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I understand that by definition dimension is defined by just another coordinate to pin-point something in space-time. Therefore we need to know not only where but when. At the same time, this somehow over the time changed to imply that there's a "copy" of universe at each time. Meaning if we had a time machine we could go back to in time by just reversing vector's time component.

But how can this be, if time is relative and dependent on speed of reference frame? Does this assume some universal speed the whole space-time is quantified? Is there some constant Planck distance of time?

More over spatial dimensions are constantly exponentially expanding. So if we imagine the time as for example 2D cartoon, it's frame would be ever expanding as the movie goes on. But what effect would relativity/quantum fluctuation have on the frame and it's pixels? A distortion of some kind, surely.

I understand it is just a model and works OK on Earth (meaning locally), and with relativity accounted for in a nearby space. But how about as a whole? Why is this model then expanded to hypothetically allow time-travel? I'm not talking about sci-fi movies, but about scientific papers trying to achieve this (hypothetically).

Is there even a possibility to pin-point a coordinate in this mess? Doesn't that disprove that time is a dimension, not only to travel in, but also just as a coordinate definition? It doesn't have any stable coordinates (except in non-relativistic speeds locally). If time is measurement of the curve an object took in a time dimension, what is this curve tight to? Any spatial coordinate? But those can't be fixed in time, they change all the time (expansion).

If I wanted to go back in time to 1950, I would have to account not for only speed of all the entities (Earth, Sun, Milky Way, Universe?), expansion of the Universe, but also my speed (time velocity) relative to what? Some arbitrary point?

In short: If I have precise coordinates now in 3D [x, y, z, t(now)] and the point exists, how can time be a dimension if this point didn't existed in [x, y, z, t(before)].

Can someone help to explain?

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closed as unclear what you're asking by ACuriousMind, user36790, Gert, CuriousOne, knzhou Jun 7 '16 at 15:59

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    $\begingroup$ I don't think it's helpful to think of space-time as consisting of a long sequence of timeless universes that we're traversing. In general relativity there isn't even a 'now', space-time just exists as a single, eternal four-dimensional thing. $\endgroup$ – lemon Jun 2 '16 at 8:21
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    $\begingroup$ Study vector space, only then will you understand what is a dimension. $\endgroup$ – Isomorphic Jun 2 '16 at 8:33
  • $\begingroup$ Isomorphic: But how is it a vector space if one axis is not linear? $\endgroup$ – SmartK8 Jun 2 '16 at 9:00
  • $\begingroup$ @SmartK8: That's where differential geometry comes in. Differential geometry is the mathematical framework that connects general affine coordinates (house numbers) with local physics in the tangent spaces. Crudely speaking tangent spaces are the formal description of the "stuff" that happens in the lab and inside Einstein's famous trains and elevator cars. I can only advise you to take a bunch of classes on differential geometry, that is, if you are doing university level physics... it would be a little bit much to ask you to do it as a hobby. It's serious math. $\endgroup$ – CuriousOne Jun 2 '16 at 9:19
  • $\begingroup$ I will check it out. I'm a programmer, so this would be my hobby. But I'll give it a try. $\endgroup$ – SmartK8 Jun 2 '16 at 9:31
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Time is that which the clock shows. Any one clock. Clocks do not all show the same time but their readings are related to each other and that relation is what the theory describes. In non-relativistic theory any two (perfect) clocks can only differ by a constant time difference but they all progress at the same rate. In relativity any two clocks that are in inertial relative motion can differ by a constant time difference and the rate at which they are progressing. That ratio in rates can be calculated from the relative velocity of the clocks.

That time is a dimension is an often misunderstood and, equally often, poorly explained meme. Time is not a dimension, the theory of special relativity merely treats any one clock-time as a dimension of an abstract construct called Minkowski space. Minkowski space is NOT the affine space you live in with an added fourth dimension. It's a local tangent space that describes how relativistic four-vectors and -tensors transform under changes between inertial systems. It is a mathematical construct that makes perfect sense given how clocks and all other physical quantities (!) behave when seen from non-co-moving observers, but it is not a physical space that you can move in.

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  • $\begingroup$ OK, I can understand that. I can understand that locally it makes perfect sense to have it as a model/calculation. But why is there even a notion of travelling in time then? It can't be possible, this would imply there's only spatial now and movement. Leaving time to be just a tool to predict coordinates of moving objects in their own reference frame. What could be at best called a "personal" time "dimension" of given object. $\endgroup$ – SmartK8 Jun 2 '16 at 8:33
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    $\begingroup$ @SmartK8: There is no notion of traveling in time in physics. I do regret to inform you that a lot of what has recently been "advertised" on the internet and even in some books about the topic is a poorly conceived attempt to "help" the student to get a feeling for how relativity works. IMHO it's a very poor attempt, indeed, that confuses people about both the theory and the actual phenomenology of time. Try to purge it from your mind, if you can. All you can actually do is to move in space while your own clock ticks away at the same merciless rate. $\endgroup$ – CuriousOne Jun 2 '16 at 8:36
  • $\begingroup$ I don't know, I've seen many BBC documentaries where well-known physicists are talking about worm-holes potentially (hypothetical of course) getting you in back in time. Some even talking about time travel by rotating universe. But I was skeptical, so I'm inclined to believe you that there's not officially this notion. $\endgroup$ – SmartK8 Jun 2 '16 at 9:03
  • $\begingroup$ @SmartK8: There is a huge disconnect between mathematical physics, theoretical physics and physics, the science. Physics the science is where people perform observations and experiments and theory explains those observations and experiments. Theoretical physics is where people come up with general frameworks for those observations and mathematical physics is where (often the same people) go out on a limb and see where the math takes them. What you have seen on tv, lately, was a lot of mathematical physics... Why? Because it's a heck of a lot more colorful than physics, the science. $\endgroup$ – CuriousOne Jun 2 '16 at 9:15
  • $\begingroup$ I guess you're right. I'm just surprised that theoretical physicists are taking their models (in some cases just GR) so seriously to a point they are willing to say that you can actually travel in time under some (albeit almost impossible) conditions. When in reality, you probably won't able to do it, even if these conditions were satisfied. Well thanks for a quick answer. Don't know why I got -2, but oh well. :D $\endgroup$ – SmartK8 Jun 2 '16 at 9:21
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The universe is a four dimensional object i.e. to locate any point within it you need four numbers. Most commonly we use a coordinate system $(t, x, y, z)$ and the four numbers give location of the spacetime point in this coordinate system.

