Can SR be derived from causality alone?

In summary: I forget the exact limit. I think it was something like 6 dimensions.In summary, it seems that causality is not enough to derive the Minkowski metric and the Lorentz transformations.
  • #36
TrickyDicky said:
This might also be helpful:
E. C. Zeeman
Causality Implies the Lorentz Group.
J. Math. Phys. April 1964 Volume 5, Issue 4, pp. 490-493

Along this line of reasoning...

A.A. Robb's (1914) axiomatic approach (using the notion of an ordering relation 'after') should be mentioned
http://en.wikipedia.org/wiki/Alfred_Robb

http://books.google.com/books?id=vp...hthUGyh&sig=csSzPceSNPGd4uoGmPMUKloDtU0&hl=en (comment by Torretti)


There are implicit assumptions of continuity.

friend said:
I found the following paper on the arXiv:
http://arxiv.org/abs/1005.4172

This makes reference to Rafael Sorkin's (1987) "Causal Sets", a fundamentally-discrete approach to Quantum Gravity
http://en.wikipedia.org/wiki/Causal_sets


Aimless said:
I remember hearing in a talk once upon a time that knowing the casual structure of spacetime was sufficient to give you the metric up to a (constant?) scale factor; however, I've been unable to track down a reference for that statement.

See Finkelstein's (1969) "Space-Time Code"
http://prola.aps.org/abstract/PR/v184/i5/p1261_1
http://streaming.ictp.trieste.it/preprints/P/68/019.pdf [preprint]

"The causal order C determines the conformal structure of space-time, or nine of the
ten components of the metric. The measure on spacetime fixes the tenth component."
[per spacetime event in 3+1 dimensions] (p. 1262, or p.3 in the preprint)
 
<h2> What is SR and how is it related to causality?</h2><p>SR stands for Special Relativity, which is a theory in physics that describes the relationship between space and time. Causality is the principle that every event has a cause, and SR uses this principle to explain how the laws of physics are consistent for all observers in different frames of reference.</p><h2> Can SR be derived solely from causality?</h2><p>This is a highly debated topic in physics. Some scientists argue that causality is a fundamental principle that is necessary for the development of SR, while others argue that SR can be derived from other principles such as the principle of relativity and the constancy of the speed of light.</p><h2> What evidence supports the idea that SR can be derived from causality alone?</h2><p>There is no direct evidence that supports the idea that SR can be derived solely from causality. However, many scientists believe that the consistency of the laws of physics across different frames of reference is a strong indication that causality is a fundamental principle in the development of SR.</p><h2> Are there any alternative theories that do not rely on causality to explain SR?</h2><p>Yes, there are alternative theories such as the Lorentz ether theory and the transactional interpretation of quantum mechanics that do not rely on causality to explain SR. However, these theories are not widely accepted and have not been able to fully explain all the phenomena that SR can.</p><h2> What are the implications of being able to derive SR from causality alone?</h2><p>If SR can be derived solely from causality, it would provide a deeper understanding of the fundamental principles that govern our universe. It would also have implications for our understanding of other theories in physics, such as quantum mechanics, and could potentially lead to the development of new theories that unify these concepts.</p>

FAQ: Can SR be derived from causality alone?

What is SR and how is it related to causality?

SR stands for Special Relativity, which is a theory in physics that describes the relationship between space and time. Causality is the principle that every event has a cause, and SR uses this principle to explain how the laws of physics are consistent for all observers in different frames of reference.

Can SR be derived solely from causality?

This is a highly debated topic in physics. Some scientists argue that causality is a fundamental principle that is necessary for the development of SR, while others argue that SR can be derived from other principles such as the principle of relativity and the constancy of the speed of light.

What evidence supports the idea that SR can be derived from causality alone?

There is no direct evidence that supports the idea that SR can be derived solely from causality. However, many scientists believe that the consistency of the laws of physics across different frames of reference is a strong indication that causality is a fundamental principle in the development of SR.

Are there any alternative theories that do not rely on causality to explain SR?

Yes, there are alternative theories such as the Lorentz ether theory and the transactional interpretation of quantum mechanics that do not rely on causality to explain SR. However, these theories are not widely accepted and have not been able to fully explain all the phenomena that SR can.

What are the implications of being able to derive SR from causality alone?

If SR can be derived solely from causality, it would provide a deeper understanding of the fundamental principles that govern our universe. It would also have implications for our understanding of other theories in physics, such as quantum mechanics, and could potentially lead to the development of new theories that unify these concepts.

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