Some questions regarding quantum fluctuations

[momo666]

First of all, would I be correct in using the following explanation?
Quantum fluctuations are not actually events but properties of the quantum vacuum, they don't have a physical cause but they are not an example of creation ex nihilo, they are created from other things.
I think of it like a shaking of a soda can. The quantum vacuum is the soda and the fluctuations are the bubbles that appear when you shake the can.

In case I have not been clear let me line up my questions:
1) Are quantum fluctuations an example of creation out of nothing (not anything) ? I am correct in saying that there is no such a thing in physics?
2) Do quantum fluctuations have a physical cause?
3) What exactly makes the quantum vacuum fluctuate?
4) What are quantum fluctuations "made of" ?

 

[jfizzix]

Quantum physics is a tool that describes the outcomes of experiments to the best possible precision. This is all that quantum physics is really prepared to do.

That being said:
Quantum fluctuations are examples of the irreducible randomness of quantum systems, and the fact that quantum mechanics ultimately gives probabilities for measurement outcomes rather than deterministic trajectories like in Newtonian physics. As one example of irreducible randomness, the Heisenberg principle rules out the possibility of a particle having both a well-defined position and momentum. Quantum mechanics can tell you what the position and momentum probability distributions will be for both position and momentum, but any measurement outcome is random, though with likelihoods obeying those distributions.
The uncertainty principle also sets a fundamental limit on the predictability of future behavior of a system. Since at any given time, one can't know both the position and momentum of a particle to unlimited precision, the future behavior as dictated by its present state of position and momentum is also undetermined.

In quantum theory, quantum fluctuations don't have a cause in the same sense that a planet's curved trajectory is caused by the presence of its local star. Quantum fluctuations are part of quantum theory itself. Particles simply don't have well defined trajectories, and are instead described by probability distributions where the actual measurement outcomes may "fluctuate" about the average predicted value.

As with the quantum vacuum, the quantum state of anything when not acted on by outside sources evolves over time in a predictable way (as can be calculated by the Schrödinger equation or relativistic versions of it). Even so, these quantum states only give probabilities of outcomes. The outcomes themselves are random, though obey the distributions predicted by theory. Whether or not pairs of particles are created from nothing is a point of philosophical debate depending on interpretation, and is outside of science's ability to resolve (i.e., by experiment). The potential for particle creation is determined by the state of the vacuum, and the equation describing the total energy of the field (which would be a minimum number in a vacuum). Since one can predict the likelihood of particles being created in a given scenario, there is at least some causal determination in these particles' creation.

Long story short, the quantum vacuum is not nothing. It's its own thing with its own properties.

 

[radium]

An example of quantum fluctuations occurs in systems which undergo a quantum phase transition. This transition is quite unlike a classical phase transition in that it occurs at zero temperature because of quantums induced by varying some parameter. There may not be any phase transition at all at finite temperature.

The canonical example is the quantum Ising model. In one dimension, this is basically an Ising model with spins in the z direction but with a transverse field in the x direction. The quantum fluctuations occur because the transverse field term is proportional to the \sigma^x Pauli matrix and this does not commute with \sigma^z which is the way the system wants to order at zero field. Therefore at zero temperature you will start with an ordered phase with zero field and then reach a critical point where the order is destroyed by the quantum fluctuations and the system becomes a paramagnet.

There is no ordered state at finite temperature, but if you are within a small distance of the critical coupling compared to the temperature of the system you will see that because of the critical point the quantum fluctuations will indeed persist at finite temperature and will compete with thermal fluctuations on an equal timescale. So the system still "feels" the presence of the quantum critical point even at finite temperature, and oddly enough, below the lattice energy scale, the imprint of this critical point grows with temperature because the quantum timescale becomes shorter.

 

[radium]

So to summarize an answer to the original question, I think the main idea (in a pragmatic sense) is that quantum fluctuations are consequences of the Heisenberg uncertainty principle. The virtual particles come from the energy time uncertainty relation (which dictates a bound on their lifetime) and also enter the idea of renormalization, most concretely in the idea of vacuum polarization since that renormalizes the electric charge so that the coupling actually flows under RG. Quantum fluctuations also appear in quantum phase transitions which happen at T=0 but also influence behavior at higher T.

A few others things are that virtual particles can in fact go on shell which is represented in the many particle spectrum which begins at M \geq 2m and an imaginary part of matrix amplitudes.

Ghosts are just a tool to get rid of the gauge dependent parts of scattering amplitudes. They get rid of the gauge dependent prefactor in the Feynman path integral since they have fermion if statistics and give a determinant. They violate the spin statistic theorem so they are definitely not real. They will not appear in final results and you technically don't need them if you gauge fix in axial gauge for example. The problem with that gauge is that it not Lorentz invariant, and if you want Lorentz invariance then you need to add ghosts.

 

[Nugatory]

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