Exploring the Possibility of Expanding Atoms

[timmdeeg]

No. That's a fundamental misunderstanding of what "expanding space" is supposed to be describing.

The usual answer is "expanding space" means increasing distances.

One could argue that in an expanding universe the volume enclosed by 4 galaxies is growing and therefor additional space is created. So on one hand the (proper) volume is growing measurable in m³ but on the other the volume is growing according the growing scalefactor $a$ which is dimensionless however.

In other words GR doesn't predict growing (in the sense of additional) space but a consequence of the growing $a$ seems to be that any arbitrary volume enclosed by comoving points is growing. Isn't this a contradiction in itself and how do you resolve that?

 

[timmdeeg]

So if space isn't expanding inside of bound systems, what is happening to the particles in space that aren't in a bound system?

In this case these particles would be comoving and thus the proper distance between them would increase.

 

[Tayler]

In this case these particles would be comoving and thus the proper distance between them would increase.

So basically, in a square metre of space, the concentration of particles will decrease over time. Correct?
But would there be any significant change to the particle itself?

 

[Will Learn]

Hi again Tayler. Hope you are well.

what is happening to the particles in space that aren't in a bound system?

would there be any significant change to the particle itself?

Well, possibly. The space could be expanding as discussed earlier. However, all ordinary matter tends to create solutions to the Field Equations of General Relativity where space does not expand. It may even contract. So just by having that bit of matter which is your atom (various protons, neutrons and electrons) in a small region of space will tend to stop that little patch of space expanding.

It has previously been mentioned that we don't know much about "dark energy". However, even if something was driving the expansion of space where your atom is located, there are some other forces that can take over and pull all the sub-atomic particles through space to keep them together. I think it was Ibix who first mentioned electromagnetic interactions. There is also something called the strong force which holds sub-atomic particles together. It is extremely unlikely that all these forces can be overwhelmed.

 

[timmdeeg]

So basically, in a square metre of space, the concentration of particles will decrease over time. Correct?
But would there be any significant change to the particle itself?

Yes, within a volume measured in cubic meters the concentration of comoving particles would decrease. Counting them a certain time and then later at a certain time would reveal that. "At a certain time" is important because we talk about proper distances.
No, the particles would remain unchanged.

 

[Ibix]

So basically, in a square metre of space, the concentration of particles will decrease over time. Correct?
But would there be any significant change to the particle itself?

Cubic meter, but yes.

Nothing happens to the particles themselves. In a sense, the "expanding universe" is just like a cloud of particles expanding as if from an explosion (but note that there isn't a single point source for all matter in the universe). They just keep moving the way they do because there are no forces on them. But all that mass curves spacetime, and that has more complex effects.

The key problem with "space being created" is that general relativity models everything as spacetime. That's a 4d structure, and "the universe, now" is a 3d slice through it. "The universe, a second later" is a different 3d slice through spacetime. So it isn't that "space was created", but that you're thinking about successive slices through spacetime that have different scales.

 

[Tayler]

Cubic meter, but yes.

Nothing happens to the particles themselves. In a sense, the "expanding universe" is just like a cloud of particles expanding as if from an explosion (but note that there isn't a single point source for all matter in the universe). They just keep moving the way they do because there are no forces on them. But all that mass curves spacetime, and that has more complex effects.

The key problem with "space being created" is that general relativity models everything as spacetime. That's a 4d structure, and "the universe, now" is a 3d slice through it. "The universe, a second later" is a different 3d slice through spacetime. So it isn't that "space was created", but that you're thinking about successive slices through spacetime that have different scales.

Sorry haha I did mean m3.

So from what you just said I imagine spacetime is like a loaf of bread where each slice is bigger then the last and each slice contains the entire universe and is a different point in time. Each slice gets bigger but its contents stay unchanged. So hypothetically if you could weigh the entire universe at any given time or say, a slice from the first few minutes after the big bang and then a slice 2 billion years later, they would be the same weight, correct?

