Meaning of Spacetime Foliations

[stglyde]

We know that we didn't go from Galilian Invariance to Lorentz Invariance by just adding length contraction and time dilation. We also added the speed limit of light as c. So Lorentz Spacetime is a completely new foundation than Galilian Spacetime. And Spacetime foliation as I understood it being a slice of different nows and lengths giving rise to relativity of simultaneity. However, I can't understand what Tim Maudlin was talking about in the article "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done" when he tried to make compatible Bohmian mechanics non-local nature by adding a new "Spacetime Foliation". Maudlin said:

If we begin with a non-Relativistic theory that makes essential use of absolute simultaneity, the most obvious (or perhaps crude and flat-footed) way to adapt the theory to a Relativistic space-time is to add a foliation to the space-time, a foliation that divides the space-time into a stack of space-like hyperplanes. One then employs these hyperplanes in place of absolute simultaneity in the original theory. If no attempt is made to produce a further account of the foliation, and it is accepted as intrinsic space-time structure, then such a theory will clearly fail, in the sense described above, to be Relativistic. But the way it fails is worthy of note: no positive part of the Relativistic account of space-time is being rejected: rather, in addition to the Lorentzian metric, a new structure is being added.

How does it differs to the normal Spacetime foliations in Lorentz Spacetime? Is Mauldin describing about adding Spacetime foliations to Newtonian absolute space and time. Or is it adding additional structure to Lorentz Spacetime? But why did he refer to it as spacetime foliations (which has generic meaning in SR as slicing of spacetime in relativity of simultaneity)? Also wouldn't this end up the same as Lorentz Spacetime? I just can't imagine how the two differs and want to know how their spacetime diagrams differ.

The following is prior to the above paragraph to give the context of what Maudlin was describing:

So for the purposes of this paper, we will adhere to two conditions for the physical theories we consider: first, each theory must have some local beables, and second, the physics must predict violations of Bell’s inequality for some possible experimental situations involving experiments performed on the localized objects at space-like separation. Bell’s result proves that this can occur only if the physics is irreducibly non-local, in the sense that the physics governing a beable at a particular space-time point cannot be exhausted by considering only the physical state in the past light-cone of that point. Even once we have conditionalized on the past light-cone, there must be further predictive improvements to be made by conditionalizing on events at space-like separation.

The central physical question, then, is which events at space-like separation must be taken into account and how they must be taken into account.

Until very recently, the only available fully articulated theories took a particular line of the “which?” question, a line that put the theories in tension with Relativity. These theories proceed in the most straightforward way to adapt non-local non-Relativistic theories to the Relativistic space-time, but in doing so, they are forced to add space-time structure, or the equivalent, to the physical picture. So if one interprets Relativity as demanding that the Lorentzian metric be all the space-time structure there is, these theories are not fully Relativistic. The theories need not reject the physical significance of the Lorentzian metric, but they do need to appeal to further space-time structure to formulate their laws. We will examine two examples of such theories first, and then turn to a recently discovered alternative theory, which is completely Relativistic. Our goal will be to assess, as far as we can, the advantages and demerits of these theories.

 

[stglyde]

To those familiar with Mauldlin article. Is he talking about putting a preferred frame in SR to define the Bohmian frame of absolute simultaneity? If not. What is he talking about?

 

[haushofer]

I don't understand

no positive part of the Relativistic account of space-time is being rejected: rather, in addition to the Lorentzian metric, a new structure is being added.

If you have a 1-dim spacetime foliation (a vector indicating the "time" direction and a 3-dim. spatial metric on the hypersurface), an absolute time will prevent you from constructing the "total metric" from these ingredients; there is no 4-dim. invariant spacetime interval. I would say there is no "Lorentz metric" to start with.

 

[stglyde]

Say, are all preferred frames in SR automatically aether frame? If not. What are the preferred frames that don't use aether in SR? Bohmian mechanics are one of the intensively researched interpretations in Arxiv more than Many world Interpretation. And back to back with it is search for spacetime structure that can allow non-locality with beables.

 

[ghwellsjr]

Any inertial frame in SR will be exactly like the presumed single aether rest state of LET. Any and all characteristics attributable to aether will also be applicable to any other inertial frame moving with respect to the aether that you want to choose. Can you think of any characteristic of the aether rest state for which this is not true?

What do you mean by "preferred frames in SR"? There is only one "preferred frame" and it's in LET, not SR, and nobody knows how to identify it.

