First, I should like to say that, although the universe is spatially flat, space-time is not flat!

Second, the problem is that ordinary quantum field theories do not enable us to calculate the vacuum energy density of the universe. Unfortunately, they do not provide any mechanism that would explain why the vacuum energy density is much much smaller than what simple dimensional analysis might suggest. As Wolfgang Pauli first pointed out, one would have an explanation why the vacuum energy density essentially vanishes if there were a matching between bosonic and fermionic degrees of freedom - which is what supersymmetry predicts. Unfortunately, there are no experimental indications that supersymmetry is a property of Nature, yet.

Thus, the problem of understanding the very large scale of the universe and the very tiny value of the cosmological constant appears to remain wide open, at present. This means that Physics has certainly not reached its endpoint and that wonderful puzzles confront the younger generation of physicists.

The short answer is Yes: vacuum energy can be consistently defined in the presence of gravity-and only then-and is given by the cosmological constant, a term that is allowed by all symmetries of general relativity. Einstein's equations then imply that their solutions depend only on the ratio of the cosmological constant and the appropriately scaled Newton's constant, not on the two separately.Therefore it isn't possible to deduce that the cosmological constant, i.e. vacuum energy, should take any particular value: there exist solutions for any value. It's an experimental fact that the value of this ratio, although ``small'', is, definitely,  non-zero.

The above statements are valid in the absence of matter. Matter, in general relativity, affects spacetime through its energy-momentum tensor only. In its presence it isn't possible to distinguish the contribution of the cosmological cnstant from the contribution of the energy-momentum tensor that is proportional to the metric. Therefore comparing the two contributions doesn't make sense: the solutions to Einstein's equations aren't sensitive to each individually, only to their sum. Furthermore, the contribution of the energy-momentum tensor makes sense only as the average value on a particular state, which, of course, evolves, too.It is the presence of gravity that allows a definition of vacuum energy for the matter sector-but, since this will, inevitably, change the initial value of the cosmological constant, it doesn't make sense to compare the value of the cosmological cnstant to the average value of the energy momentum tensor-which one? 

The *real* issue with the cosmological constant is, as mentioned, that it isn't known how to determine its ratio to (the rescaled) Newton's constant. Only a quantum theory of gravity will allow us to do that.

in other words: Even *were*, by chance, the vacuum energy contribution of matter equal to the measured value of the cosmological constant, this wouldn't have addressed the issue of the presence of such a term in the Einstein-Hilbert action, whose value is independent of the average value of the matter energy-momentum tensor.

I can see that the discussion has already exposed the gigantic difference in the perception of the vacuum between GR and QM. The discussion so far has focused on the GR perspective of the cosmological constant and dark energy. The cosmological constant is the simplest possible form of dark energy because it assumes constant energy density in both space and time. The Lambda-CDM model of cosmology has the density of dark energy at about 6.6x10-27 kg/m3 equivalent to energy density of 6 x 10-10 J/m3 which is about 70% of the "critical density" of the universe.

The vacuum energy density that I am talking about from zero point energy (ZPE) is about 10122 times larger than this at about 10113 J/m3. This energy density makes a black hole with a radius equal to Planck length. Another way of stating this is that all the observable energy in the observable universe is about 1032 times less energy than the quantum mechanical energy in a cubic millimeter of vacuum. While this seems ridiculous, there is actually support for this tremendous energy density from GR. For example, gravitational wave equations give the impedance of spacetime as c3/G ≈ 4x1035 kg/s. As shown in the link below, this is consistent with vacuum energy density of 10113 J/m3. Also zero point energy characterizes the vacuum as being harmonic oscillators with energy E = ħω/2 at all frequencies up to Planck frequency. This also gives energy density of about 10113 J/m3. Thus the large discrepancy between QM and GR is an open question.

http://onlyspacetime.com/QM-Foundation.pdf

The reason is, that, in the absence of gravity, vacuum energy, i.e. zero-point energy,  isn't defined, that's why, so it can't be measured.  Only energy differences (such as the Casimir effect) can be defined in that case.  And black holes make sense at all, when gravity is taken into account-and, for the moment, gravity can only be described in classical terms. So there isn't any discrepancy between quantum mechanics and general relativity here, because the calculation of the zero-point energy in quantum mechanics isn't defined absent a gravitational background and, as explained above, in the presence of matter, the contribution of the cosmological constant can't be unambiguously determined from such a comparison. The two values aren't expected to be related in any way, so the fact that they are different doesn't mean anything-and were they the same that wouldn't imply anything either.

@Stam,

"The reason is, that, in the absence of gravity, vacuum energy, i.e. zero-point energy,  isn't defined, that's why, so it can't be measured"

As far as I know ZPE is only a manifestation of the  "vacuum energy" . Wills Lamb won his nobel price, giving birth to QED, justifying some "excess energy" found in atom orbitals. The ZPE was used to "justify" the  Mossbauer effect too in 1960's. The Vacuum energy  is at the base of the modern QED.