 

[Ibix]

So from what you just said I imagine spacetime is like a loaf of bread where each slice is bigger then the last and each slice contains the entire universe and is a different point in time. Each slice gets bigger but its contents stay unchanged. So hypothetically if you could weigh the entire universe at any given time or say, a slice from the first few minutes after the big bang and then a slice 2 billion years later, they would be the same weight, correct?

More or less, except all the slices are infinitely large as far as we know. So "space expanding" means that the distance between any two objects is growing at the same rate everywhere rather than that the slices are getting further apart. And we don't know any way to define "a total mass of the universe", so whether or not it's changing isn't known. With dark energy, whose density doesn't change and normal matter and radiation whose density does change, and curved spacetime to make the maths extra fun it's not the straightforward question you might assume.

 

[Tayler]

normal matter and radiation whose density does change,

Change how and from what?

 

[Will Learn]

I'm loving this discussion. You're inquisitve, Tayler.
How deep do you want go?

1. The argument about space being created (I think that was MacWylie who first mentioned it) is often presented as if space is being "injected" in from elsewhere. Between any two (distinct) points in space, more space is constantly being injected in. It's also possible not to worry about it and look at things the other way (Timdeeg was one of the first to mention this), space is just space but the scale factor changes. You might like to think of it as if the co-ordinate system is getting updated and modified as time progresses. Two points in space that are said to be "co-moving" just do have an increasing distance of separation as time progresses. The arguments are two sides of the same coin and I expect there are many other ways of looking at the situation.

I prefer thinking about the expansion of space with the idea of an evolving scale factor. It avoids all problems of considering space as "stuff" that has to be created from somewhere. Space doesn't have to be "stuff" it's just distance. There is some space between A and B just means there is some distance between A and B.

2. About the changing mass of time slices through spacetime:

So hypothetically if you could weigh the entire universe at any given time or say, a slice from the first few minutes after the big bang and then a slice 2 billion years later, they would be the same weight, correct?

This is complicated and I think Timdeeg has typed an answer while I was doing this one.
Start by replacing "weight" with mass. This is a minor technical change but it will help us. Mass is an intrinsic property of matter, while weight changes according to the gravitational field you're in. I don't think we could keep a total weight of the universe constant but there's some hope of keeping constant mass.
Next consider that mass is just a concentrated form of energy, so we'd be better off considering the total energy in the time slice. Mass can certainly change as time passes, nuclear reactions convert mass into energy, for example. Total energy at least has a better chance of being conserved.
Finally, see some comments that were mentioned earlier (I think it was Peter Donis who pointed at an article in the Preposterous universe blog).

Energy isn’t conserved; it changes because spacetime does. See, that wasn’t so hard, was it?

[Taken from https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ ]​

So, ummmm... no. Hypothetically, the stuff in each time slice is different in many ways. However, the changes are predictable. A human being studying physics could identify a place in one time slice that would correspond to a place in another time slice. Your analogy about expanding slices of bread is quite good for this. Some things change their properties but that is also in a predictable way (e.g. blue light may change into red light), you could identify it as being the same light just at a later time.

Study physics and tell me the correct answers as they stand in 10 years time.

 

[timmdeeg]

@Ibix would you mind to comment on post #36? I'm not sure if I'm missing something.

 

[PeroK]

So basically, in a square metre of space, the concentration of particles will decrease over time. Correct?
But would there be any significant change to the particle itself?

Yes and no. In principle, yes; in reality, a cubic metre of intergalctic space is likely to contain no particles.

The important thing you are (still) missing is that expansion occurs on a cosmological scale, where galaxies themselves are considered as the particles (think big!). You can't apply the same equations and get expansion on the scale of anything smaller.

You should consider the galaxies and galaxy clusters as the point particles. The universal expansion drives these further apart.

The universal expansion simply does not apply even within galaxy clusters (although you may need to take the vacuum energy into account when looking at the dynamics). And the dynamics within a galaxy are almost totally matter (and dark matter) dominated.

You must somehow lose the idea that you can apply universal expansion to every cubic metre of space.

