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Comments
(t/T)^2=1-(v/c)^2
This is a pythagorean relationship as in
(cosA)^2=1-(sinA)^2
so provided that we let v/c=sinA, we will have t/T=cosA
So does this suggest that t 'axis' is at an angle A from T?? Well, it is so only when we think that v/c=sinA necesarily mean that v is moving along an axis at an angle A from the axis of c of which we know that clearly this is not the case.
Merely spoting a mathematical symmetry does not mean that there is any reality underlieing it. Physicists used to know this very well and there are myriads of such amazing symmetries in mathematics. I can show that a one octave higher wave is 'perpendicular' to the lower wave. This is called HILBERT SPACE and I can show that the peculiar relativistic relationship above stems from the same waving since a particle moving with v is realy a wave.
Even Einstein first rejected the idea as superfluous. He was correct, but he neaded Minkowski insight in generalising relativity. But this is just MATHEMATICALY not in conceptual sense.
Time dillation reads: t/T=B, This suggest that we measure speed using T and not using t. we say x/t=(x/T)x(T/t)=x/TB. Once we have done this, we have a set of FOUR, not THREE ratios. These are:
i)t/T
ii)x/T
iii)y/T
iv)z/T
We have what mathematically looks like something moving in a 4 dimensional spacetime. But then t/T is not realy a speed. It is a time dillation. This is the first insight in understanding Minkowski spacetime. The second insight is comming.
A merger of space and time, even in principle is problematic for some reasons. It necesarily put some regions, such as andromeda, millions of years 'away' hence it is imposible to reach there without spending a million years. But if we think clearly, this impossibility is only in practise not in PRINCIPLE. If we had another signal moving faster than light, then spacetime interval btwn here andromeda would be smaller, without the space interval necesarily reducing. Judge this from s^2=x^2 y^2 z^2-(ct)^2. The spacetime interval, s, tends to zero as ct, hypotenuse distance tends to equal x^2 y^2 z^2. If there is no limit as to how fast a signal can cross the cosmos, then there is no need to think that 's' reflects the true nature of space and time. It is only so as an EMERGENT phenomenon due to bridging gaps using light signals. it has been shown in quantum mechanics that IN PRINCIPLE, there is no limit as to how fast a signal can get across. So relativity is nolonger a fundamental picture of reality. It is an emergent phenomenon and we must treat such equations as just a mathematical setting.
I´m not merging space and time......I´m merging the relative and the bigger perspective...
s2=x2 y2 z2-(ct)2
s=spacetime. But this is a mathematical relationship, not a CONCEPTUAL. Donnot try to form an idea of a merger between space and time in your head, you will spoil your brain. To understand spacetime, simply take math. It has no nonmathematical meaning.
No space either.??..I´d say that from the bigger perspective it is all here now......; but, from a personal daily life view it is convenient to use the concepts of space and time. I think the trick is to jump back and forth between the two until they somehow merge and become one. The same way we can think how things are one and many simultaneously....or any of these sets of opposites that exist simultaneously depending whether we look at the large or small picture...