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Expansion as stretching

  1. Jan 10, 2015 #1
    [Mentor's note: This thread was split off from https://www.physicsforums.com/threads/observable-universe-question.79096] [Broken]

    The expansion of space can be likened to the stretching of the fabric of space time. At early epochs, that stretch was FASTER than the speed of light ...

    So the expansion of the universe initially carried ALL light AWAY from our location
    Last edited by a moderator: May 7, 2017
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  3. Jan 10, 2015 #2


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    This is a popular misconception. The expansion of space does not proceed at a given speed (it is really a rate per distance), and so it's never correct to say that the expansion was faster than the speed of light. What is typically meant by this, I'll grant, is that the expansion can be such that that objects comoving with the expansion attain speeds surpassing that of light. This is true, but it's always true in any expanding cosmology, at both early and late epochs. The distance at which objects attain a superluminal recession velocity is called the Hubble distance.
  4. Jan 10, 2015 #3
    Yes, that is what I said

    In the rubber sheet analogy, the sheet is stretching, such that, say, opposite corners held by opposing graduate students, are receding from each other faster than light propagates THROUGH the rubber sheet

    It is very important to clarify, that nearby proximate points, such as the center of the rubber sheet, are not receding from each other very quickly at all...

    At later epochs, the expansive stretching slows, such that you have to have a larger sheet, held by more graduate students, to have opposing TAs on opposite sides of the sheet running away from each other at the same faster than light speed...

    Other than that QUANTITATIVE difference, however, early and late epochs are qualitatively similar, i.e. there is always a Hubble distance
  5. Jan 12, 2015 #4


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    First of all, space-time is not expanding, space is. Space-time is what it is.

    Second, when space is expanding it is more accurate to talk about a rate of expansion than a speed. However, it may result in distances growing faster than the speed of light.
  6. Jan 12, 2015 #5


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    Again, expansion does not have a speed.
  7. Jan 12, 2015 #6

    So constant time slices, of the fabric of space-time, grow larger with time...

    But the fabric of space-TIME is static...

    Simply "floating in hyperspace" were one to use that picture...

    That makes even more sense

    So that is why there is no speed, nothing is moving in any ultimate hyperspacial sense...

    The perception of expansion actually describes the shape or structure or form of the fabric of space-time...

    Which is unchanging
  8. Jan 12, 2015 #7


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    Putting it this way can be misleading, because the word "static" means "unchanging", and the concept of "change" requires time, and time is a part of spacetime, not something spacetime exists "in". It would be better to say spacetime just "is"--it exists.

    This can be misleading too, because there is no "hyperspace"; there is no underlying medium in which spacetime exists. Spacetime just exists.

    This can also be misleading, for the same reason as above.

    This part is fine...

    ...as long as you leave this part out. Spacetime does have a geometry, a shape, and the spacetime geometry of our universe is such that "slices" cut out of it a certain way have a spatial scale factor that increases along a timelike direction orthogonal to those slices. That is the best way to describe, in geometric terms, what is usually referred to as the "expansion" of the universe. Note that I said nothing about hyperspace or spacetime being static--I just described the geometry and that's all.
  9. Jan 12, 2015 #8
    How does viewing space time as a manifold or fabric, embedded in a higher dimensional bulk or hyperspace, ever lead to any errors?

    Providing we both calculate completely correctly ...

    If I imagine a higher dimensional embedding space, and you do not, when do ever wind up with different answers?

    How is the concept of hyperspace ever actually, actively, mis-leading?

    There is a difference between "it's not a necessary concept and I don't like it or use it"...

    Vs. "it's an erroneous presupposition"
  10. Jan 13, 2015 #9


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    Occam's razor. Neither hyperspace nor higher dimensions are required to give us the right answers so we don't include them. Including them can also lead to other issues, such as what is that dimension embedded in, and that one, etc. In the end it's all a big philosophical mess, so we just avoid it all by saying that spacetime isn't required to exist within anything else. We don't claim that it absolutely cannot exist within something else, only that it isn't required to.

    It's misleading because it isn't mainstream science. Note that PF rules do not allow members to simply give their opinions as answers, regardless of whether it "leads to errors" or not. You can find the rules here: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/
  11. Jan 13, 2015 #10


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    And if you calculate completely correctly, there will be nothing whatsoever in your calculation that corresponds to "hyperspace". So on what basis would you even interpret the calculation as being about "hyperspace" if nothing in the calculation corresponds to it?
  12. Jan 13, 2015 #11
    Einstein famously reasoned visually and geometrically, so I was told

    The WMAP graphic of the fabric of space time visually suggests, or even implies, that the viewer is looking at the fabric of space-time from some higher dimensional (3D for the 2D spacetime shown) hyperspace perspective

    Hyperspace seems useful for visualizing curvature (to the extent that such is possible)

    I understand that String Theory regards space time as a membrane embedded in a higher dimensional Bulk, i.e. hyperspace

    Is that a misunderstanding?
  13. Jan 13, 2015 #12
    Is it possible to explain how to have a curved membrane or manifold or fabric, without it curving through higher dimensions?

    For the first few dimensions, curvature seems to require higher dimensions...

    A line can curve only in a plane, like the center of a football/soccer field. And the surface of the earth can curve only through 3Ds.

    What is different for 4D space time curving?
  14. Jan 13, 2015 #13


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    Yes, but you are not. You haven't even learned the basics of differential geometry, which is absolutely necessary to understanding the curvature of space.

    It most certainly does not suggest that. If you continue to make baseless assertions I will lock this thread.

    Yes, by understanding that curvature can be intrinsic or extrinsic. From wiki: http://en.wikipedia.org/wiki/Curvature#Higher_dimensions:_Curvature_of_space

    By extension of the former argument, a space of three or more dimensions can be intrinsically curved. The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.

