Meaning of Spacetime Foliations

[PeterDonis]

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?!

If the frame in which the diagram for that scenario was drawn is the ether frame, and if tachyons were assumed to be "instantaneous" in the ether frame, then yes, A and B would both fire their tachyon pistols at t = 8 sec in the ether frame, and both pistol shots would hit at t = 8 sec in the ether frame.

Of course, in any other frame, the shots would not travel "instantaneously"; in any other frame, one would appear to travel forward in time and one would appear to travel backward in time. So the term "instantaneous" is not an invariant; even in an ether theory, a tachyon can only travel between two points "instantaneously" as seen in one specific frame. That wouldn't change the result of the duel because the motion of A and B would also look different in any other frame, so it would still turn out that A's shot hit B just as B was firing, and vice versa. But the tachyons would no longer travel "instantaneously".

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.

I think you're misunderstanding ghwellsjr's comments on this. SR and LET use the same mathematics; they just put different interpretations on it. So if LET says some particular equation applies "in the ether frame", and that equation is expressed in covariant form, then that equation will apply in all frames, whether you use SR or LET to interpret the equation.

But if you explicitly violate covariance, for example by specifying that tachyon velocity is always some specific v > c relative to a specific frame, which you call the "ether frame", then the tachyon velocity will be different in some other frame, because you specified that this particular phenomenon violates covariance. (The case of "instantaneous" tachyons is just the case v = infinity relative to the ether frame.)

So we can say the Bohmian Mechanics Wave functions instantaneous velocity is a lorentz violation and it uses the Ether frame only.

Bohmian Mechanics is explicitly non-relativistic; AFAIK nobody has ever succeeded in making a relativistic version. So Bohmian Mechanics doesn't even address this question; it simply can't be applied to relativistic phenomena at all.

 

[PeterDonis]

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 should add to my previous post the important qualification that light still travels at c in all frames, even if we start considering possibilities like tachyons. Both SR and LET use the same math, as I said, including the Lorentz transformations; and the Lorentz transformations ensure that anything that moves at c in one frame, moves at c in all frames. So the stuff I was saying about tachyons does *not* apply to light.

(Of course, if you're willing to allow tachyons to explicitly violate Lorentz covariance, you could try to concoct a theory where light did too; but at that point you'd basically be starting from scratch, since if you can't rely on the Lorentz transformations being right you've basically gotten rid of all the math of SR/LET anyway, so you're on your own. I've been assuming that we aren't going to go there.)

 

[stglyde]

If the frame in which the diagram for that scenario was drawn is the ether frame, and if tachyons were assumed to be "instantaneous" in the ether frame, then yes, A and B would both fire their tachyon pistols at t = 8 sec in the ether frame, and both pistol shots would hit at t = 8 sec in the ether frame.

Of course, in any other frame, the shots would not travel "instantaneously"; in any other frame, one would appear to travel forward in time and one would appear to travel backward in time. So the term "instantaneous" is not an invariant; even in an ether theory, a tachyon can only travel between two points "instantaneously" as seen in one specific frame. That wouldn't change the result of the duel because the motion of A and B would also look different in any other frame, so it would still turn out that A's shot hit B just as B was firing, and vice versa. But the tachyons would no longer travel "instantaneously".

Thanks for your explanation. It's much clearer now. For many nights, these thoughts have consumed me.

But why is "in any other frame, the shots would not travel "instantaneously"? What principle prohibits that? Maybe because c is still the limit and tachyons just special? But if c and all particles are instantaneous. Then everything would look instantaneous in every frame, agree?
And we are back to Galilean spacetime where even gravity travels instantaneously.

I think you're misunderstanding ghwellsjr's comments on this. SR and LET use the same mathematics; they just put different interpretations on it. So if LET says some particular equation applies "in the ether frame", and that equation is expressed in covariant form, then that equation will apply in all frames, whether you use SR or LET to interpret the equation.

But if you explicitly violate covariance, for example by specifying that tachyon velocity is always some specific v > c relative to a specific frame, which you call the "ether frame", then the tachyon velocity will be different in some other frame, because you specified that this particular phenomenon violates covariance. (The case of "instantaneous" tachyons is just the case v = infinity relative to the ether frame.)



Bohmian Mechanics is explicitly non-relativistic; AFAIK nobody has ever succeeded in making a relativistic version. So Bohmian Mechanics doesn't even address this question; it simply can't be applied to relativistic phenomena at all.

 

[PeterDonis]

But why is "in any other frame, the shots would not travel "instantaneously"? What principle prohibits that?

The Lorentz transformation. As I said, I was assuming that the only violation of Lorentz invariance being proposed was the specific violation of the tachyon itself, and that everything else was still to remain as it is in SR. If you get rid of the Lorentz transformation in general, you're basically on your own.

Maybe because c is still the limit and tachyons just special? But if c and all particles are instantaneous. Then everything would look instantaneous in every frame, agree? And we are back to Galilean spacetime where even gravity travels instantaneously.

And we are also in gross violation of many, many experiments, so that's not a viable option. That's another reason why I assumed that the *only* violation of Lorentz invariance was the specific violation of the tachyon velocity being fixed relative to a particular frame.

 

[stglyde]

The Lorentz transformation. As I said, I was assuming that the only violation of Lorentz invariance being proposed was the specific violation of the tachyon itself, and that everything else was still to remain as it is in SR. If you get rid of the Lorentz transformation in general, you're basically on your own.



And we are also in gross violation of many, many experiments, so that's not a viable option. That's another reason why I assumed that the *only* violation of Lorentz invariance was the specific violation of the tachyon velocity being fixed relative to a particular frame.

Presently. Quantum non-locality has 3 explanations:

1. Many Worlds where there is really no non-locally but just a result of matching up.
2. Copenhagen where the wave functions don't exist physically.. so since there is no beables in spacetime.. then there is nothing to be non-local about. Everything is just wave function, spacetime manifolds and equations and one must simply hide it under the rug.
3. Bohmian version where the wave function is a beable existing in spacetime and non-local and has instantaneous velocity and it moving fixed relative to a particular frame.

The last is identical to the situation we were discussing about "tachyon velocity being fixed relative to a particular frame" or wave function being fixed relative to a particular frame, agree? In other words, can you equate tachyons velocity with BM wave function velocity?. And if this not viable, then only possibility 1 and 2 exist. Are you saying #3 is not viable? And why?

 

[stglyde]

I don't understand



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.

Haushofer, have you not yet understand what Maudlin was describing? In another article "Space-Time in the Quantum World" I saw at google, he described it in other words (see if you can pick up what he was referring to):

"What Bohm's theory and the collapse theories seem to need is something like the classical notion of absolute simultaneity: a fundamental physical relation between events at space-like separation. In effect, such a relation would induce a foliation (italics) of the space-time, a division of the spacetime manifold into a stack of space-like hyperplanes. Putting a measure over those hyperplanes yields an absolute time-function in terms of which the Bohmian dynamics or the collapse dynamics can be framed."

PeterDonis, any idea what Mauldlin was talking about? See thread message #1 for his other statements. Many of us are at a loss what he Mauldin was describing. Maybe you know what and can assist us.

 

[stglyde]

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

Harald.. why don't you read this Tumulka paper http://arxiv.org/abs/quant-ph/0406094 about "A Relativistic Version of the Ghirardi-Rimini-Weber Model". Many physicists are interested in it because it is completely relativistic formulation of non-locality with beables (collapse model). Can you find any flaw with it that can kill the theory?

