Category:Special Relativity (SR)

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SPECIAL RELATIVITY

Special Relativity (SR)

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1905 –


Albert Einstein's famous paper on the Special Theory of Relativity (STR, Special Relativity, SR) was published in 1905, as a paper in the journal Annalen der Physik, entitled "On the Electrodynamics of Moving Bodies".

The core equations presented by Einstein had appeared in the same journal the previous year, in a paper by H.A. Lorentz explaining how it could be possible that all simply-moving observers could agree on the existence of an undistorted stationary aether, but be unable to identify its state of motion.

Einstein took the idea of Lorent's relativised "flat" aether, and rederived the same basic equations by assuming that the lightbeam geoemtry had to be flat, and the principle of relativity had to be obeyed ... but without the concept of there being an aether.

... as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
— Albert Einstein, "Geometry and Experience", 1921    

SR as "minimal theory"

The initial attraction of special relativity was not that it made better experimental predictions than other theory – the first experimental paper to address the theory actually concluded that SR was worse – but it's extreme minimalism. During the late C19th even aether theory experts such as Oliver Lodge were forced to conclude that the subject had gotten out of control. There were so many different classes of aether theory that just trying to catalogue them and parameterise them was embarrassing. Aether theory in the 1890s had the same problem as String Theory in the 1990s - it was not that it couldn't predict, it was that it could predict anything you wanted it to, with the right choice of arbitrarily-selected parameters.

Lorentz' aether theory, with its curvature-free aether and one possible set on mathematics, with no free variables, was a breath of fresh air, and Einstein's 1905 theory then did the impossible and trumped Lorentz's model by simplifying it even more by dropping the idea of a aether altogether.

Special relativity's three postulates

Special relativity supposedly only had two postulates - that the principle of relativity held true in simple mechanics, and that the speed of light had to be constant for everyone. The theory also had a third, implicit postulate, that lightbeam geometry was totally "flat" and undisturbed by the presence and motion of the bodies embedded in it.

The assumption of flat spacetime meant that the assumption of local lightspeed constancy for all observers could be extrapolated out over the area being studied, and taken as global lightspeed constancy for all observers. The assumption that lightbeams weren't affected by the proximity of any other moving body meant that Einstein could eliminate proximity from the descriptions and derive his equations using the more abstract concept of inertial frames. It was then possible to prove from the geometry of how flat physics in one frame mapped to flat physics in another, that the only possible mathematical solution was Lorentz's.

  • If we don't assume perfectly flat spacetime other solutions become available (see Fresnel's relativistic aether-dragging model).
  • Einstein cemented the logic of his model by using inertial frame arguments - since these abstract away proximity effects, as soon as we admit the validity of inertial frame arguments, we are forced to accept the Lorentz mapping of observations between frames, and SR/LET. This was a useful way of excluding other relativistic solutions such as Fresnel's or any attempt to de-aetherise Fresnel's system similarly to how Einstein had de-aetherised Lorentz's.
  • If we assume that proximity effects do play a part, then the metric takes on the properties of a field (as in GR), and acquires gravitoelectromagnetic properties that lead to spacetime being distorted between bodies with relative motion, giving an acoustic metric and an acoustic general theory of relativity. However,constructing such a system would have been far beyond Einstein's capabilities in 1905. at this point, the most Einstein could do was to distil out the mathematical "skeleton" of LET – its core flat-spacetime relationships – and discard the unnecessary aether-theory "flesh".

Problems and limitations

... I do not believe that it is justifiable to ask: What would physics look like without gravitation?
— Albert Einstein, Scientific American, April 1950    


Special relativity is, in many ways, a "perfect" theory. It has no free parameters or fudge factors, the equations are provably the only possible implementation of relativity theory in perfectly flat spacetime, and they are "locked", allowing no adjustments or modifications.

However, this level of perfection also means that the theory is not obviously extensible to a real universe in which the observers exchanging signals are always necessarily made from particulate matter, inhabiting a region that therefore cannot ever be a perfect vacuum.

the "theory gap"

In the real world, energy-densities near particles can be high enough to make the assumption of flat-spacetime difficult – the classical radius of the electron is in the same "ballpark" as the electron's calculated r=2M event horizon, leading to a number of papers exploring the idea of an electron modelled as a black hole. This is extremally far from flat spacetime. If we assume a collection of particles with significant "up-close" gravitational field distortions, then we need to be able to model how those distortions change when there is relative motion between them.

Given that the physics of these tiny distortions needs to obey the principle of relativity, how do we model them? Special relativity is not certified for the job, as it assumes as a fundamental known law that no such distortions exist. This leaves us with our relativistic theory of curved spacetime, general relativity. But C20th general relativity cannot model the distortions either, because it assumes that simple inertial physics is supposed to be dealt with by special relativity.

What we can do is use "general" GR principles to try to model particles as tiny gravity-wells, and derive the equations of motion independently of special relativity, in the hope that we then arrive at the same SR relationships. Unfortunately, it seems that we don't – the "moving gravity-well" approach suggests an acoustic metric rather than the Minkowski metric of SR, and seems to give us redder set of Lorentzlike equations. We can derive a "Newtonian approximation" of the SR equations of motion, but this approximation is, again, redder than the SR relationships. This situation appears to leave us with no theoretical proof (last checked circa ~2007) that the equations of SR can be applied to simple particles, or that SR is using the correct set of Lorentzlike equations.

Notes

  • It is possible for an idealised theory to be definitionally perfect, but to still have a range of application to real physics that is zero.
  • A "vacuum" derivation of observerspace physics is problematic because as soon as one inserts a physical observer into a region, the region is no longer empty, by definition. It is difficult to present a theory of how matter interacts with matter in the presence of significant relative motion, if it is a geometrical prerequisite of the derivations that the region be matter-free. For the theory to be logically applicable to real physics, one needs to argue that deviations from the theory's idealised geometry do not affect the derivations or the equations. In the case of SR this seems not to have been done.