What's being curved, when mass bends the spacetime continuum?

[Rayzen]

Yes, "Kraflyn," I was referring to the second meaning of "What exactly is spacetime?"

 

[Kraflyn]

Hi.

A) Prior to special theory of relativity electromagnetism was postulating the existence of vacuum. Vacuum was carrier of all Fourier modes of electromagnetic wave. Electromagnetic wave was considered as real, as waving of electromagnetic field embedded into vacuum. Vacuum was waving with electromagnetic field. There were no photons then. Then came Einstein and special theory of relativity didn't need absolute vacuum nor could have embraced it. So vacuum as something real had to be discarded.

B) Then came QFT. What did QFT do? It introduced creators and annihilators, operators operating on zero field: the vacuum vector. And what does the quantization of creators require? Quantization uniquely requires harmonic oscillators to have minimum energy \omega /2 \ne 0 for each Fourier mode... We heard that somewhere already today, didn't we? ... When summed over all modes, one finds that the energy associated with any particle in its lowest energy state is... infinite. So, regarding to to what did we measure this infinite energy of a particle just standing still? And then quantum vacuum got introduced back again. This time it was introduced in a relativistically covariant manner. And then supernovae teams measured frequencies of photons emitted by Ia SNs and found: a non-vanishing cosmological constant! So vacuum does seem to affect geometry after all...

I hope this explains it a bit. Please do not hesitate to ask about anything related to this topic. I do sometimes mention something one might be unfamiliar with, worth explaining some more.

Cheers.

 

[Muphrid]

I'll say just one more thing and I'll be done with this thread.

The way I see it is... nothing is really being 'curved,' rather the presence of mass causes deviations in the paths of particles, bodies, photons, etc. relative to the part of our universe where there is no mass as we assume behaves in a certain way. That certain way is described by Special Relativity in which the key point is that space and time are unified into what we like to call space-time. Minkowski space-time is the areas in our universe where mass doesn't exist and special relativity works. So it's a build on to say 'curved' space-time, where paths are typically continuous curves like that of a function in math. Again, nothing is being curved.

And that's my take on it.

Interesting perspective. This is rather close to the interpretation of "Gauge Theory Gravity", where the metric and other objects are just fields on a Minkowski background and the relations between these fields give rise to particular geodesics. The predictions are in great agreement with GR for what's in our capabilities to test, and it gives a very clean and obvious footing for doing QM in a gravitational background.

 

[PeterDonis]

This is rather close to the interpretation of "Gauge Theory Gravity", where the metric and other objects are just fields on a Minkowski background and the relations between these fields give rise to particular geodesics. The predictions are in great agreement with GR for what's in our capabilities to test, and it gives a very clean and obvious footing for doing QM in a gravitational background.

This interpretation of GR as a field theory on a Minkowski background spacetime only works for asymptotically flat spacetimes. It works for the solar system, for example (or for other isolated systems like binary pulsars), but it doesn't work in, for example, cosmology. There's no way that I know of to interpret the FRW spacetime that describes an expanding universe in this way, since FRW spacetimes do not have an asymptotically flat region.

(A technical point: strictly speaking, as I understand it, you can always interpret gravity as a spin-2 field on a flat background spacetime in a small local region; what looks like "spacetime curvature" in the standard GR interpretation can always be re-interpreted as the effects of the spin-2 field. The problem arises when the local regions fit together into a global spacetime that isn't asymptotically flat, so you can't extend the local interpretation to a global one.)

(Another technical point: even for asymptotically flat spacetimes, I'm not sure if the spin-2 field interpretation always works globally. I'm not sure it works for a spacetime containing a black hole, for example.)

 

[Drakkith]

I hope this explains it a bit. Please do not hesitate to ask about anything related to this topic. I do sometimes mention something one might be unfamiliar with, worth explaining some more.

Cheers.

Ah ok, that makes more sense. To me a "vacuum" is simply an area devoid of matter.

 

[Kraflyn]

Hi.