Btw.. I also owned Maudlin 2nd edition Quantum Non-Locality and Relativity. It's now in its third edition (May, 2011) which includes Tumulka relativistic GRW. I'll review the book.

 

[PeterDonis]

3. Bohmian version where the wave function is a beable existing in spacetime and non-local and has instantaneous velocity and it moving fixed relative to a particular frame.

As I said before, this is *not* Bohmian Mechanics, which is explicitly non-relativistic and does not even deal with the matter of changing reference frames at all. Bohmian Mechanics uses the Schrodinger Equation, which is explicitly non-relativistic and can't be transformed from frame to frame, at least not without making predictions that grossly contradict experiments. So the same is true for Bohmian Mechanics.

Another way of putting this is that we know the Schrodinger Equation is not correct; it is only an approximation that is valid if everything is moving slowly compared to the speed of light. As soon as you start talking about "instantaneous" wavefunction collapse over a significant spatial distance, you are violating that restriction. For experiments confined to a single lab, you can get away with this, but it won't work in general.

The last is identical to the situation we were discussing about "tachyon velocity being fixed relative to a particular frame" or wave function being fixed relative to a particular frame, agree? In other words, can you equate tachyons velocity with BM wave function velocity?. And if this not viable, then only possibility 1 and 2 exist. Are you saying #3 is not viable? And why?

I'm saying nobody has an actual theory corresponding to #3; the theory of Bohmian Mechanics is not it because it does not deal with changing reference frames at all. AFAIK nobody has actually come up with a consistent relativistic version of Bohmian Mechanics. So there's no way to tell what the "instantaneous wavefunction velocity" would become in a version of Bohmian Mechanics that could actually deal with more than one reference frame.

 

[PeterDonis]

PeterDonis, any idea what Mauldlin was talking about? See thread message #1 for his other statements. Many of us are at a loss what he Mauldin was describing. Maybe you know what and can assist us.

I can't say for sure since I haven't read the book or article you are taking these quotes from. so I don't know if he's talking about just something speculative or if he's actually referring to a paper or papers making a serious attempt to extend Bohmian Mechanics or something similar to a relativistic theory. In the quote at the end of the OP there is a reference to a "recently discovered alternative theory", but no link or paper title is given. But I can speculate based on the quotes given.

The general meaning of the term "foliation" is clear, of course: it's a slicing of spacetime into a "stack" of 3-D spacelike hypersurfaces, each of which is viewed as a "surface of constant time" according to some family of observers. The family of observers is the described by a congruence of timelike worldlines such that each worldline passes through one and only one point of each hypersurface. Each worldline then can be viewed as labeling a "point in space" occupied by the observer traveling along it.

In general, any given spacetime will have an infinite number of different possible foliations, so it looks like what Mauldin is proposing is to label one such foliation as "preferred" with respect to wavefunction collapse. In other words, any given wavefunction collapse would have to occur "instantaneously" with respect to that particular foliation only. For example, suppose I am traveling along one particular worldline A picked from the congruence of worldlines described above; in other words, I am at rest at "spatial point A" with respect to the preferred foliation. I receive one of a pair of entangled particles, the other of which is sent off in the opposite direction. When I receive my particle, I measure it in a way that collapses the joint wavefunction of both particles; this measurement takes place at time t0 with respect to the preferred foliation, i.e., it takes place at the event where my worldline A intersects the hypersurface marked t = t0. Then, according to the type of theory Mauldin is proposing, the wavefunction of the other particle in the entangled pair also collapses at the event where its worldline intersects the t = t0 hypersurface.

Of course this violates Lorentz invariance in a way similar to the tachyon pistol when we specified that its velocity was fixed relative to the ether frame, instead of relative to the pistol. In both cases, there is an obvious question: what, physically, picks out *that* particular frame, that particular foliation, as being "special"? Just saying "it's the ether frame", or "it's the foliation my theory picks out", won't do; there should be some *physical* property that picks out one foliation over another.

 

[stglyde]

I can't say for sure since I haven't read the book or article you are taking these quotes from. so I don't know if he's talking about just something speculative or if he's actually referring to a paper or papers making a serious attempt to extend Bohmian Mechanics or something similar to a relativistic theory. In the quote at the end of the OP there is a reference to a "recently discovered alternative theory", but no link or paper title is given. But I can speculate based on the quotes given.

Oh, the recently discovered alternative theory Maudlin is referring to is the paper by Tumulka at http://arxiv.org/abs/quant-ph/0406094 about "A Relativistic Version of the Ghirardi-Rimini-Weber Model". Many physicists are interested in it because it is completely relativistic formulation of non-locality with beables (collapse model or even BM). Can you find any flaw with it that can kill the theory?

The general meaning of the term "foliation" is clear, of course: it's a slicing of spacetime into a "stack" of 3-D spacelike hypersurfaces, each of which is viewed as a "surface of constant time" according to some family of observers. The family of observers is the described by a congruence of timelike worldlines such that each worldline passes through one and only one point of each hypersurface. Each worldline then can be viewed as labeling a "point in space" occupied by the observer traveling along it.

In general, any given spacetime will have an infinite number of different possible foliations, so it looks like what Mauldin is proposing is to label one such foliation as "preferred" with respect to wavefunction collapse. In other words, any given wavefunction collapse would have to occur "instantaneously" with respect to that particular foliation only. For example, suppose I am traveling along one particular worldline A picked from the congruence of worldlines described above; in other words, I am at rest at "spatial point A" with respect to the preferred foliation. I receive one of a pair of entangled particles, the other of which is sent off in the opposite direction. When I receive my particle, I measure it in a way that collapses the joint wavefunction of both particles; this measurement takes place at time t0 with respect to the preferred foliation, i.e., it takes place at the event where my worldline A intersects the hypersurface marked t = t0. Then, according to the type of theory Mauldin is proposing, the wavefunction of the other particle in the entangled pair also collapses at the event where its worldline intersects the t = t0 hypersurface.

Of course this violates Lorentz invariance in a way similar to the tachyon pistol when we specified that its velocity was fixed relative to the ether frame, instead of relative to the pistol. In both cases, there is an obvious question: what, physically, picks out *that* particular frame, that particular foliation, as being "special"? Just saying "it's the ether frame", or "it's the foliation my theory picks out", won't do; there should be some *physical* property that picks out one foliation over another.

Thanks. I'll think about it.

 

[stglyde]

I can't say for sure since I haven't read the book or article you are taking these quotes from. so I don't know if he's talking about just something speculative or if he's actually referring to a paper or papers making a serious attempt to extend Bohmian Mechanics or something similar to a relativistic theory. In the quote at the end of the OP there is a reference to a "recently discovered alternative theory", but no link or paper title is given. But I can speculate based on the quotes given.

The general meaning of the term "foliation" is clear, of course: it's a slicing of spacetime into a "stack" of 3-D spacelike hypersurfaces, each of which is viewed as a "surface of constant time" according to some family of observers. The family of observers is the described by a congruence of timelike worldlines such that each worldline passes through one and only one point of each hypersurface. Each worldline then can be viewed as labeling a "point in space" occupied by the observer traveling along it.

