Exploring the Expanding Universe: Understanding the Stretching of Space-Time

[TEFLing]

[Mentor's note: This thread was split off from https://www.physicsforums.com/threads/observable-universe-question.79096]

The expansion of space can be likened to the stretching of the fabric of space time. At early epochs, that stretch was FASTER than the speed of light ...

So the expansion of the universe initially carried ALL light AWAY from our location

 

[bapowell]

The expansion of space can be likened to the stretching of the fabric of space time. At early epochs, that stretch was FASTER than the speed of light ...

So the expansion of the universe initially carried ALL light AWAY from our location

This is a popular misconception. The expansion of space does not proceed at a given speed (it is really a rate per distance), and so it's never correct to say that the expansion was faster than the speed of light. What is typically meant by this, I'll grant, is that the expansion can be such that that objects comoving with the expansion attain speeds surpassing that of light. This is true, but it's always true in any expanding cosmology, at both early and late epochs. The distance at which objects attain a superluminal recession velocity is called the Hubble distance.

 

[TEFLing]

...

the expansion can be such that that objects comoving with the expansion attain speeds surpassing that of light. This is true, but it's always true in any expanding cosmology, at both early and late epochs. The distance at which objects attain a superluminal recession velocity is called the Hubble distance.

Yes, that is what I said

In the rubber sheet analogy, the sheet is stretching, such that, say, opposite corners held by opposing graduate students, are receding from each other faster than light propagates THROUGH the rubber sheet

It is very important to clarify, that nearby proximate points, such as the center of the rubber sheet, are not receding from each other very quickly at all...

At later epochs, the expansive stretching slows, such that you have to have a larger sheet, held by more graduate students, to have opposing TAs on opposite sides of the sheet running away from each other at the same faster than light speed...

Other than that QUANTITATIVE difference, however, early and late epochs are qualitatively similar, i.e. there is always a Hubble distance

 

[Orodruin]

But not to the fabric of space-time itself...

Which can expand, or stretch, at hypothetically arbitrary speeds ...

First of all, space-time is not expanding, space is. Space-time is what it is.

Second, when space is expanding it is more accurate to talk about a rate of expansion than a speed. However, it may result in distances growing faster than the speed of light.

 

[bapowell]

Which can expand, or stretch, at hypothetically arbitrary speeds ...

Again, expansion does not have a speed.

 

[TEFLing]

http://www.bing.com/images/search?q...DAF1737CEBFF52DB4742B486A75872BF94EE&first=27

So constant time slices, of the fabric of space-time, grow larger with time...

But the fabric of space-TIME is static...

Simply "floating in hyperspace" were one to use that picture...

That makes even more sense

So that is why there is no speed, nothing is moving in any ultimate hyperspacial sense...

The perception of expansion actually describes the shape or structure or form of the fabric of space-time...

Which is unchanging

 

[PeterDonis]

the fabric of space-TIME is static...

Putting it this way can be misleading, because the word "static" means "unchanging", and the concept of "change" requires time, and time is a part of spacetime, not something spacetime exists "in". It would be better to say spacetime just "is"--it exists.

Simply "floating in hyperspace" were one to use that picture...

This can be misleading too, because there is no "hyperspace"; there is no underlying medium in which spacetime exists. Spacetime just exists.

that is why there is no speed, nothing is moving in any ultimate hyperspacial sense...

This can also be misleading, for the same reason as above.

The perception of expansion actually describes the shape or structure or form of the fabric of space-time...

This part is fine...

Which is unchanging

...as long as you leave this part out. Spacetime does have a geometry, a shape, and the spacetime geometry of our universe is such that "slices" cut out of it a certain way have a spatial scale factor that increases along a timelike direction orthogonal to those slices. That is the best way to describe, in geometric terms, what is usually referred to as the "expansion" of the universe. Note that I said nothing about hyperspace or spacetime being static--I just described the geometry and that's all.

 

[TEFLing]

Putting it this way can be misleading, because the word "static" means "unchanging", and the concept of "change" requires time, and time is a part of spacetime, not something spacetime exists "in". It would be better to say spacetime just "is"--it exists...
This can be misleading too, because there is no "hyperspace"; there is no underlying medium in which spacetime exists. Spacetime just exists......as long as you leave this part out. Spacetime does have a geometry, a shape, and the spacetime geometry of our universe is such that "slices" cut out of it a certain way have a spatial scale factor that increases along a timelike direction orthogonal to those slices. That is the best way to describe, in geometric terms, what is usually referred to as the "expansion" of the universe. Note that I said nothing about hyperspace or spacetime being static--I just described the geometry and that's all.

