Thanks for this post. I would expect higher energy photons to travel more slowly than low energy7 photons!
The higher the energy of a photon, the more momentum it carries p = mc, where m is the effective mass of the photon by E = mc^2. (Yes, of course everyone knows that photons have no rest mass, but photons are never at rest; thus the fact they have no rest mass is totally irrelevant to physics!)
The effective mass is the quantum gravity charge of the electron. Thus, the more energy it has, the more effective gravitational charge it has.
The vacuum contains gravitational fields from the 3 × 10^52 kg of observable stars (page 5 of http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/documents/ON_the_EXPANSION_of_the_UNIVERSE.pdf ), plus other mass contributions from dark matter like neutrinos.
These gravitational fields interact with the photon's gravitational charge (mass) in much the same way that the photon's electromagnetic field interacts with the electromagnetic fields of molecules in a block of glass, thus slowing down photons.
In the deflection of starlight by gravity, starlight is deflected with twice the Newtonian a = GM/r^2 prediction, i.e. a = 2GM/r^2. The amount of effective transit "mass" (gravitational charge) of the photon of starlight, m = E/c^2, is trivial compared to the sun's mass and thus has no effect on the deflection (similarly, as Galileo found, an apple and a lead cannon ball fall in the same time). It is purely because of (1) the really immense energy of some of these gamma ray burst photons and (2) the really immense travel times of the photons from distant gamma ray bursts to the earth, that there is now a measurable difference in velocity between photons of differing energy.
It is interesting that the vacuum is effectively scale-invariant to photons over many orders of magnitude of length scale. But I'm wondering if that is built into the way we do QFT - i.e., it is a predetermined result. I mean to say, have we ruled out any purely electrodynamic effects that might confer dispersion on the vacuum? It is unthinkable, of course, but are we precluded from even thinking it simply by our formalism?
I suppose the standard answer to my question is that QED is renormalizable and gauge-invariant (so the photon remains massless and also we don't get terms that would induce E^2 = p^2 + a * p^4 + b * p^6 + ....
There is one more hypothesis that they raise at the end, it is that the decrease in the speed of light is not an absolute quantity, distribution that peaks at a value smaller than the speed of light. In this way, high energy photons arriving sooner than what should be expected wouldn't spoil right away a variable speed of light.
11:23 PM, June 26, 2009
Rhys said...
"(Yes, of course everyone knows that photons have no rest mass, but photons are never at rest; thus the fact they have no rest mass is totally irrelevant to physics!)"
If you say so, nige. Do you know what a Casimir operator is? And more physicallY: how many polarisation states does a massless vector particle have, and how many does a massive one have?
To me Bee, it appears this article is very insightful because of the understanding of "shape being distributed by the telling photons" as if pasting a Lagrangian view of the universe in a most colourful way.
It is describing the vacuum method of discernibility. This does not depart from the idea of expression of local regions of our universe and the local description arising from those cosmological events. To me this supports the understanding of "vacuum in space" as a prime mover of geometrical considerations. It does not lessen Linde's versions either in terms of our own universe.
Again the path of "least resistance" is a clear sign of the value of the distribution of what is held in context of the geometrics of the gravitational field? Photon energy calculations?
A most interesting post and I must try to read the paper before forming any kind of opinion. The one thing it prompts though is to ask when does an entity of energy become one of matter. From Einstein’s perspective is to say that’s when it becomes subluminal in it’s speed or another way to look at it is when time becomes a dimension, which is realized as to be applicable. That would imply that as a photon becomes more energetic and resultantly having its velocity drop, would mean it no longer is solely a entity of energy in such respect.
On the surface this seems to be just a further attempt to find flaw with relativity, such that it might be removed as an encumbrance to unification. I’ve often wondered what has many so convinced that relativity must be altered, rather than quantum mechanics or perhaps both to succeed in furthering the completion to physical law.
What are the electric and magnetic fields associated with 10^14 - 10^17 eV photons? The vacuum sparks for atomic nuclei somewhere beyond Z = (1/fine structure constant). The vacuum goes dichroic for magnetic fields around a teratesla.
Perhaps the anomaly is simply the expectation, contributing low probablilty Feynman diagrams no longer being quite so improbable.
Not everyone believes in doubly-special/deformed relativity etc., but is there general support for the idea that a photon having Planck energy or above is "special" in some sense? Of course, it wouldn't be that much in some other frames which is part of the issues thereof.
