Should the Special Relativity Principle be Reduced to a Tautology?

[Perspicacious]

You have probably noticed that the full force of Poincaré's relativity principle isn't necessary to derive the Lorentz transformation and the essence of special relativity:

http://www.everythingimportant.org/relativity/
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001
http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf

You are also very likely aware of the well-known fact that spatially compact spacetimes break global Lorentz invariance and define absolute inertial frames of reference:
http://groups.google.com/group/sci.physics.research/msg/e19ac8581a6148f2

Since SR is easily generalized so as to include this interesting class of spacetimes, it's reasonable, then, to amend the relativity principle also. I propose that it be reduced to a tautology.

Proposition: All physical laws can be divided into two categories. The two great divisions are the laws that are true in all inertial frames of reference and those that aren't.

There are many conjectures, proposed experiments and searches for possible violations of Lorentz invariance. What are the possibilities? Is there a catalogue of current conjectures? Let me list a few ideas and concepts based on possible laws from the second category.

1. Superluminality (a popular favorite)
2. Perfect matter-antimatter symmetry
3. Object length dependence on frame of reference

I'm especially interested in the observed asymmetry between kaons and antikaons and whether or not their asymmetric decay is a consequence of a preferred frame. Has a test for this possibility been seriously considered?

 

[DrGreg]

Special Relativity is only a locally-valid approximation to General Relativity.

So a spatially compact but flat spacetime is an interesting theoretical idea but isn't really relevant our real spacetime which isn't flat.

Searches for violations of Lorentz invariance are for violations of local Lorentz invariance.

 

[Perspicacious]

A spatially compact but flat spacetime is an interesting theoretical idea but isn't really relevant our real spacetime which isn't flat.

My links to spatially compact spacetimes are not limited to those that are flat. My other thread, The Black Hole in a Spatially Compact Spacetime, opens with this quote:

Thus in Friedmann–Lemaıtre universes, (i) the expansion of the universe and (ii) the existence of a non–trivial topology for the constant time hypersurfaces both break the Poincare invariance and single out the same “privileged” inertial observer who will age more quickly than any other twin: the one comoving with the cosmic fluid – although aging more quickly than all her traveling sisters may be not a real privilege!

A link to that paper, which contains the foregoing statement, is listed in my references.

Searches for violations of Lorentz invariance are for violations of local Lorentz invariance.

My question about asymmetric kaon-antikaon decay is precisely in the context of a possible violation of local Lorentz invariance.

 

[JesseM]

I'm especially interested in the observed asymmetry between kaons and antikaons and whether or not their asymmetric decay is a consequence of a preferred frame.

As I understand it, this asymmetric behavior of kaons is a violation of CP-symmetry, but this is permitted in the Standard Model, which exhibits the larger CPT-symmetry and which is also Lorentz-symmetric. There are apparently some extensions of the Standard Model that allow for Lorentz symmetry to be violated, although I think the symmetry is broken by spontaneous symmetry breaking which means the theory would have been symmetric in the era when the forces were unified, and the symmetry was broken by a random decay to different vacuum state. So if I'm understanding this right, there wouldn't be any asymmetry in the fundamental laws of physics, just in the particular vacuum state which our region of the universe has, which was fixed by contingent events in the past. This article discusses such lorentz-symmetry-violating extensions of the Standard Model in more detail:

http://physicsweb.org/articles/world/17/3/7

 

[Spin_Network]

Since SR is easily generalized so as to include this interesting class of spacetimes, it's reasonable, then, to amend the relativity principle also. I propose that it be reduced to a tautology.

Proposition: All physical laws can be divided into two categories. The two great divisions are the laws that are true in all inertial frames of reference and those that aren't.

There are many conjectures, proposed experiments and searches for possible violations of Lorentz invariance. What are the possibilities? Is there a catalogue of current conjectures? Let me list a few ideas and concepts based on possible laws from the second category.

1. Superluminality (a popular favorite)
2. Perfect matter-antimatter symmetry
3. Object length dependence on frame of reference

I'm especially interested in the observed asymmetry between kaons and antikaons and whether or not their asymmetric decay is a consequence of a preferred frame. Has a test for this possibility been seriously considered?

The link provided by JesseM :http://physicsweb.org/articles/world/17/3/7

Has a sentence:An elementary particle in the presence of one of these relic fields would then experience interactions that have a preferred direction in space-time. In particular, there could be preferred directions in 3D space in any fixed reference frame, such as an Earth-based laboratory.

Emphasis on the last part relative to 3-D space.

The fundamental problem lay within the notion of 3-D + '1D' to complete the 4-D spacetime.

Its not that there is an added '+' dimension, I believe the fundamental problem lay in that Spacetime is not linear in any way all wrapped into the same bundle?..for instance we should not be looking for the 3-D connective "TIME" componant in Einsteins Relativity, it should be stated as a single spacetime, but within the context of : 4-D spacetime = 3-D in 1.

Thus, the continuation of all dimensional extensions are embedded 'within' a single 'space-time-frame', the "1" is not an added dimension branching off into hidden extensive area's such as 3+1..4+1..5+1..etc..etc?

Like a labourer who has to 'mix' the contents of sand..cement..water into "one", to produce the concrete for a building foundation, one can see the beauty of the understanding that 2D+1D, 3D+1D,4D+1D all produce a symmetry breaking (the plus 1 is what breaks the symmetry mold), but 3Din 1D or 4-D in 1D..etc..etc does not break this mold at all, 3-Dimensional matter is "in", ONE-DIMENSION, the space-time-frame.

The notion of 3-D matter, does not need the extra added componant of "plus1" in any context, by its very existence, it is already within the "1" frame.