Understanding the Measurement and Interaction of Electrons: A Beginner's Guide

[durant35]

That question does not make sense.

And what is "macroscopic light"? Light does not have a size.

The word 'spread' has the same meaning as the evolution of superpositions which ultimately result in the Schrodinger's cat. By that I mean, concretely in the case of diamonds we mentioned, does the air that surrounds one of the diamonds get in some kind of superposition depending on its interaction with the diamond that is 'vibrating and non vibrating'.

Also I need a conclusion about decoherence, does it produce an eigenstate? So a cat is hypotethically in a superposition of dead and alive and after a few fragments of time it decoheres and it becomes either dead or alive, just one of those two states.

 

[mfb]

does the air that surrounds one of the diamonds get in some kind of superposition depending on its interaction with the diamond that is 'vibrating and non vibrating'.

No, interaction with the air would lead to decoherence.

Also I need a conclusion about decoherence, does it produce an eigenstate?

An eigenstate of what? Of something that is measured: yes.

 

[durant35]

No, interaction with the air would lead to decoherence.An eigenstate of what? Of something that is measured: yes.

I read that decoherence leads to transition from a superposition state to a mixed state, but a mixed state per se implies an eigenstate as an outcome, right? That is one concrete result, like the 'cat is dead' after the decoherence proc.ess

 

[durant35]

Also, because of the environment, we are never in superposed states, right? So for instance my cat is always alive when I see it on everyday basis, there's no superposition. I read a document from a physicist Zurek which claims that decoherence saves us, but decoherence isn't instanteneous so do we everyday objects have superposed properties despite decoherence not being instanteneous?

 

[mfb]

Also, because of the environment, we are never in superposed states, right?

Right.

I read a document from a physicist Zurek which claims that decoherence saves us, but decoherence isn't instanteneous so do we everyday objects have superposed properties despite decoherence not being instanteneous?

Decoherence happens so fast, you never get something that could be seen as relevant superposition for macroscopic properties - measuring those would need some time as well.

 

[durant35]

Right.Decoherence happens so fast, you never get something that could be seen as relevant superposition for macroscopic properties - measuring those would need some time as well.

Im sorry mr mfb but I don't get it precisely, is it that we are not in a superposition a definite fact or the decoherence process kills the superpositions occurring rapidly but for a small period of time we are in one.
I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

 

[bhobba]

Im sorry mr mfb but I don't get it precisely, is it that we are not in a superposition a definite fact or the decoherence process kills the superpositions occurring rapidly but for a small period of time we are in one.
I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

Every pure state is in a superposition and in an infinite number of different ways. You need to specify superposition of position.

What's going on here in the Macro world is, without going into the technical details, we have as a result of decoherence states get converted to mixed state of position. Such mixed states can be considered to be in a definite position rather than a superposition.

Thanks
Bill

 

[durant35]

Every pure state is in a superposition and in an infinite number of different ways. You need to specify superposition of position.

What's going on here in the Macro world is, without going into the technical details, we have as a result of decoherence states get converted to mixed state of position. Such mixed states can be considered to be in a definite position rather than a superposition.

Thanks
Bill

So basically those small superpositions of location can be considered an exact position for all purposes, and the macroscopic properties like dead or alive are definite despite the uncertainty and there are no superpositions of those properties?

 

[zonde]

I can't shake my head over it, but I constantly have this thought of people being in a superposition of dead and alive for fragments of seconds without external cause but we cannot see it. Tell me please how does decoherence solve this bizarre idea?

You can meaningfully speak about superposition of dead an alive only if the two can be viewed as basically the same quantum state (technically, as states in the same Hilbert space) differing only by complex phase factor. And I don't think this is possible.

 

[bhobba]

So basically those small superpositions of location can be considered an exact position for all purposes, and the macroscopic properties like dead or alive are definite despite the uncertainty and there are no superpositions of those properties?

As I have mentioned to you a few times its next to impossible explain this linguistically. You must go into the math.

However what you said is not correct. What happens is a general state gets converted to a mixed state in the position basis. This can be interpreted as having a definite position but the position it has isn't known, but has a certain probability.

Here is what a mixed state is about. A pure state is written as |u><u|. These are the states the principle of superposition applies to which is the |u> forms a vector space. A mixed state is a generalisation of a pure state. Imagine you are presented with states |bi><bi| to observe with probability pi. It turns out such a state is mathematically ∑pi |bi><bi|. Now what decoherence does in most practical cases (technically its the Hamiltonian has radial symmetry) is it converts a state to ∑pi |bi><bi| where the |bi><bi| are states of definite position. This means you can interpret this as the system being in state |bi><bi| with probability pi. However while you can interpret it that way it was not prepared the way I told you a mixed state was prepared ie some process randomly presenting a state. There is no way to tell the difference - but it was not prepared that way. That's why its called apparent collapse. If it was prepared that way - ie randomly presenting an actual state - than it would be actual collapse.

Thanks
Bill

 

[durant35]

I think I understand it in principle but I don't understand how to practically employ it in practice and how does the classical world emerge from it, with definite macroscopic properties and not superpositions. The fact that decoherence isn't instanteneous seems to always leave room for a macro superposition without any reason and that's what makes it bizarre and gives me anxiety.

As I have mentioned to you a few times its next to impossible explain this linguistically. You must go into the math.

However what you said is not correct. What happens is a general state gets converted to a mixed state in the position basis. This can be interpreted as having a definite position but the position it has isn't known, but has a certain probability.

