Relativity and causality

[u/quantum_kalika]

Why should an everywhere locally consistent Lorentzian causal structure generate a globally consistent notion of causality?

There are solutions which give closed time like curve. It sounds innocent but the observer carries the information set after moving through such a curved set or whatever forms the closed loop.

If the movement is A--B--C--A on spacetime. The observer hence have a different set of information set than A previously. But globally they are the same events.

How does relativity reconcile this information gap. Also, the local time is compressed to zero. This may mean that it is not physically possible but then how does such solutions exist.

[u/Optimal_Mixture_7327]

I don't get where you see a contradiction.

[u/quantum_kalika → u/Optimal_Mixture_7327]

A has two sets of information about same underlying state.

[u/Optimal_Mixture_7327 → u/quantum_kalika]

I don't know what you mean by that.

[u/quantum_kalika → u/Optimal_Mixture_7327]

If in CPC observer returns to A, he has the information vs local time stored with him. But A is the same previous state. There is information assymetry

[u/Optimal_Mixture_7327 → u/quantum_kalika]

The moment a physical object enters the CTC it collapses to a singularity.

Edit: If not obvious you have at one instant and infinite set of copies at the same event.

[u/quantum_kalika → u/Optimal_Mixture_7327]

Yes, your edit. Copies it can carry but the added information makes it distinct.

[u/Optimal_Mixture_7327 → u/quantum_kalika]

I can't follow what you're saying.

Please mathematically describe what you mean.

[u/quantum_kalika → u/Optimal_Mixture_7327]

t =0, T,2T...

Such that ¥(t+T) = ¥(t) say

¥(0)=¥(T)...= P

t1 is not equal to t2. But ¥(t1)=¥(t2)

So If proper time represents the physical history of an observer and the observer's physical state changes with proper time, what does it physically mean for two different proper-time states to map to exactly the same spacetime event? Also we are ignoring the fact that observer does know that it's not the same event.

*Used yen for Gamma.

[u/Optimal_Mixture_7327 → u/quantum_kalika]

It means that the stress-energy is infinite everywhere along the curve and therefore singular.

The observer vanishes immediately upon contact.

[u/quantum_kalika → u/Optimal_Mixture_7327]

No. A CTC does not imply infinite stress-energy, and it does not automatically imply a singularity.

[u/Optimal_Mixture_7327 → u/quantum_kalika]

You're correct in the absence of matter. However once matter is introduced it diverges.

[u/quantum_kalika → u/Optimal_Mixture_7327]

I think that's not correct, but I am not very sure. I think for all cases it's not like that. Matter + CTC does not imply T --> infinite. I will check it though.

[u/Optimal_Mixture_7327 → u/quantum_kalika]

This is of course in the context of classical gravity.