Defining Special Frame: Math & Limitations of Preferred Frames in BM

[Tomahoc]

This is to understand about the mathematics and possible limitations of the concept of preferred frames in BM and why entanglement couldn't use one.

Supposed you have a cruise missile sent out from Earth to a distant planet traveling at 0.99999 the speed of light. 30 Seconds after sending it out.. you got order to cancel and self destruct the missile. But you can't use even light speed signal to catch it. Now you use emergency tachyon beam to contact the missile at a certain v > c with respect to a preferred frame common to Earth and the missile. But in the frame of reference of the missile. The space is contracted between it and the distant planet so it takes only say 3 seconds to reach it. Now when you use tachyons traveling with respect to the preferred frame (not with respect to earth). How does the preferred frame synchronize your 30 seconds with the missile when it takes only 3 seconds for it to reach the target?

I understand the tachyons should travel with respect to the preferred frame. This is because if it travels with respect to earth. It can't reach the missile (or too late) or can even receive the signal before it sents out (by the missile sending back instantaneously to Earth's past). But in a preferred frame, not only can the Earth not receive it before it sends out. But it might be able to catch the missile halfway before it reaches the target, can it?

Of course I don't believe in tachyons. This is just to work out the math to prove preferred frames are never feasible in BM and entanglement and I have been thinking of this for over a day. Thank you.

 

[bcrowell]

I assume BM refers to Bohmian mechanics: http://en.wikipedia.org/wiki/Bohmian_mechanics , which is an interpretation of quantum mechanics. However, nothing in your question has anything to do with quantum mechanics. It seems to be purely a question about special relativity, dealing with tachyons and frames of reference. Although you mention entanglement, it doesn't seem to play any actual role in the scenario you describe. Could you give us a revision of your question that would clarify this? I.e., either (1) give us a question that eliminates the irrelevant quantum stuff, or (2) give us a question that makes it clear why quantum mechanics and Bohmian mechanics are relevant.

 

[Tomahoc]

I assume BM refers to Bohmian mechanics: http://en.wikipedia.org/wiki/Bohmian_mechanics , which is an interpretation of quantum mechanics. However, nothing in your question has anything to do with quantum mechanics. It seems to be purely a question about special relativity, dealing with tachyons and frames of reference. Although you mention entanglement, it doesn't seem to play any actual role in the scenario you describe. Could you give us a revision of your question that would clarify this? I.e., either (1) give us a question that eliminates the irrelevant quantum stuff, or (2) give us a question that makes it clear why quantum mechanics and Bohmian mechanics are relevant.

ok.. i'll rephrase the question...

Supposed on Earth two ships A & B left Earth at opposite direction.. one traveling at 0.8c, which from the lorentz transformation formula is 1 second for it but is 1.66667 second for you on earth. The other B traveling at 0.995c, which 1 second for it is 10 seconds for you on earth. Now supposed A sends a tachyon signal after 3 seconds and it travels not with respect to A but with respect to you on Earth (which stands for the referree or the special preferred frame). This means it should also reach B at its 3 seconds too (to prevent signal being received before it is sent out). Now what is the formula to define the preferred frame location such that the 3 seconds of A is the same frame as 3 seconds of B?

 

[bcrowell]

OK, making progress. The next thing I'm unclear on is what you have in mind in terms of a preferred frame. SR doesn't have a preferred frame. (And you can have tachyons in SR without having a preferred frame.) Since you refer to a preferred frame, do you have some other theory in mind rather than SR, one that does have a preferred frame? If so, then what is that theory?

Now supposed A sends a tachyon signal after 3 seconds and it travels not with respect to A but with respect to you on Earth (which stands for the referree or the special preferred frame).

What do you mean by "it travels not with respect to A but with respect to you on earth?" If it doesn't travel with respect to A, do you mean that it's at rest relative to A? But that would seem impossible, since a tachyon is never at rest relative to any non-tachyonic matter.

