# B Gravity and expansion

1. Dec 16, 2017

### PeroK

That would be normal positive pressure. A model where a gas is expanding and pushing things with it. That's not what's happening here.

Negative pressure means that energy is required to expand the vacuum - rather than energy required to compress it.

Note that vacuum energy is positive: if a vacuum expands and its energy density remains constant - as it must, assuming vacuum is vacuum and you can't dilute a vacuum - then that implies more total energy.

The other energies (matter and radiation) have the obvious property that as space expands, their energy densities must decrease. Vacuum energy has what seems the extraordinary property that this does not happen and, as space expands, the total vacuum energy goes up and up.

As I understand it, that is where we reach the mystery of dark energy.

2. Dec 16, 2017

### PAllen

Simple. Comoving bodies, by any reasonable definition, are moving away from each. Meanwhile, position has no meaning beyond coordinate choice in relativity. Consider just SR: every distinct frame entails a different definition of what constant position means, and they are all equally valid. Constant position cannot possibly have more meaning in GR than it does in SR. Expansion is the feature of spacetime geometry that makes it possible for comoving bodies to continue moving apart. Using my simple 1x1 analogy, if the universe is cone shaped, you are able to have comoving bodies moving apart forever. A cylinder, or a cone whose sides bent to asymptote a cylinder would not allow this.

Specifically, it is trivial to define constant position such that positions don't move apart. Pick a particular galaxy. Define that world lines that show no redshift as seen by this galaxy are lines of constant position. Just as valid as any other choice. No matter how far away some other comoving galaxy is, if a light source in that galaxy is moving towards us with a speed relative to that galaxy (this relative velocity, being local, is well defined) corresponding to the galactic redshift interpreted as SR Doppler, then light from that source will show no red shift. Define constant position lines by such light sources rather than comoving galaxies. Even with Dark Energy, this is still possible, but such light sources will need to move more and more non-inertially to maintain absence of redshift as observed by us, the more Dark Energy there is. But as long as we can see a comoving object, there is colocated non-superliminal velocity trajectory which would have no redshift as observed by us.

Note, this is also a justification why I consider the phrase "superluminal recession velocities" misleading.

Last edited: Dec 16, 2017
3. Dec 16, 2017

### PAllen

Note, I stated the same as Susskind, that with Dark energy there is tiny shift of equilibria even for bound systems. The difference in how we phrase interpretation is a matter of which side of an equation we are focusing on. Assuming you put the cosmological constant on the right hand side of the GR field equation (e.g. to allow the possibility for it to be a dynamical field rather than a constant), then as a field contributing to stress energy it has a natural interpretation as negative pressure. However, possibly paradoxically, the effect of negative pressure on the metric corresponding the Einstein tensor (the left hand side of the equation) is to produce a homogeneous tendency of geodesics to diverge (and positive pressure produces the opposite gravitational effect). To me, this is just as much gravity as the tendency of geodesics in Schwarzschild spacetime to converge in two directions while diverging in the third. Gravity is effect of the metric tensor on inertial stucture. Negative pressure produces a certain form of gravity.

Last edited: Dec 16, 2017
4. Dec 16, 2017

### Staff: Mentor

"Space" doesn't contract in SR. Objects appear to have shorter lengths to observers moving relative to them.

Once again: I agree that electromagnetism is consistent with SR. That's not the issue. The issue is that you are using the word "contraction" to refer to how electromagnetic fields transform under a Lorentz transformation. That word is not appropriate because fields do not have a "length" or a "size", so they can't contract. So there's no point in you continuing to say that SR has to be valid; nobody is disputing that. You need to show what property of fields can be properly said to be a "length" and to "contract".

You are confused. Spacetime is curved in the presence of gravity. You are trying to use intuitions from SR, that only work in flat spacetime, in the presence of gravity. That doesn't work.

Also, the "speed of light" you refer to is a coordinate speed, not a physical speed. You don't appear to understand the distinction; it's crucial.

From where? Can you give an actual textbook or peer-reviewed paper as a reference?

Where are you getting this understanding from? Again, can you give an actual textbook or peer-reviewed paper as a reference?

