Can a universe form from a true vacuum through quantum tunneling?

[mattattack]

So, a true vacuum is a vacuum devoid of space/time and any form of particles, correct? Is it correct that a true vacuum can have an energy state, even if it is devoid of particles?

According to the uncertainty principle, a system has unstable energy (and cannot have 0 energy because of this), so given this can a universe form from a true vacuum spontaneously? I've heard Vilenkin say a universe can 'quantum tunnel' into existence. Even though I thought quantum tunneling was restricted to quantum particles tunneling through already existing material. He also said that when a false vacuum forms from this, the change in states causes an explosion of energy, and also commented that "well you might ask why there is a true vacuum state, and I will talk about that later", but he didn't say much else about it.

Is there anywhere I can get good information on what we know about true vacuums and quantum tunneling in this context, or anyone that knows much about this explain it here briefly? I can't really find anything on the internet on the subject.

 

[sadraj]

Yeah, actually vacuums have energy , say infinite amount of energy, because the lowest energy level of quantum state of a particle ( as an example harmonic oscillator)has infinite energy. But true and false vacuum corresponds to classical fields , as an example a scalar field like Higgs can have some minimums , the lowest one is the true one since otherwise it may decay to lower minimums by quantum tunneling process until gaining the lowest. The amazing infinite energy of quantized field is an open question in the context of Cosmological constant debate.

 

[ZapperZ]

Yeah, actually vacuums have energy , say infinite amount of energy, because the lowest energy level of quantum state of a particle ( as an example harmonic oscillator)has infinite energy.

Where in the world did you get that? The lowest energy of a quantum harmonic oscillator is $1/2 \hbar \omega$. This is NOT "infinite".

Zz.

 

[Jilang]

Where in the world did you get that? The lowest energy of a quantum harmonic oscillator is $1/2 \hbar \omega$. This is NOT "infinite".

Zz.

It becomes infinite when you integrate over all w.

 

[ZapperZ]

It becomes infinite when you integrate over all w.

But that's the total energy, not the energy of a particular ground state, as erroneously stated.

Besides, in a simple harmonic oscillator, where I only have ONE particular frequency, what are you integrating over?

Zz.

 

[sadraj]

The ground state (vacuum) of the Hamiltonian corresponding to a particular field not the Hamiltonian of a harmonic oscillator.

 

[ZapperZ]

The ground state (vacuum) of the Hamiltonian corresponding to a particular field not the Hamiltonian of a harmonic oscillator.

I'm not the one made that connection. You did!

Yeah, actually vacuums have energy , say infinite amount of energy, because the lowest energy level of quantum state of a particle ( as an example harmonic oscillator)has infinite energy.

That was what I was responding to. When you say something like that, and then we have students in QM classes looking at their text and seeing the energy eigenvalue at n=0 as being finite, there's a lot of explanation needed here!

Zz.

 

[sadraj]

Ok you are right!
;)
I have to write precisely!

 

[ChrisVer]

Isn't the problem due to the Hamiltonian density?
I mean it is related ~(1+N), with N being the number operator... even if it's zero for the vaccum, the 1 is being integrated over all space to give us the Hamiltonian, leading to infinity.

 

[WannabeNewton]

I mean it is related ~(1+N), with N being the number operator... even if it's zero for the vaccum, the 1 is being integrated over all space to give us the Hamiltonian, leading to infinity.

Yes you get an infinite sum (resp. integral) over all possible harmonic oscillator modes solely of the energy eigenvalues mentioned earlier by Zz after acting the Hamiltonian density on a given state (so the 1 that you were referring to) on top of the terms corresponding to the number operator.

 

[mattattack]

Yes you get an infinite sum (resp. integral) over all possible harmonic oscillator modes solely of the energy eigenvalues mentioned earlier by Zz after acting the Hamiltonian density on a given state (so the 1 that you were referring to) on top of the terms corresponding to the number operator.

Yeah, I don't think I understand any of these terms (like 'harmonic oscillator', or eigenvalues). But are you saying a true vacuum state has potential infinite energy?

 

[bhobba]

But are you saying a true vacuum state has potential infinite energy?

A naive application of the theory yields an infinite vacuum energy.

Its really an example of the infinities that plague QFT.

Such infinities are handled by what's called renormalization, which was initially viewed with suspicion - you would hear jokes about physicists having infinities hidden under their rugs.

But a lot of research has been done, and guys like Wilson, who got a Nobel prize for it, sorted it all out with what's called the Effective Field Theory approach:
http://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/

Basically these days our theories are viewed as low energy approximations to deeper theories we may or may not know about. We get infinities by pushing them into regions they are invalid. It is hoped, and suspected, deeper theories will fix the issue.

It was mentioned its infinity if you integrate over all possible energy modes in the vacuum. But Wilson's idea is simplicity itself. Since the theory is only a low energy approximation there is some energy above which its not valid - so they should not be included.

Thanks
Bill

 

[Jilang]

The introduction about zero point energy in this article is worth reading and mentions how the cut off might work.
http://www.calphysics.org/zpe.html