After reading the paper you referred to I can appreciate as to understand its motivation more so then its content. That being the authors are most concerned that not only the theorists pay more attention to the data, yet rather they look to their theories to see if they can be more definitively made to predict the consensus that will be eventually formed by the results. That’s best brought out when in the summation of the paper they say:
“To quantum gravity theorists we suggest urgent attention be given to any possibility of deriving predictions for these observations from theories of quantum gravity, otherwise it may be only a matter of months to a year or two before we theorists are demoted to the role of postdictors of great experimental discoveries.”
I find the authors concern and level thereof a trifle unwarranted, as for instance the unexplained orbit of Mercury didn’t lessen the significance of GR when it was shown to actually be able to account for it, whereas the Newtonian approach had failed. That’s like saying the Copernican model had no advantage over Ptolemy’s without making predictions beyond what was then known.
I thus feel too often science rushes to find consensus before the dust has settled. The most important thing is that the theories be logically consistent in relation to what we observe as to be able to be understood being more important then what they may seem to predict. I am thus reminded of a quote of John Bell’s I recently read in the book I just finished entitled “ The Age of Entanglement by Louisa Gilder” where when addressing John Wheeler in regards to this he said:
“I’d rather be clear and wrong than foggy and right.”
Smolin above all others in relation to his objections about string theory should be most sympathetic to this and such I find this comment a bit out of character in terms of consistency.
Best ,
Phil
P.S. I must lend thanks to Doug Hemmick for pointing out this most wonderful book I mentioned.
Thanks Bee. What I meant was, in conventional relativity the photon energy would not be the same in different frames. Hence if there's something special or "troublesome" about a photon having Planck energy in any frame at all, then wouldn't we need DSR etc. to deal with that? IOW, DSR should be considered a likely or necessary prospect and no. And if so, how does that fit in with quantum gravity schemes etc.
As far as I am concerned, from a quantum gravitational perspective there is no reason to expect an effect to set in at a particular distance or energy. The reason is that qg effects become relevant in the high curvature regime, not at a large energy (energy is not a local quantity, it's an integrated one). You will thus look for curvature invariants that reach Planckian size to determine whether qg effects become relevant. By construction, these invariants are independent of the reference frame. In an effective description then you would replace what would actually "really" be quantum gravity effects that we don't know how to deal with by a model, but still the effect should become important when the background would have a high curvature. (You can find more details on this point of view here and here).
So, the short answer is, no, DSR in the form considered by the authors is not necessary, and in my opinion not very well motivated either. But then, they are frequently quoting evidence from the 2+1 dimensional case. It probably depends on your taste how convincing you find that. Either way, the question isn't so much how likely I or anybody else thinks this scenario might be. What I find more important is that it be self-consistent and testable.
I think the sentence you are quoting isn't so much about reaching consensus, as about putting the cards on the table before it's clear what cards are the winning ones. That is to say a pre-diction is generally considered more convincing than a post-diction. I would agree with you that one can overstate this though. What will happen if you push people is simply that they will try to cover all possibilities and consequently be right whatever the data says, which isn't helpful either. (You see, the photons could arrive earlier, or later, or it could be stochastic and it could be both. And oh, if the modification is second order, they arrive neither earlier nor later. Thus, our model is consistent with everything.)
Keep in mind however that there have been alternative explanations for the perihelion precession of Mercury. The deciding factor was the prediction for the light deviation (whether or not that wasn't originally as decisive as it was claimed to be). Best,
B.
2:05 PM, June 28, 2009
Giotis said...
What do you mean by that Bee? The gravitational coupling which determines the strength of the gravitational interaction becomes strong at very high energies (at Planck scale) and thus qg effects become important in that regime. Or you want to say something else maybe?
I meant exactly what I said. I wasn't talking about the running of the coupling, I said qg effects become strong not at Planckian energies, but in the strong curvature regime. The Planck mass is about 10^-5 g, some molecules have masses in that range. Needless to say, there's nothing quantum graviational about them (in DSR there is btw). Best,
B.
