View Full Version : The postulate that the laws are the same in all inertial frames

Ken G

2010-Feb-07, 12:27 AM

Special relativity embodies a postulate that the laws of physics are the same in all inertial frames. What are the full ramifications of this? Often, SR also uses a postulate that the speed of light is isotropically c, but that postulate is more like a constraint on how we coordinatize spacetime, and it is over-specified-- we don't actually need to limit to such coordinatizations to get the right predictions. So what is it about the postulate that the laws are the same that gives us a predictive theory, and how much do we need to attach to that single postulate to connect it to measurables in a way that we can really call testable physics?

antoniseb

2010-Feb-07, 12:48 AM

On a practical basis, it is in the detectors at our colliders where this is really relied upon AND tested.

grav

2010-Feb-07, 12:50 AM

Special relativity embodies a postulate that the laws of physics are the same in all inertial frames. What are the full ramifications of this? Often, SR also uses a postulate that the speed of light is isotropically c, but that postulate is more like a constraint on how we coordinatize spacetime, and it is over-specified-- we don't actually need to limit to such coordinatizations to get the right predictions. So what is it about the postulate that the laws are the same that gives us a predictive theory, and how much do we need to attach to that single postulate to connect it to measurables in a way that we can really call testable physics?Good question. I'd be interested in the answers to that myself. :)

Strange

2010-Feb-07, 01:04 AM

Presumably, it is only those laws of physics which are directly relevant to SR that must be the same in all inertial frames? For example, if the strong force had a different value I guess that wouldn't affect the derivation of SR so the postulate shouldn't require that to be the same.

hhEb09'1

2010-Feb-07, 01:18 AM

Presumably, it is only those laws of physics which are directly relevant to SR that must be the same in all inertial frames? So, inertial forces, and electromagnetic forces?

Ken G

2010-Feb-07, 01:24 AM

On a practical basis, it is in the detectors at our colliders where this is really relied upon AND tested.Everything that happens at our colliders can be tested and understood without using a coordinatization where the speed of light is isotropic. It's all in how you set the clocks, i.e., the chosen coordinatization. But you're right, that would be a perfectly good application to pose the OP question.

Ken G

2010-Feb-07, 01:27 AM

Presumably, it is only those laws of physics which are directly relevant to SR that must be the same in all inertial frames? For example, if the strong force had a different value I guess that wouldn't affect the derivation of SR so the postulate shouldn't require that to be the same.You're right, although I think the strong and weak forces also obey those rules, hence grand unification. But to keep it simple, we should just stick with what we understand, so no gravity, no strong, no weak, and no quantum mechanics.

loglo

2010-Feb-07, 10:35 AM

I think the predictivity, if that is the correct word, of SR comes from the symmetry imposed by the relativity postulate. Symmetries imply conservation laws via Noether's theorem and conservation laws restrict the allowable states and interactions and outcomes. (and make the math more tractable. :) )

Once you have symmetry you at least start on the road to predictability.

tusenfem

2010-Feb-07, 12:01 PM

Everything that happens at our colliders can be tested and understood without using a coordinatization where the speed of light is isotropic. It's all in how you set the clocks, i.e., the chosen coordinatization. But you're right, that would be a perfectly good application to pose the OP question.

Of course it would have to be isotropic, at least in the x-y direction of the circular accelerator. If c would vary in either direction, than this would immediately have been noticed in the requirements of the magnets that bend the orbit of the accereated particle, as the gamma factor would change over the orbit. And there is no need for clocks.

Ken G

2010-Feb-07, 02:02 PM

I think the predictivity, if that is the correct word, of SR comes from the symmetry imposed by the relativity postulate. Symmetries imply conservation laws via Noether's theorem and conservation laws restrict the allowable states and interactions and outcomes. (and make the math more tractable. :) )

Once you have symmetry you at least start on the road to predictability.Yes, and indeed the postulate in the OP is a symmetry, and is the core of the predictability of SR. However, this still leaves open the OP question, in particular, is the symmetry of saying that all the laws are the same for all inertial observers sufficient to make a predictive theory? I don't think it's quite enough because it lacks sufficient information to connect different observers' measurements, and a predictive theory is going to have to do that. However, if we go further and assert what looks like another symmetry principle, that the speed of light is isotropic, it is more like a coordinate symmetry than it is like a physical symmetry. It certainly overspecifies the required physics, as physics can be done fine in other coordinates.

I suspect that the second postulate has to be there, but can be in a weaker form, such as a postulate that there needs to be some way to set clocks such that the measured speed of light is isotropic in all frames. What is not clear to me is the relative importance of this postulate compared to the first postulate, it seems much less fundamental like it is only ruling out pathological cases. For example, it seems to me the finiteness of the speed of light has greater consequences than its isotropy.

Ken G

2010-Feb-07, 02:21 PM

Of course it would have to be isotropic, at least in the x-y direction of the circular accelerator. If c would vary in either direction, than this would immediately have been noticed in the requirements of the magnets that bend the orbit of the accereated particle, as the gamma factor would change over the orbit. And there is no need for clocks.You'd think that, naturally enough, but it just shows how deeply ingrained in our psyche is the Einstein simultaneity convention. That also shows how ready we are to "reify the coordinates" (to borrow a nice phrase from grant hutchison).

It is all about the clocks, because you are tallking about speed. So I can take the clock settings you are imagining, and simply go around and reset the clocks any way I like. That way I can make the coordinate speed of the particles as anisotropic as I choose, by introducing what you would interpret as a spatial gradient in the clock settings. Now, you might argue that this is just a kind of silly exception, because such coordinate speeds don't mean anything, but I will simply respond that the only way coordinate speeds ever mean anything is if you adopt a philosophical stance that some kinds of clock settings are "more real" than others-- none of which has anything do to with any testable predictions you can make with the apparatus. That's why I underscore the philosphical content of the second postulate as it is normally used.

tusenfem

2010-Feb-07, 02:59 PM

No, I am talking about the Lorentz force vxB that needs to be provided by the magnets of the circular collidor. There would be a difference in the power needed for magnet A and magnet B a quarter circle further down the tube. The magnets knows nothing about the velocity of the particle. So I am not at all having clock settings in my head, don't put your own ideas into what I say. I don't care about clocks, I care about forces.

Ken G

2010-Feb-07, 04:19 PM

No, I am talking about the Lorentz force vxB that needs to be provided by the magnets of the circular collidor. There would be a difference in the power needed for magnet A and magnet B a quarter circle further down the tube. The magnets knows nothing about the velocity of the particle. So I am not at all having clock settings in my head, don't put your own ideas into what I say. I don't care about clocks, I care about forces.That won't get you there either. The Lorentz force is just a piece of a more general force, the electromagnetic force. The interpretation that we can separate that force into electric and magnetic components is also an example of "reifying the coordinates." All physically testable expressions can interchange magnetic and electric forces willy nilly in the different coordinatizations. That's why the physical invariants are expressed as dot products of four vectors (and more general tensor animals that are just generalized versions of dot products).

There is no experimental test that the speed of light is isotropic, just as there is no experimental test what is magnetic and what is electric. When we "reify the coordinates", we imagine that we know more than we can actually know. This is a more general lesson than the standard one we take from relativity, and it is somewhat ironic that although the core message of relativity is that some observers may imagine reality contains more content than can be demonstrated (i.e., absolute notions of space and time), the way it is often conceptualized continues to propagate an untestable perception of additional content of reality (the isotropic speed of light). It is no less philosophically unnecessary to imagine that the speed of light is isotropic than it is to imagine that there is an aether.

The answer to the OP might help illuminate the following question: Given the above, why do we tend to vilify those who like to interpret relativity in terms of an aether, yet we embrace those who tend to interpret it in terms of an isotropic speed of light? Both interpretations are philosophical stances that go beyond what is experimentally demonstrable, so if we were really true to our own claims, we would reject them both and just stick with the invariants in predicting our measurable outcomes.

macaw

2010-Feb-07, 05:39 PM

There is no experimental test that the speed of light is isotropic,.

Yet, there are many tests (http://www.exphy.uni-duesseldorf.de/Publikationen/2009/Eisele%20et%20al%20Laboratory%20Test%20of%20the%20 Isotropy%20of%20Light%20Propagation%20at%20the%201 0-17%20Level%202009.pdf) that limit the anisotropy to very small numbers converging to zero.

Google:

C.Laemmezahl

M.Tobar

H.Hermann

H. Muller

A.Peters

S.Schiller

Ken G

2010-Feb-07, 05:48 PM

Yet, there are many tests (http://www.exphy.uni-duesseldorf.de/Publikationen/2009/Eisele%20et%20al%20Laboratory%20Test%20of%20the%20 Isotropy%20of%20Light%20Propagation%20at%20the%201 0-17%20Level%202009.pdf) that limit the anisotropy to very small numbers converging to zero.True enough, but that's a different form of isotropy than saying that light must move at a speed that is isotropic, that's the form that says the same outcome must occur in an experiment if the apparatus is rotated. Remember that experimental outcomes in a theory that has Lorentz invariance are derivable from dot products (and their tensor generalizations), so what these experiments actually say is that you can do physics with dot products-- not that the speed of light is isotropic. The latter does not hold expressly because any actual speed is going to be a coordinate speed-- c itself is just a parameter in the theory. Interpreting c as an isotropic speed of light is a philosophical stance that involves constraining to certain types of coordinates (basically, setting clocks via the Einstein convention, which is not required for predicting experiments, including predicting the experiments you linked to).

macaw

2010-Feb-07, 05:55 PM

True enough, but that's a different form of isotropy than saying that light must move at a speed that is isotropic, that's the form that says the same outcome must occur in an experiment if the apparatus is rotated. Remember that experimental outcomes in a theory that has Lorentz invariance are derivable from dot products (and their tensor generalizations), so what these experiments actually say is that you can do physics with dot products-- not that the speed of light is isotropic. The latter does not hold expressly because any actual speed is going to be a coordinate speed-- c itself is just a parameter in the theory. Interpreting c as an isotropic speed of light is a philosophical stance that involves constraining to certain types of coordinates (basically, setting clocks via the Einstein convention, which is not required for predicting experiments, including predicting the experiments you linked to).

Yes, this is what I explained to you earlier when I introduced you to several mainstream test theories that admit anisotropic coordinate light speed , yet their predictions are indistinguishable from SR.

Ken G

2010-Feb-07, 06:00 PM

All of which I understood years before you even entered this forum (you might even find posts of mine to that effect from years ago). You also said that there was no need to set the clocks. So let's not reprise that rather pointless exchange from that ATM thread!

nokton

2010-Feb-07, 06:06 PM

Special relativity embodies a postulate that the laws of physics are the same in all inertial frames. What are the full ramifications of this? Often, SR also uses a postulate that the speed of light is isotropically c, but that postulate is more like a constraint on how we coordinatize spacetime, and it is over-specified-- we don't actually need to limit to such coordinatizations to get the right predictions. So what is it about the postulate that the laws are the same that gives us a predictive theory, and how much do we need to attach to that single postulate to connect it to measurables in a way that we can really call testable physics?

Hi Ken,

Questions, questions, most which challenge what we are taught, but challenge not

the asker, whos mind now blows away the mists of what was once sacred learning.

To answer you, SR predicts, but does not explain, a black hole. You are correct in

how we view lightspeed within our current understanding of physics, and how we not

understand how our concept of it is limited.

Lightspeed is fixed in one concept, there are others, spacetime can be distorted for one.

Hope you understand my path.

Nokton

Ken G

2010-Feb-07, 06:20 PM

Except for the black hole bit, I do understand you. Let's not bring in black holes though-- this thread is a gravity-free zone!

macaw

2010-Feb-07, 06:22 PM

All of which I understood years before you even entered this forum (you might even find posts of mine to that effect from years ago). You also said that there was no need to set the clocks. So let's not reprise that rather pointless exchange from that ATM thread!

