Is the Universe infinite?

[AbstractDreamer]

 

1 hour ago, Strange said:

Well, I'm not going to get into a discussion about whether quantum theory is correct or not.

But for the many theories of quantum mechanics that are correct or not, that describe interactions of the forces, and have useful applications; these models are not dependent on the absence of non-local interactions.  To state that no information is transferred during entanglement decoherence is an assumption that, either true or false, does not contradict the principles of quantum theory.  I did not mean to imply that quantum theory is incorrect, neither is that my argument.

What I'm trying to say is: Is it possible the universe may have an infinite number of sizes, with respect to coherent states, depending on the boundaries of the volume in question at a specific time.

[Carrock]

26 minutes ago, AbstractDreamer said:

But for the many theories of quantum mechanics that are correct or not, that describe interactions of the forces, and have useful applications; these models are not dependent on the absence of non-local interactions.  To state that no information is transferred during entanglement decoherence is an assumption that, either true or false, does not contradict the principles of quantum theory.  I did not mean to imply that quantum theory is incorrect, neither is that my argument.

If there is superluminal information transfer then there are effects contrary to quantum theory and quantum theory is wrong. You can't have it both ways.

[Strange]

33 minutes ago, AbstractDreamer said:

Is it possible the universe may have an infinite number of sizes, with respect to coherent states, depending on the boundaries of the volume in question at a specific time.

What?

[taeto]

I know the topic is old hat. I have read through the thread, and notice that most answers do not speak of this question in the same spirit as I naturally tend to think of it. That is, coming from the mathematics side.

Mostly it is perceived as a question of size, and that is fair enough. If the volume of the space part of the universe is infinite, then it is reasonable to consider it to be infinite. Even if that is not the case, then it is still possible that the volume of the entire spacetime is infinite. 

Suppose though, that the volume of space is finite, and maybe even of spacetime as well. Could not the contents of space still be an infinite amount? In particular, is the amount of physical content within a 1x1x1 cube (resp. 1x1x1x1 spacetime cube) necessarily finite?

I have to add some motivation to that question.

First, in mathematics, I am absolutely happy with the fact that in Euclidean space, the modest straight line segment between 0 and 1 contains an infinite amount of single points, even an infinite amount of rational valued points. And if you consider all the Euclidean points in this segment, there is the same amount of them as in the entire Euclidean space \(R³\). It seems to me that space itself easily contains an infinite amount of things, namely of single points. After all, even physicists keep referring to a geometry of space and spacetime that necessarily consists of a continuum of points.

Some physicists that I met, though I am not sure if they are just pop-sci types, explain that even in the interval between 0 and 1 there is only a finite number of Planck lengths available, hence the interval itself should count as finite. To me that sounds pretty simplistic, as it seems presupposed that you can determine the beginning and end of each interval of Planck length in which something uniformly happens throughout. Whereas you can never hope to figure out what happens on a smaller scale. This is quite reasonably true in QM, but it is not one of those things that you confirm experimentally, and it seems it could be changed by a quantum gravity theory that extends current QM.

Second, when I listen to Susskind explaining BHs, he explains the concept of a condensate so that it has the property to contain an infinite number of identical particles. And this concept is used to explain how QM works in some situations. Is there any reason that has to be b****cks? It seems fine if the particles are massless with a momentum that adds up to near zero, or not?

And if the universe contains an infinite amount of individual particles, then it also has to count as being infinite? 

[Strange]

On 24/06/2018 at 9:18 PM, taeto said:

First, in mathematics, I am absolutely happy with the fact that in Euclidean space, the modest straight line segment between 0 and 1 contains an infinite amount of single points, even an infinite amount of rational valued points. And if you consider all the Euclidean points in this segment, there is the same amount of them as in the entire Euclidean space R³ . It seems to me that space itself easily contains an infinite amount of things, namely of single points. After all, even physicists keep referring to a geometry of space and spacetime that necessarily consists of a continuum of points.

This is true. But I don't think the coordinates (or points) count as "contents" of space. I would think of the contents as being matter, photons, etc. The amount of these must, surely, be finite if the volume of space is finite otherwise the density would be infinite. No?

On 24/06/2018 at 9:18 PM, taeto said:

Second, when I listen to Susskind explaining BHs, he explains the concept of a condensate so that it has the property to contain an infinite number of identical particles.

