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This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity. That aside, my favourite quirk from r

This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity. That aside, my favourite quirk from relativity is this: "The more you move in space, the less you move in time." Like relativity in general, it sounds simple enough, but it's consequences are profoundly shocking. (That is, if you take the time to understand it, and don't leap to the conclusion that you know relativity better than Einstein or Penrose ;) Take the case of two people on Earth, one stationary and one travelling past in a car. They each have a different reference frame, and a different set events which make up their present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. In the reference frame of the person on Earth who is moving, the debate is still going on. But, in the reference frame of the stationary person, it is a day or so later in Andromeda, and the invasion fleet is already on it's way! In nature there is no absolute reference frame we can call base reality, and both observers reference frames are equally valid. Then the outcome of the invasion debate is a foregone conclusion. How can there be any room for free will in the deliberations of the alien government? This is the crux of the Andromeda Paradox and the Reitdijk-Putnam-Penrose argument. BTW: "Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment." https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argume... More info https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity https://en.m.wikipedia.org/wiki/Relativity_of_simultaneity Edit: If you know of any serious alternatives to the 4D spacetime/ block universe theory then I would love to read it. Rescuing free-will from the jaws of spacetime would be cool!

Ma8ee 5y ago
Isn't the whole point that talking about "the present moment" about something very far away isn't particularly meaningful when simultaneity for spatially separated events depends on the observer?
- awb 5y ago
  Correct, check the criticisms on the Wikipedia page: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu...
elcomet 5y ago
You can check https://unrollthread.com/t/1482811504424542211/ https://unrollthread.com/t/1482811504424542211/ to view it as a blog post
3pt14159 5y ago
Well, another way of looking at it is that the observer is not the same as the decider. So ultimately your reference frame is only current within the locus of your own mind and any decisions you make get broadcasted out to observers in the universe. They make their own decisions about where to be, how fast to be, and so on, and from their perspective it could be yesterday from when the decider decided, but its irrelevant just as much as being farther away in 3d space gives a longer delay in ping time. Whether or not the decider has free will or not I don't think can be argued by this specific example.
- mannykannot 5y ago
  FWIW, I feel this is the right way to look at it. Furthermore (or perhaps I should say equivalently) the "observers" on Earth have not observed the decision, and thinking of them as such seems to be a Galilean fallacy.
darkerside 5y ago
Wouldn't all that matters here be their relative velocities to Andromeda, and not to each other? And relative to Andromeda, the person in the car might actually be going slower. Separately, I don't think chronology is broken. It's ok that there is predestination because there is no way for actions taken here to propagate back there in time to change things. If a change does somehow propagate back through a wormhole or something, it's all good, just spinning up another dimension probably...
ajuc 5y ago
At least when you think of objects moving slower than light there can't be reversing of casuality. But relativity allows for that, we just drop the faster than light solutions usually as non-physical. Recently there's been an interesting paper about what happens when we don't drop these solutions: https://arxiv.org/abs/1910.02780 https://arxiv.org/abs/1910.02780 Imagine the Andromeda fleet can move faster than light. When you look at it from Earth POV suddenly it manifests near Earth out of nothing. Looks very similar to quantum mechanics indeterminism - if alien general decided to send the fleet it's there, if he didn't - it's not there, and there's no local cause for it appearing suddenly. What the paper above explores is - starting from relativity including faster-than-light objects and trying to prevent paradoxes they derive quantum mechanics.
naasking 5y ago
> "The more you move in space, the less you move in time." Even better IMO: everything is moving at the max speed (c) through spacetime, and accelerating along one dimension means decelerating along other dimensions; for example, stationary objects have 0 speed in spatial dimensions but move at c through time, and photons move at c through space but are stationary along the time dimension.
- cropcirclbureau 5y ago
  Yeah, the video [0] by Fermilab that taught me this explanation blew my mind. [0] https://www.youtube.com/watch?v=A2JCoIGyGxc&list=LL&index=94 https://www.youtube.com/watch?v=A2JCoIGyGxc&list=LL&index=94
- jules 5y ago
  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.
thedstrat 5y ago
Both observers are just seeing what already happened millions of miles away. Though they see the alien fleet arriving at different times, it's not possible that the aliens are doing different things in different reference frames. They made one decision and then the two people see the results of that decision at different times
