Is Poincaré's Space Dilemma the Key to Understanding Gravity?

[Wes Tausend]

...

This thread is an offshoot from post #55 on a previous thread called, "Freefall isn't acceleration?".

In a nutshell, Equivalence principle. The earth, consisting of matter as cause, acts just as though it's surface is moving upward, or at least outward in an accelerated manner. The floor rises to meet "falling" objects.

The movement of a piece of surface is frame dependent, but the surface definitely doesn't move outward as a whole because the radius is constant. The frame invariant proper acceleration of the surface doesn't imply movement.

A.T.,

From good reference, I'm not so sure "constant radius" is that easy to pin down. We may take it upon ourselves to assume that there is no surface movement, no "spatial inflation" change in the general space between and within the atoms comprising earth, but how do we know that for a fact? Afterall, here on PF, students and members alike can expect extraordinary claims to require extraordinary proof. Around 1898, the great mathematician, Poincaré, explored this very principle in his publication, The Relativity of Space, which we may find useful today.

Below, consider the following excerpt from Poincaré's The Relativity of Space in his Science & Method essays:

Part of it reads:
"...Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a metre long will now measure a kilometre, and what was a millimetre long will become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I awake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure. In reality the change only exists for those who argue as if space were absolute..."

From the above, we can logically surmise that Poincaré's "recreational" observation of human cluelessness seems to ring true, if the "jerk of such an abrupt change" did not awaken one (which he left unsaid). Accordingly, even the Earth's "new" radius would apparently not yield a clue. That concludes part 1.

Following, in part 2, we can reason our own additional observation:
Our own observation might be the one Poincaré also left unsaid... that perhaps we could not easily detect such an obscure growing dimension even if it were somehow ongoing... as long as a steady growth occurred at uniform motion. Such uniform motion is the same smooth motions of Earth traveling around the sun and rotating every 24 hours, none of which are easily noticeable in spite of both occurances together, being a rather complicated combination in the minds eye. The complications of uniform motion have temporarily fooled humans before in geocentricity vs heliocentricity and due care has since been heralded.

But more ominous, further suppose the proposed "growth" of this "fantasy" motion were not uniform? What if the motion were steadily speeding up (accelerating) as it occurred? In that case, we may surmise all living inhabitants of Earth would perhaps merely now notice, only an acceleration. Depending on rate, we must reluctantly admit, this "rising ground" phenomena might feel exactly like Einstein's (or even Newton's) gravity. It seems absolutely everything else, the entire universe, would appear exactly the same.

As per Feynman, we can be fooled, but nature cannot. So are we fooled in this case? No, but only because of SR which hadn't been invented in 1898.

As far as I can see, the sole basic item preventing this particular scenario from becoming a legitimate general relative coordinate system is the limiting speed of light which must naturally be included. Matter simply cannot accelerate faster and faster indefinately, and that seems to settle it.

Does anyone else have some other more simple form of basic proof? Agree, disagree?

Wes
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[Ibix]

I don't think there's anything stopping you from changing coordinates to ones such that a particular family of freely falling observers are at constant radial coordinate. But it cannot be done globally. Hold two balls one above the other. Drop the higher one and release the lower when the upper one reaches it. Both are free-falling through the same point, but at different velocities. You can't rescale to keep both at a constant distance from the centre of the Earth, which is what I think you are proposing.

 

[Wes Tausend]

...



This post is one more offshoot from post #63 on a previous thread called, "Freefall isn't acceleration

A.T.,

I expected a healthy argument and I replied one more time in the former thread out of courtesy to inertiaforce, the OP. So here, I have repeated this post from the other thread to maintain continuity.

The proper physical radius doesn't change according to GR, which we should stick to in this forum.

I agree. I am merely pointing out the extent of Equivalence by simple observation. Equivalence, along with SR are definitely always part of GR. My references to acceleration and motion are Einstein's thought experiment (see post #33) which resulted in Equivalence and therefore GR. Do you have an equally good reference why we cannot refer to such equivalent motion in GR?

No, it's space-time curvature that allows proper acceleration in opposite directions, without changing the proper distance. The speed limit c is irrelevant here, because the opposite surface pieces don't move at all relative to each other.

I disagree. I see the curvature as the direct result of the bending of light, therefore incorporating SR, also discussed in post #33.

