B Understanding the Expansion of Space: Galaxies Moving Away and Proving Expansion

[timmdeeg]

Can you define what being in “free fall” means?

If an object is in free fall its trajectory is a 'geodesic'. In this case the object doesn't feel a force acting on it. This is true for Galaxies, planets orbiting around a star and apples falling down to Earth.

 

[PeterDonis]

I found it a good way to conceptually think of expansion that fits with what we see in observation and has some basis in physics. (E.g. QFT, the FRW equations, inflation theory etc.)

As @timdeeg has pointed out, this does not fit with observation because your model predicts that galaxies should feel a force, and they don't.

The reason the concept of "space expanding" doesn't make sense is that "space" is frame-dependent, and the laws of physics are frame-independent. So whatever is going on in the universe, "space expanding" can't be a good description of it.

 

[rede96]

If an object is in free fall its trajectory is a 'geodesic'. In this case the object doesn't feel a force acting on it. This is true for Galaxies, planets orbiting around a star and apples falling down to Earth.

If I understood you correctly your saying that expansion is due to space time curvature. Correct?

 

[rede96]

As @timdeeg has pointed out, this does not fit with observation because your model predicts that galaxies should feel a force, and they don't

I was using ‘force’ in very loose terms just to indicate there was something going on to cause objects to move apart. I wasn’t implying they felt any force from acceleration. The way I thought about it wouldn’t be any different.

 

[PeterDonis]

I was using ‘force’ in very loose terms just to indicate there was something going on to cause objects to move apart.

Then you shouldn't use the word "force", because it will only lead to confusion. Not just for others, but for you. It leads you to think that "there was something going on to cause objects to move apart". There isn't. There is just the geometry of spacetime.

To illustrate what I mean, consider tidal gravity: two objects free-falling radially above a gravitating mass (like the Earth), starting from slightly different altitudes. These objects will move apart as they fall. Is there "something going on" that causes this? If so, what is this "something"? If not, how is this case different from the expansion of the universe?

 

[timmdeeg]

If I understood you correctly your saying that expansion is due to space time curvature. Correct?

Well, to know what geodesic means is not the clue to have a notion of what expansion means. But you can imagine two neighboring geodesics describing the trajectories of two objects. If the spacetime is curved then their geodesics accelerate relative to each other, in the case of an expanding universe they accelerate away from each other. Whereas if the spacetime is flat their relative acceleration is zero (which doesn't exclude of course that these particles move relative to each other with constant speed).

 

[PeterDonis]

If the spacetime is curved then their geodesics accelerate relative to each other, in the case of an expanding universe they accelerate away from each other.

This is not quite right. In a matter-dominated universe the expansion is decelerating, and the geodesics in question (the worldlines of comoving objects) are converging, not diverging. But the universe is still expanding.

The correct definition of "expanding" for the universe is that the congruence of worldlines of comoving objects has a positive expansion scalar. Unfortunately, that's already getting beyond the "B" level of this thread. But you can find more information here:

https://en.wikipedia.org/wiki/Congr...atical_decomposition_of_a_timelike_congruence

 

[PeterDonis]

your saying that expansion is due to space time curvature.

The expansion is due to the positive expansion scalar of the congruence of comoving worldlines (see my previous post). But the fact that such a congruence exists and has the properties it has (not just positive expansion, but every comoving observer sees the universe as homogeneous and isotropic) is due to the particular geometry of the spacetime in question (FRW spacetime).

 

[timmdeeg]

This is not quite right. In a matter-dominated universe the expansion is decelerating, and the geodesics in question (the worldlines of comoving objects) are converging, not diverging. But the universe is still expanding.

Ah yes, it follows from the second Friedmann equation that the second derivative of the scale factor is negative in this case (what I didn’t take into account). Thanks for correcting and for the link.

 

[Dan White]

This is an old thread but my understanding is that there is an idea from quantum physics that says that empty space may be teeming with activity at a quantum level. I thought this might be of interest to the OP if he is still around.

 

[PeterDonis]

This is an old thread but my understanding is that there is an idea from quantum physics that says that empty space may be teeming with activity at a quantum level.

This appears in our current cosmological model as dark energy. We don't fully understand why its density is so small (about 120 orders of magnitude smaller than the value that the basic quantum physics calculation you refer to gives), but it is there in the model.

 

[Orodruin]

This appears in our current cosmological model as dark energy. We don't fully understand why its density is so small (about 120 orders of magnitude smaller than the value that the basic quantum physics calculation you refer to gives), but it is there in the model.

I think that is taking things for granted a bit too far. In the cosmological model the cosmological constant is just a parameter without any particular origin. In the quantum zero point energy could theoretically contribute to this but is, as you say, 120 orders of magnitude off which if anything is an indication that the connection to the cosmological constant is not well understood. Ideally a theory of quantum gravity should of course address this.

 

[PeterDonis]

In the cosmological model the cosmological constant is just a parameter without any particular origin.

True, but any "activity of empty space" of the sort the poster I responded to was describing would have to appear in our cosmological model in this parameter. So our cosmological model already takes into account the possibility that such a thing exists. The value we use in our model is based on empirical observation and we don't have a good theoretical understanding of why that is the value we observe, but that doesn't mean our model doesn't take the possibility into account.

 

[vanhees71]

I think that is taking things for granted a bit too far. In the cosmological model the cosmological constant is just a parameter without any particular origin. In the quantum zero point energy could theoretically contribute to this but is, as you say, 120 orders of magnitude off which if anything is an indication that the connection to the cosmological constant is not well understood. Ideally a theory of quantum gravity should of course address this.

Well, in principle our Standard Model of HEP doesn't tell us at all what the absolute value of the vacuum energy (density) is. In the usual perturbative treatment it's set to 0 by imposing "normal ordering" or equivalently by renormalization of the vacuum diagrams. This introduces a renormalization scale, and when using the renormalization group to go from the low-energy scale to very high scales (GUT scale or even the Planck scale) you get these huge 120 orders of magnitude discrepancies.

I think in this sense the vacuum-energy/cosmological-constant problem is the least understood "today observable part" on the crossroad between GR and QT. Maybe it's solved one day when a consistent formulation of "quantum gravity" is found.

 

[timmdeeg]

I think in this sense the vacuum-energy/cosmological-constant problem is the least understood "today observable part" on the crossroad between GR and QT.

Do we have at least a hint why it acts as "repelling" gravity?

 

[PeterDonis]

Do we have at least a hint why it acts as "repelling" gravity?

We have more than a hint. What you are calling "repelling gravity" is what the Einstein Field Equation says you get when you have the stress-energy of a perfect fluid with an equation of state $p = - \rho$. And that's exactly what you have with a cosmological constant.

 

[timmdeeg]

We have more than a hint. What you are calling "repelling gravity" is what the Einstein Field Equation says you get when you have the stress-energy of a perfect fluid with an equation of state $p = - \rho$. And that's exactly what you have with a cosmological constant.

Thanks. I have another question in this context.

The value of the Cosmological Constant according to the Quantum Field Theory is much to high. But apart from this it's sign due to QFT seems correct. In other words QFT having no link to General Relativity doesn't just predict a vacuum energy density, it predicts the vacuum energy density with the correct sign to act like the CC. Is that correct?

 

[PeterDonis]

QFT having no link to General Relativity doesn't just predict a vacuum energy density, it predicts the vacuum energy density with the correct sign to act like the CC. Is that correct?

AFAIK yes, QFT predicts a positive sign for the vacuum energy density.

 

[StandardsGuy]

Space without matter still has fields: electromagnetic field, gravitational field, Higgs field, etc. It also has energy, so "empty" space isn't nothing.