Does he mean that it could (in principle) contain an infinite number of particles, rather than it does?

[taeto]

4 hours ago, Strange said:

This is true. But I don't think the coordinates (or points) count as "contents" of space. I would think of the contents as being matter, photons, etc. The amount of these must, surely, be finite if the volume of space is finite otherwise the density would be infinite. No?

I agree that this is what should be the idea, physically. There is still room for confusion, because the questions whether "space" or "spacetime" is finite or infinite appear ambiguous. Surely space, as a mathematical abstract that serves to keep track of the coordinates of things that are happening, has continuum size, regardless of geometry. That is the way it is used in theoretical physics. No? You would probably explain that "the universe" consists of both "the space(time)" and the stuff that occupies it, but space itself is just one single thing, as opposed to the entire totality of its points? After all, space is there in the universe, so it should count in some way to the totality of things.

5 hours ago, Strange said:

Does he mean that it could (in principle) contain an infinite number of particles, rather than it does?

When it is explained that a condensate has the property that adding or removing a single particle does not change it in any way, it is clear that this means an infinite amount of single particles have to be present. But I have to perceive this statement as just an approximation, to say that it is close enough to what actually occurs. It seems to me that he never explains this latter part, but, after all, he mostly just lectures to old people that are not necessarily keen to actively force the distinction. So yes, the exact definition that he usually gives definitely does imply the infinite amount. Whether confined to a finite part of space is however not completely clear; because of SR I would guess that finiteness is implicitly implied.

I can come up with spontaneous particle-antiparticle formation and annihilation as a mechanism to quickly create lots of stuff in a small space. Is there any known bound to how many pairs may be created within given space and time? Are there more reasonable/effective candidates?

[Strange]

7 hours ago, taeto said:

Surely space, as a mathematical abstract that serves to keep track of the coordinates of things that are happening, has continuum size, regardless of geometry.

Ah. Perhaps we are thinking of "size" in two different sense: the cardinality of the coordinate system (which is, in GR at least, the continuum); versus the physical extent (volume) of the universe, which could be finite or infinite.

Does that make sense?

8 hours ago, taeto said:

When it is explained that a condensate has the property that adding or removing a single particle does not change it in any way, it is clear that this means an infinite amount of single particles have to be present.

I can't comment as I am not familiar with the context...

[Mordred]

On ‎2018‎-‎06‎-‎24 at 3:18 PM, taeto said:

I know the topic is old hat. I have read through the thread, and notice that most answers do not speak of this question in the same spirit as I naturally tend to think of it. That is, coming from the mathematics side.

Mostly it is perceived as a question of size, and that is fair enough. If the volume of the space part of the universe is infinite, then it is reasonable to consider it to be infinite. Even if that is not the case, then it is still possible that the volume of the entire spacetime is infinite. 

Suppose though, that the volume of space is finite, and maybe even of spacetime as well. Could not the contents of space still be an infinite amount? In particular, is the amount of physical content within a 1x1x1 cube (resp. 1x1x1x1 spacetime cube) necessarily finite?

I have to add some motivation to that question.

First, in mathematics, I am absolutely happy with the fact that in Euclidean space, the modest straight line segment between 0 and 1 contains an infinite amount of single points, even an infinite amount of rational valued points. And if you consider all the Euclidean points in this segment, there is the same amount of them as in the entire Euclidean space R³ . It seems to me that space itself easily contains an infinite amount of things, namely of single points. After all, even physicists keep referring to a geometry of space and spacetime that necessarily consists of a continuum of points.

Some physicists that I met, though I am not sure if they are just pop-sci types, explain that even in the interval between 0 and 1 there is only a finite number of Planck lengths available, hence the interval itself should count as finite. To me that sounds pretty simplistic, as it seems presupposed that you can determine the beginning and end of each interval of Planck length in which something uniformly happens throughout. Whereas you can never hope to figure out what happens on a smaller scale. This is quite reasonably true in QM, but it is not one of those things that you confirm experimentally, and it seems it could be changed by a quantum gravity theory that extends current QM.

Second, when I listen to Susskind explaining BHs, he explains the concept of a condensate so that it has the property to contain an infinite number of identical particles. And this concept is used to explain how QM works in some situations. Is there any reason that has to be b****cks? It seems fine if the particles are massless with a momentum that adds up to near zero, or not?