Dear All,

The ZPE or Vacuum energy of QFT has nothing to do with presence or absence of gravity. It exists and the traditional textbook line that Stam adheres to is simply an easy escape route for experts to avoid uneasy questions from others. That only energy differences are measurable does not in anyway take away the ZPE, unless we really set up our scales like that. Since we have no knowledge of the exact amount of ZPE of all the fields, we cannot set up and calibrate our energy scales in that manner.

Just look at the double standards in Physics. They say because of zero-point fluctuations the third law of thermodynamics remains valid and there will always be some energy of zero-point motion at absolute zero (Statistical mechanics and thermodynamics).  Same zero point energy becomes inconsequential in QFT! It seems there is some real problem here that we are unable to address farely and honestly.

Of course presence of Gravity would make it impossible to set it to zero. But even in the absence of gravity, energy is energy and it will have its quantum mechanical/QFT consequences as in Lamb shift and vacuum polarization.

Regards,

Rajat

What I stick on is how is it possible to have a zero point energy without a corresponding zero point momentum for most observers? 

John,

I think one of the biggest problems is that are definitions are all over the place and we do not all "if you will" talk the same language.  I am not talking the math either.  If we could all start with the definitions of the ideas and theories and all agree on them then we could all talk the same language.

For instance to me vacuum energy and the cosmological constant are the same thing just expresses in different ways.

When we start thinking of all the different things to consider in the way we all look at the equations and the reality of our universe we start adding in component that make things seem like the density is infinite and yet that is not reality. 

Another one is the presents of a field.  To me this is the essence of the Spooky Action at a distance that Albert Einstein posed more than one hundred years ago.  It is also one of those things that we assign a physical quality to that seems to add to the density of things in the universe. 

I think that this is a mistake and one of the reasons that we do not have a unified field theory.

So I think that defining things very carefully is the most important thing that we should start with.  This way we are all talking about the same thing when we say "Field" or "Vacuum Energy".

It is not that we do not understand.  Each of us understands the concepts and ideas but each of us has differing thoughts on the implications of those ideas.  This leads sometime to the bazaar conclusions such as an infinite amount of energy in a field.  

For instance: If we look at the Casimir affect and the infinite number of wavelengths that are in the vacuum we come up with bazaar thoughts on the density that is there.

Now if instead we think of this affect and we look at it as the number of wavelengths is limited by the density of the number and that Probability plays the main role in determining the actual wavelengths that are there it makes more sense that there is only a chance that each one of them is there and it is determined by probability but that in reality they are not "all" there at any one time.

I think that you see my point that the perception and definition are as important to the talk as the talk itself.

What we are talking about here is why General Relativity and Quantum Mechanics do not match.  The problem is in the definitions of the two.  

General Relativity is for the most part a simple look at the two parts of the universe that where unexplained by Newton 100 years ago.  Why we see the speed of light at that speed and are all reference frames the same.  This leads us to how does that affect gravity.   The conclusions were far from simple in the field equations of general relativity but the concepts were simple.

Relativity was based on only to postulates.

The principle of relativity which states that there are no privileged reference frames and that all of physics and its laws are the same regardless of your movement through space and time.  The second was that light always appears to travel at the same speed "c" in a vacuum irregardless of the source that seemed to emit it.

John,

You have put these questions up and we have started these talks about this but I think that most of us do not understand even the light postulate.

I would argue that the only thing that we can truly say about us only seeing light at the speed that we see it at is that it always is at that speed in the presents of matter.  This would change the way we look at light.

The Lamb shift-as its name indicates-is a *shift*, an energy difference. That is measurable, in the absence of gravity. The Mößbauer effect, similarly, involves the measurement of an energy difference. Zero point fluctuations are, just that: energy differences. That's why they can be defined and, thus, measured, while neglecting the backreaction on spacetime. The reason is that, energy is the conserved quantity related to time translation invariance, that is a global symmetry in the absence of gravity and is a local symmetry in its presence. 

The axiom that you can only measure energy differences implies an abstract concept of energy that lacks the nuance of the real world. For example, the proposal is that the quantum vacuum contains ZPE at all frequencies up to Planck frequency. Even though this is a homogeneous background energy present everywhere in the universe, it is not energy in the abstract. It has specific properties and consequences that indicate its presence. For example, the Lamb shift of energy levels in the hydrogen atom was a predicted and experimentally proven consequence of the vacuum having energy. Many aspects of quantum electrodynamics and quantum chromodynamics require an energetic vacuum.

