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worzel
2004-Oct-16, 12:47 AM
Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

Grand Vizier
2004-Oct-16, 01:46 AM
Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

Weird, worzel. I was just thinking about starting a thread to ask about the current status of Mach's Principle when I read your post (I was pondering all that geocentric stuff). I know that the term was coined, not by Mach, but by Einstein. And I know that it means that, if true, the properties of mass, including inertia, can only be defined with regard to the 'Fixed Stars' (as Mach would have put it). But it still seems like 'spooky action at a distance', (as Einstein would have put it).

And I've seen it described as obsolete on several sites. But if Mach's Principle is metaphysical nonsense, what have we replaced it with, exactly?

Grey
2004-Oct-16, 01:46 AM
Is this true? I thought it was just an idea.
My understanding is that although Einstein was intrigued by Mach's Principle, and it was part of the inspiration for general relativity, general relativity does not in fact incorporate it. That is, it's entirely possible to accept general relativity without considering Mach's Principle to be true.

I've always wondered if it's more of a philosophical point anyway. The obvious experimental test would be to check and see whether an object still shows inertial effects if you remove everything else from the universe, but it seems like that would be difficult to arrange. :D

Of course, if the Higgs boson is eventually found and indeed proves to be the cause of inertia, that would seem to show this to be false, but it might still be possible to reconcile the two ideas, I suppose.

Grand Vizier
2004-Oct-16, 02:27 AM
Is this true? I thought it was just an idea.
My understanding is that although Einstein was intrigued by Mach's Principle, and it was part of the inspiration for general relativity, general relativity does not in fact incorporate it. That is, it's entirely possible to accept general relativity without considering Mach's Principle to be true.

I've always wondered if it's more of a philosophical point anyway. The obvious experimental test would be to check and see whether an object still shows inertial effects if you remove everything else from the universe, but it seems like that would be difficult to arrange. :D


Depends how big the funding we can get is... :)



Of course, if the Higgs boson is eventually found and indeed proves to be the cause of inertia, that would seem to show this to be false, but it might still be possible to reconcile the two ideas, I suppose.

Thanks. I understand that the Higgs Boson 'may be responsible for many of the properties of matter', but I have not seen it linked with, or opposed to, Mach's Principle on this forum, or anywhere else, come to that. The 'God Particle' has somehow failed to interest me to date, but if these are the stakes...

George
2004-Oct-16, 04:08 AM
Mach's principle, as this bucket story exemplified, was taken up by Einstein in his theory of general relativity. The gravitational effects of the distant stars and planets, Einstein showed, do provide the inertia of masses.

Is this true? I thought it was just an idea.

That doesn't sound right to me. Newton felt the bucket water would become concave due to absolute space. Einstein showed space is not absolute, but spacetime is absolute. I think he called it "invariance theory" but others, media especially, liked calling it relativity instead.

The bucket test would work independent of other stars. However, their mass/energy affect spacetime. It is this interaction with space that gives some connection to Mach.

Unfortunately, I am not a GR person, but thought I'd throw that out at you anyway. Hopefully, others will elaborate and correct. :)

dgruss23
2004-Oct-16, 01:19 PM
Bondi discussed this in his 1952 Cambridge Monographs on Physics book titled Cosmology.

He began the Chapter IV titled "The Problem of Inertia" by noting that the Earth's rotation speed can be measured by terrestrial experiments such as the focault pendulum and by astronomical measurements with respect to the fixed stars. Since both measurements agree, Bondi asks if this can be a coincidence or if it requires a dynamical explanation.

In Mach's view an explanation is required.

Bondi then proposes that if it is assumed the coincidence of the terrestrial and astronomical reference frames is not a result of Newton's laws or GR, then it becomes necessary to postulate a causal connection between the motions of the stars and the motions of local inertial frames. Bondi concludes that since the local frame cannot be influencing the motions of the stars, then the stars must influence the local inertial frame.

This is Bondi's statement of Mach's Principle: "the local inertial frame is determined by some average of the motion of the distant astronomical objects."

It seems quite philosophical.

worzel
2004-Oct-16, 03:44 PM
It seems quite philosophical.
Yes, I always thought it was. But what I read suggested that it is implicit in GR. As you can explain all the local phenomena on a stationary earth using GR, it wouldn't suprise me if it were true, except that I've never heard it claimed before.

Evan
2004-Oct-16, 05:03 PM
My understanding is not that the "distant remote fixed stars" actually somehow cause inertia. Thet are simply what was considered an absolute reference point for the frame of motion locally.

Mach wrote: "All masses and all velocities, and consequently all forces, are relative. There is no decision about relative and absolute which we can possibly meet, to which we are forced, or from which we can obtain any intellectual or other advantage. (Mach, The Science of Mechanics, ch.2, vi-3, Open Court, 1960, 279)"

http://www.bun.kyoto-u.ac.jp/~suchii/mach.pr.html

Since all bodies locally can be observed to be moving relative to one another we need a reference that is not observed to be moving. Unfortunately it was not appreciated that the universe was expanding and the distant "fixed" stars are no such thing.

