Exploring the Expansion of the Universe: The Role of Gravity

[Gedanken]

If the Universe is expanding, wouldn't it be common sense to think everything inside it is expanding too?

 

[Morgan Patranella]

No. the space in between objects is expanding but not the objects like Earth themselves... This is what you asked, correct?

 

[Comeback City]

And to add on, this is pretty much just happening at the intergalactic level.

 

[David Lewis]

If spacetime is expanding then new heres and nows are being created.

 

[Drakkith]

If the Universe is expanding, wouldn't it be common sense to think everything inside it is expanding too?

The expansion of the universe is about the distance between objects increasing over time. Note my choice of words there. The distance between objects. Objects bound together by strong forces, such as the atoms in molecules or planets to their stars, are not expanding as far as we know. But, given a large enough distance, these forces drop off far enough to allow expansion to take place and the objects get further away from each other over time.

 

[PeterDonis]

If spacetime is expanding then new heres and nows are being created.

This is not correct. Spacetime is a 4-dimensional manifold; it already contains all "heres" and "nows". "Expanding" just labels a particular feature of the geometry of this 4-dimensional manifold.

Also, since as far as we can tell spacetime is a continuum, even if we adopt a particular coordinate chart (such as standard FRW coordinates), expansion does not create new "space" in these coordinates. Each "point in space" can be labeled in FRW coordinates and the labels are the same at every instant of time.

 

[Albrecht]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

 

[rede96]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

It is true, at least according to the dark energy model, that expansion does exert a very small ‘negative pressure’ on objects which causes them to expand more than they would without the pressure from expansion. But the effects are so small I don’t think it’s possible to measure on such small scales. And in any case it’s no where near enough to overcome the forces that hold objects together.

 

[Albrecht]

I do not mean any pressure or any force.
If there is for instance relativistic contraction (in SRT) then there is contraction for all objects and for all fields and for everything. There is no force involved. - My question is whether expansion in case of the whole universe is the same or is it different so that the distances of objects expand but fields of any kind do not change.

 

[phinds]

I have not really understood this. If the space expands, do fields like the electrical field and the gravitational field expand by the same amount? - That would mean that any objects and also galaxies expand in the same way as the space and are so unchanged in relation to the space.

No, it would not mean that at all. Again, objects on the order of galactic clusters and smaller do not expand. EM radiation BETWEEN such bound systems does change. Light drops in frequency and loses energy when traveling between bound systems.

 

[my2cts]

No, it would not mean that at all. Again, objects on the order of galactic clusters and smaller do not expand. EM radiation BETWEEN such bound systems does change. Light drops in frequency and loses energy when traveling between bound systems.

Interesting discussion. Are you saying that electromagnetic fields inside atoms do not expand but such fields in between galaxy clusters, galaxies, stars perhaps or even planets , do ? At what scale does this transition from expansion to non-expansion occur ?

 

[Drakkith]

The value of the field at any particular point in space will likely change as expansion causes charges to move away from each other, but whether or not that means that the "field itself" is expanding is difficult to answer.

 

[PeterDonis]

If the space expands, do fields like the electrical field and the gravitational field expand by the same amount?

Fields don't have a size, so asking whether or not they expand makes no sense.

That would mean that any objects and also galaxies expand in the same way

Since you are starting from a mistaken premise, you can't expect to reason correctly from it.

If your question is whether bound systems expand due to the universe's expansion, the answer has already been given in this thread: no.

If there is for instance relativistic contraction (in SRT) then there is contraction for all objects and for all fields and for everything.

For objects, yes. Fields don't have a size so they can't "contract". The components of fields are affected by a Lorentz transformation, yes, just like the components of any vector or tensor.

My question is whether expansion in case of the whole universe is the same

No. You're trying to compare apples and haircuts. They're not even the same kind of thing.

Length contraction is an effect of changing your choice of coordinates.

