Apparent 'stillness' of macroscopic systems

[Oudeis Eimi]

Hi fellow PFers, long time reader here. I have a query that was motivated
by a comment on another thread (“Decoherence question”).
It is about the quantum properties of decohered macroscopic systems.

In my (incomplete and perhaps misapprehended) understanding, a macroscopic
object, say a chair, that is almost unavoidably strongly interacting
with its environment, will be in a (mixed) quantum state in which its
position and (linear) momentum are described by close to minimum uncertainty
packets, always of course obeying the HUP. We would say that the strong
interaction with the environment tends to “select” with overwhelmingly
preference states in which the object is rather well localised in both
configuration and momentum space.

Now, although the spatial and momentum distributions are macroscopically
very small, they can obviously never be null. The way I understand it,
the environment is permanently monitoring both the position and momentum
of the system, which should lead to the system approaching what in
classical terms we would describe as Brownian motion of some sort. This is
what I would expect would be the (approximate) motion of the centre of mass
of the system in deep space, free from any gravitational influence.

However, when the chair is resting on my (also approximately localised)
floor, it seems to be at perfect rest. I´m having a hard time reconciling
the non infinitely small momentum distribution with this apparent stillness.

Can anyone shed some light on this issue?

 

[DaveC426913]

...what in
classical terms we would describe as Brownian motion of some sort. This is
what I would expect would be the (approximate) motion of the centre of mass
of the system in deep space, free from any gravitational influence.

However, when the chair is resting on my (also approximately localised)
floor, it seems to be at perfect rest. I´m having a hard time reconciling
the non infinitely small momentum distribution with this apparent stillness.

It sounds like you're assuming that Brownian motion gets scaled up. i.e.:
"...if a pollen grain can get knocked about by energetic atoms then it stands to reason that 10²⁶ pollen grains stuck together should get knocked about by 10²⁶ as much..."

Fact is, 10²⁶ atomic-scale collisions do not accumulate into one (10²⁶-atoms)-sized collision.

They average out: An atmospheric atom hits the left leg and one or two atoms jiggle in response, sending a tiny wave of vibration into the chair, which dies out after a short distance.
A vanishingly short time later, another atom hits the right leg, and one or two atoms jiggle in response, sending a tiny wave of vibration into the chair, which dies out after a short distance.

The chair is being knocked about, but at atomic scales.

What are you expecting to see?

 

[dslowik]

I think your OP was asking about purely QM effects, rather than thermal effects due to collisions with surrounding particles, i.e., assuming the chair was in a vacuum at 0K. But I think the reasoning is qualitatively the same: the momentum uncertainties of each of the individual constituent particles get actualized upon interacting/observing with their neighbors, but there are so many of these on such a small scale (just like the atomic, thermal collisions of post #2), that they would average out and the chair would maintain a momentum very near 0.

But if the chair was truly in a vacuum, couldn't you represent IT by a wave function between interactions with external fields?...

 

[bhobba]

However, when the chair is resting on my (also approximately localised)
floor, it seems to be at perfect rest. I´m having a hard time reconciling
the non infinitely small momentum distribution with this apparent stillness.

Here is the book to get at what I think your level is:
https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

Whats really going on with the chair is it interacts with the environment and decoherence occurs. After decoherence you have a range of probabilities for its position - but that range is of the order of atomic distances ie the distance between atoms. You never notice it. It keeps interacting which means its constantly having its position measured but that its position varies slightly is never noticed. Since its position varies slightly by the Heisenberg uncertainty principle its momentum isn't completely unknown either and it varies only slightly - but so slightly you never notice. Or another way of looking at it is by interacting with the environment it acts as a position measurement - but not a 100% accurate one - but its variance is so small you never notice it and the Heisenberg uncertainty principle skirted because its such a small variance in momentum as well (you can't know both with 100% accuracy at the same time - but you can know their approximate values) - so small you don't notice that either.

Thanks
Bill

 

[Oudeis Eimi]

Here is the book to get at what I think your level is:
https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

Whats really going on with the chair is it interacts with the environment and decoherence occurs. After decoherence you have a range of probabilities for its position - but that range is of the order of atomic distances ie the distance between atoms. You never notice it. It keeps interacting which means its constantly having its position measured but that its position varies slightly is never noticed. Since its position varies slightly by the Heisenberg uncertainty principle its momentum isn't completely unknown either and it varies only slightly - but so slightly you never notice. Or another way of looking at it is by interacting with the environment it acts as a position measurement - but not a 100% accurate one - but its variance is so small you never notice it and the Heisenberg uncertainty principle skirted because its such a small variance in momentum as well (you can't know both with 100% accuracy at the same time - but you can know their approximate values) - so small you don't notice that either.

Thanks
Bill

Thanks Bill. I knew that book (considered it for someone else in fact), but never read it myself. My level is a Physics MSc, but my specialty is Materials Science, not open quantum systems. That's why I don't (yet) have Schlosshauer's book, which I have been told is the book to get on decoherence, because I'm not conversant on open quantum systems, Lindbladt equations, etc. But I'm thinking of getting it anyway and fill in the gaps through some self study.

I will think of your answer - it's more or less the same thing I suspected was going on, but I wasn't quite sure myself.

 

[haael]

which should lead to the system approaching what in
classical terms we would describe as Brownian motion of some sort

No. If you have a system and you measure it again and again using the same observable, you will get the same result all the times. You would have to do alternating measurements using non-commuting observables to get some random effects. If the momentum of the chair is zero then you will get the value 0 every time you measure it.

The thing that might interest you however is the quantum Zeno effect. Indeed continuous observations of a system have stabilizing effect on that system.

 

[Oudeis Eimi]

No. If you have a system and you measure it again and again using the same observable, you will get the same result all the times. You would have to do alternating measurements using non-commuting observables to get some random effects. If the momentum of the chair is zero then you will get the value 0 every time you measure it.

The thing that might interest you however is the quantum Zeno effect. Indeed continuous observations of a system have stabilizing effect on that system.

Ahhh yes, of course. However, is the environmental monitoring equivalent to an ideal measurement? I would say (but might very well be flat wrong) that it's more like a simultaneous, *imperfect* measurement of both position and momentum (to within HUP restrictions obviously). What do you think?

 

[bhobba]

That's why I don't (yet) have Schlosshauer's book, which I have been told is the book to get on decoherence, because I'm not conversant on open quantum systems, Lindbladt equations, etc.

I have the book and it is THE book.

You don't need to know that stuff - all you need is an intermediate course on QM at the level of say Griffiths which I think you likely have done.

Thanks
Bill

 

[bhobba]

Ahhh yes, of course. However, is the environmental monitoring equivalent to an ideal measurement?

You are on the right track. You need to investigate generalised measurement theory:
http://www.quantum.umb.edu/Jacobs/QMT/QMT_Chapter1.pdf

Schlosshauer's book is the book you want - you won't be sorry.

Thanks
Bill

 

[Oudeis Eimi]

Thanks again Bill. I have NR QM at the level of Cohen-Tanoudji (plus a smattering of QFT which is probably of little use here), so I will get the book. Thanks also for the link, I will study it.