Redshift, blueshift, one shift, two shift

A reader writes:

A thought struck me while driving home one night: If relativity means the speed of light is absolute, how is it possible for there to be a Doppler shift of light?

As I understand it, Doppler occurs when a wave source is moving and the peaks/valleys of the wave get scrunched up/stretched out.

The theory of relativity states that light shining from a moving vehicle is NOT traveling c (light speed) plus the speed of the vehicle, because time slows down relative to the stationary observer.

If all the crests of the wave are traveling at c and Relativity implies that the point source can't go any faster than c, then it would seem there's no way for there to be any shortening of the frequency.

How does relativistic time dilation not cancel out the Doppler effect much like the added speed of a vehicle is canceled out?

Add in the wibbly-wobbly-timey-wimey grey area of light being both a particle AND a wave at the same time and my brain is hurting me for trying to visualize how the Doppler shift works for light.


You are, and this is not something that's often said to people coming to grips with Einstein's theories, overthinking this.

Yes, as special relativity says and as everybody who talked to Einstein about it firmly understood until the concept slithered out of their brain about ten minutes after the end of the conversation (relativity is even worse than tax brackets in this regard), the speed of light is indeed a universal constant. No matter how fast the observer, or the source of the light, are moving relative to each other or relative to anything else, everybody always sees the speed of light in a vacuum as the same 299,792,458 metres per second.

(Things get a little more complicated when the light is moving in a medium other than vacuum, but our universe, at least, is conveniently largely made of vacuum. This is a useful thing to remember if someone attempts to persuade you that the universe has been fine-tuned just for us; if this were actually the case, 99.9999-and-several-more-nines-per-cent of the universe might fairly be expected to not be instantly lethal to humans... but it is. Oh, and just to make things a little more confusing again, Einstein also came up with a theory of general relativity, which has to do with gravity and is different from special relativity.)

So, as you say, light doesn't go past you any faster if the light source is coming at you, or any slower if the light source is moving away.

But when the source of a sound is coming at you, the sound doesn't pass you any faster, either.

The speed of sound is much less constant than the speed of light. Sound travels faster the "stiffer" the material it's travelling through is, so it's zero in a vacuum, around 343 metres per second in dry air at sea level, but about 1500m/s in water. Unlike the speed of light, it is of course possible for things to travel faster than the speed of sound, especially in air. But even when a sound-emitting thing, like a jet fighter, is travelling faster than sound, the sound it emits still travels at whatever the speed of sound in that part of the atmosphere is.

(This is why you don't hear a supersonic plane, or a supersonic bullet, coming...

...until it's already gone past you. In the case of a bullet, the noise it makes is pretty much entirely the "sonic boom" created by pushing air out of the way faster than sound. The shock wave around a supersonic aircraft, bullet or explosion can travel faster than sound, but the shock wave slows as it spreads out, and soon becomes a regular sound wave.)

But, as you say, the Doppler effect clearly changes the pitch of sound made by an approaching, departing or...

...passing sound source.

The reason for this is that when a sound source is approaching you, each new oscillation of whatever sound it's making is emitted when the source is a bit closer to you than the last, which puts the compressions and rarefactions of the sound waves closer together. This is, from your point of view, exactly the same as if you were listening to a stationary sound source making a higher-pitched sound. And if the sound source is moving away, the opposite happens.

Light is, once again, a somewhat more squirrelly concept, because as you say, photons have characteristics of both particles and waves. In this case the analogy still works fine, though; once again, the source of each new particle-photon or wave-photon is closer to you, or further away from you, when each new photon is emitted, creating the same effect you'd see if the light were coming from a stationary source with a higher or lower frequency, respectively.

It's often misleading to apply observations in the everyday world of modest velocities, masses and timescales to the much greater velocities, far larger masses, and/or much longer timescales which cause Newtonian physics calculations to give you clearly wrong answers, so that Einstein's refinements become necessary. In this case, the trap lurking in the speed-of-sound to speed-of-light analogy is that if you move towards a sound source, the speed at which the sound waves pass you, in your frame of reference, really will increase.

Sound waves can also pass you faster, or slower, than the speed of sound in a given medium if that medium (air, for instance) is itself moving from your point of view (because you're standing still and the wind is blowing, for instance). If you and the sound source are both stationary and a steady wind is blowing from the source to you, you'll encounter the peculiar situation in which the sound waves are passing you faster than sound, but the pitch is staying the same!

If you assume a stationary listener, no wind and perfectly spherical and inelastic cows, though, the light-to-sound analogy works.

Time dilation is irrelevant, here. If you're in a spaceship with red headlights and you're travelling at close to the speed of light, time will pass slower for you, from the point of view of a stationary observer, and your headlights will look blue, to a stationary observer in front of you. But the time-dilation affects everything on and within your spaceship, including you, your headlights and the tiny 32,768Hz quartz tuning-fork resonator...

Quartz tuning-fork oscillator
(Source.) your wristwatch. So from your point of view, your wristwatch still counts one second per second, and your headlights are still red. (But the universe in front of you will look bluer, and the universe behind redder. The sound analogy works here, too; if you're in a car driving past a stationary car that's beeping its horn, the horn will sound higher as you approach and lower after you pass by.)

But if you assume a stationary listener, the speed-of-sound to speed-of-light analogy works OK. The sound, or light, passes you at the same speed no matter how fast the source is travelling, but the sound, or light, waves arrive closer together when the source is approaching, and further apart when it's departing.

Psycho Science is a regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.

9 Responses to “Redshift, blueshift, one shift, two shift”

  1. juanito Says:

    It occurred to me one day while driving that if you went quickly enough, doppler shift would make red traffic lights appear to be green. I figured out how fast you'd have to go, but don't have the math-fu to figure out how long before your car ablates away from atmospheric friction.