Expansion of the universe is a way of describing the overall spacetime geometry of the universe in terms of the behavior of the worldlines of comoving objects.

the distances of objects expand but fields of any kind do not change

The distances between comoving objects increase. That has nothing to do with the behavior of any fields (at least as far as I can tell what you mean by that term; you don't seem to be using it in the usual way).

At what scale does this transition from expansion to non-expansion occur ?

There is no "transition". The spacetime geometry of the universe is what it is. Comoving objects have particular worldlines in this geometry. Individual parts of bound systems (like stars in a galaxy or planets in a solar system) have other worldlines. That's all there is to it. You can't pick out regions and say that "expansion" is happening in some but not others. Once you've described all the worldlines of objects and the geometry of spacetime, you've described everything; there's nothing left over.

 

[PeroK]

Interesting discussion. Are you saying that electromagnetic fields inside atoms do not expand but such fields in between galaxy clusters, galaxies, stars perhaps or even planets , do ? At what scale does this transition from expansion to non-expansion occur ?

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per
year.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

At an intermediate scale - The Milky Way and Andromeda galaxies say - although still gravitationally bound, the effects of expansion would be more noticeable.

On a larger scale, the gravity between distant galaxies is so small compared to the expansion that gravity becomes negligible and you have effectively only expansion.

 

[Bandersnatch]

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per year.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

Looks like you're using Hubble's law for these calculations. I.e. you took the Hubble constant, and calculated the Hubble flow for 1 AU, which over 1 year gives about 10 metres.
It's not the right way to go about, as you're mixing expansion with acceleration. Expansion by itself (w/o dark energy) is similar to inertial motion, rather than a force - i.e. it can't make Earth's orbit larger. The 10 m/year increase is what you'd get if only if the Earth and the Sun were moving with the Hubble flow. They aren't - they're gravitationally bound. They had long decoupled from the Hubble flow, which has as much bearing on the size of Earth's orbit today as the velocity of gas particles in the molecular cloud from which the Solar system coalesced. There's no equilibrium to talk about with expansion (without DE).

What does increase the orbit is dark energy, but that's many orders of magnitude less pronounced than what you calculated. At 1 AU it should result in acceleration of something like $~10^{-25} m/s^2$. Compare with centripetal acceleration in Earth's orbit: $~10^{-2} m/s^2$.
So, unless I borked the calculations, that means the orbit is one picometre larger than it'd be without it.

But again, that's the effect of DE. Without it, the expansion itself wouldn't have any effect.

 

[PeroK]

Looks like you're using Hubble's law for these calculations. I.e. you took the Hubble constant, and calculated the Hubble flow for 1 AU, which over 1 year gives about 10 metres.
It's not the right way to go about, as you're mixing expansion with acceleration. Expansion by itself (w/o dark energy) is similar to inertial motion, rather than a force - i.e. it can't make Earth's orbit larger. The 10 m/year increase is what you'd get if only if the Earth and the Sun were moving with the Hubble flow. They aren't - they're gravitationally bound. They had long decoupled from the Hubble flow, which has as much bearing on the size of Earth's orbit today as the velocity of gas particles in the molecular cloud from which the Solar system coalesced. There's no equilibrium to talk about with expansion (without DE).

What does increase the orbit is dark energy, but that's many orders of magnitude less pronounced than what you calculated. At 1 AU it should result in acceleration of something like $~10^{-25} m/s^2$. Compare with centripetal acceleration in Earth's orbit: $~10^{-2} m/s^2$.
So, unless I borked the calculations, that means the orbit is one picometre larger than it'd be without it.

But again, that's the effect of DE. Without it, the expansion itself wouldn't have any effect.

Fair enough, but you then still have to answer the question at which point do you transition from a gravitationally bound system to one where expansion applies.

How far from the Sun must you be to measure a non-zero recessional red-shift?

