Can Quantum Mechanics Really Support Time Reversibility?

[binbots]

I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is a particle always a particle once observed?
Sorry if this question has been asked before but searching for this topic on the internet just leads to a bunch of pseudo-science.

 

[Ninyes]

I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is a particle always a particle once observed?
Sorry if this question has been asked before but searching for this topic on the internet just leads to a bunch of pseudo-science.

Collapse of a wave function happens when a wave meets an impenetrable barrier. Slowed time observation will lead to rise of potential barrier height, hence those barriers that were penetrable will slowly rise to being impenetrable.

I don't know if this is correct.

 

[atyy]

I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea? If we could see time go backwards would we see particles turning back into waves? Is a particle always a particle once observed?

Quantum mechanics does have a time direction because of the collapse of the wave function when a measurement occurs. In between measurements, the wave function evolves reversibly, which is what people are usually talking about when they say that quantum mechanics has no time direction. However, there is no collapse of the wave function in an approach like the Many-Worlds interpretation, so a direction of time may not be fundamental in that approach.

 

[ZapperZ]

I have often heard that in quantum mechanics time has no direction. That the physics works the same going backwards in time than forwards.

This starting premise is false. Classical mechanics may have that property, but QM doesn't. There are many phenomena that are described via broken time-reversal symmetry.

Zz.

 

[binbots]

Thank you. I assumed this to be the case. It seems particles are always used to describe this time reversal though. If we knew the position and momentum of every particle etc etc. I guess this is where I am getting my CM and QM mixed up.

 

[AlexCaledin]

... the physics works the same going backwards in time than forwards. How does the wave function collapse of a particle follow this idea?

But why the physics must necessarily go somewhere in time? It may well be that the wavefunction simply exists in the space-time, stretched far into past and future; and, when we observe some local event, the whole wavefunction, past and future, reduces instantly, according to the new measurement. So it's only the build-up of our observations that grows from past to future...

 

[bhobba]

But why the physics must necessarily go somewhere in time?

Because in physics time is what a clock measures and they always go forward.

It may well be that the wavefunction simply exists in the space-time, stretched far into past and future; and, when we observe some local event, the whole wavefunction, past and future, reduces instantly, according to the new measurement. So it's only the build-up of our observations that grows from past to future...

The very nature of a wave-function as used in the Schroedinger Equation precludes such a peculiar view. If it simply exists in space-time (whatever that is supposed to mean) how do you take its derivative wrt to time?

Thanks
Bill

 

[binbots]

But Doesn't time only appear to move forward because we are using it as a measuring tool? A clock repeats over and over again. Is the number sequence 1,2,1,2,1,2,1,2 etc moving forward? If you don't count the tics does it have a direction? If we think of time in the block universe way then time is more like a ruler than a clock. Every tic already exist. A ruler doesn't have a direction. It can be used backwards, upside down, or at any starting point. But because we always put a zero in the same place we start to believe it has a direction. Maybe the fact that we are constantly using time as a measurement is perpetuating the illusion of time.

 

[atyy]

But Doesn't time only appear to move forward because we are using it as a measuring tool? A clock repeats over and over again. Is the number sequence 1,2,1,2,1,2,1,2 etc moving forward? If you don't count the tics does it have a direction? If we think of time in the block universe way then time is more like a ruler than a clock. Every tic already exist. A ruler doesn't have a direction. It can be used backwards, upside down, or at any starting point. But because we always put a zero in the same place we start to believe it has a direction. Maybe the fact that we are constantly using time as a measurement is perpetuating the illusion of time.

In the Copenhagen interpretation of quantum mechanics, it certainly could be that the arrow of time is an illusion. However, the Copenhagen interpretation assumes we see the illusion, and gives us a theory that makes use of our illusion.

In other interpretations such as Bohmian mechanics or Many-Worlds (BM has open problems, MWI may have problems), the Copenhagen interpretation is emergent from something which may not have a fundamental arrow of time.

Take a look at Sean Carroll's Arrow of Time FAQ.
http://preposterousuniverse.com/eternitytohere/faq.html

 

[bhobba]

But Doesn't time only appear to move forward because we are using it as a measuring tool?.

Appear to move forward? It moves forward from its very definition - time is what a clock measures. There are things called clocks and they have a readout that increases - it never goes back.

Why do clocks never go back- that is a deep question - the answer having to do with thermodynamics:
http://www.informationphilosopher.com/solutions/scientists/feynman/past_and_future.html
http://en.wikipedia.org/wiki/Arrow_of_time#The_thermodynamic_arrow_of_time

Note the thermodynamic analysis of a ratchet and pawl in the first link. It can only go forward - and the reason is thermodynamics. The same with clocks.

Thanks
Bill

 

[atyy]

Appear to move forward? It moves forward from its very definition - time is what a clock measures. It's a primitive - its not measured by anything else.

Why do clocks move forward - that is a deep question - the answer having to do with thermodynamics:
http://www.informationphilosopher.com/solutions/scientists/feynman/past_and_future.html
http://en.wikipedia.org/wiki/Arrow_of_time#The_thermodynamic_arrow_of_time

Note the thermodynamic analysis of a ratchet and pawl in the first link. It can only go forward - and the reason is thermodynamics. The same with clocks.

I'm not sure, but I think Feynman's analysis is consistent with classical physics, where the second law does not necessarily reflect fundamental irreversibility in the dynamics. The second law reflects special initial conditions and our lack of knowledge. So a classical clock doesn't have to move forward by definition.

On the other hand, in the Copenhagen interpretation, it seems we can't run the dynamics backwards, because of collapse.

 

[bhobba]

I'm not sure, but I think Feynman's analysis is consistent with classical physics, where the second law does not necessarily reflect fundamental irreversibility in the dynamics.

