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Does relativity of simultaneaty imply determinism? Let's say an alien in a distant part of the universe travels towards us at a certain speed at this moment(i.e. from our perspective that alien is moving 'now').

To make the question more rigorous let me introduce some math here. Let's say an alien spaceship is moving towards us at speed v, and let v be measured as a fraction of the lightspeed to simplify things a bit. Then according to relativity that alien will have a now slice that is slanted toward the future in the following way:

$$\Delta t=\Delta x v^{2} $$ Measured in my frame of reference. Now imagine the alien is 200 lightyears from earth and travels towards us with a speed of Sqrt[2]/2 c, then that alien will consider events that lie 100 years in our future as part of his present. Now consider 3 events:

A: Me thinking about this potential alien.

B: that alien travelling and thinking about earth.

C: Donald Duck getting elected president in the year 2117.

A and B are simultaneous for me, while B and C are simultaneous for the alien. Now here comes my main point, if whatever happens in the future isn't determined than whatever goes on 'now' for that alien isn't well defined either. The issue at hand isn't that the alien can't know what happens on earth 'now'(and for him that's 2117), witch he absolutely can't since info can't travel faster than light, the issue is something must happen now and that something ought to be well defined.

I get the feeling here that if we drop determinism we should also drop the notion of a well defined concept of 'now'. If the future isn't determined, someone else could win the presidential election in 2117. So we genuinely have 2 options, either he wins or his challenger and both can happen. But that implies that from the POV of the alien, the statement 'Donald Duck has won the election' can't even be true or false, not only can't he know this but it's in some sort of superposition of the 2 until the event reaches his lightcone. Even an statement like 'now president Donald Duck is president or he isn't president of a powerful country on earth' can't be true now! Neither is true even from his POV, since if one was true the reality for someone on our now slice would contain that future event on our planet implying it would have to happen!

Even beter we should even drop any notion of 'then' for all events outside our lightcone. If the future isn't determined, whatever that alien considers to have happened 50 years ago on earth isn't definite either. But then the same goes for us. Whatever the curiosity rover is doing on Mars now isn't well defined, until the light from Mars reaches earth. I can't talk about events on the Andromeda galaxy that are happening now, since those events are considered the future for a guy in the bus that happens to be moving away from that galaxy(and for him my 'now' is his 'future', if only by a tiny amount).

Philosophically, having a now and past that isn't well defined seems very troubling and seems to point to a POV similar to that that certain things haven't happened until they are observed. I think the scientific consensus is that we can say something is going on on the surface of the sun 'now' even though that light hasn't reached us. In 8 minutes we may know if that statement was true experimentally, but if it is at least you would think that that scientist could say: 'See I was correct 8 minutes ago'.

However I don't see how we can reconcile in determinism with a well defined concept of now and even of past events outside your lightcone. But if we accept determinism we run into quantum mechanical trouble. Let's say I put a particle in some potential and just let it be. I don't know anything about where it is, I may now something about the probability to measure it's position in a certain range but that's it. Now say i'm going to measure it's position in 10 minutes and drink a cup of coffee in the meantime. I can't predict it's position, even in principle according to Heisenberg's interpretation. Even if I know literally everything about the system I still can't calculate(within a margin of error) where I will find that particle like in classical systems.

However, there does exist a frame of reference in the universe on my now slice where that measurement(that will happen in 10 minutes) is part of the present or past, but that implies the measurement is determined all along! I am definately, with 100% certainty going to measure it in a definite spot, I only don't know where. That right there just went right against the conventional interpretation of QM...

So what are your thoughts on this? Am I missing something here, is it true that if we drop determinism we should drop the concept of 'now' and 'the past' outside my lightcone as well? And not in the sense that I shouldn't say anything about it because I don't know anything about it(because FTL travel is impossible), but because much much more fundamentally it doesn't have a definite state.

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  • $\begingroup$ I'm voting to close this question as off-topic because it is philosophical and should be moved to Philosophy SE. $\endgroup$
    – Conifold
    Nov 25, 2017 at 4:22
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    $\begingroup$ I understand why some may argue this is philosophical, but I don't agree. I think the experimentalist POV that leads to that conclusion is too strict. I am asserting a logical relation here, that if SR is true something else must logically follow, even if that something can't be tested experimentally. I don't see hoe discussing the logical consequences of a well tested theory is not a physics discussion, even if those particular consequences can't be tested directly. Discussing spaghettification and internal black hole events falls in the same category, yet isn't regarded as phylosofy. $\endgroup$
    – Dirkboss
    Nov 25, 2017 at 12:39
  • $\begingroup$ Until you analyze the situation in terms of the time-like or space-like nature of the interval involved (I think which is Lorentz invariant) you're just going to confuse yourself. Of course you can do nothing to influence the outcome of events that are space-like separated from you; that has nothing to do with determinism or lack thereof, it's just about the parts of space-time that you are able to communicate with in time to affect events. $\endgroup$
    – dmckee --- ex-moderator kitten
    Nov 25, 2017 at 18:14
  • $\begingroup$ If you are asserting that determinism follows from SR logically then you are making a logical mistake, and a trivial one. Not even relativity of simultaneity follows from SR logically as Lorentz's alternative interpretation shows. You may have better luck saying that SR makes determinism more plausible, but that depends on non-logical (heuristic, epistemic, aesthetic) assumptions and preferences which exactly make the issue philosophical. And a major problem for you is that QFT is based on SR but is interpreted as indeterministic. $\endgroup$
    – Conifold
    Nov 26, 2017 at 21:33
  • $\begingroup$ A local event that hasn't happened yet locally cannot be part of the alien's present, even if the alien is traveling at a significant speed toward earth. That seems to be part of your logic based on what is "simultaneous" for each participant. The alien cannot influence or even see Donald Duck's election until after it has happened, and the election cannot affect the alien until after it has happened. Simultaneity is relative, but since causality is not relative, relativity cannot prove determinism. $\endgroup$
    – Asher
    Nov 26, 2017 at 22:42

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What you have formulated here is essentially a version of the Rietdijk-Putnam argument (or, as Penrose puts it, the "Andromeda Paradox"). See wikipedia for discussion: https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument

As a physical theory, Special Relavity does not prove or disprove anything. That's not how physical theories work. Physical theories make concrete predictions and then we see if those predictions correspond with experimental observations. Whether special relativity says anything about determinism based on this argument is more in the realm of the philosophy of science than actual science. What special relativity does give us is a way to predict the outcome of experiments, and those outcomes have always held up.

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    $\begingroup$ Prove may be the wrong word, imply would be a better choice. Since FTL is impossible this particular aspect of reality defies experimental verification, still I do consider the question to have some physical significance. Even if A can't be experimentally proven, the fact that A follows from theory B of whom a lot of other aspects have been verified experimentally is still very significant $\endgroup$
    – Dirkboss
    Nov 25, 2017 at 3:56

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