It is possible to characterize this energy further because the uncertainty principle and GR imply that Planck length (Lp) is a fundamental limit in the accuracy of a distance measurement between two points (references 3-7 in the link below). This uncertainty can be interpreted as caused by the "noise" produced by vacuum energy (waves) which modulate distance. This concept can be tested because we now can quantify wave amplitude ± Lp and we know the impedance of spacetime (Zs = c3/G) from GR. The analysis in the link below shows that the energy in these waves indeed corresponds to the energy in the harmonic oscillators of zero point energy. This amplitude and impedance analysis ultimately leads to the gravitational force between particles and a previously unknown connection between the gravitational force and the electrostatic force. These insights give support to the model of vacuum energy.

http://onlyspacetime.com/QM-Foundation.pdf

It's not an axiom that one can only measure energy differences-it's a consequence of what energy means, when it can be sensibly defined, in the absence of gravity.  In any vacuum, in the absence of gravity, the expectation value of the Hamiltonian is ambiguous, precisely due to the uncertainty principles and can be consistently defined to vanish. What this means, operationally, is that the degrees of freedom that carry this  ``zero point energy'' don't do any work, on average, on any apparatus-that's what the vanishing of the expectation value means. What is measurable is ``the specific heat''-that's what  energy fluctuations describe and mean.

(The Lamb shift doesn't have anything to do with this discussion, because it concerns the lifting of the degeneracy of two excited energy levels of the electron in the hydrogen atom,  due to quantum fluctuations of the electromagnetic field.)

The uncertainty principle doesn't single out any length or say anything particular about the Planck length. The only thing that general relativity has to say about the Planck length is that, if one has an object, of  mass greater than or equal to the Planck mass, whose size is less than or equal to the Planck length, then this object would be a black hole, if it were electrically neutral. That's all. And since at those scales quantum effects and gravitational effects are expected to be  comparable, even this statement isn't completely under control, since it isn't known what gravity means at those scales, as described by general relativity, since it isn't known how to take into account quantum effects in a controlled way in that context: It might be that Hawking radiation is so rapid, that such an object couldn't form, it would evaporate too quickly. On the other hand, Hawking's derivation isn't applicable, precisely, when the gravitational field changes too quickly-and it's, still, not known how to extend it.

The Planck system of units is just that-a convention. Additional physical input is required to establish that these quantities actually can be given physical meaning.

Stam,   We obviously disagree on several points. First, I gave 5 references which concluded that distance measurements have a fundamental limiting accuracy of Planck length (device independent). Most, if not all the references, utilize GR in addition to QM, to support their conclusions involving Planck length. As you know, scientists can be quite creative and extend GR to draw conclusions about QM and Planck length.

     Secondly, you often make a distinction about whether gravity is present or absent in measurements of energy. When you talk about "gravity" are you implying that there needs to be substantial gravitational acceleration or do you include the gravitational effects on the rate of time and proper volume? There are parts of the universe which have virtually no gravitational acceleration but all parts of the universe experience an enormous gravitational effect on the rate of time and proper volume. For example, we think of the Andromeda galaxy as having no substantial gravitational effect on earth. However, the rate of time at the earth’s surface is slowed 1,000 times more by the gravity of the Andromeda galaxy than by the earth’s own gravity. All parts of the universe experience an enormous gravitational effect from all the distant mass/energy. Measurements of energy always are made in the presence of gravity.

     The final point is harder to explain in this short post. I am proposing a physical explanation for zero point energy (quantifiable waves in spacetime). This is far more than mere speculation because this model passes several different types of tests which extend far beyond ZPE. For example, it leads to 7 equations (#17 to 23 in the linked paper) which show a previously unknown exponent relationship between the electrostatic force and the gravitational force. These equations were derived from the vacuum energy model of the universe. Also, pages 13 to 15 of this paper proposes and tests a new constant of nature which converts electrical charge and electric field into a quantifiable distortion of spacetime. All of this is derived from a model of vacuum energy.

http://onlyspacetime.com/QM-Foundation.pdf

One should distinguish limitations of principle, from limitations of technique. The limitations about measuring distances at better than Planck length accuracy are, at the present moment, limitations of technique, since it isn't known whether something physically relevant happens at that length scale. In fact, on past experience, we expect that interesting effects should happen *before* that scale, even though we can't predict the details.  (On the other hand, the speed of light in vacuum realizes a limit of principle: we *do* know that speeds greater than the speed of light in vacuum can't represent the speeds of physical excitations.) 

Gravity means deviations of the spacetime metric from Minkowski-I think that's the clearest way to talk about it-as your examples, also illustrate.  It's possible to quantify when these deviations aren't significant: measurements at particle accelerators show conclusively that those processes can be consistently described by quantum field theory in flat spacetime, where energy is a globally defined observable. 

While the electron does have electroweak interactions, at the scales probed up to now it behaves like a point-like object. Of course, when gravitational interactions become significant, this approximation will break down-since a massive, point-like object, would be a black hole. It isn't known how to describe an electric charge in this case. ( In the attached paper, however, the equations are valid in the non-relatvistic and classical limits.)