I will say that if we do not allow some argument and a variety of perspectives of observation here, we might as well refer all PF member questions to Wikipedia. Please reply only in the new thread.

Wes
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[Wes Tausend]

I don't think there's anything stopping you from changing coordinates to ones such that a particular family of freely falling observers are at constant radial coordinate. But it cannot be done globally. Hold two balls one above the other. Drop the higher one and release the lower when the upper one reaches it. Both are free-falling through the same point, but at different velocities. You can't rescale to keep both at a constant distance from the centre of the Earth, which is what I think you are proposing.

In Einstein's "elevator" thought experiment (see post #33), the "scientists" may release one ball from a seemingly higher table and another from the seemingly lower table as the first ("higher") ball passes it. Or rather the second ("lower") ball is released during a later period when it has now achieved a greater "inertial starting velocity" from it's respective continuously accelerating table top. The greater difference between the starting velocity of the first ("higher") ball (released at lower earlier acceleration) means it will be hit by the "rising floor" sooner and harder. I think Equivalence holds again in this case.

Wes
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[Wes Tausend]

I think you have things backwards. Bending of light doesn't cause curvature, it's the other way around.

Of course "bending of light doesn't cause curvature". But curvature of light in the elevator first caused Einstein to mathematically treat it that way in his coordinate system. We sometimes mix up the order of geometry and math. One must first imagine the geometry, and only then apply suitable math for proofs, which in this case later turns out to be a mathematical curvature of spacetime... after Einstein has observed that light bends in an accelerating elevator. I believe GR and SR are locked inextricably together in this manner.

Wes
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[stevendaryl]

In Einstein's "elevator" thought experiment (see post #33), the "scientists" may release one ball from a seemingly higher table and another from the seemingly lower table as the first ("higher") ball passes it. Or rather the second ("lower") ball is released during a later period when it has now achieved a greater "inertial starting velocity" from it's respective continuously accelerating table top. The greater difference between the starting velocity of the first ("higher") ball (released at lower earlier acceleration) means it will be hit by the "rising floor" sooner and harder. I think Equivalence holds again in this case.

Wes
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I'm not sure I understand what the disagreement is about. The principle of equivalence is only a local notion. If you confine your experiments to a tiny region where the change in gravity is negligible throughout the region, then the principle of equivalence states that experiments in that region cannot distinguish between being at rest in a gravitational field and accelerating through empty space. So in an elevator sitting on the ground, it will seem just like an elevator accelerating upward in empty space.

But now, if you consider a large region that includes the entire Earth, then it is not equivalent to anything accelerating in empty space. A rule of thumb is this: take two objects, say two apples, and drop them. If their paths remain parallel as they drop, then you might be accelerating through empty space. If the paths diverge, then you are definitely not just accelerating through empty space. Divergence of the paths of freefalling objects is a sign of spacetime curvatures, which is due to the presence of matter and energy.

 

[Wes Tausend]

I'm not sure I understand what the disagreement is about. The principle of equivalence is only a local notion. If you confine your experiments to a tiny region where the change in gravity is negligible throughout the region, then the principle of equivalence states that experiments in that region cannot distinguish between being at rest in a gravitational field and accelerating through empty space. So in an elevator sitting on the ground, it will seem just like an elevator accelerating upward in empty space.

But now, if you consider a large region that includes the entire Earth, then it is not equivalent to anything accelerating in empty space. A rule of thumb is this: take two objects, say two apples, and drop them. If their paths remain parallel as they drop, then you might be accelerating through empty space. If the paths diverge, then you are definitely not just accelerating through empty space. Divergence of the paths of freefalling objects is a sign of spacetime curvatures, which is due to the presence of matter and energy.

I think you might mean convergence instead of divergence. Two apples, or balls, will converge over time in real gravity if dropped from a significantly distant point in space. They will not do so if dropped in Einstein's isolated elevator, but rather seem to fall parallel. But in Poincaré's fantasy non-uniform motion universe (see post #1), the balls will again converge as they seem to fall. It takes some thought to realize this. Perhaps reference to another thought experiment will help:

The convergence comes to light in post #59 in this other past thread started by inertiaforce. In my opinion, the ability to visualize the "falling" convergence is served far better by an experimental gravitational model of expanding bubbles in an evacuated bell jar (or aquarium) than by the disgusting old bowling ball sagging a sheet of cloth. I got the "bubble idea" partially from Poincaré, or at least he confirmed my line of thinking. I even mentioned Poincaré later in the thread, but did not elaborate as I have done here. In my opinion, Equivalence is much more equivalent, more global and useful, than we once thought.

