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I Spacetime relativity

  1. Mar 15, 2017 #1
    When the universe is expanding then why not we are expanding along with it
     
  2. jcsd
  3. Mar 15, 2017 #2

    phinds

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    Because expansion is so incredibly weak that gravitationally bound systems, and systems (such you you and me) bound by additional forces are not affected. Things as large as galactic clusters, and anything smaller, do not expand
     
  4. Mar 15, 2017 #3
    But according to the general relativity of Einstein the whole universe is a fabric of space and time and when this fabric of the space time is expanding then the effect must also occur in such a large structure because universe has a homogeneous entropy of space and time
     
  5. Mar 15, 2017 #4

    phinds

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    Well, if you don't like my answer don't accept it. I do suggest you do some research (which will show you that I have given you the correct answer). And by the way, "fabric" is a TERRIBLE way to describe the universe. Yes, I know Einstein used it, but he knew what he was talking about. For most people, it just leads to confusion.
     
  6. Mar 15, 2017 #5
    But strong forces are short range forces ,and they only effective up to Fermi of distance
     
  7. Mar 15, 2017 #6

    PeroK

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    The expansion is too small to notice in any case. For example:

    The lifetime (80 years) expansion per meter is about ##6 \times 10^{-9}m##. Which would be hard to detect.

    And, for the Earth's orbit round the Sun. The expansion of space would amount to about ##1km## in a lifetime. That would also be hard to detect, even if gravity didn't counteract it.

    Expansion at the atomic level would also be undetectable and counteracted by other forces in any case.
     
    Last edited: Mar 15, 2017
  8. Mar 15, 2017 #7

    phinds

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    Yes, but my understanding is that the issue is NOT that it is hard to detect, the issue is that it just doesn't happen. It's like an ant pushing on a house. It's not that the ant moves the house such a small amount that it's undetectable, it's that the ant doesn't move the house at all. The ant simply can't exert enough force to change the balance of the rest of the forces
     
  9. Mar 15, 2017 #8
    I don't think that reasoning is correct

    Certainly, molecules won't expand. That's because they are in a ground state which is a stable equilibrium. If they are temporarily excited, then they will decay through electromagnetic emission, so small perturbations cannot ever eventually build up into large changes. For a chemical bond, you have a binding energy versus distance between atoms, and the bond will pull the atoms to a distance where the binding energy is minimized (as a negative value).

    The situation is different for gravity, since the orbits aren't in a stable equilibrium. You can nudge an orbit and you get another orbit--it doesn't bounce back. So a tiny shift can accumulate into large one over time. The question is, is there a tiny shift? There seems to be some disagreement over it according to the introduction of http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652015000501915.

    I'm no expert, but I think planetary orbits are not expanding, but for a different reason than above. The universe is only homogeneous on very large scales, averaging over smaller structures like superclusters. The solar system is very much smaller, so the fluid approximation is not at all valid. The average density in the solar system is much, much higher than in the universe, but it's also not smooth, being concentrated in the Sun.
     
  10. Mar 15, 2017 #9

    PeterDonis

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    This is true for ordinary matter and dark matter (and radiation), but not for dark energy. The density of dark energy really is constant everywhere, as far as we can tell. So there is a very, very tiny force exerted by dark energy on objects in the solar system; it's just way too small to overcome the binding forces between those objects (let alone the binding forces between their atoms).
     
  11. Mar 15, 2017 #10
    As I said in my previous post, gravitational orbits are different than electromagnetic orbits. What do you mean by "binding forces" for a gravitational geodesic orbit? Expansion could conceivably make planetary orbits get larger over time. At the same time, the orbital velocity of the planets would decrease due to cosmological redshift consistent with the increase in radius from the Sun.
     
  12. Mar 15, 2017 #11

    PeterDonis

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    In Newtonian terms, the gravitational force between the Sun and the planet (or planet and satellite, or whatever). In GR spacetime curvature terms, the spacetime curvature due to the Sun and planets.

    No, because the effect of the dark energy on the spacetime curvature in the solar system is constant, and so is the effect of the matter in the solar system. The reason dark energy has a noticeable effect on cosmological scales is that the density of ordinary matter and radiation dilutes with the expansion, while the density of dark energy does not; therefore the effect of dark energy on the spacetime curvature, relative to other effects, gets larger with time. But on the scale of the solar system, the density of matter does not change with time; it doesn't dilute with expansion, because the solar system is gravitationally bound. So the effect of the matter in the solar system on its spacetime curvature does not get smaller with time, it remains many orders of magnitude larger than the effect of dark energy and the relative impact of the two doesn't change.
     
  13. Mar 15, 2017 #12
    Yes, I agree with you.

    I'm not qualified to treat this with GR, but let me take a Newtonian approach and treat dark energy as a fictitious force directed away from the center of the coordinate system, where we place the Sun.

    A planet in a circular orbit (very approximately) will have centripetal acceleration v^2/R which is equal to the sum of the gravitational force of the Sun pointing inward and the gravitational force of dark energy which points outward. So, the presence of dark energy means that the orbital velocity needs to be a very tiny bit less for a given radius than expected just from the gravity of the Sun to execute a stable circular orbit. There's no "accumulation over time" effect.
     
  14. Mar 15, 2017 #13

    PeterDonis

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    Yes, that's my take as well. And the "very tiny bit" is something like 30 orders of magnitude smaller than the base value due to the Sun's gravity.
     
  15. Mar 16, 2017 #14

    PeroK

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    Or, to put it another way, the current orbit is stable given the effects of both gravity and expansion. It's not, as some might suppose, a stable orbit taking only gravity into account, which gradually spirals outward due to expansion.
     
  16. Mar 24, 2017 #15
    How do you know we are not?
     
  17. Mar 30, 2017 #16
    Because we do not measure it, except with our accelerators.
     
  18. Mar 30, 2017 #17

    Drakkith

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    I'm not sure I see what accelerators have to do with this.
     
  19. Mar 30, 2017 #18
    We measure an accelerated expanding Earth at the surface, we do not measure this with our ruler, but we do measure it with our accelerators.
     
  20. Mar 30, 2017 #19

    Drakkith

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    No, we haven't measured an expanding Earth. The Earth is not expanding.
     
  21. Mar 30, 2017 #20

    jbriggs444

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    The term is accelerometer.
     
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