How does viewing space time as a manifold or fabric, embedded in a higher dimensional bulk or hyperspace, ever lead to any errors?

Providing we both calculate completely correctly ...

If I imagine a higher dimensional embedding space, and you do not, when do ever wind up with different answers?

How is the concept of hyperspace ever actually, actively, mis-leading?

There is a difference between "it's not a necessary concept and I don't like it or use it"...

Vs. "it's an erroneous presupposition"

 

[Drakkith]

How does viewing space time as a manifold or fabric, embedded in a higher dimensional bulk or hyperspace, ever lead to any errors?

Providing we both calculate completely correctly ...

If I imagine a higher dimensional embedding space, and you do not, when do ever wind up with different answers?

There is a difference between "it's not a necessary concept and I don't like it or use it"...

Vs. "it's an erroneous presupposition"

Occam's razor. Neither hyperspace nor higher dimensions are required to give us the right answers so we don't include them. Including them can also lead to other issues, such as what is that dimension embedded in, and that one, etc. In the end it's all a big philosophical mess, so we just avoid it all by saying that spacetime isn't required to exist within anything else. We don't claim that it absolutely cannot exist within something else, only that it isn't required to.

How is the concept of hyperspace ever actually, actively, mis-leading?

It's misleading because it isn't mainstream science. Note that PF rules do not allow members to simply give their opinions as answers, regardless of whether it "leads to errors" or not. You can find the rules here: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

 

[PeterDonis]

Providing we both calculate completely correctly ...

And if you calculate completely correctly, there will be nothing whatsoever in your calculation that corresponds to "hyperspace". So on what basis would you even interpret the calculation as being about "hyperspace" if nothing in the calculation corresponds to it?

 

[TEFLing]

And if you calculate completely correctly, there will be nothing whatsoever in your calculation that corresponds to "hyperspace". So on what basis would you even interpret the calculation as being about "hyperspace" if nothing in the calculation corresponds to it?

Einstein famously reasoned visually and geometrically, so I was told

The WMAP graphic of the fabric of space time visually suggests, or even implies, that the viewer is looking at the fabric of space-time from some higher dimensional (3D for the 2D spacetime shown) hyperspace perspective

Hyperspace seems useful for visualizing curvature (to the extent that such is possible)

I understand that String Theory regards space time as a membrane embedded in a higher dimensional Bulk, i.e. hyperspace

Is that a misunderstanding?

 

[TEFLing]

Is it possible to explain how to have a curved membrane or manifold or fabric, without it curving through higher dimensions?

For the first few dimensions, curvature seems to require higher dimensions...

A line can curve only in a plane, like the center of a football/soccer field. And the surface of the Earth can curve only through 3Ds.

What is different for 4D space time curving?

 

[Drakkith]

Einstein famously reasoned visually and geometrically, so I was told

Yes, but you are not. You haven't even learned the basics of differential geometry, which is absolutely necessary to understanding the curvature of space.

The WMAP graphic of the fabric of space time visually suggests, or even implies, that the viewer is looking at the fabric of space-time from some higher dimensional (3D for the 2D spacetime shown) hyperspace perspective

It most certainly does not suggest that. If you continue to make baseless assertions I will lock this thread.

Is it possible to explain how to have a curved membrane or manifold or fabric, without it curving through higher dimensions?

Yes, by understanding that curvature can be intrinsic or extrinsic. From wiki: http://en.wikipedia.org/wiki/Curvature#Higher_dimensions:_Curvature_of_space

By extension of the former argument, a space of three or more dimensions can be intrinsically curved. The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.

We do not conceive of spacetime as being embedded in a higher dimension, so the curvature is intrinsic.

For the first few dimensions, curvature seems to require higher dimensions...

This only appears to be true because you're used to seeing the first few dimensions from your vantage point in 4d spacetime. They happen to be embedded into higher dimensional space, but in general they are not required to be.

 

[TEFLing]

Yes, but you are not. You haven't even learned the basics of differential geometry, which is absolutely necessary to understanding the curvature of space.

Can you be more specific?

It most certainly does not suggest that. If you continue to make baseless assertions I will lock this thread.

Can I be more specific?

In every rubber sheet analogy, and in every picture of a space-time fabric...

The viewer seems to be looking at said space-time from some "position" or some "where" OUTSIDE of the fabric...

Doesn't that imply that the viewer resides in a higher dimensional ambient space (to try to use the term you quoted)? Am I the only person who winds up with that impression?

 

[bapowell]

In every rubber sheet analogy, and in every picture of a space-time fabric...

