What is Vacuum energy: Definition and 86 Discussions

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.

The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10−9 joules (10−2 ergs), or ~5 GeV per cubic meter. However, in quantum electrodynamics, consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10113 joules per cubic meter. This huge discrepancy is known as the cosmological constant problem.

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  1. S

    I Vacuum up-tunneling with high-energy events?

    I was reading these papers by Sean Carroll (https://arxiv.org/abs/1405.0298; https://arxiv.org/abs/1505.02780) in which, among other things, he argues against vacuum up-tunneling occurring in the universe. He only acknowledged that it would be possible in the first moments of the universe while...
  2. S

    I Is Vacuum Decay from a False to True State Impossible or Just Unlikely?

    I found this paper (https://arxiv.org/pdf/hep-th/0211160.pdf) which argues against the possibility of a decay from a metastable vacuum to a true vacuum state. However, this is the first time I've read this. Is it then impossible that a vacuum decay from a false vacuum may occur (even in...
  3. hyksos

    I Exploring the Casimir Effect: The Archimedes Experiment

    Vacuum energy is predicted by Quantum Field Theory, and also independently corroborated by recent observations in cosmology involving accelerated expansion. More corroboration occurs in superconducting cuprates exhibiting quantum criticality, and in the Casimir effect The island of Sardinia...
  4. S

    I Exploring the Potential of Vacuum Energy & Gravity

    I was reading this, but am confused: https://nautil.us/the-remarkable-emptiness-of-existence-256323/
  5. JandeWandelaar

    A Has a calculation of the vacuum energy density been done with strings?

    The calculation of the vacuum energy density gives us a discrepancy with reality. There should be a mass equivalent of about $10^{96}$ kilograms. I'm wondering if the assumed point-like "structure" of particles could be the cause of this wrong value. Since string theory doesn't assume a...
  6. D

    I Questions about Negative Pressure and Vacuum Energy

    Currently, dark energy is described as a being that exerts a negative pressure while having a positive energy density. {\rho _\Lambda } + 3{P_\Lambda } = {\rho _\Lambda } + 3( - {\rho _\Lambda }) = - 2{\rho _\Lambda } However, there seems to be a problem with the negative pressure assertion...
  7. S

    I Is it a fact that vacuum energy exists?

    I have always read that vacuum energy and zero point energy are established facts of physics supported by various observations of their effects both indirectly and even directly. But I have also read some comments from various physics discussion sites where they say that it is not a fact that...
  8. Ebi Rogha

    I Vacuum energy and Energy conservation

    Also, I have heard from physicists that vacuum energy fluctuation (creation and destruction of virtual particles) violates energy conservation. The reason, they justify, is based on uncertainty principle (energy-time form of uncertainty principle), energy can exist and disappear for a very short...
  9. LeoChan

    I When was the matter density equal to the vacuum energy density?

    In ΛCDM, H(t0) = 70km/s/Mpc, Ωd(t0) = 0.3, Ωr(t0) = 0 and ΩΛ(t0) =0.7, so that Ω(t0) = Ωd(t0) + Ωr(t0) + ΩΛ(t0) = 1and the universe is spatially flat. I want to know the t and z when the matter density equal to the vacuum energy density. By total energy density equation, I think Ωd(t) +...
  10. A

    B Fundamental fields and vacuum energy

    Please forward to appropriate subforums as I wasn't sure where to post it.In the standard model there are the composite particles and elementary particles, for the elementary particles there is said to be an associated field and the particle is the excitation of that field. Apart from asking how...
  11. The black vegetable

    A How to find the gamma function for a fermion vacuum energy calculation?