Wes
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[WannabeNewton]

I don't think there's anything stopping you from changing coordinates to ones such that a particular family of freely falling observers are at constant radial coordinate. But it cannot be done globally.

It can certainly be done globally. Whether or not the resulting constant spatial coordinates can be interpret as having a "radial" component is another story since coordinates do not need to have any intrinsic geometrical interpretation. Furthermore, the resulting coordinates won't be rigid but that doesn't mean such a coordinate system doesn't exist. All I have to do is take the tetrad $e_{\hat{\alpha}}$ attached to the family of observers and apply the exponential map to it. Obviously this will only work if the associated Jacobi field has no caustics.

 

[PeterDonis]

Obviously this will only work if the associated Jacobi field has no caustics.

But this requirement won't be met in the case under discussion, will it? Suppose we take the family of tetrads attached to observers who are all free-falling towards the center of the Earth from the same altitude. Suppose also that the objects are idealized test objects that do not interact with the Earth's substance. Then their worldlines will all cross at the center of the Earth, and, I believe, this will cause the Jacobi field associated with your construction to have a caustic there, no?

 

[PeterDonis]

We may take it upon ourselves to assume that there is no surface movement, no "spatial inflation" change in the general space between and within the atoms comprising earth, but how do we know that for a fact?

Um, because we are continually making measurements of the geometry of the Earth, and it stays the same? For millennia we have been sending ships around the oceans, using navigation methods that depend on the geometry of the Earth staying the same; now we have spacecraft constantly orbiting the Earth whose orbits depend on the geometry of the Earth staying the same. If any "spatial inflation" were going on, we'd know it soon enough.

 

[Wes Tausend]

Um, because we are continually making measurements of the geometry of the Earth, and it stays the same? For millennia we have been sending ships around the oceans, using navigation methods that depend on the geometry of the Earth staying the same; now we have spacecraft constantly orbiting the Earth whose orbits depend on the geometry of the Earth staying the same. If any "spatial inflation" were going on, we'd know it soon enough.

Peter,

First thank you for your kind remark about no-controversy-worry in the other thread. I really do want to remain in compliance here on PF, yet resolve some long held, deep questions as well as help other PF members see further.

You queried, "Um, because we are continually making measurements of the geometry of the Earth, and it stays the same?" That is precisely the "dilema" crux of Poincaré's Space Dilema, thus the title. Let me repeat his observation (from post #1) in his own words with appropriate emphasis added. Poincaré wrote:

"...Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a metre long will now measure a kilometre, and what was a millimetre long will become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I awake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure. In reality the change only exists for those who argue as if space were absolute..."

I took the liberty to further observe that if any "spatial inflation" continuously occurred in uniform motion that we would likely still neither measure nor "notice anything at all". If non-uniform motion, such as a form of global Equivalence took place, we would not casually measure any difference either. However we would notice the acceleration. It would seemingly be identical to gravity, as well it should considering our thought experiment about comprehensive Equivalence.

My take on all this is that Poincaré is arguing that a steady size of space (or the radius of Earth etc) can not properly be considered Absolute any more than Absolute Rest is assured. I don't see global Equivalence as a problem, but a wonderful opportunity to expand the academic reach of Einstein's two Relativities in a simple, dynamic, geometric model.

No one must make such a choice by todays standards. But if you had to make a choice into the future, would you insist space is Absolute, or would you acknowledge that all coordinate systems are more likely relative? We are reminded to consider such related concepts as Big Bangs, singularities and more recently, cosmological inflation.

To me, it seems everything should obey the Copernican principle. Recently, the principle has been generalized to the relativistic concept that humans are not privileged observers of the universe. Our atoms, consisting of space and mass, have their own small amount of built-in gravity/Equivalence. We observe with this built-in handicap.

The only obstacle to increasingly speeding floors/surfaces seems to be the limiting speed of light (SR), but I believe this, too, can be easily dealth with using simple, common observation, to allow Equivalence to still mathematically function as needed and keep GR and SR intact. I have yet to directly ask about this and it is a daunting task.

Wes
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[A.T.]

