Travelling between two light sources, how different are the photons hitting the front vs the back?

Imagine a spaceship travelling between two identical light souces. The ship has photon detectors in the front and back of the ship. What differences would the front and back sensors show about the photons hitting them? Would there be a red/blue shift? Would the number of photons hitting the sensors be the same? Would the force of the photons hitting the sensor be the same? Are there other things that would be different about the photons in the front and back?

If this was something with regular objects, it might be like driving your car between two tennis ball launchers shooting balls at each other. In that case, more balls would hit the front of your car vs the back, and the impact of the balls in the front would be greater than those in the back. Is it the same way with photons, or is there some weird relativistic effect which makes the situation dissimilar?

The photons hitting the front would be blueshifted, and they would strike more often, compared to a stationary* ship. And likewise, the photons hitting the back would be redshifted, and would strike less often, than for a stationary ship. Bluer photons have greater momentum, and light pressure scales with the number of photons hitting you, so the force from the front photons would certainly be greater than the force from the rear photons (in principle, exerting an effect similar to air resistance, which would tend to slow the spaceship down).

The exact formulas for pressure and so on would require relativity, but qualitatively, yes, it’s the same.
*(“Stationary” here meaning “in the reference frame where the light sources are identical”).

If you could rig some apparatus to measure the speed of light, would the photons from the front give the same result as the photons from the rear?

This seems almost paradoxical! All photons are intrinsically the same as each other: the difference between a high-energy X-ray and a low-energy radio-wave photon is just in the “eye of the beholder”!

I don’t know what you mean by this. All photons are not alike. The energy and momentum carried by a photon is proportional to its frequency and inversely proportional to its wavelength. Blue photons are more energetic than red photons. Standing in front of a beam of x-rays will do damage to you, but standing in front of a beam of infrared photons will just warm you up (unless it’s a really intense beam).

And all photons, in any frame of reference, will be moving at the speed of light.

The red/blue shift thing, aka theDoppler effect. At relativistic speeds, the formulas need adjustment, but a passing train gives an idea of the frequency shift whether something is approaching or receding.


Every experiment we’ve attempted so far has verified this, and it is a defining postulate of relativity.

ETA: as noted above, the velocity measured is the same but the frequency of the EM radiation is not necessarily the same.

Yes- ninjaed - I assume he is talking about the Doppler effect, or gravitational effects, in which a photon may be red-shifted or blue-shifted. Or perhaps the fact that identical photons can be quantumly indistinguishable.

I assume septimus means that the energy measured in a frame that’s moving relative to the photon emitting source will vary according to that relative velocity. Photons that are emitted as infra-red could be detected as X-rays by an observer moving toward the emitter at relativistic speeds.

But I’m not sure why septimus finds this part surprising. The kinetic energy of a particle in classical mechanics will also vary under these circumstances, along with the relative speed. The surprising part of relativistic mechanics is not that the energy of the photons varies for an observer moving relative to the emitter, it’s that the speed stays the same.

The “paradox” I refer to is that an isolated photon can’t “know” what its frequency or energy is. Traveling unmolested at the speed of light it has no frame of reference except itself.

I do not find this “surprising,” and even “paradox” was too strong a word. But it is “nifty” that, as Riemann points out, the same photon might be viewed as infra-red and X-ray by two different observers.

That’s hardly unique to photons. The momentum and kinetic energy of any object/particle is dependent on the frame of reference.

^including in classical mechanics, of course. It’s no more than saying if two cars collide head-on at 60mph, there’s a much bigger bang than if a car traveling at 60mph hits a parked car.

…Which, in turn, is more severe than when a car traveling at 61 MPH rear-ends a car going 60 in the same direction.

But for massive particles, the measured velocity changes. An electron and and airplane behave similarly in this respect.

Massless particles don’t have this degree of freedom, and change frequency instead. It’s not a shock that the KE would have to go somewhere, but it doesn’t have an analog with macroscopic objects. Rather, it’s more like a wave.

Is there any difference between a “speed adjusted” photon and a “naturally produced” photon? That is, if the ship is travelling fast enough that the forward light source is blue shifted so much that it appears as x-rays, are those photons indistinguishable from photons that were originally produced from photon source that emitted x-rays?

In the tennis ball example, it might be how if you drove fast enough, the balls in the front hit with the force of bowling balls while the ones in the back hit with the force of ping-pong balls. But there would be other ways to know that the balls were really tennis balls, such as impact size, color, etc. Is there any thing similar with photons? Or is it that if they hit like bowling balls, they are bowling balls in all aspects.

No there’s no way to tell the difference from just the photons. However, it would be obvious if you were traveling at a considerable fraction of the speed of light. Here’s a page describing the effects you’d see. (That page is from the sci.physics FAQ. Note the date: 2002. The good old USENET days…)

Your phrasing here could be slightly confusing because the only thing that we can see to makes it obvious is… the photons.

An isolated photon that was originally emitted as an X-ray looks no different from a photon that was emitted with lower energy but is detected as an X-ray because you’re moving toward the emitter. So I think I’m correct in saying that if the only emitters were directly in front of us or directly behind us, we could not distinguish between a lower frequency less intense emitter moving toward us vs a higher frequency more intense emitter moving away from us.

But in reality there are stars around us in all directions emitting entire spectra, so if we’re moving relativistically relative to the background stars there are very significant effects on the distribution of and energy of the photons in aggregate, i.e. the sky looks very different.

The cosmic background radiation originated at a 3000° Kelvin temperature and now has less than 3° temperature. So those photons have “lost” 99.9% of their energy if you treat them in the ordinary way! Yet each of those photons has wandered blithely on, “unaware” of this huge energy loss, or even of the passage of time.

You’re right, that was bad phrasing. Thank you for clearing it up.

Although… I don’t know if the details of what I wrote are quite correct?
I’m not sure what restrictions are necessary for sources directly in front and behind for the difference to not be detectable. Perhaps they need to be single frequency emitters, unlike a realistic star with a spectrum

In principle, you also couldn’t distinguish between a star with a normal spectrum at rest relative you, and a star moving quickly relative to you with a weird spectrum. It’d take a lot of work to produce a stationary light source that had the same spectrum as redshifted hyrdrogen, or whatever, but if you really wanted to, it could be done.

When we see stars and measure their spectra, though, we implicitly assume that there’s no one out there going to all of that work to deliberately deceive us.