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Special Relativity and Time

Up till now I've discussed a few arguments for or against a cosmic beginning, so I thought I'd continue to and turn to a famous paper "Time and Physical Geometry" by the philosopher Hillary Putnam. Therein Putnam was the first to argue that the special theory of relativity implies an eternal universe. The meaning of the word "eternal" refers to "eternalism" or the block-universe, a timeless static view of time where temporal becoming is an illusion. Such a universe may still exist eternally, in a timeless sense without needing to extend back to past infinity. 

There are philosophical arguments in favor of this proposal like the paradox of how "time flows" without introducing a meta-physical time. There's also an argument to be made in general relativity and quantum cosmology for a bock universe but I want to restrict our scope to Putnam's argument from special relativity. The spacetime relevant for special relativity, is Minkowski spacetime a 4-dimensional manifold endowed with a Minkowski metric.

The relativity of simultaneity allows us to carve up space and time into different foliations, so that if we imagine two different observers that cross at even e.

Using a principle called the Einstein-Poincare synchronization the observers A and B will observe the epoch in the history of c that is perpendicular to their spacetime trajectory at e to be simultaneous with their hyper surface at e. Both reference frames of the observes A and B disagree on which event is simultaneous with e but there is no preferred frame of reference.

The disparity in measurement will be great given a greater relative velocity between A and B such that A measures judges the ontological status of c differently to B. If one accepts even the most basic interpretation of the tensed view of time that two events can be co-present on the same hyper surface, then special relativity must imply a tenseless view of time. 

Several strategies have been adopted one would be to relativise ontology to one's state of motion. Another would be the flat out denounce special relativity as false which a few people have been bold enough to do (Karl Popper, John Bell and Quentin Smith) by replacing it with a Lorentz aether theory. Both of these are clearly radical proposals but lets linger on the latter one a little further.

The proposal of Lorentz, Poincare, FitzGerald, Larmor, is a theory of relativity, it includes both time dilation 

And length contraction, the occurrences of each event are relatable in one person's frame of reference to another's through Lorentz transformation equations. The equation for Length contraction is

Lorentz and FitzGerald attributed these effects to the dynamics of a system traveling through an electric field rather than the spatio-temporal structure of spacetime. The Lorentz transformation equations which are present in both versions of relativity are

Einstein removed any reference to Galileo's privileged frame of reference whereas Lorentz kept them in as a part of relativity towards which we have epistemic ambivalence. Lorentz's version of relativity is a very elegant and beautiful theory that is empirically equivalent to the Minkowski approach. Most arguments against it are purely philosophical and so far no experiment has been able to distinguish between the two, much akin to contrary interpretations of quantum mechanics. I think this is by far the best way to respond to the argument (though it must be admitted that Lorentz's approach is not nearly as advanced as the Minkowski approach). No general theory of relativity has so far been developed off of Lorentz's theory, nor any approach to quantum field theory.


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