Does the wavefunction evolve only to the future?

[Gerinski]

Layman here. It is often said that the pure fundamental theories do not contain any arrow of time, they are fully reversible in time.

But regarding Shrodinger's equation, it describes the evolution of the wavefunction in time. As I understand it, if we consider a static particle after a measurement, let's say event A, its wavefunction will start spreading from that spacetime event location in a spherical shape at the speed of light until it undergoes a new measurement, at which the wavefunction sphere will collapse at some point given probabilistically by the equation.

Is such a sphere expanding at light speed truly spherical, pointing also towards the past as well as to the future? So that there would be a probability of the next measurement finding that particle in a spacetime coordinate which lies in the past of event A, as much as finding it in a spacetime coordinate which lies in the future of event A?

Because if the answer is no, that the wavefunction evolution is not really a sphere, but only a hemisphere from event A towards the future but not towards the past, wouldn't it mean that the very arrow of time is already contained in such a wavefunction evolution equation? Selecting that only coordinates in the future can be canditates to finding the particle from event A, but never coordinates in the past?

Thanks !

 

[BvU]

Hello intermediate layman,

You are mixing up tidbits from QM with tidbits from relativity. If the detection of a particle is event A, the next detection is an event in the future of A. Hence the word next.

Wavefuctions do not spread with the speed of light.

And the Schroedinger equation doesn't say anything about the direction of time. You can replace t by -t and all you have to do is put that sign on the other side too.

 

[A. Neumaier]

the Schroedinger equation doesn't say anything about the direction of time.

But he was talking about measurement to make his case.

The measurement process, however, is a dissipative process that prefers a time direction since it only works from the past towards the future.

Thus while the fundamental processes (described by relativistic quantum field theory) are reversible in time, measurement is not a fundamental process. It involves approximations that are valid only under the assumption of the observed arrow of time and a corresponding increase of entropy with time.

 

[Jilang]

Quantum evolution is reversible. The rest not so.

 

[atyy]

Yes, if you include collapse, wave function evolution is not time reversible.

Whether the unitary, time reversible Schroedinger evolution is more fundamental than collapse is a matter of interpretation.

 

[A. Neumaier]

Whether the unitary, time reversible Schroedinger evolution is more fundamental than collapse is a matter of interpretation.

No.

One can derive collapse in open systems related to measurement as an approximation form unitary dynamics, while one cannot derive the unitary, time reversible Schroedinger evolution from collapse but has to postulate it in addition. This tells what is fundamental.

Moreover, collapse is tied to measurement, and it is not even possible to say on the fundamental level what the latter means without having already a valid dynamics.

 

[atyy]

No.

One can derive collapse in open systems related to measurement as an approximation form unitary dynamics, while one cannot derive he unitary, time reversible Schroedinger evolution form collapse but has to postulate it in addition. This tells what is fundamental.

Moreover, collapse is tied to measurement, and it is not even possible to say on the fundamental level what the latter means without having already a valid dynamics.

Sorry, don't agree.

 

[A. Neumaier]

Sorry, don't agree.

What does it mean to measure a position, in fundamental terms?
What counts as a measurement?
When precisely does the measurement happen?
Is it instantaneous or does it take time?
If the latter, at which time does the collapse happen?
Is is objective, or does it depend on the judgment of an observer?
Which observer?
If unobserved, does a system collapse?
Why, if it depends on measurement?
Before the first physicist existed to take a measurement, was there collapse?
If yes, on the basis of what did the collapses happen?
If no, why do we base our theory of stellar evolution on dissipative laws?

Lots of unresolved and basically unsolvable questions if measurement and collapse are taken as fundamental!
This doesn't make collapse an acceptable basis for a fundamental process.

Of course you may disagree, but then your understanding of what is fundamental is very strange.