Well, maybe they are fixed. Here is a different interpretation of redshift.

http://www.halos.com/reports/arxiv-1998-redshift.pdf

A Thousand Pardons
2004-Oct-16, 05:24 PM
My understanding is not that the "distant remote fixed stars" actually somehow cause inertia.
If you are talking about Mach's Principle, I would have to disagree. Here's a short pithy statement of it from Mathworld (http://scienceworld.wolfram.com/physics/MachsPrinciple.html):
What this implies is that the inertia of a body here is influenced by matter far distant.

Evan
2004-Oct-16, 06:38 PM
I dunno about that. It seems Einstein was "putting words" into Mach's mouth.

"The above version of the principle is largely due to Albert Einstein, who brought the principle into mainstream physics whilst working on general relativity. Indeed it was Einstein who first coined the phrase Mach's principle. There is much debate as to whether Mach really intended to suggest a new physical law since he never states it explicitly. He is more concerned with criticising Newton's mechanics, in particular the idea of absolute space."

http://www.wordiq.com/definition/Mach's_principle

I would like to find a copy of Mach's work in the original German and see what he really wrote. A lot can be lost in translation. I have found quite a few references and excerpts here (http://idefix.physik.uni-freiburg.de/~aufgabe/Skripte/RaumZeit.pdf)

"Was fuer ein Ziel will und kann die Wissenschaft erreichen, der ich mich hingebe? Inwiefern sind deren
allgemeine Ergebnisse ”wahr“? Was ist wesentlich, was beruht nur auf Zufaelligkeiten der Entwicklung?"

Here Einstein asks Mach what results can he expect to use from the work (Mach's) . What has been shown to be "true" and what actually useful developments can he expect.


In "Die Mechanik" Mach claims the "Fixsternhimmel" as a reference frame. This is where subtle translation errors can creep in. That means "Fixed star sky" or the universe, NOT necessarily the fixed stars themselves.

I don't have time now to do more reading on this now but I believe there is room to interpret what Mach meant differently from what is given as accepted.

A Thousand Pardons
2004-Oct-16, 07:07 PM
I dunno about that. It seems Einstein was "putting words" into Mach's mouth.
more or less, but the result was what we know as Mach's Principle.

Einstein thanked Mach for his contribution to general relativity, but I think Mach disowned the results, so you probably won't find a lot of support for Mach's Principle in Mach's works, other than a general push in that direction.

Normandy6644
2004-Oct-16, 07:15 PM
Didn't Einstein eventually abandom Mach's principle with GR anyway?

A Thousand Pardons
2004-Oct-16, 07:30 PM
Didn't Einstein eventually abandom Mach's principle with GR anyway?
It doesn't seem to be that Einstein abondoned Mach's Principle with General Relativity. Pais says Einstein was disappointed that General Relativity didn't lend strong support to Mach's Principle, and eventually quit his insistence on Mach's Principle. However, there are still physicists today who accept General Relativity, and support Mach's Principle.

ToSeek
2004-Oct-16, 10:04 PM
My explanation of inertia is that stuff is lazy.

A Thousand Pardons
2004-Oct-16, 10:21 PM
My explanation of inertia is that stuff is lazy.
Close to my own--my answer to inertia is a stuffed lazyboy

worzel
2004-Oct-17, 11:58 AM
I guess the lack of a resounding "yes" means that it isn't implicit in GR.

Grand Vizier
2004-Oct-17, 12:22 PM
The whole issue seems like a major dangling loose end to me. But Grey mentioned the Higgs Boson. While Googling gives few link-ups between this and Mach's Principle, there are a few more with regard to the Higg's Field. Like this AIP abstract:

A vacuum—generated inertia reaction force (http://content.aip.org/APCPCS/v573/i1/89_1.html)

My physics isn't that great, but it seems to me that the authors here are suggesting that the Higgs Field resists acceleration like air resistance with velocity, which would make inertia a local phenomenon, I guess. But I'm not sure how the Higgs Field provides some sort of reference framework. (I'm getting muddled.)

They do seem very definite:


This analysis strongly supports the concept that inertia is indeed an opposition of the vacuum fields to any attempt to change the uniform state of motion of material bodies. This also definitely shows that inertia should be viewed as extrinsic to mass...

And then go on to say that:


It is also briefly discussed why a strict version of Mach's Principle does really contradict this view, though a broad sense version of Mach's Principle may be in agreement.

So it seems the Principle is still with us in some form...

A Thousand Pardons
2004-Oct-17, 12:26 PM
I guess the lack of a resounding "yes" means that it isn't implicit in GR.
yes and no (http://www.badastronomy.com/phpBB/viewtopic.php?p=348799#348799) :)

worzel
2004-Oct-17, 12:39 PM
I guess the lack of a resounding "yes" means that it isn't implicit in GR.
yes and no (http://www.badastronomy.com/phpBB/viewtopic.php?p=348799#348799) :)
:D Philosophical then.

Padawan
2004-Oct-17, 01:53 PM
I would define Inertia as


The reluctant force within you that strongly prevents you from doing your job, studying, or carrying out any other task you know that you have to do.

Inertia is also known as lazyness :P

A Thousand Pardons
2004-Oct-17, 02:34 PM
Philosophical then.
You mean me? Of course. Just ask soupdragon2. :)

Evan
2004-Oct-18, 05:38 AM
A small reminder. General Relativity deals with gravity, how it results and the effects that are due. It does not deal with the speed of light. General relativity incorporates the laws of motion as stated by Newton and expands upon them.

