# Thread: How real is general relativity?

1. ## How real is general relativity?

How real is general relativity?

To me it is totally real and makes sense, but others seem to think of it as more of an illusion.

So, two cube shaped clocks, one on surface of a neutron star the other in deep space.
The clock has a side length of 1 light-nanosecond (299mm or 11.8 inches)

If the clock on the surface is slowed by a factor of 2 relative to the one in space then its light nano-second is twice as long as the light nano-second measured by the clock in space.
So, one clock is twice the size of the other. (I think all observers agree on this)

Is this real or just a magnification or illusion caused by curved space?

2. Originally Posted by PetTastic
Is this real or just a magnification or illusion caused by curved space?
If it's caused, it's real.

3. To quote “curved space” you are already referring to general relativity! GR is a mathematical model which better explains the more esoteric observations we can make in cosmology and a better explanation of how gravity works than Newton provided. Neither Newton nor Einstein provided a mechanistic cause and effect explanation but rather a set of calculations which makes better predictions of the large-scale phenomena we can observe. To use the word real takes you into that very long thread about reality, where GR has often been discussed.

4. By any sensible measure, it's real: every experiment -- and there is no alternative method to confirming reality -- to date has confirmed its validity.

5. It is possibly the most real (accurately and precisely tested) theory in physics. It is possible (likely) that there is some underlying thing going on, and that relativity is an artifact of that in the same way that thermodynamics is easily tested and demonstrated correct, but springs from statistical mechanics.

6. Originally Posted by PetTastic
How real is general relativity?

To me it is totally real and makes sense, but others seem to think of it as more of an illusion.

So, two cube shaped clocks, one on surface of a neutron star the other in deep space.
The clock has a side length of 1 light-nanosecond (299mm or 11.8 inches)

If the clock on the surface is slowed by a factor of 2 relative to the one in space then its light nano-second is twice as long as the light nano-second measured by the clock in space.
So, one clock is twice the size of the other. (I think all observers agree on this)

Is this real or just a magnification or illusion caused by curved space?
Odd that you would use a clock as your object- and then measure its size.

If only there were some other thing a clock did that you could measure! Hmm.

7. Originally Posted by DaveC426913
Odd that you would use a clock as your object- and then measure its size.

If only there were some other thing a clock did that you could measure! Hmm.
I might take some time to think about that.

I am interest in the size and speed of the protons, neutron & electrons the clock is made from.

The mass of the clock also seems a interesting issue.
Thinking about conservation of mass/energy, if you dropped the clock onto the neutron star there would be a huge release of energy on impact?
Also, photons leaving lights on the two clocks have a fixed energy or mass ratio to their clock.
Does the clock on the neutron star have the same mass as the one in space?

8. Originally Posted by PetTastic
How real is general relativity?
Is "real" a scientific term?

I ask because I don't think it is.

9. Originally Posted by Cougar
Is "real" a scientific term?

I ask because I don't think it is.
Sure it is .. wherever a scientist has defined the term by way of using the scientific method, that is.

10. Before discussion falls down that rabbit hole, there's already a real thread for real discussion about what real is or is not...and this thread ain't it. Really.

11. Originally Posted by PetTastic
Thinking about conservation of mass/energy, if you dropped the clock onto the neutron star there would be a huge release of energy on impact?
Likely any solid object would spaghettify before reaching the surface.

12. Originally Posted by PetTastic
I might take some time to think about that.

I am interest in the size and speed of the protons, neutron & electrons the clock is made from.

The mass of the clock also seems a interesting issue.
Thinking about conservation of mass/energy, if you dropped the clock onto the neutron star there would be a huge release of energy on impact?
Also, photons leaving lights on the two clocks have a fixed energy or mass ratio to their clock.
Does the clock on the neutron star have the same mass as the one in space?
I think, the point is that the clock will show a time dilation.

