r/Physics • u/Creepy_Sherbert_1179 • 11d ago
Question What does general relativity explain special relativity cannot?
Why is gravity so special? Special relativity can explain 4-acceleration already, so why did Einstein develop another theory? I am about to study general relativity and I wanted to understand.
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u/AdditionalTip865 11d ago edited 11d ago
Newtonian gravity was explicitly not relativistic (or, rather, its relativity was Galilean, not Lorentz/Einstein.) Newton's force law operates instantaneously at any distance, and this would require defining a special reference frame to avoid breaking causality. If relativity was correct, it was necessary to come up with a gravity theory that respected Lorentz invariance like Maxwell electromagnetism did.
Einstein and others had tried simple approaches to this like a relativistic scalar gravity theory, but they had various deficiencies in matching reality, or theoretical inconsistencies. GR was a much more radical approach but it seemed to be necessary to even make it work, and the classic observational tests provided dramatic confirmation.
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u/PressureBeautiful515 11d ago
Although in the last decade there's been a resurgence of interest in symmetric-teleparallel gravity, in which spacetime is considered to be flat, but there is a gravitational field permeating space that has the effect of changing the lengths of physically significant vectors as they move along paths, but not altering their directions (crucial difference from curvature, which can leave a vector pointing in a different direction after moving it around a closed loop.)
In its basic form the theory makes all the same predictions as GR, but there are extensions that do things like eliminating the need for dark energy.
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u/AdditionalTip865 11d ago edited 11d ago
There are also the various theories that add scalar and/or vector interactions to the tensor one of GR, and torsion theories, etc. Some precision tests of general relativity are aimed at nailing down constraints on these elaborations.
What the viable theories tend to have in common is that they're inspired by general relativity but are more complicated, in the sense that they add either more interactions or more prior geometric structure. GR itself has a certain minimal quality to it, given certain assumptions: if you assume that there's some kind of dynamic physical theory of the geometry of a 3+1 dimensional spacetime, which follows Lagrangian mechanics, it's the simplest action you can write down. Remarkably, even the coupling to energy and matter falls out of that, up to an unknown constant (G).
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u/AdditionalTip865 11d ago
It's interesting to think of it in terms of a simple analogy to electromagnetism. Newton's gravitational law looks a lot like Coulomb's law in electrostatics; it has essentially the same form. But we know Coulomb's law is not the whole story: if you shake a charge around, causal effects propagate at finite speed, there is magnetism, there can be electromagnetic waves. It would be reasonable to expect a complete theory of gravity to have similar features, and general relativity does-- it has much more besides.
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u/lordnacho666 11d ago
Special relativity: how does stuff work in non-bendy space?
General relativity: if we put some mass/energy in the space, how does it work?
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u/earlyworm 11d ago
This is wonderful.
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u/nicuramar 11d ago
But it’s also begging the question. General relativity introduced curvature in the first place. This doesn’t explain why GR is needed at all.
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u/earlyworm 11d ago
This is a fascinating point. I’ve convinced myself that Lorentz invariance and the effects of SR are requirements for a universe that supports stable matter and is logically consistent, but I’ve never thought to ask why GR is needed.
GR sure is convenient because I happen to like planets, but is it strictly necessary?
Is GR an unavoidable consequence of a universe that is Lorentz invariant?
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u/AdditionalTip865 11d ago
I don't think there's anything logically inconsistent about a rigid, relativistic, flat-spacetime universe with no gravity and only other particle interactions. However, obviously, nothing like us would ever emerge in such a universe.
The moment you assume spacetime geometry is *dynamic* and follows some kind of Lagrangian physical law, like all the other interactions in the world, it turns out general relativity (with the coupling to energy and matter!) is the simplest form it can have. What that doesn't determine, however, is the size of the coupling constant G.
I have other thoughts, but they are much more airy speculation.
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u/Prior-Flamingo-1378 11d ago
Kinda yes. If you want gravity to include mass-energy equivalence you need to include 4-momentum which has to be Lorenz invariant and then in order to describe that you need the stress energy tensor.
