The arguments against macroscopic quantum states are

[skynelson]

I am aware and well read on the decoherence approach to understanding how conglomerations of micro quantum systems will tend to lose quantum coherence via interaction with the environment. The cross terms in the density matrix for the system will tend to zero (due to the partial trace operation), leaving us with a (diagonal) mixed state, representing a classical form of uncertainty rather than a quantum form of uncertainty (we don't know which state the system is in, but it is definitely in a state).

My reading on decoherence has largely been Zurek's papers. (for instance http://arxiv.org/abs/quant-ph/0306072).

At a conference recently, however, somebody mentioned to me the "thermodynamic argument" for why macroscopic quantum states can't exist. I have a vague sense of what he meant, based on thermodynamics and probablility, but I am not clear on the exact argument or its basis.

Is it different from decoherence theory, or essentially the same? What is the thermodynamical reasoning for why MQS states are not viable?

 

[skynelson]

And are there any other approaches to this argument that I am unaware of?

 

[mfb]

Macroscopic quantum states can exist (and are realized), but they are very sensitive to any interaction with the environment - even thermal fluctuations. Maybe that is meant with "thermodynamic argument"?

 

[kith]

I would say this is just a sloppy formulation for decoherence. The framework for this is the theory of open quantum systems. If you couple a system to a thermal environment, you usually get irreversible decoherence on a very short timescale. This could be dubbed the "therodynamical argument" for the fact that macroscopic quantum states are rarely observed.

 

[Oudeis Eimi]

I am aware and well read on the decoherence approach to understanding how conglomerations of micro quantum systems will tend to lose quantum coherence via interaction with the environment. The cross terms in the density matrix for the system will tend to zero (due to the partial trace operation), leaving us with a (diagonal) mixed state, representing a classical form of uncertainty rather than a quantum form of uncertainty (we don't know which state the system is in, but it is definitely in a state).

My reading on decoherence has largely been Zurek's papers. (for instance http://arxiv.org/abs/quant-ph/0306072).

At a conference recently, however, somebody mentioned to me the "thermodynamic argument" for why macroscopic quantum states can't exist. I have a vague sense of what he meant, based on thermodynamics and probablility, but I am not clear on the exact argument or its basis.

Is it different from decoherence theory, or essentially the same? What is the thermodynamical reasoning for why MQS states are not viable?

Mmmmm, I don't know if this is what that person was hinting at, but *maybe* his or her argument was against _pure_ (ie, kets) macroscopic quantum states, not states in general (which are generally mixed). The argument might be that a system in equilibrium with an environment with a well defined temperature would tend to be in a (mixed) state proportional to exp(-βH), and that since β is always finite, this cannot be a pure state. Again, not sure whether this is what that person was referring to.

 

[kith]

The argument might be that a system in equilibrium with an environment with a well defined temperature would tend to be in a (mixed) state proportional to exp(-βH), and that since β is always finite, this cannot be a pure state.

This is not enough, because this is also true classically. There, we frequently observe non-equilibrium states. The question is "is it possible to prepare a pure state for a macroscopic object" and "how fast would it turn into a completely mixed state". The transition from the initial state to the equilibrium exp(-βH)-state is not faster than for classical systems, but the timescale for decoherence is usually extremely short.

 

[Oudeis Eimi]

This is not enough, because this is also true classically. There, we frequently observe non-equilibrium states. The question is "is it possible to prepare a pure state for a macroscopic object" and "how fast would it turn into a completely mixed state". The transition from the initial state to the equilibrium exp(-βH)-state is not faster than for classical systems, but the timescale for decoherence is usually extremely short.

This makes sense.

 

[StevieTNZ]

A macroscopic quantum system is in a quantum state, ie. governed by QM laws, regardless of its interactions and thermodynamic heat state. It is more difficult to see the quantum behaviour, but is still present. A mixed state does not accurately describe the situation - a mixed state is where the system is in either one or another of the possible states it may be in - but when you have ALL the information you need, it is in a superposition of states.

 

[kith]

A macroscopic quantum system is in a quantum state, ie. governed by QM laws

The question "can macroscopic objects be in a quantum state" is different from the question "can we describe every macroscopic object by a quantum state at arbitrary times". Most noteworthy, a macroscopic system consisting of a measurement apparatus and the system it is measuring doesn't evolve by Schrödinger's equation. So here we need input from an interpretation. Many worlds say yes to the second question, Copenhagen says no.

A mixed state does not accurately describe the situation - a mixed state is where the system is in either one or another of the possible states it may be in - but when you have ALL the information you need, it is in a superposition of states.

A mixed state is the right description because it correctly predicts the results of all measurements you can do at the system.

 

[mfb]

Most noteworthy, a macroscopic system consisting of a measurement apparatus and the system it is measuring doesn't evolve by Schrödinger's equation. So here we need input from an interpretation. Many worlds say yes to the second question, Copenhagen says no.

MWI let's the macroscopic system (measurement apparatus+measured system + everything else) evolve according to the Schrödinger equation.

 

[kith]

MWI let's the macroscopic system (measurement apparatus+measured system + everything else) evolve according to the Schrödinger equation.

Yes, my phrasing was not correct. What I meant is that in a measurement, I always get a definite outcome, not a mixed one. So the assumption that the macroscopic system evolves according to Schrödinger's equation alone is not sufficient to explain what happens in a measurement, I need additional assumptions provided by interpretations.

 

[audioloop]

The question "can macroscopic objects be in a quantum state" is different from the question "can we describe every macroscopic object by a quantum state at arbitrary times"

or rephrased, do macroscopic states exist in superposition ?


and has to be established formally first (size).

Phys. Rev. Lett. 106, 220401 (2011)
Quantification of Macroscopic Superpositions
http://prl..org/abstract/PRL/v106/i22/e220401

...we propose a novel measure to quantify macroscopic superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space...