Uncertainty principle for a sitting person
up vote
16
down vote
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If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.
What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?
heisenberg-uncertainty-principle estimation
edited 18 hours ago
Qmechanic♦
99.3k121781105
asked 2 days ago
Fakrudeen
334310
|
show 5 more comments
up vote
16
down vote
favorite
If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.
What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?
heisenberg-uncertainty-principle estimation
edited 18 hours ago
Qmechanic♦
99.3k121781105
asked 2 days ago
Fakrudeen
334310
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
2
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
18
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday
|
show 5 more comments
up vote
16
down vote
favorite
up vote
16
down vote
favorite
If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.
What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?
heisenberg-uncertainty-principle estimation
edited 18 hours ago
Qmechanic♦
99.3k121781105
asked 2 days ago
Fakrudeen
334310
If a person is sitting on a chair his momentum is zero and his uncertainty in position should be infinite. But we can obviously position him at most within few chair lengths.
What am I missing? Do we have to invoke earth's motion, motion of the galaxy etc. to resolve the issue?
heisenberg-uncertainty-principle estimation
heisenberg-uncertainty-principle estimation
edited 18 hours ago
Qmechanic♦
99.3k121781105
asked 2 days ago
Fakrudeen
334310
edited 18 hours ago
Qmechanic♦
99.3k121781105
asked 2 days ago
Fakrudeen
334310
edited 18 hours ago
Qmechanic♦
99.3k121781105
edited 18 hours ago
Qmechanic♦
99.3k121781105
edited 18 hours ago
Qmechanic♦
99.3k121781105
99.3k121781105
asked 2 days ago
Fakrudeen
334310
asked 2 days ago
Fakrudeen
334310
asked 2 days ago
Fakrudeen
334310
334310
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
2
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
18
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday
|
show 5 more comments
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
2
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
18
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday
7
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
2
2
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
2
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
7
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
18
18
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday
|
show 5 more comments
2 Answers
2
active
oldest
votes
up vote
98
down vote
If a person is sitting on a chair his momentum is zero...
How close to zero?
The uncertainty principle says that if $Delta x$ is the uncertainty in position and $Delta p$ is the uncertainty in momentum, then $Delta x,Delta psim hbar$. So, consider an object with the mass of a person, say $M = 70$ kg. Suppose the uncertainty in this object's position is roughly the size of a proton, say $Delta x = 10^{-15}$ meters. The uncertainty principle says that the uncertainty in momentum must be
$$
Delta psimfrac{hbar}{Delta x}approxfrac{1 times 10^{-34}text{ meter}^2text{ kg / second}}{10^{-15}text{ meter}}approx 1times 10^{-19}text{ meter kg / second},
$$
so the uncertainty in the object's velocity is
$$
Delta v=frac{Delta p}{M}approx frac{approx 1times 10^{-19}text{ meter kg / second}}{text{70 kg}}sim 1times 10^{-21}text{ meter / second}.
$$
In other words, the uncertainty in the person's velocity would be roughly one proton-radius per month.
This shows that the uncertainties in a person's position and momentum can both be zero as far as we can ever hope to tell, and this is not at all in conflict with the uncertainty principle.
answered 2 days ago
Dan Yand
2,319115
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
|
show 3 more comments
up vote
27
down vote
If we pretend that person is a quantum mechanical particle of mass $m=75$ kg and we localize him in a box of length $L=1$ m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velocity to within one Planck length per second?
Applying quantum mechanical principles to classical systems is always a recipe for disaster, but this underlying point is a good one - in macroscopic systems, the uncertainty principle implies fundamental uncertainties which are so small as to be completely meaningless from an observational point of view. If you were moving at a planck length per second for a hundred quadrillion years, you'd be about halfway across a hydrogen atom.
answered 2 days ago
J. Murray
6,6312722
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
98
down vote
If a person is sitting on a chair his momentum is zero...
How close to zero?
The uncertainty principle says that if $Delta x$ is the uncertainty in position and $Delta p$ is the uncertainty in momentum, then $Delta x,Delta psim hbar$. So, consider an object with the mass of a person, say $M = 70$ kg. Suppose the uncertainty in this object's position is roughly the size of a proton, say $Delta x = 10^{-15}$ meters. The uncertainty principle says that the uncertainty in momentum must be
$$
Delta psimfrac{hbar}{Delta x}approxfrac{1 times 10^{-34}text{ meter}^2text{ kg / second}}{10^{-15}text{ meter}}approx 1times 10^{-19}text{ meter kg / second},
$$
so the uncertainty in the object's velocity is
$$
Delta v=frac{Delta p}{M}approx frac{approx 1times 10^{-19}text{ meter kg / second}}{text{70 kg}}sim 1times 10^{-21}text{ meter / second}.
$$
In other words, the uncertainty in the person's velocity would be roughly one proton-radius per month.