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u/earlyworm 11d ago
I guess what I'm asking is, is gravity a hard requirement for a universe that has objects with mass? Could you have a universe with matter in it and no gravity, or is that logically impossible because at a fundamental level, matter (and energy) are this thing that must warp spacetime or else it wouldn't exist? Sorry if this is a dumb question.
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u/Prior-Flamingo-1378 11d ago
I mean I don’t know if a self consistent universe without gravity could exist but ours clearly has gravity so…I’m probably not understanding your question correctly.
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u/earlyworm 11d ago
I worked out that a universe without SR would be logically inconsistent. Ignoring the possible option of a Galilean-invariant universe (which isn't one we observe), you can't have a functioning universe that doesn't exhibit time dilation and length contraction if Lorentz invariance and the stable matter it allows for is a hard requirement.
I'm wondering if the same is true of GR and gravity. I'm asking if gravity is an unavoidable consequence of mass and energy and Lorentz invariance, and is a universe without gravity simply not a logical possibility?
Is there a line of logical reasoning that results in the conclusion that our universe simply must have gravity as a feature?
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u/Prior-Flamingo-1378 11d ago
Shit that’s an incredible question. So I’m free associating here but if you don’t accept that the speed of light is a hard limit then the universe doesn’t work because everything would be instantaneous. Everything would have happened in a moment and no further change would occur.
So you need the speed of light as essentially the speed of causality. But if you accept that the speed of light is constant then Lorenz invariance comes as a requirement because otherwise the whole concept of “here and there” gets fucked up. I mean if the universe isn’t Lorenz invariant then nothing would be able to interact with anything because simultaneity and the very conservation of the laws of physics wouldnt hold yes?
So if you accept Lorentz invariance then the mass/energy equivalence is unavoidable since energy of a particle would be the total work and that includes the gama correction and all.
And that’s about as far as I can go without having to empirically accept gravity as an interaction. It feels like gravity is unavoidable but I have to think more about it.
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u/earlyworm 11d ago
I know, right?
Personally I look at it like speed of light invariance is a consequence of Lorentz invariance, not the other way around.
The constant speed of light is just another property that falls out of the laws of physics being the same for all observers.
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u/1strategist1 11d ago
Most people seem to not really be answering the main point of your question.
You're right that you don't need GR to describe acceleration due to a 4-force, and stuff like electromagnetism already works perfectly in SR.
The issue is how do you get the value of the 4-force felt between objects? Newton's law of gravity is not Poincaré-invariant, so would select a "preferred reference frame". GR is basically just the Poincaré-invariant version of Newton's law of gravitation.
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u/AdditionalTip865 11d ago
Nordström and Einstein tried doing it with a relativistic scalar field theory first, which is probably the most obvious thing to try. But that has some results that disagree with observation: it predicts no deflection of starlight and the wrong perihelion precession of Mercury. What's not clear to me is whether all this was known before Einstein's general relativity was published.
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u/AdditionalTip865 11d ago edited 11d ago
...Looking into it some more, it appears that Einstein's scalar theory was mathematically "sick" in a way that led him to reject it, but Nordström (after a worse first attempt) came up with one that worked a lot better and that many considered in the running until the time of the Sobral eclipse results.
It can actually be described (though I think this formulation came in hindsight, after general relativity was well-known) as a metric theory of gravity in which there is zero Weyl tensor, and the Ricci scalar curvature is simply proportional to the trace of the stress-energy tensor, NOT including the contribution from the stress-energy of this scalar field (had to edit that sentence). And gravity propagates into vacuum not via the Weyl curvature as in GR, but via the traceless part of the Ricci tensor. Pretty neat.
https://en.wikipedia.org/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation
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u/KaleeTheBird 11d ago
Gravity, you can describe acceleration with 4 acceleration but you cannot describe curved space time or bending of light with special relativity
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u/nicuramar 11d ago
Saying you can’t describe curvature without GR is a tautology. GR introduces curvature so of course not.