    Following the method by Peskin and Shroesder 11.4 Trying to calculate the vacuum energy of a fermion. If my method is correct so far the next step is to find gamma function , the formula I have for gamma fuctions doesn't match this equation. Can anyone help with the next step? Starting with the...
  12. DrInfinity

    A Effect of Spin on Vacuum Energy

    In equation (3) of this article https://arxiv.org/pdf/astro-ph/0605418.pdf , on page 3, you can see an expression for the vacuum energy density of a field as a function of its particle spin, particle mass and the wave number k. It is fairly straight forward to derive the integral portion of...
  13. G

    A Vacuum energy density after spontaneous symmetry breaking

    If we start with the Lagrangian \begin{equation} \begin{split} \mathcal{L} = & \frac{1}{2}(\partial_\mu \phi)^2 + \frac{1}{2}\mu^2 \phi^2 - \frac{1}{4}\lambda^2 \phi^4\\ \end{split} \end{equation} and give the scalar field a VEV so that we can define the field ##\eta##, where $$\eta = \phi...
  14. A

    A Confusion about 2016 Unruh paper - fluctuating vacuum energy density?

    Hi all, Just had a look at the 2016 paper by Wang, Zhu, and Unruh, "How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe," Qingdi Wang, Zhen Zhu, and William G. Unruh, Phys. Rev. D 95, 103504 – Published 11 May 2017 The paper states...
  15. Cathr

    I On Hubble's constant, the expansion of the Universe and vacuum energy

    Recently I was thinking about the Hubble's constant (which, actually, is not Hubble's and not constant...) and wondering: if the universe is expanding at 70 km/s each Mpc, then there's possible to calculate some expansion of space, say from me to a person 1 meter away from me (theoretically)...
  16. J

    I Vacuum energy length scale detectable by the Casimir effect?

    According to Sean Carroll's The Cosmological constant(https://arxiv.org/pdf/astro-ph/0004075.pdf) (Eqn.20) cosmological observations imply that the magnitude of the vacuum energy density in natural units is given by $$|\rho^{(obs)}_\Lambda|\le (10^{-12}\ \rm{GeV})^4.$$ Does this imply that the...
  17. J

    I Does the Friedmann vacuum equation have a linear solution?

    Does the Friedmann vacuum equation have a linear solution rather than an exponential one? Using natural units one can write Friedmann's equation for the vacuum as $$ \begin{eqnarray*} \left(\frac{\dot a}{a}\right)^2 &=& \frac{8\pi G}{3}\rho_{vac}\\\tag{1} &=& L^2 \left(\frac{\rho_0}{L^4}\right)...
  18. J

    I Is the ground state energy of a quantum field actually zero?

    I start by outlining the little I know about the basics of quantum field theory. The simplest relativistic field theory is described by the Klein-Gordon equation of motion for a scalar field ##\large \phi(\vec{x},t)##: $$\large \frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0.$$ We...
  19. nomadreid

    I CMB and the reference point for vacuum energy

    From the basic definition of vacuum energy as being tied in with the Uncertainty principle, I would expect this not to include the Cosmic Background Radiation. Right? On the other hand, in figuring out (a) the Casimir effect, one attributes the force to the field between the plates carrying...
  20. S

    B What Impacts Could Arise When Particle Mass Is Less Than Vacuum Energy Density?

    If mass of a particle is less than the vacuum energy density.. what would happen.. is this possible (also for some dark matter species)? How about photons.. are they more or less than the vacuum energy density? And what exactly is the value of vacuum energy density?
  21. Marrrrrrr

    A Virtual Fermions and Pauli Principle

    Hi guys, Do virtual particles, when they are fermions, obey Pauli exclusion principle as real fermions do? More specifically, what I am wondering is the following: Fermion fields would have some energy at every point in spacetime due to the uncertainty principle. Now, is it possible for the...
  22. S

    I Are quantum harmonic oscillators and radiation modes equal?

    Are quantum harmonic oscillators, vacuum fluctuations and radiation modes the same? Is vacuum energy caused by vacuum quantum fluctuations?
  23. davidge

    I Relativity Matter & Vacuum Energy: Stress-Energy Tensor

    Matter is responsible for the stress-energy tensor. What is included in "matter"? Does vacuum energy contributes somewhat to the stress-energy tensor? Would it be correct to include all forms of energy in the stress-energy tensor, through the mass-energy equivalence?
  24. newjerseyrunner

    B Why is vacuum energy assumed to be uniform?