danbruc 5y ago
Rescuing free-will from the jaws of spacetime would be cool! Free will does not exist. It is logically inconsistent. Either your choice is some function of your current state and the environment you are in, then the choice is not free, or it is independent of your current state and the environment you are in, then it is not your choice in any meaningful way, it is just the result of a coin flip. You can do some mental gymnastics, define free will as being able to do what you want, define it as being free of various kinds of constraints, call it free if the choice is not computable in advance, if you can not measure all necessary variables, in practice or in theory, ... If you are happy with any of those definitions, fine, then you might have this kind of free will, but I would not consider any of those particularly interesting.
- wruza 5y ago
  I prefer to think that it's a soulspace dynamically mapped onto a physical space at stochastic points designated by a wave function density distribution. So that at any point in time we have zero, one or more random souls influencing our behavior. So it wasn't particularly me, your honor.
- V-2 5y ago
  The typical source of confusion is conflating "free" with "unpredictable". But they're not the same thing at all.
  - vidarh 5y ago
    "Unpredictable" is imprecise to the point of being meaningless. If a black box is fully deterministic to the point that you can construct a model that is entirely accurate, then there's nothing "free" about it. What you're modelling has no agency. For the notion of "free will" to have any meaning at all, it doesn't need to be "unpredictable" in the sense that it keeps confounding someone trying to predict it all the time, but it does need to deviate from predictions sometimes or you have just an automaton, and it needs to do so in a way that is fundamentally impossible to model, and it needs to do so without just injecting randomness. I've yet to see anyone present a definition of "free will" that doesn't reduce to smoke and mirrors, because that would mean coming up with some fourth category in a venn diagram of determinism, randomness and the combination of the two where they intersect, that is non-deterministic in a way that can't be explained by layering a deterministic model and randomness.
jahnu 5y ago
> "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-december-2021/ 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."
- ctw 5y ago
  Disclaimer: I’m interested in relativity and have been reading about it lately but I’m no authority. > 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.
  - jahnu 5y ago
    That's my understanding too but I am also saying that "less you move in time" needs to be more rigorously defined. As it stands above I'm not sure it makes sense, even though it might be a useful fiction to get a handle on the weirdness of it all. I'm also no authority whatsoever on the topic :)
    - 5y ago
vidarh 5y ago
"Rescuing free-will" would depend on there being something to rescue in the first place. I've yet to see a definition of free will that a casual observer would agree is "free" once you strip it of the smoke and mirrors. To me the Andromeda Paradox isn't very interesting, because the question is only problematic if you consider time as a process that events happen within simultaneously in a way that you can precisely globally order by positing some way of counting objective units of time backwards from the point the two people on earth both see the invasion force. If you instead look at the passage of time as simply the propagation of cause and effect where the propagation rate may differ depending on features of the events being propagated, then you get a dependency graph where when you interact different cause-effect chains meet. Only the nodes (events happening) matters, not the edges (the unobservable-because-nothing-interacted other than propagation). The notion of something happening simultaneously then becomes abstract - you have no objective matter of measuring something being simultaneous except by whether or not they directly interact in a given moment. You're relying on your universe behaving in a way that means you can count events to try to maintain a chronology on the basis you know how they're spaced apart. But the best we can do is count the number of such events that happens in different frames under different conditions between causal chains merging. Once you ditch the idea of "global ordering time" the "paradox" is nothing of the sort. Because in that respect talking about "when" the event in Andromeda happened is meaningless, because it is a conversation based on projecting a model of the world as it appears from one local part of that cause-effect graph to another on the basis that there's an objective global ordering outside of what we can impose by counting chronology comparing clock time when we directly interact. It may make your mental model of what happened when messy, but that is because thinking of what happened when instead of what interacted with what in which order is messy. (if there's any way of achieving faster than light travel, my totally-usupported-by-any-theory bet is that it would show our notion of time to be too static, and that it'd "bypass" the cause-and-effect paradoxes by affecting the laws of physics at the points of FTL interactions)
