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What is the value addition of GR?

  1. Jun 26, 2015 #1
    What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same.

    I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of objects as geodesic equations instead of gravitational potential, force law and acceleration vectors like defined in Newtonian Gravity.

    But apart from the nice way of reformulating the field equations, force law, Equations of motion in terms of geometry, did it explain/predict stuff which cannot be explained through the original gravitational field equation, force laws and SR like the bending of light due to gravity.
     
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  3. Jun 26, 2015 #2
    This appears to be a very generic question. GR gave a wealth of new insights into topics such as gravitational waves, shifting orbital precessions, redshifting of EM waves as they travel away from gravitational potential wells, and pretty much wrecked the idea of gravity being a "force", alongside forcing us to rethink about performing calculations which would otherwise be elementary in the Newtonian framework (and I haven't even pointed out 10% of the ideas [introduced or tweaked] that GR contributed to yet). You can read plenty more by a quick Google search :wink:

    EDIT: Unlike SR, not all calculations in GR are "tweaks" of non-relativistic formulae.
     
  4. Jun 26, 2015 #3

    PAllen

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    Also, there is really no such thing as SR + Newtonian gravity. Its action at a distance in incompatible with SR, and this was immediately seen by physicists after 1905. Thus many were working on a resolution, some of which worked well enough (e.g. Nordstrom's second theory), but conflicted with experiment. GR won out because of match over time with observations (elegant logical basis was nice, but would have been irrelevant if there was conflict with observation).
     
  5. Jun 26, 2015 #4

    pervect

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    Newtonian gravity, with instantaneous action at a distance, isn't really compatible with special relativity. Which is why GR was developed in the first place, to have a theory of gravity that was truly compatible with special relativity rather than just a make-do hack that would work in limited circumstances.



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    Yes. Aside from the theoretical considerations, GR has predicted a lot of observed phenomenon, the harvard tower experiment for gravittional time dilation being one of the more famous. In a similar vein, see the scout rocket experiments. Timekeeping has gotten so precise that we need to routinely adjust for these effects.

    Some of the other effects, such as increased light bending, perihelion precession, the shapiro effect, and most recently frame dragging (gravity probe B), are more in the nature of minor corrections but have been observed accurately enough to confirm them. GR has had a great impact on cosmology, as well - it did not quite predict Hubble expansion, but was instrumental in explaining it.
     
  6. Jun 26, 2015 #5

    phinds

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    Uh ... the right answer when you do cosmological gravitational calculations, as opposed to the wrong answer.
     
  7. Jun 26, 2015 #6

    Nugatory

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    The precession is particularly interesting (well, at least to me) because it was observed in the orbit of Mercury shortly after Newton. It puzzled people for the next two centuries, until GR was discovered and we could say "Aha! So that's what's going on!".
     
  8. Jun 26, 2015 #7

    atyy

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    For things like the orbit of mercury, GR and be thought of as SR + "Newtonian Gravity modified" - the important point is that Newtonian Gravity without modification is not compatible with SR.

    For things like the accelerated expansion of the universe, GR goes beyond SR + "Newtonian Gravity modified", because the background is no longer flat spacetime.
     
    Last edited: Jun 26, 2015
  9. Jun 26, 2015 #8
    Thanks for the responses.
    1. I see the "action at a distance" problem was resolved
    2. Mercury's orbit was explained well
    3. Gravitational time dilation is a good one apart from increased light bending and other such experiments got confirmed
    But from what I get from your responses, apart from the different stuff related to how Gravity acts on light, the theory found most use in explaining or bringing about breakthroughs in cosmology I suppose and I see there are additional experiments created to confirm GR. I understand GR is the most correct theory until now but my question was more related to what additional value it brought in explaining things around us and providing breakthroughs in understanding more about the universe and resolve things which have been puzzling us like say Mercury's orbit. For instance solving actual physical problems which werent resolved (and could never have been resolved through existing physics) or adding accuracy to existing solutions.

    I understand that there is a competitor theory called Brans-Dicke theory which also uses Metric Tensor based approach. But is there any other theory which had tried explaining these above effects without invoking curvature but modifying newtonian theory, incorporating the constancy of speed of light and maximum speed of transmitting change ... but retaining flat space time?

    @Nugatory - To explain Mercury do we necessarily need GR or is it just that it was a slick tool which could churn out answers easily. I am not aware of the nitty gritties of the calculation and hence curious. Like for instance the results of double slit experiments cannot be explained without quantum mechanics - it was not a slick tool but just that the normal classical approach was just plain wrong and wouldnt work whatever you do.
     