 

[PeroK]

PS the $10m$ per annum clearly doesn't equate to a $10m$ increase in orbit I could equally well have calculated the hypothetical expansion per second, which would be a fraction of a metre.

 

[PeterDonis]

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

No, it's very, very, very slightly larger than it would be if there were no dark energy. In an expanding universe with zero dark energy the size of the Earth's orbit would be unaffected by the expansion.

In this case, the solar system is gravitationally bound. Which means gravity is the dominant factor.

At an intermediate scale - The Milky Way and Andromeda galaxies say - although still gravitationally bound, the effects of expansion would be more noticeable.

On a larger scale, the gravity between distant galaxies is so small compared to the expansion that gravity becomes negligible and you have effectively only expansion.

None of this is correct as regards expansion in the absence of dark energy.

at which point do you transition from a gravitationally bound system to one where expansion applies.

There is no such "transition". See the last paragraph of my post #13.

 

[Albrecht]

For objects, yes. Fields don't have a size so they can't "contract". The components of fields are affected by a Lorentz transformation, yes, just like the components of any vector or tensor.

Yes, fields can contract, and that is (as you say) described by the Lorentz transformation.

And you can measure the contraction. If you have a charge, then at a distance r from the charge you may have a field strength E. If now the field contracts (by whatever cause) by a factor of 2, then at the position r you will measure a field of E/4. That is a clear indication of the contraction.

This is particularly visible for multipole fields like the electrical fields in objects. The molecules in an object are bound to each other by electrical multipole fields. The size of the object is mostly given by the extension of these fields. So, if the object contracts in motion (special relativity) then this is only possible because the fields contract. This causes for instance the MM apparatus to contract in motion and that causes, as we know, the null result of that experiment.

A similar thing happens in a gravitational field. If space contracts which contains a gravitational field, also objects contract there because the binding fields inside contract.

Now cosmology tells us that the space of the universe expands. That is the opposite to contraction but understood to be fundamentally the same phenomenon like relativistic contraction. And if it is the same phenomenon then the rules and consequences have to be similar. But this would now mean that also gravitational fields expand, and so the size of planetary orbits has to increase and also the size of galaxies, as the constituents of a galaxy are bound gravitationally to each other.

So the assumption that the distance of galaxies (which are maintained by inertia and so fixed to the space) on the one hand and the size of galaxies on the other hand behave differently (as some has said in this discussion) does not look logical.

 

[PeterDonis]

If you have a charge, then at a distance r from the charge you may have a field strength E. If now the field contracts (by whatever cause) by a factor of 2, then at the position r you will measure a field of E/4.

Please give a reference for the experimental results that demonstrate this.

Please note that I am not disputing that electromagnetism is consistent with SR; of course it is. I am asking for a specific experimental situation that merits the description "the field contracts" as you have described it, in order to justify the further claims you are making.

A similar thing happens in a gravitational field. If space contracts which contains a gravitational field, also objects contract there because the binding fields inside contract.

Same comment here: please give a reference for the specific experimental results that demonstrate this.

cosmology tells us that the space of the universe expands.

No, it doesn't. That is pop science, not real science. Real cosmology tells us that comoving objects in our universe are moving apart. That is not the same as "space expands".

That is the opposite to contraction but understood to be fundamentally the same phenomenon like relativistic contraction.

No, it isn't. It has nothing to do with length contraction in SR.

The rest of your post just builds on these misconceptions.

 

[my2cts]

Expansion is only measurable on large scales. If you do the calculation then the expansion between the Earth and Sun is about 10m per
year.

Small but nonzero. What is not measurable today, is tomorrow. See the LIGO case.

The Earth, however, cannot keep drifting further away each year. Instead, gravity and any expansion settle into a stable equilibrium, with expansion slightly reducing the effect of gravity.

Indeed. Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.
However that argument holds at any scale.

The Earth's orbit, therefore, is slightly larger than it would be if there were no expansion.

Do you have a reference for this ?

 

[PeroK]

Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.
However that argument holds at any scale.