5:34 AM, June 29, 2009
Giovanni Amelino-Camelia and Lee Smolin have a new paper on the arXiv:
Prospects for constraining quantum gravity dispersion with near term observations arXiv:0906.3731v3 [astro-ph.HE] By Giovanni Amelino-Camelia, Lee Smolin
We discuss the prospects for bounding and perhaps even measuring quantum gravity effects on the dispersion of light using the highest energy photons produced in gamma ray bursts measured by the Fermi telescope. These prospects are brigher than might have been expected as in the first 10 months of operation Fermi has reported so far eight events with photons over 100 MeV seen by its Large Area Telescope (LAT). We review features of these events which may bear on Planck scale phenomenology and we discuss the possible implications for the alternative scenarios for in-vacua dispersion coming from breaking or deforming of Poincare invariance. Among these are semi-conservative bounds, which rely on some relatively weak assumptions about the sources, on subluminal and superluminal in-vacuo dispersion. We also propose that it may be possible to look for the arrival of still higher energy photons and neutrinos from GRB's with energies in the range 1014 - 1017 eV. In some cases the quantum gravity dispersion effect would predict these arrivals to be delayed or advanced by days to months from the GRB, giving a clean separation of astrophysical source and spacetime propagation effects.In their paper, Giovanni and Lee summarize the status of extracting information about quantum gravitational effects from gamma ray bursts. The idea is that quantum gravity could affect the propagation of photons; we previously discussed this possibility here and here. Such modifications are quite generic and appear in various approaches to describe quantum graviational effects, some of which are inspired by loop quantum gravity, some are inspired by string theory, some are inspired by God-knows-what. There are however no derivations of such effects from a fundamental theory, at least not yet. At the present status, one should thus understand these models as examinations of specific features the to-be-found underlying theory could have.
While the discussed effects on the propagation of photons are extremely tiny and way too feeble to be observable in experiments on Earth, they could add up when the travel is very long distance. In the models the authors consider, the strength of the effect depends on the energy of the photon. The speed of light is then no longer a constant but a function of the energy of the photon. In the low energy limit, photons travel with what we usually call THE speed of light, c [1].
To first approximation there are two cases: either the high energetic photons are faster than the low energetic ones, or the high energetic photons are slower than the low energetic ones. I would have guessed the majority of people had thought if such a scenario is true then the photons with higher energy should be faster. If only because we are secretly all dreaming of traveling faster than the speed of light. But that's not what the data seems to suggest to me.
These scenarios can be tested with signals from gamma ray bursts, highly energetic flashes of light originating in faraway Galaxies. Their spectrum covers a large range of energies. If one records photons of different energies with an exact timing, one can compare their arrival time. In my previous post we had been discussing the gamma ray burst GRB 080916C (the number encodes the date). In this burst, the high energy photons seem to be arriving with a delay relative to the lower energetic ones. However, the statistics of that one burst isn't very convincing. Yes, there was that one lazy high energy photon with 13 GeV that arrived 16.3 seconds after the onset of the burst. And okay, there were a couple more photons that seemed to be delayed, but then the low energy signal had two peaks rather than one. This might have indicated it was a fairly uncommon burst.
However, Giovanni and Lee sifted through some databases and found a couple more gamma ray bursts that were recorded during the last year that show similar characteristics, if not so pronounced. In all cases, the high energetic photons were delayed. Their paper offers a neat table summarizing these events, but unfortunately no statistical analysis for how significant the patterns are.
In the following sections of the paper they constrain several models with that data, most notably those who break and those who only deform Lorentz Invariance. In the first case, the universe has a preferred frame relative to which the energy of the photons is defined. In the second case there is no such preferred frame [2]. They further distinguish between the case where high energetic photons are faster (superluminal) and those in which they are slower (subluminal), and extract bounds on the quantum gravity scale for both cases. It is somewhat unintuitive to extract bounds also on the superluminal case when there is a trend in the data for higher energetic photons to arrive later, but it could be an astrophysical effect that is hiding superluminal propagation. The bounds on the superluminal case however are weaker.
There is quite a lot of astrophysics involved in the emission of these photons and the most conservative explanation for the delay is certainly that the photons were emitted with delay. While Giovianni and Lee's analysis offers useful first estimates, what would be needed is a procedure that allows to cleanly separate astrophysical source effects from effects during propagation. To do so, one had to extract the dependence of the signal on the distance to the source.
In the final section of the paper, Giovanni and Lee suggest to obtain further experimental data by looking for photons of even higher energies (that could be delayed up to months) or neutrinos that are emitted from the same source. In both cases, I wonder whether it is feasible to obtain any sensible statistic within the lifetime of the average physicist.
Altogether it is a very useful paper that summarizes the status. It leaves one wanting though for a more thorough data analysis.
"Constraining Modified Dispersion Relations with Gamma Ray Bursts"
20 Comments -
Thanks for this post. I would expect higher energy photons to travel more slowly than low energy7 photons!
The higher the energy of a photon, the more momentum it carries p = mc, where m is the effective mass of the photon by E = mc^2. (Yes, of course everyone knows that photons have no rest mass, but photons are never at rest; thus the fact they have no rest mass is totally irrelevant to physics!)
The effective mass is the quantum gravity charge of the electron. Thus, the more energy it has, the more effective gravitational charge it has.
