Four-vectors and related concepts

[Austin0]

I'm not sure I'd agree it's "beyond our logic or comprehension". If we can write down equations that correctly predict the outcome of any experiment, then, arguably, we do understand what is happening. But there comes a point when we can't give any further reasons why the Universe behaves the way it does. We just have to accept that's the way it is.

It appears you may have thought I was referring to SR when I used those terms.
I was not at all. I was talking about block time as conceived by many within SR.
When I said beyond our logic I meant in the sense that you cannot logically verify or support concepts like block time or Wheelers worlds . You cannot logically derive a physics that would make them actual possibilities.Or comprehend them beyond the most simplistic verbal descriptions [equivalent to paper galaxies on an expanding balloon].
At the same time you cannot logically refute or reject them on any basis of reason or physics that applies to our reality. It would be silly to even try.
Dont misunderstand me. When I use the term Metaphysical , I don't mean that in any negative sense. I have plenty of ideas and feelings regarding this realm. I would hope that any final theory of physics would somehow bring it all together, pointing to some higher reality , have resonance with the human spirit as well as the intellect.
But the point I was trying to convey is that even if SR block time is a reality , it is a many worlds concept. And any entity at a spatial remove is effectively in another universe. It does not provide any meaningful information or helpful concepts. It does not resolve any paradoxes ,it IS a paradox.
So if the Lorentz dilation calculation tells us that Fred is 100 while Bill is 13 and also tells us that Fred is 13 while Bill is 100 , what does this mean? To give any validity to either one, is to attempt to apply an absolute simultaneity. To assume that there is a definite, quantifiable , instantaneous relationship between them over a large distance.
No , actually two ,different, mutually exclusive, definite , quantifiable instantaneous temporal relationships. Yet SR has made it clear that we cannot assume any real simultaneity even at much closer distances. So I just don't know?

Also I'm not quite sure of your use of the word "transitivity". My understanding of that word is the mathematical definition. In this context we could ask, if A is simultaneous with B, and B is simultaneous with C, is A simultaneous with C? The answer to that (for all possible A, B and Cs) determines whether "simultaneous" is a transitive relation or not.

This is the definition I was using but I see that I may have been ,at best, using it obscurely, if not actually incorrectly.

SO point [A ] graphs the colocation event of (t=12.5 ,x=0) and (t'=20.8 , x'=16.67)

Blue IS simultaneous with Red


graphs the event (t'=7.5 ,x'=0 ) and (t=12.5 ,x=10 )

Green IS simultaneous with Red

But: Green IS NOT simultaneous with Blue

And:

(t=12.5 ,x=0) and (t'=20.8 , x'=16.67) IS NOT simultaneous with

(t'=7.5 ,x'=0 ) and (t=12.5 ,x=10 )

Therefore it would appear that :
(t=12.5 ,x=0) CAN NOT be simultaneous with
(t=12.5 ,x=10 )

Except withiin a limited ,conditional definition when applied to the measuring of physical phenomena within the frame. In this context, it self-evidently works perfectly ,without problem, but also without the neccessity of any assumption or implication of actual or absolute simultaneity.

I have studied the hyperbola and lightcone diagram. I can't really conceive of the shape of the hyperbola if it is fully realized in 3 D with the lightcone being a light sphere.
It seems like it would not be a bounded shape but would be some kind of complex gradient or something. But I will keep trying.
Thanks



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