Planck scale fluctuations
Edward C. Jones
Letters (http://www.journals.uchicago.edu/ApJ/rapid.html).
The Phase Coherence of Light from Extragalactic Sources: Direct Evidence
against First-Order Planck-Scale Fluctuations in Time and Space
Richard Lieu and Lloyd W. Hillman
... We show that the Hubble Space Telescope detection of Airy rings from
the active galaxy PKS 1413+135, located at a distance of 1.2 Gpc,
excludes all first-order (alpha = 1) quantum gravity fluctuations with
an amplitude a_0 > 0.003. The same result may be used to deduce that the
speed of light in vacuo is exact to a few parts in 10^32.
What do you all think of this?
John Eastmond
news:<b2br3p$ob5$1...@bob.news.rcn.net>...
I'm no expert but it seems an important and surprising result to me.
It will be interesting to see how the quantum gravity people respond.
John Baez
John Eastmond <east...@yahoo.com> wrote:
>"Edward C. Jones" <edcj...@erols.com> wrote in message
>news:<b2br3p$ob5$1...@bob.news.rcn.net>...
>> I just saw an abstract in the Rapid Release Astrophysical Journal
>> Letters (http://www.journals.uchicago.edu/ApJ/rapid.html).
>>
>> The Phase Coherence of Light from Extragalactic Sources: Direct Evidence
>> against First-Order Planck-Scale Fluctuations in Time and Space
>>
>> Richard Lieu and Lloyd W. Hillman
>>
>> ... We show that the Hubble Space Telescope detection of Airy rings from
>> the active galaxy PKS 1413+135, located at a distance of 1.2 Gpc,
>> excludes all first-order (alpha = 1) quantum gravity fluctuations with
>> an amplitude a_0 > 0.003. The same result may be used to deduce that the
>> speed of light in vacuo is exact to a few parts in 10^32.
>>
>> What do you all think of this?
As usual the fine print is important: until you figure out
what "alpha = 1" means, you can't tell what they've really done!
>I'm no expert but it seems an important and surprising result to me.
>It will be interesting to see how the quantum gravity people respond.
Valerie Jamieson, reporting for the magazine New Scientist,
asked me what I thought about this. After looking at their paper,
here's what I said:
.......................................................................
Thanks for bringing their work to my attention. As always, you
have to read the fine print. They assume that if time were
quantized, there would be a tiny uncertainty when we measure a
very short time, but that these tiny uncertainties would "add up"
following a certain formula when we measured a very *big* time -
which is closer to what they are actually doing. As they point out
in this paper:
http://www.arXiv.org/abs/astro-ph/0301184
there are a number of proposed formulas for how these uncertainties
might "add up". For example, they could add up linearly, or more
slowly, or faster - hence the quotes in my phrase "add up", which suggests
something linear.
Their work rules some of these formulas but not all. In particular,
they claim to rule out 2 of the formulas that Jay Olson and
I already have claimed are wrong:
http://www.arXiv.org/abs/gr-qc/0201030
But, they don't claim to rule out all the formulas!
So, I would not say their work proves that time isn't quantized.
I would say their work proves that uncertainties in time don't
add up to be very big, even for very long times.
.......................................................................
Actually I shouldn't have said their work "proves" this!
But that's what it suggests.
The mysterious phrase "alpha = 1" refers to a rule where the
uncertainties add up linearly. They actually study a variety
of different rules, corresponding to different values of alpha.
John Eastmond
This is my understanding of Lieu and Hillman's argument.
They argue that the wavelength, lambda, of light from the distant
galaxy is uncertain by the Planck length, l_p, which is 10^-35 m. They
make the assumption that this discrepancy grows linearly as the light
propagates. Thus if the distance from the galaxy to us is L then the
total discrepancy in the distance the light travels, DL, is given by:
DL = (L / lambda) * l_p.
They argue that if DL is of the order of the wavelength of light
lambda then one would not expect to see interference effects in the
image of the galaxy.
If the galaxy is one billion light-years away then L is given by:
L = 10^9 * 10^7 (seconds in a year) * 10^8 (speed of light) metres
L = 10^24 m
If we take lambda = 10^-6 m and l_p = 10^-35 m we find that DL is
given by:
DL = (10^24 / 10^-6) * 10^-35
DL = 10^-5 m
As this is roughly the same order of magnitude as the wavelength one
would agree with Lieu and Hillman that interference effects should not
occur.
But I think the assumption that the discrepancy grows by the Planck
distance every wavelength is not realistic. Surely it is more likely
that a random walk process would occur so that sometimes the
wavelength grows by l_p and sometimes it shrinks by l_p with equal
probability? If this was the case then the total discrepancy in the
distance, DL, would be given by:
DL^2 = (L / lambda) * l_p^2
thus
DL = sqrt(L / lambda) * l_p
If we put in the values L = 10^24 m, lambda = 10^-6 m and l_p = 10^-35
m we find:
DL = sqrt(10^30) * 10^-35
DL = 10^-20 m
This is 14 orders of magnitude less than the wavelength lambda = 10^-6
m so that, contrary to Lieu and Hillman, one would still expect to see
interference effects in the galaxy's image. Even if one managed to
observe in X-ray frequencies (lambda = 10^-10 m) DL would still be 8
orders of magnitude less than lambda.
