What is the Fabric of Spacetime Made Of?

[Sammyg]

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.

 

[Ignoramus]

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.

 

[Naty1]

Spacetime can be envisoned as Penrose spin networks with integer edges representing areas and integer value nodes representing volumes..and these can be shown to evolve from string theory, although that's not how they were discovered. It can also be envisoned as membranesof vibrating energy; these are analalogous to strings moveing through space and sweeping out two or three or n dimensional spacetime...these are theoretical mathematical constructs, not proven experimentally.

Right now nobody knows what spacetime is made of. Nobody knows what time is made of either, nor mass, nor energy...in fact you could claim it's rather embarassing or you could say:

"We know much; we understand little"

 

[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.

Right. So what does that mean exactly? What is space and what is time?

 

[john 8]

Spacetime can be envisoned as Penrose spin networks with integer edges representing areas and integer value nodes representing volumes..and these can be shown to evolve from string theory, although that's not how they were discovered. It can also be envisoned as membranesof vibrating energy; these are analalogous to strings moveing through space and sweeping out two or three or n dimensional spacetime...these are theoretical mathematical constructs, not proven experimentally.

Right now nobody knows what spacetime is made of. Nobody knows what time is made of either, nor mass, nor energy...in fact you could claim it's rather embarassing or you could say:

"We know much; we understand little"

I guess the real question is, are space and time real physical things? What do you think?

 

[jnorman]

after reading the response above, i am wondering what Naty1 is... anybody that can "envison (spacetime) as Penrose spin networks with integer edges representing areas and integer value nodes..." is a few points beyond me on the IQ scale.

anyway, Yes, Virginia, there is an "aether" that is anaolgous to the fabric of spacetime (not that anyone has a clue what the aether is). but after dispensing with the original aether with SR, einstein, after the development of GR, finally decided that there was an aether after all which rather represented the "spacetime" which GR indicates is warped by the presence of mass. there has to be something that is being warped if GR is correct. and IMHO, GR is basically the correct approach, whereas i do not believe a "graviton" theory of gravity based on the exchange of particles is reasonable (which of course does not mean it won't be found correct at some point in the future, but it is very complex and confusing and far less elegant compared to envisioning a warped spacetime - not that warped space is not confusing, just less confusing...)

here is a paper einstein delivered in 1920 discussing ether and relativity:
http://www.mountainman.com.au/aether_0.html

 

[chis]

I am a layman and not qualified.
Space time is the dimention we percive in. Imagine a blind person reading brail where their hands are the spacetime or as I see it the matter dimention. On its own it is infinite nothing, but introduce the brail lumps and bumps and you have perception. The brail is two other dimentions antimatter and light hence why we percive a 3D world. Gravity or the pressure of the matter dimention which we exsist in, is the process of smoothing the intrusional bumps. This universal force of gravity or you may think of it as decay is percived as time.
So Spacetime is the matter dimension that we live in and percive in, but cannot see and can only view or percive objects or mass as indentations they make in our dimension.
Gravity is time.

 

[Naty1]

after reading the response above, i am wondering what Naty1 is... anybody that can "envison (spacetime) as Penrose spin networks with integer edges representing areas and integer value nodes..." is a few points beyond me on the IQ scale.

I wish! unfortunately not so. Just sharing a conceptual picture I read about ...

I was referring to a diagram and explanation I saw in a recent book on physics...can't find it right now...May have been by Dr Kaku...anyway, the dynamic curving of spacetime was described as variations in a geodesic shaped framework of nodes and links...as mass/energy/pressure evolves and moves and modifys the shape of spacetime ,an edge may grow or shorten and nodes values vary in integers of Planck length...

 

[jnorman]

kaku=wizard :-)

 

[Naty1]

What is space and what is time?

I guess the real question is, are space and time real physical things? What do you think?

You can find discussions and some measure of working definitions via Wikipedia...

They appear to be real and physical but nobody knows their fundamental consitutents. Space appears to be something; so does time; relativity implies both curve and expand and contract with velocity...maybe velocity is fundamental?? Maybe light, according to Penrose Twistor theory...nobody knows...

It's like asking what is mass? Mass is made of atoms. Atoms are made of elementary particles...let's say quarks and electrons...They may be made of vibrating strings of energy. may be made of other undiscovered particles. Are particles wavelike or particle like? What are strings made of? fundamentally there is a lot we don't not know; we have mathematical based models that pretty well depict what we observe and explain most experimental results. But there is also a lot we don't understand.

 

[tiny-tim]

Welcome to PF!

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.

Space time is the dimention we percive in. Imagine a blind person reading brail where their hands are the spacetime or as I see it the matter dimention. On its own it is infinite nothing, but introduce the brail lumps and bumps and you have perception.

