If you have a free electron and an atom, at the same temperature, the free electron will be much larger.
At the quantum scale our intuition that “light=small, heavy=big” gets flipped—it’s actually the heavy things that tend to have smaller size. This is because the size of sufficiently tiny things is dominated by how spread out the wavefunction is (and light things have a more spread out wavefunction), while the size of e.g. a bowling ball is set by separation of the packed atoms it’s made of, not by the sharpness of its wavefunction.
So not only is the question undefined (can’t answer without more details), the intended answer is actually counter to the intuitions you get taught when learning quantum mechanics.
I would accept the position ‘this question is not well-defined’. However, I don’t think I accept the position ‘actually an electron is bigger once we define things this way’.
(For one thing, I think that definition may imply that an electron is bigger than me?)
Also, I think this overall argument is a nitpick that is not particularly relevant to Scott’s article, unless you think that a large percentage of the respondents to that survey were quantum physicists.
(For one thing, I think that definition may imply that an electron is bigger than me?)
An electron’s wavefunction is actually more spread out than yours is (if we could do a quantum measurement on the position of your center of mass—which we can’t because it’s too hard to isolate you from the environment—it would be very precise).
But because you’re a macroscopic object, how big you are isn’t determined by your center of mass wavefunction, but by the distance between the different atoms comprising you. So you’re bigger than a standard electron.
For a hydrogen atom at room temperature, the size of the electron orbital and the size due to a spread-out wavefunction are actually about the same. So for interactions involving hydrogen atoms, the wavefunction size is really important.
If you have a free electron and an atom, at the same temperature, the free electron will be much larger.
At the quantum scale our intuition that “light=small, heavy=big” gets flipped—it’s actually the heavy things that tend to have smaller size. This is because the size of sufficiently tiny things is dominated by how spread out the wavefunction is (and light things have a more spread out wavefunction), while the size of e.g. a bowling ball is set by separation of the packed atoms it’s made of, not by the sharpness of its wavefunction.
So not only is the question undefined (can’t answer without more details), the intended answer is actually counter to the intuitions you get taught when learning quantum mechanics.
I would accept the position ‘this question is not well-defined’. However, I don’t think I accept the position ‘actually an electron is bigger once we define things this way’.
(For one thing, I think that definition may imply that an electron is bigger than me?)
Also, I think this overall argument is a nitpick that is not particularly relevant to Scott’s article, unless you think that a large percentage of the respondents to that survey were quantum physicists.
An electron’s wavefunction is actually more spread out than yours is (if we could do a quantum measurement on the position of your center of mass—which we can’t because it’s too hard to isolate you from the environment—it would be very precise).
But because you’re a macroscopic object, how big you are isn’t determined by your center of mass wavefunction, but by the distance between the different atoms comprising you. So you’re bigger than a standard electron.
For a hydrogen atom at room temperature, the size of the electron orbital and the size due to a spread-out wavefunction are actually about the same. So for interactions involving hydrogen atoms, the wavefunction size is really important.