3
$\begingroup$

I read the page here: Is the Uncertainty Principle valid for information about the past?, but I am still somewhat confused.

If you measure the momentum/position (with uncertainty) of a particle, what could you infer mathematically about its past? Its past momentum/position? Or rather some wave function as there could be infinite different systems with different possible wave functions that are collapsed to generate the measured result?

$\endgroup$
  • 1
    $\begingroup$ Keep in mind that in the uncertainty principle, "uncertainty" does not mean "there is a definite value, but we are just unsure about it." $\endgroup$ – Aaron Stevens Oct 1 '19 at 23:01
  • $\begingroup$ @AaronStevens Einstein tried to show what you said but the evidence suggested that there is more likely than not no hidden variables. $\endgroup$ – frt132 Oct 2 '19 at 1:22
  • $\begingroup$ "Uncertainties" in the uncertainty principle are just standard deviations of measurements of observables of a quantum system. $\endgroup$ – Aaron Stevens Oct 2 '19 at 2:41
  • $\begingroup$ I understand it as a result of limitation from Fourier transforms. Regardless, so far there has been no evidence that hidden variables exist. $\endgroup$ – frt132 Oct 2 '19 at 5:05
  • 1
    $\begingroup$ @Andrei, local explanations for EPR-type correlations is something that realists wish for, but the Bell inequalities and related experiments do indicate that hidden variables cannot explain the observed correlations, no? $\endgroup$ – Marius Ladegård Meyer Oct 2 '19 at 7:30
1
$\begingroup$

No, the uncertainty principle is a statement about the localization of a quantum state when represented in position vs. momentum space (more generally, the eigenbases of two non-commuting observables). So long as no measurements take place, the quantum state can be evolved completely deterministically forward and backward in time if you know the Hamiltonian. This is what physicists mean when they say quantum mechanics is deterministic.

Any state, even one translated forward or backward in time using the Hamiltonian, will obey the uncertainty principle: namely the spread of the state in position space must obey a certain inequality in union with the spread of the state in momentum space. This does have some net effect on the outcome of measurements of that quantum state, but that is not the same thing as the state itself.

The state itself evolves determanistically forward or backward until a measurement occurs. Of course, measurements on the state like "what's your position" or "what's your momentum" will also obey the uncertainty principle, because the outcome of measurements (the part of quantum mechanics that is random) are probabilistically determined by the amplitude of the wavefunction over the eigenspace of the measurement operator. That is to say, the uncertainty principle is not related to randomness of quantum mechanics in any way other than requiring that the state will always have some spread over the eigenbases of non-commuting operators.

$\endgroup$
  • 1
    $\begingroup$ I saw a quote on research gate that 'The question whether from a complete knowledge of the past we can predict the future, does not arise because a complete knowledge of the past involves a self-contradiction.', how can you know the Hamiltonian of the system? $\endgroup$ – frt132 Oct 2 '19 at 15:11
  • $\begingroup$ By measuring a particle, can you infer how the system evolved to that particular state (past Hamiltonian)? $\endgroup$ – frt132 Oct 2 '19 at 15:18
  • $\begingroup$ you know the Hamiltonian because we understand the particles/fields involved and we know how to construct a Hamiltonian based on their mutual and self interactions. A single measurement on a particle is never enough to determine the entire superposition. Quantum State Tomography should point you in the right direction. Paraphrasing: "A single measurement on a system determines the system's current state after the measurement (a measurement alters the state), quantum tomography works to determine the complete state(s) prior to measurements." $\endgroup$ – Bobak Hashemi Oct 3 '19 at 4:38
  • $\begingroup$ Thanks, but from the Wikipedia article you linked, 'By measuring one of the quadratures of a large number of identical quantum states will give us a probability density corresponding to that particular quadrature.', it seems somewhat mostly impractical/impossible to know the past superposition as one would need to measure copies of same thing involved. $\endgroup$ – frt132 Oct 3 '19 at 9:31
0
$\begingroup$

If you happened to know the quantum state of the universe as well as the Hamiltonian, then you could use the Schrodinger equation to know the quantum state at both past and future (!) times.

However, that quantum state would still not have both well-defined position and momentum, for instance.

$\endgroup$
  • $\begingroup$ The history is not unique to an observer as infinite ways of quantum states evolvement could correspond to the same outcome one measures? $\endgroup$ – frt132 Oct 2 '19 at 1:48
  • $\begingroup$ @frt132 that is considering a different set up. What I said is true. $\endgroup$ – Ryan Thorngren Oct 3 '19 at 18:16
0
$\begingroup$

The uncertainty principle puts a limit on what can be known, not on what can exist. It is possible that nature is deterministic but our description of it it is probabilistic due to our incomplete knowledge. So the answer to your question is "no". This is also true about the future. Heisenberg's principle does not imply that the future is undetermined, only that we cannot predict it with certainty.

In principle you could infer the past of a particle by performing successive position measurements. Two such measurements, together with an accurate timing of them, allow you to also calculate the momentum of the particle. But this is only possible for the time before the first measurement and the second one, because each measurement alters the momentum. You also need to make some assumptions about how the particle moves, say in straight lines.

$\endgroup$
  • $\begingroup$ "Heisenberg's principle does not imply that the future is undetermined, only that we cannot predict it with certainty." We certainly can predict the values of compatible variables with certainty, and we can determine the wave function with certainty. $\endgroup$ – Marius Ladegård Meyer Oct 2 '19 at 7:33
  • $\begingroup$ Sure, but what you can predict with certainty does not allow you to predict the future in general with certainty, so my original statement is correct. $\endgroup$ – Andrei Oct 2 '19 at 11:42
  • $\begingroup$ Say you detect an electron, could you calculate the possibility that a second ago the electron was created by photon decay somewhere? Or that the electron has been existing and moving for a long time? $\endgroup$ – frt132 Oct 2 '19 at 15:26
  • $\begingroup$ frt132, no, I don't think you can. $\endgroup$ – Andrei Oct 3 '19 at 3:55

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.