What is the Fabric of Spacetime Made Of?

[marmot]

A lot of the misunderstandings of physics arise from the idea that mathematical models are nature, and therefore makes someone imagine that there is a tangible fabric called spacetime that fills the cosmos. its a beautiful mental image, but I doubt it is true. It is the fault of physicists because a lot of physicists believe that the equations in their sheet are somehow nature, and that these laws are followed by the universe, as if the universe were somesort of mind. only human beings can make and follow laws, the universe is not a mind.

In order to understand how GR deals with spacetime, its useful to understand what a spacetime diagram is. There was a clever mathematician called Minkonski that came with a diagram that could show a particle[s movement versus time. Thus, if a particle went in a straight line, it meant it was advancing in a constant velocity in the diagram.



Now imagine this spacetime diagram filling all the universe. Einstein said that massive objects would deform and warp this spacetime diagram. For example, in flat spacetime, a particle could be moving in a straight path, at constant speed. If a star deforms this spacetime, the fabric gets wrinkled to the point that the straight line now seems to point to the star, and curves and therefore now it looks like it is accelerating. Hence why massive objects have strong gravitational fields.

Remember that these are clever mathematical tools to make predictions. Spacetime is an invention of physicists, not something that is part of the cosmos.

 

[inquisitive_i]

thankyou all

 

[G Hathaway]

A lot of the misunderstandings of physics arise from the idea that mathematical models are nature, and therefore makes someone imagine that there is a tangible fabric called spacetime that fills the cosmos. its a beautiful mental image, but I doubt it is true. It is the fault of physicists because a lot of physicists believe that the equations in their sheet are somehow nature, and that these laws are followed by the universe, as if the universe were somesort of mind. only human beings can make and follow laws, the universe is not a mind.

In order to understand how GR deals with spacetime, its useful to understand what a spacetime diagram is. There was a clever mathematician called Minkonski that came with a diagram that could show a particle[s movement versus time. Thus, if a particle went in a straight line, it meant it was advancing in a constant velocity in the diagram.



Now imagine this spacetime diagram filling all the universe. Einstein said that massive objects would deform and warp this spacetime diagram. For example, in flat spacetime, a particle could be moving in a straight path, at constant speed. If a star deforms this spacetime, the fabric gets wrinkled to the point that the straight line now seems to point to the star, and curves and therefore now it looks like it is accelerating. Hence why massive objects have strong gravitational fields.

Remember that these are clever mathematical tools to make predictions. Spacetime is an invention of physicists, not something that is part of the cosmos.

If 4-D spacetime is curved doesn't that imply there must be a 5th physical dimension in which this, our 4-D spacetime, is curved?

 

[Mentz114]

If 4-D spacetime is curved doesn't that imply there must be a 5th physical dimension in which this, our 4-D spacetime, is curved?

No, it's not necessary to have a fifth dimension. The 'curvature' can be expressed mathematically with a metric tensor.

 

[G Hathaway]

No, it's not necessary to have a fifth dimension. The 'curvature' can be expressed mathematically with a metric tensor.

We can mathematically model reality. The metric tensor is not reality.

In what dimension is space curved? Sure, we can see the 2-surface when folded into a sphere is a closed 3-space. It is curved or folded or closed in a higher dimension.

What is the dimension if it is 4-space that is folded? If it is 3-space (sans t) that is folded, what is the dimension into which it is folded? One of the string-theory dimensions?

 

[Phrak]

We can mathematically model reality. The metric tensor is not reality.

In what dimension is space curved? Sure, we can see the 2-surface when folded into a sphere is a closed 3-space. It is curved or folded or closed in a higher dimension.

What is the dimension if it is 4-space that is folded? If it is 3-space (sans t) that is folded, what is the dimension into which it is folded? One of the string-theory dimensions?

The kind of curvature that Mentz was referring to, the curvature described by derivatives of the metric tensor, is called intrinsic curvature. The kind you're familiar with is extrinsic curvature. Intrinsic curvature is purposely defined so as not to depend upon other dimensions--embedments.

One standard example to show the difference between them is the side of a cylinder. Consider a circle drawn around the cylinder. It's extrinsic curvature is defined as 1/R, R=radius of cylinder.

Now draw a triangle on the side. It's internal angles add up to 180 degrees. If you sliced opened the cylinder and laid it flat, the internal angles would still add up to 180 degrees. The surface has zero intrinsic curvature. If the angles don't add to 180 degrees as triangle is shrunk to a point, the curvature at that point is other than zero. I'm simplifying a little. It takes three numbers, not one, to fully specify the curvature of a two dimensional surface.

