A delightful quirk of relativity theory

https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu...

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.

[0] https://www.youtube.com/watch?v=A2JCoIGyGxc&list=LL&index=94

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?

Also, the concept of free will is bound up with the concept of consciousness. What is the entity that may or may not have free will? Until we define and understand that, free will will be an ill-defined concept not amenable to proper analysis

Is it not essentially equivalent to "actual" free will? I am perfectly happy with just this.

[0] https://plato.stanford.edu/entries/incompatibilism-theories/...

1) Define “free”

2) How do you test your hypothesis?

You’re trying to apply logic to an untestable philosophical debate. If you believe free will doesn’t exist, you can’t design an experiment that would invalidate that belief. And if your theory is untestable and unfalsifiable, then what good is it other than a creative exercise?

However, we do know from Quantum Mechanics that the universe is probabilistic and not deterministic:

https://www.thegreatcoursesdaily.com/quantum-universe-fundam....

So, we do know that the universe is not pre-determined and cannot be calculated in advance, but if you want to believe in humans as fully deterministic (or some other definition of no free will) inside of a non-deterministic environment, I haven’t heard anyone propose an experiment that could test that, at which point the debate of “free will” is relegated to the realm of thought experiments rather than science.

So, perhaps the better question is: Does it serve you better to believe there is free will or no free will? And leave it at that.

This is as free as you can get and I don't think anyone ever posited "free will" as something other than this.

Also, I wonder if your either/or line of reasoning depends on the Law of the Excluded middle. What happens to your reasoning if that law is not true?

And given that the free will and now are connected it is easy to see why we cannot describe the free will using physical equations. Well, at least until we will manage to describe now.

At a first approximation there are obviously limits to our “free” will as no one has yet been able to will themselves to float through the air without support, go without food or water indefinitely, pop a pet dragon into existence, survive the physical destruction of their brain, etc.

So it’s hard to start from a position that anyone ever seriously thought “free will” meant no limits or dependencies.

Which is what makes the question kind of unknowable. Because we can't rerun our lives to see if we could make different decisions with all of the exact same conditions as before. Even running the choice twice isn't the same. Because the second time you do it, you're now a person who has previously made this choice. And that makes the scenario different, because you are different. We have no real way of testing free will.

But better still: the question does not matter at all.

Either free will exists or it doesn't. There's no spectrum of "50% will" or whatever. You can either make choices or you're essentially the result of all the forces acting upon you.

So, what are the consequences of both scenarios?

If free will exists, then fine, we can make choices. We can choose to do whatever. There's nothing really interesting to be said about this branch.

However. If free will does not exist, then there's something weird going on. Because if free will does not exist, I don't have any choice in whether or not to post this message. I post this message because your post elicits that response in me. Just like you made your post for the same reason. And we just keep pulling this thread all the way back to the big bang.

But we also don't have the choice in how we feel about this discussion either. You will either accept this or not based on the various physical, biological, and chemical processes going on inside of and around you. So you will either agree or disagree and that decision itself is preordained. Regardless if it is true or not. You're either the type to believe in free will or not and you can't choose that. Because if you could choose that, you'd have free will.

Even if you believe you are making a change, you're not. Because you were going to make that change due to the forces at work on you. Forces that were eventually going to interact with you because those forces themselves are the products of other forces, etc. So if you hear all this, take it to heart, and decide to live a life of apathy because you have no free will and nothing matters. Then that's what was going to happen at this point and time regardless.

It is quite interesting in fact, as it lets you sensibly assign moral responsibility to those who were acting of their own free will, even if the world is deterministic. Arguably that's the only kind of free will worth having, and what people mean when they talk about free will (not what people say they mean).

Why do "I" have this experience of having a viewpoint and making decisions? That is a mystery that I am not close to solving. However why would any of that define how the universe must work?

Much like a finite being can hold thoughts of Cantor's classes of infinities in her finite brain. The domains in question are unrelated.

That line of argument makes no difference between the free will of humans and that of animals, insects, bacteria or rocks. But that can't possibly be true: we humans invented free will after all. That's the mental gymnastics that keeps me mentally strong. No beast, nor angel. "Freedom evolves" (DD).

It's like in chess. If you are running an algorithm that plays chess, you will just play the moves mindlessly, so no free will right? Except that per my definition your internal state is influencing your moves, so, you are free (in this sense).

But there are situations where you're forced into a move. For example, the king is in check, there is only one move possible, then this move is forced. It's precisely in this forced case where there is no free will: you are being compelled to move by forces beyond your internal state.

