Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

GR effects

  1. Mar 27, 2010 #1
    According to SR theory, relative motion leads to
    -length contraction
    -mass inflation
    -time dilation.

    In GR theory, gravity leads to time dilation. Does it also lead to
    -length contraction?
    -mass inflation?
     
  2. jcsd
  3. Mar 27, 2010 #2

    ia_

    User Avatar

    Special relativity is a subset of general relativity. In a region of space without large masses, the geometry of that space will become flat. That is, it will reduce to the minkowski metric of special relativity. So, all of the effects that occur in special relativity can also occur in general relativity.

    In addition, there are a host of new, but it some cases analogous effects. Perhaps the most often observed new effect is that time runs more slowly for objects in a large gravitational potential. This is magnified in the case of a black hole. The rate of progression of time for an object falling into a black hole (as viewed by a distant observer) will slow to zero as that object approaches the event horizon.

    For GPS satellites, which orbit the Earth at a high velocity, both special and general relativistic effects occur:

    effect due to sr:
    As GPS satellites move fast relative to us, their time is dilated, and runs more slowly, by about 7 microseconds/day.

    effect due to gr:
    Because gps satellites are further away from the center of the Earth's gravitational field, their time runs faster than ours, by about 45 microseconds/day.

    According to wikipedia (http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity), if neglected then these effects would cause uncertainties in position to grow by around 10km/day.

    There are dozens of other new effects: frame dragging, event horizons, the penrose process, cauchy surfaces, schwarzschild and kerr black holes, expanding cosmologies, even messier differential equations, and so on:D
     
    Last edited: Mar 27, 2010
  4. Mar 28, 2010 #3
    In GR there are no such things as "length contraction" and "mass inflation" caused by gravity but rather now there exists a new concept "curvature" by which one can feel the presence of a gravitational field and matter.

    AB
     
  5. Mar 28, 2010 #4
    Really? Funny how Einstein seemed to START with Special Relativity, then moved on to GR. Are you positive you're not just blowing smoke?

    @Altabeh: Hmmmm... do you mind if I quote you to a friend of mine who's been struggling with this concept? You said that very succinctly!
     
  6. Mar 28, 2010 #5
    Yeah sure!:wink:

    AB
     
  7. Mar 28, 2010 #6

    Janus

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, really. Einstein started with SR because it was easier to start with the limited "special" case. But he also knew that the theory would not be complete until it could be further expanded to deal with the more "general" case.
     
  8. Mar 28, 2010 #7

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I.e, Einstein condsidered more general situations for which special relativity is a special case. If, in general relativity, one considers the special case of a simply connected spacetime with [itex]g_{\mu \nu} = \eta_{\mu \nu}[/itex], one gets Minkowski spacetime. In this case, Einstein's equation is [itex]0 = T_{\mu \nu}[/itex], so energy and matter have to be (in some sense) negligible ("test" particles only).
     
  9. Mar 28, 2010 #8
    I understand, but I don't think you can call a theory published while GR was still being formulated a "subset". I understand the physics, I disagree with the semantics. To be blunt, Einstein's first paper describing SR was published in 1905, and GR formulated between '07-'15.

    I wouldn't call it a subset of anything, just "The Special and General Theories of Relativity".
     
  10. Mar 28, 2010 #9

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Why not?
    To me, the phrasing doesn't seem so bad. It is clear what is meant.
    For me, the dates are irrelevant.
    Again, I don't think that the terminology is so bad.
     
  11. Mar 28, 2010 #10

    dx

    User Avatar
    Homework Helper
    Gold Member

    Electrostatics was formulated before the full electromagnetic theory of Maxwell. Yet, electrostatics is logically a special case of electrodynamics, in the sense that under specialized conditions, electrodynamics reduces to electrostatics. The relationship between special relativity and general relativity is the same.
     
  12. Mar 28, 2010 #11
    I don't see how this argument over semantics, which I will gladly cede, can go anywhere useful. I aknowledge the point that General Relativity is a complete theory in which there is a "Special" case, as a subset. I would point out that a person in 1906, would of course have no way of appreciating that. It is logically organized in the manner you describe, but that isn't how it evolved. ia_'s language assumed prior knowledge that some people may not have on an educational site, not an entirely uncommon occurence.

    There are some brilliant people here, but the communication skills are occasionally lacking in terms of liasing between common parlance and various formalism and terms of art of mathematics and physics. This does lead to some extended misunderstandings and pointless detours such as this.

    This is a situation in which, as with dx's example: there's more than one way of establishing a logical hierarchy. There is a historical context, in which theories evolve from one another, and then the formal (and useful) manner of classifing them ad hoc. I'm not disputing the latter, but let me ask you this: How would you establish a hierarchy for the major branches of mathematics?

    @George Jones: "Again, I don't think that the terminology is so bad." Fair enough; I don't think the terminology is that great.
     
  13. Mar 28, 2010 #12
    So back to my original question - is there length contraction and/or mass inflation in GR - Altabeh said:

    Then there must be no such things as length and mass, or they do not contract and inflate.