cormacrelf 5y ago
> 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.
- simsla 5y ago
  I've found that people also respond to thoughtful comments on blogs.
stared 5y ago
A real paradox is if you can reach two mutually-exclusive conclusions. In the special relativity theory, the order of events depends on the frame of reference. It is not much unlike 2D space if something is left or right to each other depending on a rotation. "I don't like how does the special relativity/quantum physics works" is not a paradox on its own. In this case, it just challenges our pedestrian view of time.
- vidarh 5y ago
  It's a paradox in the same sense that Zeno's paradox is. As in "if we assume the world is how we intuit it to be without thinking it through and having the proper understanding, this problem seems self-contradictory" rather than in the sense of something actually self-contradictory.
awb 5y ago
> Take the case of two people on Earth, one stationary and one travelling past in a car. They each have a different reference frame, and a different set events which make up their present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. In the reference frame of the person on Earth who is moving, the debate is still going on. But, in the reference frame of the stationary person, it is a day or so later in Andromeda, and the invasion fleet is already on it's way! I’m pretty sure this is wrong (or misleading) on multiple levels: 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. 2) The car would need to be moving at a non-insignificant fraction of the speed of light to have an observation dilution of a day or more. It’s physically impossible for humans to move that fast with our current technology. https://www.quora.com/Does-time-slow-down-in-a-moving-vehicle#:~:text=According%20to%20the%20theory%20of,to%20the%20speed%20of%20light%20 https://www.quora.com/Does-time-slow-down-in-a-moving-vehicl...! You’d have to be traveling at 0.86c for an entire day to be observing 1 day slower than a stationary person.
- Jeff_Brown 5y ago
  The reason the scenario posits an invasion from so far away is that that's about how much distance it takes for a small speed difference here to translate into a day long time difference there.
  - awb 5y ago
    You could imagine an event happening a day later from a traveling car, but that’s about it. Two people can’t actually observe an event a day later from the same reference point (Earth), and naturally the event occurs at a singular time at Andromeda’s reference point. Same with any point between Earth and Andromeda. So, if you can’t observe it at different times from the same reference point did it actually happen at different times? From the Wikipedia page on the thought experiment, check out Criticisms: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu... > The interpretations of relativity used in the Rietdijk–Putnam argument and the Andromeda paradox are not universally accepted. > Howard Stein[5] and Steven F. Savitt[6] note that in relativity the present is a local concept that cannot be extended to global hyperplanes. > Furthermore, N. David Mermin[7] states: That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity. — David Mermin, It’s About Time
irthomasthomas 5y ago
If you think about this in the quantum-mechanical framework, it appears to contradict this free-will problem. In relativity, reality is a solid block, and future events are as immutable as past (no free-will). But in QM this statement would be expressing a level of certainty which violates the measurement problem and Heisenberg's Uncertainty principle. In Penrose's recent book he posits an interesting hypothesis on the Big Bang based on this. Roughly... stuff in the observable universe appears to be slowing down, getting colder, and further away from each other. Things start hot and energetic, and slowly lose energy, slow down and disperse. So, taking this model of the universe and winding it back, you get to the Big Bang, when the universe was infinitely hot and dense. Winding the model forward, you eventually reach a state when the universe is infinitely cold and empty. This is the heat death of the universe, a state of oblivion where there is absolutely no interaction, and no stuff. This violates Heisenberg, but QM is the map, not the territory, right? So maybe, in practice, reality has a way of beating Heisenberg? Thanks to technology, we have been able to probe this question quite recently. Scientist tried to create a near-perfect vacuum, with all the energy and stuff removed, and isolated from the rest of the universe. Inside the vacuum they created an electrical circuit fed to a computer. The circuit was broken by two floating polished plates, separated by an incredibly small gap, roughly the size of a short wavelength of light. So in this test chamber photons of all sizes could exist around the two plates, but between the plates only the smallest photons could fit. If any large photons enter the chamber they would create positive pressure around the plates, pushing them together, closing the circuit and registering a result. As the scientists pushed the vacuum closer and closer to a perfect vacuum, would Heisenberg get in the way? Maybe the experiment is not powerful enough to push the vacuum close enough to really challenge him? The experiment was a success. As the vacuum increased, eventually large photons showed up outside of the plates and pushed them together. Photons where appearing out of thin air to