Special Relativity deals with the speed of light and the concepts of simultaneity, the constancy of the speed of light and time.

Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity. Special relativity deals with the relative motions of objects up to and including the speed of light.

It is amazing to me to think that these people, Einstein, Mach, Lorentz et al were formulating these fundamental concepts that still hold true today when thier likely primary mode of transportation was a horse and buggy.

The two theories are related but not the same. General relativity went through many revisions by Einstein until its final form as published in 1916.

Jerry
2004-Oct-18, 08:38 AM
...Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity. Special relativity deals with the relative motions of objects up to and including the speed of light...

The two theories are related but not the same. General relativity went through many revisions by Einstein until its final form as published in 1916.
This is not correct, Special Relativity is a linear application of GR that shows up when you drop out all the unneeded terms. One can argue you can pull GR out of SR, but you must first define gravity as a tensor with space and time bending attributes.

However, if mass is assumed to slow the speed of light via a Lorentz transform, rather than bending time and space, a variant form of (time constant) SR can be expanded to (time constant) GR without introducing any new parameters.

We should not consider this unfathomable: We change the speed of light inside dense molecular structures without a second thought. Why isn't this EM effect assumed to be the same as gravitational lensing? Are not the results the same?

A Thousand Pardons
2004-Oct-18, 01:15 PM
A small reminder. General Relativity deals with gravity, how it results and the effects that are due. It does not deal with the speed of light. General relativity incorporates the laws of motion as stated by Newton and expands upon them.
General relativity incorporates the laws of special relativity as well.


Special relativity is most notable for the concept that physics is the same for all observers. This is not addressed in General Relativity.

O yes it is. Special relativity restricts itself to observers in inertial reference frames, as a basis, whereas general relativity expands that to all observers, even those in non-inertial reference frames.

It is amazing to me to think that these people, Einstein, Mach, Lorentz et al were formulating these fundamental concepts that still hold true today when thier likely primary mode of transportation was a horse and buggy.
And (gasp) wrote letters and posted them, as their primary means of communication :)

Evan
2004-Oct-18, 03:10 PM
General relativity incorporates the laws of special relativity as well.

Implict, yes. Explicit, no.

I have a small puzzle for anyone to explain...

Einstein was particularly fond of what he called a "thought experiment". In
his explanation of the General Theory he refers to a "man in a chest" (read
elevator) being drawn at a constant rate by a never ending force, that is,
the elevator is being accelerated at a constant rate. He further postulates
that the man within the "chest" cannot perform any experiment that will
permit him to distinguish that he is in an accelerating frame of reference
rather than in a gravitational well created by matter. Einstein specifically
makes reference to a mass suspended from a hook on the ceiling of the
"chest" by a rope. This constitutes a pendulum.

When the pendulum in the accelerating frame of reference is swung it will
have a period that is determined by the length of the rope and the degree of force caused by the acceleration of the closed frame of reference (the elevator). In the spirit of Einstein we shall ignore friction, internal heating of the fibers of the rope etc. We concern ourselves with only the elements of the problem that are relevant to the Theory.

Here follows what may be a flaw in Einstein's theory, or, is it not a flaw, and if
not, please explain why.

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing. It describes an arc as it
swings. At the end of the arc it is closer to the "roof" of the elevator
than when it is at the mid-point of the swing, yet the force due to
acceleration is exactly the same at all points within the closed frame of reference.

When a pendulum swings in a gravitational field this is not the case. We
imagine the "chest" as resting on the surface of a gravitational body so
that the pendulum "feels" exactly one gee gravity at the mid-point of the
swing. Since gravity is created as a consequence of the existence of matter
and agglomerations of matter take a spherical shape when present in large
quantities, the pendulum experiences a different gravitational force when it
is at the ends of the arc as opposed to the force experienced at the
mid-point. Gravity decreases as the inverse square of distance from the body
that produces the field. At the ends of the arc of the pendulum it is
further from the centre of the gravitational mass and therefore experiences
less gravitation. Einstein was well aware of this. It would seem that the
pendulum swinging in the gravitational well should have a slightly longer
period. Does it?

If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?

ngc3314
2004-Oct-18, 03:19 PM
General relativity incorporates the laws of special relativity as well.

Implict, yes. Explicit, no.

I have a small puzzle for anyone to explain...

Einstein was particularly fond of what he called a "thought experiment". In
his explanation of the General Theory he refers to a "man in a chest" (read
elevator) being drawn at a constant rate by a never ending force, that is,
the elevator is being accelerated at a constant rate. He further postulates
that the man within the "chest" cannot perform any experiment that will
permit him to distinguish that he is in an accelerating frame of reference
rather than in a gravitational well created by matter. Einstein specifically
makes reference to a mass suspended from a hook on the ceiling of the
"chest" by a rope. This constitutes a pendulum.

(...snip...)

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing. It describes an arc as it
swings. At the end of the arc it is closer to the "roof" of the elevator
than when it is at the mid-point of the swing, yet the force due to
acceleration is exactly the same at all points within the closed frame of reference.