In general, any given spacetime will have an infinite number of different possible foliations, so it looks like what Mauldin is proposing is to label one such foliation as "preferred" with respect to wavefunction collapse. In other words, any given wavefunction collapse would have to occur "instantaneously" with respect to that particular foliation only. For example, suppose I am traveling along one particular worldline A picked from the congruence of worldlines described above; in other words, I am at rest at "spatial point A" with respect to the preferred foliation. I receive one of a pair of entangled particles, the other of which is sent off in the opposite direction. When I receive my particle, I measure it in a way that collapses the joint wavefunction of both particles; this measurement takes place at time t0 with respect to the preferred foliation, i.e., it takes place at the event where my worldline A intersects the hypersurface marked t = t0. Then, according to the type of theory Mauldin is proposing, the wavefunction of the other particle in the entangled pair also collapses at the event where its worldline intersects the t = t0 hypersurface.

Of course this violates Lorentz invariance in a way similar to the tachyon pistol when we specified that its velocity was fixed relative to the ether frame, instead of relative to the pistol. In both cases, there is an obvious question: what, physically, picks out *that* particular frame, that particular foliation, as being "special"? Just saying "it's the ether frame", or "it's the foliation my theory picks out", won't do; there should be some *physical* property that picks out one foliation over another.

I think this is what Maudlin meant. So you are saying that instead of referring to LET and its ether frame. One can just speak of Preferred Foliation to refer to the same idea without mentioning a word about LET?? In other words, Preferred Foliation is the same Ether frame in LET? In our examples. We use tachyons moving at v>c relative to the aether frame. Translating this to language of Preferred Foliation. One can say the tachyons moving at v>c relative to the Preferred Foliation (which doesn't necessarily involve the aether frame)? If the two are different. Then what is the Preferred Foliation equivalent in LET that is in addition to the aether frame?

 

[PeterDonis]

So you are saying that instead of referring to LET and its ether frame. One can just speak of Preferred Foliation to refer to the same idea without mentioning a word about LET??

I'm not sure they're the same idea. LET does claim that there is some Lorentz frame that is an "ether frame", but it doesn't claim that the existence of this frame has any physically detectable consequences. The kind of "preferred foliation" that Mauldin is talking about would have physically detectable consequences; you could in principle detect the "preferred frame" defined by the preferred foliation by accurately timing wavefunction collapses using detectors in different states of motion.

In our examples. We use tachyons moving at v>c relative to the aether frame. Translating this to language of Preferred Foliation. One can say the tachyons moving at v>c relative to the Preferred Foliation (which doesn't necessarily involve the aether frame)?

If we specify that tachyons always move at some fixed v > c relative to the aether frame, then the aether frame is physically detectable (just fire tachyon pistols in different states of motion); so it would count as a "preferred foliation" in Mauldin's terminology (if I have correctly captured what he intended by that term).

 

[stglyde]

I'm not sure they're the same idea. LET does claim that there is some Lorentz frame that is an "ether frame", but it doesn't claim that the existence of this frame has any physically detectable consequences. The kind of "preferred foliation" that Mauldin is talking about would have physically detectable consequences; you could in principle detect the "preferred frame" defined by the preferred foliation by accurately timing wavefunction collapses using detectors in different states of motion.



If we specify that tachyons always move at some fixed v > c relative to the aether frame, then the aether frame is physically detectable (just fire tachyon pistols in different states of motion); so it would count as a "preferred foliation" in Mauldin's terminology (if I have correctly captured what he intended by that term).

Uhm. We commonly use the term "Preferred Frame" and "Preferred Foliation" is not commonly use. So Is "Preferred Frame" and "Preferred Foliation" exactly the same meaning or is there any subtle difference between them?

 

[PeterDonis]

Uhm. We commonly use the term "Preferred Frame" and "Preferred Foliation" is not commonly use. So Is "Preferred Frame" and "Preferred Foliation" exactly the same meaning or is there any subtle difference between them?

I don't know that "preferred foliation" has a commonly accepted meaning; as you say, it's not in common use. The term "preferred frame" is used fairly often, but people seem to mean different things by its use; some use it to indicate a frame that is in principle physically detectable, others use it to indicate a frame like the LET aether frame that can't be physically detected even in principle. The best advice I can give is to ask for clarification whenever you see either of these terms used.

 

[stglyde]

I don't know that "preferred foliation" has a commonly accepted meaning; as you say, it's not in common use. The term "preferred frame" is used fairly often, but people seem to mean different things by its use; some use it to indicate a frame that is in principle physically detectable, others use it to indicate a frame like the LET aether frame that can't be physically detected even in principle. The best advice I can give is to ask for clarification whenever you see either of these terms used.

But foliation has same meaning has frame as when you mentioned in message #76 in the other thread:

a "frame" is a particular way of *describing* the 4-D spacetime by slicing it up (in Gardner's terminology) into 3-D slices (which are then called "surfaces of simultaneity" or "slices of constant time" or something like that) such that (a) each 3-D slice is labeled by a unique value of a fourth coordinate, "time" ("fourth" because it takes three coordinates to specify a point in each 3-D slice), and (b) each event in the spacetime appears in one and only one 3-D slice. Particular objects are then 4-D subregions of the whole 4-D spacetime, and different ways of slicing will "cut" the subregions at different angles, so the shapes of the slices of the objects will be different.

So it is also right that "a "foliation" is a particular way of *describing* the 4-D spacetime by slicing it up (in Gardner's terminology) into 3-D slices (which are then called "surfaces of simultaneity" or "slices of constant time" or something like that)..."??

So frame and foliation has same meaning... but why do the word "foliation" is not used much?


About LET ether being undetectable and the Preferred Foliation being detectable. First read the following by John Bell:

" I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare ´ thought that there was an aether – a preferred frame of reference – but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether. . . . that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant. . . . what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincare´, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether – that is a perfectly coherent point of view. . . . The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backward in time. . . . [this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether. (‘‘John Bell,’’ (1986) interview in Davies and Brown; cf. Bell 1987: 279; see also Bell 1984: 66–76)

Now the LET ether is said to be undetectable. But can't we say that Entanglement experiments make it detectable because it uses the LET ether frame as Bell wanted to suggest?

In other words. Particles like fermions and bosons are ruled by SR and don't use the aether frame, while only wave function use the aether frame. Is this not possible?

Well. I know gauge theory which says locality and gauge principle is what created the gauge bosons in the first place (when you have to add cheating terms to the wave function to make it vary from place to place.. i got this very clear from Schumm book Deep Down Things). So this gauge principle is what make it impossible that the wave function use the aether frame right?

This is the reason Maudlin is so excited about the completely relativistic GRW with flash (in the paper shared a few message prior to this). But I think it is very much in infancy.

So right now the safest bet is Copenhagen where since the wave function is just in the equations, there is nothing to be non-local about. This means one must only see Spacetime as equations and wave functions and spacetimes are models about reality and we only have models to reality and nothing further that can be know... end of story. We must not think of any physical sense to them or we may not be able to reconcile non-local equations. Is this what you also believe?

 

[bohm2]

".Bohmian Mechanics is explicitly non-relativistic; AFAIK nobody has ever succeeded in making a relativistic version. So Bohmian Mechanics doesn't even address this question; it simply can't be applied to relativistic phenomena at all.