No problem. Do ask if You are interested in any particular detail here. For instance, I briefly mention supernovae teams and accelerated expansion of universe. This topic of supernovae suggesting acceleration deserves a thread on its own. However, if one is interested in it in order to clear some points connected to the current topic - why not explaining it, then. A good answer starts with a good question!

Cheers.

 

[buzzdiamond]

Space is made up of magnetism. That's what holds the universe together. Magnetic forces bend and warp due to the constant motion of the objects in the universe. The whole universe pulsates back and forth, expanding and contracting, bound all together by magnetism. Its that simple, or complicated, how ever you want to look at it.

 

[buzzdiamond]

I've been wondering about this for a while now. In order for space to be warped, space itself has to be made of something or have something affecting it which will incline it NOT to be warped in the absence of mass... Sucks that all we can reall say is, "well it's math, get over it." haha

I honestly know next to nothing about physics, but the way I look at it is this, if Space were made up of - or was being affected by something theoretical like (X) and I mean it was just completely jam packed full of (X), and mass has very little (X) or even none at all, then a rock (which has mass) would have equal pressure from all sides pushing on it at all times by (X). Then, when that rock passed close enough by another rock which was also being squished on all sides by (X), there would be less pressure acting on each rock in the area between the two making them move towards each other.

So if I'm right, your question is: what is this (X) which keeps space pushing all this mass together. No idea.

I kinda like those analogies which use the rubber sheets with metal balls on them where the ball kinda sink in showing "warping". Thing is, we know that the connection and elasticity of the rubber is what makes the sheet a sheet and able to support the weight of a ball instead of a bunch of pellets of rubber the ball falls though or breaks apart. If I'm right, what you're asking is: what is this elastic force keeping mass from breaking space or falling through instead of just bending it. No idea. I definitely think (X) is a thing though, probably no one interested in entertaining the idea because it's probably unprovable. Shoot, following this line of reasoning, it's possible black holes are literally where all that mass actually did break through. I'm sure this sounds like complete rubbish to everyone, keep in mind it's all theorizing and speculation :)

Either way, that's the question I'd like to know. If space IS made of something like (X) which keeps it together and nice and taut, I've got lots of theories that would change the way we looked at the big bang.

Space is made up of something, it's called magnetism. Everything in space is moving back and forth, bending and warping, pulsating like a beating heart,
The universe expands and contracts, albeit bound together by magnetic force. It's that simple, or complicated, however you want to make it.

 

[Kraflyn]

Hi.

There are some prominent theories on the electric universe, true. There's even a movie about those theories on electric universe. This might be true in the end, I guess.

Cheers.

 

[Kraflyn]

Hi.

Philspazer, this is exactly what happens in Casimir effect: http://en.wikipedia.org/wiki/Casimir_effect. Your X = quantum vacuum.

Cheers.

 

[harrylin]

Interesting perspective. This is rather close to the interpretation of "Gauge Theory Gravity", where the metric and other objects are just fields on a Minkowski background and the relations between these fields give rise to particular geodesics. The predictions are in great agreement with GR for what's in our capabilities to test, and it gives a very clean and obvious footing for doing QM in a gravitational background.

What is the difference of those perspectives (if any) with Einstein's GR?
'According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration' and ' The existence of the gravitational field is inseparably bound up with the existence of space'. (A.E.1920)

 

[Kraflyn]

Hi.

No impact on GR whatsoever. The question asked about the causal physical theoretical origin and foundation of GR.

Cheers.

 

[StationZero]

I'll let you guys in on a little secret...the aether actually does exist. Long live the aether!

 

[Drakkith]

Space is made up of magnetism. That's what holds the universe together. Magnetic forces bend and warp due to the constant motion of the objects in the universe. The whole universe pulsates back and forth, expanding and contracting, bound all together by magnetism. Its that simple, or complicated, how ever you want to look at it.

Space is made up of something, it's called magnetism. Everything in space is moving back and forth, bending and warping, pulsating like a beating heart,
The universe expands and contracts, albeit bound together by magnetic force. It's that simple, or complicated, however you want to make it.