:lol: Agreed.

Ken G

2010-Feb-07, 06:37 PM

We have a truce! Excellent, because I'm actually curious to get your take on the OP question.

macaw

2010-Feb-07, 06:43 PM

Special relativity embodies a postulate that the laws of physics are the same in all inertial frames. What are the full ramifications of this? Often, SR also uses a postulate that the speed of light is isotropically c, but that postulate is more like a constraint on how we coordinatize spacetime, and it is over-specified-- we don't actually need to limit to such coordinatizations to get the right predictions. So what is it about the postulate that the laws are the same that gives us a predictive theory, and how much do we need to attach to that single postulate to connect it to measurables in a way that we can really call testable physics?

This guy (http://www.physicsforums.com/showpost.php?p=2568253&postcount=20) got it dead on. Therefore, it doesn't deserve the rank of postulate, it is simply a consequence of PoR. As I mentioned earlier, there are many mainstream proofs of my statement. Here (http://groups.google.com/group/sci.physics.relativity/msg/a1b1aa766a22394b?hl=en&lr=&c2coff=1) is my favorite, by Tom Roberts. I also like this (http://arxiv.org/abs/0710.3398) one, it is very well written.Many more such papers here (http://www.google.com/search?hl=en&source=hp&q=Einstein%27s+synchronization&aq=f&aqi=&oq=)

Another very good one is:

N.D.Mermin "Relativity without light", Am.J.Phys (1984)

Here are some other good ones, relatively recent:

[8] H. M. Schwartz: Deduction of the general Lorentz transformations from a

set of necessary assumptions, Am. J. Phys. 52 (1984) 346—350.

[9] H. M. Schwartz: A simple new approach to the deduction of the Lorentz

transformations, Am. J. Phys. 53 (1985) 1007—1008.

[10] S. Singh: Lorentz transformations in Mermin’s relativity without light, Am.

J. Phys. 54 (1986) 183-184.

astromark

2010-Feb-07, 07:08 PM

From the point of view of the 'ordinary man'. Its a absolute that I ask science to confirm as true those standards. 'The rules of this Universe.'

Ken's question casts doubt upon the very fabric of our structure. Please explain from where a discrepancy found real exists ?

Ken G

2010-Feb-07, 07:09 PM

This guy got it dead on. The second postulate is , in fact, a direct consequence of the first one. As I mentioned earlier, there are many mainstream proofs of my statement. Here is my favorite, by Tom Robers.

I agree with "this guy" from physicsforums in noticing the fundamentally philosophical character of the distinctions made in your second link. The second link is actually not quite what it is cracked up to be-- it is not a proof that the speed of light must be isotropic just given that the laws of physics are the same in all inertial frames. The OP really centers on the question, "what additional philosophical stances must be added to the first postulate to get the second." Your link helps us see what those philosophical stances are, because it is very clear in the assumptions it is making, i.e., what philosophical commitments it is making. What that proof really shows is that if you adopt certain contraints on what kinds of coordinate systems (i.e., what kinds of prescriptions for setting clocks) you will "allow" (i.e., those that respect the isotropies we encounter in the lab, as your earlier link demonstrated to an astonishing precision of 1 in 1017), then you get a definite contraint on the coordinates that will satisfy those philosophical commitments. When you make the commitments that the coordinates themselves should be isotropic (and so on), you get the Lorentz transformation.

However, that doesn't actually answer the OP question, because it makes the same mistake I am pointing out-- it is guilty of coordinate reification. Any form of philosophical stance that is required to be reflected in the allowable coordinates is an example of doing essentially the same thing as believing in an aether-- it is assuming that reality must or should obey certain criteria that are actually not verifiable by experiment. We cannot say that light has to be measured to travel at isotropic speed, because measurable speed depends on coordinates, and non-isotropic coordinates are allowed. More importantly, this means that if we discover some physics that did break Lorentz invariance (the fundamental isotropy of space), we could be led to use, in the new physics, a coordinate system in which the speed of light was vastly different from isotropic (i.e., not just different to 1 part in 1017).

So the question becomes: what happens to relativity rhetoric if we really stick to our guns and force ourselves to use language that is entirely stripped of anything we cannot test by experiment? Isn't that the point of eliminating the aether? I'm just asking, what happens if we take aether-expunging to its logical limit?

macaw

2010-Feb-07, 07:13 PM

I agree with "this guy" from physicsforums in noticing the fundamentally philosophical character of the distinctions made in your second link. The second link is actually not quite what it is cracked up to be-- it is not a proof that the speed of light must be isotropic just given that the laws of physics are the same in all inertial frames. The OP really centers on the question, "what additional philosphical stances must be added to the first postulate to get the second." Your link helps us see what those philosophical stances are, because it is very clear in the assumptions it is making, i.e., what philosophical commitments it is making. What that proof really shows is that if you adopt certain contraints on what kinds of coordinate systems (i.e., what kinds of prescriptions for setting clocks) you will "allow" (i.e., those that respect the isotropies we encounter in the lab, as your earlier link demonstrated to an astonishing precision of 1 in 1017), then you get a definite contraint on the coordinates that will satisfy those philosophical commitments. When you make the commitments that the coordinates themselves should be isotropic (and so on), you get the Lorentz transformation.

However, that doesn't actually answer the OP question, because it makes the same mistake I am pointing out-- it is guilty of coordinate reification. Any form of philosophical stance that is required to be reflected in the allowable coordinates is an example of doing essentially the same thing as believing in an aether-- it is assuming that reality must or should obey certain criteria that are actually not verifiable by experiment. We cannot say that light has to be measured to travel at isotropic speed, because measurable speed depends on coordinates, and non-isotropic coordinates are allowed.

So the question becomes: what happens to relativity rhetoric if we really stick to our guns and force ourselves to use language that is entirely stripped of anything we cannot test by experiment? Isn't that the point of eliminating the aether? I'm just asking, what happens if we take aether-expunging to its logical limit?

Read the third link.

loglo

2010-Feb-07, 07:17 PM

Yes, and indeed the postulate in the OP is a symmetry, and is the core of the predictability of SR. However, this still leaves open the OP question, in particular, is the symmetry of saying that all the laws are the same for all inertial observers sufficient to make a predictive theory? I don't think it's quite enough because it lacks sufficient information to connect different observers' measurements, and a predictive theory is going to have to do that. However, if we go further and assert what looks like another symmetry principle, that the speed of light is isotropic, it is more like a coordinate symmetry than it is like a physical symmetry. It certainly overspecifies the required physics, as physics can be done fine in other coordinates.

I suspect that the second postulate has to be there, but can be in a weaker form, such as a postulate that there needs to be some way to set clocks such that the measured speed of light is isotropic in all frames. What is not clear to me is the relative importance of this postulate compared to the first postulate, it seems much less fundamental like it is only ruling out pathological cases. For example, it seems to me the finiteness of the speed of light has greater consequences than its isotropy.

I tend to agree since it is the finiteness of the speed of light which creates the invariant regions of the light cone and so preserves the uniqueness of ordering of cause and affect for all observers.

I can imagine constructing a light "cone" with invariant regions using a theory with a non-isotropic light speed. The cones would just be skewed and different for different points in space-time. (I have an image in my mind of Bizarro world from an old Superman comic!)

However I think the isotropy of the speed of light is just a statement of the rotational symmetry of our universe having three spatial dimensions, so as long as we are talking about theories in our universe I don't see how it can be dropped or weakened.

Ken G

2010-Feb-07, 07:28 PM

Ken's question casts doubt upon the very fabric of our structure. Please explain from where a discrepancy found real exists ?The issue is the difference between a structure that works, and one that is required. The aether provides a structure that works, but with current data, it holds certain superfluous elements that are philosophically repugnant to maintain in the presence of that superfluousness. So we got rid of it, because we don't need it. But we also don't need to restrict to coordinates that produce a measurable speed of light that is isotropic, so why keep that as a requirement?

DrRocket

2010-Feb-08, 01:12 AM

I also like this (http://arxiv.org/abs/0710.3398) one, it is very well written..

This one is basically the derivation presented in Rindler's Introduction to Special Relativity.

In that book he observes that the Lorentz transformation follows, with "q" in place of "c" if one simply assumes that there is something that propagates with speed "q" in all inertial reference frames. Then one simply notes that experimentally the speed of light fits the bill.

From the perspective of a mathematician, I would note that the first postulate is worded rather loosely -- it is not abundanlty clear what it means for "the form of the equations of physics to be the same in all inertial reference frames". It seems to be utilized to replace the second postulate by simply decalring the speed of light of light to be a fundamental constant of physics and therefore the same in all reference frames. That works, but there is clearly therein an additional overt assumption that the speed of light is more fundamental from a physical perspective than the speed of a Chevy pickup.

I think the point here is that arguments over whether or not one can derive SR from a single loose postulate or whether another one is required are not particularly fruitful. Neither approach meets standards of high rigor from a logical perspective and both produce a very accurate physical theory.

If you would like a very rigorous postulate that produces SR, but is not particularly philosophically satisfying, it is simply that the quantity ct -x-y-z is invariant between inertial reference frames and causality is preserved. The Lorentz (or Poincare) transforms are precisely the transforms that preserve this quantity and that preserve order in the "t" coordinate -- This is a theorem of Zeeman from 1964 and does not a priori assume linearity or even continuity (see The Geometry of Minkowski Spacetime by Naber for a complete treatment and proof).

Lightwave

2010-Feb-08, 03:13 AM

The Lorentz (or Poincare) transforms are precisely the transforms that preserve this quantity and that preserve order in the "t" coordinate -- This is a theorem of Zeeman from 1964 and does not a priori assume linearity or even continuity (see The Geometry of Minkowski Spacetime by Naber for a complete treatment and proof).

It would seem that SR considers both frames invariant. The Lorentz/Poincare COvariance does lead to the Zeeman Effect, which is in effect the underlying principle proposed by KenGs question concerning the falloff?

macaw

2010-Feb-08, 06:03 AM

IThe Lorentz/Poincare COvariance does lead to the Zeeman Effect,

Huh?

Lightwave

2010-Feb-08, 07:08 AM

Huh?

Perhaps I am mistaken but it would seem by definition that SR considers BOTH frames to be Invariant (the same)? What if they were'nt physically the same but Covariant? Graduating into each other? Lorentz Poincare Covariance relates to such things in the way of the Zeeman Effect, specifically the splitting of the spectral line.

Dr. Rocket had mentioned Zeeman. I was merely pointing out the Zeeman Effect or Stark Effect and its relationship to absorption along spectral lines in contrast to the falloff of light.

astromark

2010-Feb-08, 07:19 AM

The issue is the difference between a structure that works, and one that is required. The aether provides a structure that works, but with current data, it holds certain superfluous elements that are philosophically repugnant to maintain in the presence of that superfluousness. So we got rid of it, because we don't need it. But we also don't need to restrict to coordinates that produce a measurable speed of light that is isotropic, so why keep that as a requirement?

"Superfluousness...elements...aether... we can not prove it is real, throw it away.

But its my understanding there are rules and we have no proof of any ' other '

Do I have the understanding of what you are telling me ? No. can we fix this ? I am still listening.

forrest noble

2010-Feb-08, 07:23 AM

Ken G,

...So what is it about the postulate that the laws are the same that gives us a predictive theory, and how much do we need to attach to that single postulate to connect it to measurables in a way that we can really call testable physics?

Since Lorentz equations and Einstein's SR involve equivalent math providing the same results I think Einstein needed these postulates to explain reality without an aether. At the time he was trying to explain the meaning of motion in the absence of a background aether field which seemed to be "not there" based upon experiment. Lorentz Transforms provided a mathematical explanation in the presence of an aether but how could the same mathematics explain motion in the absence of an aether. Einstein probably realized both of the postulates were needed and made them part of his theory to explain reality without needing a physical aether.