ensure that no perfect vacuum could be attained. We call these Virtual Particles. They usually annihilate themselves before becoming "real" and observable, but if local conditions are just right, like near a black-hole, some virtual particles are lucky enough to get pulled and stretched, and this process lends them enough energy to materialize. The virtual particles are of course random, and this apparatus is actually used now to generate proper random values. You can actually tap in to the vacuum energy with an API to get your source of entropy! https://en.wikipedia.org/wiki/Casimir_effect Vacuum energy quantum RNG: https://qrng.anu.edu.au/ Back to Penrose... when the universe approaches this infinitely cold empty state, it turns out to be the same, mathematically, as the hot dense state. With everything being so distant and disconnected, the universe sort of forgets that it is big and empty. Then all it takes is the enough quantum fluctuations and virtual particles to appear in some small region of space, that they pull on each other and become real. This might, according to Penrose, trigger another Big Bang. What does this have to do with relativity and free will? If it is true that nature, at the smallest level, is fundamentally random, then the block universe containing a predetermined future cannot be real. So free will is safe? Not quite. If the Andromeda people are anything like us, their brains are subject to same laws. The electrical activity in the firing synapses, that we call thinking, must also be subject to the random fluctuations of quantum mechanics. How can they have free will, when the electrical impulses driving that will are fundamentally random and unpredictable? Weird, eh?
yoaviram 5y ago
Two alternatives for 4D spacetime: - Julian Barbour argues for timeless physics in his book...Timeless Physics. No spacetime but you don't get back free will. - David Deutsch will get you free will back, if you are willing to go along with the many-worlds interpretation. https://en.wikipedia.org/wiki/Julian_Barbour https://en.wikipedia.org/wiki/Julian_Barbour https://en.wikipedia.org/wiki/David_Deutsch https://en.wikipedia.org/wiki/David_Deutsch
philipov 5y ago
There is no room for free will in physics, period. All processes are completely deterministic. Even quantum processes might appear to be probabilistic if you look at individual particles, but the statistics are nevertheless completely deterministic: if you look at enough particles, a predictable shape will emerge. The future is set in stone and not only is there no way to change it, but the concept of changing the future doesn't even make sense. Free will is not something that exists in nature, it is something that exists in the psychology of agents with limited information about the world they operate in. Attempting to find a physical basis for free will is like trying to use an optical drive to read data off a pancake.
- time_to_smile 5y ago
  You can even leave out the 'physics' part there. "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).
  - whatshisface 5y ago
    Free will might be hard to define but it has plenty of very well-defined corollaries. For example, if there is such a thing as free will, it would not be possible to reliably predict a human being's actions in advance.
    - time_to_smile 5y ago
      > not be possible to reliably predict a human being's actions in advance. That's also true for purely deterministic systems. Basically any complex deterministic system (and quite a few relatively simple ones) you very quickly get to a point where you can't predict future behavior. On top of that, showing exactly the issues with metaphysical "free will", this corollary has a lot of constraints that are also poorly defined. For example if a person's behavior were entirely unpredictable (i.e. completely random) we would also say that they don't have free will. Therefore there is only a subset of unpredictable behaviors we would say follow from free will but that subset is just as tricky to pin down as the notion of free will itself. "Free will" only makes sense in a particular moral world view with plenty of axioms most people would agree don't hold for them. It's also worth clarifying that "free will" only becomes problematic to define in when it is posed as a metaphysical issue. We clearly have very useful, practical definitions of free will such as not holding people accountable for doing something when held at gun point.
destitude 5y ago
I was going to post this exact comment. I gave up following the twitter thread because it was so annoying.
logifail 5y ago
> Twitter is a fucking horrible format for [..] ... any intelligent thought which takes more than a couple of sentences to type out?
bmitc 5y ago
Maybe subtle, but shouldn't this be: > "The more you [are observed to] move in space, the less you [are observed to] move in time."
pxmpxm 5y ago
"This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity." My very first sentiment, having read the whole thing.
michaelcampbell 5y ago
> Twitter is a fucking horrible format for... Anything requiring more than about 350 chars, IMO. I'm really interested in that thread, but gave up after 5-6 tweets. My loss, I guess.
lofatdairy 5y ago
I was thinking the same thing about this working better as a blog post. It's so frustrating for each sentence to be it's own line and to be interrupted every moment. The content itself is excellent, but I really wish there was a better platform for it than Twitter.