Hi Sammyg! Hi chis! Welcome to PF!

I quite like chis's answer (if I'm interpreting it right) …

we can't "see" the fabric of space-time, we can only experience the imperfections, or bumps, in it …

it's like the canvas that a painting is painted on or a tapestry is woven on … the canvas itself doesn't matter.

So Spacetime is the matter dimension that we live in and percive in, but cannot see and can only view or percive objects or mass as indentations they make in our dimension.
Gravity is time.

No, I don't follow that … why is gravity time?

 

[Naty1]

Gravity is NOT time acording the relativity.

But an argument could be made that gravity is the fabric of spacetime...that gravity is the geometry of spacetime...

 

[inquisitive_i]

Gravity bends Space-Time?

hi everyone...
i had a doubt regarding how light bends owing to a gravitational field as gravity is a property of mass and light (photon) is a massless entity..
experts here suggested that light follows a geodesic path and its the Space-time continuum that bends not d light itself..
Now the question that perturbs me is how cud the space bend at the first place??
even if it does.. what happens in the case of a black hole where d light emitted by it is engulfed by itself.. is the space curving all around it self?
if it is so.. than there must form a cavity in the continuum...! this whole thing struggles to ascend to my faculties...
please help.


P.S. : I am a graduating student and m not savvy to all the cosmological termnologies, its a humble request that u keep the reasoning down to simplest of levels.. thankyou

 

[iRish_waKe]

hi everyone...
i had a doubt regarding how light bends owing to a gravitational field as gravity is a property of mass and light (photon) is a massless entity..
experts here suggested that light follows a geodesic path and its the Space-time continuum that bends not d light itself..
Now the question that perturbs me is how cud the space bend at the first place??
even if it does.. what happens in the case of a black hole where d light emitted by it is engulfed by itself.. is the space curving all around it self?
if it is so.. than there must form a cavity in the continuum...! this whole thing struggles to ascend to my faculties...
please help.P.S. : I am a graduating student and m not savvy to all the cosmological termnologies, its a humble request that u keep the reasoning down to simplest of levels.. thankyou

Here's what I think:

Gravity is caused by the 'pressure' space-time exerts on a body, such as the Sun or Earth. The simplest way to describe it is the trampoline model. Imagine a trampoline flat on the ground, and you place a 20lb bowling ball in the center, the "space-time" or fabric of the trampoline is going to warp around the ball, causing everything that gets just a little to close to be pulled in. Now you have to imagine that the fabric of space-time is not just horizontal, but vertical, and every degree in between, so it folds "space-time" all around it. The same thing happens in space, we feel not a pulling force from the earth, but pressure from space-time actually pushing against us from above.

A black hole is just a super dense object in space, with so much gravity that it's pulling everything into a singularity.

So, that leaves the question, what is space-time? Space-time = Dark Matter. We simply don't have the the tools to detect it or prove it's existence, but we will, hopefully sooner than later. The properties of dark matter, once discovered, will prove the theory I'm explaining above, which is essentially GR. It also explains why as you approach the speed of light, the pressure from DM is what slows you back down and would require you to have infinite power. It's like trying to go too fast in an airplane, the friction from the air is what's holding you back from going faster.

This is simply my perception on GR and DM, and how I would like to believe everything works. Hopefully one day I find out this is true, because at these levels anyway, it works.

 

[Crazy Tosser]

Here's what I think:

Gravity is caused by the 'pressure' space-time exerts on a body, such as the Sun or Earth. The simplest way to describe it is the trampoline model. Imagine a trampoline flat on the ground, and you place a 20lb bowling ball in the center, the "space-time" or fabric of the trampoline is going to warp around the ball, causing everything that gets just a little to close to be pulled in. Now you have to imagine that the fabric of space-time is not just horizontal, but vertical, and every degree in between, so it folds "space-time" all around it. The same thing happens in space, we feel not a pulling force from the earth, but pressure from space-time actually pushing against us from above.

A black hole is just a super dense object in space, with so much gravity that it's pulling everything into a singularity.

So, that leaves the question, what is space-time? Space-time = Dark Matter. We simply don't have the the tools to detect it or prove it's existence, but we will, hopefully sooner than later. The properties of dark matter, once discovered, will prove the theory I'm explaining above, which is essentially GR. It also explains why as you approach the speed of light, the pressure from DM is what slows you back down and would require you to have infinite power. It's like trying to go to fast in an airplane, the friction from the air is what's holding you back from going faster.

This is simply my perception on GR and DM, and how I would like to believe everything works. Hopefully one day I find out this is true, because at these levels anyway, it works.

Now in your theory you would have to define what this 'pressure' is, you cannot just say what it does...
For example, space-time pressure is a tendency of space-time to...

