# If space curves what is it?

1. Jun 3, 2014

### Duhoc

Is there such a thing as a spatial field containing energy or mass? How do you bend something without either?

2. Jun 3, 2014

### Mordred

space is simply geometric volume, it has no substance or energy it is simply volume filled with the energy-mass contents of the universe. Space curvature is a term used to describe the gravitational influence on matter contained in that volume. On cosmological scales, space geometry is a distibution relation between of matter (positive pressure) and the cosmological constant (negative pressure). The energy-density relations to pressure is determined by its corresponding equation of state

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

the comparison between the universes actual density and its calculated critical density determines if the universe is flat, or positive/negative curved.

http://cosmology101.wikidot.com/universe-geometry
page 2 is here (covers in more detail how geometry affects distance measures in the FLRW metric
http://cosmology101.wikidot.com/geometry-flrw-metric/

3. Jun 3, 2014

### Staff: Mentor

Spacetime curvature is a way of describing of how real objects behave in relation to each other using advanced geometry. In other words, the way objects move and react to each other through the framework of space and time can be very well described using certain mathematical rules, specifically rules derived from geometry. The theory incorporating these rules and explaining how to use them is called General Relativity.

Note that a field is also a mathematical way of explaining how objects interact with each other. Different field theories use different types of math, but like GR, they all serve the purpose of helping us understand the universe around us. Just because GR doesn't use a field doesn't mean it's any more or less correct than other field theories.

Also, to answer your questions, yes, there are fields that contain energy. The EM field contains energy in the form of EM waves. Without energy and mass (or stress), you cannot curve alter the curvature of spacetime.

4. Jun 3, 2014

### Duhoc

I think general relativity describes the curvature of space time. Information, I thought, follows a straight path, which is in fact a curvature of space time. I believe this effect is exaggerated near a black hole where light travels in a circle. How would mass influence the path of an object to which it was not connected unless the space around the massive object was curved. I believe the paradox of force at a distance was what general relativity was designed to resolve.

5. Jun 3, 2014

### Staff: Mentor

Correct.

I don't know what you mean by information following a straight path. GR talks about physical objects and light.

6. Jun 4, 2014

### Mordred

The term space-time has special meaning

"In physics, spacetime (also space–time, space time or space–time continuum) is any mathematical model that combines space and time into a single interwoven continuum"
http://en.wikipedia.org/wiki/Spacetime

" the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations."

http://en.wikipedia.org/wiki/General_relativity

neither GR nor SR tells us that space is made of some fabric, both GR and SR are geometric models that describe the above relations.

here is a good article on GR covering how the mathematical relations work in terms of pressure etc.

http://math.ucr.edu/home/baez/einstein/einstein.pdf

see section 3 where is discusses pressure and the flow of momentum

forgot to mention we did have an extremely lengthy thread that took forever (far too long) to explain the actual meaning of space. Glad that thread eventually got closed lol

7. Jun 4, 2014

### Duhoc

There is obviously a distinction between space and space time. But even so, if spacetime is curved it must have a physical nature because only a physical think can curve. Also, my perception of general relativity, which may be wrong, and which you are free to disabuse me of, is that an object or light is following a path that goes from point to point in space time. Information is passing to light and the object telling it where the next point is. But over a distance this point to point path is curved which is why objects followed a curved path in curved spacetime, in my opinion. What else could be telling an object or light to travel in a curved path? That was an issue Newton ignored and I thought Einstein was trying to answer. You could say gravity, but how does gravity impart that information to the object or light if not through information. I thought they had developed some type of geodesic geometry to illustrate this point, or field tensor, and I am not completely sure what that is. In consonance with this idea, (and incidently, I have heard this idea put forth it is not my impression) that the region around a black hole is so warped that light actually travels in a circle. Then, taking these wild assertions one step further, how could gravity waves propagate if they were not curving space or space time?

8. Jun 4, 2014

### phinds

I think you're missing the point here. "Curvature" is a description of how things move due to the nature of spacetime. There is no "ether" or "medium" through which they move so there is no substance to be "curved", it's all just geometry.

Also, you're right about the curvature being a description of the geodesics which are "curved" when compared to mathematically straight (i.e. Euclidean geometry) lines.

9. Jun 4, 2014

### D H

Staff Emeritus
No, it doesn't. There are several misconceptions here.

One problem is that you are implicitly looking at things from a perspective of Newton's absolute space and absolute time as if that is the "correct" way to view things. Physicists have known for over a century that that view is only approximately correct, and then only when objects are moving very slowly compared to the speed of light, and distances between objects are very large compared to the Schwarzschild radii of those objects. When velocities become large or distances become small you have to completely abandon those Newtonian notion. They aren't even approximately correct to any reasonable definition of "approximate". They are just wrong.

Forgot gravity for a bit. (I'll get back to it later.) I'll start with special relativity. Stealing an idea from the new Cosmos series, let's suppose we have a ship of the imagination, but one that is a bit more bound to reality than Tyson's. Our ship can't go faster than light, it can't backwards or forwards in time. What our ship can do is accelerate wildly (1000 m/s2, or a bit over 100 g), and without rockets. By our watch, our ship will leave the Milky Way behind in a couple of months. In ten more days we'll have reached the Andromeda galaxy. In just three more days we'll have left the Local Group behind. Along the way, we'll see something funny happening to the stars to the side of us and behind us. They'll start migrating towards our front. By the time we've left the Local Group behind, almost all of the observable universe will appear to be directly in front of us, and what was visible light will have become very deadly gamma radiation. (Our ship needs some good shielding, which it has. It's made of unobtainium.)

