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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?

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  • Note that quantum mechanics, which is just as relevant, has a very different conception of time, and the way to reconcile both has not been found yet. – armand Jan 27 at 10:28
  • But doesn't quantum field theory treat time and space at par? (Disclaimer: I am still in early stages of learning QFT so my understanding of it can be way off) – prateek Jan 27 at 10:41
  • All I know is that time in QM and in relativity is irreconcilable. The stakes for a unified theory are so great that if someone had found it we would have heard of it. I am a layman too, just wanted to note that concurrent theories of time do exist. – armand Jan 27 at 10:51
  • Unified theory aims to assimilate general relativity within quantum framework while quantum field theory has assimilated special relativity within itself. Though QFT is still incomplete for other reasons. The question here is about the relation between space and time which should be prior to any theory of mechanics. – prateek Jan 27 at 11:04
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    @armand Treatments of time in QM and general relativity are in tension, but QFT is set in special relativistic spacetime, so it already unifies QM with SR. Taking SR spacetime as basis, there are no two entities to be the same or not ontologically, there is only one. It approximately splits into what we call space and time only in special types of frames we are used to (slow moving), and the split is not ontological, it is an artifice of our limited perspective. But, of course, it is controversial that treatment of time in physics (within spacetime or not) reflects its ontological nature. – Conifold Jan 27 at 12:10
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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.

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    Godel's point was not that closed timelike curves indicate general relativity is flawed, rather his point was that this shows that if general relativity is correct, time as traditionally conceived is a kind of illusion (basically discarding 'time' construed in terms of presentism or McTaggart's A-series, where there is some objective universal 'present moment'). See the book "Godel Meets Einstein: Time Travel in the Godel Universe" by Palle Yourgrau for a good discussion of Godel's argument. – Hypnosifl Jan 27 at 21:11
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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.

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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.

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  • Physics tries to explain the phenomena we all experience while the role of philosophy is broader it not only aims to clarify and put in context what labours of physics yield but also delve deep into the questions of noumena (on what there is). And philosophers in every culture and epoch have questioned the nature of time. So, this question is of fundamental importance to any philosophy of science/physics student. Also, the field that is concerned with thoughts, feelings and opinions is essentially psychology while philosophy's role is to interpret and clarify truths which all sciences generate – prateek Jan 29 at 12:33
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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.

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  • Please leave a comment why, if you consider this a bad answer, or the physics to be incorrect. – CriglCragl Jan 29 at 1:59
  • Even in CCC model there must be a beginning, if not of this universe but of the universe from which this universe began. And "but being nothing it couldn't be certain about itself" - are you hinting towards a primordial being or consciousness that was uncertain and led to the beginning? – prateek Jan 29 at 12:38
  • @prateekagarwal: Why? I would say an eternal multiverse determined by geometry makes more sense, generated by the uncertainty principle only. I was only trying to frame that idea. Some notion of nowness is needed, at least to keep track of particular places in all possible. – CriglCragl Jan 29 at 12:57
  • Multiverse is the simultaneous of multiple universes. "In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next." (wiki) It doesn't explain the start of the first universe. So the problem of time stands. And moreover, the question here is about the relationship of time and space. Also, for uncertainty principle to be the basis of beginning is controversial for it only allows to be borrowed for a some amount of time, at the end of which it must be annihilated. – prateek Jan 29 at 13:23
  • Again, why must there be a beginning? I like the uncertainty principle as key, because it neither asserts being nor nonbeing, elegantly avoiding either as the default. If there is low enough entropy, borrowing is enough. See deep inelastic scattering & matter over antimatter. – CriglCragl Jan 29 at 15:36

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