How are space and time related?

Question

We know from Einstein's special theory of relativity that space and time together form a spacetime continuum and are interdependent. They share a mathematical structure and any fundamental theory of Physics must found itself on this mathematical structure but what I want to understand is whether space and time are ontologically different or not?

Do two entities which share a mathematical structure have to be same? If not, then which of space or time is fundamental? Did at the beginning one emerge from the other or there was a rupture in something fundamental which resulted in simultaneous creation of space-time?

Answer 1

I want to understand is whether space and time are ontologically different or not?

Well, given that nobody has a really good and persuasive conception about what is time and what is space it seems even less likely to have an answer about their ontological difference. The whole perspective might be faulty: Newtonian mechanics functions as a 4 dim geometry, as it was noted in the 18th. c. (by d'Alambert and Lagrange); however as model of the real world it misses a fundamental empirical fact: there is an upper limit for propagation. The obvious consequence is that colinear speeds are not to be added simply as as geometric segments. Actually it is the existence of this constant of nature (popular as the "speed of light") which seems to be the real puzzle.

Kurt Goedel famously demonstrated that relativity allows closed timelike trajectories and his point was that if in principle they are possible, the theory must be flawed. [see Yourgau P.,A World Without Time (2006)]. CPT symmetry hints that it is not space itself which is somehow a counterpart of time. In recent years Craig Callender has argued that it is hyperbolic PDE which allow a structuring of the world such as physics discovers. He has a published a book (Callender C.,What Makes Time Special? Oxf.2017) advancing from an earlier attempts e.g. Skow B. What Makes Time Different from Space Noûs 41 (2007), p.227–52; for a synoptic view see Baron S and Evans P., What so spatial about time.

Disentangling what is in the fine structure constant could help understanding the speed limit trough 2 others constants without appealing to spatiality.

Answer 2

In the beginning, there was nothing. Even outside of our universe or multiverse, there would be nothing in which the universe is said to be expanding. In the beginning, nothing keeps on fluctuating creating particle/anti-particle pairs, and those can annihilate each other or may go sufficiently apart. We can visualize space consisting of contiguous particles. Initially the process of creation and annihilation of particles, antiparticles goes on in such a way that time doesn't have any meaning. In a way, we can visualize where the time goes back and forth. After all, we can imagine the initial universe with a state1 going to state2 going to state3 which falls back to state1. So time t1 with state1 moves forward till state3 and again starts back from t1. Unless there is any change in space, the time has no meaning. So time is an entity depending on space. Space keeps on changing with time and we may say space depends on time but it is just playing with words.

Answer 3

Within the context of relativity, it is not true that spatial dimensions and the time dimension are on equal footing. If they were, you could go back and forth in time like going up and down a ladder, which our universe doesn't allow.

This is a subject of physics and not philosophy, in that physics deals with the way things are and in that description of the world, every effort is made to boil out of it what our thoughts, feelings and opinions about that description might be- whereas philosophy is concerned with thoughts, feelings and opinions.

Coming to grips with this is a difficult task even for people who are trained in the field, and if you want more insight into this topic you'll need to make a deep dive into the math. I recommend you try posting this question on the physics stack exchange and see if one of the experts over there can help you without unleashing a torrent of equations.

Answer 4

I would say it seems like both space and time are emergent rather than fundamental. The clue to this is that time irreversability is about state spaces, probabilities, rather than geometry.

The fundamental laws are all time reversible (except deep inelastic scattering, involving the weak nuclear force). But quantum-states that start out pure, tend to become mixed; information spreads out. This asymmetry, directionality, is a type of pattern, that our minds need to perceive in one direction, because that represents information reaching us - moving differently through the state space would see information do the opposite of spreading out, which we would perceive as time going backwards; ie the reverse of perception, ie. we can't percieve it.

Looking at cyclical cosmologies like say Conformal Cyclic Cosmology, we can see this quality of time as linking together a LOT more states than if there was 'just' perfect symmetry.

I went into more detail in a recent answer here Why is the universe governed by very few laws of high generality instead of lots of particular ones?

To summarise in relation to your question:

In the beginning there was nothing, but being nothing it couldn't be certain about itself, and so the universe began. Gigantic state spaces that we can understand using just geometry, like E8, suggest our universe is something like a fracture plane in the state space of all possible universe-timelines, where the neat smoothness got 'caught' at an essentially random point. The anthropic principle requires to be in a fracture plane with certain properties, to be here to puzzle ourselves about it.