What is space-time made out of ?

[scott]

What is space-time "made out of"?

A thread in another forum about the definition of "nothing" got me thinking. I know matter is composed of molecules, which are composed of atoms, which are composed of electrons, neutrons and protons, which are composed of quarks, etc ...

But what about space-time itself? Since in General Relativity space-time is said to be curved, it must exist as a thing in some way. If mass or matter is thought of as "clumps" in space time, and matter is composed of clumps of atoms and so forth, does "empty" space, i.e. space with no rocks, gas or dust clouds, etc .. just a vacuum, contain sub-atomic particles as well, just perhaps not as bunched together?

And I also understand that in our universe matter is neither created nor destroyed, only rearranged. Was all the matter in the universe created in the Big Bang, or was it already there, and the Big Bang merely changed its form?

 

[GRQC]

Originally posted by scott
does "empty" space, i.e. space with no rocks, gas or dust clouds, etc .. just a vacuum, contain sub-atomic particles as well, just perhaps not as bunched together?

Some simplified answers to your questions: empty vacuum has been shown to not really be "empty", but instead to be a sea of quantum energy fluctuations. That is, tiny energy-anti-energy "bubbles" appear randomly, but only last for a specific period of time imposed by uncertainty principles. As to what the actual "fabric" of spacetime is -- who knows!

And I also understand that in our universe matter is neither created nor destroyed, only rearranged. Was all the matter in the universe created in the Big Bang, or was it already there, and the Big Bang merely changed its form?

Very good question, to which no one has a clear answer (and if they claim to, they're lying!). In fact, to further complicate matters, the notion of "before" the Big Bang is not well-founded (unless you subscribe to cyclic bang/crunch theories, or other bizarre brane-world ones).

 

[wolram]

https://www.physicsforums.com/archive/topic/5732-1.html

this topic has been discused on PF before, have a
look at this link.

 

[Deeviant]

Sugar and spice and everything nice?

 

[chroot]

The terms "space-time" and "gravitational field" are basically interchangeable. If it weren't for mass, there would not really be any space-time.

But I guess that doesn't really help answer the question.

- Warren

 

[pmb_phy]

But what about space-time itself? Since in General Relativity space-time is said to be curved, it must exist as a thing in some way.

Spacetime is not made out of anything.

In General Relativity a region of spacetime may or may not be curved. Its curved only when there are tidal forces present. A region in which there is a uniform gravitational field the spacetime is flat.

Originally posted by chroot
The terms "space-time" and "gravitational field" are basically interchangeable.

In an inertial frame of referance in flat spacetime there is still spacetime. However there is no gravitational field in that case so the terms are not synonymous

 

[chroot]

Originally posted by pmb_phy
In an inertial frame of referance in flat spacetime there is still spacetime. However there is no gravitational field in that case so the terms are not synonymous

It's semantics. Some authors would say that in the absence of mass, space and time are "separate," and thus space-time does not really exist. Some authors (Wald, etc.) have made the point that "space-time" and "gravitational field" are synonymous -- I'm not the first person to say it. Whether or not it's a useful thing to say, however, is certainly up for debate.

- Warren

 

[GRQC]

Originally posted by pmb_phy
Spacetime is not made out of anything.

In General Relativity a region of spacetime may or may not be curved. Its curved only when there are tidal forces present. A region in which there is a uniform gravitational field the spacetime is flat.

This isn't true. Tidal forces are strictly determined by a non-zero Weyl tensor. The Ricci tensor can exist for constant curvature (where the Weyl tensor is zero). After all, that's the basis of the cosmological principle: vanishing Weyl tensor (no tidal forces, no gravitationally preferred direction -- and thus isotropy).

 

[pmb_phy]

Originally posted by chroot
It's semantics. Some authors would say that in the absence of mass, space and time are "separate," and thus space-time does not really exist. Some authors (Wald, etc.) have made the point that "space-time" and "gravitational field" are synonymous -- I'm not the first person to say it. Whether or not it's a useful thing to say, however, is certainly up for debate.

- Warren

Do you have a referance for where Wald said that? I'd like to see the context in which he said it so I can understand exactly what he meant.

Thanks

 

[chroot]

Originally posted by pmb_phy
Do you have a referance for where Wald said that? I'd like to see the context in which he said it so I can understand exactly what he meant.

Thanks

I'll try to find the passage when I get home tonight -- I don't have the book with me here at work. It might have actually been in Foster and Nightingale's "Short Course on General Relativity." I'll try to find it.