The viewer seems to be looking at said space-time from some "position" or some "where" OUTSIDE of the fabric...

Doesn't that imply that the viewer resides in a higher dimensional ambient space (to try to use the term you quoted)? Am I the only person who winds up with that impression?

Yes, but that's where the analogy breaks down. As a good exercise in differential geometry, you should work through the derivation of the intrinsic curvature of the 2-sphere. You will find, along the way, the amazing result that the 2-sphere can exist perfectly fine in only 2 dimensions -- no need for a 3rd dimension within which to embed it! This is what it means for curvature to be intrinsic (another example, working the other way, is that of a cylinder -- it has zero curvature despite how it "appears" when it is embedded in 3D. The cylinder can be constructed from the plane by suitably connecting edges in such a way that the geometry is not disturbed).

The conclusion is that spacetime is not required to be embedded in a higher dimension.

 

[Drakkith]

Can you be more specific?

One of the branches of differential geometry is Riemannian geometry, which what General Relativity is based upon. This geometry is nothing like what you've ever dealt with, so even though you are trying to think in terms of geometry, you are basically held back to the middle-school/high-school level which uses flat geometry, aka Euclidean geometry. We surpassed Euclidean geometry almost 200 years ago.

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

 

[PeterDonis]

Am I the only person who winds up with that impression?

No, but that doesn't mean it's a correct impression. The diagrams you are talking about are attempts to help people visualize what the mathematics is saying; doing that often involves adding extra elements that are not required by the mathematics or the physics, but might be helpful given humans' limited ability to visualize things. The higher-dimensional ambient spaces you are referring to are examples of this: there is nothing in the mathematics or the physics that corresponds to them, but they are added into make it easier for people to visualize a curved space or spacetime. This is a good illustration of why, if you really want to understand a physical theory, you have to actually look at the underlying math; you can't depend on second-hand methods like the diagrams you refer to.

 

[phinds]

In every rubber sheet analogy, and in every picture of a space-time fabric...

You might find it interesting to read the page linked to in my signature. It was written with a lot of help by people here on the forum.

 

[John_QPublic]

Paul Davies, Nature, 1978

"...his [Ellis] cosmic model is supported by the Big-Bang and Expanding Universe concepts, which in turn are buttressed by the simple observation that astronomers see redshifts wherever they look.

These redshifts are due, of course, to matter flying away from us under the impetus of the Big Bang. But redshifts can also arise from the gravitational attraction of mass. If the Earth were at the center of the universe, the attraction of the surrounding mass of stars would also produce redshifts wherever we looked! The argument advanced by George Ellis in this article is more complex than this, but his basic thrust is to put man back into a favored position in the cosmos..."

 

[PeterDonis]

If the Earth were at the center of the universe, the attraction of the surrounding mass of stars would also produce redshifts wherever we looked!

This does not seem right; gravitational redshift does not work this way. I suspect that Davies was misinterpreting something Ellis said in his article. Does anyone know if Ellis's article is available online?

 

[John_QPublic]

I have not found it online. I do not think Ellis was using the FLRW metric, but I am not sure. He plays all over Bianchi space.

 

[TEFLing]

I'd like comments and constructive criticism of the following...

Current understanding
------------------------------

http://scienceblogs.com/startswithabang/files/2011/12/darkenergyfr.jpeg

The fabric of space-time is static and unchanging in some sense

The space-time of the past and the fabric of the future already exist

We occupy a thin spatial slice of the fabric

And it so happens that the slices are becoming bigger

Moment by moment the stage becomes larger

Seemingly stretching apart and carrying all of the actors apart too...

BUT ...

The stage we occupied yesterday was a SEPARATE stage = space like slice of fabric...

Than the one we occupy today...

And both of these are separate from the stage we will occupy tomorrow

It is NOT ONE STAGE stretching...

But rather a series of sequential stages which happen to be becoming bigger

Nothing is growing
Nothing is stretching
There is no one thing that is enlarging

Rather
In the above figure
Space as we know it
Is like a vertical stack of rings
Each larger than the prior previous
Moment by instant
We step from a smaller ring to a larger ring
And we look around and notice we have more room now
And so we conclude one space stretched...
But NO...
We parted from the smaller ring
And entered another bigger one

The future is fated in some sense
All of the fabric of future space-time ALREADY EXISTS

Even as all of the fabric of past space time STILL EXISTS

The fabric of SPACE TIME is unchanging
What IS changing is the spatial slice of the fabric we occupy NOW
In the above figure, we're moving upwards
As if in an elevator
Going up a building
Whose floors were becoming bigger and larger
At each new level

 

[TEFLing]

Yes, but that's where the analogy breaks down. As a good exercise in differential geometry, you should work through the derivation of the intrinsic curvature of the 2-sphere. You will find, along the way, the amazing result that the 2-sphere can exist perfectly fine in only 2 dimensions -- no need for a 3rd dimension within which to embed it! This is what it means for curvature to be intrinsic (another example, working the other way, is that of a cylinder -- it has zero curvature despite how it "appears" when it is embedded in 3D. The cylinder can be constructed from the plane by suitably connecting edges in such a way that the geometry is not disturbed).