I don't see global Equivalence as a problem, but a wonderful opportunity to expand the academic reach of Einstein's two Relativities in a simple, dynamic, geometric model.

Is there a published quantitative theory based on this wonderful model?

 

[PeterDonis]

My take on all this is that Poincaré is arguing that a steady size of space (or the radius of Earth etc) can not properly be considered Absolute any more than Absolute Rest is assured.

My take on it is that the concept of "size of space" as Poincare and you are using it here is physically meaningless. What matters is the relative sizes of different objects. If I have a standard 1-meter ruler, the standard ruler defines what "1 meter" means. If somebody claims that the universe just increased in size by a factor of a thousand, so that the standard ruler is now "1 kilometer" in length, my response is that such a claim is meaningless, because "1 meter" or "1 kilometer" is not defined by somebody's abstract claim but by some well-defined physical thing--in this case, the length of the standard ruler.

 

[Mentz114]

Poincaré wrote:

"...Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a metre long will now measure a kilometre, and what was a millimetre long will become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I awake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure. In reality the change only exists for those who argue as if space were absolute..."
...

I cannot follow Poincaré at all. If something happens that no-one can ever detect - why are we even talking about it. My friend Ginger the twelve-foot hedgehog agrees completely with me.

I mean how does 'something happen' that cannot be detected. It is a contradiction. If nothing can be detected then it is pretty safe to assume that nothing happened.

Hang on ... call from Ginger.

 

[A.T.]

I cannot follow Poincaré at all. If something happens that no-one can ever detect - why are we even talking about it. My friend Ginger the twelve-foot hedgehog agrees completely with me.

I mean how does 'something happen' that cannot be detected. It is a contradiction. If nothing can be detected then it is pretty safe to assume that nothing happened.

Hang on ... call from Ginger.

Reminds me of the hollow Earth idea, based on spherical inversion:
https://en.wikipedia.org/wiki/Hollow_Earth#Concave_hollow_Earths

Purportedly verifiable hypotheses of a "concave hollow Earth" need to be distinguished from a thought experiment which defines a coordinatetransformation such that the interior of the Earth becomes "exterior" and the exterior becomes "interior". (For example, in spherical coordinates, let radius r go to R²/r where R is the Earth's radius.) The transformation entails corresponding changes to the forms of physical laws. This is not a hypothesis but an illustration of the fact that any description of the physical world can be equivalently expressed in more than one way.[46]

 

[Mentz114]

Reminds me of the hollow Earth idea, based on spherical inversion:
https://en.wikipedia.org/wiki/Hollow_Earth#Concave_hollow_Earths

Purportedly verifiable hypotheses of a "concave hollow Earth" need to be distinguished from a thought experiment which defines a coordinatetransformation such that the interior of the Earth becomes "exterior" and the exterior becomes "interior". (For example, in spherical coordinates, let radius r go to R²/r where R is the Earth's radius.) The transformation entails corresponding changes to the forms of physical laws. This is not a hypothesis but an illustration of the fact that any description of the physical world can be equivalently expressed in more than one way.[46]

Yes that's where Ginger goes on holiday.

(I apologise for my levity and I'll cease and desist from now).

 

[Ibix]

It can certainly be done globally. Whether or not the resulting constant spatial coordinates can be interpret as having a "radial" component is another story since coordinates do not need to have any intrinsic geometrical interpretation.

Isn't that kind of the point? My reading of the OP was that was trying to find a way to regard any free-falling observer as being at a constant radial coordinate. If your scheme doesn't have an identifiable radial coordinate, it's not the one I think he's looking for.

His response to my post suggests I may be mis-interpreting him.

 

[Ibix]

In Einstein's "elevator" thought experiment (see post #33), the "scientists" may release one ball from a seemingly higher table and another from the seemingly lower table as the first ("higher") ball passes it. Or rather the second ("lower") ball is released during a later period when it has now achieved a greater "inertial starting velocity" from it's respective continuously accelerating table top. The greater difference between the starting velocity of the first ("higher") ball (released at lower earlier acceleration) means it will be hit by the "rising floor" sooner and harder. I think Equivalence holds again in this case.

I think I misunderstood you. I thought you were seeking a system in which all freely-falling observers are at rest while the floor accelerates up at them. Instead you seem to be looking for one in which all freely-falling observers are moving at constant coordinate speed while the floor accelerates up at them.

