Meaning of Spacetime Foliations


by stglyde
Tags: foliations, meaning, spacetime
TrickyDicky
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#19
Dec22-11, 04:59 AM
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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
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#20
Dec22-11, 11:46 AM
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Quote Quote by harrylin View Post
Quote Quote by ghwellsjr View Post
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
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#21
Dec22-11, 03:02 PM
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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
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#22
Dec22-11, 08:47 PM
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What if the rest state is "C" and mass is a reduction of "c"?
harrylin
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#23
Dec23-11, 04:07 AM
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Quote Quote by ghwellsjr View Post
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
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#24
Dec23-11, 07:49 AM
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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 travelling twin light mirror lightspeed as travelling 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 travelling 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
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#25
Dec23-11, 08:19 AM
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Quote Quote by stglyde View Post
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 travelling twin light mirror lightspeed as travelling 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 travelling 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 possess 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_Ev...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
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#26
Dec23-11, 08:43 AM
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Quote Quote by harrylin View Post
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_Ev...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/ar...out-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
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#27
Dec23-11, 09:39 AM
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Quote Quote by stglyde View Post
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 travelling twin light mirror lightspeed as travelling 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 travelling 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 travelling twin light mirror lightspeed as..." What exactly is the measurement you are describing here?
stglyde
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#28
Dec23-11, 05:31 PM
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Quote Quote by ghwellsjr View Post
I'm afraid I don't understand what you mean by "The home twin will measure the travelling 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 travelling 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
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#29
Dec23-11, 07:16 PM
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Quote Quote by stglyde View Post
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.
Quote Quote by stglyde View Post
But it would still measure the light travelling 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.
Quote Quote by stglyde View Post
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
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#30
Dec23-11, 07:47 PM
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Quote Quote by ghwellsjr View Post
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
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#31
Dec23-11, 08:36 PM
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What experiment involving tachyons are you proposing that gives different measurements in different frames?
stglyde
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#32
Dec23-11, 09:00 PM
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Quote Quote by ghwellsjr View Post
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
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#33
Dec23-11, 09:44 PM
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Quote Quote by ghwellsjr View Post
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?
DaleSpam
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#34
Dec23-11, 10:27 PM
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Quote Quote by stglyde View Post
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
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#35
Dec23-11, 10:43 PM
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Quote Quote by DaleSpam View Post
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.
PeterDonis
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#36
Dec23-11, 11:47 PM
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Quote Quote by stglyde View Post
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".

Quote Quote by stglyde View Post
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.)

Quote Quote by stglyde View Post
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.


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