# B Irreversibility vs reversibility

1. Mar 31, 2017

### Blue Scallop

Decoherence is when the system is entangled with the environment irreversibile...

But when it is reversible.. is it still called Decoherence?

However, the universe is said to be a closed system. Does the irreversibility in decoherence means it is just our ignorance that we cant track it. For example. In the ocean. It is chaotic, when a big boat surfs it.. the wave disturbance it bestowed to the water is complex and our ignorance can't make us track all the wave interferences of the boat and the ocean. Is this also the case in Decoherence where we can't track all the massive degrees of freedom of the environment hence we call it irreversible? But like the ocean which in principle still has all the wave interferences there and in principle reversible.. is this also the case in environmental decoherence where the universe in principle still can keep tract of all degrees of freedom and hence in principle reversible?

2. Apr 1, 2017

### Demystifier

Yes, like the ocean, it's reversible in principle but irreversible in practice.

3. Apr 1, 2017

### Blue Scallop

But there must be a new degree of freedom. So my ballpoint can still be in superposition of left and right.. only the information is in the environment. So from Noether Theorem.. whenever something is conserved.. there is a new degree of freedom. What is that new degree of freedom in the environment? Or something along this line...

4. Apr 1, 2017

### Demystifier

States of each atom of the environment. Many atoms means many degrees of freedom.

5. Apr 1, 2017

### Blue Scallop

No relation to gauge invariance? Remember electromagnetic field came from U(1) local gauge invariance.. is there no corresponding symmetry in the quantum? And why is that? Thank you.

6. Apr 1, 2017

### hilbert2

A good way to demonstrate why some processes are practically irreversible is to consider a simple heat conduction problem: suppose there's a thermally insulated 1D object between endpoints x=0 and x=L, and the temperature field T(x,t) on that interval obeys the heat equation

$\frac{\partial T}{\partial t} = c\frac{\partial^2 T}{\partial x^2}$.

If the initial temperature field is Gaussian: $T(x,0) = Ce^{-a(x-L/2)^2}$, it is possible to calculate the temperature distribution $T(x,t')$ at any later time $t'$, and the distribution approaches a constant: $T(x,t) \rightarrow C$, when $t \rightarrow \infty$. However, if you try to do that other way around, trying to calculate $T(x,0)$ from $T(x,t')$ where t' is very large, you'd have to know the function $T(x,t')$ as a function of x to a very large number of significant figures to even see that it deviates from a constant distribution at all, let alone deduce what the distribution has been at some much earlier time. So, here we see that the idea of irreversibility is that you'd need to know the state of a system with unrealistic accuracy to be able to calculate what the state was before the irreversible process.

Last edited: Apr 1, 2017
7. Apr 1, 2017

### Demystifier

There is gauge invariance in quantum theory, but I don't see how is that relevant to (ir)reversibility.

8. Apr 1, 2017

### Blue Scallop

Demystifer stated that like the ocean, decoherence is reversible in principle but irreversible in practice

Although Decoherence is reversible in Bohmian Mechanics, MWI. Decoherence is Irreversible in Copenhagen... is this correct folks?

Now time is symmetric in quantum mechanics. Using MWI, can you time reverse the Universal Wave function and make the dead cat become alive again? Is this possible in principle but only In practice??

I think in Copenhagen it is not possible to bring dead cats back to life.. I'm not sure in Bohmian,, but in MWI.. is this possible since the Universal Wave Function is time symmetric?

Or what I'm asking is whether when branches in MWI have occurred.. whether you can initiate global time symmetric principle universally and reverse the universal wave function so the branches can revert back to original before they became two.

I think this is a question about MWI that Demystifier who is a Bohmian may not be able to answer so I'm inviting others to give their feedback. Thanks!

9. Apr 1, 2017

### Stephen Tashi

The following two definitions of "reversible" appear to be different. Is there an argument that they are equivalent?

1)To say a process is reversible means that the previous states of the process can be deduced from the current state of the process.

2) To say a process is reversible means that it is physically possible to have another process whose states are those of the first process, but taking place in reverse order as time passes.

10. Apr 1, 2017

### Blue Scallop

After collapse (or branching in MWI). The wave function that starts evolving deterministically again after it is NOT the same as the wave function that evolved deterministically to the state just before the collapse (or branching). But they say time is symmetric in QM. Does this symmetric time means you can reverse the wave function from the state after the collapse (branching) to the stae prior the collapse (or branching). Or does QM time symmetry only work for the same wave function? But then in universal wave function.. can't we say the wave function that starts evolving deterministically again after the collapse (or branching) IS the same as the wave function that evolved deterministically to the state just before the collapse (or branching).

And what is the connection of time reversibility in QM to Demystifier statement that decoherence is not irreversible in principle? Thanks!

11. Apr 2, 2017

### stevendaryl

Staff Emeritus
That's a good point. Certainly it's conceivable to have a physics where those two are not the same. For example, if there were a "time" variable that incremented by 1 each second, then that would be irreversible in the sense of 2) but not 1).

12. Apr 2, 2017

### Staff: Mentor

More precisely, unitary evolution is time reversible in QM. So in a no collapse interpretation like the MWI, where it's all unitary evolution, yes, you can in principle reverse the branching. (Remember that all of the branches of the wave function are still there, so all you're doing is reversing the unitary operator that entangles the state of the measuring device with the state of the measured system.) Note that this is true even in the presence of decoherence; decoherence, as Demystifier said, is not irreversible in principle, because it's just more unitary evolution that entangles more things (degrees of freedom in the environment) with the measured system.