 

[Tomahoc]

OK, making progress. The next thing I'm unclear on is what you have in mind in terms of a preferred frame. SR doesn't have a preferred frame. (And you can have tachyons in SR without having a preferred frame.) Since you refer to a preferred frame, do you have some other theory in mind rather than SR, one that does have a preferred frame? If so, then what is that theory?

Imagine the ships traveling at opposite directions have equal velocity. If A can send tachyons to B at its own frame. B can receive it at half the time, if B would send it back to A, A can receive it before sending it out. So tachyons are against SR and would have problems in causality. But if tachyons can use a special preferred frame common to both A and B. Then A and B would both receive it at the same time. Without this. Imagine you thought it's 1 minute in your frame and send the tachyons to B, B would receive it in 30 seconds. And from B point of view. If it sends back the tachyons to you.. you would receive it at 15 seconds or 45 seconds before you send it out. This automatically makes tachyons not possible in SR. But it is said that if preferred frame is used common to both A and B. Then when A sends it out at 1 minute, B would also receive it at 1 minute. This is fine. The preferred frame is exactly located between them. Now what if the velocity of A and B vary, then how do you locate the preferred frame. This is my question. I just want to know how the math works to understand the concept of SR better and why preferred frame can't exist.

 

[bcrowell]

If A can send tachyons to B at its own frame.

What do you mean by sending "at its own frame?"

So tachyons are against SR and would have problems in causality.

No, tachyons violate causality, but there is nothing in SR that forbids them.

But if tachyons can use a special preferred frame common to both A and B.

What do you mean by "use a special preferred frame?" A tachyon isn't a person or an observer who "uses" anything...?

I just want to know how the math works to understand the concept of SR better and why preferred frame can't exist.

I think the problem is that you're not understanding what a preferred frame is. Some theories are described by equations that have the same form in all frames of reference. Newton's laws are like this. For instance, Newton's second law, a=F/m, has the same form no matter what frame you're in. This is because a, F, and m all stay the same when you switch to a different (inertial) frame using a Galilean transformation. Some other theories lack this property. Their equations have the simplest form in a certain frame of reference (e.g., the frame of reference in which the ether is at rest), but if you switch to some other frame, the equations become false, and you need to change their form to make them true. An example would be Aristotelian physics, in which an object with no force acting on it would naturally move to the Earth and then stop.

 

[Tomahoc]

What do you mean by sending "at its own frame?"

For there to be causality violation, the tachyon at A has to travel with respect to A, then let's say it sees B traveling at only 5 seconds instead of 10. And B receiving it at 5 seconds and seeing A time at only 2.5 seconds when it resends it back. It would end up in A before he sent it. Classical causality violation. But if tachyon at A has to travel with respect to the preferred frame (or preferred foliation) common to both A and B. Then both A and B can see it at simultaneous time. I just want to know how to model this preferred frame in spacetime diagram to see its limitation and why it is not possible in SR.. because there is nothing that physically picks them as special. I know.

No, tachyons violate causality, but there is nothing in SR that forbids them.What do you mean by "use a special preferred frame?" A tachyon isn't a person or an observer who "uses" anything...?

Aren't you familiar with the concept of preferred foliations? My preferred frame is similar to it. If A and B velocity is equal, the referee frame can be the preferred frame. But if it varies, that's what I can't imagine.

I think the problem is that you're not understanding what a preferred frame is. Some theories are described by equations that have the same form in all frames of reference. Newton's laws are like this. For instance, Newton's second law, a=F/m, has the same form no matter what frame you're in. This is because a, F, and m all stay the same when you switch to a different (inertial) frame using a Galilean transformation. Some other theories lack this property. Their equations have the simplest form in a certain frame of reference (e.g., the frame of reference in which the ether is at rest), but if you switch to some other frame, the equations become false, and you need to change their form to make them true. An example would be Aristotelian physics, in which an object with no force acting on it would naturally move to the Earth and then stop.