Ma8ee 5y ago

Isn't the whole point that talking about "the present moment" about something very far away isn't particularly meaningful when simultaneity for spatially separated events depends on the observer?

awb 5y ago
Correct, check the criticisms on the Wikipedia page: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu...

elcomet 5y ago

You can check https://unrollthread.com/t/1482811504424542211/ https://unrollthread.com/t/1482811504424542211/ to view it as a blog post

3pt14159 5y ago

Well, another way of looking at it is that the observer is not the same as the decider. So ultimately your reference frame is only current within the locus of your own mind and any decisions you make get broadcasted out to observers in the universe. They make their own decisions about where to be, how fast to be, and so on, and from their perspective it could be yesterday from when the decider decided, but its irrelevant just as much as being farther away in 3d space gives a longer delay in ping time. Whether or not the decider has free will or not I don't think can be argued by this specific example.

mannykannot 5y ago
FWIW, I feel this is the right way to look at it. Furthermore (or perhaps I should say equivalently) the "observers" on Earth have not observed the decision, and thinking of them as such seems to be a Galilean fallacy.

darkerside 5y ago

Wouldn't all that matters here be their relative velocities to Andromeda, and not to each other? And relative to Andromeda, the person in the car might actually be going slower. Separately, I don't think chronology is broken. It's ok that there is predestination because there is no way for actions taken here to propagate back there in time to change things. If a change does somehow propagate back through a wormhole or something, it's all good, just spinning up another dimension probably...

ajuc 5y ago

At least when you think of objects moving slower than light there can't be reversing of casuality. But relativity allows for that, we just drop the faster than light solutions usually as non-physical. Recently there's been an interesting paper about what happens when we don't drop these solutions: https://arxiv.org/abs/1910.02780 https://arxiv.org/abs/1910.02780 Imagine the Andromeda fleet can move faster than light. When you look at it from Earth POV suddenly it manifests near Earth out of nothing. Looks very similar to quantum mechanics indeterminism - if alien general decided to send the fleet it's there, if he didn't - it's not there, and there's no local cause for it appearing suddenly. What the paper above explores is - starting from relativity including faster-than-light objects and trying to prevent paradoxes they derive quantum mechanics.

naasking 5y ago

> "The more you move in space, the less you move in time." Even better IMO: everything is moving at the max speed (c) through spacetime, and accelerating along one dimension means decelerating along other dimensions; for example, stationary objects have 0 speed in spatial dimensions but move at c through time, and photons move at c through space but are stationary along the time dimension.

cropcirclbureau 5y ago
Yeah, the video [0] by Fermilab that taught me this explanation blew my mind. [0] https://www.youtube.com/watch?v=A2JCoIGyGxc&list=LL&index=94 https://www.youtube.com/watch?v=A2JCoIGyGxc&list=LL&index=94
jules 5y ago
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.

thedstrat 5y ago

Both observers are just seeing what already happened millions of miles away. Though they see the alien fleet arriving at different times, it's not possible that the aliens are doing different things in different reference frames. They made one decision and then the two people see the results of that decision at different times

danbruc 5y ago

Rescuing free-will from the jaws of spacetime would be cool! Free will does not exist. It is logically inconsistent. Either your choice is some function of your current state and the environment you are in, then the choice is not free, or it is independent of your current state and the environment you are in, then it is not your choice in any meaningful way, it is just the result of a coin flip. You can do some mental gymnastics, define free will as being able to do what you want, define it as being free of various kinds of constraints, call it free if the choice is not computable in advance, if you can not measure all necessary variables, in practice or in theory, ... If you are happy with any of those definitions, fine, then you might have this kind of free will, but I would not consider any of those particularly interesting.