Do I understand you right? If I do, is it possible to describe both orbitting bodies and radially falling bodies as having constant coordinate speed in this scheme?

 

[harrylin]

...

This thread is an offshoot from post #55 on a previous thread called, "Freefall isn't acceleration?".
[..]

from Poincaré's The Relativity of Space in his Science & Method essays:

Part of it reads:
"...Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself, if we give the word similitude the meaning it has in the third book of Euclid. Only, what was formerly a metre long will now measure a kilometre, and what was a millimetre long will become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I awake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all. The most exact measures will be incapable of revealing anything of this tremendous change, since the yard-measures I shall use will have varied in exactly the same proportions as the objects I shall attempt to measure. In reality the change only exists for those who argue as if space were absolute..."
[..] From the above, we can logically surmise that Poincaré's "recreational" observation of human cluelessness seems to ring true, if the "jerk of such an abrupt change" did not awaken one (which he left unsaid). Accordingly, even the Earth's "new" radius would apparently not yield a clue.

I don't think that he meant a change that leads to physical phenomena; quite the contrary I would say that he was imagining an expansion of space that has no noticible effects.

[..] What if the motion were steadily speeding up (accelerating) as it occurred? In that case, we may surmise all living inhabitants of Earth would perhaps merely now notice, only an acceleration. Depending on rate, we must reluctantly admit, this "rising ground" phenomena might feel exactly like Einstein's (or even Newton's) gravity. It seems absolutely everything else, the entire universe, would appear exactly the same.
[..]

As far as I can see, the sole basic item preventing this particular scenario from becoming a legitimate general relative coordinate system is the limiting speed of light which must naturally be included. Matter simply cannot accelerate faster and faster indefinately, and that seems to settle it.

Does anyone else have some other more simple form of basic proof? Agree, disagree?

Wes
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It's obvious that you got your inspiration from the video in the other thread and for completeness I'll cite here below* the full warning of Einstein against such ideas here below.

Suppose that the Earth expands to double its radius. Then the distance Earth-moon must also expand to double the distance in order for us to not notice it. But then the distance Moon-Sun should also double at the same rate. If I'm not mistaken, this implies a linear acceleration of the universe outward from the Earth that replaces the Earth's gravitational acceleration. Physically it makes no sense to assume that the Earth is by chance the center of the universe in such a way. Even more, the Sun has a different gravitational acceleration so that it has to expand at a different rate, and the space around it as well, including the Earth. And the same for other planets. [Edit:] And this does not even take into account the required different gravitational accelerations of bodies at different distances from the Earth. It seems obvious to me that such contradictory requirements cannot be fulfilled. Perhaps that is also what others have in mind.

* From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation. In point of fact, the systematic pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field. Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations. 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. 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. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.[emphasis mine] - https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II

 

[Wes Tausend]

Is there a published quantitative theory based on this wonderful model?

Yes, GR is based on Equivalence. I make no other claim other than observation of it's usefulness.

One might feel that simple Equivalence only applies locally, but on the other hand GR itself is a global application derived from it. If the current coordinate math allows a global application, then we might agree somehow there exists an irrefutable pictoral geometry since the accepted math is based in said geometry. In essence, Einstein appears to take the bent (curved) path of the accelerating elevator light beam and apply it as a curved space (spacetime) around the mass of the globe. I agree that this geometry may be difficult to envision, but there is no reason we might not attempt to see further using perhaps untried but simple, logical observations. Good science is also better understood by attempts and occasional observations in error. And, inspired by Poincaré, that is all I'm doing... observing as best I can.

Equivalence is a solid, grand principle and like many here, I see the universe-machine is built of geometry, math and staid philosophical principles. Einstein's principle is solid as a tree and we have already harvested the fruit from the bottom branches. If some other curious primate were to possibly observe more fruit higher up, well we must thoroughly investigate. Perhaps the higher fruit is spoiled, perhaps not, but we can climb, look closer and qualitive questions can and should be asked.

First, as a group, we must all make the same complete observation or it won't mean much. Overall IMO, this thread seems to be proceeding satisfactorily. The concept certainly does not come quickly.

Wes
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[Wes Tausend]

...
Wes Tausend said: ↑
My take on all this is that Poincaré is arguing that a steady size of space (or the radius of Earth etc) can not properly be considered Absolute any more than Absolute Rest is assured.

