# Uncertainty principle and vacuum fluctuations

## Main Question or Discussion Point

I saw in some sites that vacuum fluctuations are due to uncertainty principle but i couldnt understand how these two are related...uncertainty principle speaks about the uncertainty about particle's position and momentum..vacuum fluctuations speaks about creation of particle pairs and annihilation...it seems both are different to me...can anyone explain how both are connected?

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neu
Are you familiar with the violation of energy conservation by the "vitual" mediating bosons.

For the same reason fluctuations are allowed as long as energy conservation is only violated for time $$\Delta t \sim \frac{\Delta E}{h}$$.

THe uncerntainty principle is more general than just $$\Delta x \Delta p \sim h$$, it applies to all pairs of observables whose operator do not commute. If two quatities don't commute then you the order of their operation affects the measurement outcome so necessarily you are not able to meaure thier eigenvalues perfectly simultaneously.

eg since $$[\hat{L_{x}},\hat{L_{y}}]=\hat{L_{x}} \hat{L_{y}}-\hat{L_{y}} \hat{L_{x}} = -i \hbar\hat{L_{z}}$$ then there is a corresponding uncertainty principle between these two quantities.

The uncertainty principle is a fundamental principle of quantum mechanics, it is not to do with technological ability. Hence, where applicable, it it allows for the violation of energy conservation since $$\hat{E}$$ and $$\hat{t}$$ don't commute.

I just wrote this off the top of my head so don't take anything I've said as Gospel, check it yourself (and correct me please).

tiny-tim
Homework Helper
I saw in some sites that vacuum fluctuations are due to uncertainty principle but i couldnt understand how these two are related...uncertainty principle speaks about the uncertainty about particle's position and momentum..vacuum fluctuations speaks about creation of particle pairs and annihilation...it seems both are different to me...can anyone explain how both are connected?
Hi spidey!

The uncertainty principle also speaks about the uncertainty about energy and time.

See http://en.wikipedia.org/wiki/Uncertainty_principle#Energy-time_uncertainty_principle:
A state which only exists for a short time cannot have a definite energy.
Loosely speaking, energy for a permanent state cannot be "borrowed", because permanent states have zero margin-of-error of energy (time everywhere => energy fixed);
but short-lived states have a non-zero margin-of-error of energy … the shorter-lived, the greater the margin-of-error (time very restricted => energy not very restricted) … so the uncertainty principle allows the vacuum to produce temporary states out of fluctuations of energy.

if we were to look at a volume and sum all the energy of pairs created, would we still find that this does not violate HUP?

and what about time dialation effects? do moving volumes allow for more energy to be created?

Are there any known way for virtual particles arising from quantum foam to gain existence/mass from the Higgs field?