wruza 5y ago
I prefer to think that it's a soulspace dynamically mapped onto a physical space at stochastic points designated by a wave function density distribution. So that at any point in time we have zero, one or more random souls influencing our behavior. So it wasn't particularly me, your honor.
V-2 5y ago
The typical source of confusion is conflating "free" with "unpredictable". But they're not the same thing at all.
- vidarh 5y ago
  "Unpredictable" is imprecise to the point of being meaningless. If a black box is fully deterministic to the point that you can construct a model that is entirely accurate, then there's nothing "free" about it. What you're modelling has no agency. For the notion of "free will" to have any meaning at all, it doesn't need to be "unpredictable" in the sense that it keeps confounding someone trying to predict it all the time, but it does need to deviate from predictions sometimes or you have just an automaton, and it needs to do so in a way that is fundamentally impossible to model, and it needs to do so without just injecting randomness. I've yet to see anyone present a definition of "free will" that doesn't reduce to smoke and mirrors, because that would mean coming up with some fourth category in a venn diagram of determinism, randomness and the combination of the two where they intersect, that is non-deterministic in a way that can't be explained by layering a deterministic model and randomness.

jahnu 5y ago

> "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-december-2021/ 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."

ctw 5y ago
Disclaimer: I’m interested in relativity and have been reading about it lately but I’m no authority. > 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.
- jahnu 5y ago
  That's my understanding too but I am also saying that "less you move in time" needs to be more rigorously defined. As it stands above I'm not sure it makes sense, even though it might be a useful fiction to get a handle on the weirdness of it all. I'm also no authority whatsoever on the topic :)
  - 5y ago

vidarh 5y ago

"Rescuing free-will" would depend on there being something to rescue in the first place. I've yet to see a definition of free will that a casual observer would agree is "free" once you strip it of the smoke and mirrors. To me the Andromeda Paradox isn't very interesting, because the question is only problematic if you consider time as a process that events happen within simultaneously in a way that you can precisely globally order by positing some way of counting objective units of time backwards from the point the two people on earth both see the invasion force. If you instead look at the passage of time as simply the propagation of cause and effect where the propagation rate may differ depending on features of the events being propagated, then you get a dependency graph where when you interact different cause-effect chains meet. Only the nodes (events happening) matters, not the edges (the unobservable-because-nothing-interacted other than propagation). The notion of something happening simultaneously then becomes abstract - you have no objective matter of measuring something being simultaneous except by whether or not they directly interact in a given moment. You're relying on your universe behaving in a way that means you can count events to try to maintain a chronology on the basis you know how they're spaced apart. But the best we can do is count the number of such events that happens in different frames under different conditions between causal chains merging. Once you ditch the idea of "global ordering time" the "paradox" is nothing of the sort. Because in that respect talking about "when" the event in Andromeda happened is meaningless, because it is a conversation based on projecting a model of the world as it appears from one local part of that cause-effect graph to another on the basis that there's an objective global ordering outside of what we can impose by counting chronology comparing clock time when we directly interact. It may make your mental model of what happened when messy, but that is because thinking of what happened when instead of what interacted with what in which order is messy. (if there's any way of achieving faster than light travel, my totally-usupported-by-any-theory bet is that it would show our notion of time to be too static, and that it'd "bypass" the cause-and-effect paradoxes by affecting the laws of physics at the points of FTL interactions)

cormacrelf 5y ago

> 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.

simsla 5y ago
I've found that people also respond to thoughtful comments on blogs.

stared 5y ago

A real paradox is if you can reach two mutually-exclusive conclusions. In the special relativity theory, the order of events depends on the frame of reference. It is not much unlike 2D space if something is left or right to each other depending on a rotation. "I don't like how does the special relativity/quantum physics works" is not a paradox on its own. In this case, it just challenges our pedestrian view of time.

vidarh 5y ago
It's a paradox in the same sense that Zeno's paradox is. As in "if we assume the world is how we intuit it to be without thinking it through and having the proper understanding, this problem seems self-contradictory" rather than in the sense of something actually self-contradictory.