    Considering that all energy gravitates, why is it assumed that the vacuum energy that we measure inside the gravity well of the Milky Way is consistent throughout space? Is there any real way to know? Would it make any difference in the problem that QM and GR differ in the vacuum energy...
  25. A

    I Lorentz violation, multiple preferred frames, vacuum energy

    Hi all - hope I'm not beating a dead horse here, but I'm following up on at least two other threads (made sense to consolidate): There are theories of quantum gravity (or the Standard Model Extension) that allow for local Lorentz violation. So, my first question: is there any reason why there...
  26. A

    I Vacuum energy cutoff and Lorentz invariance....

    One more question before Santa comes. There are a number of different related threads, so hopefully I'm not repeating this - however, I haven't found a crisp answer yet. If one introduces a UV cutoff in the vacuum energy (in an attempt to avoid having infinite vacuum energy), is it possible at...
  27. N

    B Is dark/vacuum potential energy infinite?

    And virtual particles potential energy is infinite too? As more and more dark energy is created does this mean that the potential energy of dark energy is infinite? Does that happen for virtual particles in vacuum and vacuum energy too?
  28. N

    I Is vacuum energy infinite? If it is, how and why?

    https://en.m.wikipedia.org/wiki/Vacuum_energy And it is this type of energy dark energy or a form of it?
  29. K

    I Can you extract useful work from vacuum energy?

    I know that you couldn't extract work from vacuum fluctuations without violating the laws of thermodynamics, but what if there was a gradient in the vacuum energy. If you did work on the vacuum by applying some field you could then extract this work from the gradient, but if the gradient was...
  30. A

    I Casimir effect and vacuum energy and a bit of relativity....

    Hi all, Silly question perhaps: I had understood that the energy density of the vacuum is constant throughout spacetime. But, with the Casimir effect, for example, the geometry of (real) matter (i.e., parallel plates), changes the vacuum energy density in between the plates - is this correct...
  31. R

    B Understanding Vacuum Energy: A Key to Unifying QFT and GR?

    I often wonder about how little I understand vacuum, and only recently I've been paying attention to this "vacuum energy" hypothetical. I see it being associated with things as small as spontaneous emissions to things as large as the expansion of the universe. This is a huge range of length...
  32. Italian_Mike

    I Vacuum energy versus expansion of the Universe

    If vacuum energy has a non-zero value, is the vacuum energy density (vacuum energy over a given volume of void space) being reduced over time due to the expansion of the Universe? If so, is there any consequence on the particle-antiparticle creation/annihiliation process? Will there ever be a...
  33. W

    I Vacuum energy density after inflation

    Its said that if there are different pocket universes made by inflation then this solves the alleged fine tuning of dark energy. My question is this: can the idea of different values for the vacuum energy density in these different pockets be derived from quantum field theory or does it need...
  34. F

    I Relation between quantum fluctuations and vacuum energy?

    As far as I understand it, the non-zero vacuum energy attributed to a quantum field (at each point in space-time) is precisely due to the Heisenberg uncertainty principle (and the fact that the energy of the quantum field at each space-time point is quantised). Accordingly (in order to satisfy...
  35. marcus

    A Effective cosmo const explained w/o vacuum energy

    http://arxiv.org/abs/1603.04170 Effective cosmological constant induced by stochastic fluctuations of Newton's constant Marco de Cesare, Fedele Lizzi, Mairi Sakellariadou (Submitted on 14 Mar 2016) We consider implications of the microscopic dynamics of spacetime for the evolution of...
  36. diegzumillo

    Partition function and vacuum energy (basic stuff)

    Hi all This is a fairly basic QFT question but it's bothering me. And Peskin/Schroeder fails at explaining basic stuff, so here I am. After calculating Z for a particular theory I know this can be used to calculate all kinds of correlation functions. Itself, however, is the probability...
  37. A

    Vacuum energy spectrum, density and constant term....