Do you have a reference for this ?

See the comments above. The difference, if there is one, would be immeasurably small.

I still think you are missing the point that - even if hypothetically the solar system or a hydrogen atom was "trying" to expand - the other factors would simply override this. I think you are looking for an ongoing unstoppable expansion at scales below which the expansion of the universe is not a relevant factor.

 

[my2cts]

See the comments above. The difference, if there is one, would be immeasurably small.

Define immeasurable. Besides immeasurable is not the same as nonexistent. We cannot measure planets in distant galaxies, but we know they are there.

I still think you are missing the point that - even if hypothetically the solar system or a hydrogen atom was "trying" to expand - the other factors would simply override this. I think you are looking for an ongoing unstoppable expansion at scales below which the expansion of the universe is not a relevant factor.

"trying" to expand ? And how would "other factors [] override this"?
I hope you mean conservation of energy and momentum.
That's my point.

 

[PeterDonis]

Expansion of a hydrogen atom, or the orbit of the Earth, requires energy.

You are sweeping a lot of complexities under the rug. That's not a good idea. Even though this is a "B" level thread, we still have to pay attention to the fact that there are more advanced details.

 

[PeroK]

Define immeasurable. Besides immeasurable is not the same as nonexistent. We cannot measure planets in distant galaxies, but we know they are there."trying" to expand ? And how would "other factors [] override this"?
I hope you mean conservation of energy and momentum.
That's my point.

Let's say you dropped a 1kg ball from a height of 10m. Technically, the Earth moves a small distance. But, that's immeasurable, not least because lots of other things are happening around the Earth at the same time. You can't stop all other changes that are happening to try to measure something as small as that - even if, theoretically, you could measure a distance of that magnitude, which I doubt.

The same is true of the Earth's orbit. There are changes and variations due to the gravity of everything in the solar system. These effects will be many orders of magnitude larger than the expansion of space on the scale of the Solar system. Jupiter, for example, moves the Sun about the same as the Sun's diameter over a year. That's a variation of about $1.5$ million $km$ in the position of the Sun. How do you set up an experiment to measure a change of, say, $1mm$ in amongst that? It's absurd. It's immeasurable.

 

[my2cts]

You are sweeping a lot of complexities under the rug. ... there are more advanced details.

Please specify the complexities and more advanced details, if necessary with references.
Keep the quality of this

"B" level thread"

up !

 

[my2cts]

There are changes and variations due to the gravity of everything in the solar system. These effects will be many orders of magnitude larger than ...

than for example the effect gravitational waves.
"Attempting to measure a change in arm length 1,000 times smaller than a proton means that LIGO has to be " etc.
https://www.ligo.caltech.edu/page/ligos-ifo
Yet LIGO measures GWs.
Immeasurability is a practical problem and does not imply non-existence.

 

[PeroK]

"Attempting to measure a change in arm length 1,000 times smaller than a proton means that LIGO has to be " etc.
https://www.ligo.caltech.edu/page/ligos-ifo
Yet it works.

That's a "controlled" environment. The solar system is not.

 

[my2cts]

That's a "controlled" environment. The solar system is not.

I would need a definition of that as well.
LIGO is a tool to observe systems much less "controlled" than the solar system, namely coalescing black holes. It does not get any worse.
Besides, whether physicists are able to measure it or not, is irrelevant to the question if cosmic expansion implies expansion of atomic hydrogen or of the Earth's orbit. That is a different thread.
I think here the question is: does cosmic expansion expand literally everything to expand or only really large stuff. A related question is: if anything expands cosmologically, does this increase its energy ?

 

[PeterDonis]

Please specify the complexities and more advanced details, if necessary with references.

Not in a "B" level thread; that's why I pointed out the thread level. If you are genuinely curious about the complexities, please start a separate thread at the "I" or "A" level.