This shows that the uncertainties in a person's position and momentum can both be zero as far as we can ever hope to tell, and this is not at all in conflict with the uncertainty principle.
answered 2 days ago
Dan Yand
2,319115
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
|
show 3 more comments
up vote
98
down vote
If a person is sitting on a chair his momentum is zero...
How close to zero?
The uncertainty principle says that if $Delta x$ is the uncertainty in position and $Delta p$ is the uncertainty in momentum, then $Delta x,Delta psim hbar$. So, consider an object with the mass of a person, say $M = 70$ kg. Suppose the uncertainty in this object's position is roughly the size of a proton, say $Delta x = 10^{-15}$ meters. The uncertainty principle says that the uncertainty in momentum must be
$$
Delta psimfrac{hbar}{Delta x}approxfrac{1 times 10^{-34}text{ meter}^2text{ kg / second}}{10^{-15}text{ meter}}approx 1times 10^{-19}text{ meter kg / second},
$$
so the uncertainty in the object's velocity is
$$
Delta v=frac{Delta p}{M}approx frac{approx 1times 10^{-19}text{ meter kg / second}}{text{70 kg}}sim 1times 10^{-21}text{ meter / second}.
$$
In other words, the uncertainty in the person's velocity would be roughly one proton-radius per month.
This shows that the uncertainties in a person's position and momentum can both be zero as far as we can ever hope to tell, and this is not at all in conflict with the uncertainty principle.
answered 2 days ago
Dan Yand
2,319115
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
|
show 3 more comments
up vote
98
down vote
up vote
98
down vote
If a person is sitting on a chair his momentum is zero...
How close to zero?
The uncertainty principle says that if $Delta x$ is the uncertainty in position and $Delta p$ is the uncertainty in momentum, then $Delta x,Delta psim hbar$. So, consider an object with the mass of a person, say $M = 70$ kg. Suppose the uncertainty in this object's position is roughly the size of a proton, say $Delta x = 10^{-15}$ meters. The uncertainty principle says that the uncertainty in momentum must be
$$
Delta psimfrac{hbar}{Delta x}approxfrac{1 times 10^{-34}text{ meter}^2text{ kg / second}}{10^{-15}text{ meter}}approx 1times 10^{-19}text{ meter kg / second},
$$
so the uncertainty in the object's velocity is
$$
Delta v=frac{Delta p}{M}approx frac{approx 1times 10^{-19}text{ meter kg / second}}{text{70 kg}}sim 1times 10^{-21}text{ meter / second}.
$$
In other words, the uncertainty in the person's velocity would be roughly one proton-radius per month.
This shows that the uncertainties in a person's position and momentum can both be zero as far as we can ever hope to tell, and this is not at all in conflict with the uncertainty principle.
answered 2 days ago
Dan Yand
2,319115
If a person is sitting on a chair his momentum is zero...
How close to zero?
The uncertainty principle says that if $Delta x$ is the uncertainty in position and $Delta p$ is the uncertainty in momentum, then $Delta x,Delta psim hbar$. So, consider an object with the mass of a person, say $M = 70$ kg. Suppose the uncertainty in this object's position is roughly the size of a proton, say $Delta x = 10^{-15}$ meters. The uncertainty principle says that the uncertainty in momentum must be
$$
Delta psimfrac{hbar}{Delta x}approxfrac{1 times 10^{-34}text{ meter}^2text{ kg / second}}{10^{-15}text{ meter}}approx 1times 10^{-19}text{ meter kg / second},
$$
so the uncertainty in the object's velocity is
$$
Delta v=frac{Delta p}{M}approx frac{approx 1times 10^{-19}text{ meter kg / second}}{text{70 kg}}sim 1times 10^{-21}text{ meter / second}.
$$
In other words, the uncertainty in the person's velocity would be roughly one proton-radius per month.
