I'm having a hard time figuring out how to properly phrase this question so bare with me, but I am trying to understand the apparent differences between space and time in the context of special relativity. The theory points towards a fundamental symmetry between the two, and demonstrates this in some very beautiful ways, but I cannot seem to escape the fact that time and space are two very different things. My primary concern is this:

I am able to conceive of (and indeed observe) two events happening at the same time in different spacial locations. I can - in other words - "see" a domain of space, a range if you will. I can see what is in front of me, to the left of me, etc... And yet, I am unable to "see" into the future or the past in such a direct manner... Now I am aware that this is the kind of topic in which intuition and experience can often get in the way and trick me. I am fully prepared to accept that my experiences are distorted and wrong, but is there some physical explanation for why we experience time so differently than space? Why is it that I can move through space in any direction I want but have no control over how I move through time (except implicitly by my motion through space).

Why do we seem to be free to travel about space however we please but all are constrained to follow the arrow of time together? Reading about simultaneity, they speak of events occurring at the same time in different places, or how one event will occur sooner than the other in a different frame of reference. I am totally fine with this. But if time and space are so symmetric, should there not be an equivalent argument for events seperated in time but seeming to occur in different places in different frames?

If space and time are to be treated on the same footing, then why are there such clear differences between the two? Why does time appear only to flow in one direction? Why is there no equaivalent principle of simultaneity for space as there is for time? (or is there?) If the two are equivalent, why are they so different?!

  1. The key relevant asymmetry built into SR is that worldlines are required to be timelike. This means, for example, that it's possible (in a given coordinate system) for you to be in one place at many different times, but not possible for you to be in many different places at one time. This accounts for a substantial chunk of what you're asking about.

  2. Time does not "flow in one direction" because time does not flow. If you think of Minkowski space $M$ as a Lorentzian manifold with a choice of time orientation, and if you reverse that time orientation, you get a different Lorentzian-manifold-with-time-orientation that is isomorphic to $M$. This means, in effect, that the only difference (at least according to SR) between the past and the future is that we've arbitrarily chosen one of them to call "the past" and one to call "the future".

  3. It happens to be the case that we live in a Universe where there was a Big Bang, i.e. a moment of very low entropy, and that we use the phrase "toward the future" to mean "away from the Big Bang" or, pretty much equivalently, "in the direction of increasing entropy". So there is an asymmetry there that you wouldn't know about from SR alone, but surely plays into what you're asking about.

  4. As for the rest of the stuff about our sensations --- why we perceive a flow of time, etc, etc --- I think that you might as well ask why we perceive the colors red and green as we do instead of the opposite way around. The answers (if any) must depend on the detailed structure of the way our brains work, and this is a question for the biologists and psychologists, not for the physicists.

  5. A qualification to point 4: On the other hand, there are several levels at which you can ask "why". One could interpret parts of your question as "Why does evolution select for creatures who have the perceptions about time that we do?". This, at least, has a better chance of an being answerable than "Why does evolution select for creatures who perceive red and green the way we do, rather than the other way round?". It's still looks like more of a biology question than a physics questions, though.

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    $\begingroup$ Your 1 just really says you can't travel faster than a certain speed c. And neither can anything else. Thus, there is causality, with later depending on earlier and how fast. That is basically no difference than 2, which is admittedly a statement and no explanation and no justification, and basically a non scientific statement. 3 is just one theory about the arrow of time, with no more backing than others. 4 and 5 are clearly just non physics related, and not very critically informative or useful. Perhaps you should admit you don't know the answer. $\endgroup$ – Bob Bee May 16 '17 at 4:40

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