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In the special theory of relativity, each event is a point in 4d spacetime. And we can represent our life as a world line in the spacetime. Then, if we somehow find out the mathematical equation of somebody's world line, then can his future be predicted?

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    $\begingroup$ How is this question not about mainstream physics?! Although the OP has used the words "if we somehow find out", the fact remains that people have already found out the exact equation that is followed by a timelike word-line, namely, $\dfrac{d^2x^\mu}{d\tau^2}=f^\mu$. Of course, if one actually intends to find an explicit solution to this equation of motion then they should concern themselves with what the $f^\mu$ actually is (and that would also not help because the world is ultimately quantum mechanical!)--but the OP is not asking anything outside of mainstream physics! $\endgroup$ – Dvij Mankad Nov 5 '18 at 17:27
  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/63811/2451 and links therein. $\endgroup$ – Qmechanic Nov 5 '18 at 19:24
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As Anna v has pointed out, this is not something unique to SR. Even classical physics allows for us to "predict the future". Anna's answer gives why this is unreasonable due to QM, but even if that could be overlooked (it can't though), there are other problems.

You are made up of cells, which are made of molecules, which are made of atoms, and so on. To predict your future you would need to know the world lines of all of your parts. All of your biochemical reactions and decisions would need to be predicted (assuming that your decisions can be determined from the interactions of these different parts, but biology is very complex, so this is pretty much an impossible task already). You (I'm assuming) interact with others on a daily basis, so you would need to do this for them as well. But they interact with others as well. And on and on. Nothing is in isolation. To predict the future of one thing we must essentially predict the future of all things.

So really it's impossible to predict the future this way. It doesn't come down to finding a single math equation for a single world line. I would say you have better luck consulting a psychic at this point.

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    $\begingroup$ To perfectly model the universe, you're gonna need a second, bigger universe to hold the computation. Having just an exact copy which you could then observe probably won't work: inside it, there will be a copy of you, observing... the third universe? The original one? And of course, the behaviour of the combined system is again computationally unpredicatble. $\endgroup$ – Joker_vD Nov 5 '18 at 12:05
  • $\begingroup$ @Joker_vD we're still not sure that there is no system that irreversibly loses information. If such a system would exist, we could create a universe to hold the computation for our universe, minus all the parts that would be lost anyway. Then we would possibly be able to simulate the entire interesting universe (the part that isn't lost forever, for which we have no reason to care). We're also not 100% sure of the efficiency of the universe. We assume it's efficient and optimal, because existing observations suggest so, but what if it isn't entirely optimal? $\endgroup$ – Andrei Nov 5 '18 at 14:07
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    $\begingroup$ This is similar to why we can only predict the weather moderately well. It's hard to model a large number of complex interactions in a way that produces decent predictions in the future. $\endgroup$ – JMac Nov 5 '18 at 16:26
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    $\begingroup$ @JMac Don't forget about chaos and precision of our knowledge about the "initial conditions" $\endgroup$ – Aaron Stevens Nov 5 '18 at 16:28
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    $\begingroup$ I thought maybe the calculated metric could take into account Jupiter's position as it depends on time. I am just curious because all the exemple I saw was an interaction between only 2 bodies, where was is usualy static. This might be better suited for a new question. $\endgroup$ – Maxter Nov 5 '18 at 19:17
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If you have the mathematics of a moving body then its future is predictable in classical mechanics. It would be the same in the extension of special relativity though for a person it is a big IF.

Nature though is not classical, classical emerges from an underlying level of quantum mechanics, which is inherently probabilistic. Therefore there is no mathematical equation of somebody's world line. One could fit a world line up to the present after the fact, but the future is probabilistic because it is quantum mechanical and only probabilities can be predicted . The Heisenberg uncertainty, HUP is a convenient summary.

To clarify after comments:

Any recording of a world line means an interaction has to take place. The world line of the past has been recorded , left a trace of interactions that were picked up from the probability distributions according to the quantum mechanical laws. A future world line will be one instance at each (x,y,z,t) picked from a probability distribution, decided at each point.

The HUP is a convenient envelope in describing uncertainties, as any world line of a particle or an object will have both a space envelope and a momentum/energy envelope. If there is no momentum there is no activity, and according to the HUP the space dimensions will be undefined.

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    $\begingroup$ which still does not explain all observations that we can make, so there's still a chance that god doesn't play dice, although it sure looks like it has quite a gambling problem. $\endgroup$ – Andrei Nov 5 '18 at 13:55
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    $\begingroup$ I still understand the Heisenberg uncertainty principle the way that we cannot measure both the position and the momentum of an object (especially small one like an elementary particle) precisely at the same time. But this does not mean that the world is inherently non-deterministic. As I understand it, hidden variable theories (like De Broglie–Bohm) are still possible. $\endgroup$ – pabouk Nov 5 '18 at 14:52
  • $\begingroup$ @pabouk No , hidden variable theories are not compatible with special relativity and data see also en.wikipedia.org/wiki/Bell%27s_theorem . The HUP is just an envelope of the commutation relations of the operators of quantum mechanics, which are inherent in the probabilistic system that describes the underlyng level of nature. $\endgroup$ – anna v Nov 5 '18 at 15:13
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    $\begingroup$ Could you just refer to the probabilistic nature of measurements in QM? I think that is a stronger point, since outcomes of measurements are still uncertain in the absence of any sort of uncertainty principle that relates the measurements of two observables whose operators do not commute. $\endgroup$ – Aaron Stevens Nov 5 '18 at 15:23
  • $\begingroup$ @AaronStevens To record something, there should be an interaction. To record a world line in the future means future interactions, which are inherently probabilistic. There is a probability for an interaction to happen. I see all these as equivalently provable from each other, the HUP, commutation realations, probabilities of interaction, $\endgroup$ – anna v Nov 5 '18 at 15:33
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Your thoughts are similar to that of Laplace's Demon, and may be better suited for a philosophy board.

Wikipedia sums it up well:

According to determinism, if someone (the Demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated ...

Laplace notably refers to the best model(s) of physics available to him at the time (he refers to the "tiniest atom").

Despite our better models now, the sensor and computational capabilities required for a perfect model to predict the future faster than realtime are quite unrealistic.

It's still a wonderful thought experiment.

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  • $\begingroup$ While you are correct that this is an old philosophical discussion, an aspect of the concept of "free will", it only applies to deterministic physics. Because quantum mechanics is not deterministic, it would be impossible to calculate the actual future from the present even with infinite computing power. $\endgroup$ – Paul Sinclair Nov 5 '18 at 17:26
  • $\begingroup$ There is a 365 Tomorrows story around where this experiment was constructed, with the observational (and predictional) volume constrained to a box with a volume comparable to the ISS. It did not end well. $\endgroup$ – Draco18s no longer trusts SE Nov 5 '18 at 18:33

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