# Uncertainty principle asymmetric with respect to time?

We take for granted the fact that we can infer more about the past than the future. Considering the only difference between past and future is entropy, I wonder if the reason it is possible to have records of the past and not the future is entropy related.

At the quantum level is the uncertainty principle asymmetric with respect to time?
For example, if we have snapshot of a moment of time(with no data of the past or future) does the uncertainty principle permit us to infer more knowledge in the direction of decreasing entropy(i.e the past)?

No. The double slit experiment is a clear example of past uncertainty. The interference pattern demonstrates that each particle that hits the detector took all possible paths to get from source to detector. The inference from this is that the present is the result of the sum over all possible histories.

Considering the only difference between past and future is entropy, ...

That is already incorrect. There are many asymmetries that don't involve entropy. Also, the universe is not in a thermal equilibrium, so it's questionable if the concept of thermodynamic entropy is applicable at all. The problem of the physical arrow of time is much more complex than you suggest here.

Cheers,

Jazz

That is already incorrect. There are many asymmetries that don't involve entropy.

Jazz

Ok, thanks.

What other laws of physics are time asymmetric?
(I thought it was just the 2nd law of thermodynamics)

cgk
What other laws of physics are time asymmetric?
(I thought it was just the 2nd law of thermodynamics)
The 2nd law of thermodynamics is not time-asymmetric either. If you propagate a macroscopic ensemble backwards in time, entropy *also* increases.

Entropy is not a property of the microscopic physical system, it is a property of the macroscopic ensemble-description of a system of which we have only limited information; and the microscopic information loss per time increment, in the macroscopic description, is equal in both directions.

Maybe you have to separate the Uncertainty Principle as a concept from the probability as a calculation of an attribute?
Probability attributes seem to be asymmetric with respect to time in the sense that the probability attribute before the fact of an event kind of dissappears or becomes irrelevant after the fact of an event, which takes a final known state.

Jano L.
Gold Member
For example, if we have snapshot of a moment of time(with no data of the past or future) does the uncertainty principle permit us to infer more knowledge in the direction of decreasing entropy(i.e the past)?
This perhaps depends on the interpretation of quantum theory. Heisenberg in his book talked about something similar. He suggested that when we prepare ray of electrons of known momentum ##p## and measure the position of the electron ##r^*## and time of its detection ##t^*##, assuming the electron had the momentum ##p## prior the measurement we can calculate the trajectory of the electron for values ## t < t^*## (although he said this trajectory is only hypothetical), but not for future values ##t > t^*##, since the measurement influences the subsequent momentum in an unknown way and leaves it at uncertain value.

vanhees71
Gold Member
Interestingly enough, there has been a new paper in PRL, where the authors give a definition for the $\Delta x$ and $\Delta p$ such that a Heisenberg-uncertainty principle of the usual form $\Delta x \Delta p \geq \hbar/2$ can be interpreted as a measurement-disturbance relation in Heisenberg's sense. The problem with Heisenberg's original article is that it is not well defined what's meant by "disturbance" of one observable by the measurement of another observable that is incompatible to it. It depends on how you define the "disturbance measure", whether an uncertainty relation of the above form holds or not:

Paul Busch, Pekka Lahti, Reinhard F. Werner, Proof of Heisenberg's error-disturbance relation
http://dx.doi.org/10.1103/PhysRevLett.111.160405
http://arxiv.org/abs/1306.1565

Some time ago, I tried to discuss the contrary point of view that the error-disturbance relation does not hold: