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So gravity and accel can be transformed into eachother, but what about

  1. Oct 25, 2009 #1
    ...forces? I admit, I can't come up with a torough understanding or mathematical background of general relativity yet, and my thought solely roots in my current reading of Brian Greene's elegant Universe, but still, from the limited - and, admitted, superficial at best - description given there, I wonder why the great theory of gen. relativy focuses so exclusively on gravity and acceleration.

    So, I beg your pardon if this is getting to "popular" for this part of the forum, but where is the reasoning in that? Assuming that Greene is giving a somewhat accurate abstract of the whole situation physics were confronted with back then, one found the unexplained nature of gravity troubling. General relativy linked gravity to a warping of space, according to some variance-principle (I reckon, from my background) the trajectories of objects in space time warped by massive objects suddenly became apparent and everybody went whoohoo.

    But at least to me, from my today's standpoint and judging the rough outline of the line of thought, it appears almost ridiculous how one could possibly have stopped thinking there. admitted, the search for a unifying theory, not to mention a toe, was not to be forseen, but from the above "finally someone provided a reason for the oh-so-mysterious gravitational force and everybody felt how great it was" I'd say that no one really could tell what the colomb force etc. was composed of either (if im not mistaken the s/m wasnt as advanced back then to speak about virtual photons etc, was it?)?

    So, gravity warps space and time and objects move in the curvature? Why wouldnt one have tried to apply the same principle to charge? seems to me that einstein, to name him at least once, was really happy with his newly found explanation for gravity, but somewhat daunted to try to apply the same idea to other forces, leaving the latter to the already established models. the unifying-mood struck some of a lot years later, only?

    so, two forces. both steming from fundamental properties of matter: mass and charge. both inverse proportional to the distance between the interacting objects. both dependent on the amount of fundamental "property". and then, one is sposed to be the phenomenical result of a warp of space and time, making objects move according to a variance principle while the other ... just is there?

    where is the consitency in that?

    please, enlighten me.
    Last edited: Oct 25, 2009
  2. jcsd
  3. Oct 25, 2009 #2


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    Force does exist in GR, but gravity is in the standard formulation explained as a curvature of space-time, not as a force.

    "curvature of space-time" is a bit abstract, you can think of it as drawing your space-time diagrams on curved surfaces.

    If you draw a space-time diagram of two objects with different velocities on a flat sheet of paper, they will depart from each other at a constant rate. Not so if you draw the diagram on, for example, a sphere.

    If, for example, you have two different paths on a sphere, starting at the south pole, and going north, they will follow geodesics on the sphere. Tracing their path, you will see that they initially start to move away from each other. They move apart more and more slowly, and then stop relative to each other when they reach the equator. As you continue north, they stop moving away from each other, and instead approach each other.

    If you explained this with force, you'd say that the bodies were attracting each other - that they intially were moving away, and their mutual attraction caused them to stop moving away from each other and start approaching each other.

    Some references that have more: "Exploring black holes". Sample chapters are online at http://www.eftaylor.com/general.html

    http://www.bun.kyoto-u.ac.jp/~suchii/apple.html [Broken] has some of the explanations of how curved space-time geometry mimics forces as well.
    Last edited by a moderator: May 4, 2017
  4. Oct 25, 2009 #3
    I seem to have made myself not clear enough or you misunderstood me. Either way, your reply is off-topic, sorry. Thanks for taking your time, though.
  5. Oct 25, 2009 #4


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    If you drop a feather and a one tonne weight on the moon (or anywhere else in vacuum), both fall at the same rate. The "acceleration due to gravity" does not depend on the mass of the falling object, and thus can be regarded as a property of spacetime ("curvature"), not a property of the object.

    In contrast, the "acceleration due to charge" is not independent of the "falling" object. Objects with a different charge-to-mass ratio will fall at a different rate.
  6. Oct 25, 2009 #5


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    If I understand your question correctly, you're asking why gravity is treated differently than the other fundamental forces in our current theories of physics--gravity is said to be "not really a force" because it's just spacetime curvature, whereas the other forces (electromagnetic, weak, and strong) are treated as "really being forces".

    There are a couple of ways to answer that question. The first would be to point out some unique feature of gravity, compared to the other forces, that caused it to be singled out for special treatment in GR. As DrGreg pointed out, the equivalence principle is such a unique feature.

