How do quantum fluctuations originate?
Quantum mechanics says that nature is intrinsically statistical (non-deterministic) and any statistical system is subject to fluctuations.
But don't quantum fluctuations violate the conservation of energy?
No, they don't. That to me is one of the amazing things about the formalism.
If quantum particles were just like classical particles except with slightly randomized position and momentum then the energy would not be conserved. But the way that it actually works conserves energy.
So you're talking about virtual particles and real particles alike?
Its a by-product of Quantum Field Theory (QFT)
It's a subject I have been making attempts to really understand for a while - I have gone through some books but not to the depth I personally would like.
Recently I have come across a VERY good book that is just at the right level for me, and am enjoying going through it right now:
Highly recommend it.
Any insights, if you could state some?
Not from that book because I am going through it now.
But from my previous readings there is a deep sickness in QFT that has to be resolved by what is called renormalisation at all levels.
Right at the start you get an infinite energy for the so called no particle state which is blatantly absurd. So you need to have a cut-off and say our theories are true only up to a certain energy.
To me that is very deep and profound. This is the modern version of how we look at renormalisation:
The above paper I have studied to a level I am happy with, and believe is a very deep insight about fundamental physics.
Do you know this article by Matt Strassler ?
Let's say we have an ensemble of similarly prepared systems. If we make a measurement of the energy of each system then in general we will get a different answer because the energy is stochastic.
But this doesn't mean there is a violation of energy conservation because such a violation entails that the system actually possesses a definite energy that changes discontinuously which is not what we have here; rather we have a system with an inherently probabilistic value of energy that isn't known until we make a measurement.
And if we make measurements on a sufficiently large ensemble then eventually the measurements of energy will converge towards the average value. QM states that this average value, or "expectation value", will remain conserved.
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