And btw, air friction doesn't put any limit your speed - you could still travel at a relativistic speed in air, but you would just burn out pretty fast...

 

[iRish_waKe]

I thought I did describe what the pressure was, but I will clarify. The pressure is the pushing of the fabric of space-time against a body within it.

Space-time pressure is the tendency of space-time to fold around objects within it.

How can you say air friction does not put a limit on speed? I understand that air can be moving independently of the objects within it, but as soon as you travel faster than the air is moving, if at all, it causes friction. This isn't my theory, this is my take on the principles of GR.

 

[Crazy Tosser]

Space-time pressure is the tendency of space-time to fold around objects within it.

Are you sure that you are talking about the same space-time as Einstein did? He said space-time was majorly curved by stars and planets, and since objects tend to take the shortest paths in space-time, they accelerate towards that star/planet. Now, what you are saying, that space-time tends to fold around objects in it, could explain gravity, but I don't see how it puts a constant c-limit on speeds

How can you say air friction does not put a limit on speed? I understand that air can be moving independently of the objects within it, but as soon as you travel faster than the air is moving, if at all, it causes friction.

It does cause friction, but you can still move against it... at any speed you want slower than c

 

[inquisitive_i]

Here's what I think:

Gravity is caused by the 'pressure' space-time exerts on a body, such as the Sun or Earth. The simplest way to describe it is the trampoline model. Imagine a trampoline flat on the ground, and you place a 20lb bowling ball in the center, the "space-time" or fabric of the trampoline is going to warp around the ball, causing everything that gets just a little to close to be pulled in. Now you have to imagine that the fabric of space-time is not just horizontal, but vertical, and every degree in between, so it folds "space-time" all around it. The same thing happens in space, we feel not a pulling force from the earth, but pressure from space-time actually pushing against us from above.

A black hole is just a super dense object in space, with so much gravity that it's pulling everything into a singularity.

So, that leaves the question, what is space-time? Space-time = Dark Matter. We simply don't have the the tools to detect it or prove it's existence, but we will, hopefully sooner than later. The properties of dark matter, once discovered, will prove the theory I'm explaining above, which is essentially GR. It also explains why as you approach the speed of light, the pressure from DM is what slows you back down and would require you to have infinite power. It's like trying to go too fast in an airplane, the friction from the air is what's holding you back from going faster.

This is simply my perception on GR and DM, and how I would like to believe everything works. Hopefully one day I find out this is true, because at these levels anyway, it works.

thanx iRish WaKe..
ur explanation cleared my doubts pretty well..
but one thing still remains tangled is.. this 'pressure' pushes 'bodies' within the space-time.. but LIGHT is certainly NOT a body.. y does and how does a black hole eats up (its own) light??

 

[Crazy Tosser]

thanx iRish WaKe..
ur explanation cleared my doubts pretty well.. n ya.. that pressure thing.. i understood it at ur first effort.. thanks for ur time..

but one thing still remains tangled is.. this 'pressure' pushes 'bodies' within the space-time.. but LIGHT is certainly NOT a body.. y does and how does a black hole eats up (its own) light??

Space-time curvature around a black hole (inside the event horizon) is so great that the shortest path in space-time that light traveling away from it could take is back into it.

And I do believe (unless it's all messed up in my head) that Hawking proved that black holes radiate because otherwise it would've contradicted the Second Law of Thermodynamics.

 

[iRish_waKe]

Are you sure that you are talking about the same space-time as Einstein did? He said space-time was majorly curved by stars and planets, and since objects tend to take the shortest paths in space-time, they accelerate towards that star/planet. Now, what you are saying, that space-time tends to fold around objects in it, could explain gravity, but I don't see how it puts a constant c-limit on speeds



It does cause friction, but you can still move against it... at any speed you want slower than c

I was essentially talking about 2 different things, guess I shouldn't have? I didn't say that the folding of space time put a limit on speed. If that is what you or anyone else is thinking that's what I said, then sorry for the confusion, because I wasn't.

I was simply saying that space-time is something, it's not just empty space. It is dark matter. Empty space, space-time, the vacuum of space, dark matter, whatever you want to call it, they are all one in the same. This is what I got out of Einsteins theories. That 'something' is what causes you to need infinite power to accelerate to c.

 

[iRish_waKe]

Space-time curvature around a black hole (inside the event horizon) is so great that the shortest path in space-time that light traveling away from it could take is back into it.

And I do believe (unless it's all messed up in my head) that Hawking proved that black holes radiate because otherwise it would've contradicted the Second Law of Thermodynamics.

Yes ^ That stuff has to go somewhere, it's what expelled from black holes at near the speed of light, they are called jets. Everything that the black hole has gobbled up is expelled as gamma rays, if I recall correctly.

