What is the true nature of vacuum energy in quantum physics?

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Discussion Overview

The discussion centers around the nature of vacuum energy and zero-point energy in quantum physics, particularly in the context of an electron confined in a one-dimensional potential well. Participants explore the implications of the Heisenberg uncertainty principle, the behavior of electrons under confinement, and the concept of energy transfer in quantum systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants discuss how confining an electron in a potential well increases its kinetic energy, raising questions about where this energy comes from.
  • Others propose that the energy used to compress the well is provided by the external force, maintaining that this energy does not directly affect the electron but rather increases the potential energy of the wall's atoms.
  • A participant introduces the concept of radiation pressure as analogous to the pressure exerted by the electron wave on the walls of the well.
  • Some participants mention zero-point energy as a concept that might be relevant to the discussion, with one suggesting it could be harnessed, while another argues it cannot be used as it represents the lowest energy state of a system.
  • There are claims that the Heisenberg uncertainty principle (HUP) relates to the statistical outcomes of measurements rather than directly to energy levels, with some emphasizing the implications of wave behavior in quantum mechanics.
  • One participant questions whether the electron actually accelerates, leading to a discussion about the nature of acceleration in quantum mechanics.
  • Another participant expresses skepticism about the understanding of vacuum energy, linking it to the discovery of dark energy and suggesting that the work done to increase pressure in a confined space is more significant.
  • There is a mention of the Casimir effect and its perceived weakness in terms of harnessing vacuum energy, along with a proposal for a model that considers vacuum fluctuations as interactions within a compound system of charge and electromagnetic fields.

Areas of Agreement / Disagreement

Participants express multiple competing views on the nature of vacuum energy, the implications of the Heisenberg uncertainty principle, and the behavior of electrons in potential wells. The discussion remains unresolved, with no consensus reached on key points.

Contextual Notes

Some participants highlight limitations in understanding the relationship between energy levels and the uncertainty principle, as well as the implications of wave behavior in quantum mechanics. There are also references to specific models and theories that may not be universally accepted.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in relation to vacuum energy, zero-point energy, and the implications of confinement on particle behavior.

eoghan
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Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than [tex]\frac{h}{L}[/tex], which means that the electron has a velocity (and so a kinetic energy) greater than [tex]\frac{h}{L*m_e}[/tex]. If I "press" the well, L becomes smaller and smaller, so the kinetic energy of the electron becomes greater and greater; according to the conservation of energy, the electron must take this energy somewhere: where does the electron take the energy needed to increase its kinetic energy?
 
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eoghan said:
Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than [tex]\frac{h}{L}[/tex], which means that the electron has a velocity (and so a kinetic energy) greater than [tex]\frac{h}{L*m_e}[/tex]. If I "press" the well, L becomes smaller and smaller, so the kinetic energy of the electron becomes greater and greater; according to the conservation of energy, the electron must take this energy somewhere: where does the electron take the energy needed to increase its kinetic energy?

You "press" so you yourself provide the energy. If you do it sufficiently slowly, the ratio energy/frequency remains constant (an adiabatic invariant).

Bob_for_short.
 
Bob_for_short said:
You "press" so you yourself provide the energy. If you do it sufficiently slowly, the ratio energy/frequency remains constant (an adiabatic invariant).

But the energy used to press the wall is used to press the wall... I mean, the energy is used to make the atoms of the wall nearer, increasing their potential energy. So the energy I use to press the wall it's transformed in potential electrostatic energy and doesn't affect the electron
 
eoghan said:
But the energy used to press the wall is used to press the wall... I mean, the energy is used to make the atoms of the wall nearer, increasing their potential energy. So the energy I use to press the wall it's transformed in potential electrostatic energy and doesn't affect the electron

No, if the walls are neutral, then there is no interaction potential between them. They serve just to reflect the electron so they are under pressure of the electron wave.
 
Sorry.. I don't uderstand:confused:... what do you mean by "to be under pressure of electron wave"?
 
For simplicity imagine a classical particle reflecting from the left and right walls. It makes pressure on walls and likewise.
 
Ah, ok... do you mean something like a radiation pressure?
 
eoghan said:
Ah, ok... do you mean something like a radiation pressure?

Yes, the radiation pressure in a limited system (with reflecting walls) is of the same nature.
 
eoghan said:
Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than [tex]\frac{h}{L}[/tex], which means that the electron has a velocity (and so a kinetic energy) greater than [tex]\frac{h}{L*m_e}[/tex]. If I "press" the well, L becomes smaller and smaller, so the kinetic energy of the electron becomes greater and greater; according to the conservation of energy, the electron must take this energy somewhere: where does the electron take the energy needed to increase its kinetic energy?

