Why is the fabric of space and time always portrayed flat?

[DastardlyBliss]

The concept of the fabric of time and space is confusing to me. I understand that an object with large mass can warp it, but that only makes sense to me if the fabric had only two spatial dimensions (assuming no warps).

The space-time fabric is always explained visually as a flat plane, but i know this isn't the case.

Can you help me understand? I've read theories that it's more like a loaf of bread or a bubble, but they did not clear things up for me.

Thank you

 

[A.T.]

I understand that an object with large mass can warp it, but that only makes sense to me if the fabric had only two spatial dimensions

You have basically answered your own question. Humans cannot visualize intrinsic curvature for manifolds with 3 or more dimensions. That's why usually only a 2D slice of 4D space time is shown.

 

[Dale]

The space-time fabric is always explained visually as a flat plane, but i know this isn't the case.

You are correct. Spacetime is 4D (3 dimensions of space plus 1 dimension of time). Since it is hard to draw a 4D figure, for visualization purposes things are simplified down usually to 2 dimensions. But that is just for visualization, the actual theory and math is that of a 4D curved spacetime.

 

[DastardlyBliss]

thanks for the responses

ok, but what about this? Assume there is a massive object warping the space-time fabric. Would the warp be infinite? or maybe gradually declining. In my head i am imagining a wormhole... with the space-time fabric folded over to meet at the wormhole, but suppose there are objects creating large warps on both sides of the fold which happen to meet each others warps. I am picturing the 2d model, and not sure if it really works that way in 4d. I am probably overthinking. Any simple explanations for a layman?

 

[newjerseyrunner]

The amount space bends is dependent on how massive the object is. If you use the flat sheet analogy, a ball would make a tiny dent in space, a star creates a massive dent. Neither would be infinite in depth because neither have infinite mass, but both would be infinite along the length of the sheet... sort of. The range of gravity is infinite (we think) but it's affects travel at the speed of light (we think.)

 

[PeterDonis]

Assume there is a massive object warping the space-time fabric. Would the warp be infinite?

It's more complicated than that. The curvature of a 4-dimensional manifold can't be described by a single number, the way the curvature of a 2-d surface can. In general it takes 20 numbers for a 4-d manifold; there are cases with special symmetries where fewer numbers than that are sufficient, but it's never just one number.

The other thing to keep in mind is that the curvature is of spacetime, not just space. So one of the dimensions of the fabric is the time dimension. Most visualizations, such as the "ball denting the rubber sheet" one, or even the "wormhole" one, are only showing you the curvature of space, not spacetime. But much of the important information about spacetime curvature requires looking at time, so it's being left out in those visualizations.

Instead of trying to visualize the "fabric" all in one go, another avenue that is open is to think of what spacetime curvature means, physically. It's often equated to "gravity", but it's really more specific than that: it's tidal gravity. For example, suppose I have two rocks hanging motionless above the Earth at some instant; both of them lie along a single radial line from the center of the Earth, but one is a little bit higher than the other. As the rocks start to freely fall, their separation will increase (because, in Newtonian terms, the lower one will fall slightly faster than the higher one). This is an example of tidal gravity. Or, if we have two rocks that are both at the same altitude but separated a little bit horizontally, and they start to fall, their separation will decrease (because, in Newtonian terms, they are both falling towards the center of the Earth, and that is a slightly different direction for the two of them). That is also an example of tidal gravity.

If we now try to translate what I just described into a visualization, we will find that it can't be done with a single "sheet" of fabric, so to speak--at least, not in any way that will be easy to interpret. But we can do it with two "sheets". For one "sheet", we have the time direction along one axis, and the radial (vertical) direction along the other; and we draw the worldlines (paths through spacetime) of the two radially separated rocks on the sheet. We find that the rocks separate, which means the "grid lines" on the sheet must get further apart in the radial direction as we move along the time direction. This means the sheet will be shaped something like a saddle.

For the other "sheet", we have the time direction along one axis, and the tangential (horizontal) direction along the other, and we draw the worldlines of the two rocks. We find that they get closer together, which means that the "grid lines" on the sheet get closer together as we move along the time direction. This means the sheet will be shaped something like a section of a sphere.