When a pendulum swings in a gravitational field this is not the case. We
imagine the "chest" as resting on the surface of a gravitational body so
that the pendulum "feels" exactly one gee gravity at the mid-point of the
swing. Since gravity is created as a consequence of the existence of matter
and agglomerations of matter take a spherical shape when present in large
quantities, the pendulum experiences a different gravitational force when it
is at the ends of the arc as opposed to the force experienced at the
mid-point. Gravity decreases as the inverse square of distance from the body
that produces the field. At the ends of the arc of the pendulum it is
further from the centre of the gravitational mass and therefore experiences
less gravitation. Einstein was well aware of this. It would seem that the
pendulum swinging in the gravitational well should have a slightly longer
period. Does it?

If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?

This is why Einstein (or at least his later interlocutors I've read) specify that the equivalence is local - that is, the experiment is specified to encompass such a small region that the nonparallel direction of gravitational acceleration due to proximity to the center of attraction, or "vertical" extent changing the acceleration, are not measurable. The issue is not whether you can decide from a finite experiment whether you are near a mass or accelerating, but (as I understand it, the main point) that as one approaches a truly local set of measurements, the effects become indistinguishable. Thought experiments can be such wonderful things - you seldom need to get a proposal funded...

Evan
2004-Oct-18, 03:29 PM
as one approaches a truly local set of measurements, the effects become indistinguishable.

Don't think so. As a thought experiment you have at your disposal instruments of infinite sensitivity. Was Einstein wrong or did he just oversimplify in some manner? Or, is there a reason that the pendulum DOES have exactly the same period in both cases?

ToSeek
2004-Oct-18, 03:29 PM
Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

worzel
2004-Oct-18, 03:32 PM
Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.
But the equipment available in this thought experiment could be an infinitely large planet with a fintie gravitional pull :)

Evan
2004-Oct-18, 03:36 PM
Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

Care to explain?

A Thousand Pardons
2004-Oct-18, 04:13 PM
Implict, yes. Explicit, no.

I would have said explicit, yes, but that's just me. :)


Here follows what may be a flaw in Einstein's theory, or, is it not a flaw, and if not, please explain why.

The pendulum in the elevator experiences the exact same degree of
accelerational force at all points in its swing.

That's not quite true (see the discussion on this board about the rope paradox), but it's true enough for these purposes.


If the elevator is accelerating at one gee and the gravitational field is
one gee there appears to be a discrepancy in the forces "felt" by the
pendulum in the two frames of reference. Yet Einstein postulates there is
none. Why is this so?
Einstein was well aware of the discrepancy, he did not postulate that there was none. Just as before, above, the discrepancy is small enough that it doesn't matter in the case at hand.

Grey
2004-Oct-18, 04:22 PM
But Grey mentioned the Higgs Boson. While Googling gives few link-ups between this and Mach's Principle, there are a few more with regard to the Higg's Field.
The link you'd found is more or less what I was suggesting. That is, if it's an interaction with the Higgs boson that's the cause of inertia, then it would seem to be a purely local phenomenon. However, since one can view the Higgs partical as a disturbance in the Higgs field (and indeed, I believe that it's possible for there to be a Higgs field without a particle manifestation, though that's not the way most particle physicists are betting), one could at least postulate that the field has whatever properties it has because of interactions with all the matter in the universe. It seems unlikely to me, but that doesn't mean that it isn't the way the universe works. :D

I do wonder if the reason for the small number of references is that Mach's Principle is more of a philosophical position, whereas those searching for the Higgs particle are hard-core particle physicists, who may be less concerned about philosophical matters. But that's pure speculation on my part.

Evan
2004-Oct-18, 04:24 PM
he did not postulate that there was none.

Yes he does.

Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?

Grey
2004-Oct-18, 04:31 PM
Yes he does.

Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?
Yes he is. The "suitably chosen gravitational potential" that would be equivalent would be that created by an infinite flat plane, which gives an attractive force that doesn't vary in direction or fall off with distance.

Of course, there aren't any such objects, but since he's talking about a small region, any gravitational field that could be considered constant within that region would work, too. How well the two situations agree depends on just how quickly the real gravitational field varies, and how small you're willing to make the region of interest.

A Thousand Pardons
2004-Oct-18, 04:31 PM
he did not postulate that there was none.

Yes he does.

No, I disagree. As I said before, he was aware of the discrepancy.


Quote from Einstein: "Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

That's not exactly "postulating" :)


Further he states: "It is not possible by experiment to distinguish between an accelerating frame and an inertial frame in a suitably chosen gravitational potential, provided that the observations take place in a small region of space and time"

Is he right? Why?
Yes, the key words are "small region of space and time". If you limit your measurements to a small enough region of space and time, you won't be able to measure the difference. If you don't limit it, then you would be able to measure the difference. Einstein's point in saying it that way is essentially the same point that you are making.

As I say, he was aware of the difference.

Evan
2004-Oct-18, 04:37 PM
There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.

A Thousand Pardons
2004-Oct-18, 04:40 PM
There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.
That's right. It has nothing to do with the pendulum thought experiment.

worzel
2004-Oct-18, 05:00 PM
There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.

