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Old Sep 19th 2017, 09:28 PM   #1
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Looking for pressure on a "bubble."

I am currently working two problems. The one here is my current priority, if only because I should be able to reason it out better.

Problem:
I have a "bubble" (ie small region of space) that has as one of its properties that photons have a first order small mass. I am looking for an argument to show that the rest of space is going to put a pressure of sorts on the bubble that will collapse the bubble. I am currently working semi-Classically so I'm not looking for a quantum argument for now.

Honestly I don't even know how to start this one. Clearly if I can find a free energy to work with then I'm home free. But trying to find reasonable properties for a "wall" around the bubble is driving me nuts. I just can't figure out an approach.

Thanks!

-Dan

PS In case you were wondering about the other problem: I'm playing around with the Higgs potential in electro-weak theory and the possibility of having a massive photon comes up as a vacuum fluctuation.
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Old Sep 20th 2017, 04:59 AM   #2
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Sounds very similar to a previous problem you posted about:

<Phase Boundaries>

Similar questions present themselves:

What happens when a photon tries to cross the boundary, from either side?
do the photons change (acquire or loose mass) and what does that imply?
do they "reflect" and what does that imply?
do they pile up at the boundary?

Also what is the implication of a massive photon for other aspects of physics?
While it may be allowed as a solution to the particular equation you are studying,
it may be forbidden by another equation which would (in practice) form one of a set of "simultaneous equations" required for a universal solution.
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Old Sep 20th 2017, 02:07 PM   #3
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Originally Posted by Woody View Post
Sounds very similar to a previous problem you posted about:

<Phase Boundaries>
Yeah, sorry about that. I know a lot more than I did since that thread.

Originally Posted by Woody View Post
What happens when a photon tries to cross the boundary, from either side?
do the photons change (acquire or loose mass) and what does that imply?
do they "reflect" and what does that imply?
do they pile up at the boundary?

Also what is the implication of a massive photon for other aspects of physics?
While it may be allowed as a solution to the particular equation you are studying,
it may be forbidden by another equation which would (in practice) form one of a set of "simultaneous equations" required for a universal solution.
This is actually the kind of thing I'm working on in the other problem. I have been hoping that I can treat them as individual problems. Any (massive) photon will encounter a discontinuity in its first derivative but will be continuous across the boundary to the "normal" Universe. As I've set things up it would be a spherical delta function barrier problem. There is the possibility that a bound state could exist, but the difference in the Higgs potential inside the bubble is first order small so if we could get a bound state in there it would be extremely short lived. The masses of the other electro-weak particles are different in the bubble as well but crossing over shouldn't cause any major change. I haven't dived in on this yet as the photon problem is more severe. Also the bubble is defined as a region of space due to a random fluctuation so the bubble should only have a short life. Unless Nature says it should expand. The bubble should have some kind of external pressure on it that will collapse it. That's what is motivating the question.

I may be wrong but the setup here just screams Thermodynamics to me.

I'm still working on the theory but the essence of what I am trying to do is this: I am allowing the Higgs field to experience a first order small fluctuation. The fluctuation appears in the Lagrangian in the Higgs sector. Normally we use the "sombrero" potential to describe the Higgs. A fluctuation of the Higgs field can destroy the symmetry such that the remaining Higgs potential has no symmetries left. The result of this is that the photon (which normally is massless due to a remaining symmetry after spontaneous symmetry breaking) gains a mass. So far I'm sticking to just the photon sector.

-Dan
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Old Sep 20th 2017, 02:48 PM   #4
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So in effect what your thinking is something along the lines of:
Why is the Higgs potential so perfectly symmetrical, when it would appear that random fluctuations could fairly readily distort it?
There must be some kind of resistance to any such distortions which avoids them becoming extant in the universe as a whole.
Such as; any region of space wherein such a distortion occurs will be "pushed" closed by the "normal" space around it.