My take on it is that the concept of "size of space" as Poincare and you are using it here is physically meaningless. What matters is the relative sizes of different objects. If I have a standard 1-meter ruler, the standard ruler defines what "1 meter" means. If somebody claims that the universe just increased in size by a factor of a thousand, so that the standard ruler is now "1 kilometer" in length, my response is that such a claim is meaningless, because "1 meter" or "1 kilometer" is not defined by somebody's abstract claim but by some well-defined physical thing--in this case, the length of the standard ruler.

Part of Poincaré's point is that absolutely everything could change in size overnight, remaining so the next day and being indeterminent in the morning. What he did not say is that such a change would necessitate a set of accelerations (start-stop jerks), which he would, of course, conveniently not realize since he was asleep.

What I observed in following, then, was that if the entire universe, including Earth and all it's much later born inhabitants, were imagined to be "inflating" in uniform motion by the same principle, we would not realize it was happening, nor would we be able to measure it. This principle is very much like the remark I made to the OP (inertiaforce) in his original thread that uniform motion could indicate rest as well as the motion of smooth sailing. This is also the reference frame you are adopting above, where the inflation process becomes meaningless.

But just to make things interesting, I then suggested that we may observe that if the imaginary "universal inflation" were to be of an accelerated motion, we could again casually realize, neither the size of our steadfast atoms (and all space) were apparently so absolute afterall, nor could we seemingly measure this sort of motion. But, in the absence of real gravity, this instance of Equivalence might furnish a nice, artificial inertial reaction that would allow us to walk on Earth's surface. Fully perceiving this, and we ever agree it works, one might think this the epitome of the usefulness of Equivalence then.

A bit more on Poincaré from http://web.mit.edu/redingtn/www/netadv/SP20130604.html .
"Poincaré's insistence that the world is self-similar defies common sense, and yet it is one of his most profound contributions to science. At the very least, it anticipates the fractal analysis that will play such a role in Twenty-first Century physics. We will discuss conformal transformations in the notes to Delbœuf's essay; for now we need only observe that scale invariance plays a key role in what physicists usually mean by "relativity", to which Poincaré will next turn."

I must attend a reunion. I will try to address other posts soon. There is also a complimentary mating observation on SR, part 3.

Wes
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[A.T.]

Yes, GR is based on Equivalence.

GR is based on local equivalence, and space-time curvature which reconciles the local equivalences everywhere. The significance of space-time curvature apparently escapes you completely, if you think the local equivalences require some "space inflation" that causes proper acceleration, but no increase of proper distance. That is not GR.

 

[PeterDonis]

Einstein appears to take the bent (curved) path of the accelerating elevator light beam and apply it as a curved space (spacetime) around the mass of the globe.

No, that's not what GR does. Curvature of a path (proper acceleration) is not the same as curvature of spacetime (tidal gravity). They're two different things.

 

[PeterDonis]

Part of Poincaré's point is that absolutely everything could change in size overnight, remaining so the next day and being indeterminent in the morning. What he did not say is that such a change would necessitate a set of accelerations (start-stop jerks), which he would, of course, conveniently not realize since he was asleep.

Not only did he not say the change would result in start-stop jerks, he explicitly said it wouldn't. He said it would have no observable consequences at all. Start-stop jerks are observable consequences. My comments were entirely about "changes" that have no observable consequences, since that's what Poincare was describing. If you are talking about a "change in size" that does have observable consequences, Poincare's quote is irrelevant.

Also, if you are talking about a "change in size" that does have observable consequences, then, since we don't observe start-stop jerks here on Earth, it would seem that things are not changing in size in the manner you describe. So whatever theory you think you are expounding appears to be ruled out by observation.

if the entire universe, including Earth and all it's much later born inhabitants, were imagined to be "inflating" in uniform motion by the same principle, we would not realize it was happening, nor would we be able to measure it.

But if an "inflation" of this kind would cause start-stop jerks, then we could measure those. So now I'm really confused about what kind of "change" you are talking about. But actually, it doesn't really matter, because neither kind leads to a viable theory, as I have already shown: if the "change" has no observable consequences, then it's physically meaningless; and if it does have observable consequences, then it's ruled out because we don't observe those consequences.

I think you need to rethink your entire position in the light of the above. Whatever theory you think you are expounding, it does not appear to be GR.

