It’s a really interesting question actually. In my previous answer I was alluding to the fact that computers typically use pseudorandom number generators, whose output appears random but is actually entirely deterministic.
In real life I think a similar situation holds. First we have to make a distinction between a system having randomness; a completely unpredictable outcome and being chaotic; where the outcome is theoretically predictable but varies significantly with even tiny changes in input.
For instance, most people would say a dice roll is random, but physics would suggest it is chaotic instead. If you could role the dice twice in exactly the same way, you’d get the same result both times as there is nothing that could change the outcome.
For there to be true randomness, something would have to change the energy level of the dice, and we’ve controlled for that by requiring both throws to be exactly the same.
However, you cannot role the dice exactly the same way twice as exactly means having the entire universe the same, which is obviously impossible.
Applying this reasoning to everything leads to the conclusions that a) there is no randomness, just chaotic results, and b) that this is indistinguishable from true randomness as we cannot determine the starting condition of any chaotic system accurately enough to predict its outcome.
I know that quantum physics has something to say about this, but I’m not sufficiently knowledgeable to fully grasp what it is saying.
So, ultimately I don’t believe in ‘true randomness’, but in a chaotic universe instead.
In real life I think a similar situation holds. First we have to make a distinction between a system having randomness; a completely unpredictable outcome and being chaotic; where the outcome is theoretically predictable but varies significantly with even tiny changes in input.
Yes, thank you for putting it so nicely into words. I was already aware of that distinction.
I’m studying physics right now and trying to organize my thoughts around that. I remember we talked about some mechanical contraption that exhibits non-deterministic (i.e. purely random) behavior due to the equations of motion having non-unique solution. If I remember correctly, it was a kind of “knife standing on its tip right at the edge of a cliff”-edge condition. There’s two solutions to that: It stands still or it falls down. There’s two distinctly different solutions because the equations of motion are non-continuous, i.e. even for the tiniest change in position, the net force changes from 0 to 1g.
Apart from that, there’s some more “pure random” stuff that I’m investigating into right now, like quantum stuff (as you mentioned). But there’s at least one more example that I’d like to think about:
A human/robot cannot fully predict their own future. That is because if they could, they could become aware of it and decidedly act against it. For example, if I predict that I will eat an avocado tomorrow, I might stop myself from doing that. So the prediction becomes wrong. In a certain sense, therefore one cannot predict their own actions. This isn’t due to a lack in accuracy, but it’s fundamentally impossible. I guess. Let me hear your thoughts! Your words are calm and collected; you seem to know stuff.
As I said, it’s an interesting question! I think I’ve found a paper describing something like the scenario you mentioned (Dhar, A. (1993). Nonuniqueness in the solutions of Newton’s equation of motion. American Journal of Physics, 61(1), 58–61. doi:10.1119/1.17411). It’s a apparently shows that for certain conditions (such as the balanced knife you mentioned, or a particle in a field that would accelerate it away from the origin proportionally to it’s distance) Newton’s equations of motion have non-unique solutions, although I confess that the author rather lost me during some of his leaps in mathematics. The discussion section is interesting, a couple of key conclusions stood out to me: ‘In this sense we may say that Newton’s equation has a unique solution even for singular forces like x1/3 but x(0)=0 and derivative(x(0))=0 in such cases do not uniquely specify the initial state.’ and ‘Infinitesimal disturbance in position or velocity will change the state and one of the other solutions will become effective.’
From what I have understood from the paper, the author seems to be mostly pointing out that there are certain conditions under which Newton’s equations do not have a unique solution, but that in reality a deterministic, but chaotic, outcome will occur due to infinitesimal disturbances. Ultimately, no matter how carefully you balance the knife, it’s going to fall over, and the direction it falls will be determined by a multitude of forces rather than pure chance.
@[email protected] has also made a thoughtful reply regarding quantum field theory and it’s implications on determinism, and I need to respond to that too as it’s a fascinating, if baffling, topic.
Your question about predicting your own future is interesting; you’re making the assumption that a prediction must continue to be true after the point at which it is made, but I would suggest that you can resolve the apparent contradiction by considering that any prediction of the future is only true at the instant it is made. After all, if someone else predicted your future, wrote it down, but did not tell you, you would eat the avocado, however seen as you changed the conditions of your future by gaining additional information the result changed. If you predicted your future a second time, directly after having resolved to not eat the avocado, the prediction would have you not eating it.
If we assume the universe is deterministic, and that we have the ability to perfectly replicate it and run that replica forward in time without time passing in our universe it would seem that we could accurately predict the future of our universe just be seeing what happened in the replica. However, that would involve the replica creating it’s own replica as it would evolve in exactly the same way as our universe. That replica would create it’s own replica, and so on. I’m not quite sure of what the implications of that are, and it’s late here, so I’m going to have to call it a night, but if if could be done it would be a clear way to distinguish between a random or non-deterministic universe and a chaotic one. If the predictions sometimes proved incorrect it would suggest true randomness rather than just a chaotic system.
