I Do we still experience quantum effects in decohered systems?

[jaydnul]

As I understand it, decoherence is when the quantum system becomes entangeld with the measuring quantum system. If most of the macroscopic systems we experience are all decohered, then why do we still see quantum effects like in a transistor? Is it position AND momentum that decohere?

 

[Denis]

No, decoherence is when the quantum system interacts with the environment, and this effectively destroys superpositions. One can, if one likes, describe this as something similar to a measurement - one where the measurement results are "stored" in an uncontrolled environment and ignored.

What is measured depends on the particular physics. If, say, the physics is described by something like H= H_{system} + H_{environment} + V(q_{system}, q_{environment}), then it is position which is effectively measured. If the main influence is radiation, exchange of light quanta, the result may be an effective energy measurement.

 

[jaydnul]

...one where the measurement results are "stored" in an uncontrolled environment and ignored.

Could you explain this further? What do you mean by ignored? Also, are these measurements happening at a rapid pace, the particle is constantly in a cycle of being measured and falling back into a quantum superposition for some time? Or once it is measured, does it stay classical? I'm curious because these decohered particles still seemingly display quantum properties (like in a transistor).

 

[PeroK]

Could you explain this further? What do you mean by ignored? Also, are these measurements happening at a rapid pace, the particle is constantly in a cycle of being measured and falling back into a quantum superposition for some time? Or once it is measured, does it stay classical? I'm curious because these decohered particles still seemingly display quantum properties (like in a transistor).

A particle remains a quantum object with a wavefunction. Every wavefunction is always a "superposition" of something. It never becomes classical.

 

[jaydnul]

A particle remains a quantum object with a wavefunction. Every wavefunction is always a "superposition" of something. It never becomes classical.

Even at the instant of measurement?

 

[PeroK]

Even at the instant of measurement?

You have a quantum state before a measurement: the state is evolving with time. A measurement changes the quantum state (to an eigenstate of the observable being measured); the new quantum state continues to evolve.

To what extent you can ask what is happening at the "instant of measurement" is a moot point.

 

[Denis]

A measurement is also a process which needs some time. An "instant of measurement" is an idealization. And, of course, even in this idealization the state as before, as after is some wave function. Only after the measurement, it is an eigenstate of the operator which is measured.

 

[PeroK]

Could you explain this further? What do you mean by ignored? Also, are these measurements happening at a rapid pace, the particle is constantly in a cycle of being measured and falling back into a quantum superposition for some time? Or once it is measured, does it stay classical? I'm curious because these decohered particles still seemingly display quantum properties (like in a transistor).

You are still misunderstanding QM fundamentally to the extent that no understanding of decoherence is possible. There is no process that makes an electron into a "classical" particle. Classical physics is a different theory. You cannot mix the two up.

 

[jaydnul]

You are still misunderstanding QM fundamentally to the extent that no understanding of decoherence is possible. There is no process that makes an electron into a "classical" particle. Classical physics is a different theory. You cannot mix the two up.

Ya I guess so. Let me make some broad claims and see if they are correct.

1. A particle is always described by its wave function. When the wave function isn't being measured, its behavior is described by amplitudes which can interfere and cancel out (and the amplitudes are what we consider superposition).
2. If you decide to measure the particle, it will return a single value of whatever observable you try to measure. The probability of possible outcomes is given by the square of the amplitudes.
3. After measurement occurs, the particle continues to evolve in a superposition of states until measured again.

If those are true, my question is the time it takes a particle to go from step 2 to 3, then back to 2 (in a macroscopic system like a table).

 

[PeroK]

Ya I guess so. Let me make some broad claims and see if they are correct.

1. A particle is always described by its wave function. When the wave function isn't being measured, its behavior is described by amplitudes which can interfere and cancel out (and the amplitudes are what we consider superposition).
2. If you decide to measure the particle, it will return a single value of whatever observable you try to measure. The probability of possible outcomes is given by the square of the amplitudes.
3. After measurement occurs, the particle continues to evolve in a superposition of states until measured again.

If those are true, my question is the time it takes to go from step 2 to 3, then back to 2 (in a macroscopic system like a table).

First, let me make 1-3 slightly more precise:

1) A particle is always described by its wave function, which evolves over time.

2) A measurement of an observable will return an eigenvalue of the observable's operator. The particle's wavefunction will change to the corresponding eigenfunction (*).

3) The particle's wavefunction continues to evolve.

(*) Every wavefunction can be expressed as a linear combination (superposition) of the eigenfunctions of any observable. The probability of getting a certain eigenvalue is the modulus squared of the coefficient (amplitude) of the corresponding eigenfunction in this expression.

That's a good starting point.

 

[Nugatory]

If those are true, my question is the time it takes a particle to go from step 2 to 3, then back to 2 (in a macroscopic system like a table).

The question is not as clear as you're thinking it is. The problem is that your points #1 and #3 are claims about what is happening when nothing is being measured; and the theory says nothing about that. To get a question that can be properly answered, you'd need to reframe it in terms of measurements performed during those "in-between" periods.

 

[jaydnul]

The question is not as clear as you're thinking it is. The problem is that your points #1 and #3 are claims about what is happening when nothing is being measured; and the theory says nothing about that. To get a question that can be properly answered, you'd need to reframe it in terms of measurements performed during those "in-between" periods.

I'm just confused when the "collapse" happens. When I touch the table, the range of possible position values for each particle is much much smaller than the size of my finger, so I most likely will feel the table push back. But saying "the range of possible values" makes it seem like the table particles are "collapsing" to one of these possible values. Am I measuring table when I press my finger on it?

 

[jaydnul]

First, let me make 1-3 slightly more precise:

1) A particle is always described by its wave function, which evolves over time.

2) A measurement of an observable will return an eigenvalue of the observable's operator. The particle's wavefunction will change to the corresponding eigenfunction (*).

3) The particle's wavefunction continues to evolve.

(*) Every wavefunction can be expressed as a linear combination (superposition) of the eigenfunctions of any observable. The probability of getting a certain eigenvalue is the modulus squared of the coefficient (amplitude) of the corresponding eigenfunction in this expression.

That's a good starting point.

Maybe this will help clear this up for me. Would it be right to insert a step 2.5 that says the particle's wave function has now become entangled with the measuring equipment's wave function? Would it also be right to say that my body's wave function is entangled with this keyboard's wave function, which is entangled with the desk's wave function, which is entangled with the world's wave function, etc...? So in essence, it is a precise setup that creates a particle that is unentangled (like in a double slit)?

 

[stevendaryl]

1. A particle is always described by its wave function. When the wave function isn't being measured, its behavior is described by amplitudes which can interfere and cancel out (and the amplitudes are what we consider superposition).

Actually, I don't agree with this first statement. If a particle is interacting with other particles, then the entire system is described by a wave function, but each particle doesn't independently have a wave function.

That's what makes measurement and decoherence so messy. If you try to use quantum mechanics to analyze a macroscopic system such as a measuring device, you run into the problem that the macroscopic system doesn't have a wave function, because it is always interacting with the environment (the electromagnetic field, the atmosphere, the room the device is located in, etc.)

 

[jaydnul]

Ohhh ok. So does the apparent "collapse" only happen when two separate, unentangled quantum systems become entangled? So I am already entangled with my environment, so nothing is "collapsing" in that sense when I touch the desk in front of me?