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From special relativity, we know that there is no length contraction transverse (lateral) to the velocity. As pointed out in an answer here:

it is a property of spacetime not of objects as such

Poisson's ratio is defined as (negative) lateral strain divided by longitudinal strain.

Question: Related somewhat to this question: given the above axioms, the Poisson's ratio of spacetime (or at least, minkowski spacetime) must be zero?

EDIT - and btw this does not invalidate all the previous responses below, which I am grateful for, this edit simply provides more context to the question. People can still agree or not with previous answers...

Based on the answers below:

  • General relativity reduces to special relativity in flat spacetime, and GR can be considered as the hydrodynamic (the low energy, long wavelength) regime of a more fundamental microscopic theory of spacetime.
  • Poisson’s ratio is a property of a material and depends on the microstructure of the material. Therefore, even simply treating spacetime as a calculation tool, it’s valid to consider spacetime properties$^1$.
  • While the proper length doesn’t change with length contraction, there is contraction in the observer’s frame$^2$ – this apparent value is real.

Given the above, it is still a valid question - what is the Poisson ratio of spacetime?

1 This paper the mechanics of spacetime derives the Poisson ratio of spacetime as 1, however referenced work in that paper assumed anisotropic properties. Minkowski (and FLRW) spacetime is isotropic. As this paper on the theoretical limits of Poisson's ratio points out, Poisson’s ratios for isotropic materials is [−1, 0.5].

2 Trying to actually view length contraction...no...although, there is little doubt that Lorentz contraction occurs if length is measured – that is, when different points on a moving object are all measured at the same instant of time in the observer’s stationary frame of reference....

Mr Anderson
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2 Answers2

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No -- length contraction does not correspond to stretching or compression of spacetime, and it especially does not correspond to stretching or compression in response to a force. Length contraction is just a projection effect in spacetime. It is similar to how the apparent length of a long, thin object depends on the angle from which you view it.

Sten
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Poisson's ratio is a property of a material and depends on the microstructure of the material. It is a measure of how easy it is to shear the material relative to how easy it is to compress it. But spacetime is not a thing - it is a mathematical object and doesn't have material properties. In this sense it is meaningless to talk about a Poisson's ratio for spacetime.

As mentioned in Sten's answer, Lorentz contraction is not actually a contraction as there is no change in the proper length of the object. See my answer to the question "Reality" of length contraction in SR for more on this. Nothing is being compressed in Lorentz contraction so properties like the Poisson's ratio are not involved.

John Rennie
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