And in case we wonder whether that's simply some "optical illusion" of being remote from us near and a neutron star, we can haul the clock back up - and observe it at point-blank range and it will retain that discrepancy in time.

Yes, GR is real. It has predictable, extant, lasting effects.

In case you have any doubts of this, and how hypothetical it might be - you don't need a neutron star to see its very real effects.

This guy demonstrated time dilation with a camper van, a road trip up a mountain, a couple of atomic clocks and his young family in tow.

http://leapsecond.com/great2005/

Last edited by DaveC426913; 2020-Mar-20 at 03:33 AM.

13. Order of Kilopi
Join Date
Sep 2005
Location
Metrowest, Boston
Posts
4,809
I think Einstein loses to Feynman, Schwinger, and Tomonaga for the most precise theory, QED,( 11 sig figs for the anomalous moment of the electron),but his range and imagination in theoretical physics is unsurpassed. Like " Billy the Kid", there's always a new gunslinger in town....more clever, more imaginative , coming in the future.Einstein himself commented that he expected the theory to one day be overthrown, but here we are, 100 years plus, and there he is yet.
If you had a pair of watches, which kept time to 40 significant figures, and you synchronized them, on the ground floor of your house, you'd notice that if you went upstairs, and came back down hours later, they differed....proving your head is aging faster than your feet. But it takes a physicist to show that with atomic masers, because watches are only good to several sig figs.
When Einstein formulated his GR, he was careful to note that the constant acceleration in his spaceship, matches the acceleration due to gravity only at an infinitely thin height around a perfectly round homogeneous spherical body. One atom width higher, or lower, it doesn't match up.
Last edited by trinitree88; 2020-Mar-20 at 05:41 AM.

14. Order of Kilopi
Join Date
Mar 2010
Location
United Kingdom
Posts
7,277
Originally Posted by PetTastic
Thinking about conservation of mass/energy, if you dropped the clock onto the neutron star there would be a huge release of energy on impact?
Also, photons leaving lights on the two clocks have a fixed energy or mass ratio to their clock.
Does the clock on the neutron star have the same mass as the one in space?
Energy conservation is not a simple topic in GR:
http://math.ucr.edu/home/baez/physic...energy_gr.html

15. Originally Posted by Shaula
Energy conservation is not a simple topic in GR:
http://math.ucr.edu/home/baez/physic...energy_gr.html
If we limit things to where all observers agree, have I got the following right?

If all observers agree the clock on the neutron star is running half the speed of the one in space.

The energy required to lift the clock from the surface into space is equivalent to the mass-energy of the clock on the star or half the mass-energy of the clock in space.
One clock is half the mass of the other?
Or, using external energy to lift the clock into space increases the mass of the system.

All observers agree, relative to the clock in space the subatomic particles the clock on the neutron star is made from are:
* running at half the speed
* scaled to twice the size
* half the mass-energy
* half the electric charge

16. Order of Kilopi
Join Date
Jan 2010
Location
Wisconsin USA
Posts
3,166
Interesting

17. Order of Kilopi
Join Date
Aug 2008
Location
Wellington, New Zealand
Posts
4,413
Originally Posted by PetTastic
All observers agree, relative to the clock in space the subatomic particles the clock on the neutron star is made from are:
* running at half the speed
* scaled to twice the size
* half the mass-energy
* half the electric charge
Is Energy Conserved in General Relativity? is not about your clocks and neutron star scenario.
All observers agree, relative to the clock in space
• The clock on the neutron star is running at half speed because that is part of your scenario.
The cause will be gravitational time dilation. There could also be SR time dilation but we can have a hypothetical non-rotating neutron star.
• The clock on the neutron star has a different height.
Not "scaled to twice the size" since GR time/length transformations are not as symmetrical as SR time/length transformations. See How to calculate spatial distance in space-time? and replace the two particles with the top and bottom of the clock.
• Both clocks have the same mass-energy.
There is no process converting energy to mass or vice versa.
• GR does not change the charges of subatomic particles because it has none. GR only has mass and energy.

