Uncertainty principle for a sitting person
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
|
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
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
Nov 12 at 1:16
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
Nov 12 at 11:22
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
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
Nov 12 at 19:44
|
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
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 2 days ago
Qmechanic♦
99.4k121781109
99.4k121781109
asked Nov 12 at 1:05
Fakrudeen
334310
334310
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
Nov 12 at 1:16
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
Nov 12 at 11:22
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
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
Nov 12 at 19:44
|
show 5 more comments
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
Nov 12 at 1:16
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
Nov 12 at 11:22
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
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
Nov 12 at 19:44
7
7
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
Nov 12 at 1:16
I wonder if the quantum phenomena can still be observed in such a large scale system...
– K_inverse
Nov 12 at 1:16
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
Nov 12 at 11:22
@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
Nov 12 at 11:22
2
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
7
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
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
Nov 12 at 19:44
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
Nov 12 at 19:44
|
show 5 more comments
2 Answers
2
active
oldest
votes
up vote
101
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.
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
Nov 12 at 15:09
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
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
Nov 13 at 10:33
|
show 3 more comments
up vote
29
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.
19
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
Nov 12 at 17:50
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
101
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.
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
Nov 12 at 15:09
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
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
Nov 13 at 10:33
|
show 3 more comments
up vote
101
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.
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
Nov 12 at 15:09
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
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
Nov 13 at 10:33
|
show 3 more comments
up vote
101
down vote
up vote
101
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.
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.
edited Nov 12 at 1:42
answered Nov 12 at 1:22
Dan Yand
2,6071115
2,6071115
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
Nov 12 at 15:09
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
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
Nov 13 at 10:33
|
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
Nov 12 at 15:09
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
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
Nov 13 at 10:33
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
Nov 12 at 15:09
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
Nov 12 at 15:09
2
2
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
@Draco18s Isn't that a marching column?
– Pilchard123
Nov 12 at 15:57
2
2
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
@Pilchard123 Yeah, but they don't maintain their momentum uncertainties when walking through double doors.
– Draco18s
Nov 12 at 16:20
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
Nov 12 at 23:03
+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
Nov 12 at 23:03
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
Nov 13 at 10:33
@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
Nov 13 at 10:33
|
show 3 more comments
up vote
29
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.
19
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
Nov 12 at 17:50
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
add a comment |
up vote
29
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.
19
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
Nov 12 at 17:50
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
add a comment |
up vote
29
down vote
up vote
29
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.
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 Nov 12 at 1:19
J. Murray
6,6512722
6,6512722
19
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
Nov 12 at 17:50
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
add a comment |
19
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
Nov 12 at 17:50
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
19
19
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
Nov 12 at 17:50
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
Nov 12 at 17:50
7
7
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
@DavidRicherby I'd be more concerned if you had convinced a hydrogen atom to stay still
– SGR
Nov 13 at 13:34
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
Nov 12 at 1:16
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
Nov 12 at 11:22
2
If it is a rocking chair you don't have zero uncertainty in the position even at macroscopic level :-)
– Francesco
Nov 12 at 11:48
7
You're confusing the momentum with the uncertainty in momentum.
– mkrieger1
Nov 12 at 13:54
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
Nov 12 at 19:44