No, this is not true. Magnetism is but one aspect of electromagnetism and it is NOT what spacetime is "made of", nor does the universe work the way you think it does.

I'll let you guys in on a little secret...the aether actually does exist. Long live the aether!

I'll show you an aether! *shakes a fist*

 

[Kraflyn]

Hi.

Well, according to quantum field theory, all fields are quantized in the end and collapsed into particles. There are no electromagnetic fields there; there are only photons. But this kind of thinking takes us into realm of quantum gravity once we try to embed a photon into curved metric. There is no standard description of quantum gravity yet, and the question "what is curved exactly" still remains there... If we say: "metric is curved", the question becomes: "what is metric physically?" If we say: "magnetism is curving", the question becomes: "what is magnetism physically?" If we say: "XYZ is curving", the question becomes: "what is XYZ physically?" ... If we say "my fist is curving space" ... It's a tricky little question...

Cheers.

 

[bahamagreen]

I suppose what constitutes a geometric explanation has come a long way since Leibniz wrote:

"If the mechanical laws depended upon Geometry alone without metaphysical influences, the phenomena would be very different from what they are." XXI Discours de métaphysique - Baron Gottfried Wilhelm von Leibniz, 1686.

These influences he described as "preserving always the same force and the same total direction".

I suppose we call these metaphysical influences conservation of energy and momentum now and hold them to be subsumed into geometry as the manifestation of certain mathematical symmetries.

 

[Kraflyn]

Hi.

Yes, indeed. Hm... There are issues with general theory of relativity regarding conservation... There are actually 3 issues:

A) Changing potential energy reference level changes physics of objects immersed in geometry. Namely, the constant term that changes referent potential energy level acts as a cosmological constant \Lambda g_{\mu \nu}. And we all know what this does to expanding universe.

B) impulse-flow-density tensor of graviton, t_{\mu \nu} is not conserved, energy is not conserved under co-ordinate transformations... which is maybe a consequence of A)...

C) Both A) and B) might prove to be just consequences of general theory of relativity being non-linear. Namely, in relativity, the energy of a system is not simply sum of energy of constituents. Just consider special theory of relativity: E^2-p^2 =m^2. Not quite linear, is it... On the other hand, in Hamilton-Lagrange formalism, everything is linear. If constituent have well defined actions and lagrangians and hamiltonians, the action or lagrangian or hamiltonian of a system is simply sum of actions of lagrangians or hamiltonians of constituents. And yet, general theory of relativity uses action principle... For instance, if matter and radiation and vacuum field are all present, we just add impulse-flow-density tensors, linearly, and it's all good. Just like quantum theory too: however, quantum theory is linear theory through and through! No wonder we can't really make relativistic extension of linear theories in an acceptable manner. For instance, there are virtual particles in a theory of relativistic quantum fields. My point is simply: there is something wrong with current geometric description known as general theory of relativity. It's not a secret.

So yes, use of geometry has gone a long way since Leibniz.

A discussion on issues regarding general theory of relativity are most welcome on my part, of course.

Cheers.

 

[philspazer]

Holy balls, I just looked up Casimir effect, then quantum vacuum, then

http://www.newscientist.com/article/dn16095-its-confirmed-matter-is-merely-vacuum-fluctuations.html

then LHC, and further and further...
I got to tell ya, I'm just a musician who watches discovery and history channel and I'm feelin really good about myself for figuring out some of this stuff. Thanks for putting science to my imagination and theories Kraflyn, you rock.

 

[Muphrid]

What is the difference of those perspectives (if any) with Einstein's GR?
'According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration' and ' The existence of the gravitational field is inseparably bound up with the existence of space'. (A.E.1920)

GR is a general theory of curved manifolds, and it allows for geometries that aren't topologically flat--stuff with wormholes, for instance.

