# What's the physical relevance of vacuum energy?

1. Jul 14, 2006

### maxB

Hi folks,

There are many claims that vacuum energy has a physical relevance: in Casimir effect, in the Cosmological constant. But it seems, vacuum energy is a quantity we are not able to measure. It seems like a energy potential: the absolute value has no physical relevance, but the difference has a meaning: energy.

In any theory (except supersymmetry) the absolute value of vacuum energy has no physical meaning. Why it should have a meaning in gravitation? The point is: vacuum energy is not a energy, it is a energy potential. Only differences of of the potential have a physical meaning, like in the Casimir effect: The effect do not measure the absolute vacuum energy, it measure die change of vacuum energy - a force.

The value of vacuum energy is myriads to large for explaining the dark energy - the rational reaction would be: away with the vacuum energy and looking for a new source of dark energy. Why the majority of physists believe in vacuum energy - a quantity we can not measure and any quantum field theory is invariant against a renormalization of the vacuum energy which has a infinite value in the most cases?

Last edited: Jul 14, 2006
2. Jul 14, 2006

### Mike2

What about the thermal radiation of black holes? If as they say the radiation is caused by ripping apart the virtual pairs of the vacuum energy, then if the absolute value of the vacuum energy is greater, wouldn't the thermal radiation of black holes be greater?

3. Jul 15, 2006

### john baez

You should have said: in any theory except Einstein's theory of general relativity, the absolute value of the vacuum energy has no physical meaning. Einstein's equations

G = T

say that spacetime is curved in a way that's proportional to the energy-momentum tensor T. The density of energy at any point causes spacetime to curved in a specific way. So, if you believe this theory, the
density of energy in the vacuum is something we can measure.

And, astronomers have measured it to be about 0.9 billionths of a joule per cubic meter, by seeing how the expansion of the universe is accelerating.

You might enjoy my webpages:

http://math.ucr.edu/home/baez/vacuum.html" [Broken]

and

http://math.ucr.edu/home/baez/einstein/" [Broken]

It's indeed surprising that general relativity differs from other theories in giving results that depend on the energy density, not just differences in energy density. That's just one more way it's a revolutionary theory. It may eventually need to be fixed somehow, but it seems to work darn well.

Last edited by a moderator: May 2, 2017
4. Jul 15, 2006

### Mike2

Wouldn't a direct measurement of the Unruh effect measure the energy density of the vacuum energy - the more the local vacuum energy the more thermal radiation observed by accelerating, right?

Last edited: Jul 15, 2006
5. Jul 16, 2006

### maxB

I believe in in this theory and I fully agree with your answer 1. in http://math.ucr.edu/home/baez/vacuum.html" [Broken](very appreciated). Every energy contributes via T to Einsteins's eq. sure! But thats not the question. The question is:

Is the "quantum field vaccum energy" a energy in the meaning of Einstein's equation, i.e. is this a physical quantity which causes a change in curvature?

A quantity which causes a real change in curvature should be have a real cause in every theory. I disagree with your statement that

This is not a revolutionary advantage, this is the core of the problem. Why should a quantity, real in GR, be virtual in other theories? My answer is simple:

The vaccum energy is a energy potential. Energy which contibutes to T is a potential difference. For instance in Weinberg (1998) he set

$$V = <0|H|0>$$
and then
$$\rho = V$$
But V is not a measurable quantitiy in QFT only potential differences are measurable. Thus we should set

$$\rho = V - V_0 = 0$$
Only this $$\rho$$ contributes to $$T = \rho g_{ik}$$

The consequence is that $$T = \Lambda g_{ik} \neq 0$$ is caused by a other form of energy, not by the vaccuum energy of particle physics.

This picture is consitent with the common meaning of "energy" in GR. For instance: matter with mass m = E/c^2. E is a difference $$E = V - V_0 = <1|H|1> - <0|H|0>$$, the difference between no particle and one particle. This seems circuitous but in case of matter we implicite assume V_0 = 0 - no matter, no energy.