You should be able to apply these tests and see that a sphere is an example of a surface with both intrinsic and extrinsic curvature.

 

[A.T.]

We can mathematically model reality. The metric tensor is not reality.

Well, in that sense intrinsic curvature is also just a mathematical concept, and not reality. It is used as a model that fits the reality quite well.

 

[G Hathaway]

I will try to understand what intrinsic curvature could mean.

It is a little like the problem of an expanding universe. If all scales are expanding uniformly at all scales then the expansion would be undetectable.

There is a difference between a circle (or other intersection of a plane with a cylinder) that goes around the cylinder and one drawn on the cylinder. The conic section is curved and closed outside the surface in a sense (extrinsic?) while the circle drawn on the surface (intrinsic?) closes without going 'around.'

The inhabitants of a cylindrical universe could, in theory, test for this. On their surface, sufficiently large circles can intersect themselves. Similarly, we could test for a non-flat universe by testing large triangles and see if their angles sum to 180.

Now with that surface 'understanding' of intrinsic curvature, I still find the situation unexplained. Forgive my lack of mental speed.

The metaphor of Space as a distorted Fabric is rife with extrinsic curvature unless I am mistaken.

A ball rolling on a surface with indents due to presence of mass is the thought experiment. This is stretched in an external dimension. Extrinsic, right? And a uniform acceleration orthogonal to the undistorted surface is presumed.

Unless the curvature of our universe is extrinsic the analogy fails it seems to me.

Am I getting closer?

 

[G Hathaway]

Well, in that sense intrinsic curvature is also just a mathematical concept, and not reality. It is used as a model that fits the reality quite well.

Since mathematics is derived from human experience via metaphor we feel that we can trust it to model reality. (See Lakoff and Nunez, Where Mathematics Comes From)

Models of the solar system with the Earth as the center led to a mathematics of cycles and epicycles that fit reality quite well.

Newton's laws fit reality quite well.

Special Relativity fits reality quite well.

General Relativity fits reality quite well.

Quantum Mechanics and/or QED fit reality quite well.

Of the list, how can we tell which of these is sufficiently robust to cover every reality?

Thoughts like this that shake my confidence in today's math as being fully real. They may be true of a universe that is not ours but only close.

 

[Phrak]

I will try to understand what intrinsic curvature could mean.

It is a little like the problem of an expanding universe. If all scales are expanding uniformly at all scales then the expansion would be undetectable.

Oh, no, not at all. Intrinsic curature is meaurable. It's not easy, but it's not impossible like a global gauge symmetry.

There is a difference between a circle (or other intersection of a plane with a cylinder) that goes around the cylinder and one drawn on the cylinder. The conic section is curved and closed outside the surface in a sense (extrinsic?) while the circle drawn on the surface (intrinsic?) closes without going 'around.'

The inhabitants of a cylindrical universe could, in theory, test for this. On their surface, sufficiently large circles can intersect themselves. Similarly, we could test for a non-flat universe by testing large triangles and see if their angles sum to 180.

Now with that surface 'understanding' of intrinsic curvature, I still find the situation unexplained. Forgive my lack of mental speed.

So this is the first you've heard of it? I didn't mean to explain it too well, or give you a good deal of intutive understanding. I don't know if there's any visual, or geometrical way to understant intrinsic curvature well. I don't have one.

The metaphor of Space as a distorted Fabric is rife with extrinsic curvature unless I am mistaken.

A ball rolling on a surface with indents due to presence of mass is the thought experiment. This is stretched in an external dimension. Extrinsic, right? And a uniform acceleration orthogonal to the undistorted surface is presumed.

It's a graphical model (metaphor is a dirt word, don't you know?) usefull to Program Directors for producing TV science. As you can now appreciate, explaining intringic curvature should take some time. So falling back on the rubber sheet model is the best they do.

Unless the curvature of our universe is extrinsic the analogy fails it seems to me.
Am I getting closer?

You've got it.

I must say, there have been many who have been very annoyed with intrinsic curvature (I was for a long time), and tried to embed spacetime in more than four dimensions that are nice and Euclidian, where the Pythagorean Theorem holds. I don't know how successful they've been. You can probable find some references on the web.

 

[A.T.]

I will try to understand what intrinsic curvature could mean.

Some people like the metaphor of varying density. I compare the two views here:
https://www.physicsforums.com/showpost.php?p=2003340&postcount=20

It is a little like the problem of an expanding universe. If all scales are expanding uniformly at all scales then the expansion would be undetectable.

This expansion doesn't affect the distances between masses bound by gravity or electromagnetic forces. Planets are not expanding with the universe.