awb 5y ago

> Take the case of two people on Earth, one stationary and one travelling past in a car. They each have a different reference frame, and a different set events which make up their present. Now imagine that there is an alien government in Andromeda debating a possible invasion of Earth. In the reference frame of the person on Earth who is moving, the debate is still going on. But, in the reference frame of the stationary person, it is a day or so later in Andromeda, and the invasion fleet is already on it's way! I’m pretty sure this is wrong (or misleading) on multiple levels: 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. 2) The car would need to be moving at a non-insignificant fraction of the speed of light to have an observation dilution of a day or more. It’s physically impossible for humans to move that fast with our current technology. https://www.quora.com/Does-time-slow-down-in-a-moving-vehicle#:~:text=According%20to%20the%20theory%20of,to%20the%20speed%20of%20light%20 https://www.quora.com/Does-time-slow-down-in-a-moving-vehicl...! You’d have to be traveling at 0.86c for an entire day to be observing 1 day slower than a stationary person.

Jeff_Brown 5y ago
The reason the scenario posits an invasion from so far away is that that's about how much distance it takes for a small speed difference here to translate into a day long time difference there.
- awb 5y ago
  You could imagine an event happening a day later from a traveling car, but that’s about it. Two people can’t actually observe an event a day later from the same reference point (Earth), and naturally the event occurs at a singular time at Andromeda’s reference point. Same with any point between Earth and Andromeda. So, if you can’t observe it at different times from the same reference point did it actually happen at different times? From the Wikipedia page on the thought experiment, check out Criticisms: https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument#Criticisms https://en.m.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argu... > The interpretations of relativity used in the Rietdijk–Putnam argument and the Andromeda paradox are not universally accepted. > Howard Stein[5] and Steven F. Savitt[6] note that in relativity the present is a local concept that cannot be extended to global hyperplanes. > Furthermore, N. David Mermin[7] states: That no inherent meaning can be assigned to the simultaneity of distant events is the single most important lesson to be learned from relativity. — David Mermin, It’s About Time

irthomasthomas 5y ago

If you think about this in the quantum-mechanical framework, it appears to contradict this free-will problem. In relativity, reality is a solid block, and future events are as immutable as past (no free-will). But in QM this statement would be expressing a level of certainty which violates the measurement problem and Heisenberg's Uncertainty principle. In Penrose's recent book he posits an interesting hypothesis on the Big Bang based on this. Roughly... stuff in the observable universe appears to be slowing down, getting colder, and further away from each other. Things start hot and energetic, and slowly lose energy, slow down and disperse. So, taking this model of the universe and winding it back, you get to the Big Bang, when the universe was infinitely hot and dense. Winding the model forward, you eventually reach a state when the universe is infinitely cold and empty. This is the heat death of the universe, a state of oblivion where there is absolutely no interaction, and no stuff. This violates Heisenberg, but QM is the map, not the territory, right? So maybe, in practice, reality has a way of beating Heisenberg? Thanks to technology, we have been able to probe this question quite recently. Scientist tried to create a near-perfect vacuum, with all the energy and stuff removed, and isolated from the rest of the universe. Inside the vacuum they created an electrical circuit fed to a computer. The circuit was broken by two floating polished plates, separated by an incredibly small gap, roughly the size of a short wavelength of light. So in this test chamber photons of all sizes could exist around the two plates, but between the plates only the smallest photons could fit. If any large photons enter the chamber they would create positive pressure around the plates, pushing them together, closing the circuit and registering a result. As the scientists pushed the vacuum closer and closer to a perfect vacuum, would Heisenberg get in the way? Maybe the experiment is not powerful enough to push the vacuum close enough to really challenge him? The experiment was a success. As the vacuum increased, eventually large photons showed up outside of the plates and pushed them together. Photons where appearing out of thin air to ensure that no perfect vacuum could be attained. We call these Virtual Particles. They usually annihilate themselves before becoming "real" and observable, but if local conditions are just right, like near a black-hole, some virtual particles are lucky enough to get pulled and stretched, and this process lends them enough energy to materialize. The virtual particles are of course random, and this apparatus is actually used now to generate proper random values. You can actually tap in to the vacuum energy with an API to get your source of entropy! https://en.wikipedia.org/wiki/Casimir_effect Vacuum energy quantum RNG: https://qrng.anu.edu.au/ Back to Penrose... when the universe approaches this infinitely cold empty state, it turns out to be the same, mathematically, as the hot dense state. With everything being so distant and disconnected, the universe sort of forgets that it is big and empty. Then all it takes is the enough quantum fluctuations and virtual particles to appear in some small region of space, that they pull on each other and become real. This might, according to Penrose, trigger another Big Bang. What does this have to do with relativity and free will? If it is true that nature, at the smallest level, is fundamentally random, then the block universe containing a predetermined future cannot be real. So free will is safe? Not quite. If the Andromeda people are anything like us, their brains are subject to same laws. The electrical activity in the firing synapses, that we call thinking, must also be subject to the random fluctuations of quantum mechanics. How can they have free will, when the electrical impulses driving that will are fundamentally random and unpredictable? Weird, eh?