 

[harrylin]

I cannot follow Poincaré at all. [..] It is a contradiction. If nothing can be detected then it is pretty safe to assume that nothing happened. [..].

And I cannot follow that. It seems extremely unlikely to me that we can detect everything that happens. Consequently, if nothing can be detected it is pretty unsafe to assume that nothing happened.

 

[harrylin]

[..] In essence, Einstein appears to take the bent (curved) path of the accelerating elevator light beam and apply it as a curved space (spacetime) around the mass of the globe.[..]

Would that not result in fully replacing the gravitational field by acceleration? If so, then that appearance is faulty, as I cited.

 

[Mentz114]

And I cannot follow that. It seems extremely unlikely to me that we can detect everything that happens. Consequently, if nothing can be detected it is pretty unsafe to assume that nothing happened.

I'm just saying that If something is undetectable by any means - how can we ever know it happened ?

 

[A.T.]

Einstein appears to take the bent (curved) path of the accelerating elevator light beam and apply it as a curved space (spacetime) around the mass of the globe.

No, that's not what GR does. Curvature of a path (proper acceleration) is not the same as curvature of spacetime (tidal gravity).

Note that he doesn't even mean the path in space-time but the spatial path of the light beam, which is of course also different from the intrinsic space-time curvature.

 

[Mentz114]

...
Einstein appears to take the bent (curved) path of the accelerating elevator light beam and apply it as a curved space (spacetime) around the mass of the globe
...

As A.T. has said, this is not true. The spatial path of the light is bent for a certain observer. See Ehlers&Rindler's paper

http://pubman.mpdl.mpg.de/pubman/item/escidoc:152994/component/escidoc:152993/330688.pdf

 

[yoron]

I'm not sure why this is discussed again? It's simple, as long as you can transform away your gravitational acceleration, being in a 'free fall' by changing observer, then it's not a acceleration. The guy inside the can feels no acceleration, although we on Earth see him 'accelerate'.
=

the point to notice here is that a acceleration always must be 'first person', meaning that you will notice when inertia acts on you, and you accelerate. And that is what gravity does to you too as I read it, 'accelerating you', in terms of GR. And no, if you 'expand', your mass staying the same according to all measurements you can make, how would you prove a acceleration? (Mass as I presume us imagining particles to 'move/grow' in a expansion, otherwise we can stay with weight, as measured by a accelerometer.)

 

[PeterDonis]

that is what gravity does to you too

No, it isn't. If you are moving solely under the influence of gravity, you feel no acceleration; you do not notice any inertia acting on you.

 

[yoron]

Well, if we use that spaceship at one constant gravity the same will hold true, will it not? But yes, inertia may be what defines a change in acceleration, whereas gravity is what we have when without change.

 

[PeterDonis]

if we use that spaceship at one constant gravity the same will hold true, will it not?

What do you mean by "spaceship at one constant gravity"? Do you mean a spaceship that is firing its engine to produce a 1 g proper acceleration? Such a ship is not moving solely under the influence of gravity.

More generally, an observer who feels a nonzero acceleration (like one at rest in the spaceship firing its engine) is not equivalent to an observer who feels zero acceleration (like one who is freely falling in a gravitational field). If you are trying to think of them as equivalent, you are doing it wrong.

 

[yoron]

I was thinking of the equivalence principle Peter, between a constantly accelerating, uniformly moving spaceship, at one gravity versus a planetary gravity at one G. Ignoring spin.

 

[PeterDonis]

I was thinking of the equivalence principle Peter, between a constantly accelerating, uniformly moving spaceship, at one gravity versus a planetary gravity at one G.

Here is what you originally said:

the point to notice here is that a acceleration always must be 'first person', meaning that you will notice when inertia acts on you, and you accelerate. And that is what gravity does to you too as I read it

And I replied that no, that is not what gravity does to you. If you are moving solely under the influence of gravity, you feel no acceleration, you notice no inertia acting on you, etc.

If you are in a spaceship with its engine firing, or standing on the surface of a planet, then yes, you feel acceleration, and you "notice inertia acting on you"--but the reason you feel those things is not gravity; it's the spaceship's engine firing, or the planet's surface pushing on you. In short, something other than gravity is acting on you, preventing you from being in free fall. So feeling acceleration, noticing inertia acting on you, is not what gravity does to you; it's what something other than gravity does to you.