# Does h-bar change in gravitational waves?

1. Apr 25, 2015

### friend

Heisenberg's Uncertainty Principle (HUP) tells us that the standard deviation in position times the standard deviation in momentum is equal to Planck's constant divided by 4π. And HUP also causes there to be a zero point energy in the fields of QFT. This is because position and moment can not both be zero. And since the position is constrained to be finite, there must be some momentum. And with momentum there must be some non-zero energy. We are also told that the zero-point-energy is also called the vacuum energy or dark energy that is causing the universe to accelerate in its expansion.

However, even in gravitational waves, spacetime stretches and then returns to normal. Yet there must be some acceleration in spacetime expansion in order for it to stretch and contract as a gravitational wave goes by. So if the acceleration of expansion of spacetime is caused by a change in dark energy, a.k.a zero-point-energy, then there must also be a corresponding change in the multiplication of entities in the HUP. This would mean that the value of h-bar would have to be changing as a gravitation wave goes by.

I'm not stating that this is the case. I'm asking if this is correct. Thanks.

Last edited: Apr 25, 2015
2. Apr 25, 2015

### Staff: Mentor

More precisely, this is one theory about what dark energy is. It is not the only theory, and none of the theories can explain why the dark energy density takes on the value that it does. (The "vacuum energy is dark energy" theory predicts, at least to the extent we currently know how to do the calculation, that the dark energy density should be about 120 orders of magnitude larger than it is observed to be. So clearly we still have a lot to learn in this area.)

No, this is not correct. What you are calling "acceleration in spacetime expansion" due to the gravitational wave going by is not the same as what is called "acceleration of expansion of the universe" due to dark energy. They're two different things.

3. Apr 26, 2015

### friend

One difference I see is that one is global expansion in the metric and the other is local expansion (and contraction).

4. Apr 26, 2015

### ZapperZ

Staff Emeritus
Wait, who told you this?

We know quite a bit about vacuum energy. This is even exploited in Casimir effect. On the other hand, we know very little about dark energy that is attributed to the accelerated expansion.

There are clear indications that these may not be the same thing. At the very least, making such a connection right now is highly dubious. So who has been telling you these things?

Zz.

5. Apr 26, 2015

### friend

According to wikipedia on the cosmological constant, "A common assumption is that the quantum vacuum is equivalent to the cosmological constant." And the problem is that the calculated vacuum energy is 120 orders of magnitude larger than what is observed. I agree that this is not a good start to answer whether h-bar might change. However, it makes me wonder if vacuum energy (h-bar?) might increase inside gravitational wells and decrease greatly in intergalactic space. This might happen if vacuum energy is linked to accelerated expansion and if gravity can be associated with accelerated (expanding?) frames of reference.

Has observation ruled out that vacuum energy in deep intergalactic space is much less (120 orders of magnitude) than that found deep inside a galaxy? We'd probably have to observe processes in these great voids that do not occur inside deep gravitational well. That might be a contradiction since we can only measure massive objects in intergalactic space, right?

6. Apr 26, 2015

### Staff: Mentor

Observation certainly ruled out the value you would get from QFT, which is 120 orders of magnitude above the observed value. If this value would be realized anywhere, it would completely break the universe as we know it.

7. Apr 26, 2015

### friend

ASIDE:

Does the calculation of the Casimir effect use all the fields and frequencies used in the calculation of the vacuum energy density? Or is it that at some high enough frequency the energy is the same on both sides of the plates so that they cancel out?

8. Apr 26, 2015

Staff Emeritus
The Casimir effect can be calculated without recourse to any of the properties of the vacuum. So it cannot tell us anything about those properties.

9. Apr 26, 2015

### friend

Can it be calculated WITH properties of the vacuum?

10. Apr 26, 2015

### Staff: Mentor

$\hbar$ has nothing to do with vacuum energy.

You are confusing several different notions of "acceleration". An "accelerated frame of reference" is a frame in which an object at rest feels an acceleration, i.e., feels weight. Objects at rest in comoving coordinates in our universe do not feel weight; they are in free fall. The "acceleration" of the universe's expansion is just the second derivative of the scale factor with respect to comoving coordinate time being positive, which can only be true if dark energy is present; but this "acceleration" is present even if no object in the universe feels any acceleration.

Finally, the "acceleration" due to gravitational waves is tidal acceleration: nearby freely falling objects that start out at rest relative to each other don't stay at rest relative to each other. They move apart, then together, then apart, then together... This motion is a manifestation of gravitational waves; but once again, it is present even if all the objects in question are in free fall, feeling no acceleration.