- Warren

 

[scott]

So are you saying then, that massive objects which exist create a field between them, a gravitational field, and this field can be flat or curved depending on the mass of the objects? Is the gravitational field anything like an electrical field or a magnetic field?

Is the gravitational field at all analagous to the fields (forces)which attract electrons to nuclei and which keep protons and neurtrons together?

So space-time is just this gravitational field?

 

[chroot]

Originally posted by scott
So are you saying then, that massive objects which exist create a field between them, a gravitational field, and this field can be flat or curved depending on the mass of the objects?

Yes. Mass curves spacetime, and curved spacetime makes masses move. According to the general theory of relativity, gravitation -- the attraction of two masses to each other -- is the result of those objects moving through curved spacetime.

Is the gravitational field anything like an electrical field or a magnetic field?

In some respects it is, but in other it is not. Gravity is like E&M in that forces fall with the square of the distance. It is unlike E&M in that the forces are "ficticious." It is also unlike E&M in that (so far, anyway) no one has been able to determine a suitable gauge group for gravity. E&M, on the other hand, has just about the simplest possible gauge group.

Is the gravitational field at all analagous to the fields (forces)which attract electrons to nuclei and which keep protons and neurtrons together?

Not really, no. There are very, very many differences between gravity and the other three forces.

So space-time is just this gravitational field?

In a sense -- but don't snarled up in the definition of the words.

- Warren

 

[lethe]

Originally posted by chroot
The terms "space-time" and "gravitational field" are basically interchangeable.

i would say spacetime is a manifold, and the gravitational field is the metric on that manifold.

in other words, i do not think they are quite interchangable

Originally posted by chroot
If it weren't for mass, there would not really be any space-time.

oh? so what is the meaning of vacuum solutions to Einstein's equation which are not Minkowski space? these can have nontrivial gravitational fields. you can have gravitation even in the absense of all matter.

and of course, see my above objection: spacetime is not the same as metric. Einstein's equations cannot even be formulated in the absence of a spacetime.

 

[pmb_phy]

Originally posted by lethe
i would say spacetime is a manifold, ...

There is a manifold which is the mathematical representation of spacetime if that is what you mean?

...and the gravitational field is the metric on that manifold.

Now that I agree with!

 

[lethe]

Originally posted by pmb_phy
There is a manifold which is the mathematical representation of spacetime if that is what you mean?

well, i don't really like arguing semantics, so i will just say that all these things are words that we use to represent elements of our models. these elements of our models are mathematical structures, like the manifold.

an implicit assumption in science is that we expect our models to accurately describe the real world. the more starry-eyed among us begin to not distinguish the model from the real thing, and then we freely abuse the language and say things like:

"spacetime is a manifold"

 

[rocketcity]

I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory.

Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do we not use the fact that gravitational fields are conservative to develop a scalar potential, formulate gauges, obtain Maxwell-esque equations, etc.?

How is it that photons come tantalizingly close to having mass--they are affected by grav fields, they have a non-zero momentum and can impart some of it to massive objects--but have no charge-like properties?

To put my question another way (reminiscent of Jackson's Chapter 0), grav and e-static potentials can both be written as some function of r times r^$$\epsilon$$, where $$\epsilon$$ is some number. Why is it that, in both cases, the 'some function' is just the number one, and the epsilon is (confirmed to a very high degree of precision) exactly negative one?

Just wondering.

P

 

[lethe]

Originally posted by rocketcity
I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory.

the fact that in the static limit, the gravitational and electric force both obey the inverse square law is not at all surprising. it has nothing to do with similarities between the two forces.

any long range isotropic force must obey an inverse square law. this is because we live in 3 spatial dimensions. there is no choice about it.

but put the objects in motion, introduce dipoles, and you will see that the way the forces act are actually very different, when you are not looking at a static isotropic problem.

Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do we not use the fact that gravitational fields are conservative to develop a scalar potential, formulate gauges, obtain Maxwell-esque equations, etc.?

because there is no equivalence principle for electric forces.

if you put a piece of charged styrofoam and a piece of neutral metal in an electric field next to each other, they will follow different paths. and we therefore cannot attribute their paths to curvature of spacetime.

however, if you put two objects next to each other, any two objects, made of anything at all, in a gravitational field, then they will follow the same path. does not matter how much charge, mass, or spin they have.

