curved space - real or interpretation?

[R. U. Serious]

I'm a layman and have some superficial "knowledge" about relativity and its' effects. However once formulas get into it, I am easily confused.
In popular-science books the authors usually use illustrations and thought experiments to convey some concepts, such as "flatlanders" to explain how we would perceive 4D objects or the bouncing-photon-between-mirrors clock to illustrate time dilation.

Now I am wondering whether "curved space" is also an illustration, one (of several) possible interpretation of mathematical formulas or whether it is the "only"(*) accurate description of reality?

[(*) according to relativity; leaving aside quantum-mechanics for now]

[Surlethe]

AFAIK, general relativity is a result of spacetime curvature, not the other way around: Einstein conceived of gravity as a result of such curvature, and then taught himself the mathematics needed to describe it: mathematics which, incidentally, had been invented some fifty years before by Swedish mathematician Georg Riemann. I'm sure some of the more knowledgeable members will jump in and guide you through Einstein's thought process and the mathematics of Riemannian Manifolds.

[Braedley]

Space is curved around gravity. This is best seen with gravitational lenses predicted by Einstein, and verified through numerous experiments. Also, the results from Gravity Probe B (due in about a year) will also (hopefully) verify more of Einsteins theories.

[R. U. Serious]

Oh, I know about the effects of mass/gravity on light.

But can this not be explained without having to call space "curved"? I thought so.

I have a feeling that my question may have as much to do with semantics and words, as with physics...

[Molyneux]

Oh, I know about the effects of mass/gravity on light.

But can this not be explained without having to call space "curved"? I thought so.

I have a feeling that my question may have as much to do with semantics and words, as with physics...

I'm not sure of the math, but as far as I understand it, gravity is caused by the curvature of space.

[Surlethe]

Oh, I know about the effects of mass/gravity on light.

But can this not be explained without having to call space "curved"?

No. The velocity of light is c: a constant. Thus, according to special relativity, light cannot accelerate. This provides a problem: what happens in a gravity well? Well, gravity obviously can't accelerate light; so, light must travel a straight path. This, in turn, implies a curved line is actually a geodesic, which, in turn, implies spacetime is non-Euclidean. Thus, what we perceive as gravity is nothing more than spacetime curvature.

Does that clear up your question?

[Wyrm]

Oh, I know about the effects of mass/gravity on light.

But can this not be explained without having to call space "curved"? I thought so.

Curving space neatly explains nearly all the experimentally verifiable effects of gravity. It makes sharp predictions about those effects, so when the effects are seen as predicted, GR gets a huge payoff from taking this greater risk of falsification.

The most straightforward way that gravity can deflect light (by giving the deflection as a limit as the mass of light goes to zero) predicts a deflection only half as big as is actually observed. Also, Newtonian gravity fails to fully account for the perhelion precession of Mercury; there is 43 seconds of arc per century discrepency between the Newtonian prediction and the actual observation. Theories that seeks to explain both of these discrepancies using a Newtonian-esque theory all have one thing in common: the introduction of fudge factors.

By assuming space was curved, Einstein's general relativity sharply predicts the magnitude of both the deflection of light and the precession of Mercury's orbit sharply, all without the help of additional fudge factors. Indeed, the limits of the prediction was only the limits of how accurately the gravitational constant G was known.

For this, and other tests sucessfully passed, such as more stringent hurdles for both light deflection and precession rates, the gravitational redshift of light, detectible even in weak fields like Earths (the operation of the GPS depends on knowing the gravitational redshift to a high degree of accuracy more than anything else), and the inspiral of neutron stars (due to energy lost due to gravitational radiation). At cosmological scales, there does seem to be a few discrepencies now explained by dark matter and dark energy, but at smaller scales the agreement of experiment and GR is so good that only a major revolution will overturn GR.

[Kuroneko]

Now I am wondering whether "curved space" is also an illustration, one (of several) possible interpretation of mathematical formulas or whether it is the "only"(*) accurate description of reality?

That spacetime is or can be curved is the only possible interpretation of general relativity, since it was formulated explicitly in the framework of differential geometry. That kind of winner-by-default, however, isn't very interesting. Perhaps your intended meaning is to ask whether GTR is only one of many possible mathematical models that accurately describe observations. The answer to that is "yes," although the the question of which one is "correct" is more philosophical than experimental.

