A delightful quirk of relativity theory

I got it now. Yes, Twitter is a walled garden, even if it has large windows to see most of things, there is definitely a wall there.

The tricky part is that if this was published in a static html page it would be less likely that it would reach us (even if the page was linked in the thread). Distribution is hard.

A good compromise I think is keeping the thread but having a link to a blogpost with the same content in the first (or second) tweet.

A Twitter thread formatting tool that also publishes a web version and automatically link to it in the second tweet is a good micro Saas idea if anyone is looking I think.

> "The more you move in space, the less you move in time."

Isn't that missing a bit at the end? The less you appear to move in time from a different frame of reference?

We all move through time at exactly 1 second per second, don't we?

For reference: Here's Sean Carrol saying exactly that (but in reply to a different question)

https://www.preposterousuniverse.com/podcast/2021/12/15/ama-...

"...it always goes by one second per second. That’s the only speed at which time can possibly go by, and that’s true whether you’re speeding or staying still or in a gravitational field or not. There’s no such thing as the speed with which we move through space-time, the idea of a speed is the amount of distance we travel as a function of time, that’s what speed is. So it just doesn’t apply to going through space-time, it’s a different kind of thing."

You've put the dilemma nicely - it can't be both 'free' and 'your will' by your definitions (well, without admitting supernatural beings that can affect and be affected by the natural world, but are not part of it).

Personally I'm happy with other definitions, not because I feel I'm doing mental gymnastics, but because the version you give is clearly not what normal people mean by it when they refer to it. It might well be related to what philosophers argue about, but normal people who offer you a 'free choice' or who say that you did something 'of your own free will' do not mean anything like 'your choice was not a function of the state of the universe'.

Despite being happy with those other definitions that you aren't, I'm equally skeptical of the idea that free will has to be rescued just because different points in time can be observed simultaneously. What does someone even mean by free will if it can't cope with that?

I think this conveys the right intuition but it's a bit finicky and artificial to make that concept precise so I think it's better to say that the concept of moving through spacetime at a given speed is not well-defined.

Particles have a trajectory through spacetime. They don't move along the trajectory because the time dimension is already part of the trajectory. So the speed at which they move along their spacetime trajectory seems to be a meaningless concept.

What is true however is that if the particle takes a clock with it, and you mark a tick every second the clock ticks, then the ticks will be equally spaced along the trajectory (where distance is measured using the Minkowski metric).

This makes a bit more precise what it means for photons to be stationary along the time dimension. It does not mean that they move horizontally in a space-time diagram. They move diagonally at speed c, as you expect, so for an outside observer they do move through time. However, the Minkowski distance between any two points on photon trajectories is zero. So if you wanted to annotate their trajectory with the clock tickmarks you could start somewhere and put your first tick there, but then your second tickmark would be infinitely far away on their trajectory.

Thus, for an outside observer, a clock approaching the trajectory of a photon would appear not to tick.

From a different point of view, we can reason by analogy to Euclidean geometry. When we have a curve through space we can talk about the tangent vector at any point. But the length of the tangent vector is not a well-defined concept. Only its direction is. You can define the length of the tangent vector for a particular parameterisation p(t) but for the curve itself, i.e. the set {p(t) : t in R}, the length of the tangent vector is not defined.

It is similar for a curve through spacetime. We can parameterise a curve with some variable x and write the curve as {p(x) : x in R} but this is just a set and the length of the tangent vector of p(x) depends on which parameterisation you chose for the curve. But the data of how a particle moves through spacetime is only the curve {p(x) : x in R} itself, not the function p(x): different parameterisations describe the same physical situation as long as the set {p(x) : x in R} is the same.

> Twitter is a fucking horrible format for a complex analysis of special relativity.

Keep in mind that regular people can and have simply replied to the theoretical physicist who posted it and received replies helping them understand better. In this sense it’s a fantastic medium. The same magic that keeps reliably producing spectacular “ah, actually I have a phd in the thing you’re arguing with me about” moments is at play here lowering the barrier to talk to really smart people.