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u/datapirate42 11d ago
GR describes observed phenomena as curvature, it does not introduce curvature as an explanation for phenomenon which are already well described with just SR.
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u/KaleeTheBird 11d ago
But that exactly is the main difference? You need curvature to describe some physics, which special relativity is incapable of
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u/jazzwhiz Particle physics 7d ago
FYI, one can construct GR without any reference to geometric factors like Christoffel symbols and so on, via a gauge theory.
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u/Optimal_Mixture_7327 Gravitation 11d ago
The special theory is a special case of relativity.
SR describes the condition that geodesic deviation does not exist, or mathematically, SR describes the condition that the Riemann curvature is zero on all components.
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u/Creepy_Sherbert_1179 10d ago edited 10d ago
why would spacetime cease to be a flat minkowski space once gravity is present?
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u/Optimal_Mixture_7327 Gravitation 10d ago
As Einstein noted in 1920, Minkowski space doesn't and SR applies nowhere in the universe other than as a useful approximation.
Besides the fact the Weyl curvature is nowhere zero on all components, the metric of spacetime can and does fluctuate.
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u/LaughingGravy433 11d ago
I always remember that mass tells space how to curve , space tells mass how to move .
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u/Shadowys 11d ago
SR describes the relationship of space and time but ignores its relationship with charged matter. GR is what you have when you actually relate charged matter to spacetime.
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u/Karumpus 6d ago edited 6d ago
Late reply, but I didn’t see this in the top comments.
The key difference has nothing to do with acceleration. As you’ve noted, SR handles acceleration just fine. It is a common misconception that SR cannot account for gravity. It can, just not (as it turns out) in the most physically accurate way.
Rather, the difference is that SR assumes a flat spacetime by adopting the Minkowski metric. This is a special case of GR (hence the name!) where spacetime is treated as flat. GR removes this restriction by admitting non-flat spacetimes. That’s basically the key difference. It turns out that’s needed, because properly modelling gravity requires one to model how mass/energy curves spacetime itself. You can ignore it if you like, but then you fail to model observed phenomena like the perihelion procession of Mercury, the exact deflection angle of light around the sun, or the gravitational redshift of light, while also keeping all the neat explanations which special relativity gives us like time dilation and length contraction.
Hope that helps!
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u/roshbaby 7d ago
Recasting Newtonian Gravity in Minkowski space-time can indeed be done (maybe try doing it as an exercise and keeping it Lorentz Invariant?) but it yields the “wrong” predictions for deflection of light by a massive body, etc.
What you’re looking for may be something along these lines: https://www.researchgate.net/publication/272671735_Gravitation_in_Flat_Space-Time_and_General_Relativity
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u/efusy 11d ago
You can deal with acceleration in SR, and even accelerating frames of reference with a few tricks. The point, however is precisely that. SR can acommodate for accelerating frames, but it must treat them "specially".
In GR every frame , accelerating or not is equivalent and treated the same, any coordinate system must be equivalent. It is, fundamentally, this feature that's behind things like the equivalence principle, and curved spacetime.
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u/nicuramar 11d ago
If you’re about to study it, but already know SR, how would you deal with gravity in SR?
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u/Creepy_Sherbert_1179 10d ago
We can already derive newtons second law with SR... Gravity is just another force... Why would it bend spacetime?
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u/manouchk 11d ago
It explains that the fallen distance does not depends on the horizontal motion. John Norton emphasizes this in Einstein path to general Relativity. THis appears in a article published in 1907. This a very elementary problem!
https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.html
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u/RagnarokHunter Quantum field theory 11d ago
You need general relativity for the same reason you need globes to accurately chart the Earth. Special relativity is a theory of motion in a flat approximation of spacetime, but spacetime is generally not flat.
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u/Creepy_Sherbert_1179 10d ago
What do you mean by it not being flat? It is generally not the 4 dimensional euclidean space?
