# Is wave function collapse the only source of 'randomness' in QM? What about field fluctuations? Are these two even distinct?

Basically I want to know the validity of the statement, "All randomness originates from wave function collapse" or maybe "The only true random event is the collapse of wavefunctions"

This seemed to jive with me initially, but then I thought about the random fluctuations in underlying quantum fields, as well as the idea that the quantum fluctuations at the big bang combined with hyperinflation may have caused the uneven distribution of matter we see today. Those effects aren't due to wave function collapse, right?

Are there more sources of randomness? Is there a general statement we can make about randomness and where it physically originates from?

It is important to understand that fields don't fluctuate. This is explored in the question Are vacuum fluctuations really happening all the time? (spoiler: the answer is no).

The randomness you are talking about is due to measuring some quantity when the wavefunction is not an eigenstate of that quantity. For example suppose we are measuring energy. If our wavefunction is not an eigenstate of energy we can write it as a sum of energy eigenstates:

$$\Psi = a_1 \psi_1 + a_2 \psi_2 + a_3 \psi_3 + ~ ...$$

where the $$\psi_i$$ are the energy eigenfunctions. Then measuring the energy randomly collapses the wavefunction to one of these eigenstates $$\psi_i$$ with probability $$\left| a_i \right|^2$$. This is the random element in QM, and it applies to quantum fields in exactly the same way.

• Oh I see, so quantum fields not being in an eigenstate (thus introducing randomness when measured) is totally analogous to particles not being in one since they are both represented by a wavefunction anyway. – Ozaner Hansha Dec 5 '18 at 10:33
• @OzanerHansha yes, exactly. – John Rennie Dec 5 '18 at 10:34
• – Andrew Steane Dec 6 '18 at 10:21

This problem is common to physics where the observations are always sets of "points".

When the number of points is big, one has a clear "image"; otherwise several or one point are not representative.

In Classical Mechanics one makes an average over the set of points at a "time" (=time interval) and finds a "deterministic" behavior of such "mean values" (coordinates of the Moon, for example). When the number of points is small (the light intensity is small), the observation results are vague or useless. One always has to have a good statistics to say something certain about observations.

Note also , the observed body must change (radiate or absorb) in order to be observed, so we attribute the image of an "objective" entity to something that is not objective (intact), but changing! The primary thing is a set of points due to exchange of energy; the produced image is some sort of avatar rather than the true entity, so it depends on the way we process (treat) the obtained data.

Even without collapse, a wavefunction provides and intrinsically random description. Knowing it is just providing the building bl ock to know the probability of a measurement. I.e. the result of a measurement is a random variable. What else?

As a side remark, I would add that there is no intrinsic necessity for a quantum field to fluctuate. That is a misconception. Would you say that a wavefunction would fluctuate?

• "Would you say that a wavefunction would fluctuate?" It is very important to remember that quantum fields are not the analogue of the wavefunction in QFT, but the analogue of the position variable. You could say (loosely) that the position of a particle "fluctuates" in 1D QM, and so the same language could be applied to field configurations (but probably shouldn't). – Bob Knighton Dec 5 '18 at 13:26
• From the technical point of view a quantum field could be seen as a field of operators on a Fock space. Do the operators fluctuate? – GiorgioP Dec 5 '18 at 14:49