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Is it possible that Mass is the /same thing/ as curved spacetime?

  1. Jan 3, 2012 #1
    It's fairly easily to visualize space bending as a result of the mass of an object, and that the bending of space is effectively gravity.

    But if mass always results in bending space (how else could it hold it in this universe?), is it possible that mass and the bending of space is precisely the same thing?

    IOW, if I were to wave a magic wand and place a bend distortion in space, did I just create mass? It would behave as a gravitational field and pull things toward its center, no?

  2. jcsd
  3. Jan 3, 2012 #2
    not a crazy idea...but no. Waving you arm and a wand causes gravitational waves...distortions in SPACETIME but not mass.

    Turns out that momentum, energy, pressure all contribute to gravity...the distortion in SPACETIME .

    Note 'SPACETIME': if you bend time, you create gravity, too. In general relativity all these are part of the stress energy tensor which is the source of the gravitational field.
  4. Jan 3, 2012 #3
    I'm fairly sure not. As far as I'm aware, the bending of space is purely a gravity thing which acts on a mass. Mass itself, however, effects how all forces (EM, Gravity, Strong and Weak) are applied to a body.

    You can mimic a massive object with your magic wand and things would be gravitationally drawn towards it, but if that area of curved space-time didn't actually contain mass, it wouldn't react to external forces in the same way that a massive object would (note that I'm assuming your magic wand doesn't just use energy to make its distortion, which would just be mass in a different form).
  5. Jan 3, 2012 #4
    So given my magic wand: would'nt the external forces act on that bent region as if there were a mass there? <----broken way of saying it, I'll rephrase.

    It sounds as if you both are in concert with that there are things that can act upon a mass independent of gravity. I suppose I have to wonder about this: Aren't the fact that "momentum/energy/pressure" are all issues related to matter make it such that there would be a momentum/energy/pressure the moment that space was bent?

    I believe you both, but I'm not sure that I understand how what you're saying actually flies in the face of what I'm saying.
  6. Jan 3, 2012 #5
    Quick note on this. In all things, it's easiest for me to view time as just another dimension---makes more sense to me. So I'm assuming that bending space along any one of the (for now, say 4) axes will beget (or be) gravity.
  7. Jan 3, 2012 #6
    The problem with what you are asking is that it isn't well defined. How do you propose to generate spacetime curvature without any non-zero components of the stress-energy tensor? A "magic wand" isn't a valid answer; you're asking a physics question based on the false premise that magic exists. We don't know the physics of magic, so we can't give you a well defined answer.
  8. Jan 3, 2012 #7
    Entirely incorrect. It's entirely valid to use an absurd postulation as an alternative way of explaining a prior question about something real. The notion of a "magic wand" has *nothing* to do with a magic wand per se. The question is not about magic, nor is it in particular "what does a magic wand do."

    Example: Suppose someone questions whether or not an angry cat and it's ears pointing back is a causal relationship or two facets of precisely the same phenomenon. They would be perfectly valid in saying:

    "Is it possible for an angry cat to not have its ears point backward, or for a cat with its ears pushed forward to be angry? In other words, if I were to wave a magic wand and have an obviously angry cat's ears moved forward would it cease to be angry?"

    It would not be appropriate then to question the nature of magic wands.
  9. Jan 3, 2012 #8


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    There is a sense in which you can do this. Posit a metric tensor for a manifold (spacetime). Derive the Einstein tensor (no assumptions about matter needed). Now, by equality (and a few constants), you have stress energy tensor that can be interpreted as mass-energy, pressure, etc. If you choose an 'arbitrary' metric, you will get physically implausible stress energy tensors (and there is an active and unresolved research effort into how to characterize physically plausible stress energy tensors). However, you can still view this approach as instantiating the idea of geometry producing mass.
  10. Jan 3, 2012 #9

    I interpret the question along the lines of these descriptions floating about regarding spacetime and gravity:

    1) The effect of gravity is to create a "depression" in spacetime that then causes objects to roll into it, like marbles to a low spot.