Einstein developed GR as a theory of spacetime, not space.

Are these actual peer-reviewed papers, or popular articles? Please give specific references.

5. Dec 17, 2017

### Albrecht

Fields cannot contract? How can you say this?
Example: There may be a field E of a charge q described by the equation: E = q/r2. Then assume that conditions change so that now there is E = q/(2r). So, if one looks to the spatial distribution of the field, the field (i.e. its shape) is contracted by a factor of 2. What is the problem here?

Historically Oliver Heaviside has in 1888 deduced from the Maxwell equations that an electrical field contracts for a moving charge by the equation E --> E' = E / gamma, where gamma = sqrt(1/(1-v2/c2)). This was a well known result and an important step towards relativity.

This fact of a "contraction of a field" is well known and was never questioned by the physical community to my knowledge.

6. Dec 17, 2017

### Albrecht

Of course I know the distinction. All this is the view of an observer from outside the field. For the observer in the field there is no difference visible. This is demanded by the principle of relativity.

First about time: There is time dilation in a gravitational field. An observer can put a clock into the field and after a time take it back again. The clock in the field compared to a clock which stayed outside is retarded according to the dilation formula for gravity. And now the case of contraction; here again as said for SRT: the contraction can only be determined indirectly. I have proposed the case of a light clock. This light clock has to represent the dilation in gravity. And this dilation can only be explained if contraction is assumed and a reduction of the speed of light. Where speed of light means of course the coordinate value. And that is appropriate because all this is viewed by an observer outside the field.

You say correctly that space-time is curved. This curvature includes of course the contraction of space in the radial direction for a radial field (like for a star). In case of the light clock the calculation depends on the orientation of the clock.

7. Dec 17, 2017

### Albrecht

That is in general correct. But as said before: in a radial field or in general in a radial situation curvature means contraction.
And in the case of the expanding universe: this is also a radial situation and so the change of the space means expansion.

8. Dec 17, 2017

### Albrecht

Einstein died in 1955. So there are no actual papers from him.

In the years 1925 until 1955 he developed his understanding of space which means his understanding of those properties of the space which he called the "new ether". He published a series of papers and also books about this topic. I do not know which of his papers were peer-reviewed. But I know that Einstein did not like this peer-reviewing. Because he said "I am Einstein and any peer-reviewing is inappropriate".

I do not have a list of his papers and books about this topic at hand. But university libraries should have them.

9. Dec 17, 2017

### Staff: Mentor

Because, as I have said several times and you have apparently not grasped, "fields contract" is not the same as "fields transform according to Lorentz transformations". You keep giving arguments for the latter. Those are not arguments for the former.

Which does not describe "contraction" unless E is a length. Which it isn't. It describes the relativistic transformation of the field strength when you change frames. Field strength is not length.

10. Dec 17, 2017

### Staff: Mentor

Yes.

No, it's not appropriate because it's just a coordinate effect. No physics can depend on how you choose your coordinates.

No, it doesn't. The coordinate effect you are describing is not "contraction of space". It's just a coordinate effect. No physics can depend on how you choose your coordinates.

If you actually look at the "space" in question, and compare it to a Euclidean space enclosed by a 2-sphere with the same surface area, you will find that it is more appropriate to describe the "space" around a massive body as "expanded" rather than "contracted"; the 3-volume enclosed by a 2-sphere of a given surface area is larger if there is a gravitating mass inside the 2-sphere than if there is only vacuum there.

No, it doesn't. See above.

I'm not sure what you mean by "a radial situation". The universe is homogeneous; spacetime around a gravitating mass is not. They're not the same.

Also, as I have already said, the expansion of the universe is not properly described as a "change of space".

11. Dec 17, 2017

### Staff: Mentor

Um, you do realize that Einstein published scientific papers for at least 50 years before he died, right? Apparently you do, since you go on to say:

Please give a reference for where you got this quote from.

Then how can you so confidently assert what Einstein said or didn't say? Either you have references to support your claims, or you don't. Either give specific references or stop making the claims.

12. Dec 18, 2017