I think there is one by a member in this forum:

It is often argued that hypothetic nonlocal reality responsible for nonlocal quantum correlations between entangled particles cannot be consistent with relativity. I review the most frequent arguments of that sort, explain how they can all be circumvented, and present an explicit Bohmian model of nonlocal reality (compatible with quantum phenomena) that fully obeys the principle of relativistic covariance and does not involve a preferred Lorentz frame.

Making nonlocal reality compatible with relativity
http://xxx.lanl.gov/abs/1002.3226

 

[PeterDonis]

But foliation has same meaning has frame as when you mentioned in message #76 in the other thread:

You're right, "foliation" does mean pretty much the same thing as "frame" the way I defined it. But putting the word "preferred" in front changes the meaning; there are lots of different possible frames/foliations, but saying that one of them is "preferred" is giving that one a special status that needs justification.

why do the word "foliation" is not used much?

"Foliation" is used a lot in the technical literature of GR when talking about the global structure of spacetime and various theorems about it. Being able to find a global foliation of the spacetime with the properties we've been assuming is actually a pretty strict condition on the spacetime, if "spacetime" is considered simply as a mathematically valid solution to the Einstein Field Equations.

Now the LET ether is said to be undetectable. But can't we say that Entanglement experiments make it detectable because it uses the LET ether frame as Bell wanted to suggest?

No, because the entanglement experiments don't pick out any particular frame as the ether frame. Bell was suggesting that the viewpoint that there is an ether frame even though it's physically undetectable was "coherent"; he wasn't suggesting (at least not as I understand him) that the ether frame was actually detectable.

In other words. Particles like fermions and bosons are ruled by SR and don't use the aether frame, while only wave function use the aether frame. Is this not possible?

I don't think this is what Bell was trying to say. If by "wave function" you mean the standard wave function as defined in standard quantum mechanics, it is not something separate from the particles, and it has to obey the same rules as the particles do. If you are talking about the "wave function" as it is used in Bohmian Mechanics, remember that that theory is explicitly non-relativistic, as I said before, so the question of whether it selects a "preferred frame" can't really even be asked, since relativistic phenomena are outside the theory's domain to begin with.

Well. I know gauge theory which says locality and gauge principle is what created the gauge bosons in the first place (when you have to add cheating terms to the wave function to make it vary from place to place.. i got this very clear from Schumm book Deep Down Things). So this gauge principle is what make it impossible that the wave function use the aether frame right?

I don't see a connection here. Can you give some more specfics about what the book says about gauge theory?

This is the reason Maudlin is so excited about the completely relativistic GRW with flash (in the paper shared a few message prior to this).

I've only skimmed the paper so I can't say much about it at this point.

So right now the safest bet is Copenhagen where since the wave function is just in the equations, there is nothing to be non-local about. This means one must only see Spacetime as equations and wave functions and spacetimes are models about reality and we only have models to reality and nothing further that can be know... end of story. We must not think of any physical sense to them or we may not be able to reconcile non-local equations. Is this what you also believe?

I think the Copenhagen interpretation is obviously incomplete; the fact that it works well in practice may just be because we haven't gotten sophisticated enough yet in running experiments that reveal its limitations.

I think that EPR-type experiments show that reality does not work the way our classical intuitions say it "should" work, but I don't see this as a problem, since I don't expect our classical intuitions to accurately tell us how reality works outside of the limited domain in which those intuitions evolved. Our brains are not built to understand quantum phenomena or relativistic phenomena intuitively the way we understand classical non-relativistic phenomena like thrown baseballs intuitively.

I don't think the observed violations of the Bell inequalities in EPR-type experiments indicate any violation of causality or Lorentz invariance, even "behind the scenes". I think it just indicates that we are still learning how to understand causality and Lorentz invariance. If you look at the actual math of quantum field theory, it does not place any restrictions on how spacelike-separated measurements can be correlated; the only thing actually required for causality and Lorentz invariance to be maintained is that spacelike-separated measurements must commute; that is, the results can't depend on which one happens first. The EPR-type results satisfy this criterion. So again, I don't think these results indicate anything "mysterious"; they just indicate that we don't yet fully understand how reality works.

 

[stglyde]

You're right, "foliation" does mean pretty much the same thing as "frame" the way I defined it. But putting the word "preferred" in front changes the meaning; there are lots of different possible frames/foliations, but saying that one of them is "preferred" is giving that one a special status that needs justification.



"Foliation" is used a lot in the technical literature of GR when talking about the global structure of spacetime and various theorems about it. Being able to find a global foliation of the spacetime with the properties we've been assuming is actually a pretty strict condition on the spacetime, if "spacetime" is considered simply as a mathematically valid solution to the Einstein Field Equations.

You said earlier that "In general, any given spacetime will have an infinite number of different possible foliations, so it looks like what Mauldin is proposing is to label one such foliation as "preferred" with respect to wavefunction collapse." But Maudlin appears to be referring to label all foliations as preferred. Maybe the following passages in his article "Non-Local Correlations in Quantum Theory: How the Trick Might Be Done" will hold the key to what he meant:

Since the exact outcome of the experiment depends on which x-spin measurement is made first, the notion of “first” and “second” has an ineliminable physical role in Bohm’s theory. In the non-Relativistic theory, which measurement comes first and which second is determined by absolute simultaneity. And if one is to transfer the Bohmian dynamics to a space-time with a Lorenzian structure, one needs for there to be something fit to play the same dynamical role. Since no such structure is determined by the Lorentzian metric, the simplest thing to do is to add the required structure: to add a foliation relative to which the relevant sense of “first” and “second” (or “before” and “after”) is defined. The foliation would then be invoked in the statement of the fundamental dynamical law governing the particles.

So is Maudlin referring to label one such foliation as "preferred" with respect to wavefunction collapse or referring to label all the foliations or using all of them in the wavefunction collapse? The argument perhaps being that since there is nothing that chooses just one of them as special... may as well choose all of them. In all his attributions of "foliation". He never mention about labelling one of them as preferred, but just mentioned it like doing it to all foliations (refer to message #1 again to get the context of what I mean he refer to a singular and general 'foliation'). Is this what he was saying all along. You can know perhaps by the context of what he described above.

Let's settle this first as it is the most vague and focus of this thread "Meaning of Spacetime Foliation".

I'll address the other points below in another post.

No, because the entanglement experiments don't pick out any particular frame as the ether frame. Bell was suggesting that the viewpoint that there is an ether frame even though it's physically undetectable was "coherent"; he wasn't suggesting (at least not as I understand him) that the ether frame was actually detectable.



I don't think this is what Bell was trying to say. If by "wave function" you mean the standard wave function as defined in standard quantum mechanics, it is not something separate from the particles, and it has to obey the same rules as the particles do. If you are talking about the "wave function" as it is used in Bohmian Mechanics, remember that that theory is explicitly non-relativistic, as I said before, so the question of whether it selects a "preferred frame" can't really even be asked, since relativistic phenomena are outside the theory's domain to begin with.



I don't see a connection here. Can you give some more specfics about what the book says about gauge theory?



I've only skimmed the paper so I can't say much about it at this point.



I think the Copenhagen interpretation is obviously incomplete; the fact that it works well in practice may just be because we haven't gotten sophisticated enough yet in running experiments that reveal its limitations.

I think that EPR-type experiments show that reality does not work the way our classical intuitions say it "should" work, but I don't see this as a problem, since I don't expect our classical intuitions to accurately tell us how reality works outside of the limited domain in which those intuitions evolved. Our brains are not built to understand quantum phenomena or relativistic phenomena intuitively the way we understand classical non-relativistic phenomena like thrown baseballs intuitively.

