Forms of the Relativity Postulate

Special Relativity is taken as a postulate in physics (and has been well experimentally justified). An important example is that modern QFT can be derived from SR invariance (along with a few other assumptions: hilbert space quantum states, and locality (cluster- decompostion)). However, it is interesting to note that the relativity postulate can take two basic forms that are not identical, and I propose, not yet distinguished by experiment.

Some notes are in order: Postulate type II does not exclude EPR-style non-local correlations, because these are not "interactions". That is, the quantum states become entangled initially (in the photon emission, or whatever), and the entanglement persists to large separation, but persistent entanglement is not an interaction.

The type III postulate is more positivistic than type II, but it is hard to think of forces that are allowed by type III and forbidden by type II. In particular, I suspect any kinematic-style force (i.e. created by a potential V(x,p) is treated identically by postulates II and III). However, interactions of type III do exists.

One is the "long-range EPR". I will assume you are familiar with the ordinary EPR experiment : a pair of correlated spins are sent far apart to observers A and B. Either observer will think they have measured a random spin, but when they get together and compare results, they find exact correlation (they always measure the same thing, though whether that be up or down is random). Now, if we use type II then we agree that the correlation of the spins must have been established when they were in contact. However, let me offer another possibility :

the two spins were emitted uncorrelated, both with random up/down states ( |up> + |down> over sqrt2). At some spacelike separation L they felt a nonlocal interaction with transformed them into the perfectly correlated state. So if observer A and B were moving around at spacelike separation, they would each independently think they measured random spins, whether or not they were closer than L (whether or not the interaction had occurred) so that this interaction is not locally detectable. However, they could get back together and find that every time they made measurements at spacelike separations greater than L their results were perfectly correlated. Note that this interaction preserves the expectation value of all local operators (at A or B) but does not preserve expectation values of nonlocal operators (on both A and B). (see also my bit on quantum measurement

This type of interaction is assumed to be non-existant by most physicists, but I see no a-priori reason to exclude it. It seems to violate no physical principle except the "strong" relativity postulate, which I see no reason to prefer over the "weak" relativity postulate; I stress that current experiments have only checked my statement I and cannot distinguish between II and III.

Also note that this type of interaction could not be mediated by the gauge bosons which carry every currently known force. Also note that the "strong" relativity postulate is equivalent to the "gauged-force postulate", that every interaction must be expressable as being carried by a (non-tachyonic) particle.

Charles Bloom / cb at my domain
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