It is certainly possible to reproduce all of the predictions of GTR by working in the flat spacetime of special relativity only simply by introducing some cleverly designed fields that interact with energy. Upon doing so, however, the original Minkowski structure of spacetime becomes unobservable. So, in the end, it would be a choice between "spacetime is curved" and "spacetime is flat, but we can't see that because it acts as if it was curved due to some fields." The former turns out to be simpler both in the Ockhamian sense and having much simpler to for calculating predictions. With sufficient ingenuity and determination, one could also repeat this process for special relativity and have an aether theory instead (interestingly, Lorentz was inventing mechanisms for this before relativity, which is why the "Lorentz transformation" bears his name and not Einstein's), but that's doesn't mean that the resulting monster would be worthwhile. The systems would be observationalyl equivalent, but scientists prefer to think of one as simple and straightforward while the other as an exercise in futility full of ad hoc rationalizations to make the answers match observations.

[Darth Wong]

On a side-note relating to the thread title: from a philosophical standpoint, no physics concept is "real"; they are all just "interpretations". Some of them are just simpler and/or more accurate than others, that's all.

[R. U. Serious]

No. The velocity of light is c: a constant. Thus, according to special relativity, light cannot accelerate. This provides a problem: what happens in a gravity well? Well, gravity obviously can't accelerate light; so, light must travel a straight path. This, in turn, implies a curved line is actually a geodesic, which, in turn, implies spacetime is non-Euclidean. Thus, what we perceive as gravity is nothing more than spacetime curvature.

Does that clear up your question?

Indeed. That seemed elegant and easy to understand. But still feels almost a little bit "like a trick". I though that light sometimes behaves like a particle, and thus gravitys effect on light could be explained. But given that c is constant, that would probably mean, as Wyrm put it, introducing odd fudge factors and the like.

Thanks, Wyrm, for the further proofs and explanations. Some of them were a bit over my head, but the keywords provide good starting points for further delving into the topic.

That spacetime is or can be curved is the only possible interpretation of general relativity, since it was formulated explicitly in the framework of differential geometry. That kind of winner-by-default, however, isn't very interesting.

I didn't know that, at least not epxlicitly like that, so thanks for clearing that up.

Perhaps your intended meaning is to ask whether GTR is only one of many possible mathematical models that accurately describe observations. The answer to that is "yes," although the the question of which one is "correct" is more philosophical than experimental.
[...]

Thanks, I guess I would have asked that question now, if you hadn't already answered it.

On a side-note relating to the thread title: from a philosophical standpoint, no physics concept is "real"; they are all just "interpretations". Some of them are just simpler and/or more accurate than others, that's all.

Good point. It's hard formulating precisely in this area if one is not experienced/practiced, because so much of it is outside/opposite the everyday-experience and "common sense".

Again, thanks to all, you're an amazing bunch in this regard.

[Eleas]

AFAIK, general relativity is a result of spacetime curvature, not the other way around: Einstein conceived of gravity as a result of such curvature, and then taught himself the mathematics needed to describe it: mathematics which, incidentally, had been invented some fifty years before by Swedish mathematician Georg Riemann. I'm sure some of the more knowledgeable members will jump in and guide you through Einstein's thought process and the mathematics of Riemannian Manifolds.

Irrelevant nitpick though it may be, he was German, not Swedish.

[Kuroneko]

Indeed. That seemed elegant and easy to understand. But still feels almost a little bit "like a trick". I though that light sometimes behaves like a particle, and thus gravitys effect on light could be explained.

That's quantum mechanics, not general relativity. What may help is the realization that general relativity rejects the common-sense answer to what reference frame is inertial (non-accelerated). Let's say you are on the surface of the Earth (seems like a reasonable assumption) with a ball in your hand. You throw it and watch the ball fall towards the ground in a parabolic path. Who is stationary and who is inertial? The most obvious answer is found in Newtonian gravity--you are stationary with the respect to the Earth and the ball was accelerated to its center, thus curving what would otherwise have been a straight path (as per Newton's first law).