I don't think the observed violations of the Bell inequalities in EPR-type experiments indicate any violation of causality or Lorentz invariance, even "behind the scenes". I think it just indicates that we are still learning how to understand causality and Lorentz invariance. If you look at the actual math of quantum field theory, it does not place any restrictions on how spacelike-separated measurements can be correlated; the only thing actually required for causality and Lorentz invariance to be maintained is that spacelike-separated measurements must commute; that is, the results can't depend on which one happens first. The EPR-type results satisfy this criterion. So again, I don't think these results indicate anything "mysterious"; they just indicate that we don't yet fully understand how reality works.

 

[PeterDonis]

So is Maudlin referring to label one such foliation as "preferred" with respect to wavefunction collapse

Yes; he has to be, because he needs to make the time ordering of the measurements determinate, and that can only be done for spacelike-separated measurements by picking a particular simultaneity, which means picking a particular preferred foliation.

 

[stglyde]

I don't see a connection here. Can you give some more specfics about what the book says about gauge theory?

What I learned from the book is that Quantum Mechanics as originally formulated is phase invariant... meaning changes in phase won't affect it... that is global gauge invariance. However, "locally" it's not invariant so one has to add a cheating function or factor to the equation to make it invariant under local changes of phase. By adding a "cheat" factor. It surprisingly describes the field of the photon, the quantum of the electromagnetic field and so the QED U(1) and explaining why the charge is conserved.

Now the weak force. From the doublets (muon, antimuon thing for example). They consider something like weak isospin orientation as well as the qm-phase. Now to compensate
for the problems caused by the derivator operator that vary from point to point, "cheating" terms must be added. This time, one is not enough. 3 cheating terms must be added (to make it invariant). And bingo, this creates the force carriers of the weak force, the +W, -W and Z.

This also works fo the SU(3) strong force with the Lie Group having 8 generators.

So gauge theory has to do with the fact that the wave function is local. Therefore making it non-local may undo everything gauge theory teaches us. If you don't agree, then how do you make the wave function non-local?

I think the Copenhagen interpretation is obviously incomplete; the fact that it works well in practice may just be because we haven't gotten sophisticated enough yet in running experiments that reveal its limitations.

I think that EPR-type experiments show that reality does not work the way our classical intuitions say it "should" work, but I don't see this as a problem, since I don't expect our classical intuitions to accurately tell us how reality works outside of the limited domain in which those intuitions evolved. Our brains are not built to understand quantum phenomena or relativistic phenomena intuitively the way we understand classical non-relativistic phenomena like thrown baseballs intuitively.

I don't think the observed violations of the Bell inequalities in EPR-type experiments indicate any violation of causality or Lorentz invariance, even "behind the scenes". I think it just indicates that we are still learning how to understand causality and Lorentz invariance. If you look at the actual math of quantum field theory, it does not place any restrictions on how spacelike-separated measurements can be correlated; the only thing actually required for causality and Lorentz invariance to be maintained is that spacelike-separated measurements must commute; that is, the results can't depend on which one happens first. The EPR-type results satisfy this criterion. So again, I don't think these results indicate anything "mysterious"; they just indicate that we don't yet fully understand how reality works.

Yes, quantum entanglement doesn't violate causality or lorentz invariance but we don't have physical picture of it. The wave function is in the equation, the spacetime manifold is also in the equation.. yet when you walk down or up the stairs, you feel physicality.. our physics doesn't explain how the transition from equations to reality work. "Shut up and calculate" kind of physicists just accept it is so. Bohmians and Many Worlders and those not satisfied with simply shutting up and calculate (dumb down mode).

 

[PeterDonis]

What I learned from the book is that Quantum Mechanics as originally formulated is phase invariant... meaning changes in phase won't affect it... that is global gauge invariance. However, "locally" it's not invariant so one has to add a cheating function or factor to the equation to make it invariant under local changes of phase. By adding a "cheat" factor. It surprisingly describes the field of the photon, the quantum of the electromagnetic field and so the QED U(1) and explaining why the charge is conserved.

...

So gauge theory has to do with the fact that the wave function is local. Therefore making it non-local may undo everything gauge theory teaches us. If you don't agree, then how do you make the wave function non-local?

The "global" and "local" here don't refer to the wave function; they refer to the gauge transformations. A "global" gauge transformation is one that is the same at every point in spacetime. A "local" gauge transformation can vary from point to point in spacetime. So having the laws of physics be invariant under "local" gauge transformations is a much stricter condition than just having them be invariant under "global" gauge transformations; and it turns out that, as you say, we have to add gauge fields ("cheating" is a bit strong a term to use to describe what they do) to make the laws of physics meet the stricter condition.

The terms "global" and "local" to describe the transformations are rather unfortunate since they invite confusion about what is being referred to, but those are the standard terms and we're stuck with them.

Yes, quantum entanglement doesn't violate causality or lorentz invariance but we don't have physical picture of it.

Yes, we do. What we don't have is a physical picture *that matches our "classical" intuitions.* My view is that this is a problem with our intuitions, not with the physical picture. A good expression of this viewpoint is in the article "Think Like Reality" by Eliezer Yudkowsky, here:

http://lesswrong.com/lw/hs/think_like_reality/

He says:

The universe was propagating complex amplitudes through configuration space for ten billion years before life ever emerged on Earth. Quantum physics is not "weird". You are weird. You have the absolutely bizarre idea that reality ought to consist of little billiard balls bopping around, when in fact reality is a perfectly normal cloud of complex amplitude in configuration space. This is your problem, not reality's, and you are the one who needs to change.

We should not expect the "physical picture" of quantum reality to look like our intuitive picture of everyday reality.

The wave function is in the equation, the spacetime manifold is also in the equation.. yet when you walk down or up the stairs, you feel physicality.. our physics doesn't explain how the transition from equations to reality work.

Physics is not a science of consciousness, it's a science of fundamentals way below the level of consciousness. When you ask for an explanation of why you "feel physicality" when you walk down or up the stairs, you should not be asking physics; you should be asking the theory of consciousness, which is hardly in a state to give a coherent reply at this stage of our knowledge, true, but that's not the fault of physics.

 

[stglyde]

The "global" and "local" here don't refer to the wave function; they refer to the gauge transformations. A "global" gauge transformation is one that is the same at every point in spacetime. A "local" gauge transformation can vary from point to point in spacetime. So having the laws of physics be invariant under "local" gauge transformations is a much stricter condition than just having them be invariant under "global" gauge transformations; and it turns out that, as you say, we have to add gauge fields ("cheating" is a bit strong a term to use to describe what they do) to make the laws of physics meet the stricter condition.

The terms "global" and "local" to describe the transformations are rather unfortunate since they invite confusion about what is being referred to, but those are the standard terms and we're stuck with them.