Note that by saying that the clocks are made of normal matter you are making your scenario almost certainly moot. The clock in the neutron star will be pancaked into a thin layer of matter. It would be better to get rid of the neutron star and have a clock on Earth + clock in space scenario if you want to retain real clocks. Or ideal clocks if you want to keep a neutron star.

18. Banned
Join Date
Oct 2005
Posts
27,229
Originally Posted by PetTastic
Is this real or just a magnification or illusion caused by curved space?
Actually, there is not any thread on this forum about what the OP means by "real", since only the OP can know the intended meaning there and no thread could answer that. We'd have to ask them, but it might be a hard question to answer, so I will interpret what I suspect the intended meaning is. There is no other reference for that meaning-- there is not a consensus even among scientists as to what that word should mean, you have to ask the person using it what they mean. (And if you use a dictionary, you will of course find inclusive meanings that are too vague and general to be of any use, try it.)

My guess is, by "real", what is intended is along the lines of "has objectively observable consequences that cannot be as easily attributed to anything else." So that is the meaning I will also use, and when that meaning is taken, gravitational time dilation and length contraction are not real, nor are they some kind of illusion. Neither of those is the right way to think about them. The same holds for special relativistic time dilation or length contraction, a fact that is quite poorly understood from what I've seen.

To make this clearer, let me stick with special relativity-- it's easier and makes the point well. Imagine two identical rockets, one in front of the other, attached by a flimsy thread. The two identical rockets fire a short burst from their identical engines at the same time in the initial rest from of both rockets. Let's say in a very short time both rockets achieve speed v and shut off the engine bursts. Does the thread break when it tries to length contract according to v/c? Many people who think length contraction is some kind of illusion would say no, since it is only an illusion that the thread contracts. This is wrong, the thread would break.

Now, many other people who regard the length contraction of the thread as a "real thing" are quite happy to note that the thread does break, due to that real contraction. However,the problem is that, using the meaning I described above, we do not need to regard the thread as needing to contract, nor do we need to use that to understand why it breaks. We can simply choose a reference frame that was always moving at the speed v the rockets eventually achieve, and in that reference frame the thread loses its length contraction, so is trying to expand! Yet of course it still breaks. So why does an expanding string need to break? It's because in that frame, the lead rocket fired its burst first, breaking the thread.

The moral of the story is, what is an invariant that all observers must agree on is that the thread breaks. What is not an invariant is why it broke, or what happened to the length of the thread, or if anything happening to that length has anything to do with why it broke. Thus, it would seem wise to regard as "objectively real" only three types of things:
1) the invariants.
2) the fact that the observers saw what they saw, even when what they actually see is different.
3) the fact that any two observers with the same perspective (same location, time, and motion) will see the same things, if they are objectively real.
All observers agree, relative to the clock in space the subatomic particles the clock on the neutron star is made from are:
* running at half the speed
* scaled to twice the size
* half the mass-energy
* half the electric charge
No. The central lesson of all types of relativity, above all GR, is that we must distinguish between an observation and a language based on a coordinate system. The former is what all observers must agree on, the latter depends on the choice of coordinate so can only be agreed on if the choice of coordinate is agreed on. The main accomplishment of GR is to produce a way to make predictions about the former that don't care what the choice of coordinates is.

It helps to think of coordinates as like a language, say English or French. When someone writes a poem about love in French, then what aspects of that poem depend on French, and what aspects can be translated into English? The latter is what all observers agree on, the former is coordinate dependent.

The list you gave are all like elements of the French poem that are lost when translated into English. The safest way to attain observer-independent truths is to allow the observer to have a perspective, that is, keep track of the location, time, and motion of the observer. Then saying "all observers agree" means they all get the same answer from the same perspective. It does not mean they get the same answer from different perspectives, which in fact they don't (other than the local speed of light). So the "invariant" measurements are those that include the observer perspective, and the only one that doesn't need that is the local speed of light. The mass of an object, and its size, do depend on perspective.