    Or if you'd even escape Earth's gravity well...

    Either way, i haven't tried that excuse out on any traffic cops.

    • klightspeed Says:

      Forget about the earth's escape velocity at that speed. You'd well exceed the galaxy's escape velocity.

      Of course, for every metre of travel in the atmosphere at that speed, your car would have to convert a couple of kilograms of matter into kinetic energy to stay at that speed. Not to mention the couple of hundred kilograms of matter your car would have to instantaneously convert into kinetic energy to get to that speed in the first place.

      • Stark Says:

        I come up with about 85739km/s or ~.286c (back o' the napkin calculation) to change your typical red light (~700nm) to green (~500nm).

        Galactic escape velocity is - at the upper range - ~650Km/s or .002168c

        So... yeah... right on out of the galactic neighborhood you'd go. Hope you brought snacks!

        At this speed you could make a quick run to a 7-11 on mars and back in a mere 35 minutes allowing for 10 minutes to browse the junk food aisle. Mars is currently .83AU away (Jan26,2012).

        Alternatively you could go from LA to Syndney in 0.14 seconds. Don't forget to switch to the other side of the road when you get there - head on crashes at .286c are ugly. Really try to avoid hitting anything substantial. In fact, assuming you had a hefty car (I'm thinking an SUV will be needed for this kind of travel) weighing in around 2250 kilos a crash with, say, a mountain, would be bad. Very very bad.
        Like a roughly 2200 Megaton explosion bad. By way of comparison the most powerful weapon ever tested, the Tsar Bomba was a mere 50 Megatons.

        Its rough when traffic accidents can end the world as we know it.

        • juanito Says:

          Awesome! I remember my napkin-back calculations put a collision with earth as slightly less energetic than the Tsar bomb. But i drive a little KIA, and like i said, my math-fu is not good.

          Okay, so if i was moseying along at .283c, and managed to aim very well for that traffic light and go under it, what angle would my vector change as my mass interacts with Earth's gravity? You know, ignoring pesky things like friction... A tiny fraction of a degree?

        • TwoHedWlf Says:

          Let's assume you manage to locate a bottomless pit and drive your car off it to accelerate to that velocity...Then it would take you 101 days to reach that speed.

          And you'd travel roughly 2500 AU or still only .04 light years.

  2. Anne Says:

    I have to quibble with many of your statements about the vacuum. Vacuum's a pretty slippery concept; personally I consider the one atom per cubic centimeter of the interstellar medium a fairly substantial density, but it is admittedly emptier than anything we can pull off on Earth. But light - or at least, radio waves - does not travel at c in the interstellar medium. It has a refractive index different from one, which delays, in particular pulsar signals. In fact, because it's a plasma, that refractive index goes like (approximately) 1/f^2. This means that if you want to listen to a radio pulsar, adding all the power from 1.1 GHz to 1.8 GHz, the pulses will be delayed at the lowest frequencies compared to the high frequencies. Correcting for this so that you can avoid the pulses being smeared out is a major computational task.

    As for the speed of sound in a vacuum, it's not clear what would be meant by sound in a "true" vacuum (whatever that is in this quantum-mechanical Casimir-force world). In the interstellar medium, though, sound can propagate. Well, since it's a magnetized plasma, there are at least four distinct kinds of waves that can propagate, and the distinction between sound waves and radio waves is a little ambiguous. But you can get sound waves propagating in a vacuum; the classic bell in a bell jar demo is just showing that a ringing bell isn't really able to transfer its motions to motions of the tenuous medium (it's a mismatch of acoustic impedance).

  3. Simon Says:

    > the source of each new particle-photon or wave-photon is
    > closer to you, or further away from you, when each new
    > photon is emitted, creating the same effect you'd see if the
    > light were coming from a stationary source with a higher or
    > lower frequency, respectively.

    That's kinda misleading - equating sound wavefronts with photons in your analogy, I mean.

    Redshift would still work just as well with a source that only ever emits a single photon (wheras it wouldn't make sense to talk about the frequency of a sound wave only consisting of one wavefront). You'd still measure that photon as having a lower frequency than what the source was set to emit it at, if the source was travelling away from you. Frequency of light is nothing to do with how regular the photons come - it's an intrinsic property of *each* photon (proportional to the photon's energy).

    • Stark Says:

      Well, yes, red-shifting of a single photon is perfectly reasonable... but that observed red-shift is a product of the frame of reference of the observer and not intrinsically related to the energy of the photon itself.

      The energy of a photon comes from its frequency which is different for observers in different frames of reference. So for example, we see our sun as yellow (yes, I know it isn't actually yellow - but for arguments sake here it is) and emitting yellow photons in our frame of reference but someone in a starship receding at relativistic speeds would see that light as red - however, the actual energy of the photon is unchanged even though it measures differently for each observer.

      I thought Dan's explanation was fine considering that most folks heads, at least initially, translate the idea of light being both photons and waves as meaning that light is waves of photons.... which is understandable but wrong. The fact that a single photon can and does create a wave of light is rather hard to grasp if you haven't worked your way up the physics knowledge chain... and even then it messes lots of people up.

      When measuring the red-shift frequency of light we are ignoring the particle properties and just looking at the wave... which is in fact squashed much like sound waves in doppler shift (otherwise it wouldn't change color!). But you are right: when we look at the photons - redshift has nothing to do with how often they arrive.

      Ahhh... I love the smell of relativity in the morning! Smells like... crazy ideas that are both simple in concept and devilishly tricky in practice! :)

  4. RyanJ Says:

    Now do evolution. :)

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