According to general relativity, if you think in this way, you're delusional. The ball experiences freefall (neglecting atmospheric drag), and it is the freefalling frames that are inertial. On the other hand, you are in an accelerated frame of reference, provided to you by the electromagnetic forces between the atoms of your feet and the ground. The ball's path in spacetime is completely straight--but yours isn't, so the ball's trajectory looks curved relative to you. Your environment is similarly accelerated and hence stationary relative to you, reinforcing the appearance that your trajectory is straight in spacetime.

To put it more simply, the light goes straight, and it is you who curves because you deviating from the natural path in spacetime.

Irrelevant nitpick though it may be, he was German, not Swedish.

On an equally irrelevant note, the spacetime manifold under general relativity is Lorentzian or "semi-Riemannian", not Riemannian.

[Ariphaos]

Indeed. That seemed elegant and easy to understand. But still feels almost a little bit "like a trick". I though that light sometimes behaves like a particle, and thus gravitys effect on light could be explained. But given that c is constant, that would probably mean, as Wyrm put it, introducing odd fudge factors and the like.

Light is considered a particle because it has discrete energy steps. That is, there is such a thing as "one photon" (a single photon has an intensity, which is an integer). In most other respects, it is clearly a wave of some sort - you can look up the two-slit experiment for an example of this, and perform it yourself.

Some like to insinuate multiple Universes out of the fact that the photon seems to instantly know when you cover one of the slits. Running through it myself I never found any reason why the photon couldn't just get split in two - the effects of the two-slit experiment do break down at low intensities IIRC, and light behaves more like a particle.

[drachefly]

The two slit result does not break down at low intensities. Indeed, many experiments have been performed which operate on one photon passing through the device at a time. It's harder to get lower-intensity than that.

[Ariphaos]

The two slit result does not break down at low intensities. Indeed, many experiments have been performed which operate on one photon passing through the device at a time. It's harder to get lower-intensity than that.

The single photon doesn't produce the diffraction pattern on its own, instead producing a scatter effect that, with enough such single-firings, produces the diffraction pattern over time instead of over space. Some consider this to be a more particle-like behavior.

My main point was I see no reason to consider it the result of nearby Universes interfering with the photon in question.

[Wyrm]

The two slit result does not break down at low intensities. Indeed, many experiments have been performed which operate on one photon passing through the device at a time. It's harder to get lower-intensity than that.

The single photon doesn't produce the diffraction pattern on its own, instead producing a scatter effect that, with enough such single-firings, produces the diffraction pattern over time instead of over space. Some consider this to be a more particle-like behavior.

They're wrong. The interference pattern is classic wave-like behavior. That it comes in discrete little chunks over a period of time doesn't matter. The photographic film looks exactly the same, a diffraction pattern over space, no matter how fast it is built up. Classical particles don't behave like this.

My main point was I see no reason to consider it the result of nearby Universes interfering with the photon in question.

You're the only one who's bringing up the nearby Universes, dearheart.

[Eris]

The two slit result does not break down at low intensities. Indeed, many experiments have been performed which operate on one photon passing through the device at a time. It's harder to get lower-intensity than that.

The single photon doesn't produce the diffraction pattern on its own, instead producing a scatter effect that, with enough such single-firings, produces the diffraction pattern over time instead of over space. Some consider this to be a more particle-like behavior.

They're wrong. The interference pattern is classic wave-like behavior. That it comes in discrete little chunks over a period of time doesn't matter. The photographic film looks exactly the same, a diffraction pattern over space, no matter how fast it is built up. Classical particles don't behave like this.

It's classic wave-like behaviour when there's another wave nearby to interfere with it. The messy bit with the one photon experiment is that it produces the interference pattern when there's nothing else around to interfere with it. That's where all those nasty little concepts about superposition and the Schroedinger evolution of the universal wavefunction come in.

The problem here is that there's no real consensus on how this happens anyway. Especially so due to the tension produced by the linear Schroedinger evolution (I think) and the very non-linear process of collapse, and despite work in things like decoherence we still have no solid grounding to say what's really going on in quantum mechanics.

So yes, light behaves as a wave... to the point of causing interference patterns even when it shouldn't. Photons are after a fashion doubly so not classical particles.