Quantum Decoherence: Understanding Contradictions

[Alfrez]

Try to pick out a harmonic wave from the wave you get when throwing a stone into water.



You are using the words without assigning to them the right meaning. Most of what you write here is incomprehensible to me. Do you know what a Hilbert space is, an eigenstate, or complex spacetime? What is meant by a component state?

It doesn't make sense to ask for clear answers to fuzzy questions? The first thing you need to get wright is that you learn the standard meaning of standard notions - otherwise communication is next to impossible.

Isn't there any device or gadget that can home in the harmonic wave from the wave when one throw a stone into water?

Anyway.

Hilbert Space = complex vector space
Eigenstate = allowed states
Complex spacetime = a special kind of spacetime that holds complex numbers

The third is the key, what if Hilbert Space were real and located in a netherland region of spacetime. That is. What if Complex Numbers have its own physical space and not just a mathematical expression. Then the photons from the environment can navigate Hilbert Space and lock on to the components of the Eigenstates. Right?? I wonder if this is what the author of the website thinks. I'll contact him anyway and tell him what you told me.

 

[A. Neumaier]

Hilbert Space = complex vector space
Eigenstate = allowed states
Complex spacetime = a special kind of spacetime that holds complex numbers

You need to be much more precise if you ever want to understand decoherence in a better than just entertainment fashion.

Please look up these terms in Wikipedia, compare, and correct your concepts.

 

[Alfrez]

A pure N particle state psi is unentangled only if it has the form
psi = psi_1(x_1) tensor psi_2(x_2) tensor ... tensor psi_N(x_N)
But the most general pure N particle state can be an arbitrary linear combination of states of this form - all these are called entangled. The Hamiltonian dynamics of a system generally (i.e., except under specially prepared conditions) turns an unentangled state immediately into an entangled state. Therefore in a pure state, N particles are almost always entangled.

Ok. So Andrew Thomas with Ph.D. in Electrical Engineering is wrong. His incorrect stuff sidetracked me for a while. Now going back to 100 photons in the environment and how it entangled with the one single electron in the double slit experiment causing decoherence. You said above that the entire 100 photon + 1 electron is in pure state. I have difficulty with this concept.

A pure state is when there is quantum coherence, meaning there are interferences amongst the phase relationships such that in the double slit, there are interferences, so pure state automatically means there is interference in the quantum state, agree?

Also I presume entanglement automatically means being in pure state. In other words, Superposition, entanglement, and pure state are always together.

When the 100 photons in the surrounding got entangled with the single electron, Schlosshauer described the the coherence being "carried" away to the environment, or the coherence being delocalized from the system. Now you described it as still being in pure state.

But pure state means there is interference. However, this wikipedia article says "Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the system+environment's wavefunction from interfering with each other."

Now since there is no more interference, then it can't be pure state. But you said it's still pure state. There's the contradiction.

Unless you mean that in pure state, it is possible the interference can be hidden amongst the many degrees of freedom and still call it pure state? This means pure state doesn't automatically means there is interference that can be measured, is this it?

 

[Alfrez]

I think you will agree (see post above) that in pure state, interference can be hidden amonst many degrees of freedom in the environment and beyond the realm of measurement, right?

If so, Next inquiry. Since the 100 photons + 1 electron system-environment stuff is in contact with other particles in the surrounding. In fact, since everything is connected to everything in say your living room. Can you say the entire living room is in pure state?
If not, what prevents the 100photons + 1 electron from being entangled with other objects in the environment? What's the dividing line?

 

[A. Neumaier]

Your statements are too vague to allow them to be properly discussed.

You said above that the entire 100 photon + 1 electron is in pure state.

It may or may not be in a pure state. My assumption was just for simplicity.

A pure state is when there is quantum coherence, meaning there are interferences amongst the phase relationships such that in the double slit, there are interferences, so pure state automatically means there is interference in the quantum state, agree?

A pure state means that the system can be described by a wave function psi, while mixed states must be described by a density matrix rho. (The density matrix can also describe pure states, namely when it is of the form rho = psi psi^*.)

This is completely independent of a discussion of phase relationships or interference.
In particular, you can observe interference only for a small system, not for a system and its environment together.

Also I presume entanglement automatically means being in pure state. In other words, Superposition, entanglement, and pure state are always together.

One usually assumes a system to be in a pure state when discussing superpositions and entanglement. But pure states neither need to be entangled nor be in a superposition.

When the 100 photons in the surrounding got entangled with the single electron, Schlosshauer described the the coherence being "carried" away to the environment, or the coherence being delocalized from the system. Now you described it as still being in pure state.

Yes. A unitary dynamics preserves the pureness of a state.

But pure state means there is interference.

No. pure state means not mixed, and nothing else.

 

[Alfrez]

Your statements are too vague to allow them to be properly discussed.



It may or may not be in a pure state. My assumption was just for simplicity.



A pure state means that the system can be described by a wave function psi, while mixed states must be described by a density matrix rho. (The density matrix can also describe pure states, namely when it is of the form rho = psi psi^*.)

This is completely independent of a discussion of phase relationships or interference.
In particular, you can observe interference only for a small system, not for a system and its environment together.




One usually assumes a system to be in a pure state when discussing superpositions and entanglement. But pure states neither need to be entangled nor be in a superposition.



Yes. A unitary dynamics preserves the pureness of a state.



No. pure state means not mixed, and nothing else.

Hi, I have thought of what you said for quite a time and read many references in the internet and elsewhere trying to refute your statement "pure states neither need to be entangled nor be in a superposition". But I found this at Wikipedia

"Applying the superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space. The coefficients of the linear superposition are a wave which describes the particle as best as it possible, and whose amplitude interferes according to the Huygens principle"

You see, quantum mechanics always involves waves, and from the above where it was mentioned "the configurations of the particle are all positions, so the superpositions make a complex wave in space", so superpositions are automatically part of QM where waving is part of it. Now you mentioned "pure states neither need to be entangled nor be in a superposition". How can that be. Give an example of pure state where there is no quantum wave involved.

 

[A. Neumaier]

Hi, I have thought of what you said for quite a time and read many references in the internet and elsewhere trying to refute your statement "pure states neither need to be entangled nor be in a superposition". But I found this at Wikipedia

"Applying the superposition principle to a quantum mechanical particle, the configurations of the particle are all positions, so the superpositions make a complex wave in space. The coefficients of the linear superposition are a wave which describes the particle as best as it possible, and whose amplitude interferes according to the Huygens principle"

You see, quantum mechanics always involves waves, and from the above where it was mentioned "the configurations of the particle are all positions, so the superpositions make a complex wave in space", so superpositions are automatically part of QM where waving is part of it. Now you mentioned "pure states neither need to be entangled nor be in a superposition". How can that be. Give an example of pure state where there is no quantum wave involved.

''quantum wave'' is a term not used by professionals, but the use in your sources seems to be synonymous with that of pure state.

The subsystems P (particle) and E (environment) of the system P+E are unentangled = not in a superposition if the system is in the state psi_P tensor psi_E for states psi_P of the particle and psi_E of the environment. In all other cases (the usual cases) they are entangled.

I leave it to you to translate this precise statement into your fuzzy language.