So how can we take that list of yours and turn it into a set of invariants that observers agree on? By including the perspective. The easiest way to do that is use observers who not only have the same perspective, but they also share the perspective of the object being observed. By that I mean, they are at the time and location, and in the rest frame of the system or object being observed. When you put observers at the location of, and at rest with respect to, the clocks in your scenario, you find that all observers agree the clocks are ticking at the same rate-- the rate at which a clock should tick. They also agree that all the subatomic particles have the mass subatomic particles should have. No clocks are ticking fast, no particles have twice the size or half the mass as they should.

So what is meant by "gravitational time dilation"? It is simply a choice of coordinate system, nothing more. It is a mode of analysis, a choice of quantitative language-- like French or English. It does not rise to the level of "objectively real" any better than the length contraction of the thread between the rockets, and it is not required to understand what we do observe, because what we do observe depends on our perspective and can be explained in other ways using other coordinates. Often, the "other ways" sound completely different physically-- that's the amazing accomplishment of relativity, it allows us to see completely different sounding explanations as being valid for the same phenomenon. And this is exactly what people are not used to, and have so much trouble understanding. The phenomenon is real, but the explanations are not-- nor are there any illusions involved, other than the illusion that explanations need to be unique.
Last edited by Ken G; 2020-Mar-27 at 09:14 PM.

19. Originally Posted by Ken G

To make this clearer, let me stick with special relativity-- it's easier and makes the point well. Imagine two identical rockets, one in front of the other, attached by a flimsy thread. The two identical rockets fire a short burst from their identical engines at the same time in the initial rest from of both rockets. Let's say in a very short time both rockets achieve speed v and shut off the engine bursts. Does the thread break when it tries to length contract according to v/c? Many people who think length contraction is some kind of illusion would say no, since it is only an illusion that the thread contracts. This is wrong, the thread would break.
Thank you for this example which I do not understand.
I understand the contraction, or expansion, is “real” but not that the thread breaks. Any more than the contracting, expanding rockets fail to break. I would have thought the thread is not observed to break in any reference frame, It is observed to change under v/c depending on frame, but it, the (massless) thread, experiences Acceleration in the first static frame. Is it the acceleration toward v that breaks it?
Last edited by profloater; 2020-Mar-28 at 09:42 AM.

20. I don't understand it either. The best I can do is envision the two rockets and the thread as constituting an object which is operated in such a way that the thread does not break.

21. Banned
Join Date
Oct 2005
Posts
27,229
Originally Posted by profloater
I would have thought the thread is not observed to break in any reference frame,
It breaks in all reference frames-- but for different reasons.
This tells us the reasons are coordinate-dependent, an obvious form of mind dependence. That isn't philosophy, it's pure physics. The philosophical question posed by the OP was, are reasons real? Now we see the answer to that depends on what requirements one puts on one's desired meaning of "real." Most people want reality to be objective, and so we now discover that if one tries to use that restricted version of reality, then reasons aren't in it. You see the problem-- people want to say 'things happen for a reason", and they want to say "reality is objective", but they don't know they are contradicting themselves. Physics does know that.
Is it the acceleration toward v that breaks it?
The explanation for why it breaks depends on the coordinates you choose to provide that explanation. This is the key point here-- we tend to imagine that explanations are part of the objective truth of the situation, but that turns out to be incorrect-- the language in the explanation itself can sound completely different for different choices of coordinates. So when you ask, why does it break, the answer is, first choose your coordinates and only then can I tell you the explanation for why it breaks.

So if one asks about why it breaks in terms of length contraction, that means one has chosen a coordinate system at rest with respect to the pre-launch rockets. In those coordinates, both rockets follow the same trajectory (they are identical) except displaced by a constant initial length L (this is a symmetry principle, independent of any form of relativity that respects translational invariance). So the question then is, can the thread span L? The answer is no, because the thread length was initially L, and at speed v, it's length in the coordinates we have chosen is L*(1-(v/c)^2)^(1/2) < L. That doesn't span L, so the thread must break.

