# De Broglie Bohm interpretation with virtual particles....

• asimov42
The vacuum fluctuation could theoretically produce an electron-position pair, but it is not guaranteed to do so.

#### asimov42

Hi all,

This question is similar to a question asked previously, but slightly different. I understand that there have now been attempts to extend the Broglie-Bohm, or Pilot Wave, interpretation of QM to QFT.

I'm a layman, but if I understand correctly, the standard method for computing the wave function involves summing all the ways a particle, say an electron, could move from A to B - including interacting with virtual particles along with way. Is this all handled by the pilot wave in the Broglie-Bohm interpretation? Since the particle 'surfing' the pilot wave always has a definite position and momentum?

The last thing I'm wondering about (and I'm not doing a good job of stating it here) - The moving particle could go from A to B without interacting with anything - but would also include the situation in which a virtual electron-positron pair pops into existence near the original, real, electron. In this latter case, the 'first' (real) electron could annihilate with the virtual positron, leaving the second electron ... which would then become 'real' (i.e. because it's forced to 'exist' due to its original partner, the positron, being annihilated with the first electron).

Could this type of thing even happen in the Pilot Wave theory? I think I'm confusing a number of different things so any insight would be really really helpful.

Thanks.

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Well first virtual particles dont' actually exist - they are simply a colourful name for terms in what's called a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

In the sum over history approach of Feynman particles don't actually go along those paths - its simply a way of looking at the math. Instead of having this abstract thing called a wave function, which is a representation of another abstract thing called a state, you plot a lot of paths and add up its value along the paths. Its a novel way of viewing QM with many insights, but particles don't actually go along those paths.

Thanks
Bill

bhobba said:
Well first virtual particles dont' actually exist - they are simply a colourful name for terms in what's called a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

In the sum over history approach of Feynman particles don't actually go along those paths - its simply a way of looking at the math. Instead of having this abstract thing called a wave function, which is a representation of another abstract thing called a state, you plot a lot of paths and add up its value along the paths. Its a novel way of viewing QM with many insights, but particles don't actually go along those paths.

Thanks
Bill
Question: the particle goes along -one- of the possible paths, in Bohemian Mechanics, right?

As far as I am aware, from my limited reading on Bohemian Mechanics, particles only have definite positions at all times. Could it then have momentum (thus violating the Heisenberg Uncertainty Principle)? -- genuine question of curiosity.

bhobba said:
Well first virtual particles dont' actually exist - they are simply a colourful name for terms in what's called a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

In the sum over history approach of Feynman particles don't actually go along those paths - its simply a way of looking at the math. Instead of having this abstract thing called a wave function, which is a representation of another abstract thing called a state, you plot a lot of paths and add up its value along the paths. Its a novel way of viewing QM with many insights, but particles don't actually go along those paths.

Thanks
Bill

Thanks bill. But I've also heard or virtual particles being described as 'disturbances' (see http://profmattstrassler.com/articl...ysics-basics/virtual-particles-what-are-they/) ... so there's some type of disturbance at least. Is it true to say the the types of disturbances encountered would not be of the type above (i.e., positron -like disturbance annihilates with real electron?)

Thanks.

I don't think this strategy is going to work - taking different people's words that they use to describe the underlying mathematics, and then trying to understand the underlying mathematics by combinations of these words.

Demystifier
I don't think this strategy is going to work - taking different people's words that they use to describe the underlying mathematics, and then trying to understand the underlying mathematics by combinations of these words.

Hi Vanadium, yes, probably right. :( Perhaps, could ask a slightly different question that's more in line with what I'm actually wondering (particle lifetime):

Again, let's say we have a electron traveling through space devoid of other matter for the moment: is it possible that a quantum fluctuation (vacuum fluctuation) would be able
to annihilate the electron at some point? I was assuming that a random vacuum fluctuation could take the form of a short lived electron-position pair, but maybe a) that's not possible or b) the pair would b off-shell, and wouldn't interact the way I think it would?

Not sure that is helpful - and thanks for your time guiding a layman.

StevieTNZ said:
Question: the particle goes along -one- of the possible paths, in Bohemian Mechanics, right? As far as I am aware, from my limited reading on Bohemian Mechanics, particles only have definite positions at all times. Could it then have momentum (thus violating the Heisenberg Uncertainty Principle)? -- genuine question of curiosity.

In BM particles have definite momentum and position at all times - you just can't know what they both are simultaneously. Uncertainties appear in that approach due to an inherent lack of knowledge of initial conditions.

I am not the best person to discuss BM - Dymystifyer is our expert.

Thanks
Bill

asimov42 said:
Thanks bill. But I've also heard or virtual particles being described as 'disturbances'

You are talking about Quantum Field Theory (QFT). One of the things about QFT is its a big step up in conceptualisation and mathematical sophistication from ordinary QM and notoriously difficult to grasp at the lay level. As one of our other science advisors says - everything you have read about QFT outside a QFT textbook is likely wrong. What I have told you is the truth about the math. Others try to give a more colourful take on it that obscures the facts. They do that to try and get across this difficult sujbect to a lay reader. It is to be taken with a grain of salt.

Thanks
Bill

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asimov42 said:
Again, let's say we have a electron traveling through space devoid of other matter for the moment:.

In QFT such a picture is incorrect. Even the concept of a single particle is moot. Everything is a field - particles are excitations of that field where what excitation means is rather sophisticated. Bottom line - virtually all your everyday pictures go out the window in QFT.

At the lay level the following is a good book to begin with on QFT:
https://www.amazon.com/dp/0473179768/?tag=pfamazon01-20

But as I said previously, while that book is good, conveying exactly what's going on in QFT is beyond lay explanation.

Thanks
Bill