# Quantum fluctuation

1. Jan 23, 2005

### wolram

In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenberg's uncertainty principle." Quote from wikipidia".
can someone tell me what caused the first, "temporary change", i am
guessing that the first temporary change came before the first virtual
particles.

2. Jan 23, 2005

### vanesch

Staff Emeritus
The problem with this kind of explanation is that the words have a meaning when one already knows what was to be expressed, and that the words are misleading and confusing when not.

"quantum fluctuations" are the spread in local field value when the field is in its vacuum state.
In fact, the "local field value" can be seen as an observable which doesn't commute with the Hamiltonian of the free field. The vacuum state is the lowest energy value of the Hamiltonian, and has thus a fixed energy value, and as such, is an eigenstate of the Hamiltonian. It is NOT an eigenstate of the 'local field value" observable, and thus there is a spread of values due to that non-commutation. If measuring the local field value, one has thus a statistical spread, and hence a "fluctuation".

It is very similar to the "momentum fluctuation" one can have in a "position state" of a particle.

cheers,
Patrick.

3. Jan 23, 2005

### marlon

You need to look at these words in a very narrow way. QFT is the unification of special relativity and QM. This means that both E=mc² (from special relativity) and the Heisenberg uncertainty principle (from QM) can be used. Now if you look at the vaccuum state, it has a non-zero energy value in QFT. This means that via E=mc² we can look at this vaccuum as being filled with particles. These particles are virtual particles. Now via the uncertainty relation we can deduce that during a very short while, we can apply a big amount of energy in order to make these virtual particles real. The question now is why these particles are virtual. The answer is this : virtual means that these particles can never be the end-result of some kind of interaction. they only exist as an intermediate stage during some interaction. The best example is the interaction between two electrons wia the exchange of virtual photons in QED. When applying lot's of energy a virtual particle becomes real. This means that it can exist on itself and it should be treated equally with other real particles. This explains how in field theory an electron can pop up suddenly and shortly after it dissapears again. During this process one can say that energy is not conserved and to some extent that is correct. However you need to incorporate the fact that this only happens during a very short time and when looking at some interaction in total, the netto-energy is always conserved. These processes are more of a local instantaneous violation of energy but looked at the time scale of the actual interaction going on (like the two electrons interaction via the virtual photons) you can say that the net-energy is conserved.

The actual fluctuation really represents a particle of some mass m in field theory, emerging from the underlying field. Basically the transition from one quantum state of the field to another, really provides the energy that represents the particle. There are several ways to excite a field, like for example other interactions going on...

regards
marlon

4. Jan 23, 2005

### Schneibster

Marlon, I am still wending my way through these descriptions of virtual particles.

My initial understanding was that they could be real, if a reaction required them to be, as long as mass/energy was conserved, but that in general they were not real. Then I got into a conversation where Jesse told me that they are not real, that they are actually just a convenient way of describing the bookkeeping so that everything comes out right, and we can properly describe the quantum field in terms of quanta, so that we can describe the quanta of the field interacting with, say, electrons in our description of how the electrons behave under, say, the EM force. So the only thing that has reality is the field sez I, and nobody disagrees with me.

Now, you are telling someone that these virtual quanta are real, but only while they are in an interaction. That makes some sense, but I'm sure you can see how I would find this confusing. Can you straighten me out some, please?

5. Jan 23, 2005

### marlon

Now, i am telling you that they can BECOME real for a very short while when enough energy is available in order to give them "a valid reason to exist"

i agree with the bookkeeping-explanation but the reason why they are virtual is that they indeed are inherent to realtime interactions going on. They are an intermediate stage of the interaction. ust look at the virtual photon-exchange example...Besides, look at the Casimir-effect and you can only conclude that they MUST somehow be real because their influence is measured in experiments...

marlon

6. Jan 23, 2005

### wolram

A fascinating subject ,and lots of educating going on here, many thanks
to all, can someone point me to a good on line read of the subject, or
maybe a personal journal?

7. Jan 23, 2005

### marlon

I have written many texts on this in my journal, check it out if you want.

I recommend the following entries :

1) introduction to string theory part 1
2) on the origin of confined species
3) on gluons and pions
4) info on the web for further reading
5) why are elementary particles massles
6) what is the Higgfield
7) why 8 gluons ?

marlon