For example, you go to a website that generates a random number. You get the number 8. What would happen if you went back in time a few minutes, and repeated the same actions. Would you get the same number, or would it change?
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5Are you trying to ask whether the universe is deterministic? Also, note that "random" numbers are usually pseudo-random. – ACuriousMind Mar 25 '16 at 20:12
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1@ACuriousMind Unless said website was random.org. – tpg2114 Mar 25 '16 at 20:14
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@ACuriousMind Yes, I mean a website like random.org. Yes, I do mean whether the universe is deterministic, but in this case in a simplified version. – The Broken Ace Mar 25 '16 at 20:18
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I think this is all about semantics and what you call random. Is a roulette wheel random to you? – Greg Petersen Mar 25 '16 at 20:34
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I assume that you mean go back in time to the same instant that you first generated the number 8? If the number generated depended on the time only (and was not determined by the number of visitors at the web site, this would change because there would be one extra visitor), even then probably not because you would presumably also have to apply the same switch dynamics to the terminal to ensure that the signal to the web site was identical to the original try. – jim Mar 25 '16 at 20:59
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That's the "free will" problem and, needless to say, all you can get out of it is to declare that "free will" and all sorts of "experiments" that would require to turn time back are outside of science. – CuriousOne Mar 25 '16 at 22:09
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A quantum number generator based on collapse of wave function could give you a different number. If your number generator is say based on measurements of spins of electrons, if you go to a point before wave function collapse I think you might get a different result. But this scenario is unrealistic so it's all just speculation. – Ilya Lapan Mar 26 '16 at 09:29
3 Answers
There are solutions to the field equations of General Relativity which support a form of time travel, but it is restricted to closed time-like loops.
In this case you would obtain the same random number each time.
The conditions required for these solutions are not physically achievable, as currently understood, and at this point quantum gravity is still in the future. If it ever is achieved, all of the random numbers will come up '42'.

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One characteristic of the universe, so far as we know, is that it is self consistent. If one observer measures the interval between two events, all other observers will get the same value.
A quantum mechanical system may not be deterministic, and outcomes must be described in terms of probabilities. But if one observer measures a value, all other observers will measure values consistent with it. E.G. an entangled pair of electrons may have total spin 0. If one is measured as spin up, the other will be measured as spin down.
"Going back in time" is usually science fiction. There are all kinds of paradoxes that matter in science fiction, but haven't been observed.
There are theoretical paths around spinning black holes that lead back in time. But nobody has tried to follow one. So we don't know what would happen. One can speculate, but usually this leads to science fiction. At best, it is opinion.

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Your question brings up the ages old debate of the deterministic vs non deterministic nature of the universe.
Computers, by themselves, are incapable of coming up with a random number because there is no mathematical function or algorithm that can produce a random number. So, we programmers were stuck using what we call pseudorandom numbers, which are numbers generated by applying an algorithm to a seed number to turn it into a value that is as random as possible.
Random number generators (or RNG for short) are procedures a program can call to obtain a pseudorandom number. RNGs are generally built into BIOSes, Operating systems, or can be specifically implemented by a programmer in his program if he has specific needs. The RNG uses a seed number to produce a random number that has more digits than the seed it was fed. however the same number being fed into the RNG will output the same value again. This is why it is called pseudorandom.
Now, for the longest time, RNGs were using the computer's internal clock, which is very precise,so it returns a number that has many decimals, as a seed for its random algorithm. This worked pretty well on old, slow computers, But computers evolve very quickly, and old RNGs based on the clock speed of old PCs weren't updated, and this quickly became a problem, because if your program needed to come up with random numbers very quickly, let's say a loop that gets a random number than prints it on screen than loops again and again you'd end up with series of 4 or 5 or even more times the same supposedly random number, following each other, before changing to another value which was repeated the same number of times and so on. (ex:22227777333399992222444433337777) This is because the program called an old random number generator, which was built for older computers that had less precise clocks, so the RNG was only looking for the first few decimals (lets say 4) of the number returned by the clock, but on today's fast computers that have far more precise clock (that have let's say eight digits instead of 4) and run many more cycles per second, when the program gets to the next iteration after printing a number and calls the RNG again only the last of the 8 digits of the clock has been incremented, but the first 4 that the RNG is looking for have remained the same, hence the same value is fed to the RNG as a seed, so it outputs the same value as before.
So, now that you understand how classic random generators are closely tied to TIME itself you'll easily understand why if you went back in time let's say before the year 2000 you'd end up in a period where the random number was directly tied to the date and time, and so using the same device at exactly the same date and time (to Planck time scale) would end up with exactly the same number.
Now, this was a MAJOR problem for us programmers. RNGs are everywhere, from Determinating who will win at a Casino's slot machine to who will win that ultra rare and expansive piece of gear in your favorite MMORPG those pieces of software need to be reliable, because an exploit could be costly for the operators of the hacked device. This is why in the recent years vendors have begun selling web based random number generation services which are based on what science considers being true random events. For example, a service called HotBits generates random numbers by timing successive pairs of radioactive decays detected by a Geiger-Müller tube interfaced to a computer. In my sense it is difficult to imagine a more random value, and programmers can call that service within their program and get real random numbers through internet.
So if you traveled back to more recent years, and requested a random number to a computer using such a service at exactly the same point in time, I'm not certain if you'd end up with a different value, IT comes to ask if the nature of the universe is deterministic or not, or if Laplace's Demon would work which is an age old question that unfortunately does not yet have an answer... Einstein and Bohr argued a lot about this....

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Thanks for the answer. I found everyone else's answer very informative as well, but I can relate to this one, as a programmer myself. – The Broken Ace Mar 27 '16 at 00:26