yoaviram 5y ago

Two alternatives for 4D spacetime: - Julian Barbour argues for timeless physics in his book...Timeless Physics. No spacetime but you don't get back free will. - David Deutsch will get you free will back, if you are willing to go along with the many-worlds interpretation. https://en.wikipedia.org/wiki/Julian_Barbour https://en.wikipedia.org/wiki/Julian_Barbour https://en.wikipedia.org/wiki/David_Deutsch https://en.wikipedia.org/wiki/David_Deutsch

philipov 5y ago

There is no room for free will in physics, period. All processes are completely deterministic. Even quantum processes might appear to be probabilistic if you look at individual particles, but the statistics are nevertheless completely deterministic: if you look at enough particles, a predictable shape will emerge. The future is set in stone and not only is there no way to change it, but the concept of changing the future doesn't even make sense. Free will is not something that exists in nature, it is something that exists in the psychology of agents with limited information about the world they operate in. Attempting to find a physical basis for free will is like trying to use an optical drive to read data off a pancake.

time_to_smile 5y ago
You can even leave out the 'physics' part there. "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).
- whatshisface 5y ago
  Free will might be hard to define but it has plenty of very well-defined corollaries. For example, if there is such a thing as free will, it would not be possible to reliably predict a human being's actions in advance.
  - time_to_smile 5y ago
    > not be possible to reliably predict a human being's actions in advance. That's also true for purely deterministic systems. Basically any complex deterministic system (and quite a few relatively simple ones) you very quickly get to a point where you can't predict future behavior. On top of that, showing exactly the issues with metaphysical "free will", this corollary has a lot of constraints that are also poorly defined. For example if a person's behavior were entirely unpredictable (i.e. completely random) we would also say that they don't have free will. Therefore there is only a subset of unpredictable behaviors we would say follow from free will but that subset is just as tricky to pin down as the notion of free will itself. "Free will" only makes sense in a particular moral world view with plenty of axioms most people would agree don't hold for them. It's also worth clarifying that "free will" only becomes problematic to define in when it is posed as a metaphysical issue. We clearly have very useful, practical definitions of free will such as not holding people accountable for doing something when held at gun point.

destitude 5y ago

I was going to post this exact comment. I gave up following the twitter thread because it was so annoying.

logifail 5y ago

> Twitter is a fucking horrible format for [..] ... any intelligent thought which takes more than a couple of sentences to type out?

bmitc 5y ago

Maybe subtle, but shouldn't this be: > "The more you [are observed to] move in space, the less you [are observed to] move in time."

pxmpxm 5y ago

"This would be more fun in a blog post. Twitter is a fucking horrible format for a complex analysis of special relativity." My very first sentiment, having read the whole thing.

michaelcampbell 5y ago

> Twitter is a fucking horrible format for... Anything requiring more than about 350 chars, IMO. I'm really interested in that thread, but gave up after 5-6 tweets. My loss, I guess.

lofatdairy 5y ago

I was thinking the same thing about this working better as a blog post. It's so frustrating for each sentence to be it's own line and to be interrupted every moment. The content itself is excellent, but I really wish there was a better platform for it than Twitter.