4 ms·

(I did not read the paper yet.) It is not much model dependent, the general idea is that a energy dependent speed of photons should be something like c_gamma=c

by yk 14y ago

(I did not read the paper yet.) It is not much model dependent, the general idea is that a energy dependent speed of photons should be something like c_gamma=c_0 + a ( E_gamma / m_p) + b ( E_gamma / m_p)^2 + ..., with c_gamma the speed of a photon of energy E_gamma, c_0 the speed of light ( for low energy photons), m_p the Planck mass and a,b are some parameters determined by your model. This style of papers then sets limits on a,b. And the general expectation of some space time foam model is, that a,b should be roughly 1. From this the way they can probe the Planck scale is then simply a huge baseline, in this case 7e9 light years, compared to a rather short duration of the event ( ~ days).

jessriedel 14y ago
Thanks. > And the general expectation of some space time foam model is, that a,b should be roughly 1. OK. Any idea how generic this expectation really is? > compared to a rather short duration of the event ( ~ days). What's this timescale have to do with it? They must be assuming they can identify photons emitted at the same time since they're measuring the arrival time difference in milliseconds.
- Steuard 14y ago
  >> And the general expectation of some space time foam model is, that a,b should be roughly 1. > OK. Any idea how generic this expectation really is? I can't comment on this case specifically, but the entire notion of the "Planck energy" is based on that idea: that once you've found the combination of fundamental constants with the right units, the numerical coefficient that multiplies it will wind up being within one or two orders of magnitude of 1. By some miracle, the vast majority of systems in physics seem to match such expectations.
  - jessriedel 14y ago
    No no, I get the basic idea of making estimates based on dimensional analysis. My question is: how generically do we expect the dispersion relation to be of this form? I could imagine, for example, that differences in speed are exponentially suppressed by the ratio E_gamma/M_p.
    - yk 14y ago
      It is just a Taylor expansion around c_0. And since we do not observe any strange effects we know that it should kind of work. (That the speed of light should be well behaved.) In addition the planck mass is the only constant, that we know of, which fits there.
- yk 14y ago
  >Any idea how generic this expectation really is? [Omitting a longish rant, that once we give up Lorence invaraiance we do no longer know anything.] AFAIK it is essentially the fine tuning argument. So not really generic but in the absence of a good argument a reasonable default value. > What's this timescale have to do with it? The timescale was essentially meant illustrative, so a short everyday timescale compared to gigayears. ( And it is conservative, in the sense that I do not need to remember the exact details of a GRB spectra to use this one ;)

by yk 14y ago

jessriedel 14y ago

Thanks. > And the general expectation of some space time foam model is, that a,b should be roughly 1. OK. Any idea how generic this expectation really is? > compared to a rather short duration of the event ( ~ days). What's this timescale have to do with it? They must be assuming they can identify photons emitted at the same time since they're measuring the arrival time difference in milliseconds.

Steuard 14y ago
>> And the general expectation of some space time foam model is, that a,b should be roughly 1. > OK. Any idea how generic this expectation really is? I can't comment on this case specifically, but the entire notion of the "Planck energy" is based on that idea: that once you've found the combination of fundamental constants with the right units, the numerical coefficient that multiplies it will wind up being within one or two orders of magnitude of 1. By some miracle, the vast majority of systems in physics seem to match such expectations.
- jessriedel 14y ago
  No no, I get the basic idea of making estimates based on dimensional analysis. My question is: how generically do we expect the dispersion relation to be of this form? I could imagine, for example, that differences in speed are exponentially suppressed by the ratio E_gamma/M_p.
  - yk 14y ago
    It is just a Taylor expansion around c_0. And since we do not observe any strange effects we know that it should kind of work. (That the speed of light should be well behaved.) In addition the planck mass is the only constant, that we know of, which fits there.
yk 14y ago
>Any idea how generic this expectation really is? [Omitting a longish rant, that once we give up Lorence invaraiance we do no longer know anything.] AFAIK it is essentially the fine tuning argument. So not really generic but in the absence of a good argument a reasonable default value. > What's this timescale have to do with it? The timescale was essentially meant illustrative, so a short everyday timescale compared to gigayears. ( And it is conservative, in the sense that I do not need to remember the exact details of a GRB spectra to use this one ;)