That's an old one.

Entropy increases - its not a law in the usual sense - its simply that the number of non orderly configurations are much much greater than the orderly ones.

That's why when we look at videos going backward we recognise immediately its going backwards eg we dont' see a glass suddenly reassemble when smashed - its not that the laws of physics forbid it - its simply very very unlikely.

Now its a while since I read that excerpt from the Feynman lectures, but if memory serves me correctly, the ratchet and pawl analysis depends crucially on this observation.

Time moves forward not because the laws of physics can't be reversed - but because chaos is coming - its written into thermodynamics. Its true because the universe tends to do the most likely thing - which is in a sense tautological - but intuitively appealing.

Thanks
Bill

 

[binbots]

Thanks for the information. You guys were answering my follow up question before I could even ask them. So let me see if I got this straight. All fundamental laws work in both directions in CM. Entropy gives time a direction but entropy is not a law just a probability. QM has irreversible processes so time may have a direction. In GR time can be viewed as no direction and past and future are real.

 

[bhobba]

In GR time can be viewed as no direction and past and future are real.

No.

But if you want to pursue it then the relativity forum is the place.

Thanks
Bill

 

[atyy]

No.

But if you want to pursue it then the relativity forum is the place.

I thought the answer was yes. There is no direction of time in GR, and as a classical theory, past and future (arbitrarily assigned) are real.

 

[bhobba]

I thought the answer was yes. There is no direction of time in GR,

I think there is a difference between the laws being time symmetric and time still goes forward.

Anyway the relativity forum is the best place to discuss it.

Thanks
Bill

 

[vanhees71]

Thanks for the information. You guys were answering my follow up question before I could even ask them. So let me see if I got this straight. All fundamental laws work in both directions in CM. Entropy gives time a direction but entropy is not a law just a probability. QM has irreversible processes so time may have a direction. In GR time can be viewed as no direction and past and future are real.

This is a very tricky question, and many things get easily mixed up with it, as is the case here ;-).

There are several "arrows of time". The most fundamental one is due to causality, which is assumed to be valid for all physics. There's no way to prove it from some simpler considerations but it is necessary to have natural laws at all and thus to have natural sciences as we understand them. Time is then a directed one-dimensional continuum, labeling the sequence of causes of dynamical processes in nature.

Another "arrow of time" is the thermodynamical one, which is defined by increasing entropy of macroscopic systems. It is independent from the question whether the natural laws are time-reversal invariant or not. Common knowledge indeed is that they are not since the weak interaction violates time-reversal invariance (as space-reflection, charge conjugation and CP invariance, while as a local microcausal QFT with stable ground state fulfills CPT invariance). The Boltzmann H-theorem, i.e., the statetment that the direction of time defined by the increase (or better non-decrease) of entropy follows from the Boltzmann equation using the weak principle of detailed balance, which is derived from the unitarity of the S-matrix, describing the transition-probability rates between asymptotic scattering states.

 

[TrickyDicky]

The Boltzmann H-theorem, i.e., the statetment that the direction of time defined by the increase (or better non-decrease) of entropy follows from the Boltzmann equation using the weak principle of detailed balance, which is derived from the unitarity of the S-matrix, describing the transition-probability rates between asymptotic scattering states.

As you probably know the H-theorem ultimately fails to derive a time arrow purely from time-reversible dynamics, there is an assumption about uncorrelated and independent of position velocities that introduces time asymmetry and doesn't follow from time-invariant mechanics(although it is an assumption that o the other hand also resembles special initial conditions and in that sense it would be also implicit in formalisms derived from a least action principle like the Lagrangian/Hamiltonian). More particularly in quantum theory there seems to always be some implicit breaking of time symmetry introduced be it in the form of collapse in measurements, series truncation in perturbative calculations or Fermi's golden rule irreversibility.

 

[vanhees71]

Yes, you do not derive another arrow of time than the causal one. It also doesn't matter whether your interactions are time-reversal invariant or not. The H theorem follows from unitarity of the S-matrix alone.

In quantum mechanics the arrow of time is also the causal one. The directedness of time is inherent in the very foundations of all dynamical models of physics.

 

[TrickyDicky]

Yes, you do not derive another arrow of time than the causal one. It also doesn't matter whether your interactions are time-reversal invariant or not. The H theorem follows from unitarity of the S-matrix alone.

In quantum mechanics the arrow of time is also the causal one. The directedness of time is inherent in the very foundations of all dynamical models of physics.

True.
My point was that the causal arrow is inherent to the dynamical models because it is an obvious empirical feature of our universe, but it is not often clear from the formalism how it is implemented because it usually slips in as some unspoken assumption besides unitarity that might be simply that a measurement has happened, or random phase or molecular chaos...

 

[TrickyDicky]

It would be interesting to clarify how is this universally valid time direction related to the concepts of explicit and implicit time-dependence. The concept of time translation invariance can be understood in two ways, and only in one of them it implies time reversibility, it is my understanding that in the classical and NRQM context the latter is the one used.

However in the context of pseudo-riemannian manifolds there is a distinction between stationary and static spacetimes, both are time translation invariant but only the static ones are time reversal invariant.

Could one conclude from the fact that Minkowski spacetime is static that the Lorentz-covariant formalism in which is based and that is explicitly time reversible is incompatible with the perturbative case where time-ordering is introduced thru the Dyson series (used in both time-dependent and time-independent perturbative solutions to quantum problems)?
And that this incompatibility may be in the origin of Haag's claim that in the context of the Lorentz covariant formalism "it is shown that Dyson’s matrix U(t1, t2) for finite t1 or t2 cannot exist” (On quantum field theories-1955 p.1)?