The inhabitants of a cylindrical universe could, in theory, test for this. On their surface, sufficiently large circles can intersect themselves.

Imagine it is not closed cylinder, but an infinite sheet rolled together. Its inhabitants have no way to detect the extrinsic curvature. It wouldn't affect them at all. But they could easily detect intrinsic curvature if there was any. The curvature types are very different, and intrinsic curvature should have a different name to avoid confusion.

The metaphor of Space as a distorted Fabric is rife with extrinsic curvature unless I am mistaken.

The GR models gravity is intrinsic curvature.

A ball rolling on a surface with indents due to presence of mass is the thought experiment. This is stretched in an external dimension. Extrinsic, right? And a uniform acceleration orthogonal to the undistorted surface is presumed.

No. GR is about straight paths (geodesics) in spacetime and not balls rolling on extrinsically curved surfaces. Try the link I posted here:
https://www.physicsforums.com/showpost.php?p=2026421&postcount=31

 

[G Hathaway]

Some people like the metaphor of varying density. I compare the two views here:
https://www.physicsforums.com/showpost.php?p=2003340&postcount=20

I will factor in the idea of density into my growing definition of intrinsic curvature.

Space becomes more compressed, in a sense.

My imagination is limited when I attempt to visualize other than flat 3-space. For example, in the density analog I find that I understand 'density' relative to a reference flat 3-space.

I can take away a space dimension (and give time a spacelike quality) and 'see' an expanding reality in which the past and future are separated by a planar 'now.' In this model there are time 'lines' for photons. These lines are not 'straight' when compared to a reference 3-space. But they are the very definition of straightness.

Einstein rings and two images of the same galaxy inform us of the reality of gravitational lensing. Is this intrinsic curvature? How could we tell intrinsic from extrinsic here?

This expansion doesn't affect the distances between masses bound by gravity or electromagnetic forces. Planets are not expanding with the universe.

So if we were to plot the expansion rate vs. scale we would find at small scales the expansion rate is small and as the scale goes up so does the expansion rate.

Interesting. Is this generally accepted?

If I understand Penrose and Hawking's proof of the necessity of a singularity, I thought it required a uniform expansion. Is this later news that invalidates their proof?

Imagine it is not closed cylinder, but an infinite sheet rolled together. Its inhabitants have no way to detect the extrinsic curvature. It wouldn't affect them at all. But they could easily detect intrinsic curvature if there was any. The curvature types are very different, and intrinsic curvature should have a different name to avoid confusion.

The inhabitants of a flat space would find that large circles never intersect. The unrolling of the cylinder and making a finite dimension infinite yields a different topology. On a cylinder a large enough circle intersects itself.

The GR models gravity is intrinsic curvature.

No. GR is about straight paths (geodesics) in spacetime and not balls rolling on extrinsically curved surfaces. Try the link I posted here:
https://www.physicsforums.com/showpost.php?p=2026421&postcount=31

Photons follow geodesics. By definition, as you say, 'straight.' How can there be those two 'straight' lines from A to B (as in gravity lensing). The shape of space is revealed to us by the equivalent of a circle intersecting itself on a cylinder.

What is spacetime curved in reference to? Or maybe, somehow, intrinsic curvature is not curvature. I suppose I demand too much. Flat 4-D spacetime is easy to imagine though. Photons move along a trace of spacetime that follows a geodesic. The direction to go is the 'easy' direction. Of all the possibilities for next location to be in some (along the geodesic) have a higher probability.

Everything (forgive the anthropomorphism) 'wants' to be someplace else as fast as possible. To go downhill. To dissipate the energy inherent in the difference between 'here' and 'down there.' Some of this downhillness is gravity. The net downhill direction is influenced by the other three forces as well. Real things demonstrate their reality by interacting when the downhill leads to another real thing. (I am real because photons affect me, but that's philosophy.) Why couldn't some particle just stand still. Be the Origin. A reference point. A singularity.

Yours in confusion yet... hopefully making progress ... any other metaphor or analogy that may aid understanding?

 

[A.T.]

Photons follow geodesics.

Not only photons. Everything in free fall follows geodesics in space time.

By definition, as you say, 'straight.' How can there be those two 'straight' lines from A to B (as in gravity lensing).

You can go 'straight' from north pole to south pole on the Earth's surface on many different paths too.

Or maybe, somehow, intrinsic curvature is not curvature.

Yes, curvature is not the best name for it.

 

[G Hathaway]

Not only photons. Everything in free fall follows geodesics in space time.

You can go 'straight' from north pole to south pole on the Earth's surface on many different paths too.