That's the so-called Zero-point energy. You can get it for "free". see this page: http://www.scientificamerican.com/article.cfm?id=follow-up-what-is-the-zer

What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?
 
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  • #10
eoghan said:
Hi! Let's suppose an electron in a mono-dimensional potential well. According to Heisenberg uncertainty principle, if L is the length of the well, then I have a momentum greater than [tex]\frac{h}{L}[/tex], which means that the electron has a velocity (and so a kinetic energy) greater than [tex]\frac{h}{L*m_e}[/tex]. If I "press" the well, L becomes smaller and smaller, so the kinetic energy of the electron becomes greater and greater; according to the conservation of energy, the electron must take this energy somewhere: where does the electron take the energy needed to increase its kinetic energy?


No HUP is about the statistical outcome of measurments, not quantum equation of motion. The quantum equation of motion is governed by the Schrödinger Equation.
 
  • #11
feynmann said:
Zero-point energy is "free". see this page: http://www.scientificamerican.com/article.cfm?id=follow-up-what-is-the-zer

What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?

The zerop point energy is per definition the lowest energy a system can have, thus we can not "use" it, e.g. we can not de-excite the hydrogen atom further down than it's ground state.
 
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  • #12
malawi_glenn said:
No HUP is about the statistical outcome of measurments, not quantum equation of motion. The quantum equation of motion is governed by the Schrödinger Equation.

Well, but does the electron actually accelerate or doesn't?
 
  • #13
eoghan said:
Well, but does the electron actually accelerate or doesn't?

Electron (or any other particle) in the ground state is a standing wave of the lowest harmonic. It should exist. If there is no wave, there is no electron and there is no wave equation for it.

You can think without contradiction that the electron do not accelerate in the ground or in any excited state. It "accelerates" and radiates while transitions from one state to another.

Bob.
 
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  • #14
eoghan said:
Well, but does the electron actually accelerate or doesn't?

define acceleration in quantum mechanics...
 
  • #15
According to HUP, things just don't like to be confined and become more and more agitated when attempts are made to confine them in ever smaller containers of any type.

One way to think about this: According to E = hf , energy increases as frequency does which means wavelength decreases; as a container is made smaller the wavelength of the contained particle is forcefully decreased...hence it's energy is forced to increase...it becomes more and more agitated

I'm unsure if vacuum energy is a source; I have always wondered if we really don't understand it whatsoever and the discovery of massive amounts of dark energy has just made me more suspicious...anyway, the work done to increase the pressure by making the container smaller seems more appealing...
 
  • #16
Naty1 said:
According to HUP, things just don't like to be confined and become more and more agitated when attempts are made to confine them in ever smaller containers of any type.

HUP is about the statistical outcome of measurements, not energy levels...
 
  • #17
malawi_glenn said:
HUP is about the statistical outcome of measurements, not energy levels...

More importantly, it relates the statistical standard deviation in the measurements, not the magnitude of the mean of the measurements.
 
  • #18
Born2bwire said:
More importantly, it relates the statistical standard deviation in the measurements, not the magnitude of the mean of the measurements.

That is correct
 
  • #19
feynmann said:
What is the 'zero-point energy' (or 'vacuum energy') in quantum physics? Is it really possible that we could harness this energy?

The Casimir effect (kind of Van der Waals force) is too weak to be harnessed, in my opinion.

I would like to give my own view on the "zero-point" or "vacuum" energy. Normally they say that the vacuum field fluctuations exist in the vacuum. In my opinion it is not exact since, for example, the quantized electromagnetic field is in permanent "interaction" with electrons (or charges). So it is more naturally to consider them as "fluctuations" in a compound system charge+EMF. Such a model of charge-field coupling (an electronium) has been advanced in "Reformulation instead of Renormalizations" and in "Atom as a "dressed" nucleus" by Vladimir Kalitvianski available in arXiv. The vacuum field wave functions are similar to the ground state atomic wave functions which also describe a compound system (an atom). Each charge has its own quantum EMF oscillators just like each nucleus in atoms has its own electrons around. This physical model seems unusual first but quite natural after analysing the atom description reported in Atom as a "dressed" nucleus". These "atomic" results are correct but are still rather unknown.

Bob_for_short.
 

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