Uncertainty principle and vacuum fluctuations

In summary, according to the uncertainty principle, energy and time can't be measured perfectly simultaneously, which allows for the violation of energy conservation. This principle is more general than just the uncertainty principle concerning the uncertainty about particle's position and momentum, it applies to all pairs of observables whose operator do not commute. Additionally, time dilation effects can also be accounted for by moving volumes. There is no known way for virtual particles to arise from quantum foam due to the Higgs field.
  • #1
spidey
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I saw in some sites that vacuum fluctuations are due to uncertainty principle but i couldn't 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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  • #2
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 [tex]\Delta t \sim \frac{\Delta E}{h}[/tex].

THe uncerntainty principle is more general than just [tex]\Delta x \Delta p \sim h[/tex], 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 their eigenvalues perfectly simultaneously.

eg since [tex] [\hat{L_{x}},\hat{L_{y}}]=\hat{L_{x}} \hat{L_{y}}-\hat{L_{y}} \hat{L_{x}} = -i \hbar\hat{L_{z}}[/tex] 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 [tex]\hat{E}[/tex] and [tex]\hat{t}[/tex] 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).
 
  • #3
spidey said:
I saw in some sites that vacuum fluctuations are due to uncertainty principle but i couldn't 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! :smile:

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. :smile:
 
  • #4
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 dilation effects? do moving volumes allow for more energy to be created?
 
  • #5
Are there any known way for virtual particles arising from quantum foam to gain existence/mass from the Higgs field?
 

What is the uncertainty principle?

The uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to know both the exact position and momentum of a particle at the same time. This is due to the nature of quantum particles which have wave-like properties and therefore cannot have a precise location and momentum simultaneously.

How does the uncertainty principle relate to vacuum fluctuations?

Vacuum fluctuations refer to the constant creation and annihilation of virtual particles in the vacuum of space. These fluctuations are a result of the uncertainty principle as they arise from the inherent uncertainty in the energy of a system. The shorter the time interval, the greater the uncertainty, and the more likely it is for virtual particles to appear and disappear.

What is the significance of vacuum fluctuations?

Vacuum fluctuations play a crucial role in quantum field theory and have been experimentally verified through various phenomena such as the Casimir effect. They also have implications for the behavior of particles in quantum systems and can give rise to various observable effects such as the Lamb shift.

Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle in quantum mechanics and has been verified through numerous experiments. It is a fundamental limitation of our ability to measure and predict the behavior of particles at the quantum level.

How does the uncertainty principle affect our understanding of the universe?

The uncertainty principle challenges our traditional understanding of cause and effect and determinism. It also highlights the probabilistic nature of the quantum world and the limitations of our ability to make precise measurements. Additionally, it has implications for various fields such as quantum computing and quantum cryptography.

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