Yes, curvature is not the best name for it.

The sphere metaphor is one of extrinsic curvature. Sorry, but that doesn't help; been arount that tree.

Even not in free fall, particles are going downhill relative to all four forces. Their going is probabilistic.

The very word -- curvature -- is a spatial thing. The concept has meaning for space-like objects and traces like geodesics on a sphere. Then this other thing ... intrinsic distortion ... intrinsic gazorninplatz ... intrinsic curvature ... It not 'really' curvature is what I am getting. The very word is misleading.

So space has gazorninplatz that defines easy directions. For some reason everything must change (shades of Heraclitus: The Essence of Reality is Change). Gazorninplatz is that which we metaphorically call the four Forces? We can speak of the Force of Gravity or the Shape of Space with a built-in downhill direction and the rule that nature abhors a gradient. Perhaps gazorninplatz can be visualized as a distortion of probability space. (For gazorninplatz, read intrinsic curvature).

 

[A.T.]

The sphere metaphor is one of extrinsic curvature. Sorry, but that doesn't help; been arount that tree.

The intrinsic curvature of the sphere surface is relevant here. That's what you can measure. You can always assume some extrinsic curvature and embed the intrinsically curved manifold in some higher dimensional manifold without intrinsic curvature.This is very useful for visualization:
http://www.adamtoons.de/physics/gravitation.swf

 

[Mentz114]

The term 'curved space' comes from the fact that the axes against which we measure off coordinates become curved and possibly non-orthoganal in the presence of matter. This leads to the definition of covariant and contravariant components from which we get an invariant measure of distance ( or proper length in 4-D) without which GR ( Riemanian geometry also) could not exist.

It's the axes that are curved, and because axes are not physical, so it seems neither is curvature of space or space-time.

 

[tiny-tim]

The term 'curved space' comes from the fact that the axes against which we measure off coordinates become curved and possibly non-orthoganal in the presence of matter.

This argument is so curved, it's circular!

wot's a 'curved axis'?

… because axes are not physical, so it seems neither is curvature of space or space-time.

Curvature of space or space-time is physical … parallel transport not working, or circles having the wrong circumference, are physical properties.

 

[Mentz114]

Hi Tiny,
let me try to straighten things out.

The physical manifestations you cite can equally be thought of as caused by changes in clocks and rulers from one place to another. This is a property of the measuring devices, not space-time. Maybe gravity acts directly on the measuring instruments to give the appearance of curved space-time.

For space-time to have physical curvature one must

1. Define space-time as physical ( a quantum vacuum sort of thingy ?)
2. define a local property that corresponds to 'curvature'.

M

 

[tiny-tim]

The physical manifestations you cite can equally be thought of as caused by changes in clocks and rulers from one place to another.

But a change in a ruler (a change relative to what, btw? ) is a change in space itself … why else does the ruler change, if not because of where it is?

And similarly a change in a clock is a change in time itself.

This is a property of the measuring devices, not space-time. …

Anything can be a measuring device …

a property of measuring devices is a property of everything!

For space-time to have physical curvature one must

1. Define space-time as physical ( a quantum vacuum sort of thingy ?)
2. define a local property that corresponds to 'curvature'.

"Physical" means that we can measure it …

what do you think it means? …

and we can measure parallel-transport and circumferences.

 

[Mentz114]

But a change in a ruler (a change relative to what, btw? ) is a change in space itself … why else does the ruler change, if not because of where it is?

And similarly a change in a clock is a change in time itself.

The clocks and rulers change because gravity varies from one place to the next. So it is relative to another place. This gives an illusion of curved space-time.

"Physical" means that we can measure it …

We only ever measure length and time intervals. Do you have 'curvometer' ?
We can't even measure mass directly, we have to use a machine that converts it into a signal our eyes etc can deal with.

What about theories of gravity that make the same predictions as GR but don't have curvature ? Curvature is a mathematical convenience and certainly isn't necessary or physical.

The problem is that I don't think there's any way to distinguish our positions experimentally so arguing is a waste of time.

 

[G Hathaway]

Never having heard of deconstructionism before, I find it hard to judge whether I inadvertently engaged in it.

 

[Phrak]

never having heard of deconstructionism before, i find it hard to judge whether i inadvertently engaged in it.

ok. .

 

[G Hathaway]

I found http://www.astro.ucla.edu/~wright/cosmo_03.htm

Does the article (at the heading Flatness-Oldness problem) conclude that at the largest scale the universe is flat to within 1 in 447,225,917,218,507,401,284,016?

If so, what would that mean?