 

[stglyde]

Any inertial frame in SR will be exactly like the presumed single aether rest state of LET. Any and all characteristics attributable to aether will also be applicable to any other inertial frame moving with respect to the aether that you want to choose. Can you think of any characteristic of the aether rest state for which this is not true?

What do you mean by "preferred frames in SR"? There is only one "preferred frame" and it's in LET, not SR, and nobody knows how to identify it.

In Bohmian mechanics, the wave function is sensitive to all configuration changes instantaneously throughout the universe. Any idea how to model this nonlocality in Special Relativity? I mentioned BM because in Copenhagen, since the wave function is not physical but just in the equations. There's nothing there to be non-local. But in BM, non-locality is its middle name. Let's avoid LET for now.

 

[ghwellsjr]

Do you agree or disagree with my statement?

Any and all characteristics attributable to aether will also be applicable to any other inertial frame moving with respect to the aether that you want to choose.

 

[stglyde]

Do you agree or disagree with my statement?

I agree but in Bohmian Mechanics, somehow the wave function can use the preferred frame, that is undetectable by us. So how does it do it?

 

[ghwellsjr]

It does it the same way light propagates at c only in the aether frame and yet it also propagates at c in any other inertial frame moving with respect to the aether that you want to choose. Since you said you ageed with my statement, why are you asking about other specific examples?

 

[stglyde]

It does it the same way light propagates at c only in the aether frame and yet it also propagates at c in any other inertial frame moving with respect to the aether that you want to choose. Since you said you ageed with my statement, why are you asking about other specific examples?

It can't just propagate at c. This is because in Bohmian Mechanics, the wave function is sensitive to any configuration changes throughout the universe instantaneously. For example. The wave function of any object on Earth can feel the configuration of any object say 20 billion light years away and instantaneously. So how does it do it?

 

[ghwellsjr]

Are you saying that in Bohmian Mechanics, light does not propagate at c in the aether frame but rather instantaneously?

 

[stglyde]

Are you saying that in Bohmian Mechanics, light does not propagate at c in the aether frame but rather instantaneously?

In BM. Light propagates at c but the wave function propagates instantaneously.

 

[harrylin]

We know that we didn't go from Galilian Invariance to Lorentz Invariance by just adding length contraction and time dilation. We also added the speed limit of light as c. So Lorentz Spacetime is a completely new foundation than Galilian Spacetime. And Spacetime foliation as I understood it being a slice of different nows and lengths giving rise to relativity of simultaneity. However, I can't understand what Tim Maudlin was talking about in the article "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done" when he tried to make compatible Bohmian mechanics non-local nature by adding a new "Spacetime Foliation". Maudlin said:

How does it differs to the normal Spacetime foliations in Lorentz Spacetime? Is Mauldin describing about adding Spacetime foliations to Newtonian absolute space and time. Or is it adding additional structure to Lorentz Spacetime? But why did he refer to it as spacetime foliations (which has generic meaning in SR as slicing of spacetime in relativity of simultaneity)? Also wouldn't this end up the same as Lorentz Spacetime? I just can't imagine how the two differs and want to know how their spacetime diagrams differ.
[..]

Interesting!
I didn't know that article (although I now had a quick look at it); but I do have (and read) his book "Quantum Non-Locality and Relativity". One of the possible options that he mentions in view of Bell's theorem (which he takes for granted) and relating to Bohm's explanation is the existence of what he calls a "preferred frame", with which he obviously does not really mean a preferred but an "absolute" frame - just as Bell did before him.

So, perhaps he means with "further space-time structure" simply the addition of a Lorentz-Einstein ether, in which, as he mentions, "absolute simultaneity" exists although we cannot detect it ("not empirically accessible"). However, he calls such an interpretation of relativity not "completely relativistic" and presents another interpretation by Tumulka which he does hold to be completely relativistic - but which I do not understand (and neither do I understand the one by Ghirardi).
Anyone else?

Harald

 

[ghwellsjr]

Are you saying that in Bohmian Mechanics, light does not propagate at c in the aether frame but rather instantaneously?

In BM. Light propagates at c but the wave function propagates instantaneously.

Are you saying that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame?

 

[stglyde]

Are you saying that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame?

They used different languages like foliating spacetime specially such that absolute simultaneity can be arranged. I'm still reading on Maudlin book. But for the purpose of this message. Yup. One can say (for purpose of discussion) that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame. What's the problem with that?

 

[ghwellsjr]

They used different languages like foliating spacetime specially such that absolute simultaneity can be arranged. I'm still reading on Maudlin book. But for the purpose of this message. Yup. One can say (for purpose of discussion) that in Bohmian Mechanics, the wave function propagates instantaneously in the aether frame. What's the problem with that?

