Predetermination in quantum theory and information theory

[Green dwarf]

TL;DR

Is the future determined by the present state of the universe?

My understanding of quantum theory and information theory is that, given complete information on the state of the universe at present, it is possible to predict its state at all times in the future and past. 3 questions: 1: is this true? 2: how are quantum-probabilistic outcomes accounted for? 3: given the uncertainty principal, is it actually possible to completely know the present state of the universe?

 

[vanhees71]

In quantum theory complete knowledge of the initial state means that you know the statistical operator of the system at time $t=0$, and then using the dynamics of quantum theory you know this state for all times. So the answer to 1 is yes with the caveat that it only applies to situations, where the quantum-theoretical laws are known. That's not the case for the gravitational interaction, and since it plays a dominating role for the evolution of the universe as a whole, we don't know how to describe it quantum theoretically to begin with.

The answer to 2 is also very simple: The very meaning of the quantum state is probabilistic, i.e., knowing the statistical operator of the system you only know the probabilities for the outcome of any measurement of an observable of the system ("Born's rule"), i.e., even with complete knowledge of the state, this doesn't imply that all observables take determined values and (answering 3) there's no state, where all observables take determined values simultaneously.

 

[Green dwarf]

Thank you vanhees71. Can I ask a further question? My understanding is that a wave function could in theory be defined for the whole universe and that this function evolves in a deterministic way. Does that mean that the uncertainty in the system doesn't increase over time? The alternative being that the outcome in the next moment has many possibilities, each of those has many possibilities in the moment after and so on, producing a sort of butterfly effect and meaning that the distant future has much greater uncertainty than the near future.

 

[Demystifier]

Summary: Is the future determined by the present state of the universe?

My understanding of quantum theory and information theory is that, given complete information on the state of the universe at present, it is possible to predict its state at all times in the future and past. 3 questions: 1: is this true? 2: how are quantum-probabilistic outcomes accounted for? 3: given the uncertainty principal, is it actually possible to completely know the present state of the universe?

Different quantum interpretations answer those questions differently and there is no consensus among experts which interpretation is the "right" one. If you are interested in various interpretations, then you have to ask the question in the foundations and interpretations subforum. The only way to answer those questions in an interpretation-independent way is to take a purely instrumental point of view, which only takes for granted those views that have a direct support in experiments. From this purely instrumental point of view, the answers to your questions are as follows.

1. No, it is not true that we can predict the state at all times in future and past. Experimentally, nobody succeeded to do that for all times.
2. At times at which we cannot predict the state, which usually happens when we measure the system, we compute the probability from a mathematical formula called "Born rule".
3. No, it is not possible to completely know the present state of the universe. To know it one would need to measure everything in the universe, which is impossible.

 

[martinbn]

I would argue that depending on how the question is understood the answers might be different.

1. Yes, you can predict the future becasue the Schrödinger's equation has a well posed initial value problem. For the past it is more complecated but in a sense you can also say yes.
2. The probabilities enter when values of observables are conserned.
3. The Heisenberg rpinciple is not an obsticle becasue in QM the state doesn't conssist of observables like on classical mechanics.

 

[PeterDonis]

1. Yes, you can predict the future becasue the Schrödinger's equation has a well posed initial value problem.

But the dynamics of QM (if we don't adopt any particular interpretation) is not just the Schrödinger equation. Solving the initial value problem for the Schrödinger equation only predicts things up to the next measurement.

For the past it is more complecated but in a sense you can also say yes.

Same issue as above: you can only "retrodict" back to the previous measurement (or preparation).

 

[martinbn]

But the dynamics of QM (if we don't adopt any particular interpretation) is not just the Schrödinger equation. Solving the initial value problem for the Schrödinger equation only predicts things up to the next measurement.

Not if it is the whole universe. You cannot get out and make a measurement on it.

Same issue as above: you can only "retrodict" back to the previous measurement (or preparation).

I meant that for some equations the forward in time initial value problem is different from the backwards in time one.

 

[PeroK]

It seems to me that talking about a property of a mathematical model that cannot feasibly be tested has little meaning. Even if the universe has a meaningful wave function within whatever theory and even if that wavefunction evolves deterministically within the theory, unless there is some way to test that aspect of the model by a theoretically plausible experiment, then it has little meaning to say that it is so.

I think the same about the classical physicists who proclaimed a clockwork universe. They confused the mathematical model with the "reality" of physical phenomena. There was and is no way to test whether the universe evolves deterministically. Whether it's classical or quantum is not the key issue. It's an untestable proposition, IMO.

 

[PeterDonis]

Not if it is the whole universe.

QM can only be applied to the whole universe under certain interpretations. In this thread we are only considering aspects that are independent of any interpretation.

 

[martinbn]

QM can only be applied to the whole universe under certain interpretations. In this thread we are only considering aspects that are independent of any interpretation.

But the question is specifically about the state of the universe.

 

[vanhees71]

Of course, we are discussing an impossible scenario here. There's no way to measure the entire universe, because it's not even clear, how to separate the entire universe from the measurement device/observer. Any prediction of such a scenario also cannot be tested, because you cannot repreat the measurement at all, because you cannot start many universes with the same initial condition to get statistics to verify the probabilistic predictions of any quantum theory.

I don't think that this is a physically well-defined scenario, and thus it belongs anyway in the more speculative subsection about interpretations (philosophy) of quantum theory.

 

[martinbn]

Of course, we are discussing an impossible scenario here. There's no way to measure the entire universe, because it's not even clear, how to separate the entire universe from the measurement device/observer. Any prediction of such a scenario also cannot be tested, because you cannot repreat the measurement at all, because you cannot start many universes with the same initial condition to get statistics to verify the probabilistic predictions of any quantum theory.

I don't think that this is a physically well-defined scenario, and thus it belongs anyway in the more speculative subsection about interpretations (philosophy) of quantum theory.

I don't think this has to be the case. There could in principle be consequences that lead to observations. For example the evolution of the state based on the equations may rule out some posibilities for the global structure of the universe simply because such a state cannot evolve from the curant sate.

 

[PeterDonis]

But the question is specifically about the state of the universe.

Then the answer to the question is interpretation dependent.

 

[PeterDonis]

There could in principle be consequences that lead to observations.

On some QM interpretations it is impossible to even have "observations" of the universe as a whole, since such observations would have to be made from outside the universe.

 

[PeterDonis]

My understanding of quantum theory and information theory is that, given complete information on the state of the universe at present, it is possible to predict its state at all times in the future and past. 3 questions: 1: is this true? 2: how are quantum-probabilistic outcomes accounted for? 3: given the uncertainty principal, is it actually possible to completely know the present state of the universe?

As my exchange with @martinbn and @Demystifier's comment in post #4 show, the answer to this question as you ask it is interpretation dependent. Discussions of QM interpretations belong in the interpretations subforum, not this one.

If you did not intend your question to be specifically about QM applied to the whole universe, but only more generally about QM applied to some physical system, I would suggest that you clarify your question.

 

[jedishrfu]

It seems this is a good time to close this thread as the OP's original question has been answered.

Thank you all for contributing here.