Understanding Joos Equations and Decoherence in Quantum Mechanics

[kye]

I read in the Stanford website on this topic "The Role of Decoherence in Quantum Mechanics"

"Indeed, while it is well-known that localised states of macroscopic objects spread very slowly with time under the free Schrödinger evolution (i.e., if there are no interactions), the situation turns out to be different if they are in interaction with the environment. Although the different components that couple to the environment will be individually incredibly localised, collectively they can have a spread that is many orders of magnitude larger. That is, the state of the object and the environment could be a superposition of zillions of very well localised terms, each with slightly different positions, and that are collectively spread over a macroscopic distance, even in the case of everyday objects.13

13 As a numerical example, take a macroscopic particle of radius 1cm (mass 10g) interacting with air under normal conditions. After an hour the overall spread of its state is of the order of 1m. (This estimate uses equations [3.107] and [3.73] in Joos and Zeh (1985).)

The equations of Joos are shared in their website at http://www.decoherence.de/J+Z.pdf

My question is this.

Why don't we see everyday objects spread over macroscopic distance? Is it because we can see experience only one of the branches or is it the case like the wavepacket of a free particle that spreads in time? Is the latter the context of what Joos is saying and not the latter about the branches? If it's the latter, what is the explanation why everyday objects are not spread over macroscopic distance (the is a consequence of decoherence)?

 

[bhobba]

As a numerical example, take a macroscopic particle of radius 1cm (mass 10g) interacting with air under normal conditions. After an hour the overall spread of its state is of the order of 1m. (This estimate uses equations [3.107] and [3.73] in Joos and Zeh (1985).)

You will need to post your calculations.

My reading indicates that's not what is being said - rather as he states just prior to equation 3.107:
'Hence under usual circumstances all macroscopic objects can be assumed to be localized within their thermal de Broglie wavelengths.'

The de Brogle wavelengths of macroscopic objects is very very small indicating high localisation.

Its almost certain you have done something wrong - or misinterpreted something - that paper has been around for yonks - that type of error would not escape attention that long.

Thanks
Bill

 

[kye]

You will need to post your calculations.

My reading indicates that's not what is being said - rather as he states just prior to equation 3.107:
'Hence under usual circumstances all macroscopic objects can be assumed to be localized within their thermal de Broglie wavelengths.'

The de Brogle wavelengths of macroscopic objects is very very small indicating high localisation.

Its almost certain you have done something wrong - or misinterpreted something - that paper has been around for yonks - that type of error would not escape attention that long.

Thanks
Bill

That calculation quote came from http://plato.stanford.edu/entries/qm-decoherence/ in reference 13 under "2.2 Exacerbating the measurement problem", but wave packet still spreads in the Schroedinger Equations. Won't decoherence cause any delocalization problem at all (since there is no collapse)?

 

[bhobba]

That calculation quote came from http://plato.stanford.edu/entries/qm-decoherence/ in reference 13 under "2.2 Exacerbating the measurement problem", but wave packet still spreads in the Schroedinger Equations. Won't decoherence cause any delocalization problem at all (since there is no collapse)?

I would seriously doubt that claim about a 10g object.

Simple calculations show:
http://en.wikipedia.org/wiki/Wave_packet
'The width eventually grows linearly in time, as ħt /m√a, indicating wave-packet spreading.'

Although I haven't done the glug and chug knowing how small planks constant is, 6.62606957 × 10-34, macroscopic objects would spread VERY VERY slowly.

To doubt this I would really need to see the DETAILED math, and not some reference to an article that claims it.

This spreading has nothing to do with decoherence which is a separate issue. But if you include that it will only make it even less likely to spread because the above is spreading assuming no interaction. Even a few stray photons from the CMBR is enough to give a dust particle a definite position. And if the equation I posted is correct (and the derivation looks pretty basic to me), even a dust particle will spread very very slowly and the chances of it not being decohered again before any quantum effect can show is utterly zero.

Thanks
Bill

 

[kye]

I would seriously doubt that claim about a 10g object.

Simple calculations show:
http://en.wikipedia.org/wiki/Wave_packet
'The width eventually grows linearly in time, as ħt /m√a, indicating wave-packet spreading.'

Although I haven't done the glug and chug knowing how small planks constant is, 6.62606957 × 10-34, macroscopic objects would spread VERY VERY slowly.

To doubt this I would really need to see the DETAILED math, and not some reference to an article that claims it.

This spreading has nothing to do with decoherence which is a separate issue. But if you include that it will only make it even less likely to spread because the above is spreading assuming no interaction. Even a few stray photons from the CMBR is enough to give a dust particle a definite position. And if the equation I posted is correct (and the derivation looks pretty basic to me), even a dust particle will spread very very slowly and the chances of it not being decohered again before any quantum effect can show is utterly zero.

Thanks
Bill

Thanks for the clarifications. I guess the author of the article forgets about the de_broglie wavelength of macroscopic objects.

Anyway, when wave packet spreads, are they forming different branches already in Many Worlds or do worlds only split (or form branches) whenever there are quantum choices (what qualify the the valid choices before branches split)?

 

[bhobba]

Anyway, when wave packet spreads, are they forming different branches already in Many Worlds or do worlds only split (or form branches) whenever there are quantum choices (what qualify the the valid choices before branches split)?

What a wavefunction is depends on your interpretation.

From the formalism nothing is said other than it encodes the probabilities of outcomes if you observed it. When it spreads it means if you observe it its position is less certain.

Thanks
Bill