How is it that photons come tantalizingly close to having mass--they are affected by grav fields, they have a non-zero momentum and can impart some of it to massive objects--but have no charge-like properties?

photons have no charge because if they did, they would not be a long range force, it would only act on subatomic scales, and we would not be able to see them.

in other words, photons have no charge because we can see them!

they don't have to have no charge. in fact, there are other bosons that are a lot like photons, except that they do have charge. they are the gluons. we can't see them because they do have charge, and so only act on short distances.

we got pretty lucky that photons have no charge.

To put my question another way (reminiscent of Jackson's Chapter 0), grav and e-static potentials can both be written as some function of r times r^$$\epsilon$$, where $$\epsilon$$ is some number. Why is it that, in both cases, the 'some function' is just the number one, and the epsilon is (confirmed to a very high degree of precision) exactly negative one?

see above. in 3 dimensions, any long range isotropic force must have inverse square law.

 

[chroot]

Excellent post, lethe.

- Warren

 

[Nudnik]

Originally posted by rocketcity
I find it interesting--and baffling--that the gravitational force and the electrostatic force can be so empirically similar and yet give rise to such completely different theory.

Why do we not explain electrostatic attraction by saying that the presense of a *charge* warps space-time? Why do we not use the fact that gravitational fields are conservative to develop a scalar potential, formulate gauges, obtain Maxwell-esque equations, etc.?

How is it that photons come tantalizingly close to having mass--they are affected by grav fields, they have a non-zero momentum and can impart some of it to massive objects--but have no charge-like properties?

To put my question another way (reminiscent of Jackson's Chapter 0), grav and e-static potentials can both be written as some function of r times r^$$\epsilon$$, where $$\epsilon$$ is some number. Why is it that, in both cases, the 'some function' is just the number one, and the epsilon is (confirmed to a very high degree of precision) exactly negative one?

Just wondering.

P

Try this on for size. Look at the shapes of the field patterns between attracting unlike charges and repelling like charges. The field is more concentrated between attracting charges and less between repelling charges. Becaues of this the attracting force is slightly greater than the repelling force. When opposite point charges are taken together as electrically neutral there is then a small residual attractive force that is independent of the polarity of other particles.

 

[yogi]

Back to Scott's 3rd Q re the origin of matter - why is it always assumed that it all got created in the so called "beginning" or near the beginning - what is wrong with the notion of matter being created by expansion - note the numerical value for the density of the universe is approximately equal to the 1/R where R is the Hubble radius, and the total mass of a critical density universe is approximately equal to 4(pi)R^2 - Is this purely coincidental ... why can't the universe be considered as existing in a state of continuing inflation - where stress energy is created consequent to the expansion of a negative pressure (false vacuum)?

 

[David]

Originally posted by chroot
The terms "space-time" and "gravitational field" are basically interchangeable. If it weren't for mass, there would not really be any space-time.

I agree.

It is not “space” that is “curved”, it is the gravity fields that are curved around spherical astronomical bodies.

Whenever light or physical objects pass near an astronomical body, their paths curve because of the curved gravity field. But is not “space” that is “curved”. For example, we could put side rockets on a spacecraft and fire them in the direction of an astronomical body, just the right amount so that the spacecraft will pass the body in a straight line. That proves that “space” is not “curved” at the body. It is the gravity fields that are “curved”. If space were “curved” around the body, there would be no way for the spacecraft to pass the body in a straight line.

You also said, “If it weren't for mass, there would not really be any space-time.”

Well, of course, if it weren’t for mass, there wouldn’t be nothin’ of any kind anyway, and we wouldn’t be here.

 

[yogi]

choot and David ...If you are saying that clumps of matter are necessary for the universe to exist, I would disagree - the cosmic energy can be uniformly distributed in the form of spatial stress - and the totality of that energy can equal that necessary to define the radius of curvature of the Hubble sphere. In fact, it may be that most cosmic energy exists as some form of stress, and that only a small fraction got distilled into the stuff called particles at some earlier era when the gravitational forces may have been greater.

The amount of curvature due to the Earth's mass is very small - a change in the effective radius of about 1.5 mm ...I don't see how redirecting a rocket to divert it from the geodesic disproves spatial curvature.

 

[FZ+]

For example, we could put side rockets on a spacecraft and fire them in the direction of an astronomical body, just the right amount so that the spacecraft will pass the body in a straight line. That proves that “space” is not “curved” at the body. It is the gravity fields that are “curved”. If space were “curved” around the body, there would be no way for the spacecraft to pass the body in a straight line.