    2) If the low spot could be created in another way (Thus far unknown) would objects still roll into that depression?

    I believe the magic wand analogy was merely used to represent the unknown way of creating that low spot without an object/mass.

    So, the answers thus far have seemed to indicate that we really don't know of another way to create that depression in the spacetime fabric, so its an experiment we can't perform yet.

    As a thought experiment, so far, we are not really offering any clue as to what the outcome would be, but, logically, if the DEPRESSION in the spacetime fabric was being used as yet another analogy, and not as an actual physical description, then, the question loses meaning.

    If the depression in the spacetime fabric is meant to be a literal physical description, or at least describe an effect that works in that fashion, then it is implied that the effect, and not the object creating it, was necessary to roll our marbles.

    IE: If the mass "creating the depression" is actually the attractive force at play, and the depression description is an analogy, then creating the depression otherwise would not attract objects.

    If the mass "creating the depression" was actually creating the moral equivalent of a depression, such the at the objects were drawn in by the depression itself, then creating the depression alone would actually be sufficient to draw in the objects.
  11. Jan 3, 2012 #10


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    It depends on what you mean by "the same thing". If you mean "the same" as in "appears the same to our experience", then certainly not: mass is a very different thing from spacetime curvature. If you mean "the same" as in "equivalent according to the laws of physics", then it's not just "possible" that they're the same, it's actual; according to the Einstein Field Equation, spacetime curvature *is* mass (more precisely, stress-energy; as other posters have pointed out, mass is not the only component of the stress-energy tensor); the one is equal to the other.

    No, it wouldn't be appropriate, it would be obfuscating a very simple issue. The question in quotes above is a simple question about the correlation, averaged over all cats, between being angry and having ears pointed backward. The way you answer such a question is to look at the observed correlation. You will find, of course, that the correlation is high but not perfect, indicating that these two phenomena are contingently closely related but are not "the same thing". If you want to go deeper and ask "why", you investigate the biology of anger and ear behavior in cats. Talk about "magic wands" does nothing but obscure the sorts of things you actually need to look at to answer the question.

    Similarly, your question about mass and spacetime curvature is a simple question about the correlation between observing mass (stress-energy) and observing spacetime curvature. In this case, the correlation is perfect, indicating a stronger relationship than just being contingently linked. General relativity explains this through the Einstein Field Equation, which requires the correlation to be perfect.
  12. Jan 4, 2012 #11


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    Given that the general mathematical representation of space-time curvature is a 4 dimensonal rank 4 tensor - the so called Riemann curvature tensor - and that mass is a scalar, I would say that they're not "the same thing".
  13. Jan 4, 2012 #12


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    Agreed, but a looser interpretation of the OP is:

    If I change the curvature of spacetime in an appropriate way, have I necessarily changed/produced mass?

    In classical GR, I would answer this: yes.
  14. Jan 4, 2012 #13
    Not quite. For #1 above, I'm already assuming (correctly or incorrectly) that a depression in spacetime *is* gravity. For #2 above, I'm already assuming that if the 4D low spot were created another way that it would draw objects toward its center.

    The question is: is bent space actually matter itself? Or perhaps: is it a misinterpretation to view matter and bent-space (or matter and gravity if you like) as separate phenomenons when they are actually the same thing.

    Yes, that's dead on.
    Last edited: Jan 4, 2012
  15. Jan 4, 2012 #14
    If that's the case, and the "yes" is reassurring, then broadening this to all of physics:

    Is it the case that whenever "thing" A (in our case, mass/momentum/etc) cannot exist without "effect" B, and "effect" B cannot exist without "thing" A, is it unreasonable to assume (generally) that "thing" A and "effect" B are "the same"? I don't view this as a semantic question.

