Meaning of Spacetime Foliations

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.

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?

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.

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?

"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.

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?

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.)

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:

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?

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.

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

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

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)?