You ask:

But how can this be, if time is relative and dependent on speed of reference frame?

and the answer is that the speed of the reference frame does not change the universe - it just changes the coordinate system that we use to measure the universe.

In fact this is a key point to understand in relativity (both special and general). If we take two spacetime points and a line connecting them then the separation of the points, i.e. the length of the line between them, is an invariant called the proper length (or proper time - same thing by a different name). It doesn't matter what reference frame you choose, the proper length always has the same value.

All that changes with the reference frame is the coordinate system. Suppose you're travelling at high speed with respect to me. If I use some coordinates $(t, x, y, z)$ and you use your own coordinates $(t', x', y', z')$ then our two coordinate systems won't match up and you and I will disagree about measurements of time and spatial intervals. But it isn't the universe that is changing. The universe is what it is and it's just our measurements of the universe that change depending on the speed.

When you say:

At the same time, this somehow over the time changed to imply that there's a "copy" of universe at each time.

Technically this refers to a foliation. If I choose a time axis then I can divide up the four dimensional universe $(t, x, y, z)$ into a series of three dimensional sub-universes $(x, y, z)$ - one for each value of $t$. But all I'm doing is choosing how I measure out the universe. You, in your reference frame, can also do a foliation of the universe and your foliation won't be the same as mine because your time axis isn't the same as mine. But that doesn't change the universe because the universe doesn't care how you and I measure it out.

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  • $\begingroup$ I think part of the confusion arises from students mistaking the four-dimensional manifold that you are describing with the coordinate system transformations that are happening on the tangent bundles of this manifold. The problem I see here, in terms of education, is that students do not understand the difference between affine coordinates and the attached vectors space in non-relativistic physics, either. To make the step from a misunderstood non-relativistic theory to an often poorly explained relativistic one is therefor double hard. $\endgroup$ – CuriousOne Jun 2 '16 at 8:48
  • $\begingroup$ But new spatial points are appearing as the Universe expands. You can make a line between two points at given [x, y] where only z differs, but you can't do the same for a t at given [x, y, z]. Because [x, y, z] might not existed in a given t as it does now. It's like a graph with one axis not being linear (in this case three axis are not linear). And even the fourth one is very shaky. Also does the speed of travelling time-dimension (having [x, y, z] stable) affects the other coordinates? IMO, it doesn't. So time is indeed seems like a special case, not much of dimension or axis. $\endgroup$ – SmartK8 Jun 2 '16 at 9:11
  • $\begingroup$ @SmartK8: No, new spatial points are not appearing as the universe expands. See Did the Big Bang happen at a point? for why not. The expansion increases the proper distance between existing points but it does not create new points. $\endgroup$ – John Rennie Jun 2 '16 at 9:21
  • $\begingroup$ @SmartK8: John Rennie's description was, of course, simplifying. What he is talking about is the affine space of non-relativistic physics, which, in relativity becomes a Riemannian manifold. Think of both as a set of house numbers. $\endgroup$ – CuriousOne Jun 2 '16 at 9:24
  • $\begingroup$ John Rennie: But when expanded enough. You can occupy this new space? Are you telling me you're outside of coordinates? IMO, new coordinates do appear as space-time is stretching. Sure, the distance is longer between points, but there must be new points (or fractions of them within this distance). Therefore if at one point there were points 0 and 1, and now it is expanded to 0,0.1,0.2..,1 and your point [x, y, z] is at one of those fractions. You can't connect it to the past. Except for some kind of rounding perhaps. $\endgroup$ – SmartK8 Jun 2 '16 at 9:26
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You're confusing concepts, as far as I can tell. Being a "dimension" doesn't imply all values of that dimension (or any of them) are arbitrarily reachable or even exist physically at a given time. It doesn't mean that the intuitive sense of all the baggage a more usual dimension comes with, are applicable to time. It doesn't imply time travel or multiple copies. Moving coordinate systems are trivial but that's a tiny part of it.

So we don't know what "actually" exists "now" for "other times" or even if they do, or if they are reachable, to take your last question about t(now) versus t(before). We just don't know.

The thing is, we don't know much about time, except that we seem to agree events happen in it ;-) so finding out what it means, and examining what laws seem to apply to it, and what they might allow, is about the only approach we have, scientifically, for now.

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