  10. Jun 26, 2015 #9

    robphy

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  11. Jun 26, 2015 #10

    Mentz114

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    Definately not a slick tool. The equations for the orbits of planets come from a strict calculation which allows no room to fiddle anything. The amazing thing is that the exact closed solution was not found until about 2002. GR is definately needed to explain the anomalous precession of the orbit of Mercury.
     
  12. Jun 26, 2015 #11

    russ_watters

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    You forgot to mention time dilation and the Harvard tower experiment. Without understanding GR's impact on the timekeeping ability of clocks, GPS would be difficult or impossible to make work.

    Whether you consider all of these things important or not is really up to your personal preference, but most science types consider the 1-2 punch of SR and GR to be among the greatest discoveries in the history of science. Enough to make Einstein a rock star on the order of Galileo or Newton.
     
  13. Jun 26, 2015 #12

    PAllen

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    As I mentioned earlier, Nortdstrom's second theory was the best attempt of this type. However, it gave no deflection of light and a much too small perihelion shift for Mercury. (Note, there are formulations of Nordstrom's second theory that use a non-flat metric, but it was originally formulated with Minkowski metric, and that is the formulation most closely meeting your desire).

    I would not consider the so called Post-Newtonian expansion approach in GR as meeting your criteria because it still uses non-flat metric, rather than the flat Minkowski metric.

    As noted, correctly predicting the perihelion and light deflection is what defeated all reasonable pure SR based approaches.
     
  14. Jun 26, 2015 #13

    pervect

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    I'm not quite sure of the intent of the question, really. Percentage-wise, the biggest inaccuracy you'll get by not using GR comes with high velocities, the error being 2:1 for light deflection. Other effects show up mostly when you need high precisision, such as (for instance) trying to get centimeter resolution out of GPS.
     
  15. Jun 26, 2015 #14

    pervect

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    If I may draw a colorul analogly, asking "why does GR need a curved space-time" is rather like saying "why do we use a globe to get accurate maps for the Earth". The answer in both cases is that the underlying geometry isn't flat. The formal mathematical details are somewhat involved, but that's the basic principle. Note that by the time you have SR, you already have (well, should have) the fundamental idea that the geometry of space and time is intertwined, into the geometry of space-time, as measured by the Lorentz interval. GR just describes the fundamental geometry of space-time near massive objects. The geometry is what it is, trying to do away with GR conceptually is rather like trying to get a working theory for navigating around the Earth with a flat Earth.
     
  16. Jun 27, 2015 #15
    Let me put this differently.

    There are three uses for any theory.
    1. Reformulation : One use of a new theory could be an effective reformulation of an existing theory to help solve problems in an easier way which otherwise would have been cumbersome if done in the original manner like say some problems could be solved easily if we choose a different coordinate system (say polar coordinates instead of cartesian) or some problems get solved easily through the Lagrangian formulation. So in this case the idea is to take an existing theory and reformulate it for easier use but not modifying the "algorithmic complexity or algorithmic content" resident in the theory.
    2. Revision: Another use of a new theory would be to explain phenomenon which otherwise cannot be explained by existing theories. It removes an inconsistency/gap between existing theories and observations by modifying existing theories, like what quantum mechanics did. This means that the existing theory has a certain "algorithimic content" to it but that doesnt match up with the "algorithimic content" of nature as observed through experiments. There is something more which is present in nature, which is not present in the existing theory. That gap or impedance mismatch is corrected by revising the theory. This is a more fundamental use than just reformulation.
    3. Interpretation: Another use of a new theory is that it helps gain greater insight into why things are the way they are. It doesnt help problems to be solved in an easier way or remove inconsistencies between existing theory and observations. It helps in understanding nature in a more graspable manner for the human mind. It is a new way to articulate mathematical symbols so that it helps us gain greater insight into the "heart' of the theory.
    Now for a thought experiment or a thought situation analysis:

    If suppose we assume light speed is not constant and there is no speed limit in the universe, then we would not have the space time concept as propounded by SR. But even in that situation, a geometric reformulation of newtonian gravitational field will make sense because of the equivalence of inertial and gravitational mass. In that context GR would just be useful as a reformulation tool rather than revision. But as experiments have vouched for constancy of the speed of light, it was imperative that the newtonian or gallilean mechanics needed to modified and so SR came about to set that right. But with the revised mechanics, newtonian gravity didnt work well and hence GR apart from its effective reformulation which was nevertheless useful as reformulation and interpretation tool, also incorporated SR into newtonian theory of gravity by revising it. So it in a way it did all three.