11. Apr 26, 2015

### friend

Thank you for your instruction. However, there is a way in which the accelerated expansion of the universe is like the acceleration of a gravitational field. And that is in the red-shift of light. An observer in the accelerating universe sees a red-shift in (star)light in correlation to the distance of the galaxy. And an observer in a gravitational field sees a red-shift in light in correlation with how deep in the well the source of that light happens to be. The reason that we don't feel an acceleration in cosmological expansion might be because it is the same in all directions. The same would hold if we were exactly in between two massive objects. Both objects would exert the same force on us in opposite directions; so we would not feel an acceleration in any one direction. So I'm not quite convinced yet.

And, no offense, but what do you mean, "ℏ has nothing to do with vacuum energy"? The first paragraph of the wikipedia article on vacuum-energy states, "Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe. They are expected to do this everywhere, throughout the Universe. Their behavior is codified in Heisenberg's energy–time uncertainty principle. Still, the exact effect of such fleeting bits of energy is difficult to quantify." And certainly the uncertainty principle relies on ℏ, right?

12. Apr 26, 2015

Staff Emeritus
It is independent of the properties of the vacuum.

13. Apr 26, 2015

### friend

The second paragraph of the wikipedia article on the Casimir effect states, "Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects."

So the Casimir effect at least depends on the QED sector of the zero-point-energy, which is the same as the vacuum energy, right?

14. Apr 26, 2015

### atyy

15. Apr 26, 2015

### Staff: Mentor

By this reasoning, the Doppler effect due to relative motion in flat spacetime is also "like the acceleration of a gravitational field", because there is a redshift of light in both cases. This is not science; it's superficial reasoning by analogy.

But he also sees a redshift correlated to the distance (actually that's not quite what the redshift is correlated to--see below) in a universe with decelerating expansion, or indeed in a universe in which the expansion rate is not changing at all; so the redshift is not due to "acceleration".

What the redshift is actually telling you is by what factor the scale factor of the universe has increased since the light was emitted; the scale factor will have increased by a factor $1 + z$, where $z$ is the redshift. For small redshifts, this correlates linearly with the distance; for larger redshifts, the linear correlation with distance no longer holds. But the correlation with the ratio of scale factors is always exact.

Yes; but here the situation is static--the gravitational field does not change with time. So it is a different situation from the expanding universe. In an expanding universe, "gravitational redshift" in this sense can't even be defined, because the situation is not static.

No, it's because there is nothing pushing on galaxies to cause them to feel acceleration. Galaxies don't have rockets attached to them, and they're not sitting on something that pushes on them.

But this would also be true if there were only one massive object and you were free-falling towards it, or in orbit around it. Do you understand what "feeling acceleration" means? It means just what it says: you feel an acceleration. An accelerometer attached to you reads a nonzero value. It has nothing to do with whether your speed relative to something else is changing.

16. Apr 26, 2015

### Staff: Mentor

Perhaps I should have clarified that changes in $\hbar$ have nothing to do with vacuum energy. See below.

Yes, but that doesn't mean quantum fluctuations due to the uncertainty principle are due to changes in the value of $\hbar$. They aren't. $\hbar$ is constant. Quantum fluctuations are due to changes in quantum fields.

17. Apr 26, 2015

### friend

If the Casimir effect can be measured within 1%, is that enough to detect a change in force from a point on the surface of the earth to some point high above the earth (I doubt it, but I can hope)?

18. Apr 26, 2015

### friend

OK. So I need to clarify. The red-shift reveals the acceleration, not just the distance. That was the whole point of the red-shift vs brightness curve for supernovae. But similarly, the red-shift of light coming from a gravitational well also reveal the change in gravitational field. I don't know, but I'd bet that you would also get a non-linear red-shift vs brightness curve coming from a heavy mass. Also, horizons are produced by acceleration, gravitation, and expansion. My question is whether the vacuum energy is affected by all these sources of acceleration.

Last edited: Apr 26, 2015
19. Apr 26, 2015

### Staff: Mentor

The first post in this thread said
That question was answered in the next few posts, so this thread can be closed.

This might be also be a good time to remind everyone that wikipedia is not an acceptable reference under the Physics Forums rules. If wikipedia is telling you one thing and a PF mentor or science advisor is telling you another thing.... Chances are that you're misunderstanding the wikipedia article, and there is a non-zero probability that you're arguing with someone who could have written it (or did!).