There are problems with both simple postulates in principle. For instance within a gravitational field the frames that move contrary to the center of the field and/ or have a relative velocity to it, are dilated (clocks move slower than those frames that are stationary relative to the center of gravity which move the fastest.) The laws of physics, however, in each frame may be applied the same way which was Einstein's point.

For two frames such as The Milky Way and Andromeda, for instance, we cannot decipher the speed of light between them unless we evaluate comparable time frames in the universe (i.e. galaxies) as well as Andromeda's blue shift to make a determination of what we presently call the expansion of space and the galaxies relative motion to each other to determine the light traveling time between them, even if we knew Andromeda's exact distance at any point in time.

Without these postulates the calculations seemingly would be the same using Lorentz transforms instead, but the theoretical concept, perspective or philosophy, seems quite different. If we really did find a physical background aether field, like dark matter, Higgs particles, gravitons, etc., the verbal explanations of Special Relativity might conceivably change or be dropped all together in favor of Lorentz transforms or another theoretical model. In the same way the concepts and postulates of General Relativity (such as warped space, etc.) or other theoretical-physics' models might change if new facts, observations, or equations are found to be contradictory or more functional.

DrRocket

2010-Feb-08, 07:39 AM

It would seem that SR considers both frames invariant. The Lorentz/Poincare COvariance does lead to the Zeeman Effect, which is in effect the underlying principle proposed by KenGs question concerning the falloff?

Utter nonsense.

What is important is the invariance of the Minkowski inner product under the Poincare group. Covariance is a word used by physicists to describe the formulation of general relativity in a coordinate-free manner, somethhing taken as matter of course in mathematics.

The Zeeman effect is a quantum effect which has nothing to do with the subject at hand. Neither is the Zeeman of the Zeeman effect the person who proved the theorem that I quoted. The Zeeman of the Zeeman effect died in 1943 at the age of 78, and was not proving any theorems in 1964.

DrRocket

2010-Feb-08, 07:40 AM

Perhaps I am mistaken but it would seem by definition that SR considers BOTH frames to be Invariant (the same)? What if they were'nt physically the same but Covariant? Graduating into each other? Lorentz Poincare Covariance relates to such things in the way of the Zeeman Effect, specifically the splitting of the spectral line.

Utter nonsense squared.

Lightwave

2010-Feb-08, 08:13 AM

Utter nonsense squared.

Perhaps? I may have been mistaken on the source. But if say ALL thermal energy resided within a darker colder background, it would seem to make sense to me.

You wouldnt need an aether if the background were the aether? And the clocks would be dependent or affected by the rate of radiative transfer wouldnt they?

Grimble

2010-Feb-08, 09:19 AM

To go return to the OP, when Einstein wrote here (http://www.bartleby.com/173/7.html)

For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference.

was he not making the second postulate a particular instance of the first?

Ken G

2010-Feb-08, 03:21 PM

I will give you my take on this (whether you want it or not!). My main contention is that special relativity, and its reliance on Lorentz transformations, has not completely rid us of what its core lesson was to rid us of: reliance on preconceived (philosophical) notions that cannot be tested by experiment. Note there's nothing wrong with doing that, but it represents a confusing mixing of theory and interpretation, and we do better to recognize the differences. Let's start by summarizing what is clear enough:

1) the postulates of special relativity succeed at generating a vastly accurate generalization of Newton's and Maxwell's dynamics to all inertial observers in a gravity-free environment, and

2) it relies on Lorentz transformations to translate the measurements of each inertial observer into a form generally usable by all such observers in a seamlessly invariant way, and

3) either the relativity principle with some seemingly innocuous additional assumptions, or an overt specification of the metric tensor, coupled with some even more innocuous assumptions (arrow of time), suffices to specify completely this Lorentz transformation.

In short, it works, that is not under dispute. But what philosophical prejudices do we continue to cling to, hidden under these three stalwart facts?

It is the role of the inertial observer, of course. You see, what the Lorentz transformation is, above all, is a mapping between the observables of variously moving rulers and clocks, subject to some prescription for setting the clocks. Note the problem here-- we want the laws of physics to transcend the observers, but they cannot transcend their measurements, because then it isn't physics-- physics has to connect to measurements. So at some level, there's no such thing as coordinate-free physics, because we can restrict our coordinates to what can be measured, but measurements are still coordinates. All we can do is create laws of physics that don't depend on the differences between the coordinate systems-- they cannot, unlike mathematical theorems, be free of coordinates altogether. What's more, when physics involves two events, there is only one inertial clock and ruler at both events, so it is impossible for anyone else to talk about those events entirely in terms of "their own" measurements-- they are going to need to combine two different sets of rulers and clocks. Hence not only do we need coordinate information, we have to be able to propagate that information meaningfully. That's the rub.

What this means in practice is, you still have to set the clocks. If you use the Einstein prescription to do that, you are forcing the speed of light to be isotropic-- it is not something you measure, it is something you create. Your philosphical basis for that creation is twofold:

1) you know that the experiment shows isotropy, so why not build that into light, and

2) if you use the Einstein convention, you don't get any fictitious forces when you combine measurements of inertial observers with no relative motion (say, observers affixed to an inertial rigid rod).

What's more, when we pick out the inertial observers (observers with no fictitious forces), we find they all move at constant velocity relative to each other, just as Newton would have it, so our philosophical prejudice is bolstered by a pat on the back from Newton himself. On the surface, that vote of confidence is reassuring, but we really should have taken it as a clue that we have not broken free of the shackles of the previous dogma-- we have not yet learned the core lesson of relativity!

Of course this is corrected in general relativity, but somewhere that story gets lost in the prevailing opinion that GR is a theory of gravity. I've argued that GR would still be here if there was no gravity, because it is the way to say SR without the philosophical prejudices imposed by the abhorrence of "fictitious forces." What's so great about inertial observers? They have no fictitious forces. What's so bad about fictitious forces? They're not real. But wait a minute, are they not perceived as real by real observers? Does relativity not tell us that what seems real is real, even if it violates a philosphical prejudice?

So the place where the philosophical prejudices of SR, which also give rise to the Lorentz transformation, appear is in an undo emphasis on observers who do not experience fictitious forces. We thus see that, sure enough, the Lorentz transformations are nothing but a subclass of the transformations between what observers will see-- the subclass that does not need to include fictitious forces. But that's just like postulating an aether! Just like with the aether, we select a fairly arbitrary subgroup and say the laws work for you, and everyone else will have to transform into your frame! The game of SR is rigged-- we set the clocks so that observers with no identifiable forces on them will not witness the presence of any fictitious forces. Part of that clock-setting prescription is the philosphical bias that the speed of light should be isotropic, and when it all works, we sweep the prejudices under the rug-- just like Newton did with absolute space and time.

Yes Einstein realized this, and he must have felt it would be the key to gravity. But somehow when we teach SR today, we ignore this lesson, and think of GR only as some really nasty things you need to do when you have gravity. It's not just that-- it's relativity that has actually learned the lesson of relativity. The irony in all this is, of course, there are a lot of people who are experts in SR who will quickly regard any reference to an aether as "ATM", without realizing that the exact same kinds of arguments that could be used against an aether can be used against their own formulation of SR: reliance on a perceived importance of something whose existence cannot be tested by experiment (the idea that "true" physics should work without fictitious forces, so some observers see a kind of distorted reality).

DrRocket

2010-Feb-08, 03:58 PM

I will give you my take on this (whether you want it or not!). My main contention is that special relativity, and its reliance on Lorentz transformations, has not completely rid us of what its core lesson was to rid us of: reliance on preconceived (philosophical) notions that cannot be tested by experiment. Note there's nothing wrong with doing that, but it represents a confusing mixing of theory and interpretation, and we do better to recognize the differences. Let's start by summarizing what is clear enough:

1) the postulates of special relativity succeed at generating a vastly accurate generalization of Newton's and Maxwell's dynamics to all inertial observers in a gravity-free environment, and

2) it relies on Lorentz transformations to translate the measurements of each inertial observer into a form generally usable by all such observers in a seamlessly invariant way, and

3) either the relativity principle with some seemingly innocuous additional assumptions, or an overt specification of the metric tensor, coupled with some even more innocuous assumptions (arrow of time), suffices to specify completely this Lorentz transformation.

In short, it works, that is not under dispute. But what philosophical prejudices do we continue to cling to, hidden under these three stalwart facts?

It is the role of the inertial observer, of course. You see, what the Lorentz transformation is, above all, is a mapping between the observables of variously moving rulers and clocks, subject to some prescription for setting the clocks. Note the problem here-- we want the laws of physics to transcend the observers, but they cannot transcend their measurements, because then it isn't physics-- physics has to connect to measurements. So at some level, there's no such thing as coordinate-free physics, because we can restrict our coordinates to what can be measured, but measurements are still coordinates. All we can do is create laws of physics that don't depend on the differences between the coordinate systems-- they cannot, unlike mathematical theorems, be free of coordinates altogether. What's more, when physics involves two events, there is only one inertial clock and ruler at both events, so it is impossible for anyone else to talk about those events entirely in terms of "their own" measurements-- they are going to need to combine two different sets of rulers and clocks. Hence not only do we need coordinate information, we have to be able to propagate that information meaningfully. That's the rub.

What this means in practice is, you still have to set the clocks. If you use the Einstein prescription to do that, you are forcing the speed of light to be isotropic-- it is not something you measure, it is something you create. Your philosphical basis for that creation is twofold:

1) you know that the experiment shows isotropy, so why not build that into light, and

2) if you use the Einstein convention, you don't get any fictitious forces when you combine measurements of inertial observers with no relative motion (say, observers affixed to an inertial rigid rod).

What's more, when we pick out the inertial observers (observers with no fictitious forces), we find they all move at constant velocity relative to each other, just as Newton would have it, so our philosophical prejudice is bolstered by a pat on the back from Newton himself. On the surface, that vote of confidence is reassuring, but we really should have taken it as a clue that we have not broken free of the shackles of the previous dogma-- we have not yet learned the core lesson of relativity!

Of course this is corrected in general relativity, but somewhere that story gets lost in the prevailing opinion that GR is a theory of gravity. I've argued that GR would still be here if there was no gravity, because it is the way to say SR without the philosophical prejudices imposed by the abhorrence of "fictitious forces." What's so great about inertial observers? They have no fictitious forces. What's so bad about fictitious forces? They're not real. But wait a minute, are they not perceived as real by real observers? Does relativity not tell us that what seems real is real, even if it violates a philosphical prejudice?

So the place where the philosophical prejudices of SR, which also give rise to the Lorentz transformation, is an undo emphasis on observers who do not experience fictitious forces. We thus see that, sure enough, the Lorentz transformations are nothing but a subclass of the transformations between what observers will see-- the subclass that does not need to include fictitious forces. But that's just like postulating an aether! Just like with the aether, we select a fairly arbitrary group and say the laws work for you, and everyone else will have to transform into your frame! The game of SR is rigged-- we set the clocks so that observers with no identifiable forces on them will not witness the presence of any fictitious forces. Part of that clock-setting prescription is the philosphical bias that the speed of light should be isotropic, and when it all works, we sweep the prejudices under the rug-- just like Newton did with absolute space and time.

I think this is basically correct.

No one has ever said that "ficticious forces" are not real. Anyone who has every experienced centripetal force knows that it is real (race car drivers for instance). However, in accelerated reference frames, Newtons laws of motion and the dynamics of special relativity, do not hold. That is a statement about the formulation of the mathematical description of dynamics, not a statement about what real massive bodies do -- it is a coordinate effect in other words.

