Imaginary Transverse Space of Superluminal Lorentz Transform

In summary: I see. Cos someone was telling me that superluminal reference frames could be easily described. Not so easy it seems.In summary, this paper discusses Lorentz transformations that involve imaginary Unit coefficients, and the implications of this for the space in which the transformations take place. It seems that the space in the x-direction is real, but the transverse space around it is imaginary.
  • #1
greswd
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I was reading this paper: http://dinamico2.unibg.it/recami/erasmo%20docs/SomeOld/RevisitingSLTsLNC1982.pdf

It is on superluminal Lorentz transformations and is too advanced for me. :confused:

But anyway, take a look at equation(s) (11). For the y' and z' transformations, there is an imaginary unit coefficient. But for the x' transformation, there is none.

So the space in the x-direction is 'real', but the transverse space around it is 'imaginary'?
 
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  • #2
greswd said:
the space in the x-direction is 'real', but the transverse space around it is 'imaginary'?

From what I can see on a quick skim of the paper, no. They are still talking about Minkowski spacetime, so all four of the spacetime directions are real. They are just using some strange conventions because they are trying to construct "inertial frames" in which an object "at rest" is moving on a spacelike worldline.
 
  • #3
PeterDonis said:
From what I can see on a quick skim of the paper, no. They are still talking about Minkowski spacetime, so all four of the spacetime directions are real. They are just using some strange conventions because they are trying to construct "inertial frames" in which an object "at rest" is moving on a spacelike worldline.
it seems like they are using a tachyonic Lorentz factor [tex]\frac{1}{\sqrt{\beta^2-1}}[/tex]
and the only way to preserve the light cone between transformations (such that a photon does not end up with a superluminal velocity) is a rotation to the complex plane.

I've got some info from: http://rspa.royalsocietypublishing.org/content/early/2012/09/25/rspa.2012.0340
but they didn't tackle the transverse spatial dimensions.
 
  • #4
greswd said:
it seems like they are using a tachyonic Lorentz factor

Yes, but that just corresponds to using a weird mathematical convention to describe the same spacetime. Nothing about the underlying spacetime or its geometry is changed.
 
  • #5
I'm wondering how to describe the transverse space in the frame of a tachyon.
 
  • #6
greswd said:
I'm wondering how to describe the transverse space in the frame of a tachyon.

Part of the issue that this paper appears to be trying to deal with is that there is no such thing as "the frame of a tachyon", if by "frame" you mean "something that works just like ordinary inertial frames". An ordinary inertial frame only works for objects traveling on timelike worldlines. A "frame" in which a spacelike worldline (that of a tachyon) is "at rest" is a fundamentally different kind of thing. (I'm not even convinced that it makes physical sense, but whether it does or not, mathematically it's a fundamentally different kind of thing.) So I would not expect any description of the transverse space to match your intuitions about what such a thing "ought" to look like. The imaginary numbers that are showing up in the paper for the transverse dimensions are, I think, a symptom of the fundamental difference.
 
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  • #7
PeterDonis said:
Part of the issue that this paper appears to be trying to deal with is that there is no such thing as "the frame of a tachyon", if by "frame" you mean "something that works just like ordinary inertial frames". An ordinary inertial frame only works for objects traveling on timelike worldlines. A "frame" in which a spacelike worldline (that of a tachyon) is "at rest" is a fundamentally different kind of thing. (I'm not even convinced that it makes physical sense, but whether it does or not, mathematically it's a fundamentally different kind of thing.) So I would not expect any description of the transverse space to match your intuitions about what such a thing "ought" to look like. The imaginary numbers that are showing up in the paper for the transverse dimensions are, I think, a symptom of the fundamental difference.

I see. Cos someone was telling me that superluminal reference frames could be easily described. Not so easy it seems.
 

FAQ: Imaginary Transverse Space of Superluminal Lorentz Transform

1. What is the Imaginary Transverse Space of Superluminal Lorentz Transform?

The Imaginary Transverse Space of Superluminal Lorentz Transform is a concept in physics that is used to describe the behavior of particles that travel faster than the speed of light. It is a theoretical construct that helps explain the effects of superluminal travel on the fabric of space-time.

2. How does the Imaginary Transverse Space affect particles traveling at superluminal speeds?

The Imaginary Transverse Space affects particles traveling at superluminal speeds by altering their trajectory and causing them to experience time dilation and length contraction. This is due to the fact that the fabric of space-time is distorted in this imaginary space, leading to changes in the fundamental properties of particles.

3. Is the Imaginary Transverse Space a proven concept?

No, the Imaginary Transverse Space is a theoretical construct that has not been proven through experiments. It is a concept that is used in certain theoretical models and hypotheses in physics, but its existence has not been confirmed through empirical evidence.

4. Can particles actually travel at superluminal speeds in the Imaginary Transverse Space?

No, particles cannot actually travel at superluminal speeds in the Imaginary Transverse Space. The concept of superluminal travel is still considered to be impossible according to our current understanding of physics. The Imaginary Transverse Space is simply a theoretical construct that helps explain the effects of superluminal travel on the fabric of space-time.

5. How does the Imaginary Transverse Space relate to Einstein's Theory of Relativity?

The Imaginary Transverse Space is related to Einstein's Theory of Relativity in that it helps explain the behavior of particles traveling at superluminal speeds, which is a phenomenon that is not accounted for in the theory. The concept of the Imaginary Transverse Space is also based on the principles of relativity and the distortion of space-time, which are the foundations of Einstein's theory.

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