Are the stars and galaxies truly moving from our rear to in front of us as we get ever closer to the speed of light? It certainly is what we see. If we turn our ship around accelerate in the other direction for 72 days they'll appear to have moved moved back to their rightful places, just shifted by 10 million light years. And how can we have gone 10 million light years in 144 days when the speed of light is the ultimate speed limit of the universe?

If we reverse this process and return home, we'll find a very different solar system and a very different Earth compared how they were when we departed. The solar system will be in a different part of the galaxy, and the continents will have moved. Our 288 day trip will have taken us 20 million years into the future. We haven't done any time traveling. Our little jaunt was the twin paradox, gone wild.

Until we develop that unobtainium-based shell and space drive, our spaceship will have to remain in the realm of the imagination. However, the mathematics and physics of that trip are very real. You have to discard your Newtonian worldview if you want to understand relativity theory.

Another problem with your view is your thinking that something physical must be happening to space-time, that space-time is a physical thing.

All of modern physics has a base below which there are no answers, just descriptions. In quantum theory that base is pretty deep, but it's still there. What does the Higgs exist? What are electrons and quarks, really? Good question. Physics doesn't have an answer. The standard model of physics is just that, a model or map to the world of the very small. In relativity theory, the base is fairly shallow. It's the Einstein field equation. General relativity is the physicist's mathematical description of what happens to moving objects with mass-energy. What makes general relativity happen? Physics doesn't have an answer. General is a map that describes what happens the world of moving objects.

The territories that those maps describe are distinct from those maps. A physicists job is mapping those territories. Don't confuse the maps for the territories.

10. Jun 4, 2014

### Duhoc

Okay, okay. So what all of you guys are saying, is that at this moment, even though we can draw a very accurate map of the curvature of space around a massive object we still have no idea what makes gravity work. Is that correct? I mean there are no gravitons jumping from atom to atom like in an electron telling the nucleus of an atom what to do. All we have is a very, very accurate mathematical description of the curved nature of a gravitational field. Am I correct? There is no intrinsic energy in space, no real curvature of space as if it were a physical object, just for some reason a construct that agrees with the mathematics we see.

11. Jun 4, 2014

### Mordred

correct, we can mathematically define the gravitational influence, we can show its geometric regions of influence. However we have not found the graviton particle as of yet. The rest of your descriptive is also correct

12. Jun 4, 2014

### Staff: Mentor

We have a mathematical way of building models that accurately describes how gravity works, along with other things. Whether space is "actually" curved or not is an unanswerable question. It behaves that way, so it is either curved or there is something else going on that gives the appearance of being curved.

13. Jun 4, 2014

### Mordred

just a side FYI, there is a gravitational quantum field specific to gravity, in much the same way as QED is for electromagnetic force, QCD is for the strong force, QFD (quantum flavor dynamics) is for the weak force. quantum geometrodynamics is for the force of gravity.

http://en.wikipedia.org/wiki/Geometrodynamics.

part of the problem detecting the graviton is the amount of energy required to produce gravitons is projected to be far higher than we can currently produce at any LHC and probably be out of our reach for quite some time. The mere fact we haven't observed a graviton does not discount its possibility.

14. Jun 5, 2014

### Duhoc

So Mordred, this goes back to our initial point. Currently, the common consensus is that there is a gravitational field which imparts information to mass and space, in which case space would have to have some energy, some reality. Perhaps it is even theorized by the standard model and the force of gravity is not a force which acts at a distance.

15. Jun 5, 2014

### D H

Staff Emeritus
The standard model of physics is moot on the nature of gravity. What Mordred didn't mention is that geometrodynamics is a work in progress, and is but one of several competing approaches to quantize gravity. None of those approaches have yet been successful.

16. Jun 5, 2014

### Mordred

yeah I guess I should have mentioned that,

17. Jun 5, 2014

### Duhoc

part of the problem detecting the graviton is the amount of energy required to produce gravitons is projected to be far higher than we can currently produce at any LHC and probably be out of our reach for quite some time. The mere fact we haven't observed a graviton does not discount its possibility.

So I am assuming that there was sufficient energy to create a graviton or gravitational waves at the time of the big bang when there was sufficient energy, and in that instant the imprint of gravity determined the organization of matter going forward. And, in essence, this is what the inflationists had predicted as the Bicep2 results. Mentor, if you don't mind me asking, what precisely do you mean by "quantizing" gravity. Are you referring to a field which exists but is beyond our current ability to observe.

18. Jun 5, 2014

### julcab12

... All things we understood to this point i.e layers of interactions are quantized at a very fine level except for gravity.

.....Although physicists have a workable theory of gravity that involves the gravitational field, and gravitational forces as a curvature of space-time. We have a shaky version of quantum gravity involving gravitons. Assuming graviton. Just as photons are 'packets' of the electromagnetic field, Gravitons would be 'packets' of the gravitational field or space-time curvature apart from the stress–energy tensor.

19. Jun 5, 2014

### D H

Staff Emeritus
You are conflating two very distinct concepts here, gravitons and gravitational waves. Gravitons are hypothetical particle that might arise in quantizing gravity. Gravitational waves are a consequence of general relativity, which is not a quantum theory. Gravitational waves and gravitons are distinct concepts.

Most importantly, physicists do not have a working theory that describes gravitons. They do have a working theory that describes gravitational waves.

Physicists developed a quantum theory of electromagnetic radiation during the first half of the 20th century. There is no quantum theory of gravitation. "Quantizing gravity" is a shorthand term that means developing a working theory in which gravitation is described as a quantized interaction at the atomic scale.