Does causality forbid time travel?

Question

If causality is an axiom or a fundamental law in physics, would the existence of causality be a reason which forbids time travel? Because time travel could break causality so we see first the effect and then the cause.

Answer 1

Physics doesn't have axioms in the same sense that mathematics does. There are no statements we take as self-evidently true. We have theories which make various assumptions, and then we test the consequences of those assumptions against experiment, and theories survive or fail based on their ability to predict experimental results (particularly results that were not known when the theory was originally written down).

That is to say, we can say that causality is an important part of our theories (and it is), but if we observed a time traveller from the future appearing in front of us who could prove they were really from the future, and we could reproduce their accomplishment, then that would be that; time travel would be possible in our universe.

Having said that, there are assumptions, and there are assumptions. (Here, we are getting into philosophy, and some people might not reasonably disagree with my point of view).

On the one hand there are assumptions like "the speed of light in vaccuum is constant" (or the more grown-up version of that statement, "the fine-structure constant doesn't change with space or time"), which we take to be true in our theories, but logically could be false -- and indeed, people have explored the consequences of giving up this assumption, and done experimental tests to look for violations of it.

On the other hand, there are assumptions like "effects should precede causes" -- which we do assume -- but it is very hard to imagine a logically consistent world in which this assumption is violated. Indeed, the point of almost every time travel story is to describe all the many paradoxes and logical inconsistencies that can arise from breaking this assumption. Because it's so hard to see how to make a theory which does not have a version of causality logically self-consistent, most physicists would say that a physical theory should be causal, and therefore that time travel should be impossible. At the very least, someone who claimed physics was not causal would need to explain why it appears be causal in every experiment we have done.

Answer 2

Causality is neither an axiom of physics nor a deduced law. It is just a common way of thinking + the metaphysical concept built on it. It is mistakenly brought into the strict, empirically verifiable laws of physics, and the idea that natural laws and phenomena should obey some sort of "causal laws" is baseless. The same is true of the temporal, only supposedly prescribed, order of cause and effect. It is also a dogmatic myth that if there is an 'acausal effect' or a 'causal paradox' in some physical model, then it cannot exist, it is not a good model. No. We can't arbitrarily dictate to the Universe what can and can't exist in it - just because our thinking can't handle it well. The fact that something is a paradox does not mean that it cannot exist, but that we do not understand it (clarification by Hungarian physicist Béla Lukács).

It follows from the foregoing that causality cannot in any sense forbid time travel, including time travel into the past, closed timelike curves, self-collisional worldlines. It only raises interesting analytical points, but nothing can be said about whether a physical process is possible on the basis of "causal laws or assumptions". Whether or not time travel, for example, can be realised. General relativity is full of spacetime and other phenomena that theoretically allow time travel. This is why it is such an exciting field of science.

If anyone wants to find out interesting information on the subject of time travel, read this, for example: TARDIS spacetime