"Forced" moves can have some shades of gray in chess as well. For example, you may be forced to sacrifice a piece to defend the Queen, because sometimes the game is just lost if you don't do so. So.. the rules of the games allow you do to something else, but you can't meaningfully choose if we suppose you're playing for winning. And, of course, you can only play legal moves: some board states have few legal moves left so you're comparatively less free. In those cases, you have your free will partially constrained.

[0] https://plato.stanford.edu/entries/compatibilism/

> We all move through time at one second per second, don’t we?

You need to define “move through time”. The only way to measure time is with a clock, and the clock’s motion relative to you affects the measurement.

If you let everyone define “time” as the thing measured by the watch on their wrist, then everyone moves through time at one second per second, but since people are in motion relative to each other and therefore have different frames of reference, their clocks will measure different times.

Since no frame of reference is privileged, there is no “absolute time”. Of course you could pick one and measure every event against that one, but that would be an arbitrary choice.

This is my understanding. If I’m wrong, I’d be happy to be corrected.

> 1) An event in Andromeda occurs at single moment, it’s our observation of the event that is warped. So there aren’t two realities, one where they’re still debating and one where they aren’t. In both realities the debate has concluded, it’s just our observation of the event takes place at different reference times.

Yeah, they're making the mistake of assuming a minute is a minute.

It's closer to the difference in angular motion vs linear motion. If you are closer to the center, you move very little linearly. If you are closer to the outer edge, you move very little angularly.

Now you look at the linear distance as time passed for the object and the angular distance as the amount of "space-time" an object has gone. The amount of "space-time" is constant. It's a bit of a wonky model, but it's probably the simplest one that encapsulates the concept.

So just because they spent 3 days debating, you spent 5 days watching, and Bob only spent 1 day watching; that doesn't mean Bob is 2 days ahead of Andromeda and 4 days ahead of you. Since we are all also traveling through space at different speeds, we've all traveled the same amount of space-time, so we're all seeing the same things.

As for our perception, that more depends on our relative positions from each other rather than speed. Because nothing is faster than light, we can never experience an event before we see it.

When you undergo an acceleration, it corresponds to a hyperbolic rotation of the spacetime around you (from your frame of reference). When the acceleration is small, the rotation is also very, very small; however at very large distances, even a small rotation can have a large effect.

In the example, that "large effect" is the alien debate moving in time forward or backwards a day (again, from the accelerated reference frame).

This has nothing to do with the observation delay, it's just an artefact of what it means for two far apart events to happen "simultaneously": simultaneity is a relative property, so two things that happen simultaneously in one reference frame might not happen simultaneously in another.

The reason this doesn't introduce a paradox is because without a specific reference frame, events only have a partial order: when you compare two events, there are three possible results:

1) Event A is in the past light-cone of event B.

2) Event B is in the past light-cone of event A.

3) Neither event is in the past light-cone of the other.

For 1+2 this means that the time between the events is greater than the distance between the events, whereas for 3 it means the reverse. For 1+2, the ordering of the events is the same for any reference frame. For 3, there will always be some frame of reference where both events appear to happen at exactly the same time, so nothing can be said about their order without choosing a reference frame.

I think the term free-will has clouded the issue a bit. Forget about free-will. Scientists, instead, normally talk about Determinism vs indeterminism, or nondeterminism in CS. These have a more precise definition than that other thing. The universe is deterministic if the outcome of events are completely determined by previous events. Or the universe is nondeterministic if the outcome of events are not certain, but follow a random distribution.

As to the precise details of the speeds and distances etc, it is a thought experiment, swap the car for a rocket traveling past at 0.86c, if you like. Or instead of aliens deliberating all day, maybe they are more efficient than we are, and they make their decision instantly by flipping a digital coin powered by the perfectly nondeterministic quantum fluctuations of the vacuum.[0]

For earth rocket man, there is a moment before the quantum dice roll when the decision is indeterminable, it's completely random. But at the same moment in the stationary frame, the fleet is already on it's way. Unless you wish to argue that a stationary reference frame is somehow more valid than a moving one, you have to accept that in the moving frame, the event of the dice roll has still not occurred and should be random, but how can it be random, if it has already happened in the stationary frame. Hence the paradox.

I hope that cleared things up some?

  [0] The vacuum has an api: https://qrng.anu.edu.au/

[1] https://www.youtube.com/watch?v=PC2JOQ7z5L0

The real question becomes one of probabilities: Unless some entity is able to introduce measurable biases that deviates from predictable probabilistic distributions relative to what could be predicted based on its complete state (including its internal physical structure) and complete inputs, it makes little sense to suggest the entity has agency.

