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doc: relativity tweak
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philiplinden committed Dec 31, 2024
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59 changes: 18 additions & 41 deletions docs/relativity/01-special.md
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Expand Up @@ -73,47 +73,9 @@ Since the speed of light is constant in all inertial reference frames, an
observer watching their clock will **always** observe the photon moving at the
speed of light, $c$, in their own reference frame.

The physics of relativity happen regardless of what we use to measure time, but
this "light clock" isn't arbitrary. We will use the fact that we are measuring
how long it takes for a photon to travel a given distance to measure time.

Let's give a light clock to `Ash` and `Brock` and see what happens.

```admonish example
`Ash` is riding a train, and `Brock` is waiting for the train to arrive at the
station. The train is moving at speed $v$ relative to the station.
`Ash` holds a light clock called `A`. `Brock` also holds a light clock called
`B`. `Ash` and `Brock` both observe the speed of light in their own light clocks
and in each other's light clocks.
**From `Ash`'s perspective:**
- The station is moving towards the train at speed $v$.
- Light clock `A` is at rest.
- The photon in the light clock `A` is moving at speed $c$.
- Light clock `B` is moving towards the train at speed $v$.
- The photon in the light clock `B` is moving at speed $c$.
**From `Brock`'s perspective:**
- The train is moving towards the station at speed $v$.
- Light clock `A` is moving towards the station at speed $v$.
- The photon in the light clock `A` is moving at speed $c$.
- Light clock `B` is at rest.
- The photon in the light clock `B` is moving at speed $c$.
```

Light clock `A` is moving at speed $v$ relative to `Brock`, but he observes the
photon inside to be moving at speed $c$, not $c+v$. How can this be?

Let's use the first postulate of special relativity and follow the math to see
how all of the observations could be true.

```admonish help
It is natural to pause at this point and ask "how can this be true?" or "why is
the speed of light constant?"---stop yourself. For a moment, accept that it is
true and instead we should ask **"what must happen for this to be true?"** Trust
the process. 🙏
```
The physics holds regardless of what we use to measure time, but this "light
clock" isn't arbitrary. We will use the fact that we are measuring how long it
takes for a photon to travel a given distance to measure time.

## The speed of light is constant

Expand Down Expand Up @@ -147,3 +109,18 @@ It is key to pin the definition of $c$ this way because as we will see later,
distance and time are _not absolute_, they are _relative_. The time or distance
can change depending on the observer's reference frame, but **distance traveled
by a photon divided by elapsed time is always $c$.**

## Time is relative

Light clock `A` is moving at speed $v$ relative to `B`, but he observes the
photon inside to be moving at speed $c$, not $c+v$. How can this be?

Let's use the first postulate of special relativity and follow the math to see
how all of the observations could be true.

```admonish help
It is natural to pause at this point and ask "how can this be true?" or "why is
the speed of light constant?"---stop yourself. For a moment, accept that it is
true and instead we should ask **"what must happen for this to be true?"** Trust
the process. 🙏
```
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