    Another way to answer your question would be to say that, actually, physicists *are* trying to come up with theories in which *all* forces, not just gravity, are treated as being "curvatures" of a manifold. The difference is that, to include other forces besides gravity, the manifold can't just be 4-dimensional spacetime; it has to have extra dimensions in order to have enough "room" (loosely speaking) for the curvatures to reflect the effects of the additional forces. When string theorists talk about their models of the universe having 10 or 11 dimensions, this is the sort of thing they're talking about.
  7. Oct 25, 2009 #6


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    As others said:

    Unlike the electrical force, gravitational force accelerates everything uniformly, even massless photons. This is usually only achieved by inertial "forces" in accelerated frames of reference. Hence the idea to view gravitational force as an inertial "force" or just an artefact of an accelerated frame of reference.

    From that follows that frames at rest in a gravitational field are accelerated upwards. Acceleration means a curved path in space-time. A curved path in space-time despite constant space position implies curved space-time.
  8. Oct 26, 2009 #7
    Hm... Does gravity actually "accelerate" photons? Really? Even beyond c? No? But they always move at c, don't they? So there isn't much room for tangetial accel... Gravity steers them, rather.

    DrGreg: Your point, to my understanding, is not valid. The equivalence principle is a result from the equivalence of inert mass and heavy mass - it's not a fundamental property of gravity, so to say (at least this vantage point is just as valid as saying that it allegeldy was).

    No doubt that besides what AT said there are difference between gravity and other forces, gravity and e/m forces being just the most similar ones so i chose them.

    yes, Peterdonis, there are unique features, but just as radon has unique features compared to hydrogen, it didn't justify for one coming up with a elaborate and exact model for describing radon, which completely neglects hydrogen. well, one could, but at least had to admit, that the model is most likely incomplete and eventually find out about radon and hydrogen being composed of the same essence.

    I know about the current efforts for unification fought at all fronts, but this topic is about why BACK THEN not even einstein - who himself heralded the search for a unifying theory - didn't bother that his description of gravity is so radically different from the description of all other forces.

    it would be naive to alege, even today, that one should be certain that unification is actually possible, but the issue is still striking. forces, some of them very similar to gravity, yet so utterly differently described? and NO ONE seemed to have bothered? why? Was there any evidence in these times beyond the fact that for other forces a rather exact model has been found already, that could have justified for gravitation being "singled out" as a space-time curvature?

    btw peterdonis: thanks for the hint on the 11 dimension thing, but once again, that knowledge is of young age :)
    Last edited: Oct 26, 2009
  9. Oct 26, 2009 #8


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    There is no physical quantity called "steering". Every change of the velocity vector is (coordinate) acceleration. In the frame of an accelerating rocket you see light rays bend with by same acceleration as every other free falling thing. The same happens locally in a gravitational field.
    "Very similar" is relative. Inertial forces are more similar to gravity then interaction forces.
  10. Oct 26, 2009 #9
    Well this is a bit misleading. Of course they all fall at same rate. You do not need spacetime curvature, just good old Newtonian physics to explain this. If something has ten times more mass it will require ten times more force to accelerate at same rate. F=ma remember?
  11. Oct 26, 2009 #10


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    But gravity like all inertial forces affects even massless objects. And F=ma doesn't work if m=0. Inertial forces primely quantify acceleration effects. From the acceleration you can derive a force via F=ma, but only for massive objects.

    The concept of force is useless to quantify the coordinate acceleration of massless particles. The concept of space time curvature is more general here.
    Last edited: Oct 26, 2009
  12. Oct 26, 2009 #11
    Both feather and one tonne weight have mass.

    It depends of product of masses in question.

    And space time "curvature" can be regarded as a property of the object (mass) embeded in it.
  13. Oct 26, 2009 #12


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    S.Vasojevic, my explanation was not intended as a rigorous mathematical proof, just an indication of why gravity is different to electromagnetism. I'm assuming the Moon is huge enough to be considered "fixed" (in reality it moves a very tiny amount upwards) and the one-tonne mass is tiny enough that we can ignore any tiny local curvature that it causes. Under those simplifying assumptions, all objects have the same acceleration towards the Moon, regardless of their own mass. The same cannot be said for electromagnetic forces.
  14. Oct 26, 2009 #13


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    Along the lines everyone has been saying, the easiest distinction to draw is between gravity and electromagnetism. Try, for example, to construct some type of theory in which electromagnetism is equivalent to some motion of some frame (a principle of equivalence for EM, if you will). I encourage to OP to really think about this example and delve into equations to attempt to confirm any suspicions about it he may have. I think actually doing such an exercise is much more demonstrative than all the explanations I could give.
  15. Oct 26, 2009 #14
    This was the point, I think. Einstein wasn't the first to realize the similarity between gravity and the pseudoforces observed in an accelerated reference frame.

    This is why gravity is different from other forces, it behaves like a pseudoforce, while EM force does not.
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