But that leaves us with the problem of explaining how something could effectively break the laws of physics in a way that doesn't just lead to infinite regress.

The day I see someone give a definition of free will that overcomes that, I'll be in awe. Not holding my breath.

"Free will" is a very poorly defined concept that mostly falls out of problems with theodicy in early moral philosophy. Since the idea of "free will" plays a major role in Christian ethics this notion has permeated a huge amount of the Western intellectual tradition, but only makes sense in the framework of other archaic philosophical questions around theodicy like "if god is omnipotent, omniscient, and omnibenevolent why is there evil?" This question is only remotely interesting if you have a cultural reason to need to believe that these three things must be true (or if you're curious about the development of the Western intellectual tradition, in which case it's a very important question to understand).

1. The universe is not deterministic (if you believe that wavefunctions collapse)

2. The mysterious thing that makes conscious entities experience high-amplitude events more often than low-amplitude events is not deterministic (if you believe in MWI).

Evidence for free will, a definition of free will; those things physics cannot provide. But there's room for it.

It's like you're trying to avoid mentioning hidden variables or bell's theorem directly. That is, you're probably not correct when you say something like that.

1. Chaos theory ensures that unless we have INFINITE precision measurements, even a perfect simulation of our universe will diverge based on even the smallest differences. A difference of one particle's velocity in the googolth decimal place will eventually cause wildly different simulation outcomes. So, in practice, it's impossible to know what's going to happen given a long enough time frame, unless we can get advanced enough to have literally infinite precision measurements.

2. Given objection 1, using the law of large numbers to explain away quantum processes' non-determinism from initial conditions seems like a cop-out to me. Yes, given enough particles, they converge around some predictable value. But given the need to have exactness in measurements to predict chaotic processes, if a SMALL number of individual particles interact with other matter, and they sometimes do, how could the probabilistic nature of those individual particles be neglected?

Let me sum it up this way. If I take a quantum random number generator and use it to generate lat-long coordinates, and visit that place, could anyone or anything predict what happens given initial conditions before I do that? No, it is not bound by initial conditions.

https://en.wikipedia.org/wiki/Superdeterminism

But otherwise I agree that "free will" is basically just a silly argument over the definition of an undefinable term, or a way to explain away loopholes in theology.

The only thing I think would be improved by having this in blogpost form is more interact-able visuals, equations and similar.

But it is literally unreadable to me. I couldn't finish reading the thread and had to find an alternative way out of twitter.

Fist trial, using my android phone with fennec fox. There is a modal that hides the content asking me to "log in"; if I close the modal I go back to the twitter homepage. Thus unreadable because I don't have a twitter account. Sometimes I have managed to read a few tweets by a "smart" combination of closing the successive modals and reloading the page, but not this time.

Second trial, using my laptop with firefox browser and heavy adblocking. I can read only the first three tweets, the rest do not load due to some third-party javascript.

No big deal. Third trial, now I open a "clean" firefox browser session with just ublock origin, and I manage to read about 30 tweets, until it starts talking about hyperbolic rotations. The thread obviously continues, but the sole link below it "show replies" does not work. When I click on it it says "Whoops! Something went wrong. Please try again!".

Typically I wouldn't bother and stop reading. Fuck twitter. But today I really wanted to read this thread because I teach these things. Thus I learned to use nitter, which gives an interface of twitter that, even if it's equally ugly, it sort of works (in that you can actually manage to read the text).

In retrospect, this is an extremely sad state of affairs. We have an excellent article which is made of a short text, a few simple formulas, and a few simple images. This could be a static html page of a handful of Kb with img tags. But it is a slow and humongous javascript monstrosity that does not even work, and may disappear at any time if twitter "bans" this user for reasons unrelated to this text.

For readers twitter threads are pretty crap tho, that's why I really like to use thread reader app.

People are correct to point out it helps material reach a wide audience, but that's not the point. The point is what could be better?

The original argument was to keep communication brief, shorter is better, etc. The fact it keeps being circumvented in this way suggests sometimes a longer format is necessary.

As a practical matter, in this case the person could have linked to a long form blog post and used Twitter as a sort of comment discussion section?

That's amazing, and it was well explained in 1908! Yet students today are learning a horrific bastardized version of it. Physics is absolutely terrible when courses and books try to to remove the "complicated" math, and in its place they put something more complicated and ambiguous.

Teach the math!

It's like Greenspun's Tenth Rule, but for math:

"Any sufficiently complicated scientific theory contains an ad hoc, informally-specified, bug-ridden, slow implementation of half of Complex Analysis."