And yeah, the light is simply following the curvature of space time, which, unfortunately for the light, does not lead away from the black hole, it just goes round and round into the center of the black hole.

 

[chis]

Hey Tiny Tim, yes you are right about the canvas analogy.
I also share a similar belief as Irish Wake that the pressure of the matter dimention in which we percive has a pressure advantage over the other two and the rate of destructive crushing is both gravity and time.
I'm a little scared to disscus my theories as I got an infraction for putting something similar on another thread.

 

[iRish_waKe]

Well discussion of your own personal theories and discussing your take on other theories, namely GR, are different. Just be careful how you are wording it. If your theory throws GR out the window, then this is not the place for it.

 

[chis]

Thanks Irish Wake i'll bare that in mind.
What's your theory on time?

 

[inquisitive_i]

Yes ^ That stuff has to go somewhere, it's what expelled from black holes at near the speed of light, they are called jets. Everything that the black hole has gobbled up is expelled as gamma rays, if I recall correctly.

And yeah, the light is simply following the curvature of space time, which, unfortunately for the light, does not lead away from the black hole, it just goes round and round into the center of the black hole.

thats what i said.. if the light is following the curvature of Space-time and goin round and round again back to the centre of black hole... than there should essentially exist a Cavity in d FABRIC at the spot of a black hole..

So should v say.. black hole is nothing but an unstitched hole in the fabric.??

 

[Crazy Tosser]

thats what i said.. if the light is following the curvature of Space-time and goin round and round again back to the centre of black hole... than there should essentially exist a Cavity in d FABRIC at the spot of a black hole..

So should v say.. black hole is nothing but an unstitched hole in the fabric.??

Let's just say... we can find out what the black hole is outside the event horizon, where it's just an extreme gravitational curvature. Talking about space-time or anything else inside the event horizon is... pointless... It is defined as something we will never know anything about.

 

[inquisitive_i]

awrite..
"it IS defined as something we would never know about.." but shouldn't we always keep trying to find it..??

 

[inquisitive_i]

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?

 

[Mentz114]

inquisitive_i :

GR suggests that any orbit around a massive body is caused due to the stretching and bending of trampoline (Space-Time).. right?

Wrong.

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..

Keplerian orbits may be circular.

So.. how do i relate that?

Study GR and you'll find out that it describes the solar system better than Newton-Kepler. Including the bending of light by the sun and the orbital precession of Mercury.

 

[inquisitive_i]

cud u please explain d "wrong" more specifically.. becoz this is what i saw before i wrote that. (http://in.youtube.com/watch?v=tpbGuuGosAY)
and it clearly mentioned that mass 'stretched & bend' space-time which we experience as gravity..

Moreover,
'keplerian orbits may b circular' but than.. if they get circular how do we find apohelion and perihelion?

 

[A.T.]

GR suggests that any orbit around a massive body is caused due to the stretching and bending of trampoline (Space-Time).. right?

No, the trampoline represents only space-space (2D space). There is no time dimension. You cannot explain gravity with this analogy. Here is a better picture:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

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?

To visualize orbits in GR you would need 2-space and the time dimension, which are all curved. To show the curvature of such a 3D-diagram you would need at least a 4D-display.

 

[inquisitive_i]

Here is a better picture:
http://www.physics.ucla.edu/demoweb/...spacetime.html

thankyou sir but d link provided me another ambiguity.. it explained why mercury's ellipse is deframmed (precessed).. but why does it precess cotinously (43 secs/century).. Is the curvature formed by Sun constantly deepening with that rate (43 secs/century)?

 

[A.T.]

thankyou sir but d link provided me another ambiguity.. it explained why mercury's ellipse is deframmed (precessed).. but why does it precess cotinously (43 secs/century).. Is the curvature formed by Sun constantly deepening with that rate (43 secs/century)?

Why do you think the curvature has to change? It is constant. The ellipse is a result of a static time curvature. The precessesion of the ellipse is caused by a static space curvature.

 

[Mentz114]

cud u please explain d "wrong" more specifically.. becoz this is what i saw before i wrote that. (http://in.youtube.com/watch?v=tpbGuuGosAY)
and it clearly mentioned that mass 'stretched & bend' space-time which we experience as gravity..

Don't believe everything at the You-niversity, it's not the best place to learn physics. The rubber sheet analogy is not accurate.

'keplerian orbits may b circular' but than.. if they get circular how do we find apohelion and perihelion?

apohelion = perihelion

A circle is a degenerate case of an ellipse, when eccentricity e=1.

 

[Dale]

than such curvatures must essentially b perfectly circular in accordance with d GR.

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.

 

[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