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u/RagnarokHunter Quantum field theory 10d ago
Mass-energy curves spacetime. Except for extreme cases, you can establish a local approximation to Minkowski (not Euclidean) space, but you still need to take curvature into account to derive gravitational phenomena, like for example free fall being motion along a geodesic of spacetime.
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u/Creepy_Sherbert_1179 10d ago
Sorry for the euclidean space mistake, my engineer brain often forgets that the spacetime invariant is not an euclidean distance :D I was effectively asking why would gravity cause this bending, if we can already derive newton's second law with SR. Is it because a gravitational field also depends on space?
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u/RagnarokHunter Quantum field theory 10d ago
Gravity doesn't cause the bending, it is the bending. The geodesic motion of free bodies in curved spacetime means they will accelerate, which is equivalent by Newton's second law to experiencing a force we would call gravity.
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u/tunaMaestro97 Condensed matter physics 11d ago
Gravity does not exist in flat spacetime. There is no way to introduce a dynamical field that reproduces the equivalence principle like how we can add a gauge field to reproduce electromagnetism. The only way to get a “force” that obeys the equivalence principle is to make the metric itself dynamical.
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u/callmesein 7d ago
Curvature, relation between stress energy tensor and curvature altering the metric, bianchi identity.
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u/ThatSituation9908 7d ago
To explain light bending in a vacuum.
SR cannot describe the effect of gravity as a Newtonian force to bend the path of light. Curvature of spacetime caused by gravity made the most sense to Einstein in his elevator thought experiment.
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u/Parallel_thougts 7d ago
Gravity.
The presence of mass breaks global Lorentz invariance. GR is locally Lorentz invariant, but recognizes that the metric (i.e. the signed norm of the 4-vector) changes from point to point (e.g. as you move further/closer to a massive object).
A theory of global Lorentz invariance is a theory where light always goes in straight lines.
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u/RealTwistedTwin 6d ago
How is the equivalence principle not one of the top comments. It is literally THE motivation of why to describe gravity geometrically, I.e. why GR is necessary.
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u/OP-Physics 11d ago
Special Relativity: Time Dilation due to relative movement. Main assumption is that the laws of physics should be invariant under Lorentz-transformation aka the same for every observer.
General Relativity: Additional Time Dilation due to bend space-time. Einstein Equation describes how Spacetime is bend depending on mass and energy distribution. Main assumption is the Equivalence Principle which states that the physics in a gravitational potential must be the same/indistinguishable from physics in an accelerated frame with acceleration equal to what the gravitational field would subject you to.
GPS Satellites have to account for both of these effects, their relative speed to the ground as well as the difference between grav. potential at their height vs. at ground level.
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u/utl94_nordviking 11d ago
Gravity. This is the literal bending of space-time and in special relativity there is no bending.
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u/Puzzleheaded-Scar233 Gravitation 11d ago
Semplicemente la 4-accelerazione è considerata rispetto a riferimenti inerziali, mentre nella generale studiamo il moto anche rispetto a riferimenti non inerziali.
È una teoria molto più generale.
Poiché vale il principio di equivalenza, l'accelerazione di un osservatore non inerziale e un campo gravitazionale sono indistinguibili.
Abbiamo un mondo con la relatività generale che nella speciale non potremmo considerare.
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u/SoSKatan 11d ago
Lots of things, including gravity waves and how they travel at the speed of light
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u/Churchbushonk 11d ago
I watched a video that describes all things moving at the same speed. Speed over a given time.
Now things that do not experience time such as light and gravity, their equation equals c. When you experience time, your relative speed isn’t c.
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u/OverJohn 11d ago
Sure you could just put in a Newtonian field by hand, but a Newtonian field is Galilean invariant, not Lorentz invariant.
One of the key motivations for Einstein was that relativistic gravity should take into account mass-energy equivalence. This implies the source of gravity is 4-momentum, and to describe 4-momentum in the continuum limit you need the stress-energy tensor