    Hi all, A question about the vacuum energy density and spectrum. The only spectrum that is frame invariant involves the cube of the frequency. Is it also possible to have a constant offset term (which would also be frame invariant), to 'adjust' the energy density so it doesn't turn out to be...
  38. A

    Vacuum energy and harmonic oscillator

    Hi everyone I was wondering, why is vacuum energy related to the zero point energy of an harmonic oscillator? The hamiltonian of an harmonic oscillator is $H= \frac{p^{2}}{2m} + \frac{1}{2} \omega x^{2}$. Where does the harmonic potential term come from in the vacuum?
  39. D

    Locality, unitarity & vacuum energy

    I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/pdf/1502.05296v1.pdf , top of page 3 under heading "What is the problem?"). My question is, why does the locality and...
  40. F

    Local measurement of the Vacuum Energy?

    Is it possible to measure the vacuum energy locally? I wonder if it might change with gravity? I'm told that we can measure the vacuum energy globally by measuring the acceleration of the universe's expansion. But can we measure it locally? Or are all local measurements independent of the vacuum...
  41. Quarlep

    Cosmological Constant and Vacuum Energy

    I was reading a book about cosmolgy.And there wrotes vacuum energy must be higher than cosmological constant 10100 times to satisfy (It may just the opposite ) observations. Is that true ?
  42. F

    How is the vacuum energy affected by nearby particles?

    When calculating the dynamics of a particle, we can use Feynman's path integral to determine the observables involved. This integrates over every possible path that the particle can take. We can even use it to calculate the vacuum energy of empty space. Now what happens to that vacuum energy...
  43. F

    Cosmological constant and vacuum energy

    Since Omega-lambda is very close to Omega-matter, what could it mean if we assume they are exactly equal to each other. Also, let's assume they were always equal since coincident problem is unnatural.
  44. A

    Vacuum energy of free scalar field

    Homework Statement I have the following task: In quantum free scalar field theory find commutators of creation and anihilation operators with total four-momentum operator, starting with commutators for fields and canonical momenta. Show that vacuum energy is zero. Homework Equations...
  45. D

    Is Dark Energy the Same as Vacuum Energy?

    Dark energy = Vacuum energy? I am working on giving a presentation on dark energy and its possible relation to vacuum energy (i.e. one and the same). I have complied information from a couple of books, as well as websites (Scientific American, NASA, Astrophysical Journal). As i understand...
  46. james.goetz

    Will space always expand when the space has vacuum energy and zero mass?

    I am examining various models of eternal inflation and I want to double check one of my assumptions, which is that space always expands when the space has vacuum energy and zero mass. Is this correct? Will space always expand when the space has vacuum energy and zero mass? Thank you.
  47. E

    Vacuum energy and principle of uncertainty

    Let us assume that harmonic oscilator has the lowest energy level equals 0, (and next one \hbar \omega and so on). Does this harmonic oscilator violates the principle of uncertainty? Let us assume that energy of vacuum equals 0 and not \hbar \omega/2. Does such vacuum violates the principle...
  48. A

    Varying Fine Structure Constant and Vacuum Energy Density

    Hi all, I have a bit of a variation of a question I asked some time ago. Webb et al. continue to publish results which suggest that the fine structure constant may vary over space and time. I realize the results are controversial - what I'm wondering: If the fine structure constant...
  49. K

    Vacuum Energy in SR: A Relativity Question

    I have just a very general question regarding the idea of vacuum energy. It seems that it exists it would have to occur such that it would be the same in every reference frame to satisfy the principle of relativity, yes? Would that suggest it would be part of a stress-energy tensor which is...
  50. S

    Earth movement and physical vacuum energy harness

    Could we harness energy from Earth movement relative to physical vacuum? Earth is moving around Sun with speed of 30 km/sec. Also there exist force of Casimir and similar effects. If we have some body (for example a ball) which is moving in some media (for example water) then to harness...