GR is a theory of gravity, but it is more. It is a coordinate-free formulation of dynamics (that is what covariance really means, and why it is a word used by physicists but not by mathematicians). I think this sometimes is lost in the presentation in physics books with an over-emphasis on various coordinate systems. I much prefer to keep things abstract and coordinate free, up until the point at which one has to produce specific numerical results or do an actual measurement, and then you simply have to impose some sort of coordinate system, at least locally. Our direct measurements are scalars, not abstract tensors, and for that you need coordinates.

You can do a similar thing with SR, and it is both easier and less illuminating. It is easier because SR is GR in flat Lorentzian space, hence in the absence of gravity. There the manifold admits an atlas with a global chart, and all of the machinery of manifold theory becomes trivial. In SR you can invoke a chart/coordinate system that covers everything and the theory becomes one of how to translate among such global coordinate systems -- each system corresponding to an observer. It is less illuminating simply because the setting is so simple. By working in a single coordinate system you lose very little, because you are simulataneously working over the complete manifold. This contrasts with GR in which coordinates are only local and cannot describe the complete tensor field or differential form over all of space time.

In SR the metric can be established in a coordinate free manner (signature is independent of the particular choice of basis for a vector space), but when you need to do measurements you need a coordinate system. The coordinate-free perspective allows one to think of spacetime as a single entity, and reference frames as the perspective of a selected observer. All observers see the same space-time, they just measure it in different ways. This is actually the critical point with SR. Objects don't shrink and time does not dilate, because there is no such thing as time or length. Time and length are simply what is measured in specific coordinate systems. We need those concepts because they correspond to what is measured by instruments, but they are not invariants of the theory. We can't measure directly, and don't apparently experience directly space-time intervals, but the theory is only truly understandable in terms of this abstract notion. Giving it up would dramatically impoverish the elegance and ultimate comprehensibility of the theory.

You do not want to rid yourself of notions that cannot be directly measured in an experiment, but rather are inferred from the results of several measurements. They are what make the theory compact, comprehensible at a deep level, and elegant.

"Shut up and calculate" doesn't really work literallyh, and nobody actually does that. It is really just "monkey see, monkey do". Monkeys don't make progress.

Ken G

2010-Feb-08, 04:12 PM

Yes, I agree-- I'm not saying expunge all philosophy from physics, because we do like to have a picture in our minds that is a way we like to think about reality. It is quite possible that Newton himself was aided in the formulation of his laws by his own interpretation of an absolute space and time, and it also may have helped him find aesthetic beauty in those laws. So perhaps we can say the lesson of relativity is not "though shalt not philosophize", it is, "though shalt not philosophize and fail to recognize you are doing it."

DrRocket

2010-Feb-08, 04:17 PM

. So perhaps we can say the lesson of relativity is not "though shalt not philosophize", it is, "though shalt not philosophize and fail to recognize you are doing it."

Good theoreticians philosophize all the time. They are WAY better at it than philosophers. But we don't need to re-start that debate for the umpteenth time.

Tensor

2010-Feb-08, 04:20 PM

Good theoreticians philosophize all the time. They are WAY better at it than philosophers. But we don't need to re-start that debate for the umpteenth time.

Awwwwww, just shut up and calculate, will ya. :whistle::lol:

Ken G

2010-Feb-08, 05:37 PM

Good theoreticians philosophize all the time. They are WAY better at it than philosophers. But we don't need to re-start that debate for the umpteenth time.That's why I said nothing about philosophers (I know it pushes your buttons). The point I am making is that we know if we rotate our apparatus, we find no change in its outcome to an astonishing precision (1 part in 1017 came up earlier), so it would be easy to imagine that we also know our best theory is always going to have the speed of light be isotropic to that same precision. That is exactly what we do not know, and that is why we need to tease out for special recognition the role of philosophy in our physical theories. We may someday obtain a theory that only alters our observations by that kind of teeny amount, but in that theory, the speed of light is nowhere close to isotropic in our current frame. How could that be possible given the success of SR? It could be possible because all we'd have to do is reinterpret SR to get rid of its suspicion of fictitious forces (and its subsequent philosophical reliance on inertial observers as the "in the know" observers), and suddenly we have equally predictive theories that do not have isotropic speeds of light.

That's why it is important to learn the lesson of relativity, and indeed the lessons of the history of physics itself: it's fine to philosophize as it gives us something to picture when we apply the theory, but we should always know the difference between what nature told us and what we heard. Do we see an appreciation for that in all the highly expert links that have already appeared in this thread? No, because it wasn't their purpose, but when it's never the purpose, we get ossification of our prejudices. Personally, I don't think we should ever teach special relativity, it should be a historical footnote on the way to the real theory: GR with and without gravity.

DrRocket

2010-Feb-08, 06:11 PM

Personally, I don't think we should ever teach special relativity, it should be a historical footnote on the way to the real theory: GR with and without gravity.

That would be an interesting approach. SR really is GR without gravity, GR in a flat spacetime, so there is no conflict.

However, one can teach SR with very little mathematics, and do it correctly. There is nothing more involved in most of it than high school algebra, and only simple calculus for the whole thing.

GR with gravity takes some serious mathematics. To do it right it takes mathematics that is way beyond what is reasonable to assume for an undergraduate, and really beyond most first-year graduate students. You can tame it down and do some hand waving (as in Rindler's Essential Relativity, Special, General and Cosmological) but to really do it right, as in Misner, Thorne and Wheeler takes some fairly sophisticated stuff.

Ken G

2010-Feb-08, 07:30 PM

However, one can teach SR with very little mathematics, and do it correctly. There is nothing more involved in most of it than high school algebra, and only simple calculus for the whole thing.

Yes, the proof would be to actually pull it off, and it's hard to know if it would work. Students generally do not do terribly well in SR, and sometimes we can be fooled about what things are actually harder for them (at the introductory general-science level, I find students understand basic GR concepts much better than they understand SR concepts, though of course all are quite watered down). My gripe is the "devil's bargain" element-- the challenge in teaching SR is to get students to let go of arbitrary Newtonian prejudices, but to replace them with arbitrary Einsteinian prejudices (that he himself advanced beyond) seems to miss the point. Do we want our students to be able to do the calculations (how many of them will ever need to, and those that do will end up regarding the textbooks as a kind of trivial application), or do we want them to get the point?

GR with gravity takes some serious mathematics.Yes, I don't even know how to do that myself, so to attempt that I'd have to learn it myself first and there wouldn't be a need. It would suffice to just say "here's an interpretation that is actually more conducive to generalization to a theory of gravity", which is more or less the best reason for motivating any interpretation.

Nereid

2010-Feb-08, 08:08 PM

In these last few posts, Ken G and DrRocket seem to have introduced a new element: how does the purpose of an undergrad university physics course relate to the purpose of people who do research in physics (or the subset for whom GR or SR is at least important, if not critical)?

forrest noble

2010-Feb-08, 09:31 PM

Ken G,

.....I'm not saying expunge all philosophy from physics, because we do like to have a picture in our minds that is a way we like to think about reality. It is quite possible that Newton himself was aided in the formulation of his laws by his own interpretation of an absolute space and time, and it also may have helped him find aesthetic beauty in those laws. So perhaps we can say the lesson of relativity is not "though shalt not philosophize", it is, "though shalt not philosophize and fail to recognize you are doing it."

When discussing these matters I prefer to use the word "perspective" rather than the word "philosophy" which seems to have too many different variant definitions which can lead to greater misunderstandings. The definition of philosophy that matches most to the word perspective seems to be this one.

Philosophy: is an academic discipline involving the study of fundamental perspectives and problems concerning matters such as logic, existence, reality, knowledge, truth, validity, aesthetics, value ...

Perspectives are absolutely essential for a general understanding of anything. Take for example something physical and complicated such as a horse. From one point of view, like a picture, it has a particular appearance that differs from another point of view. Using our mind enables us to put together many possible exterior perspectives in our mind at once. With a knowledge of a horse's internal structures we can also incorporate that into our understandings of it. If we were a animal behaviorist we could have some understanding of a horse's behavior, nature, etc. etc.

Even if we had almost all the possible perspectives of a horse and wrote it all down we would not have a "truth" of what a horse is, the reason being that there is no "truth;" all explanations of reality are a matter of perspective. All of reality carries with it perspectives that are not reality themselves. Even my explanation of this is only a perspective. All vocabulary carries with it definitions and perspectives that are put together by others with a somewhat different understanding than what one originally intended. Physics equations can provide answers but not necessarily understandings of the factors of reality involved or the answers that are determined.

The point is that the more generally valid perspectives one is able to mentally put together at the same time concerning a specific "reality," seemingly the better off one will be able to understand the "reality" itself as well as the possible "valid" perspectives of others that can exist. As a result a great deal of misunderstandings and arguments concerning opinions of reality and dogmas of theory can be avoided.

Ken G

2010-Feb-08, 09:41 PM

In these last few posts, Ken G and DrRocket seem to have introduced a new element: how does the purpose of an undergrad university physics course relate to the purpose of people who do research in physics (or the subset for whom GR or SR is at least important, if not critical)?Yes, that's the general subject of pedagogy, which is closely related to the "embedded philosophies" we find in our popularized interpretations of our theories. It is easy to imagine a simple hierarchy where theories are what get used at work, interpretations are what follow us home, and pedagogies are how we explain it all to someone else. But my suspicion is that this street is not actually so one-way, and in fact they each percolate around in important ways that guide the progress of new discoveries. If not for a single researcher, then certainly for the following generation!

StupendousMan

2010-Feb-08, 09:46 PM

In these last few posts, Ken G and DrRocket seem to have introduced a new element: how does the purpose of an undergrad university physics course relate to the purpose of people who do research in physics (or the subset for whom GR or SR is at least important, if not critical)?

They are at odds. The purpose of an undergraduate university physics course is to educate undergraduate students. The purpose of people who do research in physics is to learn more about physics. Those who teach are not doing research (during the time they teach and grade and develop materials). Those who do research are not teaching undergraduate physics courses (during the time they are chasing after new phenomena and explanations).

The gap between what undergraduates learn in a typical physics course, and what research physicists do on a daily basis, is in many cases so large that it doesn't make sense to try to connect the two in any really comprehensive way. Sure, one can draw an example here or there, but most of what the students do on homework problems and on tests is based on concepts which were worked out decades, if not centuries, ago.

An even more cynical view is that the purpose of an undergraduate physics course is to allow a student to move on to the upper-level engineering courses he needs to get a job. That has even less to do with research ....

Ken G

2010-Feb-08, 09:57 PM

When discussing these matters I prefer to use the word "perspective" rather than the word "philosophy" which seems to have too many different variant definitions which can lead to greater misunderstandings. The definition of philosophy that matches most to the word perspective seems to be this one.I agree that "philosophy" has connotations that tend to obscure the message here, but I don't shy from it, because it actually is the right word, and we should not surrender to connotations that mostly stem from those who don't really know what philosophy is. Among those whose charge is to define the term, any new discovery that dramatically changes how we think about our reality is considered philosophy. It is indeed a hard word to define, but the most general meaning is its literal translation from Greek: love of wisdom. Thus, anyone who thinks that the discovery of a new principle of nature is an example of an increase in our general wisdom is agreeing to call it philosophy; only those who would characterize such discoveries in terms of technical know-how rather than know-ledge or wisdom could hold to the position that we are not talking about philosophy here.

Philosophy: is an academic discipline involving the study of fundamental perspectives and problems concerning matters such as logic, existence, reality, knowledge, truth, validity, aesthetics, value ...

Yes, you can cull out the sub-definition that relates to perspective and associate it with the overlap with physics, separating it from, say, morality issues, but it's still philosophy.

Perspectives are absolutely essential for a general understanding of anything. Yes, the term understanding is one that is closely connected to knowledge and wisdom.

