I've red that Minkowski space is reducible and Rindler space is irreducible. How do I have to understand this? And that means further both spaces are disjoint. How can I make sense of this?
Kay,
I know Rindler coordinates. But what is Rindler space?
Regards,
Eugene.
The link of the paper is
http://arxiv.org/pdf/quant-ph/0008030.pdf
Eugene,
to be clear, Rindler space is not a space it is a representation of a Weyl-algebra W. See pages 10-12 of the paper mentioned above. The description on these pages speaks only about irreducibility and factorization of a representation of the Weyl algebra W. Question is still what is called reducible. This is the case, when the representation is the direct sum of one-particle Hamiltonians. How two representations are disjoint is explained on page 12, but why the Minkowski representation and the Rindler represenation are disjoint is not explained.
Kay,
there are many meanings of term "reducible" in Math. I'l try to understand this paper.
Regards,
Eugene.
Dear Johan,
if you refer to the publication of Einstein of 1911 when he talks about reference systems, Redshift and stuff I fully agree with you.
Stefano
And how about nuclear explosion, Johan?
Don't You reject Euclidian space? Why is Minkowski space worse than Euclidian or any other metric space?
Johan,
coordinate systems are only our way to describe reality, but not reality itself. We use those systems, which are convenient for us. Any mathematical transformation transforms nothing real. The main postulate of relativity is that reality can not depend on it's description. Don't You agree with this, Johan?
Maxwell's equations are simpler in Minkowski space and don't depend on Lorenz transformations. That is all relativity. Where is mistake?
Johan,
"time distribution within a wave" is not understandable for me.
May by your "severe" critic of QM and relativity have some sense, but your constructive program is unclear. You and I have different views on physics, reality, philosophy, ethics and so on. For example, it seems that different forces are reality for You, meanwhile, all the physics can be done without notion of force (see Heinrich Herz's book on Mechanics, 1891 year) and constructive definition of force is absent till now (see first volume of Sommerfelds famous series of monographs). Therefore, it seems to me, that further discussion has no sense.
Regards,
Eugene.
Absent any definition of what it means for a space to be (ir)reducible or disjoint, the statements, as given, are meaningless. One definition of reducibility can be found here:
http://arxiv.org/abs/1308.1685v1.pdf
so it's a straightforward exercise to check whether the spacetimes discussed here satisfy the assumptions of this definition-or not.
It should be stressed that these are mathematical, not physical issues, so the answer, as such, doesn't have anything to do whether these spaces, or these definitions are, or not, relevant for physics.
Stam,
actually, it is not spaces. It is representations. Then, evrything is understandable.
Regards,
Eugene.
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