Concluding: if we define E = V - V_0 every theory - including GR - is invariant against V -> V + constant and we can set V_0 = 0.

Sure, this is a modification of the interpretation of a very common term in QFT and no one like this way (Maybe except Pauli in the first edition of Handbuch der Physik (1933) were he state that vaccuum energy do not interact with the gravitation field. But he dropped this statement in the second edition).

The question is what are the alternatives: To accept a vaccuum energy to be real which is not measurable in QFT and its gravitational cause is 10^120 too large? Or to assume that only the transitions beetween the energy levels of the quantum system have a real meaning with regard to GR?

Last edited by a moderator: May 2, 2017
6. Jul 16, 2006

### Careful

***
This is not a revolutionary advantage, this is the core of the problem. Why should a quantity, real in GR, be virtual in other theories? My answer is simple:

The vaccum energy is a energy potential. Energy which contibutes to T is a potential difference. For instance in Weinberg (1998) he set

$$V = <0|H|0>$$
and then
$$\rho = V$$
But V is not a measurable quantitiy in QFT only potential differences are measurable. Thus we should set

$$\rho = V - V_0 = 0$$
Only this $$\rho$$ contributes to $$T = \Lambda \rho$$
***

Hi,

I see you are very eager to explain the problem of the cosmological constant''. Although I agree with your reasoning (it was also my first reaction : huh, what problem ?´´ ), it could be that there is somewhat more to it. One further aspect certainly is the choice of vacuum state (and associated particle notion) in QFT, since although the latter certainly is Lorentz invariant, it is not diff-invariant (in ordinary QFT) - this is something I appreciate about the BF treatment of gravity.
Another concern deals with naturalness; it would be nice to have a mathematical accurate formulation of QFT in which the vacuum expectation value for the energy momentum tensor *is* exactly the (tiny, but very important) value of the effective cosmological constant (usually symmetries are used for putting it to zero and a symmetry breaking mechanism for tuning it to what we observe it to be). What you are proposing is simple fine tuning - note the effective cosmological constant is not zero - so you would have to put your pin very accurately here. Doing so indicates that you are missing something deeper : in Einstein's theory it is indeed a problem to know what one should put in the right hand side of the equation since the CC is vacuum energy. Basically, one could say that the CC has to be understood in terms of a mechanism providing us with a *real* vacuum energy. The way I currently understand this is that at the Planck scale, the real degrees of freedom are always in motion (even at zero temperature), a natural energy scale for this system (which we call the particle vacuum) would be determined by its Poincare recurrence time : E is inverse proportional to delta(t) where t is a physical clock time. Now, if you can show that the vacuum has a very long recurrence time, then theoretical arguments show that the CC has to be small.

So, the cosmological constant is really pointing in the direction of a new physics...

Careful

Last edited: Jul 16, 2006
7. Jul 16, 2006

### maxB

Absolutly yes. Diffeomorphism invariance is a must. Maybe the problem in QFT is caused by missing that. Not only the vacuum energy potential is infinite, in QED also the E or B field are infinite and we need renormalization. Maybe if we could define it better, everything is ok: the fields are finite and also the vacuum energy. This would the best solution.

But again: Suppose with the new theory we get the the right value for V_vac (in accordance with \Lambda_eff). But the situation of measurement remains the same: In QFT we measure differences, in GR we measure absolute energies - why?
My feeling is, we should measure the same in any theory. When I want to measure energies of a atom, I looking for the photons it emits and absorbs, not for the absoute values of the potential levels - I can gauge this levels, but I can not gauge the level transitions.

The conceptual difference between "absolute engery level" and "transition between energy levels" would not noticed if the value of vacuum energy would not be so absurd. We should remember what we measure and call this "energy".

Yes, when I require that <0|H|0> is a potential, then I implicit say that V_0 = 0. My renormalization is a total one - not a fine tuning V_0 = Lambda. Lambda has to be explained by a different contribution, not by the vacuum energy.

It could be an other term of the form constant*g_ik, maybe a geometrical contribution - not a QFT one.