And if the universe contains an infinite amount of individual particles, then it also has to count as being infinite? 

I would like to touch upon a particular section of the above. In mathematics we are confronted by sets that are infinite in quantity etc. A good example would be all the possible paths a lightbeam can follow (geodesics.) So there is a technique that is handy called compactification. Any infinite mathematical object/set etc will contain both infinite and finite parts.

 So in the example above we can compactify the possible paths to a finite probability weighted likelihood . This is via the possible paths of least resistance, it is a weighted probability based on kinetic vs potential energy relations.

In QFT there is two boundaries Dirichlet and Neumann boundaries these correspond to many of the PDE and ODE (partial differential) and (Ordinary differentials) the Direchlet being the PDE'S.

So lets provide a QFT application to all the above. Now particles can pop in and out of existence all the time but lets stick to the Feyman path integrals.

The external lines on a Feyman diagram are observable, this is an amount of "action" of 1 or more quanta. This involves coordinate change, the path of that external line will be a probability weighted likelihood. Now what about the internal lines these are not observable Operators but the unobservable propagators. Where the VP term is often applied, but its better to simply consider it as part of the field. (particles being field excitations). So in essence there can be an infinite possible number of particles however there is a likelihood of the number depending upon the available energy potential of the fields involved. Under QFT this is the purpose of the creation and annihilation operators. Unlike QM the field is treated as an operator.

 There is a few examples of how we can apply mathematics to deal with functions we use to model our universe with infinite possible values but restrict those functions to the finite portions.

Those two boundaries are involved in gauge group such as SU(2) and U(1)

Now another compactification technique is wicks rotation. If you take say a waveform and rotate a mirror image of that waveform there will be a point where the two will meet. This provides a definitive finite coordinate or graph point.

As you expressed an interest in the mathematics I felt this will be something you would find of interest

As a visual aid here is an example of a Feymann diagram the external lines on the diagonals are the observable (on shell particles) the internal wavy line is the propagators.

[math]\array{e^+ \searrow &&\nearrow P^-\\&\leadsto &\\ e^-\nearrow &&\searrow P^+}[/math]

Edited June 27, 2018 by Mordred

[EWyatt]

On 8/12/2017 at 8:19 PM, swansont said:

Being part of a multiverse does not mean our universe must be finite.

Uh, so our universe could be "infinite" in size, but there would be room for other universes anyway??  Does that pass the logic or physics test?

[swansont]

1 hour ago, EWyatt said:

Uh, so our universe could be "infinite" in size, but there would be room for other universes anyway??  Does that pass the logic or physics test?

Yes, it does.

There are an infinite number of numbers in any interval between two values (e.g. 1 and 2), and an infinite number of intervals. It's not a problem.

[Markus Hanke]

11 hours ago, EWyatt said:

Uh, so our universe could be "infinite" in size, but there would be room for other universes anyway??  Does that pass the logic or physics test?

Sure it does. There are plenty of examples of such concepts, which are mathematically (and hence logically) sound. To pick out just one, consider a Sierpinski cube - it’s a cube with a finite and well defined edge length, yet its surface area is infinite, while covering zero volume. How is that for a mind-boggler

[mistermack]

Are the words "is" and "infinite" actually compatible? 

"is" implies a finite state at a finite instant in time to me. 

Could there "be" an infinitely long pencil at an instant in time?

[Markus Hanke]

3 hours ago, mistermack said:

Could there "be" an infinitely long pencil at an instant in time?

No, but there can be infinitely many, infinitesimally small sections of pencil at an instant in time - which add up to a finitely long pencil. This is just the basis of ordinary calculus, where you integrate up infinitesimal quantities to obtain a finite result, in a mathematically well defined and fully self-consistent manner.

3 hours ago, mistermack said:

Are the words "is" and "infinite" actually compatible?

Yes, for the above reason.

[taeto]

6 hours ago, Markus Hanke said:

  9 hours ago, mistermack said:
Could there "be" an infinitely long pencil at an instant in time?

No, but there can be infinitely many, infinitesimally small sections of pencil at an instant in time - which add up to a finitely long pencil. This is just the basis of ordinary calculus, where you integrate up infinitesimal quantities to obtain a finite result, in a mathematically well defined and fully self-consistent manner.