Since I am actively pursuing a ZPE model which is aimed at Singularity, and cycloid emergence as a process of ZPE potential and field production, I am enjoying the excellent discussion of the requirements for an excellent example. It does require imagination to find a suitable model that can exhibit all of the static and dynamic principles that are required to model quantum foam. I simply state that I am now off to a productive start using an object oriented set theory in 1 and 2 dimensional transforms.

Hi Stan

Again, I am entering an area that is not mine, but.. What mean that "it is an experimental fact that the vacuum energy is not zero"?. How is verified this fact?

Carlos,

Remember that Albert Einstein when he wrote 5 papers that changed Physics for ever had what we call today an undergraduate degree in Physics wrote a short paper that was accepted by Zurich University and became Dr. Einstein.

Do not underestimate your ability.  

I would be happy to answer this question, but I have some trouble from the very beginning trying to understand (or to find an appropriate and precise definition of)  two essential concepts which are mentioned, expressed by the words "really" and "exists".. I am not joking, it is REALLY (!) a serious matter. Parmenides (5-th century B.C.) was probably the first to discuss this issue. His views were later on developed by Plato; not all of us agree with Plato's ideas, but in spite of many centuries of animated discussions, it seems that we are still far from a consensus about what we mean by "Reality" and "Existence" (except in mathematics).

The rate of expansion of the Universe is positive, as measured by supernovae observations (Nobel Prize in Physics 2011)

This means, in general relativity, that the cosmological constant is non-zero. This term describes the vacuum energy of spacetime, the energy in absence of matter.

I think part of the problem is that in math lots of things can exist.  This does not make them real.  It only means we can calculate them or suppose that they exist.  Real means that they exist in not only our minds as a math concept can but that they have a physical meaning in the universe.

In standard QM there is an uncertainty between momentum and position. Measuring the position of a particle will under some circumstances raise the particles energy by increasing it's momentum spread. This increase in energy is real and is supplied by the measurement process. Could one view ZPE in a similar manner? ZPE only exists when measured and originates from an attempt to measure the field in question. In quantum optics the ZPE contributes to the noise one observes in a beam splitter. Likewise in the Casimir effect it is work done by the field modes established in a cavity by zero point fluctuations.   

Dear Stan.

Do you want say that, if the expansion of Universe is a wrong interpretation of data, there aren't other signals of the vaccum energy?.

And for the cassimir effect and the Lamb shift, are there other explanations?

One more time: the Lamb shift doesn't have anything to do with vacuum energy. The Casimir effect measures the energy differences between *different* vacua-obtained by varying boundary conditions, not the energy of one vacuum.(And fluctuations about a value are different than the value of a quantity: the value of energy is independent of the value of the specific heat.)

Vacuum energy (not differences) is defined *only* by gravity and that's the cosmological constant. Up until the supernovae measurements there wasn't any way of measuring it and there, still, isn't any way of calculating its value. The measurement shows the result to be non-zero and the details can be found on the Nobel Prize website, that, also, of course, discusses the supporting material. 

The uncertainty principles involve fluctuations about an average value, not the average values themselves. That's why they can't be used to measure vacuum energy, or zero-point-energy, but the fluctuations about their values.

The uncertainty principle is clearly not a measurement technique, however, it does imply that increases as a result of decreasing the position measurement error for measurements performed on a population of similarly prepared particles.    

But that doesn't say anything about the energy itself-the particle isn't free. And even less does it say something about the energy of the ground state.

That canonical coordinates don't commute dictate the ground state for free fields and give rise to the uncertainty principle. I accept that my query has a "no" in your opinion. I'm certainly not certain it has a yes answer in mine either.

The canonical coordinates don't commute for all states, not only the ground state-so they don't dictate the ground state energy: the center of mass motion isn't fixed by any condition and the uncertainty relations fix the relation between the widths only.

Yes, H and H+C where C is a c-number both work in QM and QFT neglecting gravity. That wasn't the point I was addressing.  

Just a brief footnote:  In many-body theory (which can be viewed as nonrelativistic, relatively low-energy QFT), the 'vacuum' energy is simply the ground-state energy of the system.  This, of course, does exist and is as meaningful as the chemical potential.

The ground state energy's value isn't defined up to a constant-that's the point, since the center of mass motion isn't defined, from translation invariance.  

To Stam Nicolis:  Thanks.  If you specify your reference frame, it is well-defined.  Take liquid He-3, for instance:  you can determine in your laboratory its chemical potential at very low temperature (which is essentially the ground-state energy per particle).  The results given by several many-body calculations agree with this to a satsfactory extent. So, what's the problem?!

The problem is that, even were  the statement relevant, it isn't independent of the reference frame. The chemical potential, in any case, describes something else,  namely the *fluctuation* of the number of particles in a given state, not the ground state energy.And it's not mandatory to work in the grand canonical ensemble. 

Stan.

Very interesting your positions.

I think then you aprobes the Standard Model and the Lambda CDM cosmological model. Then, what do you think about the Higgs fields and the Higgs boson?.

