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B How did spacetime pop out into existence?

  1. Aug 13, 2015 #1
    Hello,
    Cosmology for the layman says that there was a time t=0 when the universe was created out of infinitesimal length distance and before that nothing existed not even time.
    OK, but this rests on the assumption that there is always a manifold from which we cut off our space slices in the past until we reach a point where our space coordinates vanish. The space coordinates dissapear at t=0, not the manifold itself! So, the whole spacetime manifold must have popped out into existence at once!
    I don't believe that space is evolving with time right now as we speak. After all, in SR the spacetime is a unified plane and there is no distinction between space or time.
    So why layman books are saying that spacetime is expanding etc? It's only space that's expanding and any particular spacetime must be a static solution of the GR differential equations, given the initial conditions.
    And it must have popped out into existence all at once, with everything in it that has been and will become in the future.
    Is this correct or have I got it all wrong?
     
  2. jcsd
  3. Aug 13, 2015 #2

    Orodruin

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    This is wrong. Space-time is the manifold, talking about the manifold "appearing" at some time is meaningless.

    What you believe has little to do with actual physics. The expanding universe is the best model available at the present time.

    This is space-time, not space as you were referring to when talking about space evolving.

    They don't, at least not if they are at all accurate (which may be a big assumption). Space is expanding. Space-time is what it is and time is a part of it.

    No this is wrong. You need to double check the definition of what a static space-time is. The FLRW space-time is not static.

    I think your biggest problem is that you are trying to describe what space-time is in terms of time, but time is an integral part of space-time itself. Something that "pops" into existence intrinsically refers to it not existing at an earlier time, but the concept of time does not exist outside of space-time.
     
  4. Aug 13, 2015 #3
    I am not an expert, but I think you have 3 things wrong here (if someone says I'm wrong they're probably right).
    1. As space expands, so does time. As you said, they are unified as spacetime. As space expands so does time. At any place that has time, there is space, and any point in space, there is time. They expand together.
    2. Spacetime didn't come from nowhere. According to GR it was always there in infinitesimal quantities. At one point is was smaller than the Planck length (which is where we have a little conflict with QM).
    3. There is no future. Unlike marvel, there is no destiny, or time travel. What has happened has happened, and the future can't be known.
     
  5. Aug 13, 2015 #4

    Orodruin

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    No, you cannot say this. The expansion of space is that as the cosmological time parameter grows, the size of the scale factor increases. There is no corresponding thing for time.

    As I said in my post, "to come from" is intrinsically assuming a time ordering where there was an earlier time when it did not exist - but it does not make sense to talk about time outside of space-time.

    I do not see how this is at all related to the topic. Space-time is what it is, the past, future, and present are all part of it.

    Please answer only things which you are reasonably certain about.
     
  6. Aug 13, 2015 #5
    This is what I was commenting on for number 3.
     
  7. Aug 13, 2015 #6
    Orodruin, I think you haven't quite captured what I said.
    Isaac0427, on the contrary has exactly understood what I am saying, although his answer is the exact opposite of what I am saying. I am saying the space is not static, any solution of the FLRW is ( sorry for my wording here! ) Any hyperbolic spatial coordinate circle on the hyperbolic space-time sphere say, has increasing radius with time, but the sphere which is the space-time itself does not evolve anywhere. It is spacetime, unending and unborn as it was created.
     
  8. Aug 13, 2015 #7
    Ok, I have a better wording for this now. There is a manifold in FLRW solutions where at some point on its surface has all space and time coordinates vanishing and you take this as the moment of creation or big bang, right? But this manifold is all that there is, and because all the g's are vanishing somewhere in its metric this does not mean that it had a beginning.
     
  9. Aug 13, 2015 #8

    Drakkith

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    You're assuming spacetime is a substance or physical quantity which exists independently of anything else. It may be better to think of spacetime as a way of describing the relative position of objects or events using advanced geometry. In other words, don't think of the math as being a physical entity.

    This is more likely to mean that our understanding of physics is incomplete than anything else.
     
  10. Aug 13, 2015 #9

    Dale

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    Consider standard latitude and longitude coordinates on a sphere. Would you say that the manifold disappears at the south pole, or that the latitude lines disappear there? Personally, I don't think that either is a good description. I would just say that the latitude coordinate ranges from -90 degrees to 90 degrees.
     
  11. Aug 13, 2015 #10
    Please correct me if I'm wrong (I probably am) but I thought that there was never a time t=0, because spacetime could be infinitely small, which means that it has always existed.
     
  12. Aug 13, 2015 #11
    I must admit that I've made a mistake. Not only the space coordinates disappear somewhere on the manifold but the time coordinate as well. It's hard to visualize this but as an example I have the 2D hyperbolic torus x2 + y2=-r2 , z2 + w2=-r2 embedded in a 4D Euclidean space with signature (1,-1, 1,-1) as it degenerates when r=0.
     
  13. Aug 13, 2015 #12

    Drakkith

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    Forgive me if this is incorrect, as my knowledge of GR is very rudimentary, but I believe both of you are still under the impression that spacetime is a physical object and that as we look backwards in time we see spacetime shrink. When we talk about the universe expanding (or contracting in the case of looking backwards in time) we mean that the material within space moves further apart (or closer together). There is nowhere to which you can point to, "Here is where spacetime ends", you can only point to a period in time, t = 0, and say that "Here is where our equations give us infinities and other nonsense".