Even if we had almost all the possible perspectives of a horse and wrote it all down we would not have a "truth" of what a horse is, the reason being that there is no "truth;" all explanations of reality are a matter of perspective. All of reality carries with it perspectives that are not reality themselves.Yes, I agree with you here, and point out that your musings on the topic are quintessentially philosophical. There's probably a term for this way of thinking! If not, there should be: perhaps "perspectivism."

The point is that the more generally valid perspectives one is able to mentally put together at the same time concerning a specific "reality," seemingly the better off one will be able to understand the "reality" itself as well as the possible "valid" perspectives of others that can exist.Yes, that was very much the point of a recent (infamous) thread that ended up in ATM. It's kind of a hard sell!

Ken G

2010-Feb-08, 10:02 PM

An even more cynical view is that the purpose of an undergraduate physics course is to allow a student to move on to the upper-level engineering courses he needs to get a job. But we don't need cynicism, for that is a closing of an avenue for progress. I'm saying that there is a problem if the way we teach something is not the best way to think about that thing, whatever it is, because of the problem of ossification. We sometimes see the ramifications of ossification even on this very forum, when something can get classed as "ATM" for simply addressing well-known observations from an alternative interpretive standpoint.

In fact, I can't help wondering if Einstein himself expected GR to completely supplant SR, and would be somewhat perplexed about how ossified has become the latter and how generally obscure is the former.

Spaceman Spiff

2010-Feb-09, 03:37 AM

The coordinate-free perspective allows one to think of spacetime as a single entity, and reference frames as the perspective of a selected observer. All observers see the same space-time, they just measure it in different ways. This is actually the critical point with SR. Objects don't shrink and time does not dilate, because there is no such thing as time or length. Time and length are simply what is measured in specific coordinate systems.

(my emphasis)

I like that!

:clap::clap::clap:

Tensor

2010-Feb-09, 04:01 AM

But we don't need cynicism, for that is a closing of an avenue for progress. I'm saying that there is a problem if the way we teach something is not the best way to think about that thing, whatever it is, because of the problem of ossification.

But who determines what is the best way to think about something? The teacher? The student? Someone else? There may not be a best way to think about something for everyone.

In fact, I can't help wondering if Einstein himself expected GR to completely supplant SR, and would be somewhat perplexed about how ossified has become the latter and how generally obscure is the former.

While he may have expected it, during his search of a Unified Field Theory, I don't think anyone else gave it a second thought after 1928.

korjik

2010-Feb-09, 04:34 AM

But who determines what is the best way to think about something? The teacher? The student? Someone else? There may not be a best way to think about something for everyone.

While he may have expected it, during his search of a Unified Field Theory, I don't think anyone else gave it a second thought after 1928.

I think that when you get a proper theory of gravity that is compatible with quantum theory, then SR will fall into the background. It will become something covered in junior level classes as a stepping stone to quantum theory, gravitation and electrodynamics.

The only reason it is used now is that it is used in QM and ED. Once you have a decent ToE, it becomes less important.

Tensor

2010-Feb-09, 04:47 AM

I think that when you get a proper theory of gravity that is compatible with quantum theory, then SR will fall into the background. It will become something covered in junior level classes as a stepping stone to quantum theory, gravitation and electrodynamics.

The only reason it is used now is that it is used in QM and ED. Once you have a decent ToE, it becomes less important.

Oh, I agree, but since Dirac, and for the foreseeable future, the inclusion of SR in QM, without the inclusion of GR, is a stumbling block to GR supplanting SR completely.

korjik

2010-Feb-09, 05:14 AM

Oh, I agree, but since Dirac, and for the foreseeable future, the inclusion of SR in QM, without the inclusion of GR, is a stumbling block to GR supplanting SR completely.

Technically, it wouldnt be GR. Either that or it wouldnt be QM.

:)

Ken G

2010-Feb-09, 02:00 PM

Objects don't shrink and time does not dilate, because there is no such thing as time or length. Time and length are simply what is measured in specific coordinate systems. I agree with your summary of coordinates vs. coordinate-free, but I point out that in this sentence you have adopted a classical philosophical stance, so you left the strict confines of what we could safely call physics. Your stance is called rationalism, where what is "really real" is viewed as the abstract notions of the mind, not the mandates of perception. This is a common philosophical stance for mathematicians and mathematical physicists. The alternative is called empiricism, often the attitude of observational physicists, and the two have been debated for millennia. The empiricist would say that you reversed the logic-- all that is real is just what we observe, and we are free to unify our observations into abstract and elegant theories when we seek to understand our perceptions, but our understanding will never replace the perceptions as what is real.

My own personal view is that neither rationalism nor empiricism has any claim to the truth, rather truth is what emerges when these two views collide and combine, like milk and cocoa. By itself each has a flaw-- rationalism must fit in our brains so is subject to what we can make sense of, empiricism must fit in our perceptions so is subject to our five senses. Neither seems to really encompass what we might think of as reality, since it seems more natural to imagine that reality gave rise to us than the other way around. This is also why many questions in philosophy are OK to remain questions, and need not have unique answers.

Kwalish Kid

2010-Feb-09, 02:08 PM

You'd think that, naturally enough, but it just shows how deeply ingrained in our psyche is the Einstein simultaneity convention. That also shows how ready we are to "reify the coordinates" (to borrow a nice phrase from grant hutchison).

It is all about the clocks, because you are tallking about speed. So I can take the clock settings you are imagining, and simply go around and reset the clocks any way I like. That way I can make the coordinate speed of the particles as anisotropic as I choose, by introducing what you would interpret as a spatial gradient in the clock settings. Now, you might argue that this is just a kind of silly exception, because such coordinate speeds don't mean anything, but I will simply respond that the only way coordinate speeds ever mean anything is if you adopt a philosophical stance that some kinds of clock settings are "more real" than others-- none of which has anything do to with any testable predictions you can make with the apparatus. That's why I underscore the philosphical content of the second postulate as it is normally used.

Or maybe we could take the observed relationship between clocks as evidence for the isotropic speed of light. You always underscore the philosophical content at the detriment of the empirical content.

Ken G

2010-Feb-09, 02:09 PM

But who determines what is the best way to think about something? The teacher? The student? Someone else? There may not be a best way to think about something for everyone.

That is exactly the purpose of this thread, to examine that issue. There's no evidence that SR is a good way to think about the situation-- it's not really true to relativity, and students are generally not very good at it. Those who are good at it probably could handle a more general approach, that would be truer to relativity. Still, my contention has not been demonstrated.

While he may have expected it, during his search of a Unified Field Theory, I don't think anyone else gave it a second thought after 1928.But you are talking about unifying gravity and the other forces. I'm just talking about taking a general perspective to relativity.

Tensor

2010-Feb-09, 02:10 PM

Technically, it wouldnt be GR. Either that or it wouldnt be QM. :)

This demonstrates why I've stayed out of each of Ken's thread's. Ken is a master of using the precise terms for the interpretation/philosophy of theories. I'm not that good, and I sometimes get frustrated in discussions about these things for that very reason. As an aside to Ken, this is said in admiration, and is not meant as being a challenge.

Ken G

2010-Feb-09, 02:12 PM

The only reason it is used now is that it is used in QM and ED. Once you have a decent ToE, it becomes less important.I agree. The other comments seem to suggest you could not include GR in QM in the same gravity-free environments that Dirac treated, and I'm not sure that's true. If I'm right, then the very fact that Dirac retrofitted QM to SR instead of GR is an example of the concrete impact on research at the frontiers that pedagogical ossification can have.

George

2010-Feb-09, 03:23 PM

My own personal view is that neither rationalism nor empiricism has any claim to the truth, rather truth is what emerges when these two views collide and combine, like milk and cocoa.Anthropofoodmorphism. I'm in! :) [Just wanted to bookmark this excellent thread.]

I suspect something else must be added to the milk beyond just cocoa. I like Dr. Rocket's view that moves distance and time aside since it may help find another piece of the puzzle that has been lying beneath one or both of these. But they must be "real" in order for us to travel there and back with complete confidence in seeing the predicted results of the contraction/dilation, though, again, it may really be something else, such as 3d time or other weird thing.

Establishing some sort of loose constraints on what a potential new aether might be would be helpful. The old one seems beyond resurrection, even remotely, I think. One of the early problems with it as a conventional medium for wave propogation was that it would have to have tensile strengths greater than steel to allow lightspeed propogation and yet be content in a vacuum.

grav

2010-Feb-09, 03:29 PM

I haven't seen it mentioned here, so I will go ahead and state that if we were to try to derive SR from the first postulate alone, then since ballistic theory also includes the same physics in all frames, we would still need some generalized form of the second postulate, something on the order of "massless particles will always be measured to travel isotropically and not ballistically with the source, so at the same speed whether the source is stationary or moving", which I believe is pretty must how the second postulate as originally stated already reads except that massless particles is replaced with light.

DrRocket

2010-Feb-09, 03:43 PM

But who determines what is the best way to think about something? The teacher? The student? Someone else? There may not be a best way to think about something for everyone.

It is most certainly true that there is no single " best way" to think about something that applies to all people or all situations.

The "best way" is determined by the student, but the effricacy of that choice is determined by the ability of the student to utilize that "best way" in working with the theory at hand to solve problems or extend the theory. Thus the student makes the choice, but the teacher evaluates the end product of that choice.

Note that "student" and "teacher" are here taken in a very broad sense. One might equally replace them with "researcher" and "scientific community" respectively.

Not all people think in the same way. Some think verbally and some think visually. Neither is necessarily better or worse than the other.

A friend of mine (another mathematician) visited a very famous mathematician when he was in Paris. The guy started out by asking him, "Are you a picture guy or a numbers guy ?" -- meaning did he think verbally or pictorially. It turns out that he asked because he found that he could communicate only with "pictures guys" -- not overly surprising as both men are topologists. In my experience, most, but not all, mathematicians are "picture guys".

Even picture guys think about things differently -- they use different pictures. The best ones use several different pictures.

DrRocket

2010-Feb-09, 03:57 PM

An even more cynical view is that the purpose of an undergraduate physics course is to allow a student to move on to the upper-level engineering courses he needs to get a job. That has even less to do with research ....

Not only cynical, but shortsighted and wrong.

The purpose of an undergraduate physics course is to teach the student some physics. If that knowledge is useful in subsequent engineering courses, and it almost certainly will be, that is gravy.

There is a tremendous and widespread misconception among engineering students (and even some engineering faculty) that education should focus on those skills that are immediately applicable in the work place. This confuses training with education, and the two are not the same thing. Education, the aquisition of fundamental knowledge and the ability to reason so as to be able to apply that knowledge to new situations is permanent. Training, the acquisition of specific and perishable skills for use in targeted narrow applications, is transient. I made quite a good living by assuring that training was not misapplied, and that significant problems were solved by paying attention to fundamentals. A great many engineering students are over-trained in the software package du jour, and undertrained in fundamental science and mathematics. Those that are more fundamentally educated do much better in the long run.

DrRocket

2010-Feb-09, 04:09 PM

I agree. The other comments seem to suggest you could not include GR in QM in the same gravity-free environments that Dirac treated, and I'm not sure that's true. If I'm right, then the very fact that Dirac retrofitted QM to SR instead of GR is an example of the concrete impact on research at the frontiers that pedagogical ossification can have.

Dirac retrofitted QM to SR rather than GR for a simple reason. He could combime QM and SR. He did not know how to combine QM and GR, and neither does anyone else.

You really do need SR for GR anyway. GR is built on the mathematics of Riemannian (I use the term here to include pseudo-Riemannian) manifolds. Manifolds are locally based on ordinary n-space with an inner product of the requisite signature. The key is that the global theory is built by "sewing together" local charts. SR is GR in flat spacetime, or alternately SR is local GR. You need the local theory in order to "sew things together" to get the global theory.

SR is to GR as multivariable calculus is to calculus on manifolds.