In relation with vacuum energy, obviously.

I beg to disagree.  The chemical potential of a system represents one of its characteristic signatures, including its dimensionality.  At absolute zero, it is simply the ground-state energy per particle of the system; for an ideal system, we can calculate its dependence on temperature.  In the high-temperature limit (as defined relative to some characteristic temperature, say, the Fermi temperature in Fermi systems), it goes to its classical expression.  The work function of a metal can be viewed as its chemical potential.  (Please refer to how Feynman introduced the concept of chemical potential in his famous book on statistical mechanics.)  True, there is some sort of 'complementarity' between the chemical potential and the number of particles in a system (just as there is between temperature and entropy, and between pressure and volume); but this does not mean that the chemical potential describes the fluctuations in the number of particles.  Although this potential emerges naturally in the grand-(or Gibbs-)canonical-ensemble formulation of statistical mechanics, it stands on its own.  Experimentalists have compiled tables for the chemical potential of many systems.  It is a basic quantity in phenomenological physics (specifically, thermodynamics).  Kindest regards.    

I forgot!

Thanks George for your support!

Carlos.

Dear Cameron.

On the contrary. It's more possible than the impossibility of to get absolute zero with the helium samples is in relation to the impossibility of have an absolutely isolated system.

ok?

carlos.

Insofar as the Higgs field and boson are described by a quantum field theory in flat spacetime, they don't have anything more to do with vacuum energy than any other field or particle. The hierarchy ``problem'' is simply that, since the vacuum expectation value of the Higgs defines a Lorentz invariant scale, its ratio to any other, higher, energy  scale is meaningful-and how quantum corrections affect it is a major question, to which the answer isn't known yet.

This means that the vacuum energy can exist including in absence of the higgs field, that they are different things..

Of course-in the presence of the Higgs field and gravity it's not possible to invariantly distinguish the cosmological constant contribution from that of the energy-momentum contribution of the Higgs-just as for any other form of matter, also (cf. comment made previously in this thread). 

Vacuum energy exists. Absolute electric field used in Maxwell's equations includes the zero point electromagnetic field.

The evidence of this results from computation of energy which is detected at very low levels by "photon counting.

Energy is proportional to the square of the absolute field E. Following Einstein's theory which founds the laser, matter amplifies (positively or negatively) the light beams.

Set Z the zero point field. Absolute field is A=Z+F where F is the usual, RELATIVE field.

Input energy  a light beam into a photocell is proportional to A2=(Z+F)2

It remains energy  Z2, so that signal is proportional to (Z+F)2-Z2 =2ZF+F2.Thus, at low level, signal is, in first approximation proportional to F, while at high level it is proportional to F2. Often people makes errors in interpretation of "photon counting" experiments.

First, I should like to say that, although the universe is spatially flat, space-time is not flat!

Second, the problem is that ordinary quantum field theories do not enable us to calculate the vacuum energy density of the universe. Unfortunately, they do not provide any mechanism that would explain why the vacuum energy density is much much smaller than what simple dimensional analysis might suggest. As Wolfgang Pauli first pointed out, one would have an explanation why the vacuum energy density essentially vanishes if there were a matching between bosonic and fermionic degrees of freedom - which is what supersymmetry predicts. Unfortunately, there are no experimental indications that supersymmetry is a property of Nature, yet.

Thus, the problem of understanding the very large scale of the universe and the very tiny value of the cosmological constant appears to remain wide open, at present. This means that Physics has certainly not reached its endpoint and that wonderful puzzles confront the younger generation of physicists.

It is practically impossible to give an answer from present theories.

Reconciling GR and QFT or relooking at GR might give some clues.

Unification of the fundamental forces of nature might give some clues, but present string and brane theories are also quite far.

There is a single sure theory: classical theory.

You are talking about two types of "energy;" the "energy" of physical particles, and the "energy" of space (non-physical existence).

The source of the discrepancy you refer to is due to the simple-minded paradigm of physics where quantum structures are expressed in "energy" terms, analogous to the behavior of macro structures. General Relativity is a mathematical perception of macro structures, and is not a mechanical principle of itself. To speak of the "relativistic" energy of particles, as though the energy were inherent to the particle, is poetic license. 

The idea that dark matter possesses energy is also poetic license. Dark matter, by definition, does not interact with visible matter and thus it possesses zero energy and it also behaves with zero energy. Even fast moving dark matter particles, such as neutrinos, have zero energy with respect to visible matter. There is also no evidence that dark matter has energy relative to other dark matter. Dark matter appears to be nothing but a pool of strings of mass from which visible matter can be created.

The problem with the present state of fundamental physics is the lack of a structural model for the non-material structure that provides the Universe with dynamic space. The fact that physicists talk about quantum foam, zero point energy, and energy from the vacuum, is an admission that space is dynamic. Of course, this dynamic space is Aether, and due to the overuse of poetic license in the relativity theories, the concept of Aether is denied, despite the overwhelming evidence for Aether's existence. The fact that two magnets can easily repel or attract to each other without any physical structural connection is obvious evidence for a structured, non-material space, which has magnetic properties. The same applies to gravity and electrostatic force. Space must be both dynamic and structured for forces to act at a distance with no physical connections.