The principle of Equivalence means just that, equivalence. Not almost equivalent.
As someone pointed out, it is exactly equivalent to an infiinite flat plane with finite gravitional pull everywhere, or in my own words above, an infinitely large planet with finte g.

Grey
2004-Oct-18, 05:09 PM
There is a reason why you can't determine by experiment what frame of reference you are in and it isn't because the effects are too small to measure. The reason is not given by Einstein in his explanation but pertains nonetheless.
I'm curious. What is this other reason you're suggesting?

Evan
2004-Oct-18, 05:24 PM
????

The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame. In a gravitational field time is more dialated the deeper into the gravity well you go. This has the effect of equalizing the measured swing of a pendulum or the velocity of a falling body. It is tied to the concept of simultanaeity. Ironically, it is the one difference between the frames that makes them the same. He intentionally ignores the geometric difference between the frames caused by the radial distribution of gravity vs the rectilinear acceleration in the moving frame. Einstein glossed over that point as being self evident.

ToSeek
2004-Oct-18, 05:31 PM
Given instruments of unrestricted sensitivity, I can think of at least two ways of figuring out whether you're in an accelerating elevator or in a gravitational field, with the given example being one of them.

Care to explain?

Basically, in an accelerating frame, the force of acceleration will be the same everywhere in the elevator. In a gravitational frame, there are two differences:

1. There will be less gravitational force higher in the elevator than lower (this seems to be what you were alluding to).

2. Since the source of gravity is effectively a point, the direction of gravity will be slightly different from one side of the elevator to the other.

A Thousand Pardons
2004-Oct-18, 05:53 PM
The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame.

That's not strictly true. See the rope paradox discussion that I mentioned earlier.


In a gravitational field time is more dialated the deeper into the gravity well you go. This has the effect of equalizing the measured swing of a pendulum or the velocity of a falling body. It is tied to the concept of simultanaeity. Ironically, it is the one difference between the frames that makes them the same. He intentionally ignores the geometric difference between the frames caused by the radial distribution of gravity vs the rectilinear acceleration in the moving frame. Einstein glossed over that point as being self evident.
In the popular expositions, yes. Why wouldn't he? And even then, he didn't really ignore it, as I mentioned before. His wording ("in a small region of space and time") allows just enough reference to it to be accurate without having to go into the gory details.

worzel
2004-Oct-18, 06:14 PM
The reason not given by Einstein is because of the difference in time dialation in a gravitational field vs the constant time dialation in an accelerating frame.
As far as I understood it, the gravity field / acceleration equivalence menas that in the elevator clocks below you run slow while clocks above you run fast. You can also come to this conclusion by considering the acceleration as an ever increasing number of ever smaller lorentz boosts, you get the same answer.

Evan
2004-Oct-18, 06:56 PM
That is correct. In the gravitational field the clock runs slower the further into the field it is. Also, any clock used to measure the period of the pendulum swing will be affected depending on where the swing is measured. Same for a falling body. As it falls into the well time slows in direct proportion to the increase in gravity.

In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.

Grey
2004-Oct-18, 07:52 PM
In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.
I believe this is inaccurate. Observers at the top and bottom of an accelerating elevator will agree that the top clock runs faster and the bottom clock runs slower. The time dilation from gravitational/acceleration effects is based on the potential, which is different at different heights in the elevator, regardless of the fact that the force experienced is the same. Similarly, if there were an infinite flat plane, the time dilation closer to it would be more pronounced than that farther away, even though the force would remain constant.

A Thousand Pardons
2004-Oct-18, 08:25 PM
That is correct.

I believe it is correct too but I think it is the opposite of what you say here:

In the accelerating frame time dialation is equal throughout the frame. It is of course increasing as the frame accelerates but it increases equally at all points. A clock used to measure the pendulum swing experiences the same time dialation regardless of where it is in the accelerating frame.

Evan
2004-Oct-18, 08:25 PM
"The time dilation from gravitational/acceleration effects is based on the potential, which is different at different heights in the elevator"

What potential? When an object is dropped in the accelerating elevator it doesn't fall into a potential well, it is left behind.

A Thousand Pardons
2004-Oct-18, 08:38 PM
What potential?
Remember the principle of equivalence

Evan
2004-Oct-18, 09:32 PM
The principle of equivalence does not mean the two frames of reference are identical. Obviously they are not. It does mean that no test may be performed to distinguish between them and that is so. The limiting factor that prevents distinguishing any difference is imposed by the contraints of simultaneity.

worzel
2004-Oct-18, 09:54 PM
Obviously they are not.
There's that word "obviously" again :)

A Thousand Pardons
2004-Oct-19, 03:31 AM
The principle of equivalence does not mean the two frames of reference are identical.
No, but there is a difference in potential. Think about a ball held near the top, and released. It will pick up speed in that frame, and energy, as it drops from a higher potential to a lower one.

Evan
2004-Oct-19, 03:50 AM
Well, actually the frame picks up speed relative to the ball. It's the frame that has energy added to it, not the ball (until it hits the floor and is also accelerated). Imagine standing in the airlock of a spaceship accelerating at one gee and throwing the ball out the hatch. It will arc away and appear to curve "down" as if it were under the influence of gravity. But it isn't.