Theories in which gravity can be accounted for by a field on a flat spacetime background fundamentally can't reproduce any geometry that isn't topologically flat like the background. You can consider other backgrounds, but these have to be entered in "by hand."

The difference in picture is clear, though. Where GR attributes the effects of gravity to an actual curving of spacetime, a field theory will say that spacetime is still flat but the motions of particles and objects are affected by some sort of ever-present field.

 

[harrylin]

[..] The difference in picture is clear, though. Where GR attributes the effects of gravity to an actual curving of spacetime, a field theory will say that spacetime is still flat but the motions of particles and objects are affected by some sort of ever-present field.

That sounds to me as a mere difference in phrasing (except that one allows more than the other, if I correctly understand you). Einstein's GR even has both, as I cited. According to his GR the motions of particles and objects are affected by an ever-present gravitational field and he accounted for that field by means of a "conditioning" of space-time by matter.

 

[Muphrid]

I disagree. To me, GR suggests there is no gravitational field--there is simply the geometry of spacetime, which is warped and curved and which, in turn, affects the motions of test particles. Gravity as a field theory on a flat background doesn't require the conceptual middle man that is the spacetime geometry--there is a gravitational field, and it affects trajectories directly.

 

[Kraflyn]

Hi.

Yes, one may say that metric curvature can be equally well expressed as a field and vice versa. However, how equally well exactly? The difference between field description and curvature description is much like the difference between heliocentric and geocentric picture. In heliocentric picture, orbits are simple ellipses or second order curves, and in geocentric picture orbits are same those orbits plus epicycles. So heliocentric picture is more simple. In GR, gravity is not a force at all, there is no external field. Gravity of GR is a pseudo-force: it depends on Your choice of coordinates. Much like centrifugal force. Some systems have it - some may not. The field complication, much like geocentric epicycles, brings complications. Unlike innocent epicycles, field corrections tend to produce ghosts... Mythical particles that can do ... anything at all really. So field vs. curvature does not necessarily end with a draw. Fundamentally, every theory is wrong, so I'm not pro nor am I contra. I'm just having a conversation :D

Cheers.

 

[Kraflyn]

Hi.

What is exactly this mythical creature called "flat background"? Where did it come from? And why would it be more popular than, say, curved metric?

Yes, there is always a background, it's called vier-bein or tetrad, meaning four-frame. How come we prefer flat? Some of us like curvy a bit more, maybe?

Cheers.

 

[harrylin]

I disagree. To me, GR suggests there is no gravitational field [...]

Thus, as already became apparent, you disagree with Einstein's GR. That is an obvious disagreement of interpretation; the mathematics is necessarily the same.

Hi.

Yes, one may say that metric curvature can be equally well expressed as a field and vice versa. However, how equally well exactly? The difference between field description and curvature description is much like the difference between heliocentric and geocentric picture. [..] The field complication, much like geocentric epicycles, brings complications. Unlike innocent epicycles, field corrections tend to produce ghosts... Mythical particles that can do ... anything at all really. [..]

Hi, I am not aware of that kind of complication due to the field concept, in particular in view of the use of GR math tools to go with it. Does anyone have a concrete example?

 

[Kraflyn]

Hi.

Yes, examples, sorry.

OK, in order to explain precession of Mercury perihelion, field theory on flat background should invoke a force of the form F=GMm/r^2+A/r^3. There should be higher order corrections introduced. And yet, GR solves it elegantly with just V=-1/r.

Let's pay attention to more complicated system now. For example, near a black hole GR predicts an event horizon from just knowing the Newtonean approximation V=-1/r. Now imagine field theory on flat background try produce event horizon at r=2m. Field theory in zeroth approximation believes the only singularity is at origin. In order for field theory to produce another spherical singularity, field theory should begin to introduce singular corrections for no apparent reason. Singular fields should be introduced ad hoc, and You know what happens when we arrive at singularities: we can't handle them. And all that GR had to do is to say: "ah, yes, Newtonean approximation is V=-1/r and hence Schwarzschild radius is exactly at r=2m".