But the wave function is related to the gauge transformations. The best book with 44 Full 5 Star "Deep Down Things" by Bruce Schumm mentions the following for example (he used the words "cheating terms" for fancy since his audience are laymen):

https://www.amazon.com/dp/080187971X/?tag=pfamazon01-20

"Again, the gauge fields, or interactions, Ac(x) need to be introduced into the free-particle wave equation to patch up the damage caused by color-space rotations that swap the quark colors among one another by amounts that differ as you move from point to point in space-time. Over there, you rotate or transform, a blue quark into half-green, half-red quark, while over here, you transform a blue quark into a pure red quark (and maybe change the quantum-mechanical phase of the resulting wave function by some amount also). These differing transformations alter the way the wave function changes from point to point in space. This, in turn, destroys the delicate balance, required by the wave equation, between the rate of change in the wave function around any point in space and the energy of the object described by that wave function. We thus find it necessary to introduce gauge field (interaction) terms of the form gsAc(x)psi(x) as "cheating terms" that act to restore this delicate balance and thus make the wave equation and its wave function solution invariant with respect to local SU(3) color space rotations."

You see he mentioned "These differing transformations alter the way the wave function changes from point to point in space" so its local and global is related to the wave function as he emphasized numerous times in the book. Yet you emphasized it is the gauge transformation that is local and globe.. but gauge transformation involves wave function!

 

[stglyde]

I think there is one by a member in this forum:



Making nonlocal reality compatible with relativity
http://xxx.lanl.gov/abs/1002.3226

I read the paper entirely. There is one part which if debunked would debunk the entire idea. It is the following claim:

"By 2) I mean that time and space should be treated on an equal footing. Note that in
the usual formulation of QM, time and space are not treated on an equal footing. First,
for one particle described by the wave function psi(x,t), the infinitesimal probability in
the usual formulation is |psi|^2d^3 x, while from a symmetric treatment of time and space
one expects |psi|^2 d^3 x dt. Second, for n particles the wave function in the usual formulation
takes the form (x1, . . . , xn, t), while from a symmetric treatment of time and space one
expects (x1, t1, . . . , xn, tn). I formulate QM such that fundamental axioms involve the
expressions above in which time and space are treated symmetrically, and show that the
usual formulation corresponds to a special case."

Any seasoned Relativists can debunk this? PeterDonis?

 

[bohm2]

I read the paper entirely. There is one part which if debunked would debunk the entire idea. It is the following claim:...Any seasoned Relativists can debunk this? PeterDonis?

Actually, some physicists who favour the pilot-wave interpretation find that such models trying to find lorentz-invariant de Broglie-Bohmian models are misconceived for other reasons:

A number of authors insist that a realistic quantum physics should be ‘seriously Lorentz invariant’, in the sense that Lorentz invariance should be fundamental, and not merely phenomenological or emerging in some limit. This contrast is remarkable, because it is precisely in quantum foundations that there is arguably the strongest motivation of all for abandoning fundamental Lorentz invariance: the experimental detection of quantum nonlocality, through the observed violations of Bell’s inequalities. As emphasised by Bell, quantum theory is incompatible with locality, independently of any assumption about the existence of hidden variables...

Note that, in the specific hidden-variables theory given by pilot-wave dynamics, even leaving nonlocality aside, the natural kinematics of the theory is arguably that of Aristotelian spacetime E × E3, with a preferred state of rest (Valentini 1997). This is essentially because the dynamics is first order in time, so that rest is the only reasonable definition of ‘natural’ or ‘unforced’ motion. Pilot-wave theory then has a remarkable internal logic: both the structure of the dynamics, and the operational possibility of nonlocal signalling out of equilibrium, independently point to the existence of a natural preferred state of rest.

Hidden Variables and the Large-Scale Structure of Spacetime
http://lanl.arxiv.org/PS_cache/quant-ph/pdf/0504/0504011v2.pdf

To impose Galilean invariance on the pilot-wave theory is like imposing, on Newtonian mechanics, an invariance under transformations to uniformly accelerated frames. The Galilean transformation of ψ amounts to the introduction of fictitious inertial (Aristotelian) forces. Despite appearances, then, Galilean invariance is not a fundamental symmetry of the low-energy pilot-wave theory. There is then no reason to impose Lorentz invariance in the high-energy domain. Some authors, following Bell, have portrayed the current situation as a sort of two-horse race for fundamental Lorentz invariance, the contestants being the pilot-wave and dynamical-reduction theories. From the above perspective, this is quite misguided. For in the pilot-wave theory, uniform motion is not relative–so the ‘problem’ of finding a Lorentz-invariant extension simply does not arise. Whether the theory of dynamical reduction is also able to circumvent this problem remains to be seen. (Perhaps the reduction mechanism could be shown to single out a natural state of rest.)

On Galilean and Lorentz invariance in pilot-wave dynamics
http://lanl.arxiv.org/PS_cache/arxiv/pdf/0812/0812.4941v1.pdf

 

[PeterDonis]

You see he mentioned "These differing transformations alter the way the wave function changes from point to point in space" so its local and global is related to the wave function as he emphasized numerous times in the book. Yet you emphasized it is the gauge transformation that is local and globe.. but gauge transformation involves wave function!

Yes, the gauge transformations alter the wave function, but only in the mathematics, not in the physics. Saying that a theory is "gauge invariant" is actually saying that there are multiple mathematical expressions that describe the same physical state; a "gauge transformation" is a transformation that switches from one expression to another without changing the actual physical state. For example, the states that he is calling "blue quark", "red quark", etc. are not physical states per se; they are descriptions of physical states in a particular basis. The gauge transformation that changes, for example, "blue quarks" into "red quarks" is actually a change of basis, like a change of coordinate frames in SR; it doesn't change the physical states at all, it just changes the "coordinates" in which they are described. So when he says the gauge transformations are "changing the wave function", he's only talking about changing the basis; he's not talking about changing any actual physical observables.

As far as "local" and "global", read my description of what those terms mean as applied to gauge transformations again. They have nothing to do with the type of function that the transformations act on. Classical electrodynamics, which doesn't have wave functions at all (only the classical potential and fields) has the same property of gauge invariance.

Whether a wave function is "local" or "nonlocal" depends on what parameters it is a function of. If it's a function of a single spacetime point, it's local; if it's a function of multiple spacetime points, it's nonlocal. So, for example, a wave function describing a single particle in quantum mechanics is local; it's just a regular function that assigns an amplitude to every point in space (or spacetime, in the relativistic version). But a wave function describing two particles is nonlocal: it assigns amplitudes to *pairs* of points, which may be separated. If the two particles are not correlated, we can factor the wave function into a product of two local ones, one for each particle; but if the particles are entangled (e.g., if they are in an EPR-type experiment), we can't do this and the wave function is fundamentally nonlocal. But all this has nothing to do with whether our theory is gauge invariant or not.

 

[PeterDonis]

"By 2) I mean that time and space should be treated on an equal footing. Note that in the usual formulation of QM, time and space are not treated on an equal footing.

Here he's talking about ordinary non-relativistic quantum mechanics, not quantum field theory. I'm not sure why, since elsewhere in the paper he talks about QFT and says it's relativistically covariant. I'm still reading through the paper so I won't comment more until I'm finished, but this is one thing that jumped out at me.

 

[stglyde]

Yes, we do. What we don't have is a physical picture *that matches our "classical" intuitions.* My view is that this is a problem with our intuitions, not with the physical picture. A good expression of this viewpoint is in the article "Think Like Reality" by Eliezer Yudkowsky, here:

http://lesswrong.com/lw/hs/think_like_reality/

He says:

The universe was propagating complex amplitudes through configuration space for ten billion years before life ever emerged on Earth. Quantum physics is not "weird". You are weird. You have the absolutely bizarre idea that reality ought to consist of little billiard balls bopping around, when in fact reality is a perfectly normal cloud of complex amplitude in configuration space. This is your problem, not reality's, and you are the one who needs to change.