Of course, in other coordinates, the explanation sounds completely different (like the one I gave above). So when you ask does it break because of the acceleration, the answer is, it breaks because of the entire scenario, it just breaks and that's it. But if you wish to analyze why it breaks, you have left the realm of objective reality and entered the realm of language (in this case, coordinate language). To distinguish this from that other thread that has been mentioned, the other thread raises the question, is there anything that manages to be completely independent of the language (i.e., don't we need language to talk about invariants too). But here we can stick to pure physics and just point to the language itself, the language actually used in physics, and what it is-- and what it isn't. Because this is really not well understood, I see it constantly.
Last edited by Ken G; 2020-Mar-28 at 02:53 PM.

22. Originally Posted by Ken G
It breaks in all reference frames-- but for different reasons.
This tells us the reasons are coordinate-dependent, an obvious form of mind dependence. That isn't philosophy, it's pure physics. The philosophical question posed by the OP was, are reasons real? Now we see the answer to that depends on what requirements one puts on one's desired meaning of "real." Most people want reality to be objective, and so we now discover that if one tries to use that restricted version of reality, then reasons aren't in it. You see the problem-- people want to say 'things happen for a reason", and they want to say "reality is objective", but they don't know they are contradicting themselves. Physics does know that.The explanation for why it breaks depends on the coordinates you choose to provide that explanation. This is the key point here-- we tend to imagine that explanations are part of the objective truth of the situation, but that turns out to be incorrect-- the language in the explanation itself can sound completely different for different choices of coordinates. So when you ask, why does it break, the answer is, first choose your coordinates and only then can I tell you the explanation for why it breaks.

So if one asks about why it breaks in terms of length contraction, that means one has chosen a coordinate system at rest with respect to the pre-launch rockets. In those coordinates, both rockets follow the same trajectory (they are identical) except displaced by a constant initial length L (this is a symmetry principle, independent of any form of relativity that respects translational invariance). So the question then is, can the thread span L? The answer is no, because the thread length was initially L, and at speed v, it's length in the coordinates we have chosen is L*(1-(v/c)^2)^(1/2) < L. That doesn't span L, so the thread must break.

Of course, in other coordinates, the explanation sounds completely different (like the one I gave above). So when you ask does it break because of the acceleration, the answer is, it breaks because of the entire scenario, it just breaks and that's it. But if you wish to analyze why it breaks, you have left the realm of objective reality and entered the realm of language (in this case, coordinate language). To distinguish this from that other thread that has been mentioned, the other thread raises the question, is there anything that manages to be completely independent of the language (i.e., don't we need language to talk about invariants too). But here we can stick to pure physics and just point to the language itself, the language actually used in physics, and what it is-- and what it isn't. Because this is really not well understood, I see it constantly.
Yes I do understand that but the space between the rockets behaves the same as massless string, doesn’t it? So it just changes, as the massless thread changes? The change we observe depends on our frame. I am modelling the mass less thread as just an example of space between the rockets. Just as if the gravity field changed uniformly around the rockets?
Last edited by profloater; 2020-Mar-28 at 03:28 PM.

23. Originally Posted by Hornblower
I don't understand it either. The best I can do is envision the two rockets and the thread as constituting an object which is operated in such a way that the thread does not break.
If that were the case, then the rear rocket would need to accelerate faster than the front rocket, as measured in the rest frame, so as to allow the thread to undergo relativistic length contraction in the rest frame. But we have stipulated that the rockets have the same acceleration for the same time in the rest frame, so they stay the same distance apart in that frame. There is therefore no capacity for relativistic length contraction in the thread, unless it breaks, or it develops tension that pulls the two rockets together, accelerating the rear and retarding the front.
In the reference frames of the rockets, once they start accelerating the rear rocket is simultaneous with progressively later moments in the trajectory of the leading rocket--that is, the leading rocket has accelerated for longer, and has acquired a velocity directed away from the rear rocket. In the reference frame of the leading rocket, it is simultaneous with earlier times in the trajectory of the rear rocket, and so the rear rocket lags behind. So both rocket pilots understand why the thread breaks, too.

