Suppose the speed of red light was c, and that the speed of all other light was proportional to its frequency. Blue light would travel faster than c, radio would be much slower, and so on. The question is, would things look the same as they do now, or would we see a difference?
IANA Astrophysicist, but I know what would happen. In many materials (glass and water being good examples) the speed of light IS dependant on the color. This is known as chromatic dispersion, and is the reason Isaac Newton invented a telescope based on a mirror rather than a lens. Different frequencies of radio waves also travel at different speeds in many dielectric materials, causing, e.g. pulse spreading in long coaxial cables.
Many things would look different. Consider that when you “see” a star, you are actually seeing where the star was when the light left it, not where it is at the instant you view it. If you postulate that the different colors travel at different speeds, then any moving object would have a rainbow hued “tail” showing where it had been.
Another effect would be that gravitational lensing would be different for different colors because the slower light would be near the massive object longer, and so more influanced.
Now I have a question: I thought all EM radiation travelled at c, just at different wavelengths. Did my 8th grade science teacher lie to me?
In a vacuum they travel at c. EM waves slow down when propagating through a medium, though.
In a vacuum it all travels at C. You science teacher did not lie. When not in a vacuum the speed of light changes.
Gotcha. That medium business always did give me trouble.
Making the hypothetical effect proportional to frequency makes this thought experiment rather interesting. Violet light will be travelling twice as fast as red light. That’s such a big difference that the challenge becomes seeing just how simple an experiment would detect such a huge effect. Precision tests aren’t going to be necessary.
For instance, consider occulations of stars by the Moon - a point source of light disappearing behind a very distant opaque disk. Happens fairly frequently and easily observed by amateur astronomers. Light travelling at c takes about a second to reach Earth from the Moon. Thus rather than having the star instantly disappearing, the different speeds of different colours would mean that it would fade out over about a second, getting gradually redder as it did so. That’d be very obvious, even with just a simple telescope.
Such a large effect could thus at least be trivially detected. What’s intriguing me now is whether it’d actually be more obvious than that. Given the hypothetical, are there any even simpler observations we could make that would show up such an effect?
Of course, in reality there are far more sensitive tests which show that the effect can’t be that large. By a very, very, very large margin.
Of course, if the difference between the speeds of the various colors were small enough, then we’d be unable to tell the difference. It is possible that the mass of the photon is not quite zero, just very, very small. In that case, the photons with higher energies (that is to say, bluer ones) would, in fact, travel at a slightly faster speed than lower-energy (redder) photons.
It should be noted, though, that in this case, red photons would not be traveling at c. The constant c is a property of spacetime itself, not of light (or any particular sort of light). Due to the way relativity works out, any massless particle must travel at exactly c, but nothing can travel faster. So if photons have mass, then all photons would be slower than c, with the high-energy photons just being closer to c than the low-energy photons.
Is that a tau photon, or a muon photon,
And how long will it keep its flavor?
:eek:
WSPEEDY 1590 AM on the AM Dial. Get your news almost three times faster than from WSLOW 540 AM.
Thanks Kevbo. I might eventually thought about the rainbow effect, but would not have considered gravitational lensing. I wonder now–could slow enough light get trapped in gravitational fields and not escape the star emitting it (much like black holes)? Or possibly form a circular standing wave around a star?
I would not have thought of occultations either, so thanks bonzer:
The farther away the object doing the occultation was, the greater the effect would be–hours for Pluto, for instance.
Chronos, how small would the effect have to be to be undetectable? I’m not hypothesizing that light behaves in the manner we are discussing, but it would seem the difference would have to be very tiny to not show up in cases involving astronomical distances.
What about cases involving rotation? What if an object–say the sun–was dark for a few minutes, and then flashed once. We would see the violet light in about 4 minutes and the red in 8. But in the 4 minutes between seeing the violet and the red, the earth would have rotated a degree, so the sun would go through the rainbow as it moved that degree across the sky. Am I imagining that right or are there other effects to consider?
Well said, ftg.
Ergo, the OP is a bogus question. wavelength x frequency = c
The OP is positing a hypothetical world where things are not the way they actually are in real life. :smack:
Depending on which experiments you trust, the upper bound on the possible mass of the photon is somewhere between 10[sup]-14[/sup] and 10[sup]-27[/sup] eV. I’ll be conservative, and assume 10[sup]-14[/sup]. Visible light ranges from about .3 to .5 eV, meaning that light has a gamma factor of at least 210[sup]14[/sup] for red light, and 410[sup]14[/sup] for blue light. In this case, red light would have a speed of (1 - 6*10[sup]-28[/sup])c , while blue light would have a speed of (1 - 210[sup]-28[/sup])*c. Or in other words, 0.9999999999999999999999999994 c and 0.9999999999999999999999999998 c.
That is pretty tiny . . .
I got to thinking–assuming the effect were large enough–that for stars far enough away red light would not have had time to reach us yet, so most of those stars would look blue, getting redder over the next few billion years.