This shows that the uncertainties in a person's position and momentum can both be zero as far as we can ever hope to tell, and this is not at all in conflict with the uncertainty principle.
answered 2 days ago
Dan Yand
2,319115
edited 2 days ago
answered 2 days ago
Dan Yand
2,319115
answered 2 days ago
Dan Yand
2,319115
answered 2 days ago
Dan Yand
2,319115
2,319115
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
|
show 3 more comments
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
1
1
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
Reminds me that science is closing in on producing quantum effects on the macro scale. We're a ways off from a human, but a 120 carbon atom bucky ball? Smashed. (A coherent beam of humans would be an interesting engineering challenge...)
– Draco18s
2 days ago
2
2
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
@Draco18s Isn't that a marching column?
– Pilchard123
2 days ago
2
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
2 days ago
3
3
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
+1 Great job taking a joke/troll question, applying correct physics, and ending with "zero as far as we can ever hope to tell".
– AnoE
yesterday
8
8
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
@AnoE - I wouldn't say that's a joke/troll question. It's interest to grasp the basics of uncertainty principle. In fact, basic physics textbooks examples are not far away from that question.
– Pere
yesterday
|
show 3 more comments
up vote
27
down vote
If we pretend that person is a quantum mechanical particle of mass $m=75$ kg and we localize him in a box of length $L=1$ m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velocity to within one Planck length per second?
Applying quantum mechanical principles to classical systems is always a recipe for disaster, but this underlying point is a good one - in macroscopic systems, the uncertainty principle implies fundamental uncertainties which are so small as to be completely meaningless from an observational point of view. If you were moving at a planck length per second for a hundred quadrillion years, you'd be about halfway across a hydrogen atom.
answered 2 days ago
J. Murray
6,6312722
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
add a comment |
up vote
27
down vote
If we pretend that person is a quantum mechanical particle of mass $m=75$ kg and we localize him in a box of length $L=1$ m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velocity to within one Planck length per second?
Applying quantum mechanical principles to classical systems is always a recipe for disaster, but this underlying point is a good one - in macroscopic systems, the uncertainty principle implies fundamental uncertainties which are so small as to be completely meaningless from an observational point of view. If you were moving at a planck length per second for a hundred quadrillion years, you'd be about halfway across a hydrogen atom.
answered 2 days ago
J. Murray
6,6312722
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
add a comment |
up vote
27
down vote
up vote
27
down vote
If we pretend that person is a quantum mechanical particle of mass $m=75$ kg and we localize him in a box of length $L=1$ m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velocity to within one Planck length per second?
Applying quantum mechanical principles to classical systems is always a recipe for disaster, but this underlying point is a good one - in macroscopic systems, the uncertainty principle implies fundamental uncertainties which are so small as to be completely meaningless from an observational point of view. If you were moving at a planck length per second for a hundred quadrillion years, you'd be about halfway across a hydrogen atom.
answered 2 days ago
J. Murray
6,6312722
If we pretend that person is a quantum mechanical particle of mass $m=75$ kg and we localize him in a box of length $L=1$ m, then the resulting uncertainty in his velocity would be about one Planck length per second. Are you sure you know his velocity to within one Planck length per second?
Applying quantum mechanical principles to classical systems is always a recipe for disaster, but this underlying point is a good one - in macroscopic systems, the uncertainty principle implies fundamental uncertainties which are so small as to be completely meaningless from an observational point of view. If you were moving at a planck length per second for a hundred quadrillion years, you'd be about halfway across a hydrogen atom.
answered 2 days ago
J. Murray
6,6312722
answered 2 days ago
J. Murray
6,6312722
answered 2 days ago
J. Murray
6,6312722
answered 2 days ago
J. Murray
6,6312722
6,6312722
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
add a comment |
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
18
18
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
I tried doing the experiment you suggest in your last sentence but the damned hydrogen atom wouldn't sit still and I gave up after a couple of weeks.
– David Richerby
2 days ago
6
6
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
yesterday
add a comment |
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7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
2 days ago
2
@K_inverse Yes, they can. But as soon as you try that, you'd realize neither the momentum nor the position is perfectly localized, so the premise of the question is false - you decidedly don't have "zero momentum" when sitting on a chair.
– Luaan
2 days ago
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
2 days ago
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
2 days ago
18
Since I unexpectedly gained huge momentum very unexpectedly while sitting on an IKEA chair, I have never again felt any certainty about my position in the universe.
– Pavel
yesterday