Is their any evidence for non zero energy in space? The Casimir effect for two plates separated by a small distance suggests that there is little energy in space.
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I have heard  pop in and out of existence all the time, most notable being the pairs that pop out beside black holes and while one gets pulled away. But wouldn't this actually violate the conservation of energy?
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For example, the radiation dominated cosmology, the energy density of radiation is proportional to $a^{-4}$ and the volume is proportional to $a^3$, where $a$ is the scale factor. So the total energy of radiation is propotional to $a^{-1}$. So where is the loss of energy of radiation? Is it because the gravitational field has the energy? Does $\nabla_aT^{ab}_{\rm matter}=0$ represent the conservation of energy and momentum of matter field in GR?
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I'm trying to find out if black holes could be created by focusing enough light into a small enough volume.  So far I have found (any or all may be incorrect):   Maxwell's equations are linear, dictating no interaction of radiation. The Kerr effect and self-focusing has been observed in mediums, but not vacuums. Masses bending light have been observed per general relativity. Photons are said to have no rest mass, just energy and momentum (???). General relativity seems to provide for energy to energy interaction.   This leads to a more specific question:  Does electromagnetic radiation or energy curve space like mass curves space?
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For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have on the subject is . Nevertheless I suspect this question is appropriate since I don't remember it being addressed in other textbooks  Naively, computation of the Casimir pressure leads to infinite sums and therefore requires regularization. Several regulators can be used that yield the same answer: zeta-function, heat kernel, Gaussian, probably other too. The question is:     What is the mathematical reason all regulators yield the same answer?   In physical terms it means the effect is insensitive to the detailed physics of the UV cutoff, which in realistic situation is related to the properties of the conductors used. The Wikipedia mentions that for some more complicated geometries the effect is sensitive to the cutoff, so why for the classic parallel planes example it isn't?  EDIT: Aaron provided a wonderful Terry Tao ref relevant to this issue. From this text is clear that the divergent sum for vacuum energy can be decomposed into a finite and an infinite part, and that the finite part doesn't depend on the choice of regulator. However, the infinite part does depend on the choice of regulator (see eq 15 in Tao's text). Now, we have another parameter in the problem: the separation between the conductor planes L. What we need to show is that the infinite part doesn't depend on L. This still seams like a miracle since it should happen for all regulators. Moreover, unless I'm confused it doesn't work for the toy example of a massless scalar in 2D. For this example, all terms in the vacuum energy sum are proportional to 1/L hence the infinite part of the sum asymptotics is also proportional to 1/L. So we have a "miracle" that happens only for specific geometries and dimensions
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In  article it says:     The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as required by classical electromagnetics. The Bohr model of an atom was based upon Planck's quantum theory of radiation.   My question is: how can this be if it is actually impossible? Any accelerating point charge should emit radiation, as explained , for example. It is not like I can posit the existence of an orbit where the electron is stable, just out of mid air. What am I missing here?
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So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble understanding how space (a thing I conceive to be 'empty' or nothingness) can be 'warped'.  After researching books, on-line articles, and this stack exchange itself I can't seem to find any descriptions or discussions that don't immediately resort to jumping into GR and its mathematics to provide a more physical intuitive understanding of what it means to for space to be warped.  Is it space, this empty thing, that's getting warped. Or rather is it some field (Higgs field?) that exists around matter that's getting warped?  Although this question appears similar to  , it's asking if it's empty space that's being warped by matter or rather a field in space that's being warped (the Higgs Field?). The other question and all 10 answers addressing it do not address fields vs. empty space - What's really getting warped?
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In  the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in  (QED) and  (SED).  I've looked at  and references given on the  page but none of them give a clear working for how these values are derived.  Can someone point me in the right direction, as to how values like $10^{-9}$ are derived from the cosmological constant; OR $10^{113}$ due to calculations in Quantum Electrodynamics?
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Since virtual particles are disturbances in a field, and not particles in any sense, as explained , how is it that true photons arise from them when excited with kinetic energy via the dynamical casimir effect?  While the effect is described , I was hoping to get an answer that touches more with the virtual particle's role in the effect, if it is of sigificance.
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In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of the gravitational field".  But I can't find anything concrete to substantiate this claim. As a first check, I did a calculation to compute the gravitational potential energy of a sphere of uniform density of radius $R$ using Newton's Laws and threw in $E=mc^2$ for energy of the sphere, and it was by no means obvious that the answer is zero!  So, my questions:   What is the basis for the claim &ndash; does one require General Relativity, or can one get it from Newtonian gravity? What conditions do you require in the model, in order for this to work? Could someone please refer me to a good paper about this?
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Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?  If so, can quantum mechanics describe the universe at high energies where there is no spacetime?  Schrodinger equation assumes the presence of time dimension. So how can such equations be valid at extremely high energy?  And is it meaningful to do physics if there is no time dimension?  Would the concepts of Hilbert space, wavefunction collapse etc be useful in that case?