The vacuum contains gravitational fields from the 3 × 10^52 kg of observable stars (page 5 of http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/documents/ON_the_EXPANSION_of_the_UNIVERSE.pdf ), plus other mass contributions from dark matter like neutrinos.
These gravitational fields interact with the photon's gravitational charge (mass) in much the same way that the photon's electromagnetic field interacts with the electromagnetic fields of molecules in a block of glass, thus slowing down photons.
6:19 PM, June 26, 2009
In the deflection of starlight by gravity, starlight is deflected with twice the Newtonian a = GM/r^2 prediction, i.e. a = 2GM/r^2. The amount of effective transit "mass" (gravitational charge) of the photon of starlight, m = E/c^2, is trivial compared to the sun's mass and thus has no effect on the deflection (similarly, as Galileo found, an apple and a lead cannon ball fall in the same time). It is purely because of (1) the really immense energy of some of these gamma ray burst photons and (2) the really immense travel times of the photons from distant gamma ray bursts to the earth, that there is now a measurable difference in velocity between photons of differing energy.
6:29 PM, June 26, 2009
Sorry, my sentence "The effective mass is the quantum gravity charge of the electron" should end "photon" of course! (It's past my bed time!)
6:39 PM, June 26, 2009
It is interesting that the vacuum is effectively scale-invariant to photons over many orders of magnitude of length scale. But I'm wondering if that is built into the way we do QFT - i.e., it is a predetermined result. I mean to say, have we ruled out any purely electrodynamic effects that might confer dispersion on the vacuum? It is unthinkable, of course, but are we precluded from even thinking it simply by our formalism?
9:01 PM, June 26, 2009
I suppose the standard answer to my question is that QED is renormalizable and gauge-invariant (so the photon remains massless and also we don't get terms that would induce E^2 = p^2 + a * p^4 + b * p^6 + ....
9:09 PM, June 26, 2009
There is one more hypothesis that they raise at the end, it is that the decrease in the speed of light is not an absolute quantity, distribution that peaks at a value smaller than the speed of light. In this way, high energy photons arriving sooner than what should be expected wouldn't spoil right away a variable speed of light.
11:23 PM, June 26, 2009
"(Yes, of course everyone knows that photons have no rest mass, but photons are never at rest; thus the fact they have no rest mass is totally irrelevant to physics!)"
If you say so, nige. Do you know what a Casimir operator is? And more physicallY: how many polarisation states does a massless vector particle have, and how many does a massive one have?
6:56 AM, June 27, 2009
Arun: Your equation isn't Lorentz Invariant. If it was, you wouldn't have a modification on-shell. (Which btw is exactly what happens in my model).
7:27 AM, June 27, 2009
Daniel: Right, there could be a stochastic element to the propagation.
7:37 AM, June 27, 2009
To me Bee, it appears this article is very insightful because of the understanding of "shape being distributed by the telling photons" as if pasting a Lagrangian view of the universe in a most colourful way.
It is describing the vacuum method of discernibility. This does not depart from the idea of expression of local regions of our universe and the local description arising from those cosmological events. To me this supports the understanding of "vacuum in space" as a prime mover of geometrical considerations. It does not lessen Linde's versions either in terms of our own universe.
Again the path of "least resistance" is a clear sign of the value of the distribution of what is held in context of the geometrics of the gravitational field? Photon energy calculations?
Best,
11:10 AM, June 27, 2009
Hi Bee,
A most interesting post and I must try to read the paper before forming any kind of opinion. The one thing it prompts though is to ask when does an entity of energy become one of matter. From Einstein’s perspective is to say that’s when it becomes subluminal in it’s speed or another way to look at it is when time becomes a dimension, which is realized as to be applicable. That would imply that as a photon becomes more energetic and resultantly having its velocity drop, would mean it no longer is solely a entity of energy in such respect.
On the surface this seems to be just a further attempt to find flaw with relativity, such that it might be removed as an encumbrance to unification. I’ve often wondered what has many so convinced that relativity must be altered, rather than quantum mechanics or perhaps both to succeed in furthering the completion to physical law.
Best,
Phil
3:16 PM, June 27, 2009
What are the electric and magnetic fields associated with 10^14 - 10^17 eV photons? The vacuum sparks for atomic nuclei somewhere beyond Z = (1/fine structure constant). The vacuum goes dichroic for magnetic fields around a teratesla.
Perhaps the anomaly is simply the expectation, contributing low probablilty Feynman diagrams no longer being quite so improbable.