 

[granpa]

General Relativity has always fascinated me and I understand how the fudamentals of the so called fabric of Spacetime work, but never do I hear from anybody what the fabric of Spacetime is made out of. Is it some other type of natural force and if so is it related to the 4 fundamental forces.

according to quantum mechanics its made of quantum harmonic oscillators.

 

[FredericGos]

It means that the universes intrisic curvature is very very very near to zero? ^^

 

[john 8]

GR suggests that any orbit around a massive body is caused due to the stretching and bending of trampoline (Space-Time).. right?
than such curvatures must essentially b perfectly circular in accordance with d GR..
Kepler laid down that orbiting bodies always orbit in elliptical paths with controlling body essentially at one of its focii.. that's what happens in actual practice..
So.. how do i relate that?

A trampoline made of what physical substance? Are you going to suggest that space or time are actual physical things that have an atomic structure? If so please describe this assumption.

 

[john 8]

The "fabric" of spacetime is simply a clever analogy to help imagine the merging of the 3 spatial dimensions, and the single time dimension. When you see picures of spheres bending a sheet that looks like a checkerboard, the checkeroard represents spacetime.

So, Spacetime is just what it implies; it's space and time.

So is this fabric an actual physical thing? If you say that it is, then is this fabric made of particles, waves or something else? What is it made out of?

 

[john 8]

This is incorrect. Orbits are geodesics in GR. In a Swarzschild spacetime they are essentially just distorted helixes. If you "flatten" the time dimension then you get the kind of precessing almost-ellipses that are actually observed.

What do you mean flatten? Are you talking about a physical occurence? If so, are you saying time or dimensions are physical things? If so, time or a dimension are physical in what manner? Please be specific. Thank you.

 

[john 8]

If 4-D spacetime is curved doesn't that imply there must be a 5th physical dimension in which this, our 4-D spacetime, is curved?

What science are you using to make this statement?

 

[john 8]

I will factor in the idea of density into my growing definition of intrinsic curvature.

Space becomes more compressed, in a sense.

QUOTE]

Are you suggesting that space is a physical thing? If so that would mean that it is a form of energy, either a particle or a wave. Would you agree?

 

[john 8]

This argument is so curved, it's circular!

wot's a 'curved axis'?


Curvature of space or space-time is physical … parallel transport not working, or circles having the wrong circumference, are physical properties.

Please explain in what way either space or space-time are physcal things. I am using the term physical as it is defined in any dictionary or scientific reference book.

If you say space or space-time can physically be curved then that means that these things of which you speak are physical things that are being influeneced by exterior energy, which means that space or space-time come in contact with other forms of energy. So please give a scientific reference that describes how space or space-time are physical things.

 

[john 8]

But a change in a ruler (a change relative to what, btw? ) is a change in space itself … why else does the ruler change, if not because of where it is?

And similarly a change in a clock is a change in time itself.


Anything can be a measuring device …

a property of measuring devices is a property of everything!


"Physical" means that we can measure it …

what do you think it means? …

and we can measure parallel-transport and circumferences.

So are you saying that space-time is an actual physical thing? Yes/no.

If yes, please give a scientific reference that describes the physical structure of space-time. Remember that all things that we deem to be real physical things are made of energy. This energy either takes the form of a particle or a wave. if you know of a different way in which things exist please let me know. Otherwise, tell me and the rest of us participating on this discussion what form space-time exists as.

 

[granpa]

some scientists are now suggesting that 'information' is the fundamental thing that all things are made of. i'll try to find a reference.

edit:http://critical-path.itgo.com/Articlesanscover.html

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

 

[Dale]

What do you mean flatten?

Hi john 8, it has certainly been a while, welcome back. Sorry about being imprecise, by "flatten the time dimension" I meant "take a projection along the time dimension". Specifically, a 3D projection of the 4D worldline of the satellite.

 

[I. N. Stine]

So are you saying that space-time is an actual physical thing? Yes/no.

If yes, please give a scientific reference that describes the physical structure of space-time. Remember that all things that we deem to be real physical things are made of energy. This energy either takes the form of a particle or a wave. if you know of a different way in which things exist please let me know. Otherwise, tell me and the rest of us participating on this discussion what form space-time exists as.

Wow. You have said my words exactly, if I could have ever thought of a good way to say my own questions about this. I love Relativity so much, but sometimes when I try to imagine it, the words people say about it just don't help me see it in my mind. I just can not imagine a thing that is not matter or energy that can be put into a curve or be flat or be anything, because it is nothing! It is not there! If nothing is there then there is no thing that can be curved!

Thanks for saying my question that I did not know how to say!