I was reading A.P. French’s book Special Relativity; he talks about how photons have been observed to have the same speed c despite having immensely different levels of energy. He then proceeds to say “television transmission photons of about 10-⁷ eV and gamma rays of about 100 MeV have the same speed to an accuracy of 1%...”

So my question is what accounts for the difference (albeit a very small deviation) in the speed? Perhaps I’m missing something here, but shouldn’t they have the same speed?

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By the sounds of it, French was referring to the accuracy of the measurement. It doesnt mean that the actual speed of the two photon energies deviates by 1%, but that 1% is the amount of error in the measurements that were taken.

Oh - wouldn't it have to be a pretty poor experiment to have that much error?

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Light is slowed down in transparent media such as air, water and glass. When you talk about "the speed of light", this refers the speed of light in a vacuum.

When not traveling in a vacuum, every time a photon hits an atom, that atom will "absorb" the photon and excite an electron. That electron will release the energy in the form of another photon after a minuscule amount of time. With objects that are denser, there are more atoms and molecules to absorb photons and release them, which takes time, causing light to "slow down". (note that light still travels at the speed of light between molecules, but it loses some time every time it's absorbed by a molecule, so its "average speed" slows down, but it still travels at the speed of light from atom to atom)

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Check the first publication date in your book: the text dates from the 1960s, which isn't a problem for French's (excellent) description of SR, but does significantly date the experimental science described.
Consider also that, at the extremes, it gets harder to design experiments to measure the speed of light very accurately: you're either dealing with wavelengths measureable in centimetres, or with extremely penetrating radiation. Either way, these are difficult photons to pin down precisely.

Grant Hutchison

Okay, thanks for the responses. I just wanted to make sure French was saying that the small deviation was due to experimental error, not an "anomaly" of sorts.

__________________
The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
It is imperative in science to doubt.
~~~ Richard Feynman ~~~
Common sense is not so common
~~~ Voltaire ~~~

That was well put! It paints a picture I can almost understand. This will cause some further reading.

These excitations cannot be discrete though, right? A hydrogen atom, for example, absorbs only very specific wavelengths of light. And when the energy is re-emitted, there's no guarantee that the new photon will have the same direction or phase as the originally absorbed one. I've always been a bit confused by this model of light slowing down through a medium. But perhaps I am showing a bias -- I work with discrete absorptions in extremely rare gas and perhaps it is different in the realm of dense media like Earthly solids and gases.

The idea is that the photon gets hung up in the "dressed state" of the atom for a period of time limited by Heisenberg's Uncertainty Principle. The photons which behave this way have an energy that is a little less than that of a specific absorption line, and the additional energy is "borrowed" for a period limited by the HUP before the photon must go on its way again.
Most transparent materials, like glass, have absorption lines tucked just out of sight in the UV. Short-wavelength visible light is close in energy to the UV absorption line: the necessary "borrowed" energy is therefore small, and the photon can tarry in the dressed state for a relatively long period of time. Red photons fall well short of the necessary energy, therefore need to borrow more, and so can be held in the dressed state for less time. Hence the familiar result that violet light moves slower through glass than does red light, and is therefore refracted more.

Grant Hutchison

Can you cite examples of materials that have strong absorption lines
within the visible range but which are mostly transparent? Materials
that don't have any absorption lines close to the visible range?

-- Jeff, in Minneapolis

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What is a "dressed state"? And can you recommend a good book or article that discusses this in more detail?

The "dressed state" is a superposition of quantum states describing an atom's interaction with a photon: a mixture of |ground state, photon> and |excited state, no photon>. There's a quantum formalism using dressed states which has application in, for instance, laser physics. I don't pretend to be able to do the maths.
I'm afraid it's just one of those bits and bobs I've accreted over the years, so I can't make a good recommendation of a text on the subject.

Grant Hutchison

Jeff, wouldn't that necessarily make them colored due to transmission of a partial spectrum? http://books.google.com/books?id=uXC...num=1#PPA47,M1 pete

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Not sure precisely what you're after, but you may find this of interest:
http://www.rockhounds.com/rockshop/b...on_spectra.jpg

He was. But laboratory measurements of the speed of photons can be very difficult. Visible light is fairly well understood, but really short wavelengths (like gamma rays & X-rays), and really long wavelengths (like radio waves) are very hard to deal with. Indeed, "photon" becomes a hard concept to physically verify at long wavelengths. Hence, I point out an astronomical solution to the problem: Severe Limits on Variations of the Speed of Light with Frequency; Bradley Schaefer, Physical Review Letters 82(25): 4964-4966, June 21, 1999 (follow the arXiv link to a downloadable PDF). Schaefer claims an observational limit of 6.3×10^-21 on the difference in the speed of light for 30 & 200 Kev photons. You can follow the 73 citations (so far) to other papers of similar ilk. As with French, this is the limit to observational precision and not a true difference.

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Great link Tim Thompson - It helps me understand the difficulties when dealing with big or small wavelengths.

__________________
The first principle is that you must not fool yourself - and you are the easiest person to fool.
~~~ Richard Feynman ~~~
It is imperative in science to doubt.
~~~ Richard Feynman ~~~
Common sense is not so common
~~~ Voltaire ~~~