Tensor

2010-Feb-09, 04:10 PM

It is most certainly true that there is no single " best way" to think about something that applies to all people or all situations.

The "best way" is determined by the student, but the effricacy of that choice is determined by the ability of the student to utilize that "best way" in working with the theory at hand to solve problems or extend the theory. Thus the student makes the choice, but the teacher evaluates the end product of that choice.

snip...

Even picture guys think about things differently -- they use different pictures. The best ones use several different pictures.

I was specifically thinking of the difference between Feynman and Schwinger's pictures of QED. Of course, as Feynman noted in his Nobel lecture, there are many ways of representing the same thing, with a little mathematical fiddling. Kip Thorne noted in his Popular Science book that he may think of curved space on Monday, Wednesday, and Fridays. Rubber rulers and clocks on Tuesday, Thursday, and Saturday. And on Sunday, use the membrane paradigm. I would think it would depend on the particular problem you were working on.

Tensor

2010-Feb-09, 04:14 PM

I agree. The other comments seem to suggest you could not include GR in QM in the same gravity-free environments that Dirac treated, and I'm not sure that's true. If I'm right, then the very fact that Dirac retrofitted QM to SR instead of GR is an example of the concrete impact on research at the frontiers that pedagogical ossification can have.

I'm quite sure you could, the question is why bother? Why would you bother to use the tensor machinery, the differentiable manifolds and all the other advanced math, when all you need is some basic algebra?

Ken G

2010-Feb-09, 04:25 PM

But they must be "real" in order for us to travel there and back with complete confidence in seeing the predicted results of the contraction/dilation, though, again, it may really be something else, such as 3d time or other weird thing.I would say to be sure we have solid contact with empirical science that there needs to be a measurable there somewhere. What you can measure is the objective reality, the rest is in your mind. Of course, what you can measure is in your mind too, but we must accomodate some distinctions or we have idealism and nobody likes that.

Establishing some sort of loose constraints on what a potential new aether might be would be helpful. The old one seems beyond resurrection, even remotely, I think.Einstein's take was that a new aether must itself be dynamical. A purely unmoving aether never really tells you anything you need to know.

One of the early problems with it as a conventional medium for wave propogation was that it would have to have tensile strengths greater than steel to allow lightspeed propogation and yet be content in a vacuum.Mechanical models of light broke down with Faraday's observations, so I think that kind of thinking was dead long before relativity.

There is something aetherial about a field, and the very word is meant to distinguish it from mechanical analogs.

Ken G

2010-Feb-09, 04:29 PM

I haven't seen it mentioned here, so I will go ahead and state that if we were to try to derive SR from the first postulate alone, then since ballistic theory also includes the same physics in all frames, we would still need some generalized form of the second postulate, something on the order of "massless particles will always be measured to travel isotropically and not ballistically with the source, so at the same speed whether the source is stationary or moving", which I believe is pretty must how the second postulate as originally stated already reads except that massless particles is replaced with light.Not quite. You are quite right that there has to be a postulate that says light (or any massless particle) propagates at a speed that depends on the frame, not the source (and can be constant in all frames). But the specification of a constant speed is artificial, as it is purely an instruction for creating a coordinate system. There also has to be some postulate about how such coordinate systems will act, to wit, in a way we can call "inertial." But to define the meaning of inertial, we need some kind of a dynamical theory, and it has to be the same in all frames-- so you still need the first postulate. One could also assert a postulate that slow clock motion generates the same coordinates, and there would be physics in that, I don't know if it would be enough to get SR but perhaps it embodies the first postulate in important ways.

I think our conclusion is that neither postulate by itself is SR, but there are more streamlined ways (and DrRocket is right that rigor is difficult to achieve) to say the postulates that are more free of philosophical prejudice. (And note that philosophical interpretation is not a bad thing-- only prejudice is.)

Ken G

2010-Feb-09, 04:34 PM

Dirac retrofitted QM to SR rather than GR for a simple reason. He could combime QM and SR. He did not know how to combine QM and GR, and neither does anyone else.Are you sure? You are talking about gravity, but note I specifically mentioned that Dirac was working in the gravity-free environment (where the vast majority of all quantum mechanics comfortably fits), and I did not require that he leave that zone.

SR is GR in flat spacetime, or alternately SR is local GR. You need the local theory in order to "sew things together" to get the global theory.

But you don't need the Lorentz transformation, because you don't need to require inertial frames, and you don't need to excise fictitious forces from your dynamical theory. You need Minkowski geometry, but you don't need SR as it is normally axiomatized and taught. In short, you only need the coordinate-free scaffolding-- you can communicate that to observations using any coordinate system that looks locally like a measurement, which is less restrictive than SR.

Ken G

2010-Feb-09, 04:38 PM

Kip Thorne noted in his Popular Science book that he may think of curved space on Monday, Wednesday, and Fridays. Rubber rulers and clocks on Tuesday, Thursday, and Saturday. And on Sunday, use the membrane paradigm. I would think it would depend on the particular problem you were working on.This is exactly what I was attempting to convey in a recent thread that was placed in "ATM" for making that very same point (note that Thorne is effectively saying he believes in an aether on Tuesdays, Thursdays, and Saturdays, where here I use "believe in" to simply mean "adopt the working picture").

Ken G

2010-Feb-09, 04:42 PM

I'm quite sure you could, the question is why bother? Why would you bother to use the tensor machinery, the differentiable manifolds and all the other advanced math, when all you need is some basic algebra?Ah, that's the question, isn't it? The issue is, just what tensor "machinery" do you really need? A dot product is "tensor machinery." Your point brings up the fact that the way we teach tensor algebra suffers from the same basic problem as the way we teach GR-- it only gets used when you have to have it, which tends to be when the problem is difficult. People don't even realize they are also using it in much simpler problems, because it simply isn't taught that way. But what tensor algebra really is is a way of keeping track of the separations between what you need coordinates to do, and what you do not need coordinates to do. Isn't that something we need to understand, no matter how simple the problem is? Indeed, the simpler the problem, the better!

grav

2010-Feb-09, 04:47 PM

Not quite. You are quite right that there has to be a postulate that says light (or any massless particle) propagates at a speed that depends on the frame, not the source (and can be constant in all frames). But the specification of a constant speed is artificial, as it is purely an instruction for creating a coordinate system. There also has to be some postulate about how such coordinate systems will act, to wit, in a way we can call "inertial." But to define the meaning of inertial, we need some kind of a dynamical theory, and it has to be the same in all frames-- so you still need the first postulate. One could also assert a postulate that slow clock motion generates the same coordinates, and there would be physics in that, I don't know if it would be enough to get SR but perhaps it embodies the first postulate in important ways.

I think our conclusion is that neither postulate by itself is SR, but there are more streamlined ways (and DrRocket is right that rigor is difficult to achieve) to say the postulates that are more free of philosophical prejudice. (And note that philosophical interpretation is not a bad thing-- only prejudice is.)I was not stating there whether one needs the first postulate or not, but only that the second postulate is essential in deriving SR, so one cannot derive SR solely from the first postulate alone.

Nereid

2010-Feb-09, 05:10 PM

In these last few posts, Ken G and DrRocket seem to have introduced a new element: how does the purpose of an undergrad university physics course relate to the purpose of people who do research in physics (or the subset for whom GR or SR is at least important, if not critical)?Yes, that's the general subject of pedagogy, which is closely related to the "embedded philosophies" we find in our popularized interpretations of our theories. It is easy to imagine a simple hierarchy where theories are what get used at work, interpretations are what follow us home, and pedagogies are how we explain it all to someone else. But my suspicion is that this street is not actually so one-way, and in fact they each percolate around in important ways that guide the progress of new discoveries. If not for a single researcher, then certainly for the following generation!

Looking a bit more closely at this audience aspect, wrt philosophy ...

Those who 'do' GR for a living - the researchers and the designers of GPS systems (any others?) - are they unaware of the kinds of philosophical interpretations that this thread is about (in a general sense, not necessarily the specific SR sense)? Or do they, perhaps, consider this sort of categorisation trivially simple?

Ditto those who 'do' SR for a living - people who design particle colliders?

I fully agree that the approaches, tools, interpretations, etc that a teacher uses - whether in high school, or doing post-grad courses, or anything in between - can be judged by their effectiveness in terms of meeting the educational goals at hand.

But I'm wondering who the SR (and general) philosophical interpretations are for? If these were a product, what is the target market? how satisfied are the customers?

Ken G

2010-Feb-09, 05:16 PM

I was not stating there whether one needs the first postulate or not, but only that the second postulate is essential in deriving SR, so one cannot derive SR solely from the first postulate alone.Don't overlook that, even if you use both postulates, you still don't have an actual theory of dynamics. All you have is a constraint on the theory of dynamics, such that it must generate kinematics of a certain form. For one thing, the kinematics must admit the concept of an inertial frame. Once you have a dynamics that is allowed by the first postulate, if that dynamics has an isotropic speed in some inertial coordinates that does not depend on anything else (as Maxwell's equations do), then there is a way to extend those inertial coodinates to all inertial observers such that this speed is constant and isotropic (the Lorentz transformation). You can prove that from the first postulate alone (with a few hidden assumptions), so the second postulate is superfluous, unless you take the second postulate as actually associating that speed with the speed of a light particle in a vacuum. But there's no need to assert that in a postulate of relativity, that more properly belongs in amongst the laws themselves.

I think the only reason Einstein used the second postulate was to justify his clock-setting procedure as something inherent in the concept of an inertial frame, and not just an arbitrary coordinatization. Had he used slow clock transport instead of his simultaneity convention, I think he could relegate the second postulate entirely back into the realm of the dynamical laws themselves (most notably, Maxwell's equations).

Ken G

2010-Feb-09, 05:26 PM

Ditto those who 'do' SR for a living - people who design particle colliders?Here I think we have to distinguish a practitioner of a given theory from someone trying to do basic research into new theories. Alternate interpretations and pedagogies are fairly irrelevant to practitioners-- they can use any of either that works for them personally, and the only challenge they encounter is trying to communicate their successes to other practitioners. Often, a kind of "standard lexicon" develops, but it can be quite different for different subfields and quite often settles on the most convenient form of expression. Tradition also plays a role in each subfield, and there is really no guarantee that a subfield will use the interpretation that is most illuminating or insightful (for example, engineers routinely express electric and magnetic fields in different units, while mathematical physicists typically don't even express mass and energy in different units!). This can cause consternation when practitioners cross between subfields. So I don't accept the general thesis that the best way to think about things is however the people in the trenches do it-- there is still value in re-assessing whether or not there is a better way to skin the cat.

But I'm wondering who the SR (and general) philosophical interpretations are for? If these were a product, what is the target market? how satisfied are the customers?This connects with the distinction that DrRocket has made between "training" and "education." The fact is, most of the students who learn SR, or any particular subtopic of physics, will never use it in their chosen profession-- except to teach it to someone else. So education has a mission that is quite different from training-- and it is education that needs to seek out the most illuminating and insightful pedagogy, which starts by identifying what is the actual lesson there in the first place. If the lesson is that space and time are not absolute, do we really get that lesson across by hammering home an alternate coordinatization of space and time that is also not absolute?

grav

2010-Feb-09, 06:31 PM

Don't overlook that, even if you use both postulates, you still don't have an actual theory of dynamics. All you have is a constraint on the theory of dynamics, such that it must generate kinematics of a certain form. For one thing, the kinematics must admit the concept of an inertial frame. Once you have a dynamics that is allowed by the first postulate, if that dynamics has an isotropic speed in some inertial coordinates that does not depend on anything else (as Maxwell's equations do), then there is a way to extend those inertial coodinates to all inertial observers such that this speed is constant and isotropic (the Lorentz transformation). You can prove that from the first postulate alone (with a few hidden assumptions), so the second postulate is superfluous, unless you take the second postulate as actually associating that speed with the speed of a light particle in a vacuum. But there's no need to assert that in a postulate of relativity, that more properly belongs in amongst the laws themselves.In response to this, as I also stated to Fortis in the other current thread...

if we include hidden assumptions about the homogeneity of space and the isotropy of some speed for whatever reason, then the first postulate is enough. But then we need to determine whether or not those hidden assumptions should also be considered postulates. Otherwise, it would be tantamount to stating the first postulate to read something like "the laws of physics is the same in all inertial and homogeneous frames where one such law requires that some speed is always to be measured isotropically regardless of the motion of the source."