But in collapse interpretations, wave function collapse is not a unitary operation, so it can't be reversed. The problem is that, even though decoherence is reversible in principle, it isn't in practice because there are way too many degrees of freedom to keep track of in the environment. So there's no way for us to tell, experimentally, the difference between decoherence without collapse, and collapse.

13. Apr 2, 2017

### stevendaryl

Staff Emeritus
I think that they are very closely related, if not the same thing.

To illustrate classical irreversibility, imagine dropping a ball onto the floor in a closed room. The ball will bounce around but lose energy until eventually it comes to rest on the floor. That's irreversible in both of @Stephen Tashi's senses: (1) Seeing a ball on the floor, there is no way to figure out that it was once dropped at a particular location from a particular height. (2) The reverse transition never happens. It's never the case that a ball that is initially on the floor suddenly starts bouncing.

So why is that irreversible? The simple answer is that things tend to run down, and bouncing balls tend to lose energy. But that's an incomplete answer. The ball might be losing energy, but energy is conserved. So even though the ball is losing mechanical energy, that energy goes somewhere: into heating the ball or into heating the floor, or into vibrations in the floor. Why does energy tend to flow from the ball to the floor and into heat? The classical statistical mechanics answer is entropy: There is only one way for a ball to have kinetic energy, but there is an astronomical number of ways to distribute that energy among the vibrations of the molecules making up the ball and the floor. So the odds are enormously in favor of the energy finding its way into vibrations than it staying in the form of kinetic energy of the ball.

There is a similar irreversibility at work in quantum mechanics. If you start with a hydrogen atom with its electron in an excited state, the electron will tend to radiate away energy and fall into the ground state. But why? Why is there such a tendency? You can reason classically in this case, and say that the entropy of the electromagnetic field is vastly greater than the entropy of a hydrogen atom, so it's entropically favorable for the electron to give up its energy to the electromagnetic field (in other words, radiate). However, if you treat both the atom and the electromagnetic field quantum-mechanically, then what happens is that with time, the atom becomes entangled with the electromagnetic field. Which is what decoherence is about.

14. Apr 2, 2017

### Blue Scallop

Can you please give an example of reversing the branching in MWI? Is double slit or spin-1/2 particle better example of it? In the double slit, say the screen entangled with the electron giving the detection hit. So by reversing the branching. Can you make the hits disappeared and how do you do that??

15. Apr 2, 2017

### Staff: Mentor

In practice, the only operations we can actually reverse are the ones where decoherence has not happened; for example, qubit operations in quantum computing. But these are the ones where even collapse interpretations say there is no collapse--because collapse is not reversible.

So neither a standard spin-1/2 particle measurement nor the double slit experiment are practical examples of reversing branching in MWI, because they both involve decoherence, and therefore we cannot reverse them in practice.

16. Apr 2, 2017

### Blue Scallop

In message #12, you wrote that:

You wrote earlier that in MWI, where it's all unitary evolution, one can in principle reverse the branching.. even in the presence of decoherence as your emphasized. But in last message you have written that it can only happen if there is no decoherence.

However in principle you seemed to say it can happen. Can you give an example where you can reverse the unitary evolution even in presence of decoherence (in MWI) (in principle)?

17. Apr 3, 2017

### stevendaryl

Staff Emeritus
Decoherence reversing is almost exactly analogous to entropy reversing. If you have a tiny number of particles bouncing around inside a container, the entropy can go up and down, but if you have 10^{23} particles, you'll never see it go down. Decoherence basically is just entanglement involving an astronomical number of particles. For a small number of degrees of freedom, you can certainly witness entanglement reversing, but you'll never a macroscopic number of degrees of freedom disentangle itself.

18. Apr 3, 2017

### stevendaryl

Staff Emeritus
Okay, I realize that there is a bit of confusion about entanglement and decoherence. On the one hand, we say that it is irreversible. On the other hand, if it's really irreversible, then we shouldn't ever see any evidence of superpositions, at all, since everything should be maximally entangled by now.

So there is something to be explained, which is: How do we ever see unentangled systems?

If you assume wave function collapse, then that's sufficient to explain how things get unentangled:

You have an electron whose spin state is entangled with some other subsystem as follows

$|\Psi\rangle = \alpha |u\rangle |U\rangle + \beta |d\rangle |D\rangle$

where the electron's spin state is $|u\rangle$ or $|d\rangle$ and $|U\rangle$ and $|D\rangle$ are states of the rest of the other subsystem (maybe a measuring device).

You perform a measurement of the spin and find that it is spin-up. Then according to the collapse interpretation, the composite system is in the state

$|\Psi'\rangle = |u\rangle |U\rangle$

which is a disentangled state.

Without invoking collapse, you can get effective disentanglement by simply restricting your attention to the first component of the superposition. How can you get away with that? That's sort of a deep question.

19. Apr 3, 2017

### Stephen Tashi

The meaning of that, by the intuitive definition of entropy, is clear. However, technically, a specific number of particles with specific positions and velocities has no defined entropy - correct? Only "ensembles" of systems have a defined entropy and only ensembles of systems in equilibrium have a defined thermodynamic entropy. To have a Shannon type of entropy, we need to be talking about a probability distribution. So perhaps quantum mechanics can supply the probabilistic model for a specific set of particles (?)

20. Apr 3, 2017

### Blue Scallop

But restricting your attention to the first component of the superposition is using the concept of tracing out.. but tracing out automatically uses collapse, is it not.. so you invoke collapse by simply tracing out in the density matrix. So you can't say "without invoking collapse"..