Can Quantum Mechanics Explain the Expansion and Contraction of Space-Time?

[TEFLing]

I feel like there's an elephant in the room which no one has brought up yet. 4 spatial dimensions and space-time are not the same thing. It's almost more appropriate to refer to the former as "4 D" and the latter as "3+1 D". If you considered space-time to exist in the balloon analogy, then the two spatial dimensions and one time dimension would NOT be the 3 dimensions in which the sphere exists. For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension, with 2 spatial dimensions and one time dimension interacting to create the 2D surface of the sphere's relativistic effects.

In the olive artisan bread loaf analogy, each slice represents 2D of space ... And the stack of slices represents the passage of +1D of time

 

[ChrisVer]

(more precisely, what it says when you adopt a particular coordinate chart, the "comoving" chart)

I am having some conceptual problems with this, if you can enlighten me...
Why should it depend on the coordinate system itself,since coordinate systems are all equivalent ? I mean why would someone have to adopt a particular chart [the one named comoving] to get that?

 

[bapowell]

For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension, with 2 spatial dimensions and one time dimension interacting to create the 2D surface of the sphere's relativistic effects.

I don't think there's a good reason to bring time into the analogy as a dimension. The balloon exists in 3D (ambient) space, and its surface is idealized to be 2D (the surface of a 2-sphere). In making the analogy with the universe, only the surface of the balloon carries over: space is the 3D surface of a 3-sphere. The ambient 3D space of the balloon does not carry over in the analogy -- there is no 4D space within which the 3D "surface" of the universe is imbedded.

 

[gulfcoastfella]

Thanks bapowell. Why is it believed that there can't be a 4D space for which our universe is a surface?

 

[bapowell]

It's not that there cannot be such a space, only that such a space is not actually necessary. Though perhaps counter-intuitive, the surface of a 2-sphere, for example, is well-defined in 2D (i.e. the geometric properties that make it a 2-sphere don't care about any additional dimension). You can think of the geometry of the surface as being "encoded" within the surface.

 

[gulfcoastfella]

Oh, yeah, that's very cool; I haven't heard that before, even though I'm reading a book on the Calculus of Variations, and it talks about describing a 3-dimensional coordinate system constrained by a surface as really only needing 2 dimensions. Very cool.

 

[PeterDonis]

Humans have a perception of now which is so unique as to psychologically seem separate and distinct from both the past and the future

Yes, but this is a fact about human psychology, not about physics. This thread is about physics.

We feel ourselves to be evolving from one moment to the next, so I want to humor that popular perception

Why? What does it have to do with physics?

Relativity implies that we are 4D beings, whose present selves connect continuously from our past selves through our sense of now forward to our future selves

This is one way of interpreting what the mathematical model of relativity says, yes. But it could equally well be put forward as an interpretation of non-relativistic physics.

Relativity would connect our world lines to those of our parents...

To those of our ancestors...

Back ultimately ~4Gyr to the first Earth protocellular life form

None of this requires relativity. The fact that we are causally connected to our ancestors is perfectly explicable with non-relativistic physics.

 

[PeterDonis]

4 spatial dimensions and space-time are not the same thing

This is true; when we speak of "4-D" in a relativistic context, we mean "a four-dimensional manifold with three spacelike and one timelike dimension", not "a manifold with four spacelike dimensions". The difference shows up in the metric; the metric of spacetime is indefinite (squared intervals can be negative, or zero even between different points), whereas the metric of a four-dimensional space would be definite (squared intervals between different points must be positive).

For the purposes of the analogy, the balloon exists in 3 spatial dimensions and one time dimension

But one of the spatial dimensions does not represent an actual physical dimension of spacetime; it is an unphysical feature of the analogy only.