We should not expect the "physical picture" of quantum reality to look like our intuitive picture of everyday reality.

The article "Think Like Reality" is only about quantum. I'd like to create a relativistic version for those some Newtonian fellows I know who still can't accept the concept of relativity of simultaneity. They reasoned the world being physical shouldn't be based on perspective.

So what is the counterpart of complex amplitudes in GR and also configuration space. I guess differential manifold is counterpart of configuration space and lorentzian metric tensors as counterpart for complex amplitudes? If so, then the paragraph would be relativistically changed to:

"The universe was propagating lorentzian metric tensors through differential manifolds for ten billion years before life ever emerged on Earth. Special & General Relativity are not "weird". You are weird. You have the absolutely bizarre idea that reality ought to consist of absolute space and time as background when in fact reality is a perfectly normal array of lorentzian metric tensors in differential manifold. This is your problem, not reality's, and you are the one who needs to change."

But the terms lorentzian metric tensors may be awkward. So what is the GR counterpart for complex amplitudes in QM? I know the Einstein Fields Equations have changing parameters just like QM complex amplitudes. What are they exactly?

 

[stglyde]

Yes, the gauge transformations alter the wave function, but only in the mathematics, not in the physics. Saying that a theory is "gauge invariant" is actually saying that there are multiple mathematical expressions that describe the same physical state; a "gauge transformation" is a transformation that switches from one expression to another without changing the actual physical state. For example, the states that he is calling "blue quark", "red quark", etc. are not physical states per se; they are descriptions of physical states in a particular basis. The gauge transformation that changes, for example, "blue quarks" into "red quarks" is actually a change of basis, like a change of coordinate frames in SR; it doesn't change the physical states at all, it just changes the "coordinates" in which they are described. So when he says the gauge transformations are "changing the wave function", he's only talking about changing the basis; he's not talking about changing any actual physical observables.

As far as "local" and "global", read my description of what those terms mean as applied to gauge transformations again. They have nothing to do with the type of function that the transformations act on. Classical electrodynamics, which doesn't have wave functions at all (only the classical potential and fields) has the same property of gauge invariance.

Whether a wave function is "local" or "nonlocal" depends on what parameters it is a function of. If it's a function of a single spacetime point, it's local; if it's a function of multiple spacetime points, it's nonlocal. So, for example, a wave function describing a single particle in quantum mechanics is local; it's just a regular function that assigns an amplitude to every point in space (or spacetime, in the relativistic version). But a wave function describing two particles is nonlocal: it assigns amplitudes to *pairs* of points, which may be separated. If the two particles are not correlated, we can factor the wave function into a product of two local ones, one for each particle; but if the particles are entangled (e.g., if they are in an EPR-type experiment), we can't do this and the wave function is fundamentally nonlocal. But all this has nothing to do with whether our theory is gauge invariant or not.

Well, even if gauge transformations alter the wave function, but only in the mathematics, not in the physics, as you emphasize, it's still related to Special Relativity as Bruce Schumm mentioned in the following:

We know that phase is irrelevant. The choice of the phase of an object's - or a system of objects' - or the universe's wave function is arbitrary. One the one hand, the hallowed wave equation tells us that the arbitrary choice of phase must be consistent from point to point in space and time or all hell breaks loose. On the other hand, as Yang and Mills point out, this requirement appears to be incompatible with Einstein's well-supported notions of the nature of space and time. The contradiction is direct and demands a resolution, so something has to give. And, as has so often been the case in modern science, in reconciling these apparently incompatible points of views, Yang and Mills were led down a path that profoundly and fundamentally augmented the way physicists view the operating principles of the natural world (note 8.2).

So because of Einstein's well-supported notions of the nature of space and time, or Special Relativity, the equations have to conform to SR and be altered, which results in the existence of the gauge fields.. even if gauge transformation is in the equations and not in physical space.

 

[PeterDonis]

So because of Einstein's well-supported notions of the nature of space and time, or Special Relativity, the equations have to conform to SR and be altered, which results in the existence of the gauge fields.. even if gauge transformation is in the equations and not in physical space.

Do you have an online reference for the source from which this quote was taken? Since he mentions Yang and Mills, it appears that he is talking about non-abelian gauge theory, but I'm not sure about the context.

In general terms, you're correct, making quantum theory consistent with relativity appears to require gauge fields. But that may be as much a matter of the mathematical form we choose to write our physical laws in as anything else. As I said in a previous post, gauge transformations don't change any physical observables; they only change the particular "basis" we write the laws in, similar to a change of coordinates. It may be that we will someday find a better way of writing the laws, that naturally expresses relativistic quantum processes without requiring the "redundancy" of gauge fields to compensate for the fact that multiple mathematical states represent the same physical state.

 

[PeterDonis]

The article "Think Like Reality" is only about quantum. I'd like to create a relativistic version for those some Newtonian fellows I know who still can't accept the concept of relativity of simultaneity. They reasoned the world being physical shouldn't be based on perspective.

The article is using quantum mechanics to make a general point, but the point applies to relativity as well.

So what is the counterpart of complex amplitudes in GR and also configuration space.

There isn't, really, since GR is a classical theory, not a quantum theory. But your relativistic version is not a bad "translation", I think, except that metric tensors aren't usually thought of as "propagating". I would use spacetime curvature instead, perhaps something like this:

"The universe was generating spacetime curvature from stress-energy in a locally Lorentzian differential manifold for ten billion years before life ever emerged on Earth. Special & General Relativity are not "weird". You are weird. You have the absolutely bizarre idea that reality ought to consist of absolute space and time and Newtonian forces, when in fact reality is a perfectly normal curved manifold with local Lorentz symmetry. This is your problem, not reality's, and you are the one who needs to change."

 

[bohm2]

I'm not sure if what you guys are looking for is a model that's both lorentz-invariant and narrative (as discussed by D. Albert):

Albert calls a theory narratable if specifying a system’s state at all times is sufficient to specify all properties of a system. Poincare-covariant quantum mechanics is not narratable: if we give the state at all times on a given foliation, we have given something less than the complete description of the system.

http://philosophyfaculty.ucsd.edu/faculty/wuthrich/PhilPhys/AlbertDavid2008Man_PhysicsNarrative.pdf

I believe there are only 2 such models:

1. Tumulka’s GRWf ("flash") model:

The flash ontology is an unusual choice of ontology; a more normal choice would be particle world lines, or fields in space-time. The motivation for this choice lies in the fact that the GRWmodel with flashes can be made Lorentz invariant (by suitable corrections in the equations), whereas the GRW model with the matter density m(r, t) cannot in any known way.

Collapse and Relativity
http://www.maphy.uni-tuebingen.de/members/rotu/papers/losinj.pdf

A Relativistic Version of the Ghirardi–Rimini–Weber Model
http://arxiv.org/PS_cache/quant-ph/pdf/0406/0406094v2.pdf

2. The more recent Bedingham model:

Mathematical models for the stochastic evolution of wave functions that combine the unitary evolution according to the Schrodinger equation and the collapse postulate of quantum theory are well understood for non-relativistic quantum mechanics. Recently, there has been progress in making these models relativistic. But even with a fully relativistic law for the wave function evolution, a problem with relativity remains: Different Lorentz frames may yield conflicting values for the matter density at a space-time point. One solution to this problem is provided by Tumulka’s “flash” model. Another solution is presented here. We propose a relativistic version of the law for the matter density function. According to our proposal, the matter density function at a space-time point x is obtained from the wave function ψ on the past light cone of x by setting the i-th particle position in |ψ|2 equal to x, integrating over the other particle positions, and averaging over i. We show that the predictions that follow from this proposal agree with all known experimental facts.

