ParaclitosLogos

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I am not a scientist, much less a physicist. But, I will offer a summarized account of what involves the calculation of zero energy density in quantum field theory (as I understand it), which ends up predicting the vacuum energy density of space with an error of 120 (10^120) magnitudes from actual measurements.

I do this to try to spell out what are the assumptions used for such calculation, that could, perhaps, be found to be shaky.

Physicists feel free to correct, add, and clarify for us (thanks in advance).

1. Quantum field theory posits that in every point in space there is a harmonic oscillator of every possible frequency

2. They can be excited in a different way, and, a certain excitation appears to us as particles.

3. Quantum field theory postulates such view because it could be said that everything in physics is formulated in terms of harmonic oscillators.

4. Essentially any perturbative quantum field theory that is Lorentz invariant is going to be described to first approximation as a quadratic Lagrangian with  up to 2 derivatives.  This is the heart of it all.

5. This is why harmonic oscillators show up everywhere in physics. It would appear that the structure of physics is almost always approximated by a harmonic oscillator.


6. The equation of the Harmonic oscillator is roughly of the following form

H = ( n + 1/2) h Wn           n=0,1,2,3,4...

7. And what is interesting and important is that even at energy level n=0, its lowest state,its ground state (zero point energy ) H is not zero (this is due to Heisenberg´s uncertainty principle when applied to energy)

H= (1/2) h *  W0 


8. This, as far as I know, is the heart of quantum field approaches, as explained above, this  is motivated by what appears to be a pervasive fact of nature.


Then.

9. If we  wanted to compute the ground zero energy density in a given volume of space, we would add up all the energies of all the oscillators of that volume of space (for n=0).

10. This means adding all of the ground zero energy-momentum of all the harmonic oscillators in the given volume.

11. This addition is done up to around Planck scale, where we would expect Quantum field theory to break down.

12. And this yields an energy density 10^120 greater than what has been measured to be the energy density in vacuum space.




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kurros

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Re: Zero energy density calculated in Quantum field theory. Assumptions?
« Reply #1 on: August 31, 2015, 11:49:12 am »
That is the hand-waving story, more or less. The thing is, there is no formal calculation, not like there is for the "normal" predictions of say the Standard Model. And even if we assume the hand-waving story is capturing the right idea, the main problem (in my view) is that it assumes there is no new physics between what we have explored, and the Planck scale. The value of the vacuum energy depends on what particles exist, and on what symmetries govern their behaviour, since there can be various cancellations between their contributions to the vacuum energy. Even in the case of no new physics, the "prediction" for the vacuum energy is not actually a prediction; there are free parameters which can be tuned so that you get whatever value you like for the vacuum energy. The real problem is that this requires a lot of fine-tuning, so it is said that the "natural" value, or the value you get without "accidental" cancellation occurring, is this 10^120 GeV or whatever it is. But in a theory with different particles, those cancellations could happen by construction, rather than by accident, even to the point of the vacuum energy density being exactly zero (which is no good either, but you get the idea).

So anyway to believe the naive calculation, you have to believe that in the 18 or so orders of magnitude between the highest energy scales we have explored, and the Planck scale, that there is nothing to be discovered. Usually the cosmological constant problem is taken as evidence that there is indeed some new physics to be found there; physics which will produce the right number "naturally", without excessive tuning.
« Last Edit: August 31, 2015, 11:52:00 am by kurros »

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ParaclitosLogos

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Re: Zero energy density calculated in Quantum field theory. Assumptions?
« Reply #2 on: August 31, 2015, 12:55:50 pm »
I am not sure why calculated predictions of a physical model should assume there is a new physics between what we have explored, and some given limit (like the Planck scale).

If postulating a harmonic oscilator in all points of space is a key principle of QFT, it would seem that not only the calculation is naive but the whole theory is.

That there is no formal calculation might be related to the fact that the prediction appears to be ridiculous not that there is anything really wrong with the calculation principles and actual steps, from the QFT point of view.

THE COSMOLOGICAL CONSTANT

Sean M. Carroll



...
Equation 19 (19)

Field theory may fail earlier, although quantum gravity is the only reason we have to believe it will fail at any specific scale.

As we will discuss later, cosmological observations imply

 Equation 20

The ratio of (19) to (20) is the origin of the famous discrepancy of 120 orders of magnitude between the theoretical and observational values of the cosmological constant. There is no obstacle to imagining that all of the large and apparently unrelated contributions listed add together, with different signs, to produce a net cosmological constant consistent with the limit (20), other than the fact that it seems ridiculous. We know of no special symmetry which could enforce a vanishing vacuum energy while remaining consistent with the known laws of physics; this conundrum is the cosmological constant problem''. In section 4 we will discuss a number of issues related to this puzzle, which at this point remains one of the most significant unsolved problems in fundamental physics,,.



Anyone else wants to add?



« Last Edit: August 31, 2015, 01:18:41 pm by ontologicalme »

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kurros

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Re: Zero energy density calculated in Quantum field theory. Assumptions?
« Reply #3 on: August 31, 2015, 01:10:24 pm »
 Well the problem is that the calculation is *sensitive* to physics which we currently know nothing about. A key principle to emerge from the physics of the 20th century is the idea that phenomena on vastly different scales should be insensitive to each other in general. For example you don't need to know the positions of the sun and stars relative to the earth in order to compute the physics of a car engine. And we don't need to know what the Planck scale physics is to compute the low energy behaviour of electrons. But we DO need to know the high scale physics to compute the vacuum energy, and we know the answer will be wrong if we don't take this into account. This is what leads to the fine tuning problem. The hope is that some new mechanism, or symmetry as caroll alludes, will be discovered which can protect the calculation from these unknown factors (and of course correct the numerical result as well)
« Last Edit: August 31, 2015, 01:12:06 pm by kurros »

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ParaclitosLogos

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Re: Zero energy density calculated in Quantum field theory. Assumptions?
« Reply #4 on: August 31, 2015, 02:19:54 pm »
Well the problem is that the calculation is *sensitive* to physics which we currently know nothing about. A key principle to emerge from the physics of the 20th century is the idea that phenomena on vastly different scales should be insensitive to each other in general. For example you don't need to know the positions of the sun and stars relative to the earth in order to compute the physics of a car engine. And we don't need to know what the Planck scale physics is to compute the low energy behaviour of electrons. But we DO need to know the high scale physics to compute the vacuum energy, and we know the answer will be wrong if we don't take this into account. This is what leads to the fine tuning problem. The hope is that some new mechanism, or symmetry as caroll alludes, will be discovered which can protect the calculation from these unknown factors (and of course correct the numerical result as well)

Thanks Kurros, of course there are important points where I don´t agree, but, I am not interested in debating, just spelling out ideas about the matter.

Anyone else?