 

[Rocky9242]

I understand that the balloon analogy is misleading
Space is not expanding
Moment by moment, we leave behind a smaller space like slice, of the fabric of space-time...
And evolve into another, new, larger space like slice, of the fabric of space-time...
It's NOT like one balloon stretching...
Rather it's like a stack of balloons of increasing size...
To change the analogy, it's not one loaf of raisin bread rising... But a stack of slices of increasing size... Like a sliced loaf of artisan olive bread... The first slice is tiny, the next a bit bigger, and so on, up to the largest slices near the center middle...
The olives in the first few slices represent our galaxy in an ancient past life, the way it was billions of years ago...
The olives in the middle represent galaxies as they exist today
Olives towards the other end represent those same galaxies at future times
Please remember, Relativity says we are 4D beings, having "world volumes" as it were
Our past selves CONTINUE to exist in past space like slices, of the fabric of space-time...
And our future selves ALREADY exist, in future space like slices, of the fabric of space-time
The fabric of space-time is NOT expanding...
What is happening, is that what we for some reason perceive of as NOW, is a space like slice, of the fabric of space-time...
Which slices are becoming bigger and bigger, larger and larger
It's not that something is expanding or stretching...
Rather, space like slices, of the fabric of space-time, USED to be small...
And are GOING to be big...
And we're ON (relatively) medium sized slices
In a nutshell, that is what Relativity really says ... Not ONE thing stretching, but a STACK of thingS which are larger and larger

I _really_ don't understand this slice business. I thought space was expanding at the rate of the Hubble Constant. If space is not really expanding, what is the explanation of red shift?

Saying that our past selves continue to exist and our future selves already exist is a non-scientific statement. It is all right to make non-scientific statements, but we need to keep in mind that the current existence of the past and future is not subject to observation or experiment, and therefore is not scientific.

 

[PeterDonis]

I thought space was expanding at the rate of the Hubble Constant. If space is not really expanding, what is the explanation of red shift?

The redshift is evidence that distant galaxies are moving away from us, and that how fast they are moving away depends on their distance from us. (The Hubble constant, btw, is the proportionality constant between those two things; you have to multiply it by a particular galaxy's distance from us to get that galaxy's speed of recession from us.)

Whether you attribute the fact that distant galaxies are moving away from us to "space expanding" is a matter of interpretation, not physics.

 

[TEFLing]

Yes, but this is a fact about human psychology, not about physics. This thread is about physics.
Why? What does it have to do with physics?
This is one way of interpreting what the mathematical model of relativity says, yes. But it could equally well be put forward as an interpretation of non-relativistic physics.
None of this requires relativity. The fact that we are causally connected to our ancestors is perfectly explicable with non-relativistic physics.

Physics must be explained, yes?

So explaining physics requires understanding the audience

And some on this thread seem to prefer popular kinds of explanations

Also, the continuity of world lines is central to Relativity , yes? Einstein called the distinction between past present and future an illusion. I'm trying to explain Relativity using non Relativistic concepts. As long as I choose validly comparable concepts, then I should draw such comparisons, for purposes of explanation, yes?

 

[TEFLing]

I _really_ don't understand this slice business. I thought space was expanding at the rate of the Hubble Constant. If space is not really expanding, what is the explanation of red shift?

Saying that our past selves continue to exist and our future selves already exist is a non-scientific statement. It is all right to make non-scientific statements, but we need to keep in mind that the current existence of the past and future is not subject to observation or experiment, and therefore is not scientific.

Einstein called the distinction between past present and future an illusion. The ontological existence, of the past and future portions, of the worldlines of all particles, is a required and mandatory part of the theory. Space time is a fabric / manifold / membrane of 3+1D

Space like slices of that fabric are bigger and bigger at later and later times ( as measured by clocks inside the fabric )

But no single slice is stretching / growing / expanding

To try to make another analogy, it's like a movie real... Despite the illusion of motion, the movie is really a sequence of still shots... Something exploding in the movie would be a sequence of still shots, each with a bigger fire ball than the frame before...

But the frames aren't changing, and the fireball in a given frame is not changing or growing or anything

So it is not really right to say that one fireball is growing, i.e. that one space is expanding / stretching...