Matter Density and Relativistic Models of Wave Function Collapse
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.1425v1.pdf

See this thread for more detail:

Albert's narrative argument against Everett-type theories
https://www.physicsforums.com/showthread.php?t=535980

 

[stglyde]

Do you have an online reference for the source from which this quote was taken? Since he mentions Yang and Mills, it appears that he is talking about non-abelian gauge theory, but I'm not sure about the context.

In general terms, you're correct, making quantum theory consistent with relativity appears to require gauge fields. But that may be as much a matter of the mathematical form we choose to write our physical laws in as anything else. As I said in a previous post, gauge transformations don't change any physical observables; they only change the particular "basis" we write the laws in, similar to a change of coordinates. It may be that we will someday find a better way of writing the laws, that naturally expresses relativistic quantum processes without requiring the "redundancy" of gauge fields to compensate for the fact that multiple mathematical states represent the same physical state.

The author has many refereces in the book without being specific to it. Try to check out the book "Deep Down Things: The Breathtaking Beauty of Particle Physics" (as I mentioned earlier). It may be the best particle physics book for laymen on Earth because it didn't dumb down things like other popular science books. But I'm concerned about this SR law within gauge theory that works in the equations. If true. I wonder how to write a gauge theory of preferred foliations. But then the author seems to be describing spacetime points in the following (Try to go to Amazon and they have a 25 page free book preview of any pages. Just go to page 217- 330. The following is where he introduced Yang Mills predicament. Pls. comment on this:

In the mid-1950s, two physicists, C.N. Yang of the Institute of Advanced Study at Princeton University, and R.L. Mills of Brookhaven National Laborator, became deeply interested in the question of the phase invariance of quantum mechanics. What intrigued them most was that, on reflection, the idea of global phase invariance didn't quite wash with Einsten's notions of the nature of space-time. Yang and Mills were perfectly happy with the idea that the observable properties of a quantum-mechanical system should be independent of the phase of the wave function, as discussed at length above. What bothered them was that, to exhibit this independence of phase, one had to change the phase globally, by the same amount everywhere in space-time. We haven't yet demonstrated that changing the phase locally- by an amount that differs from point to point in space and time- disrupts the delicate balance of the Schrodinger equation, but we will in due course. In any regard, the need to require that quantum-mechanical systems be unaltered only by global changes of phase seemed to Yang and Mills to be very unnatural"

<skipping 7 paragraphs>

But now, Yang and Mills admonish us that we shouldn't really talk about global phase invariance because not all points in space-time are causally connected. So, it makes no sense to require that the choice of change of the wave function's phase be the same everywhere in space-time. Instead, we must consider local changes of phase, that is, changes in the phase of the electron's wave function by an amount that varies from point to point.

<skipping 18 paragraphs>

Whenever the phase of the wave function changes locally (by an amount that varies from point to point in space), the result of the derivative (rate of change) operation changes, introducing some "mistake" that cause the new wavefunction to no longer satisfy the wave equation. The thing - the only thing - we require of this new term we're going to add is that it commit precisely the same mistake, but with a negative sign, so that when the mistake from the term with the derivative is added to the mistake from the new term, they exactly cancel out, and everything is OK. In other words, Yang and Mills cheated; when nobody was looking, they added another term that got rid of the problem caused by the effect of the rate of change operation"

<skipping 12 paragraphs more include mathematical arguments>

You can read the skipped paragraphs at Amazon free preview. But from the above it is clear the author was talking about changes in spacetime points and not just in the equations in gauge transformation (as you claimed). What do you think?

 

[PeterDonis]

But from the above it is clear the author was talking about changes in spacetime points and not just in the equations in gauge transformation (as you claimed). What do you think?

I think you're reading too much into the author's attempt to describe a highly technical issue in non-technical terms. Every time a Brian Greene physics special airs again on one of the science channels, we get a spate of threads asking about things he said that sound a lot more colorful than the actual physics is. The author's use of the term "cheating" and describing what Yang and Mills did as "when nobody was looking, they added another term" strikes me as similar to the colorful ways in which Greene describes aspects of quantum mechanics; it sounds good and sells books and videos, but it can easily lead to misunderstandings.

Take a look at the Wikipedia page giving an introduction to gauge theory:

http://en.wikipedia.org/wiki/Introduction_to_gauge_theory

Note one thing in particular, which I have mentioned before: the fact that general relativity is invariant under arbitrary continuous transformations of the coordinates is an example of gauge invariance! So if Yang and Mills were "cheating" by adding terms involving gauge fields, then Einstein was also "cheating" when he added terms related to spacetime curvature to coordinate transformations in order to make the laws of physics look the same in all coordinate systems when gravity was present.

 

[stglyde]

I think you're reading too much into the author's attempt to describe a highly technical issue in non-technical terms. Every time a Brian Greene physics special airs again on one of the science channels, we get a spate of threads asking about things he said that sound a lot more colorful than the actual physics is. The author's use of the term "cheating" and describing what Yang and Mills did as "when nobody was looking, they added another term" strikes me as similar to the colorful ways in which Greene describes aspects of quantum mechanics; it sounds good and sells books and videos, but it can easily lead to misunderstandings.

Take a look at the Wikipedia page giving an introduction to gauge theory:

http://en.wikipedia.org/wiki/Introduction_to_gauge_theory

Note one thing in particular, which I have mentioned before: the fact that general relativity is invariant under arbitrary continuous transformations of the coordinates is an example of gauge invariance! So if Yang and Mills were "cheating" by adding terms involving gauge fields, then Einstein was also "cheating" when he added terms related to spacetime curvature to coordinate transformations in order to make the laws of physics look the same in all coordinate systems when gravity was present.

Forgive the author using the term "cheating". Of course he meant Yang and Mills well and we know they are honest people. The "cheating terms" were just used for sake of illustration.

Anyway. So what you were saying was that the phase of the wave function is not really located in space time but in internal space of the equations like isospin. Maybe the author use PUN too much. But then.. in Bohmian Mechanics, the phase of the wave function is really propagating in space and time!

 

[PeterDonis]

But then.. in Bohmian Mechanics, the phase of the wave function is really propagating in space and time!

Only in the simplest case of a single particle. When multiple particles are present, the space the wave function "lives" in is a tensor product of multiple copies of spacetime, one for each particle. So realistically, you can't think of a wave function even in Bohmian Mechanics as propagating in the actual spacetime we perceive.

(Actually, for standard Bohmian Mechanics, which is non-relativistic, even the single-particle wave function isn't a function on spacetime, it's a function on space that evolves in time; time is a parameter, not a coordinate. Multiple-particle wave functions are functions on a tensor product of N copies of space, one for each particle, which evolve in time. I'm assuming that a relativistic version of Bohmian Mechanics would work as I said above, since otherwise it wouldn't be able to match the predictions of standard quantum field theory; I haven't read through the paper linked to earlier that claims to develop such a relativistic version.)