harmonic universe

Yet another attempt to reduce the physics of our universe to the harmonic oscillator; An interesting paper and a pleasure to read. But there is a problem with this approach near the end imho. I do not feel that the proposed boundary conditions psi(0) = 0 and psi(infty) = 0 are natural and honestly I have no intuition what would be natural in this context.

I think that this is a general problem whenever one tries to calculate the 'wavefunction of the universe'. While we have a good intuition for boundary conditions in conventional quantum theory, this intuition is lost for quantum cosmology. But of course those boundary conditions determine everything...

neutrinos as tachyons, the Scharnhorst effect

added much later: It turned out that the OPERA results were flawed.

I leave the text below and the comments as testimony of my confusion about all that when the surprising observation seemed somehow possible.



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I wonder if neutrinos should travel slightly faster than photons according to standard physics, i.e. quantum field theory as we know it (*).

The reason would be the Scharnhorst effect.

If c denotes the 'bare' speed of light then real photons should actually travel a tiny bit slower than c, due to the interaction with virtual particles in a 'real vacuum': c(physical) < c. The bulk of the effect comes from interactions with virtual electrons and positrons (see e.g. this paper for more details).
But neutrinos interact only weakly with those and therefore the velocity of neutrinos should be closer to c; In other words neutrinos would be slightly faster than photons.

I am not sure if the OPERA experiment detected anything real, but if the results are indeed confirmed one should take a second look at the Scharnhorst effect imho; This time considering the difference between neutrinos and photons instead of looking at photons between Casimir plates.



with credit to A.M., a friend of mine and yet another quant interested in physics, who reminded me of this effect, which was discussed already in the 1990s. But if this is all b.s. the embarrassment is of course fully mine.





added later: A very simplified calculation shows that the Scharnhorst effect could have the right order of magnitude!

According to the Scharnhorst paper, equ. 10, the increase of the speed of photons between Casimir plates is to first order approximately

1 + 0.01*alpha²/(mL)⁴.

As we move the plates closer and reduce L (in a thought experiment) we eliminate more of the interaction with the virtual particles and the speed of photons gets closer to the 'bare' speed of light c.
However, we cannot reduce L below 1/m (in this approximation) and thus the Scharnhorst formula
gives a maximum correction

c = c(bare) = c(physical)*( 1 + 0.01*alpha² ).

If we assume that neutrinos travel at a speed close to the 'bare' speed c, then they would travel faster than photons in the 'real vacuum' by a factor of approximately 1 + 10^-6.

This is pretty much what OPERA measured.






(*) added even later: Heather Logan thinks this explanation cannot work and I changed the sentence to reflect that this is not 'standard' opinion; After all she is a physics professor and my last lesson in QED was about 20 years ago. On the other hand I don't see where the argument goes wrong. Obviously I appreciate any input.




added one day later: After some more thinking and reading I can now better formulate this idea as follows:

i) In QED the Ward identities ensure that after quantization of the electromagnetic field the longitudinal polarization of the photon vanishes.

ii) This implies (by comparison with classical fields?) that the photon mass remains zero and the velocity of photons is the light speed c.

iii) On the other hand, the Scharnhorst effect suggests that photons travel at a 'dressed' speed d and one can increase (in principle) d between Casimir plates (see all the above).

iv) The standard interpretation is that d = c to keep QED simple, but one has then to explain away the acausality from photons travelling at increased speed between Casimir plates.

v) In light of the OPERA experiment, the proposal is to assume d < c and (because the Ward identities hold) for all possible experiments the longitudinal polarization of the physical photon still vanishes, so that it would behave like a massless particle, although it travels slightly slower than the 'true' speed of light c. (By the way, I am not the first thinking along such lines.)

vi) The neutrino would travel very close to the 'true' speed of light c and thus slightly faster than photons. The estimate above suggests that the effect could be in the right ballpark,

see the comments for more confusion clarification.

neutrinos as tachyons

It is not surprising that there is a debate about the detection of faster-than-light neutrinos before that discovery is even announced...



It is also not surprising that there are already several arguments in favor of tachyonic neutrinos, even if there are good reasons to doubt that idea (*).



What I do find surprising is that slashdot and other news outlets are so far silent about this threat to the well being of grandfathers.



added later: They are no longer silent and OPERA's paper is here...


... as bonus material, let me mention an old joke from my home country, where it is known for a long time that bureaucrats are made from tachyons. How did we know that sometimes they travel faster than light? Because official working hours end at 4pm, but they are often at home already at 1pm.





(*) It seems to me that tachyonic neutrinos could easily resolve the information loss problem and would let us "see" the interior of black holes. They would also explain how information can be retrieved from baby universes and thus support a silly idea of mine. Obviously, this should count in favor of the tachyonic neutrinos. Simple question at this point: So what Bayesian prior should one use???

Eppley and Hannah

Every now and then somebody asks if it is really necessary to find a quantum theory of gravitation. After all, it is most likely not possible to detect single gravitons, following an argument of Freeman Dyson (because one would need a detector of planetary size for it).

Of course there are many good reasons why one would like to find a way to quantize gravity like all other fields [1, 2, 3]. But I was never worried about this sort of debate, because I knew that there was a thought experiment, published in the '70s or '80s, which settled this issue once and for all: Consistency requires that gravitation must be quantized. I remember that I read the argument and that I found it convincing at the time.



Recently, I was asked about this whole issue and I mentioned the thought experiment and that paper. Finally I promised that I would dig out the reference and I actually did.

K. Eppley and E. Hannah, Found. Phys. 7, 51 (1977)



The reason it was relatively easy to find the reference was that almost thirty years later somebody checked the argument and found that it was flawed. The problem is that the thought experiment asks for a detector so large and heavy that it cannot be built, somehow closing the circle back to Dyson's argument.