Is that somewhere close?
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Old Sep 20th 2017, 04:08 PM   #5
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Originally Posted by Woody View Post
So in effect what your thinking is something along the lines of:
Why is the Higgs potential so perfectly symmetrical, when it would appear that random fluctuations could fairly readily distort it?
There must be some kind of resistance to any such distortions which avoids them becoming extant in the universe as a whole.
Such as; any region of space wherein such a distortion occurs will be "pushed" closed by the "normal" space around it.

Is that somewhere close?
Mostly. I don't care (as far as this work is concerned anyway) why the Higgs potential is so simple, but other than that, yes this is the thing I am looking at here. The sequel is to see if we can make it do that on purpose. (Probably not.) But one thing at a time...

-Dan
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Old Sep 23rd 2017, 09:41 AM   #6
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I've had another thought about this,
Would the bubble have a "wall", or might it blend more gradually from one state to the other?
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Old Sep 23rd 2017, 12:08 PM   #7
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Originally Posted by topsquark View Post
I have a "bubble" (ie small region of space) that has as one of its properties that photons have a first order small mass.
I don't follow. You're saying that "you" have a small region of space in which photons have a " first order small" mass? What does that even mean? I.e. what does a " first order small" mean? Where is this region of space such that photons have mass? If a particle has mass then its not a photon.

Originally Posted by topsquark View Post
I am looking for an argument to show that the rest of space is going to put a pressure of sorts on the bubble that will collapse the bubble.
Space is not a thing which can act. Space cannot exert force. And you referred to "bubble" as meaning a small region of space, not an actual physical bubble which can collapse.

Originally Posted by topsquark View Post
Honestly I don't even know how to start this one.
I can see why.

Originally Posted by topsquark View Post
PS In case you were wondering about the other problem: I'm playing around with the Higgs potential in electro-weak theory and the possibility of having a massive photon comes up as a vacuum fluctuation.[
I thought that you weren't considering quantum mechanics at this point? In any case while there are "massive photons" in quantum fluctuations they aren't real photons, they're virtual photons. And virtual photons aren't really particles but a mathematical device.
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Old Sep 23rd 2017, 08:17 PM   #8
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What I am looking for in this is not QM, at this point. I'm trying to see if I can construct a semi-Classical analogy right now. I don't know much of any Quantum Thermodynamics...that seems to be Quantum Statistical Mechanics and I don't know anything about how to apply that here.

Here's the scoop of what I'm up to.

When I was working on my Masters my mentor mentioned to me that since the weak nuclear and electromagnetic forces are aspects of a single force we might be able to use electromagnetic fields to change some aspect of radioactive decay. What I chose to look at (because I am weird) was if it might be possible to effectively change the weak mixing angle over some, presumably small, region of empty space. I am calling that region of space a "bubble."

The trouble is that the calculations in my thesis were done incorrectly. I have no doubt it is impossible to change the mixing angle on a global level but I am still half convinced that it might be done on a very small region. (Volume depending on some number $\displaystyle \epsilon$ which we can take to be essentially an arbitrarily small parameter. Taking $\displaystyle \epsilon$ to 0 is what I am calling "first order small." $\displaystyle \epsilon ^2$ would be second order small, etc.)

I am currently working on two levels. The first question is "How can I even make this happen?" and the second question, which I am addressing here, "If we have such a region, what is going to happen to it?"

I have made a number of attempts at the second question and I'm pretty convinced that we can't create the bubble on purpose, but there are always some level of random fluctuations in the fields that have the potential to do so. The most simple method is to say that the Higgs potential can vary slightly such that the Higgs potential has no symmetries. This assumption effectively gives a mass to the photon over the life-time of the fluctuation.

What really bugs me about this is that the model I'm using predicts a lower vacuum energy level than in the traditional theory. This feature makes it imperative that something is going to "push" the bubble out of existence, else the fluctuation would create a more energetically favorable vacuum. The effect is similar to the idea of pressure on a wall from a reservoir in Thermodynamics so I've been calling whatever effect I need a pressure.

-Dan
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