I'm not saying it's a problem. I'm just saying that if it's true in the aether frame then it is also true in any other inertial frame moving with respect to the aether frame. What's the problem with that?

 

[stglyde]

I'm not saying it's a problem. I'm just saying that if it's true in the aether frame then it is also true in any other inertial frame moving with respect to the aether frame. What's the problem with that?

I was thinking that only FTL with aether can avoid causality problem by the BM wave function always in instantaneous speed in the aether frame. So you are saying we can use plain SR and FTL and no causality problem by making the FTL true in every inertial frame?? Hmm...

 

[harrylin]

I'm not saying it's a problem. I'm just saying that if it's true in the aether frame then it is also true in any other inertial frame moving with respect to the aether frame. What's the problem with that?

To hold that an influence can also be instantaneous in any other inertial frame creates a self contradiction: except for one specific direction, an instantaneous influence in one standard inertial reference system (the "ether frame") is determined (or defined) as an influence forward or backward in time in other such systems that are in uniform motion relative to the first one.

PS: But certainly you know that, so I guess that you meant something else than what you appeared to say.

 

[TrickyDicky]

I think one significative property such a frame has is that it seems a way (the only one I know) of reconciling Quantum nonlocality and local realism. Something that is usually considered as impossible. Then again we don't seem to have empirical evidence of such frame (though this is debatable), and it is also apparently incompatible with GR cosmological models (also a moot point IMO).

 

[ghwellsjr]

I'm not saying it's a problem. I'm just saying that if it's true in the aether frame then it is also true in any other inertial frame moving with respect to the aether frame. What's the problem with that?

To hold that an influence can also be instantaneous in any other inertial frame creates a self contradiction: except for one specific direction, an instantaneous influence in one standard inertial reference system (the "ether frame") is determined (or defined) as an influence forward or backward in time in other such systems that are in uniform motion relative to the first one.

PS: But certainly you know that, so I guess that you meant something else than what you appeared to say.

I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame, otherwise, we would have a way to identify the rest state of the aether and that would make headlines and since it hasn't made any headlines, it must not be the case.

 

[ghwellsjr]

Or to put it another way--let's suppose that instead of Michelson and Morley proposing MMX to detect aether wind, they proposed an experiment to detect the rest state of the aether by seeing if the speed of light was the same in all directions. It would be exactly the same experiment but with a different stated goal. Then, the very first time they performed their experiment they would have declared success--they had found the absolute rest state of the aether.

So whatever experiment Bohmian Mechanics wants to propose to detect the absolute preferred rest state of the aether will yield a positive result the first time it is performed.

 

[Qzit]

What if the rest state is "C" and mass is a reduction of "c"?

 

[harrylin]

I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame, otherwise, we would have a way to identify the rest state of the aether and that would make headlines and since it hasn't made any headlines, it must not be the case.

Yes - obviously that would break the symmetry of the phenomena!

 

[stglyde]

Before we get to very complicated spacetime diagrams. Let's first review some basic.

In SR between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as traveling at c all the time, right.

In LET between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as varying depending on the motion with respect to each other, right?

But according to ghwellsjr "I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame"... how do you apply this to the above? In the Twin Paradox, what is the aether frame?

 

[harrylin]

Before we get to very complicated spacetime diagrams. Let's first review some basic.

[1] In SR between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as traveling at c all the time, right.

[2] In LET between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as varying depending on the motion with respect to each other, right?

But according to ghwellsjr "I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame"... how do you apply this to the above? In the Twin Paradox, what is the aether frame?

There can be no difference between [1] and [2]: the exact same measurements are performed, and no model to explain the measurements can affect those measurements.

According to SR it is not possible to track our motion relatively to such a frame, if it exists; and it is not part of the theory. According to Langevin, his thought experiment therefore merely detects the existence of such an ether frame. Here's his summary statement preceding that thought experiment:

In all the above, the employed reference systems are supposed to possesses uniform translational motion: for only such systems, observers associated with them cannot experimentally detect their collective motion, only for such systems the equations of physics must hold their shape when switching from one to another. For such systems it is thus, as if they were stationary relative to the aether: a uniform translation in the aether has no experimental sense.

But because of this it should not be concluded, as has sometimes happened prematurely, that the concept of aether must be abandoned, that the aether is non-existent and inaccessible to experiment. Only a uniform velocity relative to it cannot be detected, but any change of velocity, or any acceleration has an absolute sense.