    My question was if suppose I am not interested in the geometric reformulation but only interested in modifying Netwtonian theory to incorporate SR could we have come up with another way of theorizing the same thing without bringing geometry into it. Why I say that is in formulating classical electrodynamics field theory, they didnt have the ability to redefine geometry due to the fact that force was not proportional to the inertial mass (ofcourse there was magnetism caused due to a moving charge and quantum mechanics later which really made it all clumsy and so inspite of the nice inverse square parallel with gravity exemplified by gauss law because of the other things which happened in EM , it developed in a completely different way and no one attempted to write field equations using metric tensors in that case). But again I suppose if there was no quantum behaviour in the world and assuming there was no SR and no magnetism, then we would have two forces dictated by inverse square laws one depending on charge and one on mass. In electrodynamics masses dont cancel out and hence a geometric formulation might not make sense but in the other it will make sense.

    In essence Newton could have attempted a geometric reformulation of his theory before Maxwell equations just that he would have dealt with a curved 3 dimensional space, curved due to the presence of mass. If suppose he had done that then, after SR came about due to maxwell's equations, then we just needed to have changed that geometric reformulation to include SR by extending the formulation from 3D space to 4D minkowski space time and curving that. In a way I am revising history to understand the value GR brought to the world or rather splitting GR into two theoretical components if you will - one the geometric formulation of gravity and the other - the inclusion of the constancy of the speed of light. Both are if you will linearly independent theoritical components. This makes me wonder if we can always create a theory of gravity which can include SR but not be a geometric formulation. I wonder if someone has attempted that.
     
  17. Jun 27, 2015 #16
    I find your question puzzling, as GR was originally presented as principle theory as well as field theory - and nevertheless it had a geometric formulation. Geometry is unavoidable in SR and GR because length measurements depend on the used reference system. How could you avoid geometry in an alternative formulation? Probably you should clarify that before meaningful answers can be given.
     
  18. Jun 27, 2015 #17

    Mentz114

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    SR is a geometric theory so it would seem a natural thing to extend it to be 'general' and include gravity. One of Einsteins key insights was the existence of a special state of motion - i.e. free fall. In this state the faller feels 'weightless'. The problem with a non-geometric (dynamic) theory is getting rid of the force of gravity in this state. GR handles this with the concept of geodesic motion. This is profoundly different from Newtons dynamic gravity.
     
  19. Jun 27, 2015 #18
    Geometry is unavoidable in SR as SR redefines the stage. But then GR is about Gravitational force/field like Maxwell's equations is about EM force/field. Both are classical forces (I am not bring in QM here - let us leave it out of the discussion now). It so happened that in case of gravitational force it is proportional to Gravitational Mass which "miraculously" was also equal to the inertial mass and so Gravitational Field theory could be formulated in a geometric way while EM field theory couldnt be - this has nothing to do with SR. Even if there we no SR, GR could be articulated in a geometric way - for instance newton could have done it but it wouldnt have accounted for SR but that will have come later. When I mean geometric way, I mean how Einstein articulated the field in terms of the modifications in the geometry of space and all objects irrespective of their masses traveled in straightlines/geodesics in that newly formulated space. In other words, he mathematically absorbed gravity into the space formation and that formulation though incorporated SR has nothing to do with SR but to do with the fact that Gravitational Mass and Inertial Mass are same and that was the beautiful "elevator" thought which inspired Einstein.

    That is not true in the case of EM as EM field or force was proportional to charge and not mass ,and so masses and charges dont cancel out and so EM field theory couldnt be formulated in an elegantly geometric way like Gravitational field theory could be. So if suppose Gravitational mass is not equal to inertial mass, then this nice geometrical formulation wouldnt be feasible. What I am saying is for a moment, let us not assume that fact (GM=IM) and formulate the field theory like how we had done for EM where (Q was not equal to IM) and lets see where we get.
     
  20. Jun 27, 2015 #19

    Mentz114

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    What you get is a theory which is GR when GM=IM is assumed, and one which gives incorrect predictions when GM is assumed not equal to IM.

    This comment is based on the Field Theory Gravity which according to Feynman, Deser and others is GR.

    See
    Field Theory of Gravitation: Desire and Reality
    Yurij V. Baryshev

    here http://arxiv.org/abs/gr-qc/9912003
     
    Last edited: Jun 27, 2015
  21. Jun 27, 2015 #20
    No it is not because SR was a geometric theory that Einstein found it natural to make GR as gravitational theory. SR's geometry insight is different from GR's geometry insight. SR geometry insight is about adding a 4th dimension and mixing time with space because of the constancy of speed of light which played havoc with the time dimension. GR's geometry insight is about baking a force into geometry - completely different inspirations and that Einstein was able to bake the force into geometry only because gravity was such a force which can be baked into geometry because GM=IM. If Einstein had lived in Newton's time, he would have done it then. And then SR would have come about and then GR would have been modified to incorporate SR. Unfortunately the order of formulations were different and hence Einstein did both at one shot - geometric formulation of gravity and incorporation of SR in gravity.
     
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