This isn't just semantics either. There is a difference in the time dialation in the two frames. It's that difference that equalizes the measured results.

A Thousand Pardons
2004-Oct-19, 04:11 AM
This isn't just semantics either.

I'll agree there. :)

There is a difference in the time dialation in the two frames.
Not according to the experts.

Evan
2004-Oct-19, 04:55 AM
Still disagree, and so do the experts. If you have a clock on the ceiling of the accelerated elevator producing flashing light pulses a detector on the floor will measure a pulse rate that is doppler shifted by the motion of the elevator to produce a shorter period. In the stationary frame in a gravitational field the same period is produced by the variance in time dilation instead of doppler shift. The clock at the top of the elevator runs faster than at the floor because of the variance of time dilation that doesn't exist in the accelerating frame. The net result is the same for both observers but the mechanism is different.

See the section on Principle of Equivalence.

http://www.astro.ucla.edu/~wright/relatvty.htm

Grey
2004-Oct-19, 01:47 PM
The principle of equivalence does not mean the two frames of reference are identical. Obviously they are not. It does mean that no test may be performed to distinguish between them and that is so.
You're saying that there are two situations which are observationally indistinguishable, but then claiming that they are obviously different? How can we tell that they are different?


Still disagree, and so do the experts. If you have a clock on the ceiling of the accelerated elevator producing flashing light pulses a detector on the floor will measure a pulse rate that is doppler shifted by the motion of the elevator to produce a shorter period. In the stationary frame in a gravitational field the same period is produced by the variance in time dilation instead of doppler shift. The clock at the top of the elevator runs faster than at the floor because of the variance of time dilation that doesn't exist in the accelerating frame. The net result is the same for both observers but the mechanism is different.
I'll agree that the mechanism is different depending on which frame of reference you choose. However, the point of the principle of equivalence is that, since I can't tell observationally which is which, I'm free to decide whether my frame of reference is accelerating or in a gravitational field, or perhaps some combination of the two. Remember that the indistinguishability is a postulate here, and the argument you're describing was the one used to show that there had to be gravitational time dilation, so that you wouldn't be able to tell the difference between these two cases.

Evan
2004-Oct-19, 02:57 PM
Grey,

We know the two frames are different. We are outside of them. It is the observer in the frame that can't tell the difference. If you go back to the original question I posed I asked what it was that accounted for the inability of the observer to distinguish the difference. The difference between the two frames is time dilation due to gravity which, as I have said, makes them seem the same. This is an important point that is not explained or touched on by Einstein in his original "Man in the Chest" thought experiment. He was certainly aware of it but he oversimplified his explanation.

Grey
2004-Oct-20, 03:20 AM
We know the two frames are different. We are outside of them. It is the observer in the frame that can't tell the difference.
And what is it that makes choosing an outside frame of reference motionless with respect to the one in the "real" gravitational field better than choosing one motionless with the one that's "obviously" really accelerating? :D Pushing it to an outside observer doesn't really help solve the problem, since under general relativity it's still technically just as appropriate to choose an accelerated outside observer as a non-accelerated one.

To be fair, the first one has the advantage that there's this obvious Earth to account for the apparent gravitational field of the stationary observer, and we can see how the field varies relative to it, but that's a decidely nonlocal consideration, and we can always choose to postulate an infinite flat plane a very long ways away to account for any extra apparent gravitational forces or accelerations.

We can also see that the "obviously" accelerating reference frame seems to be accelerating relative to the "fixed stars", whereas the "stationary" one is not (another nonlocal observation, of course), which may bring us back to the original post here. If there's something special about not being accelerated relative to the "fixed stars", are they somehow responsible for this, as Mach's Principle suggests?


The difference between the two frames is time dilation due to gravity which, as I have said, makes them seem the same. This is an important point that is not explained or touched on by Einstein in his original "Man in the Chest" thought experiment. He was certainly aware of it but he oversimplified his explanation.
I'm not sure I agree. That is, I know that the two observers will disagree about the mechanism involved, but I don't think Einstein glosses over it. In fact, I believe that it was this very thought experiment that first led him to suggest that gravitational time dilation would be observed so that the two cases would remain indistinguishable, even before he had finalized the general theory of relativity.

Evan
2004-Oct-20, 06:38 AM
And what is it that makes choosing an outside frame of reference motionless with respect to the one in the "real" gravitational field better than choosing one motionless with the one that's "obviously" really accelerating?


That is Einstein's choice. His thought experiment assumes unrealistic ideal conditions so as to consider only the matter at hand. A perfectly valid approach. However, when doing so it is then essential to consider all contributions to the matter at hand however trivial. As I said before about the Casimir effect, it's not how well the bear dances, it's that he dances at all. When assuming ideal conditions we have the luxury of assuming infinitely sensitive and perfectly accurate tools. We can and must deal with conditions that cannot be practically measured. I don't think that Einstein used this particular thought experiment to help formulate his ideas on time dilation. The particular difference between the two frames of reference should have been glaringly obvious to him. I have seen it and certainly don't claim to be in his league. He skips the geometry issue as being self evident, which it is. He cannot skip the dilation issue as it does not depend on geometry and applies even to a one dimensional consideration of the problem.

