How different can quantum vacuums be?

[quantumfunction]

For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it.

How do you derive the Cosmological Constant through something like Quantum field theory or is this something that string theory and other theories are trying to answer?

Thanks

 

[mfb]

For instance our quantum vacuum has a certain Cosmological constant and the question is can there be other vacuums with different values and if so where's the evidence for this I would like to read it.

That depends on what you call "vacuum". Particle physics usually includes the whole standard model there, so the state of the vacuum depends on all of particle physics, plus the cosmological constant, plus all unknown physics.

It is unknown where the cosmological constant comes from, therefore it is unknown if the observed value is an accident or required by some more fundamental theory.
It is possible to make an estimate for its value based on particle physics, but the result is 120 orders of magnitude above the observed value, so this estimate is clearly wrong.

 

[fzero]

The short answer to the questions is that we don't understand the interface between quantum mechanics and gravity well enough to answer the questions. To try to answer them would be to bring up some very speculative ideas, but I will try to be as conservative as possible.

To get to the second question first, in quantum field theory alone, the vacuum energy doesn't matter much, since we can always shift the energy to zero and it won't change the quantum states or their interactions. If we try to include gravity, even just at the level of the classical Einstein equation, then the vacuum energy definitely looks like a source for spacetime curvature, so we can't just shift it away anymore. As mfb mentioned, any particle physics explanation of the vacuum energy widely differs from the value of the observed cosmological constant. Therefore, we don't know whether these calculations of vacuum energy are wrong or if the observed cosmological constant isn't related to something more than the vacuum energy alone.

On the latter point, when Einstein introduced the cosmological constant, he was thinking of it just as a number that could be added to the Einstein field equation. It was only much later that particle physicists realized that a non-zero vacuum energy would act like a cosmological constant. Perhaps there is a non-zero, negative, Einstein-type cosmological constant and it is the sum of that and the particle physics vacuum energy that leads to the small observed cosmological term. This is part of the logic behind what has been come to be called the string theory landscape, though there might be an explanation along these lines in some other version of quantum gravity that I'm not aware of.

As for other vacua, as mfb also said the vacuum energy would get a contribution from every field in the Standard Model as well as anything new that might exist beyond the Standard Model. So there could be many vacuum solutions that are local minima of some grand potential energy function. In general, the constants of nature like the electromagnetic coupling and the electron mass could be different in these different vacua. From an experimental standpoint, the most we can say is that our observable universe is very isotropic, that is, the laws of physics here on Earth must be very much the same as the laws on a planet in Alpha Centauri, so we expect that our observable universe is in the same vacuum state everywhere. Conversely, it could be that there are regions of the universe at distances beyond which we can observe that could have different physics corresponding to some other vacuum solution. These possibilities are called Level 1 and 2 of Tegmark's classification of what is referred to as the multiverse. Unfortunately, since we don't really expect to interact with anything outside our observable patch, the existence of this type of multiverse is rather metaphysical rather than physical.

These are exciting questions to ponder, but I would urge that you not let the mystery and profoundness prevent you from learning more concrete facts about our universe and our vacuum state.