 

[my2cts]

Not in a "B" level thread; that's why I pointed out the thread level. If you are genuinely curious about the complexities, please start a separate thread at the "I" or "A" level.

I am fully aware of the physical complexities and advanced features of atoms and the solar system, by the way.
I just challenge that they are relevant here.
Still, I was unaware that the threads have actual levels. My mistake.
My argument ends here and now as I don't do "B" discussions.

 

[PeroK]

"trying" to expand ? And how would "other factors [] override this"?

Okay, here's a thought. Hydrogen atoms formed when the universe was much smaller than it is now. Let's assume that these atoms expand as the universe does. So, these hydrogen atoms today would be several times larger than they were when they formed. So:

Hypothesis: there are hydrogen atoms of all different sizes, depending on when they formed. Ones that formed in the early universe would be larger than ones that formed more recently - having expanded with time.

Is there any evidence for hydrogen atoms of different sizes? No. The energy levels (which are implied by the "distance" between the electron and the nucleus) are standard.

Theoretically, a hydrogen atom can only exist in certain discrete energy levels. The atom cannot exist in some intermediate state, caused by an expansion. The atom is either in one energy level or the next. It can't slowly expand into a continuous series of intermediate energy levels.

Therefore, the hydrogen atom cannot expand, regardless of what space is "trying" to do to it.

Note that the same would be true of, say, stars themselves. Even if stars "tried" to expand due to spatial expansion, gravity would just immediately pull everything back together again.

It's the same if the Earth "tries" to drift away from the Sun: gravity just won't let it go!

 

[PAllen]

I'll give my standard 'rant' on this. Expanding universe just means there is always room for comoving bodies to continue moving away from each other, not that space is pushing them, or that two 'positions' are moving apart (except in particular coordinates). Also, there is no difference in origin between the redshift between two distant comoving bodies versus a similar red shift between two distant arbitrary non-comoving bodies in the same universe. In each case, relative motion in GR is fundamentally ambiguous, but redshift between distant bodies is a function of curvature between them and what their motions are.

An analogy is lines drawn up from the apex of a cone, with the apex down. Consider the vertical time, with circles being slices for each cosmic time. Without doubt, the circles grow with cosmic time. However, angles (motion) between lines originating at the apex (comoving observers) is no different from angles between arbitrary lines on the cone. Further, two lines that start parallel will remain parallel. That successive circles are larger in no way causes lines that start parallel to move apart. This feature corresponds to what has been alluded to that without dark energy, if you had two small bodies far apart in a giant void that happen not to have any red shift between them, then even over cosmic time scales, they will continue to have no redshift, and the radar distance between them will not grow, irrespective of their not being bound.

The case of dark energy can be analogized by assuming the cone flares out from the apex. Then, two lines that start parallel will diverge, due to the hyperbolic geometry. In this geometry, if two lines remain constant distance, at least one must not be a geodesic. In the GR case with dark energy, this means that for two distant small bodies in a giant void to remain constant distance, at least one must be non-inertial. Similarly, there is a tiny affect on gravitationally bound systems.

 

[Albrecht]

Please give a reference for the experimental results that demonstrate this.

In my knowledge there do not exist any real experiments, in which contraction was directly proven. But contraction has to be assumed in special relativity to avoid conflicts. So it follows indirectly from dilation and the constancy of c. As well the contraction of fields. - One can find this in every textbook about special relativity. My favorite is: A.P French, "Special Relativity".
If space would contract in motion but fields would not follow this, then the principle of relativity should be violated. Because the observer in a moving system would see different conditions than an observer at rest.

 

[Albrecht]

Same comment here: please give a reference for the specific experimental results that demonstrate this.

The same situation here. Contraction follows indirectly.
Imagine a light clock in a gravitational field. The time indication of such clock has to show the dilation which happens there. This can only work correctly if (1) the speed of light is reduced as given by GRT and (2) the distance of the mirrors is reduced.
Again: any different behaviour would violate the principle of relativity.