I've just seen a preprint by Ng, van Dam and Christiansen at:
http://xxx.lanl.gov/abs/astro-ph/0302372
who seem to make the same point that a random walk of Planck scale
steps is more likely that Lieu and Hillman's linear model. They also
conclude that if one uses the random walk model then one would still
expect to see interference effects.
In response to John Baez's reply I would say that the above random
walk model is distinct from Lieu and Hillman's original class of
models that simply differ in their values of alpha and a_0.
John
Urs Schreiber
> They argue that the wavelength, lambda, of light from the distant
> galaxy is uncertain by the Planck length, l_p, which is 10^-35 m. They
> make the assumption that this discrepancy grows linearly as the light
> propagates.
[...]
> Surely it is more likely
> that a random walk process would occur
[...]
> so that, contrary to Lieu and Hillman, one would still expect to see
> interference effects in the galaxy's image.
In view of the current interest in speculating about the
effect of Planck-scale spacetime fluctuations on
interferometry, is anybody still considering the case of
*matter* interferometry? I am asking because in papers like
[1][2] it was argued that the mere existence of, say, C70
interferometry, puts tight bounds on the size of possible
spacetime fluctuations. The distance traveled in these
experiments is of course tiny compared to astrophysical
scales, but the (de Broglie) wave-length is much smaller,
too.
[1] quant-ph/9607011
[2]
Atom interferometry for quantum gravity? I. C. Percival and W.
T. Strunz, in M. Ferrero and A. van der Merwe (eds.), New
developments on Fundamental Problems in Quantum Physics,
Kluwer Academic Publishers, 1997
John Baez
John Eastmond <east...@yahoo.com> wrote:
>This is my understanding of Lieu and Hillman's argument.
>They argue that the wavelength, lambda, of light from the distant
>galaxy is uncertain by the Planck length, l_p, which is 10^-35 m. They
>make the assumption that this discrepancy grows linearly as the light
>propagates.
This corresponds to "alpha = 1" in their notation: the uncertainty
in a measurement of distance grows as the distance to the first power.
>But I think the assumption that the discrepancy grows by the Planck
>distance every wavelength is not realistic. Surely it is more likely
>that a random walk process would occur so that sometimes the
>wavelength grows by l_p and sometimes it shrinks by l_p with equal
>probability? If this was the case then the total discrepancy in the
>distance, DL, would be given by:
>
>DL^2 = (L / lambda) * l_p^2
This corresponds to "alpha = 1/2" in their notation: the uncertainty
in a measurement of distance grows as the distance to the 1/2 power.
This is the value of alpha that Amelino-Camelia argues for here:
G. Amelino, Quantum theory's last challenge, Nature (2000), 661-664.
http://www.arXiv.org/abs/gr-qc/0012049
Ng and Van Dam have argued for "alpha = 2/3":
Y. J. Ng and H. van Dam, On Wigner's clock and the detectability of
spacetime foam with gravitational-wave interferometers.
Phys. Lett. B477 (2000) 429-435.
http://www.arXiv.org/abs/gr-qc/9911054
Jay Olson and I have argued for "alpha = 0", i.e. *no* growth of
uncertainty as the distance increases:
John C. Baez, S. Jay Olson, Uncertainty in measurements of distance,
Class. Quant. Grav. 19 (2002) L121-L126.
http://www.arXiv.org/abs/gr-qc/0201030
Ng and van Dam have subsequently written a paper claiming to refute
ours. Unfortunately I'm too busy to refute their refutation...
I'm hoping Jay Olson will do it!
In short: we're all running around like stooges throwing cream pies
in each others faces, having a big fight over the correct value of alpha.
I *don't* think Lieu and Hillman only claim to rule out alpha = 1.
I think they claim to rule out a *range* of alpha. Could you look
at the paper again and see if I'm right or not?
Meanwhile, Ng and van Dam claim that Lieu and Hillman's analysis
is all wet, and that values of alpha up to alpha = 1 are actually
consistent with their observations:
Y. J. Ng and H. van Dam, Comment on "Where is the Planck time?",
http://www.arXiv.org/abs/astro-ph/0302372
In short, science at its finest: nobody knows what the heck is
going on! But we'll sort it out soon, and then we'll sadly
have to move on to the next question.
(I wrote the last sentence because I know from bitter experience
that otherwise some crackpot will fasten on my previous remark
and say "Baez admits that in science nobody knows what's going on!
Therefore my insane theory could be right: Mars is a neutrino! Nyeh nyeh!")
John Eastmond
From Equation (11) in Lieu and Hillman's paper one finds that the
standard deviation of the phase change of the radiation as it travels
the distance L from the galaxy is proportional to:
(L / lambda) * alpha * a_0 * (omega / omega_P) ^ alpha
This expression is always proportional to the distance L whatever the
values for alpha and a_0. Thus it seems to me that all of Lieu and
Hillman's models with different alpha make the assumption that the
uncertainty in the distance (or phase) grows linearly with distance.