Does time matter?

Question

Aside from the second law of thermodynamics it seems physics just doesn't care about the direction of time.

So does time really matter? What if instead of 3 spacial and one time dimension. 3+0 or 3+2. How would this affect physics?

Answer 1

Lee Smolin, an American physicist, orginally considered fundamental theories to be timeless going by what appeared to be the timeless inherent in GR; but recently he has tilted the other advocated a timeful theory of physics as in his book, Time Reborn. He writes:

As it happens, Einstein’s theories of relativity are the strongest arguments we have for time being an illusion masking a truer, timeless universe. Back when I believed that time is an illusion, my main reasons had to do with relativity theory.

This is mainly to do with Einsteins introduction of the simultaenity postulate in physics. By this, it only makes sense to say when two events are simulatenous only locally and not globally, that is when they are far from each other. For two events far from each other, one observer may say that the first event comes before the first, and another observer may disagree and say it is the second that comes before the first.

However he points out that:

What observers do agree about can be called the causal structure. Pick any two events in the history of the universe and call them X and Y. Then one of three things will be true. Either X could be a cause of Y, or Y could be a cause of X, or neither could be a cause of the other. These causal relations are agreed to by all observers. The causal structure is the list of all these relations, for all events in the universe. Thus you can say that what is physically real in the history of the universe includes its causal structure

and

This is a timeless picture, because it refers to the whole history of the universe at once. There is no preferred moment of time, no reference to what time it is now, no reference at all to anything corresponding to our experience of the present moment. No meaning to “future” or “past” or “present.”

However, a theory called Causal Set Theory takes this as its departure point and constructs a block time universe - so time here is real - with a causal structure compatible with GR.

Its also important to notice that the collapse postulate in QM defines a direction of time.

Further, whereas there are generalisations of physics to higher dimensions there is usually only one time coordinate. It appears to be very difficult to make sense of theories with more than one time dimension, and besides it does not make much physical sense.

Finally, whilst there are theories in which time is emergent, so one can consider, in a sense, that these theories are timeless; however there must be change in these theories. For example, in causal set theory, time is emergent, and so fundamentally it is a timeless theory, however there is fundamentally change in the theory.

Answer 2

Having different numbers of time dimensions affects the kind of initial conditions are needed to make the initial value problem well-posed for the ultrahyperbolic wave equation. In X+1 time dimensions you only need to have the position and velocity of whatever it is waving about to get solutions, but in X+Y dimensions it becomes trickier to set things up so it is solvable and solutions unique.

Max Tegmark points out that with Y time dimensions energy becomes a Y-dimensional vector and observers can end up along divergent timelines, matter becomes less stable, and of course the ultrahyperbolicity causes trouble for predictability. With 1+3 dimensions all particles are tachyons and you need initial data outside lightcones to make predictions.

Overall, the signature of spacetime has pretty deep effects on what is possible or not. But the weirdness of some of these worlds is not necessarily an argument against them being inhabitable or possible.