Grant Hutchison
Last edited by grant hutchison; 2020-Mar-28 at 07:03 PM. Reason: corrected one instance of "rear" to "leading"

24. Originally Posted by grant hutchison
If that were the case, then the rear rocket would need to accelerate faster than the front rocket, as measured in the rest frame, so as to allow the thread to undergo relativistic length contraction in the rest frame. But we have stipulated that the rockets have the same acceleration for the same time in the rest frame, so they stay the same distance apart in that frame. There is therefore no capacity for relativistic length contraction in the thread, unless it breaks, or it develops tension that pulls the two rockets together, accelerating the rear and retarding the front.
In the reference frames of the rockets, once they start accelerating the rear rocket is simultaneous with progressively later moments in the trajectory of the leading rocket--that is, the leading rocket has accelerated for longer, and has acquired a velocity directed away from the rear rocket. In the reference frame of the rear rocket, it is simultaneous with earlier times in the trajectory of the rear rocket, and so the rear rocket lags behind. So both rocket pilots understand why the thread breaks, too.

Grant Hutchison
Ah! Yes. ..thanks to both.

25. Basically, you can treat a single accelerating dimensionless point as a series of inertial frames in SR, and that's what we commonly do when considering those fictitious 1g rockets making fictitious interstellar journeys. But for an extended object undergoing acceleration (such as a rocket, or pair of rockets joined by a thread) you actually need to look at the trajectory of each point within the object. What you find is that, if the object is to maintain its shape in its own extended reference frame while it accelerates, the front must experience less acceleration than the back. And if you pay out a rope behind your accelerating spacecraft, it wil experience increasing tension forces the longer it gets, because the end of the rope must accelerate more and more rapidly just to maintain its constant length in the accelerating frame.
So the accelerating observer lives in a reference frame with a "gravity" gradient from front to back, which is mathematically described by the Rindler metric (useful search term). Take a look at Greg Egan's discussion of the Rindler horizon, for mind-meltingly more detail.

Grant Hutchison

26. Banned
Join Date
Oct 2005
Posts
27,229
Yes, that's the third explanation, the one that uses accelerating coordinates that keeps the lead rocket at rest the whole time (treating both rockets as points for simplicity). In that frame, there is an effective gravity, which involves gravitational time dilation where we could say clocks in the rear rocket are ticking slower, so the rear engine is firing slower, so it lags behind and that breaks the string. So we have three explanations already-- the string breaks because it must length contract so can't span the separation, it breaks because the front rocket takes off first, it breaks because the rear rocket burns slower and lags the front one. Ten other coordinates can give ten other reasons that combine these in various ways.

So reasons are not objectively real, though one could choose to give preference to the reasons given by observers at the scene-- in this case the observer on the string. That observer would be in an accelerating frame, and give the "gravitational time dilation" reason. So if you do give precedence to that observer, you could say that's the "real reason." But even so, I've never been a big fan of framing time dilation as any clocks "running at half the speed" of any others, because it comes with a bias that two clocks should record the same time, so if one is ahead of the other it must have "ticked faster." If we give preference to the observers at the clocks, they know the clocks are ticking normally, so the observer at the center of the string should defer to them and reject the idea that the lead engines are "burning faster", instead concluding that there is simply more time elapsed by the front engine than the rear. So given my tendency to like giving observers on the scene complete authority to say what is happening, my answer would be that the string breaks because more time elapses for the lead engine then the tail engine, so it goes farther and stretches the separation. It's like a tidal stress then, but GR does not say that any clocks are "running at half the speed" of any others, that's coordinate language. Indeed I would argue that language conceals the main point of GR, that if our watches are synchronized at one point, and when later we meet up again my watch is ahead, it does not mean my watch ever ticked faster than yours-- it means my watch experienced more time than yours. How rarely we see that kind of language in relativity, but it stems from a priority to let the observer on the scene always be the authoritative one (which does not require making any coordinate choices, but it is a choice all the same).
Last edited by Ken G; 2020-Mar-28 at 09:11 PM.