4:18 PM, June 27, 2009
Not everyone believes in doubly-special/deformed relativity etc., but is there general support for the idea that a photon having Planck energy or above is "special" in some sense? Of course, it wouldn't be that much in some other frames which is part of the issues thereof.
7:32 PM, June 27, 2009
Neil: The whole point of DSR is that the Planck energy is the Planck energy in every restframe.
10:35 AM, June 28, 2009
Hi Bee,
After reading the paper you referred to I can appreciate as to understand its motivation more so then its content. That being the authors are most concerned that not only the theorists pay more attention to the data, yet rather they look to their theories to see if they can be more definitively made to predict the consensus that will be eventually formed by the results. That’s best brought out when in the summation of the paper they say:
“To quantum gravity theorists we suggest urgent attention be given to any possibility of deriving predictions for these observations from theories of quantum gravity, otherwise it may be only a matter of months to a year or two before we theorists are demoted to the role of postdictors of great experimental discoveries.”
I find the authors concern and level thereof a trifle unwarranted, as for instance the unexplained orbit of Mercury didn’t lessen the significance of GR when it was shown to actually be able to account for it, whereas the Newtonian approach had failed. That’s like saying the Copernican model had no advantage over Ptolemy’s without making predictions beyond what was then known.
I thus feel too often science rushes to find consensus before the dust has settled. The most important thing is that the theories be logically consistent in relation to what we observe as to be able to be understood being more important then what they may seem to predict. I am thus reminded of a quote of John Bell’s I recently read in the book I just finished entitled “ The Age of Entanglement by Louisa Gilder” where when addressing John Wheeler in regards to this he said:
“I’d rather be clear and wrong than foggy and right.”
Smolin above all others in relation to his objections about string theory should be most sympathetic to this and such I find this comment a bit out of character in terms of consistency.
Best ,
Phil
P.S. I must lend thanks to Doug Hemmick for pointing out this most wonderful book I mentioned.
11:31 AM, June 28, 2009
Thanks Bee. What I meant was, in conventional relativity the photon energy would not be the same in different frames. Hence if there's something special or "troublesome" about a photon having Planck energy in any frame at all, then wouldn't we need DSR etc. to deal with that? IOW, DSR should be considered a likely or necessary prospect and no. And if so, how does that fit in with quantum gravity schemes etc.
12:25 PM, June 28, 2009
Hi Nige,
As far as I am concerned, from a quantum gravitational perspective there is no reason to expect an effect to set in at a particular distance or energy. The reason is that qg effects become relevant in the high curvature regime, not at a large energy (energy is not a local quantity, it's an integrated one). You will thus look for curvature invariants that reach Planckian size to determine whether qg effects become relevant. By construction, these invariants are independent of the reference frame. In an effective description then you would replace what would actually "really" be quantum gravity effects that we don't know how to deal with by a model, but still the effect should become important when the background would have a high curvature. (You can find more details on this point of view here and here).
So, the short answer is, no, DSR in the form considered by the authors is not necessary, and in my opinion not very well motivated either. But then, they are frequently quoting evidence from the 2+1 dimensional case. It probably depends on your taste how convincing you find that. Either way, the question isn't so much how likely I or anybody else thinks this scenario might be. What I find more important is that it be self-consistent and testable.
Best,
B.
1:52 PM, June 28, 2009
Hi Phil,
I think the sentence you are quoting isn't so much about reaching consensus, as about putting the cards on the table before it's clear what cards are the winning ones. That is to say a pre-diction is generally considered more convincing than a post-diction. I would agree with you that one can overstate this though. What will happen if you push people is simply that they will try to cover all possibilities and consequently be right whatever the data says, which isn't helpful either. (You see, the photons could arrive earlier, or later, or it could be stochastic and it could be both. And oh, if the modification is second order, they arrive neither earlier nor later. Thus, our model is consistent with everything.)
Keep in mind however that there have been alternative explanations for the perihelion precession of Mercury. The deciding factor was the prediction for the light deviation (whether or not that wasn't originally as decisive as it was claimed to be). Best,
B.
2:05 PM, June 28, 2009
What do you mean by that Bee? The gravitational coupling which determines the strength of the gravitational interaction becomes strong at very high energies (at Planck scale) and thus qg effects become important in that regime. Or you want to say something else maybe?
4:08 PM, June 28, 2009
Hi Giotis,
I meant exactly what I said. I wasn't talking about the running of the coupling, I said qg effects become strong not at Planckian energies, but in the strong curvature regime. The Planck mass is about 10^-5 g, some molecules have masses in that range. Needless to say, there's nothing quantum graviational about them (in DSR there is btw). Best,
B.
5:34 AM, June 29, 2009