- p.47 of http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

That I understand; however, as is the topic here, now Maudlin suggests something like that as well as two(?) other possible explanations. Is there anyone here who understands those other ones?

 

[stglyde]

There can be no difference between [1] and [2]: the exact same measurements are performed, and no model to explain the measurements can affect those measurements.

According to SR it is not possible to track our motion relatively to such a frame, if it exists; and it is not part of the theory. According to Langevin, his thought experiment therefore merely detects the existence of such an ether frame. Here's his summary statement preceding that thought experiment:

- p.47 of http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

That I understand; however, as is the topic here, now Maudlin suggests something like that as well as two(?) other possible explanations. Is there anyone here who understands those other ones?

Have you not read Maudlin article called "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done". Anyway. Tumulka stuff was a topic in Scientific American March 2009 edition called "Was Einstein Wrong?: A Quantum Threat to Special Relativity"

http://www.scientificamerican.com/article.cfm?id=was-einstein-wrong-about-relativity

Here's sample of what's being said:

"Hope for Special Relativity?

Two new results—pulling in curiously different directions—have emerged from this discussion in just the past few years. The first suggests a way
that quantum-mechanical nonlocality could be compatible with special relativity; the other reveals a new blow that the combination of quantum mechanics and special relativity strikes against our deepest intuitions of the world.

The first result appeared in an astonishing 2006 paper by Roderich Tumulka, a young German mathematician now at Rutgers. Tumulka showed how all the empirical predictions of quantum mechanics for entangled pairs of particles could be reproduced by a clever modification of the GRW theory (recall that this theory proposes a philosophically realist way to get the predictions of quantum mechanics under many circumstances). The modification is nonlocal, and yet it is fully compatible with the spacetime geometry of special relativity.

This work is still very much in its infancy. No one has yet been able to write down a satisfactory
version of Tumulka’s theory that can be applied to particles that attract or repel one another.
Moreover, his theory introduces a new variety of nonlocality into the laws of nature—a nonlocality not merely in space but in time! To use his theory to determine the probabilities of what happens next, one must plug in not only the world’s current complete physical state (as is customary in a physical theory) but also certain facts about the past. That feature and some others are worrying, but Tumulka has certainly taken away some of the grounds for Maudlin’s fear that quantum-mechanical nonlocality cannot be made to peacefully coexist with special relativity.

Just read the rest from Sci-Am. I don't like Tumulka's theory. If it can't even describe particles that attract or repel. I'd say it's such a long way.. much worse than Bohmian Mechanics.

 

[ghwellsjr]

Before we get to very complicated spacetime diagrams. Let's first review some basic.

In SR between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as traveling at c all the time, right.

In LET between two inertial frames moving with respect to each other for example in the Twin Paradox. The home twin will measure the traveling twin light mirror lightspeed as varying depending on the motion with respect to each other, right?

But according to ghwellsjr "I'm saying that any inertial frame you want to pick will have all the attributes of a presumed aether frame"... how do you apply this to the above? In the Twin Paradox, what is the aether frame?

I'm afraid I don't understand what you mean by "The home twin will measure the traveling twin light mirror lightspeed as..." What exactly is the measurement you are describing here?

 

[stglyde]

I'm afraid I don't understand what you mean by "The home twin will measure the traveling twin light mirror lightspeed as..." What exactly is the measurement you are describing here?

In SR, Home Twin would measure Travelling Twin time as dilated and length as contracted. But it would still measure the light traveling in Travelling Twin inertial frame as c. But in LET, the Home Twin would measure the light traveling in Travelling Twin inertial frame as varying depending on the velocity. I got this from PeterDonis where he mentioned about Frame-dependent thing in message #7 in the thread SR, LET, FTL & Causality Violation where he mentioned in the following:

There actually is one other assumption required in this scenario: that the spacelike curve the tachyon fired from the pistol follows is frame-dependent; the usual assumption appears to be that the tachyon velocity v is fixed relative to the emitter (the pistol in this case). For example, if you look at a typical scenario that uses tachyons to create closed loops, where A sends a message to B and then receives B's reply *before* he sent the original message, in order for the reasoning to go through, it has to be the case that tachyons emitted by B travel along spacelike curves that are not parallel to the curves followed by tachyons emitted by A--put another way, B's tachyons travel at some fixed v > c relative to B, while A's tachyons travel at the same v > c relative to A; but B's tachyons do *not* travel at v relative to A. (If they did, they would not be going backwards in time relative to A, so A could never receive B's reply before he sent his message.)