So this is not hard to grasp.

Now, there is something similar happening in quantum field theory. It is defined on a flat background and first ghost became known to it as "Landau ghost". The phenomenon has a standard name now: Faddeev-Popov ghost field. See, for example, http://en.wikipedia.org/wiki/Ghost_fields. Now I'm not saying ghost fields would be absent if flat background was replaced by a suitable metric. Well, ghosts would disappear if we could find such suitable metric: but we can't yet. We don't know how to do it yet. There are too many unknown details about particle interactions. The point is, rather, that there are huge difference depending on the approach one assumes. Flat background or curved geometry?

I hope this explains it a bit.

Cheers.

 

[A.T.]

I disagree. To me, GR suggests there is no gravitational field--there is simply the geometry of spacetime

But the geometry of spacetime is also described by a field. Newtons gravitation is a vector field. Einsteins gravitation is a tensor field:
http://en.wikipedia.org/wiki/Field_(physics )

 

[harrylin]

Hi.

Yes, examples, sorry.

OK, in order to explain precession of Mercury perihelion, field theory on flat background should invoke a force of the form F=GMm/r^2+A/r^3. There should be higher order corrections introduced. And yet, GR solves it elegantly with just V=-1/r.

Sorry this must be a misunderstanding - it was solved by Einstein using the GR toolbox. Thus I asked how his gravitational field concept supposedly hindered him of doing just that, or how it must have been complicating for him. See my posts #41, #50.

Let's pay attention to more complicated system now. For example, near a black hole GR predicts an event horizon from just knowing the Newtonean approximation V=-1/r. Now imagine field theory on flat background try produce event horizon at r=2m. [...]

I did not fully understand the part that I do not cite here, but the misunderstanding may be in the phrase "flat background". I think that Einstein's GR proposes just the contrary, as I cited.

[..] Now, there is something similar happening in quantum field theory. It is defined on a flat background and first ghost became known to it as "Landau ghost". The phenomenon has a standard name now: Faddeev-Popov ghost field. See, for example, http://en.wikipedia.org/wiki/Ghost_fields. Now I'm not saying ghost fields would be absent if flat background was replaced by a suitable metric. Well, ghosts would disappear if we could find such suitable metric: but we can't yet. We don't know how to do it yet. There are too many unknown details about particle interactions. The point is, rather, that there are huge difference depending on the approach one assumes. Flat background or curved geometry?
I hope this explains it a bit.
Cheers.

It does! Thanks.

 

[Kraflyn]

Hi.

You're welcome. Thank You

Cheers.

 

[harrylin]

Just a little addition: perhaps the confusion of terms can be reduced by stating that Einstein's GR models the gravitational field as a "non-flat" background.

And in this context, "non-flat" does not mean that something is literally "curved", but that, as Einstein put it, the metrical qualities of space-time are partly conditioned by nearby matter.

 

[Kraflyn]

Hi.

Yes, terminology is a bummer with GR. For instance, consider an exact solid example: Schwarzschield metric element

\displaystyle\delta s^2 = \left( 1-\frac{2m}{r}\right) \delta t^2 - \frac{\delta r^2}{1-\frac{2m}{r}} - r^2 \delta \Omega^2

Term -1/r is a scalar potential. It is defined at every point of \mathbb{R}^4. As such, it is a scalar field. So, technically speaking, curvature of space-time, i. e. geometry, is defined through fields. All world events happen on curved background. Yet curved background is curved in reference to flat background. Connection between curved coordinates and flat ones being expressed through - fields. This flat background is actually necessarily of higher dimension than the actual space-time, so this makes it even more funky. The flat background never appears in equations because we never want to refer to it. We introduced connections called Christoffel Symbols - these are not tensor, by the way - and once we introduce those, we never ever have to refer to background flat space-time ever again. But that's the second flat background associated with GR we mentioned so far...

So, yes, one should exhibit extreme tolerance and care when trying to decipher the actual and true meaning of each sentence about GR... True story

Cheers.