Here is the translation of Einstein's original thought experiment. It is intended to illustrate the principle of Equivalence. It is grossly oversimplified. He does cop out a bit with the word "approximately" but I don't feel that excuses the ommision of the effects of dilation. After all, he is speaking about relativity. It also would do well to remember this is around 1916. The part I have placed in bold is the oversimplification.


Imagine a large portion of empty space, so far removed from stars and other appreciable masses, that we have before us approximately the conditions required by the fundamental law of Galilei.

It is then possible to choose a Galileian reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus.

Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.

To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a "being" (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move "upwards" with a uniformly accelerated motion. In course of time their velocity will reach unheard-of values -- provided that we are viewing all this from another reference-body which is not being pulled with a rope.

But how does the man in the chest regard the process?

The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor.

He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth.

If he release a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment. My words here: Including light pulses...

Relying on his knowledge of the gravitational field, the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time.

The fact that the light pulses are doppler shifted is extremely significant to the theory. Einstein places us in the inertial frame of reference and therefor we need to be able to account for the reasons the observer cannot see a difference.

worzel
2004-Oct-20, 08:59 AM
The chest together with the observer then begin to move "upwards" with a uniformly accelerated motion.

This is the phrase that I think is glossing over the details. When a rigid body remains uniform in its own frame it can not be accelerating uniformly in an another frame (see ATP's earlier link to a thread on ropes and planes).

A lorentz boost makes clocks in the direction of the boost leap forward proportionally to their distance from you (one way to resolve the twin paradox). Acceleration is just an infinite series of infinitely small boosts which results in the clocks above you smoothly running faster than yours rather than leaping periodically. I think that relies on the "clocks postulate" but can't remember what that is.

A Thousand Pardons
2004-Oct-20, 10:03 AM
Here is the translation of Einstein's original thought experiment. It is intended to illustrate the principle of Equivalence. It is grossly oversimplified. He does cop out a bit with the word "approximately" but I don't feel that excuses the ommision of the effects of dilation. After all, he is speaking about relativity. It also would do well to remember this is around 1916.
That passage is from his popularization of relativity, Relativity: The Special and General Theory which was written around 1920 I think and revised many times.

Evan
2004-Oct-20, 03:05 PM
A Thousand Pardons,

This is a condensed form of the original and may have been published in 1920. The original from 1916 is much the same although longer and more detailed. It does however also omit any mention of time dilation.

Grey
2004-Oct-20, 04:25 PM
This is a condensed form of the original and may have been published in 1920. The original from 1916 is much the same although longer and more detailed. It does however also omit any mention of time dilation.
I believe that Einstein predicted gravitational time dilation as early as 1907 directly from the principle of equivalence.* I'll see if I can dig up a primary source, but it may not be until the weekend that I have a chance to find it.


* Interestingly, this means that any of the various rival theories that also espouse that principle will also feature gravitational redshift, even if other details are different.

Evan
2004-Oct-20, 09:30 PM
Here is the full text of "Relativity
The Special and General Theory" first published in 1916.

Full Text (http://www.marxists.org/reference/archive/einstein/works/1910s/relative/index.htm)

Here is the full version of the "Chest" thought experiment.

The Equality of Inertial and Gravitational Mass (http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch20.htm)


Einstein said:

A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen.

I suggest that you read the full version of the thought experiment so as to see this quote in full context. He still does not differentiate between the situation of the accelerated frame and the gravitational frame even though the mathematics clearly do for an outside observer.

He hints at it here in the following sentence:


Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it. This is by no means true for all gravitational fields, but only for those of quite special form.

Grey
2004-Oct-20, 10:42 PM
Here is the full text of "Relativity
The Special and General Theory" first published in 1916.

Here is the full version of the "Chest" thought experiment.
Thanks, but I believe the paper I'm looking for is the 1907 paper "On the Relativity Principle and the Conclusions Drawn from It", published in Jahrbuch der Radioaktivitaet und Elektronik 4. Einstein talked about lift experiments a lot. :D Take a look at the discussion of that paper here (http://www.bun.kyoto-u.ac.jp/~suchii/gen.GR.html), and you'll see that he's explicitly discussing the comparison between an accelerated frame and one at rest in a gravitational field, and using that to show that there should be time dilation under the influence of a gravitational potential. Next time I have a few minutes at the library I'll try to dig up a translation of the paper in it's entirety, to confirm that the author of the web page I posted isn't reading too much into the original paper. But here's a quote that would suggest that he's addressing the matter quite explicitly.


There exist "clocks" that are present at locations of different gravitational potentials and whose rates can be controlled with great precision; these are the producers of spectral lines. It can be concluded from the aforesaid that the wave length of light coming from the sun's surface, which originates from such a producer, is larger by about one part in two millionth than that of light produced by the same substance on earth.

Hey, it's kind of scaring me that I'm referring to an earlier paper of Einstein's, but I console myself that we're currently talking about specifically what he said, not just about what the actual predictions of general relativity are, so it's appropriate to refer to works that he wrote. You'll tell me if I start sounding like Sam5, though, won't you? :D

Evan
2004-Oct-20, 10:48 PM
I haven't looked up Sam5 Greg. Maybe I shouldn't. :D

I'm sure as I said that Einstein was aware of the time dilation and your example tends to confirm that. I am just suprised that he does not refer or even allude to it in his thought experiment.