In the context of the question the above is maybe not a fair way to answer.

In ordinary calculus you consider finitely many, say n, small sections of pencil, and you add up their lengths and get a length measure L(n) that depends on n. The integration means that you calculate a limit of L(n) as n approaches infinity, in a mathematically well defined and fully self-consistent manner. But there are not infinitely many small sections, only the fixed number n of them. The number n really is fixed and obviously finite, hence so is L(n). Calculating the limit only depends on the behavior of the function L that you consider.

Mathematically it is possible to have an infinitely long pencil with a finite volume. Maybe it stretches from x = 0 and all the way up through x > 0 so that the volume of the segment of the pencil between x and x+1 is equal to \( 1/ x^2 \).

Edited July 16, 2018 by taeto

[J.C.MacSwell]

4 hours ago, taeto said:

 

Mathematically it is possible to have an infinitely long pencil with a finite volume. 

I'm thinking pencils by definition have two ends. I am pretty sure that would make it finite...but infinite can be at times pretty counterintuitive...so maybe...but your definition seems finite.

[MigL]

As for the Susskind statement about adding or removing a particle from a condensate not changing anything...
Condensates have a particular property; they observe Bose-Einstein statistical rules.
You can stack as many as you want into the same state.

You may have misinterpreted it.

 

Edited July 17, 2018 by MigL

[Airbrush]

How many universes that are infinite in size can coexist? 

I still think only one because you can divide space in half, or quarters, or eighths, etc, and every one can be infinite in size,  but these are only theoretical.  They are divided by PLANES.   Planes don't occur in nature.   The REAL physical universes come from big bangs which are not neat and orderly like numbers, or planes in geometry.

[zapatos]

31 minutes ago, Airbrush said:

How many universes that are infinite in size can coexist? 

I still think only one because you can divide space in half, or quarters, or eighths, etc, and every one can be infinite in size,  but these are only theoretical.  They are divided by PLANES.   Planes don't occur in nature.   The REAL physical universes come from big bangs which are not neat and orderly like numbers, or planes in geometry.

Multiple universes need not be composed of the same building blocks and so could coexist in the same space.

As an analogy, a room could be a 'universe' of light, while at the same time being a 'universe' of sound.

[Airbrush]

Show me how multiple, infinite-sized universes can co-exist.  Sure universes can overlap on different dimensions.  In my thought experiment you must show how multiple, infinite-sized universes can co-exist on only 3 spatial dimensions.

Edited July 17, 2018 by Airbrush

[zapatos]

1 minute ago, Airbrush said:

Show me how multiple, infinite-sized universes can co-exist.  Sure universes can overlap on different dimensions.  In my thought experiment you must show how multiple, infinite-sized universes can co-exist on only 3 spatial dimensions.

I thought I did.

If the building blocks of Universe A do not interact with the building blocks of Universe B, why can't the two universes occupy the same three spatial dimensions?

[Airbrush]

Ok you got me there.  I accept that multiple universes can occupy the same 3 spatial dimensions as you describe. 

Now can you show me how they can co-exist IF the building blocks of Universe A must interact with B.  If it is impossible for them to NOT interact, if they must interact, then you cannot have co-existing universes that are infinite in size.

[zapatos]

2 minutes ago, Airbrush said:

Now can you show me how they can co-exist IF the building blocks of Universe A must interact with B.  If it is impossible for them to NOT interact, if they must interact, then you cannot have co-existing universes that are infinite in size.

I agree that if the building blocks must interact, that they cannot occupy the same space.

However, you can have two infinite universes that are adjacent to each other and do not overlap.

[Airbrush]

6 minutes ago, zapatos said:

…. you can have two infinite universes that are adjacent to each other and do not overlap.

That is hard to imagine.  So they end on one side and are infinite on the other side?  Vector universes?  Sounds implausible.

[zapatos]

3 minutes ago, Airbrush said:

That is hard to imagine.  So they end on one side and are infinite on the other side?  Vector universes?  Sounds implausible.

Imagine a number line starting at zero and moving right to infinity.

Now start at zero and move left to negative infinity.

Two lines that end on one side and are infinite on the other.

 

[Airbrush]

Yes, but how does a "vector big bang" happen?  That is counter-intuitive.  A big bang has to be an event that expands in all directions.  How can it expand in only one direction?