The conceptual models widely used in fundamental physics, today, are the cause of the discrepancy you can so clearly see.

Maxwell's equations explain propagations of energy using an intermediate concept which is EM field. There is no need to introduce any aether.

• In 1911, Planck showed that the formula he discovered around 1900 is wrong if the usual  EM field is used: Usual radiance of a  polarized  EM field must be increased by h(nu)3/(2c2). which is mean  radiance of all monochromatic, polarized  EM fields in a 0K furnace.
• A source increases radiance of light beams from h(nu)3/(2c2) or more. This radiance and corresponding energy do not differ from other  radiances and energy. This is showed by low energy experiments requiring, for instance photon counting:
• Set Z the field of the zero point , ( Z2 proportional to zero point radiance). A receiver (photocell) receives an energy proportional to the square of the field, that is proportional to E2 = (Z+e)2 where E is the ABSOLUTE Maxwell's field, and e the usual RELATIVE field. If the cell absorbs as much as possible, it remains an output proportional to Z2. Thus the cell gets energy 2Ze +e2.
• If e>>Z  balance of energy which is the useful (signal) energy  is proportional to e2, this is  the most frequent case.
• If  e
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Jacques - "Maxwell's equations explain propagations of energy using an intermediate concept which is EM field. There is no need to introduce any aether."

That is the point I just made. EM field IS the Aether. Simply saying you don't need to use the word does not mean the Aether does not exist. You admit Aether exists when you admit the existence of EM fields.

The answer to this question is given by the answers to two questions connected with it: 1. What is vacuum?  2. What is energy?

Very little of what people contribute to these blogs makes sense or is helpful. Why do people like to waste other people's time?

Dear Professor Fröhlich,

till science will come out with paper like this

L.I. Shiff. "On experimental tests of the General Theory of Relativity" Am. J. Phys., 28, 340–343(1960)

and many who followed, there is nothing to be surprised about.

I may agree with you about wasting time, but if some "idiots" in history of Science would have been spotted before, instead of being followed, we were in a better situation, in general...

The biggest problem I see is that we really do not have a great definition of Space, Energy, Time and so many other thing that everyone looks at it differently.  If we could all agree on the real definitions than we could talk the same language but until then we just all go away thinking that the other person does not understand. 

Here is a great example...  What is Space?  

How many think it is the absence of any think at all?

How many think that it is the absence of anything at all "BUT" there are still Quantum Fluctuations that permeate the space?

How many think that there has to be a definition but you do not know if that includes Quantum properties or if it is almost empty?

How many think that this state can not exist and there fore is irrelevant?   

How many think one time one of these and another time a different one?

My point is that with so many different thoughts no one person can talk to another without thinking they are wrong.

Science is at a turning point and without some very clear definitions that "EVERYONE" understand we will stay in this Quagmire.

Everyone out there thinks they know the real deal and yet we are all talking differnet languages.  This is complicated but not impossible.  I think we should start a forum that sets an RG definition page so that when there is a question people do not have to think this is a waste of time.

My first thing would be SPACE: It needs to start with nothing at all just dementions nothing else.  It is not Quantum it is not mass it is not energy it is nothing but the dimensions of geometry.  From this all other things start.  It does not have fields it does not have the influence of fields it is geometry in 3 dimensions.  It does not have time as a part it is only 3 dimensional.

I see people all the time thinking of space as dynamic.  This means they see it as not fixed.  I know this is because Albert Einstein showed this to be the case as we calculate things moving through space and the problem is there is no starting point if we start with something that is suppose to be nothing.... 

An ancient Greek Philosopher  Socrates, once said that "The Starting was the most important part"  If we all start at different places we will never solve the problems of the universe.

Good intent and good starting point. The problem is represented by subsequent points.

From the Nobel Lecture of Wills lamb:

"From the quantum electrodynamical point of

view, spontaneous emission could be regarded as emission stimulated by the

quantum zero-point fluctuations in the electromagnetic fields in the vacuum

or lowest energy state."

"It was pointed out by WeisskopfI  in 1934 that this ultraviolet

catastrophe could be ascribed to the above-mentioned zero-point fluctuations

in the vacuum electromagnetic field"

So who said that VACUUM ENERGY doesn't have anything to do with ZPE or Lambshift???

Unfortunately, the title of the question is ill posed in the sence of not reflecting the authors' actual question. 

It must be entitled something like "how to reconcile vacuum energy with GR" or better "how to reconcile QFT with GR". 

Then, the answer would be easy and straightforward - we do not know yet.

I do agree with Jurg Froelich.

