Relativity from a photon's point of view

kw: musings, special relativity, physics

I am between books, catching up on journal reading. Something has arisen in my thoughts from time to time, and this is as good a time as any to solidify it a little. The question: If a photon had consciousness, what would it experience?

I have read in numerous books and articles that Albert Einstein began the mental journey that led to the special theory of relativity by imagining he could ride along with a photon. Reading his own writings, though, we find that he was really thinking of riding a very fast railway carriage, and seeing how this might affect the photon's motion. Based on the Michelson-Morely experiment and on theoretical work by Lorentz, Fitzgerald and others, he concluded that no matter what speed he attained, the photon would zip by at the same speed, the one we define as c, the "speed of light". Then, taking the constancy of c as an axiom, he derived the special theory of relativity.

Supposing the photon could be endowed with the ability to observe on its own, what would it observe? Based on a wealth of experimental data, we can discuss the "career" of a photon in three sections:

1. Emission
2. Propagation
3. Absorption

Although we seldom think about the time it takes for a photon to be emitted, we can consider that the "wavicle" model implies a finite "size" that is similar to the wavelength, according to Feynman's probability-wave diagram (actually, when I saw Feynman draw this during a lecture, he only put in about 1½ or 2 cycles of the wave inside the envelope). Therefore, though we typically think of the emission as occuring "instantly"—if we think of it at all—it is reasonable to posit that it takes about the time required for one cycle to occur. In this discussion we will assume that everything occurs in a vacuum or near-vacuum, so that we don't need to consider refractive index or the reduction in the value of c within a material medium.

For a visible photon of wavelength 546.1 nm (the green Hg line), which has energy of 2.270 eV and a frequency of 549.0 THz, that emission might take 1.822x10^-15 sec, or 1.822 fs (femtoseconds). We may also assume that absorption occurs in a similar amount of time.

This photon-observer needs to have quick reactions indeed to observe anything at all during such brief periods of time! Will it, then, have more leisure for observation during propagation? No! According to the special theory of relativity, no matter the physical length of its journey, the time experienced by the photon will be zero; it will be unable to observe its own propagation.

From the photon's point of view, whether the photon was emitted by an electron transition at one end of the lab, and absorbed by inducing a similar transition at the other end, or the photon was emitted billions of years ago in a galaxy far, far away and today happens to arrive and produce an electron transition in the CCD attached to yon telescope, its experience is the same: less than 2 fs of emission immediately followed by less than 2 fs of absorption, after which it exists no longer. To us, one photon "was there" for a few nanoseconds and the other, for billions of years. The "experience" of the two photons, however, was identical: be emitted/be absorbed.

That is it! A photon of green light can at most experience 3-4 fs of emission and absorption. The rest of the universe is irrelevant to it. For a photon to have a longer "career", from its point of view, it would have to have a longer wavelength, a lot longer! For example, the power grid leaks a lot of 60 Hz (ultra-low-frequency) radio waves, photons with a wavelength of about 50,000 km and photon energies of 4.1x10^-15 eV. Such a photon might "experience" a time period of around 1/30 of a second. Pity the poor X-rays and gamma rays, with energies of thousands to millions, and even billions of eV! Their wavelengths are very short (from about a nanometer to a femtometer or less) and their frequencies are very high (from thousands to billions of THz). A one-billion-eV gamma ray photon is likely emitted in about 4 fs, and would most likely "experience" a total of less than 10^-23 seconds of existence.

Had Einstein actually spent his time thinking like a photon, I doubt much would have come of it. But instead, he thought of a very fast railway carriage observing a photon, which is much more interesting, and led to much more interesting results.