Here is what a mixed state is about. A pure state is written as |u><u|. These are the states the principle of superposition applies to which is the |u> forms a vector space. A mixed state is a generalisation of a pure state. Imagine you are presented with states |bi><bi| to observe with probability pi. It turns out such a state is mathematically ∑pi |bi><bi|. Now what decoherence does in most practical cases (technically its the Hamiltonian has radial symmetry) is it converts a state to ∑pi |bi><bi| where the |bi><bi| are states of definite position. This means you can interpret this as the system being in state |bi><bi| with probability pi. However while you can interpret it that way it was not prepared the way I told you a mixed state was prepared ie some process randomly presenting a state. There is no way to tell the difference - but it was not prepared that way. That's why its called apparent collapse. If it was prepared that way - ie randomly presenting an actual state - than it would be actual collapse.

Thanks
Bill

 

[bhobba]

I think I understand it in principle but I don't understand how to practically employ it in practice and how does the classical world emerge from it, with definite macroscopic properties and not superpositions..

That part is simple.

The macro world has definite position. Since after decoherence the mixed state is equivalent to having a definite position everything is fine.

Thanks
Bill

 

[durant35]

Thanks. So if it has a definite position does this imply that it has classical properties (like being alive) which evolve classically?

That part is simple.

The macro world has definite position. Since after decoherence the mixed state is equivalent to having a definite position everything is fine.

Thanks
Bill

 

[bhobba]

Thanks. So if it has a definite position does this imply that it has classical properties (like being alive) which evolve classically?

I am not into biology - my thing is physics using math. But I would say - yes.

Thanks
Bill

 

[durant35]

Thanks.

So let me try to conclude all of this. The system evolves from a superposition to a mixed state, but the nature observes only one state of the macro object with a definite position while other is information in the environment. So for instance the photons measure ' the cat is alive' state and the 'cat is dead' state doesn't stop existing but it is 'contained' as information in reality, and that's why it is just an apparent collapse but it is sufficient because environment only measures a definite state which for macroscopic objects then evolves classically as you mentioned in one of your previous posts.

I am not into biology - my thing is physics using math. But I would say - yes.

Thanks
Bill

 

[Bruno81]

Thanks.

So let me try to conclude all of this. The system evolves from a superposition to a mixed state, but the nature observes only one state of the macro object with a definite position while other is information in the environment. So for instance the photons measure ' the cat is alive' state and the 'cat is dead' state doesn't stop existing but it is 'contained' as information in reality, and that's why it is just an apparent collapse but it is sufficient because environment only measures a definite state which for macroscopic objects then evolves classically as you mentioned in one of your previous posts.

Nobody knows how qm connects to the classical macro world. Don't take everything for granted, as there is no higher authority on this particular subject. While we struggle to understand nature and reality, keep your expectations low and humble... if there is no classical reality existing at all times in 3 D space, there is likely lots' of room for revisions of our basic notions. Physicists used to think all of Nature was deterministic and all mysteries concerning our existence resided in the low entropy of the Big Bang(basically they thought we evolved in the only possible way given how the initial conditions were 14 billion years ago). Now we have enough eveidence that this point is almost worthless due determinism arising from indeterminism(see double slit experiement with single photons/electrons). It's more into the philosophy side of things as physicists find few or no practical aspects to these developments. If you stick around and ask the right questions, you'll see the issue in full detail.

 

[vanhees71]

To the contrary! It's pretty well known, how the "classical world" emerges from the quantum world via "coarse graining", i.e., noting that the macroscopic observables are much coarser than any microscopic resolution, and a classical state ("point in phase space") is in reality an average over many quantum states.

E.g., the fundamental quantum many-body equations for the evolution of the single-particle Wigner function, the socalled Kadanoff-Baym Equations go over into the (semi-)classical Boltzmann(-Uehling-Uhlenbeck) equations after the gradient expansion. Into that approximation goes the assumption that the macroscopic variables vary much slower in space and time than the rapid oscillations of the microscopic degrees of freedom, i.e., the macroscopic observables are given by an average over macroscopic small but microscopic large phase-space regions and times. For a pedagogic introduction into that subject, see Landau-Lifshitz, vol. X or

W. Cassing. From Kadanoff-Baym dynamics to off-shell parton transport. Eur. Phys. J. ST, 168:3–87, 2009.
http://dx.doi.org/10.1140/epjst
http://arxiv.org/abs/arXiv:0808.0715

 

[Bruno81]

Coarse graining is not an official interpretation hence it can't explain why a certain coarse graining and not another is actualised. And even if it, which it doesn't, it woud have tension with Bell and a host of experiments(double slit, DCQE, etc).

 

[vanhees71]

What do you mean by "official interpretation"? It's not an interpretation at all but a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory.

 

[bhobba]

Coarse graining is not an official interpretation

I think its fundamental to Decoherent Histories. In that interpretation QM is the stochastic theory of coarse grained histories..

Thanka
Bill

 

[Bruno81]

So it doesn't explain how a classical world emerges, doesn't explain single outcomes but instead provides a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory. I wil look into this in more detail.

 

[durant35]

What do you mean by "official interpretation"? It's not an interpretation at all but a mathematical approximation method to derive semi-classical transport equations from quantum many-body theory.

So no macroscopic superpositions are allowed, the classical world is as we see it in a definite state all the time?

 

[mfb]

Yes, especially if you "see" it (i. e. it interacts with light).

 

[durant35]

Yes, especially if you "see" it (i. e. it interacts with light).

Glad to hear that, that finally washes away some of my anxiety regarding this. I know QM is weird but to have a classical, definite state and properties of macroscopic objects at any instant which we can combine with special and general relativity is a sign of relief.