# Tag Info

0

Well, they could develop a vev, depending of the interactions you consider. Take e.g. this term in the lagrangian $L=\frac{1}{\Lambda^2}[\bar{\psi}\psi- v^3]^2$. Of course this would imply that you also break Lorentz, which you may want to avoid.

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I think it is a general fact about grassmannian field, and this has nothing to do with Lorentz invariance or other symmetries (you can invent a lot of QFTs without this kind of symmetry, but the VEV of a fermionic operator will be always zero (in the absence of sources)). In a functional integral formulation, the VEV of a grassmannian field $\psi$ is ...

3

Why can't fermions have a non-zero vacuum expectation value (VEV)? Lorentz invariance. If anything other than a Lorentz scalar has a non-zero VEV, Lorentz invariance would be spontaneously broken. For example, suppose we have a Lorentz invariant term in a Lagrangian for a vector $$\mathcal{L} \supset m^2 A_\mu A^\mu.$$ Now suppose the vector obtains a ...

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Unfortunately I cannot comment to ask you for more details. What exactly do you mean 'equilibrium point at -V'? Is this the potential, $V(\phi^* \phi)$, or the VEV, $v$ ? Is it the fact that we put $$\mu^2 < 0$$ where $$V(\phi^* \phi) = \mu^2 (\phi^* \phi) + \frac{\lambda}{4}(\phi^* \phi )^2$$ that is bothering you? The Vacuum Expectation Value ...

1

from a, b and c: An electromagnetic field is propagating by changing the field that's generated by electrically charged particles pass through the air and the space that is devoid of particles of space. An electromagnetic wave propagates, not an electromagnetic field. An EM wave is a propagating disturbance in the existing electromagnetic ...

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The electromagnetic field is mediated by the exchange of virtual photons. This is described by Quantum electrodynamics. It's this exchange that bridges the gap of empty space. I think the answer to this question has a pretty good representation of how an electromagnetic field propagates (at the speed of light) in vacuum.

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It is not empty in the sense that you still have quantum fields present. You also have quantum fluctuations happening all the time, and other quantum phenomena. Quote from wikipedia: "According to modern understanding, even if all matter could be removed from a volume, it would still not be "empty" due to vacuum fluctuations, dark energy, transiting gamma- ...

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Inside the solar system the solar wind consists of sub-atomic particles that form a plasma, one of the four states (phases) of matter along with solid liquid and gas. Plasma is basically a gas of charged particles--normal gas laws don't apply as moving charges create magnetic fields and magnetic fields influence moving charges, thermodynamic gas laws assume ...

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This creates a point of extremely focused energy at the middle point where the bubble collapses. In theory, this point focuses enough energy to trigger nuclear fusion. It is not currently accepted mainstream science to say that collapsing bubbles focus energy enough to cause nuclear fusion. Temperatures over 10,000K can be acheived, but are still well ...

3

No. Just like in Chemistry and Thermodynamics, we never get anything for free. On a mechanistic level, it's important to recognize that zero-point (vacuum) energy represents the lowest energy state waveform. I remember thinking that because the EM fields are everywhere and quantized, that there was some sort of magic taking place. Realistically, ...

3

The answer kinda is "You can, but why would you". It is indeed possible to extract energy from the vacuum. It has been studied, both theoretically and experimentally, using a variety of metal plates and other Casimiresque gizmos. The problem is just that it basically acts like a spring. To put the Casimir effect in action, you must first approach together ...

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Whether you can extract energy from this or not (and I strongly suspect not) the Casimir effect is a consequence of vacuum fluctuations. Essentially when two metallic plates are very close to each other, the wavelengths of virtual particles that can be created between the plates is restricted and hence there are fewer particles between the plates and ...

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The energy is borrowed from the Heisenberg Uncertainty Principle to create virtual particles and has to be paid back in a very short time. $\Delta{t} \geq \frac{\hbar}{2\Delta{E}}$ This is why virtual particles live for very short times (i.e pop in and out of existence). We cannot manipulate this energy.

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In a sense this could be an interpretation of gravitational waves. In this case, anything with energy or mass or momentum (relating by the stress-energy tensor in GR) could bend space-time producing gravitational waves. hopefully I'm understanding you correctly.

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