Peterdonis above mentioned that "B's tachyons do *not* travel at v relative to A", this means even light do not travel at c relative to each other in LET. Do you believe this?

 

[ghwellsjr]

In SR, Home Twin would measure Travelling Twin time as dilated and length as contracted.

Measurements are made without regard to any theory and only theories that explain all measurements will survive.

But it would still measure the light traveling in Travelling Twin inertial frame as c. But in LET, the Home Twin would measure the light traveling in Travelling Twin inertial frame as varying depending on the velocity.

No theory allows for you to measure how light travels. SR and LET have different definitions of how light travels and there is no measurement that favors one theory over the other.

I got this from PeterDonis where he mentioned about Frame-dependent thing in message #7 in the thread SR, LET, FTL & Causality Violation where he mentioned in the following:

Peterdonis above mentioned that "B's tachyons do *not* travel at v relative to A", this means even light do not travel at c relative to each other in LET. Do you believe this?

I believe anything Peter says but I don't see where he said anything different than what I'm saying.

 

[stglyde]

Measurements are made without regard to any theory and only theories that explain all measurements will survive.
No theory allows for you to measure how light travels. SR and LET have different definitions of how light travels and there is no measurement that favors one theory over the other.

I believe anything Peter says but I don't see where he said anything different than what I'm saying.

For there to be paradox, the following needs to be the case:

B's tachyons travel at some fixed v > c relative to B,
while A's tachyons travel at the same v > c relative to A;
but B's tachyons do *not* travel at v relative to A.

However, in Bohmian non-locality, the tachyon equavalent is instantaneous, then how does one make a version of the above, like:

B's insta-tachyons travel at some fixed instantaneous velocity relative to B,
while A's tachyons travel at the same fixed instantaneous velocity relative to A;
but B's instantaneous tachyons do *not* travel at v relative to A??

It should because it's instantaneous. But yet paradox still occurs as our Tachyon pistol example.

ghwellsjr, you may not understand the subtlety of what I'm describing here.

This problem has been consuming me for 5 days already. I wrote Peterdonis a private message asking it 5 days ago and no replies yet. Maybe he misses it, so hope he can address it here as it's what preventing me from fully comprehending the spacetime diagrams of Mauldin article.

 

[ghwellsjr]

What experiment involving tachyons are you proposing that gives different measurements in different frames?

 

[stglyde]

What experiment involving tachyons are you proposing that gives different measurements in different frames?

I don't know. I just want to understand for now what Peterdonis was describing. I know LET and SR is the same, and I try to understand LET so one become more conversant with SR. Going back to the following. For there to be paradox (in LET), the following needs to be the case:

B's tachyons travel at some fixed v > c relative to B,
while A's tachyons travel at the same v > c relative to A;
but B's tachyons do *not* travel at v relative to A."

In plain old SR. Can you give an example where something has to travel at a fixed velocity relative to A and B and not common to both (frame dependent)?

 

[stglyde]

What experiment involving tachyons are you proposing that gives different measurements in different frames?

After rereading again and again the other thread esp. messages by Peterdonis. I think I am seeing what he is describing. In the tachyon pistol duel scenerio we discussed. If the ether frame is used, then when A shoot the pistol at 8 seconds.. instead of B being hit at 4 seconds (due to time dilation factor of 2), B would also be hit in 8 seconds also.. because in the ether frame, both frames can be seen to be ticking at the same time. Right?! I know this is lorentz violation for at least the tachyon velocity. I know you'd say that in SR and LET, they are equivalent in that what happens in one frame in LET happens to all the frames in SR. So we can say the Bohmian Mechanics Wave functions instantaneous velocity is a lorentz violation and it uses the Ether frame only. Since our world is only composed of particles, then no problem with BM wave function having lorentz violations. Maybe this is what Mauldlin meant by foliation of spacetime in BM, isn't it. Now do you see any problem with BM wave functions having lorentz violations? Any conflict with other stuff like Quantum Field Theory or none at all?

 

[Dale]

In plain old SR. Can you give an example where something has to travel at a fixed velocity relative to A and B and not common to both (frame dependent)?

A standard pistol. The muzzle velocity is relative to the pistol, in other frames it may not travel at the muzzle velocity.

 

[stglyde]

A standard pistol. The muzzle velocity is relative to the pistol, in other frames it may not travel at the muzzle velocity.

Oh. Of course, the famous relativity of simultaneity. I remembered the train example. What changed due to the observer's velocity relative to the train is the relationship between measuring instrument and train.