Er... what?
The thing you are missing is that straight or not depends on your frame of reference. Taking the path that is apparently straight is definitely not straight for the man in the spaceship - in the same way that taking a "straight" path as seen from space on Earth will not appear to be straight when you are actually walking it, whilst walking straight forwards will plot a curved path as seen from space. Both points of view are equally valid. It is definitely possible, if space is curved, to tweak the path to make it appear straight.

 

[David]

Originally posted by FZ+
a "straight" path as seen from space on Earth will not appear to be straight when you are actually walking it, whilst walking straight forwards will plot a curved path as seen from space.

You can’t walk “straight forward” on earth, because the earth, not space, is curved.

 

[FZ+]

Yes you can, so long as you continue the analogy and see the Earth as a 2 dimensional non-euclidean surface.

 

[David]

Originally posted by FZ+
Yes you can, so long as you continue the analogy and see the Earth as a 2 dimensional non-euclidean surface.

The Earth is a 3 dimensional Euclidean sphere. The surface of a Euclidean sphere is curved.

 

[FZ+]

But we are free to move in only 2 dimensions, and so the surface of the Earth is a model of a 2d non-euclidean surface. It is not valid to consider straightness by invoking an dimension that in our model, does not exist. Similarly, in the 4 dimensional spacetime of the spaceship case, the curved model only disallows walking an apparently straight line if you invoke a fifth dimension, and prohibit motion in it.

 

[David]

Originally posted by FZ+
But we are free to move in only 2 dimensions, and so the surface of the Earth is a model of a 2d non-euclidean surface. It is not valid to consider straightness by invoking an dimension that in our model, does not exist. Similarly, in the 4 dimensional spacetime of the spaceship case, the curved model only disallows walking an apparently straight line if you invoke a fifth dimension, and prohibit motion in it.

I’m talking about reality. 3 Euclidean spatial dimensions in a Cartesian coordinate system, plus time. We are free to move in 3 spatial dimensions. What is “curved” is spherical astronomical bodies and gravity fields.

 

[russ_watters]

Originally posted by David
I’m talking about reality. 3 Euclidean spatial dimensions in a Cartesian coordinate system, plus time. We are free to move in 3 spatial dimensions. What is “curved” is spherical astronomical bodies and gravity fields.

But we are not free to move in four spatial dimensions. That's the part of the analogy you're not getting.

 

[David]

Originally posted by russ_watters
But we are not free to move in four spatial dimensions. That's the part of the analogy you're not getting.

There aren’t any 4 spatial dimensions. There are only three. There are the x, y, and z Cartesian coordinates, and that is it.

 

[FZ+]

There aren’t any 4 spatial dimensions. There are only three. There are the x, y, and z Cartesian coordinates, and that is it.

Exactly. And as long as you consider straightness by these 3 dimensions, you can easily make adjustments to move in a "straight line" with curved non-euclidean space.

 

[David]

Originally posted by FZ+
Exactly. And as long as you consider straightness by these 3 dimensions, you can easily make adjustments to move in a "straight line" with curved non-euclidean space.

My point is, with these three dimension and the x, y, and z coordinate system, that represents Euclidean space. If we insert spherical masses and their curved gravitational fields into this coordinate system, we still have the same coordinate system, and inserted into it are curved masses and curved gravity fields. It’s like inserting a spherical basketball into a cubical box. The ball remains spherical and the box remains cubical. The box doesn’t change shape to conform to the outline of the ball.

 

[yogi]

David - it isn't that space distorts into a sphere around a spherical mass - what occurs is a change in the measured radius of a sphere relative to the surface area of the sphere measured at that radius - in other words, the surface area of a spherespace encompassing a mass is no longer exactly 4(pi)R^2 For the Sun, the change (excess radius) if I remember correctly is about 1/2 a kilometer

 

[clicky]

Spacetime is simply how we describe and try to understand nature.
Spacetime is made of what the Euclidean space is made of - just a mathematical description. The space and time are created in the process of perception from multiscale sources of unifying interaction according to the emerging theory of interaction developed by the space
physicist Eugene Savov.

 

[Phobos]

Originally posted by David
There aren’t any 4 spatial dimensions. There are only three. There are the x, y, and z Cartesian coordinates, and that is it.

I think he's extending the analogy to help understanding. He's not saying there are 4 spatial dimentions in Relativity.