Kaptain K
2004-Oct-20, 11:25 PM
You'll tell me if I start sounding like Sam5, though, won't you?
No you do not sound like Sam5. You are cogent, coherent and logical. He was none of the above!

I haven't looked up Sam5 Greg. Maybe I shouldn't.
No, you shouldn't! 8)

Grey
2004-Oct-21, 12:17 AM
You are cogent, coherent and logical.
Hey, thanks! I'll try to live up to that. :D

Grey
2004-Oct-21, 12:26 AM
I haven't looked up Sam5 Greg.
Grey. You had it right earlier. Just a minor correction, though, I'm certainly not offended or anything!


Maybe I shouldn't. :D
I was about to give a brief summary of some of the discussions some of us had with him, but then I thought better of it. I'll do so only if you really want me to. :)


I'm sure as I said that Einstein was aware of the time dilation and your example tends to confirm that. I am just suprised that he does not refer or even allude to it in his thought experiment.
I guess all I was saying was that he had already done so in some detail in other papers some years earlier, so he may have felt that it was unnecessary to cover that ground again. But that's speculation as to his motivation on my part, and it's fair for you to suggest that it might have made sense to include it again for completeness.

Actually, the thing I most wanted to address originally may have been a misinterpretation on my part. From this:


The pendulum in the elevator experiences the exact same degree of accelerational force at all points in its swing. It describes an arc as it swings. At the end of the arc it is closer to the "roof" of the elevator than when it is at the mid-point of the swing, yet the force due to acceleration is exactly the same at all points within the closed frame of reference.

When a pendulum swings in a gravitational field this is not the case. We imagine the "chest" as resting on the surface of a gravitational body so that the pendulum "feels" exactly one gee gravity at the mid-point of the swing. Since gravity is created as a consequence of the existence of matter and agglomerations of matter take a spherical shape when present in large quantities, the pendulum experiences a different gravitational force when it is at the ends of the arc as opposed to the force experienced at the mid-point. Gravity decreases as the inverse square of distance from the body that produces the field. At the ends of the arc of the pendulum it is further from the centre of the gravitational mass and therefore experiences less gravitation. Einstein was well aware of this. It would seem that the pendulum swinging in the gravitational well should have a slightly longer period. Does it?
...it sounded as though you were suggesting that the time dilation observed in a gravitational field is a result of the varying strength of the field, rather than a difference in potential, which is not the case. It's true that for any real gravitational field we know about, the field strength does vary with position, but even in a hypothetical constant gravitational field, we'd see time dilation, a frequency shift in photons travelling up or down, and so forth, since there's a difference in potential between the top and bottom. I'm not actually certain that you were disagreeing with that, but it's a pretty common mistake, so I wanted to address it.

Evan
2004-Oct-21, 05:59 AM
Grey,

Yes, a hypothetical "constant" gravitational field exhibits redshift. The potential varies with distance. However the field strength in a real field also varies with distance and that affects the potential and the redshift. That must also be taken into account as it increases the change with distance. That effect becomes very important in relativistic (!) situations such as black holes.

The period of the pendulum is determined by the potential and the potential difference as the time dilation over distance is a product of both. Also, due to simultanaeity it doesn't matter where you measure the pendulum swing within the frame. If you have two clocks, one measuring at the mid point of the swing and one measuring at the endpoint of the swing which are compared to each other by means of pulses sent to each other they will appear to agree because of the effect of the dilation on the transmitted signal. The clock at the end of the swing is further out of the field than the clock at the mid point.

A Thousand Pardons
2004-Oct-21, 05:40 PM
If you have two clocks, one measuring at the mid point of the swing and one measuring at the endpoint of the swing which are compared to each other by means of pulses sent to each other they will appear to agree because of the effect of the dilation on the transmitted signal. The clock at the end of the swing is further out of the field than the clock at the mid point.
I think you've said this before, and I've disagreed before, but I'm going to have to go back through this whole thread and parse out the discussion before I'm sure. Could you go into a little more detail about what you mean here?

Evan
2004-Oct-21, 06:52 PM
The observer can't be in two places at once. If he is observing both clocks the signal transmitted from them to him (say, flashes of light) will be appropriately dilated either way to make them appear to agree regardless of where in the frame he observes them from. He cannot observe them both at the location of each clock simultaneously. Nor can any means be devised to transmit the information to him that isn't affected by the gravity field. Two separate observers at two different locations would report different results but that is not the thought experiment. This is the effect of simultaneity.

A Thousand Pardons
2004-Oct-21, 07:17 PM
Two separate observers at two different locations would report different results but that is not the thought experiment.
By two different results, do you mean, one observer would say that the clocks are synchronized, and another observer would say that they were not synchronized?

Evan
2004-Oct-21, 07:50 PM
Not exactly, they would record different apparent periods for the pendulum. However if the two observers then came together and compared their clocks they would appear to agree.

Some more on clocks here:

http://plato.stanford.edu/entries/spacetime-convensimul/#3

And simultaneity here:

http://casa.colorado.edu/~ajsh/sr/simultaneous.html