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Followup to "".  It is argued that even a tiny residual charge would result in huge amounts of electricity in bulk matter, everything would be different, etc. I do not find that a convincing answer: suppose $n$ protons plus $n+1$ electrons are neutral. Why wouldn't we also expect there to be $n$ protons to every $n+1$ electrons? That is, there is no bulk matter problem if every $n$'th atom is a negative ion (for hydrogen).  Now, what empirical lower bound can we give for $n$ in that kind of scenario?
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This  explains how energy curves spacetime. But I would like to know why energy curves spacetime, is there something like particle interaction that produce this result?
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{{Under Construction}}      Short question: What published works and what research groups are investigating the possibility of non-existence of gravity at quantum level?  Long question: I am no physicist, but of what I read and understand of the subject, no-one has been able to fit the graviton into the standard model, it seems that the equations won't re-normalize, thus it would be useless for predictions. Gravity also is undetectable at the quantum level, it seems because the force is too small. Also, about every book about the subject traces a strong distinction between "quantum level" and "classical level", almost if they were different worlds that obey different laws of nature, and how they relate to each other is an open question. Finally, at least two sources I have seen state that Einstein's General Relativity is the most well verified theory of all physics, because of something related to pulsars.  Thus there are two distinct "worlds": in one gravity is pretty much settled, while in the other, it is neither detectable nor mathematically explainable in the most successful model. From that, the most logical and simple explanation I can have is that simply there is no such thing as quantum gravity, and that it is a purely classical phenomenon that arises from whatever may be the relation between both "worlds".  I like to imagine that space coordinates of both worlds are not quite the same, although very similar locally, thus, if classical world emerges from a projection of the quantum world, like a shadow, gravity is bumps in the surface where that shadow is projected (holographic principle comes in my mind now).  It doesn't seems to be the mainstream view of the problem, with millions of dollars spent in trying to find the mythical graviton (that is what a physicist of INPE, Brazilian's spacial research institute, told me yesterday). Thus, I want to know, what are the works, and what people shares with me this view of the problem?
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Why is absolute zero considered to be ? Wouldn't regions such as massive gaps between galaxy clusters have temperatures of absolute zero?  I just do not see why our model must work the way that it does. I mean there have to be regions with no thermal energy out there, the universe is massive.
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Regarding this thread:    Why is the idea that the total energy in the universe "zero" so popular (re: Laurence Krauss) and why is the flatness of the universe used to back this up when, according to that post, an open universe would not conserve energy so the total energy of the universe cannot be "zero", can it? What's the energy being defined as zero and why is that energy used to predict things about the universe when "the" energy (as the term is used in that post) is not zero?  Additionally, I found one very good explanation here for this,    This seems to indicate that in flat space (the sort of space used in these zero energy universe theories) the mass can NOT be positive thus contradicting the notion that mass is positive and gravity negative and the whole thing winds up being zero. Did I interpret that correctly?  The MO question is cross-posted to Physics.SE here,
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It is said that since work is done by the gravitational potential itself , so at a finite distance the gravitational potential energy of the body is negative. Could someone explain why?
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Added: 5 times down vote for now! Down voter is this religion or physics, please try to explain your decision.  I'm confused about this.  In physics we know for a , but I think that there is a contradiction in this term. The  are the phenomena that  contradicts the vacuum existence because, according to them, the vacuum isn't the empty space.  In vacuum the creation of particle-antiparticle pairs is allowed for small times and this is also proven in practice.  From the other side, the relativistic theory says about space-time that interactions like gravitation bend the vacuum (empty space). There seems to be a contradiction to me. If vacuum is an empty space then we can't bend it, because we can't bend something nonexistent. In other words: we can't bend 'nothing'.  Can empty space really exist in physics?  EDIT1: quote: Luboš Motl     "By definition, the space without   energy is the space whose total value   of energy is equal to 0."   But this space is nonexistent, so it is abstract and should exist only in our mind... Why is so? My second statement of this post says that in physics we cant bend nothing because such a bending is only thinking and not physics!  Another possibility is that space is unknown kind of energy, but this is contradiction in modern physics!  EDIT2:  Can any physics believe that nothing exists? By mathematical logic no! And mathematic is elementary tool in physics. Anything other than that is religion!  Nothing (empty space without energy) is only a logical state!  EDIT3: quote: Roy Simpson:     The General Relativity Vacuum is a   space-time model region without   matter.   and Luboš Motl says: "By definition, the space without energy is the space whose total value of energy is equal to 0."  Agree...   But this is only mathematical Euclidean space + time so this is only a mathematic and not physics! With other words: this is only a method of mathematical mapping. But, in real (not theoretic) physics we can't mapping empty things. Empty is only a logical state!  EDIT4:   Roy Simpsons argumentation seems to me acceptable.   quote: Roy Simpson:     Einstein struggled with this too, and   the problem has come to be known as   the "Hole argument" within GR. You   have to decide whether you are just   interested in GR's vacuum (empty   space) or the full physical vacuum   which includes quantum aspects as   well.   Thanks