For an image of what I'm talking about, look at page 112 here:

https://books.google.com/books?id=i...K#v=onepage&q=tidal gravity spacetime&f=false

This is from Kip Thorne's Black Holes and Time Warps, which I highly recommend as a book on GR for the non-technical reader. The text is talking about the tidal gravity produced by the Moon (so the "rocks" would instead be pieces of Earth's ocean), but the tidal gravity produced by the Earth, or indeed any spherical gravitating body, is similar.

 

[DastardlyBliss]

The amount space bends is dependent on how massive the object is. If you use the flat sheet analogy, a ball would make a tiny dent in space, a star creates a massive dent. Neither would be infinite in depth because neither have infinite mass, but both would be infinite along the length of the sheet... sort of. The range of gravity is infinite (we think) but it's affects travel at the speed of light (we think.)

Thanks for the response newjersey runner. That makes sense, but I may not have been completely clear explaining the scenario in my head. What i meant about the fabric bending infinitely is in this scenario...

A brand new object either appears out of nowhere or has an extreme gain of mass...

Actually, I am not even going to continue with that scenario because I am still thinking 2d. I was thinking that any object under the 2d fabric would be forced away, and possibly everything infinitely in that direction, but the warp would really be spherical, right? So it would be more like the universe expanding, i guess?

 

[DastardlyBliss]

It's more complicated than that. The curvature of a 4-dimensional manifold can't be described by a single number, the way the curvature of a 2-d surface can. In general it takes 20 numbers for a 4-d manifold; there are cases with special symmetries where fewer numbers than that are sufficient, but it's never just one number.

The other thing to keep in mind is that the curvature is of spacetime, not just space. So one of the dimensions of the fabric is the time dimension. Most visualizations, such as the "ball denting the rubber sheet" one, or even the "wormhole" one, are only showing you the curvature of space, not spacetime. But much of the important information about spacetime curvature requires looking at time, so it's being left out in those visualizations.

Instead of trying to visualize the "fabric" all in one go, another avenue that is open is to think of what spacetime curvature means, physically. It's often equated to "gravity", but it's really more specific than that: it's tidal gravity. For example, suppose I have two rocks hanging motionless above the Earth at some instant; both of them lie along a single radial line from the center of the Earth, but one is a little bit higher than the other. As the rocks start to freely fall, their separation will increase (because, in Newtonian terms, the lower one will fall slightly faster than the higher one). This is an example of tidal gravity. Or, if we have two rocks that are both at the same altitude but separated a little bit horizontally, and they start to fall, their separation will decrease (because, in Newtonian terms, they are both falling towards the center of the Earth, and that is a slightly different direction for the two of them). That is also an example of tidal gravity.

If we now try to translate what I just described into a visualization, we will find that it can't be done with a single "sheet" of fabric, so to speak--at least, not in any way that will be easy to interpret. But we can do it with two "sheets". For one "sheet", we have the time direction along one axis, and the radial (vertical) direction along the other; and we draw the worldlines (paths through spacetime) of the two radially separated rocks on the sheet. We find that the rocks separate, which means the "grid lines" on the sheet must get further apart in the radial direction as we move along the time direction. This means the sheet will be shaped something like a saddle.

For the other "sheet", we have the time direction along one axis, and the tangential (horizontal) direction along the other, and we draw the worldlines of the two rocks. We find that they get closer together, which means that the "grid lines" on the sheet get closer together as we move along the time direction. This means the sheet will be shaped something like a section of a sphere.

For an image of what I'm talking about, look at page 112 here:

https://books.google.com/books?id=iGmPBAAAQBAJ&pg=PA111&lpg=PA111&dq=tidal+gravity+spacetime&source=bl&ots=wuZVgeCIup&sig=klK7uzpV6hLeG2eRCv2MeUtNvKk&hl=en&sa=X&ei=-u1cVYCUIYaWNt_sgHg&ved=0CCsQ6AEwAjgK#v=onepage&q=tidal gravity spacetime&f=false

This is from Kip Thorne's Black Holes and Time Warps, which I highly recommend as a book on GR for the non-technical reader. The text is talking about the tidal gravity produced by the Moon (so the "rocks" would instead be pieces of Earth's ocean), but the tidal gravity produced by the Earth, or indeed any spherical gravitating body, is similar.