Quantum Filed Theory has taught us that the vacuum is filled with energy that can be stimulated and made evident. Look at the Casimir effect. Yet, to the best of my knowledge, nodoby so far has come up with an explanation for what the astrophysics effect that goes under this name may be.

Generally the Casimir effect is considered the concrete proof on the existence of vacuum energy. The Casimir effect exists but its interpretation based upon the existence of the vacuum fluctuating energy and consequently of virtual particles is altogether ineffective because in the considered experimental system there isn't vacuum but two plates that are immersed in a physical situation of alleged vacuum. In other words, the presence of plates, i.e. matter, excludes the effect happens because of a phenomenon that is due to vacuum. Other studies and other analyses are necessary in order to explain the physics of the Casimir effect.

First I would like to note here that not spacetime which is flat but only space ! you can see this from Robertson Walker metric which we beleive describes our universe ! Also vacuum energy should always contribute to the cosmological constant, i.e, it has something to do with it, unless there is a symmetry to kill it !

Given that ResearchGate advertizes certain answers as "popular answers" one should not be surprised that people do not read all answers to a given question. The effect is that certain insights appear in several answers, i.e., they get duplicated. I propose to eliminate the notion of "popular answers".

I think that vacuum energy should be study from several new approaches, including some recuperations of old ideas. This is the case of zero-point energy, appeared between 1912 and 1913 in an awful theory by Planck. Recovered and forgotten by Einstein in 1913, just to be considered again, as virtual photons, from the point of view of the quantum mechanics. Several alternative theories have been developed and I would like to mention one of them:

According to Ch. Beck and M. Mackey (in Measurability of vaccum fluctuations and dark energy) vacuum fluctuations are gravitationally active only if they are measurable in the form of a noise spectrum in suitable macroscopic or mesoscopic detectors. Therefore, it should exist a universal low-energy cutoff frequency whose value could be 1.7Thz. If this is the case, dark energy of the universe is ordinary electromagnetic vacuum energy of virtual photons with frecuency below 1.7Thz. The point of view of these authors is completed in Electromagnetic dark energy.

Looking at the papers citing Ch. Beck and M. Mackey, their relation between Josephson junctions and dark energy is at best controversial, at worst the result of a misunderstanding.

People appear to like to take off on a tangent. This makes these blogs rather useless. Just try to focus on the question that is asked (provided it makes sense)!

There is well enough described the so called   Casimir vacuo energy, - yet  there is no data about its nature - is it only a small vacuo polarization energy part, or the structure of vacuo is more complicated and its energy is still  completely obscured for us?

Sinceerly,

Anatolij.

zero-point energy is an open question. Some people consider important to think about that. See for example: http://www.calphysics.org/zpe.html If someone does not like how each one interpret a question, then his formulation should add constrictions. For example: "We want to here something just inside the usual paradigms."

The very formulation of this question seems ambiguous to me. It contains two words, the adjective "really" and the verb "exist"; are we sure to have a unique definition of these two concepts? According to Parmenides, the "Being" is by definition all that exists, while the only thing that can be said about the "Non-being" is that it does not exist.  As a corollary, Parmenides states that there can be only ONE Being (Universe), because if there were two Beings separated by sometjing that exists, this "something" would be also a part of Being; thus, the two different Beings can be separated only by a Non-Being, which by definition does not exist, QED. ("Quod Erat Demonstrandum", not "Quantum ElectroDynamics). I am afraid that we are still not far ahead of Parmenides in what concerns the definitions of "existence" and 'reality". 

Richard

This brings us to the discussion on multiverses. If several universes exist that requires going to higher dimensions: our unverse would exist on a 4-dimensional brane in a higher-dimensional universe. The words "really" and "exist" would then have to be revised.

If vacuum energy exists it must be as 'negative' energy - as binding energy of the quantum vacuum medium where gravitation is the result of binding energy density differences giving a push force between bodies as pressure difference. Joule per cubic metre = pascal This is legitimised for the binding energy of a structured vacuum medium and energy density variation with change of 'c' explains the curvature of GR space-time rather than time dilation.

Dark matter & dark energy can be explained as the effects of defects in that structure, reducing binding energy and acting contrarily to the effects of ordinary matter.

Actually spacetime is a quantized energetic field of extremely low 'resting energy' level , propably at the level of planck's constant....all matter created is just a 'disturbance' of this resting energy level , a concentrated excitation in the form of quantized packages of field disturbance...maybe the elementary excitation of this field is the photon , which actually explains why its propagation is the fastest possible in this fabric of spacetime...the speed of light....this excitation has the form of a miniature wave which leads to the conclusion that all that exists are waves of excitation and the so called duality of light and matter is virtual in its essence and misunderstood because of the fact that it comes in quanta....all particles created are different concentrations of the elementary excitation....propably the creation of an excitation disturbes the field 'altering ' the fabric of spacetime and setting the basis for the creation of forces...in my opinion the four forces are different manifestations in different scales of ONE single elementary force propably described by the phenomena created in the fabric of spacetime  when an excitation of the field takes place....what needs to be done and proven is the correction of both general relativity and quantum theory to obtain a unified explanation of physical phenomena on these basis.....