27. I am struck by the parallel realisation that no macro object can accelerate itself the way we treat a point object. The force of the rocket motor has to be transmitted to the front of the rocket in a series of processes linked to the speed of sound in the object so that literally the front of an accelerating object Must be accelerating less than the back of that object. Likewise tension in any “real“ string has to travel at the speed of sound, so in an accelerating frame, There is literally no static force.

There are no infinitely stiff atoms or structures, so whenever we talk of acceleration we make a huge simplification.

28. Banned
Join Date
Oct 2005
Posts
27,229
What you could do is distribute the rocket thrust over the entire object, to manipulate the stresses any way you like. In this way you could accomplish "Born rigidity", which means the accelerating object will gradually length contract according to its v/c seen from an inertial frame. This is what an infinitely rigid object would do on its own, except that no such object exists, as you say. This also means that if you do not distribute the forces carefully over an accelerating object, it will not length contract in the manner of special relativity. That's why length contraction in special relativity generally only applies to objects that are not accelerating, as seen by observers that are accelerating. So all those times you were told that if you created a ruler in your own reference frame, and accelerated it to 99.99% of the speed of light, it would have a length that is only 1.4% of the length it had at rest, that is not likely to be true. What would be true is that if you saw the ruler at rest, and then you accelerated to 99.99% the speed of light, then it would be reckoned by you to have a length of 1.4% of normal. Or, it would have that length if someone else, already moving at 99.99% of the speed of light relative to you, built a standard ruler in their own frame. But if the ruler itself is accelerated, it is very difficult to retain Born rigidity-- it would require carefully distributed forces (and is not even possible if the ruler is made to rotate).
Last edited by Ken G; 2020-Mar-29 at 09:59 AM.

29. Yes a uniform spread accelerating force would be like free fall in an uniform gravity field. Except that like forces inside real objects, a proper uniform gravity field is just a handy simplification. And those handy simplifications blur understanding. I read in NS this weekend how experiments have now caught quantum events happening gradually, challenging the quantum leap to more like Brownian motion. QTT is the abbreviation. New Zealand is where the team did the experiment. I see a parallel there, but that’s just me.

30. Originally Posted by grant hutchison
Basically, you can treat a single accelerating dimensionless point as a series of inertial frames in SR, and that's what we commonly do when considering those fictitious 1g rockets making fictitious interstellar journeys. But for an extended object undergoing acceleration (such as a rocket, or pair of rockets joined by a thread) you actually need to look at the trajectory of each point within the object. What you find is that, if the object is to maintain its shape in its own extended reference frame while it accelerates, the front must experience less acceleration than the back. And if you pay out a rope behind your accelerating spacecraft, it wil experience increasing tension forces the longer it gets, because the end of the rope must accelerate more and more rapidly just to maintain its constant length in the accelerating frame.
So the accelerating observer lives in a reference frame with a "gravity" gradient from front to back, which is mathematically described by the Rindler metric (useful search term). Take a look at Greg Egan's discussion of the Rindler horizon, for mind-meltingly more detail.

Grant Hutchison
Thanks, I did read Greg Egan. I was reminded of a school question about a dog setting off the chase a passing bicycle, (light, I now realise). An hyperbolic question I was not equipped to tackle. I had not come across the Rindler Horizon, nor Born rigid motion, although the concept is included in the mechanical problem of impacts and impact damage. I am amused at the way these cosmic thought experiments play out in empirical situations where singularities are resolved by bullets hitting steel plates.!