    I understand that you can have two views of an item. The marble is not the bend in the rubber sheet it is sitting on. But that's only in the context of All Things. If you constrain the context to the marble and the rubber sheet only (that's all there is), then yes, the bend *is* the marble. Or adding an item *outside* the context (magic wand) then bending the rubber sheet does [create or beget or form or require] the marble. I'm not sure that's entirely nuts.
  16. Jan 4, 2012 #15


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    Your first question is philosophic to me, so my answer is more opinion than science. I would say just because A implies the existence of B and B implies the existence of A within some physical theory, it is not necessarily useful to think of A and B as the same thing.

    As to your second question, I have been trying to answer an underlying, more valid question implied by your 'poetic' description. However, I can't any longer. Please erase the 'rubber sheet' analogy from you mind. There is nothing analogous to a rubber sheet, with mass sitting on it and bending it. There is also nothing analogous to the space in which the rubber sheet sits (as is implied by this image). The best I can say in words is:

    There is an intrinsic geometry of spacetime (similar to a 2-d being living on a balloon can tell they have non-euclidean geometry by adding up angles of triangles). An aspect of this geometry (the Einstein tensor) can be simultaneous described as a distribution of mass/energy density and pressure/stress distribution.
  17. Jan 4, 2012 #16
    What's poetic? You seem angry.

    There's nothing mystical about, say, a 4D surface of a 5D balloon, nor the topological way of discovering it's "shape". Heck, people used to scratch their heads at walking north and getting closer to each other. But that analogy I used was just another magic wand example: don't mistake me for someone thinking that the universe is a rubber sheet with stuff pushing on it. It's just an example of me replacing the causal nature of "the marble causes the bend" with an equivalence. I don't care if that's a common description for gravity or a total mistake in many videos on the subject. I just chose it because there's a "thing" and a bend.

    The choice of a marble and a rubber sheet should have done nothing to abort the conversation.

    In any case, there's enough in this thread for me to look this up further.
    Last edited: Jan 4, 2012
  18. Jan 4, 2012 #17


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    I wasn't angry at all. The problem with the rubber sheet analogy is that the balls are completely superfluous and beg the question of why they depress the rubber sheet (gravity from outside the universe??!!).

    As for a 4d surface of a 5d balloon, what I would like you to think about is that there is no need for the 5th dimension at all. We perceive 3-d space. We have no knowledge of, nor do we care, whether this 3-d space is a hyperplane in a 4-d space (I am not talking about spacetime here). Whether it is or isn't embedded in something is undetectable to us, and completely irrelevant.

    Rather than thinking of balls outside a sheet depressing it, I want you to try to think about intrinsic geometry being also interpretable as mass/energy density and pressure/stress distribution.
  19. Jan 4, 2012 #18


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    Saying a treatment is "poetic" is usually to say that it lacks math. If you are motivated to study some of the math involved by this discussion, that's a good thing.
  20. Jan 4, 2012 #19
    The problem with the rubber sheet analogy is that too many people don't fully realize that it's just an ANALOGY, and look to it for actual explanations. The balls don't depress the rubber sheet because there are no balls and no rubber sheet. It's just an ANALOGY.
  21. Jan 5, 2012 #20
    Yes, well again, it's not because it's how I view the universe, it's an analogy involving something and a bend. This conversation got derailed by jumping on this as if it were an analogy of the universe, when I was trying to make it an analogy of causality not being causality.

    Maybe I should have used something like "fire was thought an separate entity to induce a chemical reaction when it was later realized that fire /was/ the chemical reaction", or less clumsy words to that effect.

    Even as a kid I never liked that rubber sheet analogy given in documentaries. It's interesting to see perhaps as a visual for gravitational acceleration, but the sheet is 2D, the ball is 3D, and it requires gravity to explain gravity. For me, the dumbed down visualization in my own mind of the structure of space is more like foam starting with (say) a planet shaped sphere-ish hole in the middle of it (the mass). The foam along the perimeter of that hole is pulled by me to the middle (somehow). This gives the greatest stretch at the center, and the bend lessens as you get further and further away. Perhaps items moving from bubble to bubble in the foam are now diverted toward that center. Actually, there's much more to that visual, and I make the foam 4D, but again none of this matters.

    This thread has been very informative to me about what stretches ST.
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