 

[PeroK]

PS in terms of cosmology, the basic unit of length is not the metre but the megaparsec, which is about 3 million light years.

 

[Ibix]

@Ibix would you mind to comment on post #36? I'm not sure if I'm missing something.

The first two paragraphs seem fine. The last seems to be rather confused.

There is a special class of observer in FLRW spacetimes - the so-called co-moving observer. These are people who see, and have always seen, the cosmic microwave background as isotropic. Since they see it as isotropic they have a decent claim (or as decent a claim as it is possible to make) to be "at rest with respect to the matter in the universe". (We're doing about 600km/s compared to co-moving observers, so we see the CMB blueshifted in one direction and redshifted in the other.)

But all of the matter, including all other co-moving observers, is moving away from them. So if all co-moving observers are what we define as stationary for the purposes of this discussion, yet they are moving apart, one way of conceptualising that is to say that there's more space between them - "space is expanding". The scale factor of the distance increase is $a$, as you say.

The direct measurable fact is that if a co-moving observer bounces a series of radar pulses off another one, the return time increases. Any (almost any?) sane coordinate system is going to take this fact and give you that the volume between four tetrahedrally arranged co-moving observers is increasing. It's the interpretation of this as "expanding space" that I think is a bit awkward. But I can't think of a better way to say it...

Does that help?

 

[Ibix]

Change how and from what?

Stuff is moving apart, so the density now is lower than it was yesterday (edit: on average, and very very slightly on that timescale). Radiation also redshifts (edit: ditto). That's all I meant.

 

[timmdeeg]

The direct measurable fact is that if a co-moving observer bounces a series of radar pulses off another one, the return time increases. Any (almost any?) sane coordinate system is going to take this fact and give you that the volume between four tetrahedrally arranged co-moving observers is increasing. It's the interpretation of this as "expanding space" that I think is a bit awkward. But I can't think of a better way to say it...

That's the sore point I tried to address. We agree that the proper volume increases and at the same time we agree that no additional space is created. That's why I asked in #36 "Isn't this a contradiction in itself and how do you resolve that?". You seem to call that "rather confused" but what's the difference saying its "a bit awkward"?

I think I'm missing something. What am I missing?

It is clear that the views whether space expands vs. galaxies are moving away depends on the chosen coordinates, s. the FAQ in Ned Wrights tutorial I mentioned earlier. This clarifies that GR doesn't predict that space expands in the sense that additional space is created.

 

[Will Learn]

Hi Timdeeg.

I'm not sure who you're asking, looks like you targeted Ibix.
If you're throwing the question out to anyone...
1. That Ned Wright's FAQ doesn't tell you how they define space.
2. How are you defining space? Is it just some length (or length³) in the 3-D spatial manifold?
3. You've mentioned changing co-ordinates to fit two views on something else. Are you happy to change co-ordinates here to fit two different views about the creation of space vs. an alteration in the metric?

 

[Tayler]

Stuff is moving apart, so the density now is lower than it was yesterday (edit: on average, and very very slightly on that timescale). Radiation also redshifts (edit: ditto). That's all I meant.

So "stuff" meaning matter? And are you saying the density of the space its contained in is moving apart, or of the physical object itself?

 

[PeterDonis]

all ordinary matter tends to create solutions to the Field Equations of General Relativity where space does not expand.

This is not correct. There is an expanding FRW spacetime solution with nothing but ordinary matter in it.

just by having that bit of matter which is your atom (various protons, neutrons and electrons) in a small region of space will tend to stop that little patch of space expanding.

This is wrong. Just having "matter" is not sufficient to create a bound system (unless you consider a proton or neutron to be a bound system since each contains quarks).

Also, "space expanding" is just a heuristic description, not an exact representation of the actual physics. "Space" is not a thing. This is an area where you can't just wave your hands and use heuristic reasoning if you want to get things right. You need to look at the math.

 

[PeterDonis]

hypothetically if you could weigh the entire universe at any given time or say, a slice from the first few minutes after the big bang and then a slice 2 billion years later, they would be the same weight, correct?