Many theorists speak about preferred foliation. I just want to understand it. In a preferred foliation. Time is synchronized at both A and B. But for A and B with velocities that vary. Preferred foliation is not at center. So how to model it. If you don't exactly know what I'm talking about. Please others who are more familiar please intervene.

 

[bcrowell]

For there to be causality violation, the tachyon at A has to travel with respect to A[...]

This is the same problem as the one I tried to straighten you out on in #4. Your use of language doesn't make sense.

If you don't exactly know what I'm talking about. Please others who are more familiar please intervene.

OK, seems like a situation where I'm convinced that you're confused, and you think I don't know enough to help you. I'll stop trying to help you.

 

[Tomahoc]

This is the same problem as the one I tried to straighten you out on in #4. Your use of language doesn't make sense.


OK, seems like a situation where I'm convinced that you're confused, and you think I don't know enough to help you. I'll stop trying to help you.

In the concept of preferred foliation. If you can define a preferred foliation in between A and B. Then it's clock would be simultaneous to that foliation such that even if tachyons were exchanged between the two. there will never be a causality violation. I know the concept of preferred foliation is not used by normal relativists.. so they may not know what I'm talking about.

For those who know what I'm talking about. I want just to know how to define preferred foliation in spacetime diagram with velocities in A and B that varies. This is to visualize how ad hoc it is because there is no physical principle that chose them and makes them special.

 

[PeterDonis]

I want just to know how to define preferred foliation in spacetime diagram with velocities in A and B that varies. This is to visualize how ad hoc it is because there is no physical principle that chose them and makes them special.

So there's no physical principle that chooses them, but you want to know how to choose them? That doesn't make sense. Since there is no physical theory I'm aware of with "preferred foliations" in it, I don't see how to answer your question.

 

[Tomahoc]

So there's no physical principle that chooses them, but you want to know how to choose them? That doesn't make sense. Since there is no physical theory I'm aware of with "preferred foliations" in it, I don't see how to answer your question.

Not how to choose them. I know there is no physical principle that chooses them. I want to share with my other friends this concept. But I don't know how to even explain it as I can't visualize how it works in the spacetime diagram. For A and B with equal velocities. It is easy to tell my friends that the referee frame is the preferred foliation.. but how about those with unequal velocities. Where to put the preferred foliation.. for example in the case of the missile that travels at 0.999C and the Earth stationary. How to define the preferred foliation that is common to both. This is all I want to know so I can explain to my friends how ad hoc it is.

 

[PeterDonis]

I want to share with my other friends this concept. But I don't know how to even explain it as I can't visualize how it works in the spacetime diagram.

And I think that's because the concept is not well-defined enough. You are asking questions that don't have a well-defined answer unless you have an actual theory. You appear to think that there is some such theory, or at least some rule that gives a unique answer to your question; but there isn't, at least none that I'm aware of.

 

[Tomahoc]

And I think that's because the concept is not well-defined enough. You are asking questions that don't have a well-defined answer unless you have an actual theory. You appear to think that there is some such theory, or at least some rule that gives a unique answer to your question; but there isn't, at least none that I'm aware of.

A particle here has a certain worldline. A particle elsewhere has a different worldline. Defining a preferred foliation is maybe just connecting the two worldlines together.
But what does it mean to connect two worldlines together.

Graphically.. if anyone know how to depict this in spacetime diagram. Please do. I'd like to see how ad hoc it truly is, graphically.

Or better yet. If someone has seen a spacetime representation of a preferred foliation. Please point me to it as it is simply what I wanted to see.

 

[PeterDonis]

But what does it mean to connect two worldlines together.

It could mean lots of things.

Graphically.. if anyone know how to depict this in spacetime diagram. Please do. I'd like to see how ad hoc it truly is, graphically.

It's as "ad hoc" as you want it to be.

If someone has seen a spacetime representation of a preferred foliation.

Once again, you're talking as though this is part of some existing theory and you just need a pointer to it. There is no such existing theory.