Thanks for taking the time to explain that, and for the book link peter. I can't honestly say i completely understand, but I am getting closer, and I feel a lot better about learning that it's people in general, and not just me, that has trouble visualizing curved surfaces with more than two dimensions. AND the fact that i wasn't completely factoring in time in the spacetime fabric will add a whole new dimension to my contemplations. ( bad pun intended )

 

[A.T.]

AND the fact that i wasn't completely factoring in time in the spacetime fabric will add a whole new dimension to my contemplations. ( bad pun intended )

Check out these links for more visualizations:

http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html

http://www.relativitet.se/Webtheses/tes.pdf



http://www.adamtoons.de/physics/gravitation.swf

 

[DastardlyBliss]

So basically this is saying that if a photon, for example, was traveling in an assumed straight line past a massive object, it would actually slow down while passing by it? hence the time dimension of the fabric.

The adamtoons thing was great, Thank you.

So i need to think less about the spacetime fabric warps taking up space (pushing objects away) and more about them taking up time. Its kinda like a straight path nearby a massive object is still the long way around it, if that makes sense. And when i was thinking of the warp being infinite, its because i never factored in gravitation.

I think i understand a lot clearer, even if i can't communicate it properly.

 

[A.T.]

So basically this is saying that if a photon, for example, was traveling in an assumed straight line past a massive object, it would actually slow down while passing by it?

Effectively yes:
http://en.wikipedia.org/wiki/Shapiro_delay

But a local clock would also tick slower, so you would still measure light at c locally.

 

[DastardlyBliss]

wait...sorry, just want to make sure i understand you. When you say local, you mean local to the "photon" right?

Edit - I think i got it now. You're talking about proper time. A clock on the object. I got that, but just found another cool adamstoon visualization that clarified things a bit more.

http://www.adamtoons.de/physics/relativity.swf - Relativity visualized

 

[A.T.]

wait...sorry, just want to make sure i understand you. When you say local, you mean local to the "photon" right?

By local I mean measuring light speed over a small distance, with a clock placed right at this short path.

You're talking about proper time. A clock on the object.

No, that would be rapdidity not vloecity:
http://en.wikipedia.org/wiki/Rapidity
But it's not what I meant.

http://www.adamtoons.de/physics/relativity.swf - Relativity visualized

You should try to get Epstein's book "Relativity Visualized" then.

 

[DastardlyBliss]

The amount space bends is dependent on how massive the object is. If you use the flat sheet analogy, a ball would make a tiny dent in space, a star creates a massive dent. Neither would be infinite in depth because neither have infinite mass, but both would be infinite along the length of the sheet... sort of. The range of gravity is infinite (we think) but it's affects travel at the speed of light (we think.)

Back to this. a simpler version of my question of "is the warp infinite" would have been for me to ask if dead space is also dispersed. If i throw a rock in a lake all the water has to move, basically. So if a new object pops into existence in space, the warp would only affect its surroundings in proportion to its gravity, and not expand the whole universe as in displacement.

 

[DastardlyBliss]

Thanks again to everybody for your responses. I can see that my original question could give birth to a million more. I am new at this. I think i need to do some reading and get my fundamentals down.

 

[newjerseyrunner]

If you drop a new object in spacetime, the it would create a depression in the fabric that would radiate outward like the ripple on a pond at the speed of light. If you popped a super massive star into existence one light year away from our star, we would not see a change in our star's trajectory until we first saw the light from it. Given infinite time it's presence would be felt throughout all of space.

 

[PeterDonis]

If you drop a new object in spacetime

You can't. This violates local stress-energy conservation. Objects cannot just appear out of nowhere; the stress-energy they contain has to come from somewhere. So thought experiments of this sort that claim to show how gravity would propagate are not correct.