Rather instead there are a sequence of fixed frames, i.e. space like slices of the fabric of space-time, that increase in size from one to the next as defined by a time like coordinate

If you prefer the regular rising raisin bread analogy, then what you should ought to imagine...

Is a sequence of SEPARATE loaves, each flash frozen after a progressively increasing amount of baking time in the oven ... And set out on separate shelves of a tall bakery rack

On the very bottom shelf is a tiny uncooked ball of dough

On the next shelf up is a barely cooked loaf baked for one minute

On the next shelf, a loaf baked for three minutes...

And so on

The fabric of space time is like all of those 3D loaves, stacked on top of each other ( in an orthogonal higher dimension )

If you actually saw such a display in some real bakery, for whatever reason...
Your eyes might scan up the rack, from the bottom shelf to the top...
Your eyes could only focus fully on one shelf at a time...
But all the shelves are always there...
That is like our illusory sense of the present... We focus on now, but past and present are both also part of the 3+1D fabric of space and time

It's not one loaf rising
It's a sequential stack of separate loaves of increasing size
( and for some reason we psychologically single out one loaf at a time for our sense of now)

 

[PeterDonis]

explaining physics requires understanding the audience

And some on this thread seem to prefer popular kinds of explanations

Are you trying to "explain" physics as in "give people an understanding of how the theory actually models things and makes predictions"? Or are you trying to "explain" as in "tell people things that fit in with their intuitions, even if it doesn't help them understand how the theory actually models things and makes predictions"?

I think a lot of people are looking for the latter type of "explanation", but that doesn't mean it should be given to them. If you're not giving people an understanding of how a theory actually models things and makes predictions, then you're not "explaining physics" IMO.

the continuity of world lines is central to Relativity , yes?

Yes. What does that have to do with what we're discussing?

Einstein called the distinction between past present and future an illusion. I'm trying to explain Relativity using non Relativistic concepts.

This seems like an oxymoron to me. Relativity uses relativistic concepts, not non-relativistic concepts.

The ontological existence, of the past and future portions, of the worldlines of all particles, is a required and mandatory part of the theory.

Here's an example of "explaining" in the wrong sense. As you state it, this is simply false: the theory of relativity models the world as a 4-dimensional spacetime continuum, but that does not mean ontological claims about the "existence" of 4-dimensional spacetime are "a required and mandatory part of the theory". But it certainly seems plausible to people's intuitions.

The reason it seems plausible to people's intuitions is that people don't understand that scientific theories are models. The 4-dimensional spacetime used in relativity is a model. Models are not the same as reality. They have to share some features with reality in order to make good predictions, but that does not mean that every feature of the model has to be a feature of reality.

 

[TEFLing]

The theory is a model, yes

According to the model, past present and future are all parts of a single fabric of 3+1D space-time ( and worldlines of particles which occupy portions of that fabric )

Einstein seemed to think that that aspect of the model also reflected reality, calling any distinctions illusory. Insofar as experiments corroborate the predictions of the theory, then judging trees by fruit for want of worthier words, the difficult to describe co existence of past present and future regions of a single fabric of space and time seems the most straight forwardly obvious and natural one ( which Einstein seemed to favor)

 

[TEFLing]

Trying to think of how QM affects the world lines of particles inside of a 3+1D fabric of space-time...

It seems like QM and GR agree that the world lines of particles in the PAST region of space-time are fixed and locked in for want of worthier words...

But GR is a fully deterministic theory , and says the same thing for the future region of space-time as well, i.e. worldlines are fixed and locked in

Whereas QM is probabilistic and says that the future region of space-time harbors wave functions which are UNCOLLAPSED and so diffused and spread out in the ghostly probabilistic sense of QM

I want to ask, what would happen if, from within the framework of GR, you replaced the fixed world lines of non-quantum deterministic ( determined ) particles...

With the quantum probability distributions...

Density ~ mass x <¥|¥>

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