In a closed universe with a finite spatial volume, yes, there is a finite conserved quantity that more or less corresponds to what you are calling the "weight" of the universe.

In a spatially infinite universe, however, this "weight" is infinite, which is another way of saying "not well defined".

 

[Tayler]

I'm loving this discussion. You're inquisitve, Tayler.
How deep do you want go?

1. The argument about space being created (I think that was MacWylie who first mentioned it) is often presented as if space is being "injected" in from elsewhere. Between any two (distinct) points in space, more space is constantly being injected in. It's also possible not to worry about it and look at things the other way (Timdeeg was one of the first to mention this), space is just space but the scale factor changes. You might like to think of it as if the co-ordinate system is getting updated and modified as time progresses. Two points in space that are said to be "co-moving" just do have an increasing distance of separation as time progresses. The arguments are two sides of the same coin and I expect there are many other ways of looking at the situation.

I prefer thinking about the expansion of space with the idea of an evolving scale factor. It avoids all problems of considering space as "stuff" that has to be created from somewhere. Space doesn't have to be "stuff" it's just distance. There is some space between A and B just means there is some distance between A and B.

2. About the changing mass of time slices through spacetime:

This is complicated and I think Timdeeg has typed an answer while I was doing this one.
Start by replacing "weight" with mass. This is a minor technical change but it will help us. Mass is an intrinsic property of matter, while weight changes according to the gravitational field you're in. I don't think we could keep a total weight of the universe constant but there's some hope of keeping constant mass.
Next consider that mass is just a concentrated form of energy, so we'd be better off considering the total energy in the time slice. Mass can certainly change as time passes, nuclear reactions convert mass into energy, for example. Total energy at least has a better chance of being conserved.
Finally, see some comments that were mentioned earlier (I think it was Peter Donis who pointed at an article in the Preposterous universe blog).

Energy isn’t conserved; it changes because spacetime does. See, that wasn’t so hard, was it?

[Taken from https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ ]​

So, ummmm... no. Hypothetically, the stuff in each time slice is different in many ways. However, the changes are predictable. A human being studying physics could identify a place in one time slice that would correspond to a place in another time slice. Your analogy about expanding slices of bread is quite good for this. Some things change their properties but that is also in a predictable way (e.g. blue light may change into red light), you could identify it as being the same light just at a later time.

Study physics and tell me the correct answers as they stand in 10 years time.

Why thankyou will. As deep as I need to get a decent idea of the universe! I'm sure I'll learn a good .00000001% in a few years

 

[PeterDonis]

A human being studying physics could identify a place in one time slice that would correspond to a place in another time slice.

Sort of. The notion of "place" that we intuitively use is not well defined in an expanding universe. It is possible to use comoving worldlines to mark out "places" that can be compared at different times, but this implies that two objects that both "stay in the same place" also move apart (since "expanding universe" just means that comoving worldlines move apart with time). So one has to be careful with intuitive reasoning like this.

 

[PeterDonis]

are you saying the density of the space its contained in is moving apart, or of the physical object itself?

Neither. "Space" is not a thing, and "the space it's contained in" is not a meaningful concept.

 

[Tayler]

In a closed universe with a finite spatial volume, yes, there is a finite conserved quantity that more or less corresponds to what you are calling the "weight" of the universe.

In a spatially infinite universe, however, this "weight" is infinite, which is another way of saying "not well defined".

I think I'm starting to understand somewhat!

 

[timmdeeg]

1. That Ned Wright's FAQ doesn't tell you how they define space.

Yes, but that is not the intention of this FAQ

2. How are youdefining space? Is it just some length (or length³) in the 3-D spatial manifold?

I would say space is nothingness which has geometric properties.

3. You've mentioned changing co-ordinates to fit two views on something else. Are you happy to change co-ordinates here to fit two different views about the creation of space vs. an alteration in the metric?