Vacuum energy enforces the natural laws, without which we would be able to change them. ZPE is largely confirmed by Casimir experiments.

Paradox does not occur when vacuum energy is partitioned into different types that compete, where in nearly flat space convex curving energy and concave curving energy are nearly equal, making net small cosmological constant.

Partition provides an exact calculation method for average energy, vibration amplitude, and frequency. The energy density is large but finite. Fields and transient events alter the partition which is expressed as a departure from flatness, and a change of amplitude and frequency.

Very interesting and important discussion, it is a basic element in my research work, but have none contributions as yet.

I will follow the running discussion.

Kurt Wraae

There are other explanations of the Casimir effect - without ZPE.

You can find an alternative explanation in the following paper:

Article Gravitational Theory of the Casimir Effect: from the Virtual...

There are indeed other explanations of the Casimir effect, and in addition, it doesn't prove the ZPE, but the variation of the ZPE when the boundary conditions are changed. That is essential, because it shows there is no absolute energy, but it remains relative. Besides, there are numerous coincidences in physics, and no experiment can settle ontological issues. It is always up to more than an isomorphism, because contrary to mathematics, physics is never finished.

More scientists should follow the discussion on the role of philosophy in science as too many seem unaware of the distinctions between ontology and epistemology.

the way I see it is that for every particle there is an antiparticle

equal and opposite charges so that, taken together, they are able to possess exactly the properties of empty space, admittedly excluding the energy. Since, however, the energy fluctuates, according to the uncertainty relation between energy and time, particle-antiparticle can appear for short times from space, and vanish into it again, analogous to momentum fluctuations in confined regions. So that the momentum can fluctuate together with energy, “something” must be its carrier whether pairs of massive electrons and positrons, or massless photons and fields.

Therefore, empty space cannot exist in any sense of the word. The emptiest space known to physics not only is electromagnetic radiation in motion, but also virtual particles together with their antiparticles.

The correlations between these objects are illustrated by Feynman diagrams, where a photon, represented by a wavy line disappears, and instead of it an electron and a positron appear. The reverse process is just as well known to physics. Added to this is the generalization to gluons instead o f photons and to quarks and antiquarks instead of electrons and positrons.

The state of a physical system in which its energy is as low as is possible is called the ground state. Take two protons, they form, according to both classical physics and non-relativistic quantum mechanics, a system that can assume different states, both physics in agreement that there are exactly two particles—the two protons. The ground state of the system is therefore that in which the total energy of the two protons is as low as Possible. In quantum field theory, the two Protons appear as states of a system, described by a Lagrangian function, that can contain arbitrarily many protons and other elementary Particles. The ground state of this system is thus one in which no real particles exist, but rather virtual particles the vacuum state, in which all charges vanish.

Maxwell showed that lines of force behaved like vortex structures in a hypothetical fluid, then ignored the logically obvious that the magnetic lines of force are the eyes of the vortexes. Collectively they rotate magnetism in either clockwise or anticlockwise vortexes around the long axes of magnets and coils. Like spins attract......The force on conductor doesn't need an axial vector to describe its direction.

The correct direction of magnetism takes us away from the illogical, where an ‘x’ event (a moving charge), perpendicular to a ‘y’ event (magnetism), causes a ‘z’ force perpendicular to both to a land of common sense.

Here magnets clearly spin their magnetism on Earth and in Space so what are they spinning? Does all the energy come from the magnet itself of do magnets and Coulomb forces organize vacuum energy in their respective ways.

Omah al-hamid; Omah, almost d'accord. The way I see it is that every particle IS its own antiparticle. E.g. a positron is an inverted electron.

The rational for magnetism could be confined to a one-verse or a universe.

The rational for coulomb forces however requires a two-verse, a bi-verse.

Regards BT. www.yowahbooks.com

Dear John, My theory is presenting Quantum Mechanics Universe. As name implies, the basics building block of universe is a QM phenomenon. I believe Space of universe has many character as well, it makes sense that space is never empty, always carries Temperature, wave, and its own character. to answer the dark energy or vacuum energy exist, please read my article Article Dark­Matter in the Quantum Mechanic Universe

PS: this new theory of mine will be presented on 2019 Quantum Physics in Paris and Osaka/japan.

On Casimir:

In ‘bi-verse theory’ where the cosmos is split into two sets of dimensions, virtual pairs have one foot in the ‘here-verse’ (the one-verse) and the other in the ‘there-verse’ (the antiverse). Here all ‘here’ particles are their antiparticles in the antiverse; they are joined at the hip but they combine to affect the whole = coulomb forces as do virtual particles = Casmir forces. Here ZPE is a combo of point anti-point energy.