The conclusion is that spacetime is NOT REQUIRED to be embedded in a higher dimension.

You could distinguish between cylinder and plane
By sending out a probe around the curved dimension of the cylinder...
It would come back to you from the other direction

That scenario could not occur in a plane
So how can one regard the cylinder as equivalent to a plane

A plane is not a cylinder
And you could in principle tell them apart
So why say they are essentially the same ?

Or did you not say that?

 

[TEFLing]

One of the branches of differential geometry is Riemannian geometry, which what General Relativity is based upon. This geometry is nothing like what you've ever dealt with, so even though you are trying to think in terms of geometry, you are basically held back to the middle-school/high-school level which uses flat geometry, aka Euclidean geometry. We surpassed Euclidean geometry almost 200 years ago.

http://en.wikipedia.org/wiki/Non-Euclidean_geometry

What books did you yourself learn from?

 

[Drakkith]

What books did you yourself learn from?

I don't know the math. I know about the math, lol. I'm about to start taking calculus 1, so I'm several years from differential geometry.

 

[PeterDonis]

You could distinguish between cylinder and plane
By sending out a probe around the curved dimension of the cylinder...
It would come back to you from the other direction

This is extrinsic curvature, not intrinsic curvature. bapowell was talking about intrinsic curvature.

 

[PeterDonis]

The fabric of space-time is static and unchanging in some sense

I already addressed this in post #7. The concept of "change" requires time as an external parameter. With reference to spacetime, time is not an external parameter; it's one of the dimensions of spacetime. So spacetime is not "changing" or "unchanging"; it just is.

The space-time of the past and the fabric of the future already exist

This would be fine if you left out the word "already". That word implies time as an external parameter. The "past" and "future" are just different parts of spacetime, like the southern hemisphere is a different part of the Earth's surface.

We occupy a thin spatial slice of the fabric

No, we don't; "we" are not points. We are worldlines (or world-tubes if you take into account that all objects have a finite size). The instant of "now" for each of us is the intersection of our world-tube with a particular spacelike slice of spacetime. But that intersection is not what "we" are, because time is a dimension of spacetime, and "we" occupy that dimension as well as the spatial ones.

And it so happens that the slices are becoming bigger

The word "becoming" is not appropriate here, because it implies time as an external parameter. See above.

It is NOT ONE STAGE stretching...

But rather a series of sequential stages which happen to be becoming bigger

You're headed in the right direction, but there's that word "becoming" again. A better way to put it would be the way I put it in post #7:

the spacetime geometry of our universe is such that "slices" cut out of it a certain way have a spatial scale factor that increases along a timelike direction orthogonal to those slices

 

[TEFLing]

This would be fine if you left out the word "already". That word implies time as an external parameter. The "past" and "future" are just different parts of spacetime, like the southern hemisphere is a different part of the Earth's surface.
No, we don't; "we" are not points. We are worldlines (or world-tubes if you take into account that all objects have a finite size). The instant of "now" for each of us is the intersection of our world-tube with a particular spacelike slice of spacetime. But that intersection is not what "we" are, because time is a dimension of spacetime, and "we" occupy that dimension as well as the spatial ones...

:

What is philosophically special about" now "

Such that we are aware of now

In a very different way from the past and future?

What is special about the present?

Can something sensible be said?

 

[PeterDonis]

What is philosophically special about" now "

Such that we are aware of now

In a very different way from the past and future?

A quick side question: why are you putting extraneous line breaks in?

If you mean this a a philosophical question, it's off topic here; this is a physics forum.

If you really mean it as a physics question, then the answer is that there is nothing special, physically, about "now". It's just a particular set of events that get picked out when you choose coordinates.

As far as what we are aware of, we are not aware of "now" because of the finite speed of light. We are only aware of our past light cone. (Actually, in practical terms, the nerve signals in our brains that instantiate our awareness travel a lot slower than light, so what we perceive as "now" is actually a time interval of something like 10 to 100 milliseconds, which is a very long time in fundamental physics terms.)

What is special about the present?

Physically speaking, nothing. See above.