Bell’s theorem demonstrates that you cannot have a deterministic theory that would also be Lorentz invariant, that is to say, compatible with special relativity and the speed of light limit. The speed of light limit is very well tested over and over again, and no one to this day has ever been able to construct even a single mathematical model that could even approximately reconstruct the predictions of quantum field theory in a way that is deterministic. That suggests that any deterministic theory would actually make quantifiably different predictions than quantum field theory, and yet we don’t have any evidence that its predictions are violated, and quantum field theory is verified to 12 decimal places of precision.
I don’t really understand your point about the dice. If you have two “quantum” dice that are exactly the same, they are not guaranteed to land on the same thing, and that is precisely what it means to be nondeterministic, that even if all the initial conditions are the same, the outcome can be different. Yes, we cannot make the whole universe the same throughout the experiment, but to make sense of this, you cannot speak in vague philosophy but need to actually specify in mathematical terms what parts of the universe you think are determining the outcome, which, again, any attempt to specify such a thing would require contradicting the predictions of quantum field theory.
My issue with your argument is that, whether or not you intended this or not, what you are undeniably arguing is that all our current physical theories are currently wrong and making the wrong predictions, and they need to be adjusted to make the right predictions, and you are basing this off of what is ultimately a philosophical criticism, i.e. that it is not deterministic and you think it should be, without even having a viable model of what this determinism would look like. It just seems far too speculative to me.
Yes, you can always make the argument that “our old theories have been proven wrong before, like Newton’s gravity was replaced with Einstein’s gravity, so we shouldn’t put much stock into our current theories,” but I just find this unconvincing, as you can make this argument in literally any era, and thus it completely negates the possibility of using science to understand the properties of nature. Every scientific theory would have to always be interpreted as just something tentative that can’t tell us anything about nature, because it’s bound to be replaced later, and instead we’re just left arguing vague philosophy not based on anything empirical.
I will readily admit that if I base my understanding of reality on our best physical sciences of the era, those can be overturned and I could be shown to be wrong. However, I still find it to be the most reasonable position as opposed to trying to “intuit” our way to an understanding of nature. The person who strongly defended the Newtonian picture of nature prior to Einstein was later shown to be wrong, yes, but he was still far more correct than the majority of those who insisted upon trying to derive an understanding of nature entirely from intuition/philosophy. I am with Heisenberg who argued that until we actually have any experimental evidence that violates the predictions of quantum field theory and can only be corrected with the introduction of hidden variables, then positing their existence is pointless metaphysical speculation, not derived from anything empirical.
It’s a really interesting question actually. In my previous answer I was alluding to the fact that computers typically use pseudorandom number generators, whose output appears random but is actually entirely deterministic.
In real life I think a similar situation holds. First we have to make a distinction between a system having randomness; a completely unpredictable outcome and being chaotic; where the outcome is theoretically predictable but varies significantly with even tiny changes in input.
For instance, most people would say a dice roll is random, but physics would suggest it is chaotic instead. If you could role the dice twice in exactly the same way, you’d get the same result both times as there is nothing that could change the outcome.
For there to be true randomness, something would have to change the energy level of the dice, and we’ve controlled for that by requiring both throws to be exactly the same.
However, you cannot role the dice exactly the same way twice as exactly means having the entire universe the same, which is obviously impossible.
Applying this reasoning to everything leads to the conclusions that a) there is no randomness, just chaotic results, and b) that this is indistinguishable from true randomness as we cannot determine the starting condition of any chaotic system accurately enough to predict its outcome.
I know that quantum physics has something to say about this, but I’m not sufficiently knowledgeable to fully grasp what it is saying.
So, ultimately I don’t believe in ‘true randomness’, but in a chaotic universe instead.
Yes, thank you for putting it so nicely into words. I was already aware of that distinction.
I’m studying physics right now and trying to organize my thoughts around that. I remember we talked about some mechanical contraption that exhibits non-deterministic (i.e. purely random) behavior due to the equations of motion having non-unique solution. If I remember correctly, it was a kind of “knife standing on its tip right at the edge of a cliff”-edge condition. There’s two solutions to that: It stands still or it falls down. There’s two distinctly different solutions because the equations of motion are non-continuous, i.e. even for the tiniest change in position, the net force changes from 0 to 1g.
Apart from that, there’s some more “pure random” stuff that I’m investigating into right now, like quantum stuff (as you mentioned). But there’s at least one more example that I’d like to think about:
A human/robot cannot fully predict their own future. That is because if they could, they could become aware of it and decidedly act against it. For example, if I predict that I will eat an avocado tomorrow, I might stop myself from doing that. So the prediction becomes wrong. In a certain sense, therefore one cannot predict their own actions. This isn’t due to a lack in accuracy, but it’s fundamentally impossible. I guess. Let me hear your thoughts! Your words are calm and collected; you seem to know stuff.