I have mentioned said FAQ. It is agreed that expansion of the universe means increasing distances between galaxies which are far away from each other so that local peculiar velocities don't play a role. Ned Wright's FAQ explains that there are two views to understand the increasing distances. In one view, choosing FRW-coordinates, the galaxies stand still and space expands, in another view choosing other coordinates the galaxies move away from each other. The point is that neither view can be "true" physics. True physics is what we observe: increasing distances.

 

[PeterDonis]

I would say space is nothingness which has geometric properties.

You could use this as a heuristic definition of spacetime, but not space, since "space" is coordinate-dependent.

 

[timmdeeg]

You could use this as a heuristic definition of spacetime, but not space, since "space" is coordinate-dependent.

I see, thanks.

 

[Will Learn]

Hi.

There is an expanding FRW spacetime solution with nothing but ordinary matter in it.

Agreed. More than one, I would think. An Einstein-de Sitter universe comes to mind first of all - but if you add an inflationary phase at the beginnning of a matter dominated universe then presumably all such universes begin with $\dot {a}$ > 0.

Just having "matter" is not sufficient to create a bound system

It's not "sufficient" - but it tends to cause deceleration of expansion and favours contraction (I hope). This worries me if it's wrong and I can only apologise to everyone, especially Tayler who was seeking advice.

 

[phinds]

It's not "sufficient" - but it tends to cause deceleration of expansion and favours contraction (I hope). This worries me if it's wrong and I can only apologise to everyone, especially Tayler who was seeking advice.

no, I'm pretty sure matter ONLY decelerates expansion if it IS a bound system. Just random bits here and there woluld BE a bound system if there was enough mass for gravity to act against expansion/acceleration but otherwise just the presence of mass is not enough.

 

[PeroK]

It's not "sufficient" - but it tends to cause deceleration of expansion and favours contraction (I hope). This worries me if it's wrong and I can only apologise to everyone, especially Tayler who was seeking advice.

That's definitely not right. A matter-dominated universe may expand indefinitely, albeit with a declerating expansion. We need the density to be greater than the critical density for the universe eventually to start contracting.

https://astronomy.swin.edu.au/cosmos/C/Critical+Density

 

[PeterDonis]

More than one, I would think. An Einstein-de Sitter universe

Also has a cosmological constant/dark energy in it.

The model I was referring to is the expanding FRW model with just matter (i.e., perfect fluid with positive energy density $\rho$ and zero pressure, and nothing else). Technically I suppose there are three such models, corresponding to the three possibilities for spatial curvature/closure (closed--will recollapse, flat--will expand forever, open--will expand forever).

 

[Tayler]

All you guys are amazing people! I definitely wish to study advanced mathematics to get my head around all the equations and have more of an understanding. This stuff is great! Love it!

 

[Will Learn]

(Einstein de Sitter Universe) ... Also has a cosmological constant/dark energy in it.

Thanks but that means I've been reading a bad set of on-line notes again.
Einstein de Sitter was defined with $\Lambda$ = 0

[University of St Andrews, http://www-star.st-and.ac.uk/~spd3/Teaching/PHYS3303/obs_cos_lecture6.pdf ]​

A matter-dominated universe may expand indefinitely, albeit with a declerating expansion

...and also @phinds with a similar comment.
Thanks for these replies. A universe may expand idefinitely, sure that's fine - but matter does tend to cause deceleration. That's not too worrying.

@Tayler
All the guys? What about the girls? Anyway, best wishes to you (and everyone).

 

[PeterDonis]

Thanks but that means I've been reading a bad set of on-line notes again.
Einstein de Sitter was defined with $\Lambda$ = 0

[University of St Andrews, http://www-star.st-and.ac.uk/~spd3/Teaching/PHYS3303/obs_cos_lecture6.pdf ]​

This might be a terminology issue. I was thinking of something more like the Schwarzschild-de Sitter model, but it does look like "Einstein-de Sitter" is also used to refer to the flat, matter-only FRW model. Sorry for the confusion on my part.

 

[PeterDonis]

matter does tend to cause deceleration

Yes, that's correct.