Unorthodox thinking. Could you explain why the recurrence time should be the crucial time scale?

Last edited: Jul 16, 2006
8. Jul 16, 2006

### Mike2

How is the thermal radiation of the Unruh effect or Hawking radiation a measure of energy differences and not a measurement of absolute vacuum energy? Or do you take these effects to be too controversal to address?

9. Jul 16, 2006

### maxB

I am not a expert in this field. Maybe someone could give a better answer. But I would expect that both effects using differences.

Recently there was an arcticle astro-ph/0406504 which states to measure the vacuum energy, but it was shown that only differences could be measured: astro-ph/0605711, astro-ph/0604265, astro-ph/0604522, astro-ph/0411034.

10. Jul 16, 2006

### Careful

*** Absolutly yes. Diffeomorphism invariance is a must. Maybe the problem in QFT is caused by missing that. Not only the vacuum energy potential is infinite, in QED also the E or B field are infinite and we need renormalization. Maybe if we could define it better, everything is ok: the fields are finite and also the vacuum energy. This would the best solution. ***

Let me add the nuance that no matter what, you will have to find an effective diff-invariant'' dynamics at the scales where GR has been tested. This does not need to imply that the latter is a fundamental ingredient of your Planck scale theory though. But diff-invariance by itself is not enough : classically, it radically cures the Maxwell field for particles at short distances (alike charges attract and opposite charges repel and the force goes to zero when the distance goes to zero) however at the cost of a singularity in the gravitational field (so the classical mass renormalization can be taken care of). Moreover, you will have to come up with nonsingular particle'' models and change Maxwell's theory at small distances (probably by defining fundamental Planck degrees of freedom as well as a correct time scale) to take care of divergences in the zero point radiation. One could hope that a quantum theory of gravity a la LQG would dynamically provide such a natural cutoff but I do not believe this to be true. However even then the problem of the huge vacuum energy persists.

***
But again: Suppose with the new theory we get the the right value for V_vac (in accordance with \Lambda_eff). But the situation of measurement remains the same: In QFT we measure differences, in GR we measure absolute energies - why?
My feeling is, we should measure the same in any theory. When I want to measure energies of a atom, I looking for the photons it emits and absorbs, not for the absoute values of the potential levels - I can gauge this levels, but I can not gauge the level transitions. ***

Sure, and you have to make a choice here ! My guess is that there is a physical clock attached to localized events which sets a natural energy scale.

***
The conceptual difference between "absolute engery level" and "transition between energy levels" would not noticed if the value of vacuum energy would not be so absurd. We should remember what we measure and call this "energy". ***

Well, here I disagree : one cannot extract energy from the vacuum by means of some physical process (we would not notice the second law of thermodynamics otherwise). The electromagnetic zero point field is expected to set a dynamical equilibrium between matter and radiation at absolute zero. Transitions between states are due to thermal (black body) radiation. But true, the natural value (with a Planck scale cutoff) for the vacuum energy of the EM field is way too high for gravity. This *could* indicate that the timescale employed is not the correct one.

***
Yes, when I require that <0|H|0> is a potential, then I implicit say that V_0 = 0. My renormalization is a total one - not a fine tuning V_0 = Lambda. Lambda has to be explained by a different contribution, not by the vacuum energy. ***

I am not a specialist in this problem (which requires a whole PhD ) neither am I aware of any plausible mechanism to achieve what you propose (in recent papers by Nobbenhuis and 't Hooft, the lack thereof became very clear).

**Unorthodox thinking. Could you explain why the recurrence time should be the crucial time scale? **

In case of the quantum harmonic oscillator we have $$E = h / T$$ where T is the recurrence time. Since quantum field theory is thought of as interacting harmonic oscillators, natural energy scales for bound states can be defined again using the recurrence times. As, you know, the latter is the classical natural measure for a system to come back to itself - a motion which basically remains within'' the same non-local quantum state. But this is speculative and certainly not well understood yet - however you have to make a proposal for a time scale at some point and this one is very natural to try out.

Careful

Last edited: Jul 16, 2006