Ken G

2010-Feb-09, 06:52 PM

I think the best way to summarize all this is that the second postulate is contained in the first, except to the extent that the second postulate leaves the realm of pure relativitistic constraints and begins to make assertions about the underlying dynamical theory itself. That would represent an awkward mixing of what is dynamics and what is relativity.

korjik

2010-Feb-09, 06:53 PM

I agree. The other comments seem to suggest you could not include GR in QM in the same gravity-free environments that Dirac treated, and I'm not sure that's true. If I'm right, then the very fact that Dirac retrofitted QM to SR instead of GR is an example of the concrete impact on research at the frontiers that pedagogical ossification can have.

Unless you can show that I am wrong, I cant imagine that Dirac didnt spend many hours trying to get GR and QM to work together.

Heck, I have to imagine at this point that combining GR and QM is the most worked on problem ever in physics.

Like Dr. Rocket said, Dirac put SR into QM cause he could. He didnt put GR in cause he couldnt. It wasnt that ossification led him to that conclusion, it was that no one, including pretty much all of the great minds of the last century couldnt beat that problem into submission.

It wasnt pedagogical ossification that was the problem, it was the upper limit of human knowldge that was the problem.

Ken G

2010-Feb-09, 07:14 PM

Unless you can show that I am wrong, I cant imagine that Dirac didnt spend many hours trying to get GR and QM to work together.

I think a crucial piece of what I am saying is getting lost in the all-too-common tendency to lump "GR" and "gravity" together. But there is a zero gravity version of GR, and that's what I'm talking about here. I would be quite surprised if QM is any harder to get to work with zero-g GR than it is to get to work with SR. Indeed, the mathematics it generates must be all the same-- but not the interpretation or language used to get there (in particular, the requirements on the coordinates used.).

It wasnt that ossification led him to that conclusion, it was that no one, including pretty much all of the great minds of the last century couldnt beat that problem into submission. The "ossification" to which I refer has nothing to do with unifying gravity and QM, indeed nothing I've said has anything at all to do with gravity! Note how effortlessly you equate GR with gravity, but my entire point here is that no such automatic association is required. Many aspects of GR are much more easily understood with no gravity at all, gravity (by which I mean, tidal gravity) makes it a much tougher problem.

It wasnt pedagogical ossification that was the problem, it was the upper limit of human knowldge that was the problem.The pedagogical ossification to which I refer is the automatic association of the Lorentz transformation with gravity-free physics, and the related automatic association of anything that does not use the Lorentz transformation as being due to the presence of gravity. You are even doing it here.

DrRocket

2010-Feb-09, 07:18 PM

Unless you can show that I am wrong, I cant imagine that Dirac didnt spend many hours trying to get GR and QM to work together.

Heck, I have to imagine at this point that combining GR and QM is the most worked on problem ever in physics.

Like Dr. Rocket said, Dirac put SR into QM cause he could. He didnt put GR in cause he couldnt. It wasnt that ossification led him to that conclusion, it was that no one, including pretty much all of the great minds of the last century couldnt beat that problem into submission.

It wasnt pedagogical ossification that was the problem, it was the upper limit of human knowldge that was the problem.

Right.

Among the books on my shelves are two by P.A.M. Dirac. One is The Principles of Quantum Mechanics. The othere is General Theory of Relativity. I imagine that if he could have written one book that unified the two, he would have done that.

Ken G

2010-Feb-09, 08:05 PM

You still are not hearing. Let me clarify further.

I could do dynamics with no relativity at all, if I had force laws that gave me the acceleration of things in a particular frame, call it frame A. I'd just say, all measurements have to be in that frame. Anybody in another frame can simply watch the clocks and rulers in frame A as they zoom by, and apply my dynamical theory to those measurements. Done, we have a complete physics.

But wait a minute, you say, the observers want a physics that works with their own clocks and rulers? Picky picky, what troublemakers. Oh all right, I suppose we're going to need relativity after all. So even in a universe with force laws like that, we'd still need relativity, so that all the observers get to play.

Now, our universe isn't actually like that, our dynamical laws don't live in a particular frame, they are expressible in coordinate-free form. That gives us another really good reason to let all the observers play that isn't just politically advisable-- the laws respect a property that they should work the same for all observers. The universe itself is democratic, and this is the particular lesson we get when we do relativity.

But wait a minute, we find something else about our laws-- all except for gravity, we can express them in a particularly convenient form, the form of that simplest of all tensor contractions, the dot product. But it comes with a price-- they only work in that convenient form for inertial observers. This is true even before we ever think about gravity, so forget that gravity even exists.

So look what we've done-- in our hunger for the simplest mathematics, that can be done with dot products (with +--- signature, of course), we have allowed ourselves to exclude some of the observers! How ethnocentric is that, we only get away with it because our own frame tends to be very nearly inertial for most applications. Did we learn the lesson of relativity I mentioned above? No! We left the lesson behind, all just to be able to use dot products. And so, we genuflect to the throne of the Lorentz transformation, even to the degree that doing anything else is considered sacrilege (I mean, ATM)!

This is all true even eithout gravity. Now comes the ultimate irony-- our laws cannot even be expressed in terms of dot products, because gravity cannot. But amazingly, because gravity cannot, we relegate the one way of thinking about all this that liberates us from dot products, and carries the true message of relativity to all observers, to problems that involve gravity, problems that are too hard for most to even understand! What we should be asking ourselves is why there should be GR even in a universe with no gravity at all. That's what I'm talking about here.

forrest noble

2010-Feb-09, 08:32 PM

korjik,

..........I cant imagine that Dirac didnt spend many hours trying to get GR and QM to work together.

Just by analyzing the equations of General Relativity compared to the mathematical system of Quantum Mechanics, philosophies and verbiage aside, it becomes apparent and is well known that behaviors of entities of the macro-world and micro-world are different so that there seems to be no value in trying to combine the two mathematical systems. Special Relativity and Lorentz Transforms, on the other hand, seem to fit in both worlds.

The underlying problem and question seems to be why this behavior difference between the macro and micro worlds exists. There have been a number of proposals why these differences exist generally involving so-far undiscovered particles. Proposals that might fit the bill may be: dark matter, gravitons, Higgs particles, Planck particles, quantum foam, strings, etc. etc. etc. all of which could be described as an aether-like omni-present background field contained within the ZPF.

Such a field of particles could influence combined molecular matter differently than micro-matter. An analogy might be a ship on a placid ocean compared to the salt within it. From this perspective there would be boundary entities in size that would be effected by both worlds such as maybe the water molecules in this analogy.

If any of the above or another new theoretical entity was discovered in the ZPF, one might expect at least changes in the verbal understandings of physics as well as conceivable changes in the mathematics involved (General Relativity, Quantum Mechanics) over time depending upon the details of the particular discovery(s). Such changes could lead to the mutual compatibility of the two theories or their predecessors. The mathematics of Special Relativity/ Lorentz Transforms, however, would seemingly remain unchanged.

DrRocket

2010-Feb-09, 09:15 PM

Just by analyzing the equations of General Relativity compared to the mathematical system of Quantum Mechanics, philosophies and verbiage aside, it becomes apparent and is well know that behaviors of entities of the macro-world and micro-world are different so that there seems to be no value in trying to combine the two mathematical systems.

1.. QM and GR are NOT mathematical systems. They are physical theories, and in fact QM at the level of quantum field theory is not mathematically well-defined or rigorous.

2. It will come as quite a shock to the best liviing theoretical physicists that there is no value in trying to unify quantum theory and general relativity. That is the single greatest outstanding problem in all of theoretical physics and it has attracted the attention of a few pretty good minds -- Witten, Weinberg, Maldecena, Wilczek, 'tHooft, Hawking, Penrose, Green, Schwarz, to name a few.

korjik

2010-Feb-09, 11:52 PM

You still are not hearing. Let me clarify further.

I could do dynamics with no relativity at all, if I had force laws that gave me the acceleration of things in a particular frame, call it frame A. I'd just say, all measurements have to be in that frame. Anybody in another frame can simply watch the clocks and rulers in frame A as they zoom by, and apply my dynamical theory to those measurements. Done, we have a complete physics.

Only if c is infinite. Otherwise you are doing Galilean relativity.

But wait a minute, you say, the observers want a physics that works with their own clocks and rulers? Picky picky, what troublemakers. Oh all right, I suppose we're going to need relativity after all. So even in a universe with force laws like that, we'd still need relativity, so that all the observers get to play.

To amplify on what I wrote above, technically, with a finite c, you still need relativity to take into the differences in observation even if everyone is using the same clock. Two different observers will see the same set of events in different orders, and the laws of physics will act to each as the order that the observer saw. The fact that one or the other can figure out the other's order is pretty irrelevant.

Now, our universe isn't actually like that, our dynamical laws don't live in a particular frame, they are expressible in coordinate-free form. That gives us another really good reason to let all the observers play that isn't just politically advisable-- the laws respect a property that they should work the same for all observers. The universe itself is democratic, and this is the particular lesson we get when we do relativity.

You are anthpomorphising the universe. It isnt political, advisable, or democratic. Not only that, the property that all laws should work the same is an assumption, not proven. If you want a real flaw in physics, it is the implicit admission that we cannot do physics when we cannot know the laws, as in we dont know how the laws would change with position, so we must assume that they dont just so we can get something done.

But wait a minute, we find something else about our laws-- all except for gravity, we can express them in a particularly convenient form, the form of that simplest of all tensor contractions, the dot product. But it comes with a price-- they only work in that convenient form for inertial observers. This is true even before we ever think about gravity, so forget that gravity even exists.

Yes, you have just pointed out what the 'Special' in Special relativity is. When you add gravity it becomes 'General', that is what the 'General' is. As a matter of fact, SR excludes gravity for most application simply because it makes frames non-inertial.

So look what we've done-- in our hunger for the simplest mathematics, that can be done with dot products (with +--- signature, of course), we have allowed ourselves to exclude some of the observers! How ethnocentric is that, we only get away with it because our own frame tends to be very nearly inertial for most applications. Did we learn the lesson of relativity I mentioned above? No! We left the lesson behind, all just to be able to use dot products. And so, we genuflect to the throne of the Lorentz transformation, even to the degree that doing anything else is considered sacrilege (I mean, ATM)!

Actually, we have excluded every other observer. We had that property from the beginning tho. The only way to get rid of that is to make the coordinate transform irrelevant by making c infinite.

You really are starting to sound like an ATMer. There is no throne SR sits on. It is simply the best fit over the largest area. It is well known to be limited and problematic. It will be tossed into the same place as Newtonian dynamics the second a complete theory explains things better. GR and QM will go that same way too. You are rapidly drifiting into an apparent belief that current mainstream is dogma, and it dosent suit you. You really should know better.

This is all true even eithout gravity. Now comes the ultimate irony-- our laws cannot even be expressed in terms of dot products, because gravity cannot. But amazingly, because gravity cannot, we relegate the one way of thinking about all this that liberates us from dot products, and carries the true message of relativity to all observers, to problems that involve gravity, problems that are too hard for most to even understand! What we should be asking ourselves is why there should be GR even in a universe with no gravity at all. That's what I'm talking about here.

Now you are prosletizing.

You say 'What we should be asking ourselves is why there should be GR even in a universe with no gravity at all. That's what I'm talking about here.'