    Which?
     
  14. Mar 28, 2010 #13
    Most physicists first get involved with a very limited and simple theory and then they try to expand the ideas brought up in the initial theory into a big framework wherein not only will the first theory work well, but the new theory will be based on some more general ideas that lead to the initial ideas in special cases. It is not at all a bad way to keep a theory going deep into broader areas of knowledge by first starting from a simple thing though this could sometimes lead to nowhere if the developed ideas are not as much compatible to the initial ideas as possible! For example, the idea of "curvature" in GR is compatibly reducible to the old implication of "force", as assumed by Newton. Sometimes there are no conditions by which the theory can be given a simplified, reduced or even generalized form. Google can help you find some examples of this.

    AB
     
  15. Mar 28, 2010 #14
    Thanks anyway.
     
  16. Mar 28, 2010 #15
    I think my post can't be put in a clearer form: Length cannot contract and mass cannot inflate due to gravity in GR.

    AB
     
  17. Mar 28, 2010 #16
    Are you by chance thinking of the old sci-fi standby, the "blueshifted 'front' of a near-c 'craft', versus the apparant long redshifted 'tail' of it? That is an effect percieved by the observer, and doesn't imply a real change in length or mass. In essence, you're seeing light "stack" in the front, and "extend" in the rear, but that's the LIGHT, not the "craft".

    I'm not even sure what you mean by "mass inflation", unless you think that the mass of an object approaching 'c' becomes "infinite", which is a common misconception. Once again, you have to remember which effects are the result of a change in something, and which are merely observational artifacts.

    @Altabeh: Yes, theories usually evolve from the simple to the more complex; and that new theory should incorporate the old, in which case from one point of view SR is clearly a subset of GR. That said, even though GR is the framework which explains SR and more, one did not evolve as a subset of the other, but rather GR is an expansion and extension (among others things) of GR.

    As I said, this is a semantic issue, with two possible views on the subject. I'll admit that mine is less useful in this context, but also it won't mislead newcomers to the subject as to how the theories were developed. To me, a subset represents a group "B" containing elements derived or taken from group "A". For that to occur, group A needs to exist for a subset to emerge, rather than B leading to A and because A encompasses B, it's being called a subset.

    As I said earlier, I would call them "SR and GR", not "GR and its subset", or "SR and its superset". There is no context in which identifying them as two theories, one leading to another, isn't preferable to "subset"
     
  18. Mar 28, 2010 #17
    A common misconception? Would you not concede that the inertia of an object (the quantity of external momentum impulse that it takes to alter its velocity a particular amount) increases without limit as the object approaches the speed of light? (After all, this is the mechanism that prevents us accelerating it to superluminal velocities. Let's just leave aside questions of precisely what the term "mass" should refer to.)

    Sure, purely optical distortions also exist, such as Terrel rotation. But the reality of length contraction is the first lesson taught on SR (regarding a barn and ladder, unfortunately under the guise of a paradox involving details of material acceleration). Regardless of how your sci-fi craft seems visually, the fact is that physical synchronised measurements of its extent (say, made by attendants along a station as the craft passes against some of them) would confirm contraction (and note that this is predicted by GR as well as by SR, regardless of whatever point Altabeh is trying to make), just as surely as atomic clocks left in different floors of a building do confirm the time-dilation predicted in GR.

    To put that another way, since the shape of atoms and molecules is basically dependent on Maxwell's theory (which exhibits Lorentz symmetry), whilst you may be familiar with notionally-spherical electron-orbital shapes for atoms at rest, the correct actual solution for the shape of the electron-cloud of a fast moving atom is more like a pancake.
     
    Last edited: Mar 28, 2010
  19. Mar 28, 2010 #18
    Really?! Wow, talk about being 180 degrees off target. Well, in that light, I'm going to skip to that portion of MTW and learn what I thought I knew. Thanks for the correction, and lesson. By the way, if it isn't too much trouble what would be a toy solution for a simple fast-moving atom (H, He)?
     
  20. Mar 29, 2010 #19
    In SR an observer measures:

    1) The length of rod parallel to the relative relative motion v, to be length contracted by sqrt(1-v^2).

    2) The length of a rod transverse to the relative motion v, to be the same length as when it is at rest.

    3) The rate of a clock with relative motion v, to be time dilated by 1/sqrt(1-v^2).

    In GR an observer at infinity in Schwarzschild coordinates measures:

    A) The length of stationary vertical rod at radial coordinate r, to be length contracted by sqrt(1-2GM/r).

    B) The length of a stationary horizontal rod at radial coordinate r, to be the same length as a local rod.

    C) The rate of a stationary clock at radial coordinate r, to be time dilated by 1/sqrt(1-2GM/r).

    As you can see from the above, 1,2 and 3 are closely related to A, B and C respectively. Is that the sort of relationship you are looking for?
     
  21. Mar 29, 2010 #20
    "Kev": Yessir! Outstanding answer!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: GR effects
  1. Tensors in GR (Replies: 2)

Loading...