    I think the problem here is that the universe has no known radius. It could very well be infinitely large. Thus, as t approaches zero, the size of the universe doesn't get smaller, it is the density of matter and energy that grows without limit. You can, of course, talk about some volume of space of radius R, such as the radius of the observable universe, and see what happens to all matter within that volume as you take t back all the way to zero, but I'm not sure you can talk about "spacetime itself" contracting.

    As always, someone correct me if I'm wrong.
     
  14. Aug 13, 2015 #13

    Orodruin

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    What coordinates you put on a manifold and whether they can take particular values are irrelevant to the physics. It is not clear what you mean by coordinates "disappearing", but anything that can be fixed through a change of coordinate chart is not physical.
     
  15. Aug 13, 2015 #14
    I think that's why I am talking about a manifold in the first place because coordinates are irrelevant. How then do you say that spacetime had a beginning since all the g's in the metric vanish somewhere, when all there is, is the manifold itself oblivious of anything around or beyond it?
    Look at my torus. It's a perfect analogue of a 2D expanding infinite flat spacetime.When r=0 both the 2 coordinates of space and time you have laid to measure vanish. There does not exist a third ultra time co-ordinate. r is the curvature so to speak. At some point r=0 and is infinite, everywhere else has a number. I do not know of any other better mathematics to explain this.
    Why should you say that a manifold was created when its curvature was infinite I cannot understand it. I think is like the interior solution of a black hole in reverse. Does the interior solution of a black hole in the universe disappear out of existence? I don't believe it.
     
  16. Aug 13, 2015 #15

    Orodruin

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    Again, you cannot use this terminology. Time is not something that exists independent from space-time and so saying that space-time was "created" is a completely vacuous statement - it has no meaning.

    When we are talking about a space-time having a "beginning", it is rather a statement of past-directed timelike curves being bounded in length (i.e., proper time).

    Yes, this is similar to approaching the singularity in a Schwarzschild black hole but in reverse, all time-like future directed curves inside the event horizon have finite length. This does not mean that space-time "disappears". Disappearing is again something requiring a time concept which does not extend beyond the space-time itself.

    When r=0, you do not have a smooth manifold. Or are you using r as a coordinate in a 2+1 dimensional space-time? It is unclear from your definition.
     
  17. Aug 13, 2015 #16
    I'm not sure if this is what you meant, but I was under the impression that spcetime described an area with both space and time, and that area could get infinitely small as we look back in time, but there would always be some area with spacetime (yes, I know that there is no such thing as an area without spacetime, I just mean it still exists no mater how small). Is that correct? Now I'm not sure if this is stupid, but about t=0 and infinites in the equations, would it be possible that there was no t=0? Time could get infinitesimaly close to 0, but if space and time were always there at unimaginably small amounts. Maybe time moved a lot slower when spacetime was smaller. Has that ever been thought of before or am I getting something really wrong here?
     
  18. Aug 13, 2015 #17

    Orodruin

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    This is impossible to answer as it is not very clear what you are intending to say. Since most popular physics induced self-interpretations seem to be quite off, the best bet would be "no". What are you basing your assertions on? Can you formulate it in a better way?

    Particularly vague statements are:
    You are getting something completely wrong. How space-time (and in particular time) behaves is described by the metric, which links to the Einstein field equations to which the FLRW metric is a solution. You can easily change your time coordinate to a coordinate which extends to minus infinity, but this will not change the proper time of the curves in the manifold, which is coordinate independent. The point of chosing the standard coordinates is that the time coordinate t equates to the proper time of a comoving observer.
     
  19. Aug 13, 2015 #18
    So what I was trying to say is I thought spacetime was like a geometrical object with all mater and light in it. As you go back in time, that object would get smaller in space, and as you go forward in time, it expanded. My other point was it would be a possibility that space could never equal 0, and nor could time. GR is fairly new to me, so I am just curious.
     
  20. Aug 13, 2015 #19

    Orodruin

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    The point is that space-time does not "go back in time". Time is a part of space time. In the FLRW space-times, you can study a surface of cosmological simultaneity, defined by the set of events which have the same cosmological time. This defines what "space" is at that cosmological time and at later times, space is bigger and so we say that space expands.

    You cannot do the same with time (there is only one time simultaneous with itself) and the correct thing would be to say that space expands, not that space-time expands. As I said in the previous post, the time coordinate is chosen precisely to correspond to the actual time of a comoving observer, you could pick a different parametrisation, but it will not change the physics.

    In the FLRW cosmolgy, the size of the Universe is proportional to the scale factor. Since t=0 really is not part of the manifold, the scale factor is never zero.
     
  21. Aug 13, 2015 #20

    Orodruin

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    Do not get me wrong, it is good to be curious. I just suggest that you try not to overinterpret or analyse popular science descriptions. Instead, if you really want to understand it and not have your ideas full of misconceptions, you need to study real textbooks (including those which are prerequisites for the ones you wish to get to), preferably at a university where you can get proper guidance from teachers.
     
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