As I said, it’s an interesting question! I think I’ve found a paper describing something like the scenario you mentioned (Dhar, A. (1993). Nonuniqueness in the solutions of Newton’s equation of motion. American Journal of Physics, 61(1), 58–61. doi:10.1119/1.17411). It’s a apparently shows that for certain conditions (such as the balanced knife you mentioned, or a particle in a field that would accelerate it away from the origin proportionally to it’s distance) Newton’s equations of motion have non-unique solutions, although I confess that the author rather lost me during some of his leaps in mathematics. The discussion section is interesting, a couple of key conclusions stood out to me: ‘In this sense we may say that Newton’s equation has a unique solution even for singular forces like x1/3 but x(0)=0 and derivative(x(0))=0 in such cases do not uniquely specify the initial state.’ and ‘Infinitesimal disturbance in position or velocity will change the state and one of the other solutions will become effective.’
From what I have understood from the paper, the author seems to be mostly pointing out that there are certain conditions under which Newton’s equations do not have a unique solution, but that in reality a deterministic, but chaotic, outcome will occur due to infinitesimal disturbances. Ultimately, no matter how carefully you balance the knife, it’s going to fall over, and the direction it falls will be determined by a multitude of forces rather than pure chance.
@[email protected] has also made a thoughtful reply regarding quantum field theory and it’s implications on determinism, and I need to respond to that too as it’s a fascinating, if baffling, topic.
Your question about predicting your own future is interesting; you’re making the assumption that a prediction must continue to be true after the point at which it is made, but I would suggest that you can resolve the apparent contradiction by considering that any prediction of the future is only true at the instant it is made. After all, if someone else predicted your future, wrote it down, but did not tell you, you would eat the avocado, however seen as you changed the conditions of your future by gaining additional information the result changed. If you predicted your future a second time, directly after having resolved to not eat the avocado, the prediction would have you not eating it.
If we assume the universe is deterministic, and that we have the ability to perfectly replicate it and run that replica forward in time without time passing in our universe it would seem that we could accurately predict the future of our universe just be seeing what happened in the replica. However, that would involve the replica creating it’s own replica as it would evolve in exactly the same way as our universe. That replica would create it’s own replica, and so on. I’m not quite sure of what the implications of that are, and it’s late here, so I’m going to have to call it a night, but if if could be done it would be a clear way to distinguish between a random or non-deterministic universe and a chaotic one. If the predictions sometimes proved incorrect it would suggest true randomness rather than just a chaotic system.
Bell’s theorem demonstrates that you cannot have a deterministic theory that would also be Lorentz invariant, that is to say, compatible with special relativity and the speed of light limit. The speed of light limit is very well tested over and over again, and no one to this day has ever been able to construct even a single mathematical model that could even approximately reconstruct the predictions of quantum field theory in a way that is deterministic. That suggests that any deterministic theory would actually make quantifiably different predictions than quantum field theory, and yet we don’t have any evidence that its predictions are violated, and quantum field theory is verified to 12 decimal places of precision.
I don’t really understand your point about the dice. If you have two “quantum” dice that are exactly the same, they are not guaranteed to land on the same thing, and that is precisely what it means to be nondeterministic, that even if all the initial conditions are the same, the outcome can be different. Yes, we cannot make the whole universe the same throughout the experiment, but to make sense of this, you cannot speak in vague philosophy but need to actually specify in mathematical terms what parts of the universe you think are determining the outcome, which, again, any attempt to specify such a thing would require contradicting the predictions of quantum field theory.
My issue with your argument is that, whether or not you intended this or not, what you are undeniably arguing is that all our current physical theories are currently wrong and making the wrong predictions, and they need to be adjusted to make the right predictions, and you are basing this off of what is ultimately a philosophical criticism, i.e. that it is not deterministic and you think it should be, without even having a viable model of what this determinism would look like. It just seems far too speculative to me.
Yes, you can always make the argument that “our old theories have been proven wrong before, like Newton’s gravity was replaced with Einstein’s gravity, so we shouldn’t put much stock into our current theories,” but I just find this unconvincing, as you can make this argument in literally any era, and thus it completely negates the possibility of using science to understand the properties of nature. Every scientific theory would have to always be interpreted as just something tentative that can’t tell us anything about nature, because it’s bound to be replaced later, and instead we’re just left arguing vague philosophy not based on anything empirical.
I will readily admit that if I base my understanding of reality on our best physical sciences of the era, those can be overturned and I could be shown to be wrong. However, I still find it to be the most reasonable position as opposed to trying to “intuit” our way to an understanding of nature. The person who strongly defended the Newtonian picture of nature prior to Einstein was later shown to be wrong, yes, but he was still far more correct than the majority of those who insisted upon trying to derive an understanding of nature entirely from intuition/philosophy. I am with Heisenberg who argued that until we actually have any experimental evidence that violates the predictions of quantum field theory and can only be corrected with the introduction of hidden variables, then positing their existence is pointless metaphysical speculation, not derived from anything empirical.