In the first place, we dont live in that universe. Second, you have gone back to doing SR, which IIRC is GR in a gravity free environment. Either that or you need GR to account for non-inertial events.

You seem to fail to understand that we know that GR is wrong, that it does not properly describe everything. We have to use what we know now to understand what we know now. Yet there are entire generations of young men and women who spend entire lives trying to change that. They are not slaves to their learning, they use that learning to be able to critique new ideas that come up. I have seen and been a part of discussions like this on levels from a bunch of undergrads BSing to a group of full professors discussing things I hardly understand. The problem is not the way we learn, it is that this isnt an easy problem. Dozens of nobel prize winners couldnt hash this one out.

macaw

2010-Feb-10, 07:10 AM

so one cannot derive SR solely from the first postulate alone.

This is demonstrably false. It has been done by many mainstream scientists. Check out the references I already gave in this thread.

Ken G

2010-Feb-10, 07:49 AM

To amplify on what I wrote above, technically, with a finite c, you still need relativity to take into the differences in observation even if everyone is using the same clock. No, if they all use the same clock, physics is done, because physics is about predicting the measurements. You are bringing in some sort of perception element that would not be part of physics in a universe where everyone does physics with the same clocks. But I'll grant you, that's not how we do physics, it's just a set-up for understanding why we don't do it that way.

You are anthpomorphising the universe. It isnt political, advisable, or democratic.Call it what you like, it respects a principle where all observers are created equal. Not just inertial ones, this is the point.

Not only that, the property that all laws should work the same is an assumption, not proven.Nothing is ever proven in science. What is relevant is that the proposition is successful, insightful, powerful, and unifying.

Yes, you have just pointed out what the 'Special' in Special relativity is. When you add gravity it becomes 'General', that is what the 'General' is.No, it really isn't, that's the point-- your statement is exactly the "ossification" I'm trying to correct! There would still be general relativity in a universe with no gravity, the "general" means "all observers, not just inertial ones." How can you agree with me what the "special" means, but not what the "general" means? Special and general are related terms.

Actually, we have excluded every other observer. We had that property from the beginning tho. The only way to get rid of that is to make the coordinate transform irrelevant by making c infinite.

Or invent a form of relativity that is more general. Wait, we did that, but apparently no one was paying close attention!

You really are starting to sound like an ATMer. Et tu? I really don't understand why this point cannot be heard.

You are rapidly drifiting into an apparent belief that current mainstream is dogma, and it dosent suit you. You really should know better.No, you just haven't understood what I'm saying.

In the first place, we dont live in that universe. Sure we do, we live in a universe where gravity can quite often either be ignored, or treated as constant (which would not require any heavy lifting, Rindler cut the trail), in very many of the problems that come up in physics. Since when is it a valid argument that a particular approach to physics is not useful unless it works in every situation?

Second, you have gone back to doing SR, which IIRC is GR in a gravity free environment. Either that or you need GR to account for non-inertial events. I need GR to describe the reality of non-inertial observers, which is not SR in exactly the same way that everyone using the same clocks is not relativity. I'm not sure what you mean by non-inertial events.

You seem to fail to understand that we know that GR is wrong, that it does not properly describe everything. I have no problem with that, I understand what physics is.

The problem is not the way we learn, it is that this isnt an easy problem. Dozens of nobel prize winners couldnt hash this one out.But that's just it, what I'm talking about here is not that difficult at all, because we're not doing tidal gravity. All it requires is bumping tensors up in our estimation of what are the important lessons of physics. We don't need to make it any harder than SR, because we can always choose to make the restrictions to inertial observers and reduce the tensor contractions to dot products any time we want. Embedding the dot products into the more general scheme is not so hard, since you're not making anyone grind out the Cristoffel symbols-- it's just insightful, and puts the Lorentz transformation into its proper perspective.

Ken G

2010-Feb-10, 07:59 AM

This is demonstrably false. It has been done by many mainstream scientists. Check out the references I already gave in this thread.That's a nitpick. You really can't get SR from the first postulate because almost everyone thinks of SR as a theory with a finite speed of light, and you indeed cannot get that from the first postulate. grav is thinking of the second postulate as the place where the speed of light is codified into the theory.

Locomotion

2010-Feb-10, 02:48 PM

Seems to me we need additional context all over the place to address this sort of question.

If literally all we have are the two postulates, is GR not a counterexample? It isn't SR, and it obeys the two postulates, doesn't it?

As for the necessity of the second postulate, Newton's mechanics obey the first postulate, but not the second, unless you go mucking around with ether trying to reconcile it with Maxwell's equations. So I would offer Newton's physics as a counterexample to the argument that the second postulate is not needed. If anyone argues that this is an unsatisfactory answer, because it doesn't explain electromagnetism, I would point out that, unlike SR, it does have gravity in it. So if it isn't good enough, how comprehensive do the "laws of physics" referenced in the first postulate have to be?

The reference to "inertial" in the first postulate suggests to me motion at a constant velocity in a straight line, so we need some definition of a straight line through space, and some measure of time so we can measure movement through space. We also have a reference to "frames", which sounds like different coordinate systems to me.

Are we to take as axiomatic flat space, and that an object moving inertially in one frame, is moving inertially in another frame? This means a straight line has to map to a straight line, and time also has to transform in a way that constant velocity maps to constant velocity. Then the transform from one coordinate system to another has to be linear. If you don't need the second postulate, then t' = t and orthogonal rotations of the spatial axis do the trick, and get the physics of Newton. Add the constraint that any motion at some particular speed in one frame, must map to the same speed in other frames, then we have something like the Lorentz transform, but with the possibility of scaling and reversal of the axis (for example, we could have time run backwards in one frame). If we treat scaling and reversal as arbitrary and meaningless, we get the Lorentz transform.

So all that follows from the requirement that constant motion in a straight line in one frame maps to constant motion in a straight line in other frames, and a velocity of c (where c is some number) maps to c in other frames. No need of the first postulate, really, because so far, there are no laws of physics in this system. I guess we could add some.

Not sure if this adds anything, I'm mostly thinking out loud here, but have I got it right?

Ken G

2010-Feb-10, 03:48 PM

Seems to me we need additional context all over the place to address this sort of question.

If literally all we have are the two postulates, is GR not a counterexample? It isn't SR, and it obeys the two postulates, doesn't it?

Good point. GR throws out the concept of global inertial frames, so one would have to interpret the SR postulates as being about global frames, not just local ones. There are certainly hidden assumptions about the nature of spacetime. But we can still look at the postulates as stating those elements of the theory which are surprising or unique to that theory.

As for the necessity of the second postulate, Newton's mechanics obey the first postulate, but not the second, unless you go mucking around with ether trying to reconcile it with Maxwell's equations. No, Newton's laws don't obey the first postulate, because Newton's laws implicitly assume that the inertial mass is observer-independent. To use Newton in our universe, even in the absence of light and Maxwell's equations, you still have to allow the inertia to be velocity dependent, which is only justified by the first postulate with a finite speed of light (which might be what we could assert is the physics of the second postulate).

So I would offer Newton's physics as a counterexample to the argument that the second postulate is not needed. I would agree that it's a very trivial form of SR if we cannot assert that the speed of light is finite, and that is pretty much where the second postulate comes in. But I've argued that the second postulate is then not interpreted as a postulate of relativity, but rather a postulate of the underlying dynamics, so it belongs in with Newton's laws in the frame comoving with the object in question.

So if it isn't good enough, how comprehensive do the "laws of physics" referenced in the first postulate have to be?The first postulate still holds in GR if it is interpreted only locally, i.e., if an "inertial frame" is one that acts locally inertially, but not globally so-- it can't handle tides.

The reference to "inertial" in the first postulate suggests to me motion at a constant velocity in a straight line, so we need some definition of a straight line through space, and some measure of time so we can measure movement through space. We also have a reference to "frames", which sounds like different coordinate systems to me.

Exactly, this is also what I've been saying. SR is fundamentally about how to coordinatize inertial frames (in the sense of frames of objects with no real forces on them) so that they are indeed inertial (in the sense that things move in straight lines at constant speed if there are no real forces). It's just instructions for making coordinates when you include the second postulate as a postulate of relativity, but coordinates aren't physics.

If you don't need the second postulate, then t' = t and orthogonal rotations of the spatial axis do the trick, and get the physics of Newton. The first postulate is not by itself a theory of physics, it requires an underlying dynamical theory that works. If you have that, the first postulate will generalize it to inertial observers, which is part of what we might call relativity (though it falls short of being real relativity as it leaves noninertial observers behind). Newton's laws with an infinite speed of light map under the first postulate into Galilean relativity for inertial observers, but if you also assert in the dynamics that the signal speed is finite, then you get Lorentzian relativity for inertial observers.

So all that follows from the requirement that constant motion in a straight line in one frame maps to constant motion in a straight line in other frames, and a velocity of c (where c is some number) maps to c in other frames. Yes, this called the "Poincare group."

No need of the first postulate, really, because so far, there are no laws of physics in this system. I guess we could add some.Yes, and the first postulate gives a constraint on those laws-- that when the laws identify an inertial observer, all other inertial observers have to be able to agree on that subclass. Otherwise, they aren't agreeing on the laws themselves, but you are right that this all assumes we have a coordinatization that picks out inertial motion for special consideration. Polar coordinates, used all the time in physics, don't even do that.

macaw

2010-Feb-10, 04:14 PM

That's a nitpick. You really can't get SR from the first postulate because almost everyone thinks of SR as a theory with a finite speed of light, and you indeed cannot get that from the first postulate. grav is thinking of the second postulate as the place where the speed of light is codified into the theory.

I don't think so. Experiment already established the speed of light as being finite, so there is no need to postulate it. This was known from the times of Olle Roemmer. Once you accept that light speed is finite you can derive SR from PoR only. It is the independence of light speed from the relative speed of the observer wrt the source that falls out straight from PoR, so "axiom 2" is definitely dependent on axiom 1.

Ken G

2010-Feb-10, 06:23 PM

I look at it that way also, but one can imagine different places where these various experimental facts get codified into the overall theory. I don't like the overall scheme SR uses to codify the experiments, so I don't see the role of the second postulate issue as being the largest problem. SR doesn't even do rotating observers.

macaw

2010-Feb-10, 06:31 PM

SR doesn't even do rotating observers.

Actually, it does. I can recommend two or three excellent papers on the subject.

Ken G

2010-Feb-10, 09:58 PM

Shall I dig up the thread where you claimed SR can't even handle accelerated observers, and now you claim it can handle rotating ones? I already know that any source you can give that treats rotating observers is not going to be SR, just as any attempt to use Newton's laws on a rotating observer is not Newton's laws, expressly because it will not follow the postulates of either theory. What it will be, of course, is a simple extension of either theory, breaking its postulates, but doing so in a clearly innocuous way, just as we do to Newton the instant we talk about "centrifugal force" or as we do to Lorentz as soon as we talk about a metric that is not the Minkowski metric. What I'm also saying is that "breaking the postulates of SR in an innocuous way" is called general relativity without gravity. That this is not SR is why I have advocated against SR in the first place.

macaw

2010-Feb-10, 10:21 PM

Shall I dig up

You'd be wasting your time looking in vain for a claim that I never made.

the thread where you claimed SR can't even handle accelerated observers,

I don't know why you feel compelled to make false statements every time I contradict you. I never claimed that SR cannot handle accelerated motion/observers. Feel free to google "the equations of hyperbolic motion in SR".

and now you claim it can handle rotating ones? I already know that any source you can give that treats rotating observers is not going to be SR,

That's too bad, since you are wrong. I can even recommend a very good book on the subject, you should read it sometimes :-)

tusenfem

2010-Feb-11, 07:01 AM

Enough bickering. byebye. thread closed.

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