    We do not conceive of spacetime as being embedded in a higher dimension, so the curvature is intrinsic.

    This only appears to be true because you're used to seeing the first few dimensions from your vantage point in 4d spacetime. They happen to be embedded into higher dimensional space, but in general they are not required to be.
  15. Jan 13, 2015 #14
    Can you be more specific?

    Can I be more specific?

    In every rubber sheet analogy, and in every picture of a space-time fabric...

    The viewer seems to be looking at said space-time from some "position" or some "where" OUTSIDE of the fabric...

    Doesn't that imply that the viewer resides in a higher dimensional ambient space (to try to use the term you quoted)? Am I the only person who winds up with that impression?
  16. Jan 13, 2015 #15


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    Yes, but that's where the analogy breaks down. As a good exercise in differential geometry, you should work through the derivation of the intrinsic curvature of the 2-sphere. You will find, along the way, the amazing result that the 2-sphere can exist perfectly fine in only 2 dimensions -- no need for a 3rd dimension within which to embed it! This is what it means for curvature to be intrinsic (another example, working the other way, is that of a cylinder -- it has zero curvature despite how it "appears" when it is embedded in 3D. The cylinder can be constructed from the plane by suitably connecting edges in such a way that the geometry is not disturbed).

    The conclusion is that spacetime is not required to be embedded in a higher dimension.
    Last edited: Jan 14, 2015
  17. Jan 14, 2015 #16


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    One of the branches of differential geometry is Riemannian geometry, which what General Relativity is based upon. This geometry is nothing like what you've ever dealt with, so even though you are trying to think in terms of geometry, you are basically held back to the middle-school/high-school level which uses flat geometry, aka Euclidean geometry. We surpassed Euclidean geometry almost 200 years ago.

  18. Jan 14, 2015 #17


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    No, but that doesn't mean it's a correct impression. The diagrams you are talking about are attempts to help people visualize what the mathematics is saying; doing that often involves adding extra elements that are not required by the mathematics or the physics, but might be helpful given humans' limited ability to visualize things. The higher-dimensional ambient spaces you are referring to are examples of this: there is nothing in the mathematics or the physics that corresponds to them, but they are added in to make it easier for people to visualize a curved space or spacetime. This is a good illustration of why, if you really want to understand a physical theory, you have to actually look at the underlying math; you can't depend on second-hand methods like the diagrams you refer to.
  19. Jan 14, 2015 #18


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    You might find it interesting to read the page linked to in my signature. It was written with a lot of help by people here on the forum.
  20. Jan 17, 2015 #19
    Paul Davies, Nature, 1978

    "...his [Ellis] cosmic model is supported by the Big-Bang and Expanding Universe concepts, which in turn are buttressed by the simple observation that astronomers see redshifts wherever they look.

    These redshifts are due, of course, to matter flying away from us under the impetus of the Big Bang. But redshifts can also arise from the gravitational attraction of mass. If the Earth were at the center of the universe, the attraction of the surrounding mass of stars would also produce redshifts wherever we looked! The argument advanced by George Ellis in this article is more complex than this, but his basic thrust is to put man back into a favored position in the cosmos..."
  21. Jan 17, 2015 #20


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    This does not seem right; gravitational redshift does not work this way. I suspect that Davies was misinterpreting something Ellis said in his article. Does anyone know if Ellis's article is available online?
  22. Jan 17, 2015 #21
    I have not found it online. I do not think Ellis was using the FLRW metric, but I am not sure. He plays all over Bianchi space.
  23. Jan 20, 2015 #22
    I'd like comments and constructive criticism of the following...

    Current understanding


    The fabric of space-time is static and unchanging in some sense

    The space-time of the past and the fabric of the future already exist

    We occupy a thin spatial slice of the fabric

    And it so happens that the slices are becoming bigger

    Moment by moment the stage becomes larger

    Seemingly stretching apart and carrying all of the actors apart too...

    BUT ...

    The stage we occupied yesterday was a SEPARATE stage = space like slice of fabric...

    Than the one we occupy today...

    And both of these are separate from the stage we will occupy tomorrow

    It is NOT ONE STAGE stretching...

    But rather a series of sequential stages which happen to be becoming bigger

    Nothing is growing
    Nothing is stretching
    There is no one thing that is enlarging

    In the above figure
    Space as we know it
    Is like a vertical stack of rings
    Each larger than the prior previous
    Moment by instant
    We step from a smaller ring to a larger ring
    And we look around and notice we have more room now
    And so we conclude one space stretched...
    But NO...
    We parted from the smaller ring
    And entered another bigger one

    The future is fated in some sense
    All of the fabric of future space-time ALREADY EXISTS

    Even as all of the fabric of past space time STILL EXISTS

    The fabric of SPACE TIME is unchanging
    What IS changing is the spatial slice of the fabric we occupy NOW
    In the above figure, we're moving upwards
    As if in an elevator
    Going up a building
    Whose floors were becoming bigger and larger
    At each new level
  24. Jan 20, 2015 #23
    You could distinguish between cylinder and plane
    By sending out a probe around the curved dimension of the cylinder...
    It would come back to you from the other direction

    That scenario could not occur in a plane
    So how can one regard the cylinder as equivalent to a plane

    A plane is not a cylinder
    And you could in principle tell them apart
    So why say they are essentially the same ?

    Or did you not say that?
  25. Jan 20, 2015 #24
    What books did you yourself learn from?
  26. Jan 20, 2015 #25


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    I don't know the math. I know about the math, lol. I'm about to start taking calculus 1, so I'm several years from differential geometry.
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