The formulation of the uncertainty principle says, as I understand it, that variables occur in conjugate pairs, and it's impossible to know both with precision. The most oft-cited example is position and momentum, though sometimes energy and duration (of a process) is also cited, and there are others.
I'm wondering whether anyone knows if the mass and volume of an object are such a pair, so that for example the more precisely one knows the mass of an object, the less precisely they'd know the volume, and vice versa.
This would help me with a thesis I'm developing on mind-matter philsophy. I've researched this online at a couple of links and I can't find any comprehentive enumeration of "conjugate" variable pairs.
Thank you very much.
Eric
Strictly speaking the uncertainty principle refers to Planck's constant which has dimensions of momentum x distance or energy x time. Breaking this down further, the dimensions are mass x distance^2/time. Volume doesn't quite fit 
There is also one for angular momentum which looks a little different.
See for example,
http://mtzweb.scs.uiuc.edu/courses/chem442...1804/angmom.pdf
http://en.wikipedia.org/wiki/Uncertainty_principle
Only certain variable pairs are conjugate.
There is also one for angular momentum which looks a little different.
See for example,
http://mtzweb.scs.uiuc.edu/courses/chem442...1804/angmom.pdf
http://en.wikipedia.org/wiki/Uncertainty_principle
Only certain variable pairs are conjugate.
QUOTE (eric+Jul 30 2005, 12:51 AM)
The formulation of the uncertainty principle says, as I understand it, that variables occur in conjugate pairs, and it's impossible to know both with precision. The most oft-cited example is position and momentum, though sometimes energy and duration (of a process) is also cited, and there are others.
I'm wondering whether anyone knows if the mass and volume of an object are such a pair, so that for example the more precisely one knows the mass of an object, the less precisely they'd know the volume, and vice versa.
This would help me with a thesis I'm developing on mind-matter philsophy. I've researched this online at a couple of links and I can't find any comprehentive enumeration of "conjugate" variable pairs.
Thank you very much.
Eric
I would suggest you look into the proof of the position/momentum pairs and see how it is derived. From what I can recall (I'm a Chemist, not a Physicist, my Physics is a little rusty). Then if you can find a relation between mass and volume (perhaps relying on density of a material?) then try and follow the same steps.
I did a bit of googling and tried to find the (simple!) basic proof for the uncertainty principle (position-momentum) and couldn't find it. These however may help:
http://en.wikipedia.org/wiki/Uncertainty_principle
I found this in my Physics notes from last year however which may be of use, and allow for a similar semi-quantitative treatment of your relationship.
These notes are by Dr J Crain at University of Edinburgh for the Phys2A course.
I'm wondering whether anyone knows if the mass and volume of an object are such a pair, so that for example the more precisely one knows the mass of an object, the less precisely they'd know the volume, and vice versa.
This would help me with a thesis I'm developing on mind-matter philsophy. I've researched this online at a couple of links and I can't find any comprehentive enumeration of "conjugate" variable pairs.
Thank you very much.
Eric
I would suggest you look into the proof of the position/momentum pairs and see how it is derived. From what I can recall (I'm a Chemist, not a Physicist, my Physics is a little rusty). Then if you can find a relation between mass and volume (perhaps relying on density of a material?) then try and follow the same steps.
I did a bit of googling and tried to find the (simple!) basic proof for the uncertainty principle (position-momentum) and couldn't find it. These however may help:
http://en.wikipedia.org/wiki/Uncertainty_principle
I found this in my Physics notes from last year however which may be of use, and allow for a similar semi-quantitative treatment of your relationship.
These notes are by Dr J Crain at University of Edinburgh for the Phys2A course.
In my introductory quantum mechanics class we learned about the generalized uncertainty principle. I do not have my text book here to tell you what it is, but take out a copy of "Introduction to Quantum Mechanics" By David Griffin. We used the second edition, so I know its in there. What it says, that the product of two observables is greater than h bar over 2 multiplied by some other factor. With momentum and position that other factor is one, as well as the one for energy and time. I don't know if you would be able to represent mass and volume both as observables in the quantum sense, but if you could, then there will be some sort of uncertainty relation (although if that other factor, which I think is some sort of derivative, but I can not remember exactly, is zero, then thats probably no help to you).
On a personal opinion though, I doubt that such an uncertainty relation exists. Theoretically for a black hole we know the mass, which is finite, and the volume, which is zero, so in my opinion there won't be one.
Anyways, hope the first part of my post helps you find the info you need, and that the second part of the post doesn't discourage you to much. lol
Cheers,
Steveo
On a personal opinion though, I doubt that such an uncertainty relation exists. Theoretically for a black hole we know the mass, which is finite, and the volume, which is zero, so in my opinion there won't be one.
Anyways, hope the first part of my post helps you find the info you need, and that the second part of the post doesn't discourage you to much. lol
Cheers,
Steveo
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