eli5: The Relativistic Doppler Effect
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The Relativistic Doppler Effect is a mind-bending concept that allows us to understand how the frequency of light and sound waves change when the source is moving at a significant fraction of the speed of light
It’s like music playing differently depending on how fast you drive – a fascinating phenomenon of physics!
So, sound (and light*) are a wave, yes? they have pluses of power, a waveform, with a wavelength and frequency. If you make that wave go “faster”, your getting more waves per second, so your frequency has gone up, and your wavelength must be shorter.
Imagine a racecar passing by you at, say 120mph, with that classic “neeee-OWW” sound as it speeds past you. The engine is actually putting out the same noise the whole time, but what you hear is affected by the relative speeds between you and the car.
as the car approaches you, the sound is travling at its based speed, but the car is moving as well, so its “catching up” to its own sound. this means the sound is getting squashed together a bit, which means that when it reaches your ear, it sounds higher pitched because the frequency is higher. once its past you, the waves are more spread out, becuase the car is moving away, so the wavelength is longer, so the engine sounds lower pitched.
now, with light, when you change the wavelength like this, you change the colour of light. you go up and down the classic “roy g biv” rainbow sprectum, with red being the slower end and blue being the faster end.
so, if you know what colour a thing “should” be, based on something like spectral absorption**, you can use this shift to work out how fast something is moving towards or away from us.
*yes, I know about light’s wave particle duality, its *complicated*, i’m glossing over it for ELI5.
** basicaly, some elements absorb light in specific patterns (say, 1 gap, then 2 very close together, then 1 gap), and these patterns stay the same relative to each other, regardless of where they are on the spectrum. So, if you see that specific 1-2-1 pattern of gaps on the spectrum, you know “ah, those are the hydrogen lines, they should be *here*, so we’ve shifted by that amount”
Light has wave properties, so think of it like a bunch of squiggles going up and down, up and down. The color of light depends on it’s **wavelength** where shorter wavelengths correspond to bluer color and longer wavelengths correspond to redder color. In other words the more squished the squiggles are to each other the bluer the light, and the more stretched the squiggles are the redder the light. Really really squished squiggles are very high energy radiation like what you see in a nuclear bomb and really really stretched squiggles are very low energy radiation like microwaves or radio waves.
Now imagine you’re doing something very repetitive, like clapping your hands. This repetitiveness has a **frequency** – how often you do it in any given amount of time. This repetitiveness can be analogous to a light wave in the sense that each clap is like a squiggle. The faster you clap the more squiggles you produced in any given amount of time and the slower you clap the less squiggles you produced in that same amount of time. The more squiggles you produce the more we have to scrunch them together and the less squiggles you produce the more we have to spread them out. So in this way you can think of it like the faster you clap your hands the bluer you’re making the light, and the slower you clap your hands the redder you’re making the light.
This is where relativistic Doppler effects come into play. Let’s imagine that you’re clapping your hands one time per second as *you measure it on your clock* – so you produce a series of squiggles that correspond to certain frequency and thus a certain color of light. Because of time dilation someone moving relative to you is going to measure that same second differently then you. For example if you’re on a rocket ship moving at near the speed of light then an observer on Earth is going to see your clock ticking considerably slower relative to theirs. While from your perspective each clap is “normal” speed – once per second – they’ll see you clapping considerably slower and consequently each clap taking considerably longer. Instead of measuring your squiggle once every one second they’ll measure it once every few seconds, because “one second” for you is a different amount of time for them. Because of time dilation they receive less squiggles in the same amount of time, so the squiggles they receive are stretched apart and thus appear a redder color then from your perspective. We call this transformation of the color of light redshift.
Alternatively there is also blue shift which is the same effect but in reverse. If you clap once per second as you measure it but I observe your clock ticking faster then mine then I will consequently observe you clapping more frequently. More claps means more squiggles and more squiggles means we have to scrunch them together. From my perspective the light you emit will look bluer then from your perspective.
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