A recent Astral Codex Ten post contained this bit:
Fewer than 50% (ie worse than chance) can correctly answer a true-false question about whether electrons are bigger than atoms.
The linked source seems to indicate that the survey’s expected answer to the question “electrons are smaller than atoms” is “true”. However, I think this is likely based on a faulty understanding of reality, and in any case the question has a trickier nature than the survey or Scott Alexander give it credit for.
There’s a common misconception that electrons (as well as e.g. protons and neutrons) are point particles, that is to say, that they can be said to exist at some precise location, just like a dot on a piece of graph paper.
Even when people talk about the uncertainty principle, they often lean into this misconception by suggesting that the wave function indicates “the probability that the (point-like) particle is found at a given location”.
However, an electron is not a point, but rather a wavefunction which has a wide extent in space. If you were to examine the electron at the tip of my pinky finger, there is in fact a non-zero (but very, very small) part of that electron that can be found at the base of the flag which Neil Armstrong planted on the moon (n.b. I’m not looking up whether it was actually Armstrong who did that), or even all the way out in the core of Alpha Centauri.
We could still try to talk about the size of an electron (and the size of an atom, which is a similar question) by considering the volume that contains 99% of the electron (and likewise a volume that contains 99% of a proton or neutron).
Considering this volume, the largest part of any given atom would be an electron, with the nuclear particles occupying a much larger volume (something something strong force). In this sense, the size of the atom is in fact coextensive with the size of its “largest” electron, and that electron is by no means smaller than the atom. There are of course in many atoms multiple electrons, and some of these may be “smaller” than the largest electron. However, I do not think the survey had this in mind as the justification for the answer it considered “correct” for the question.
I think the appropriate next step for Scott Alexander is to retract the relevant sentence from his post.
The question is not comparing electrons to protons or neutrons, or even to atomic nuclei (in which case the electron has less mass but spread over a wider area, and you’re right that the answer seems likely to be that the electron is bigger).
It is comparing electrons to atoms, which contain multiple electrons as well as protons and neutrons.
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.
Like, I’m sure the survey respondents weren’t thinking about Compton wavelength. But neither answer is good because it’s a confused/confusing question, so if the respondents were confused and didn’t remember being taught an answer in school, I would consider this a victory for their ability to be more confused by fiction than reality.
A recent Astral Codex Ten post contained this bit:
The linked source seems to indicate that the survey’s expected answer to the question “electrons are smaller than atoms” is “true”. However, I think this is likely based on a faulty understanding of reality, and in any case the question has a trickier nature than the survey or Scott Alexander give it credit for.
There’s a common misconception that electrons (as well as e.g. protons and neutrons) are point particles, that is to say, that they can be said to exist at some precise location, just like a dot on a piece of graph paper.
Even when people talk about the uncertainty principle, they often lean into this misconception by suggesting that the wave function indicates “the probability that the (point-like) particle is found at a given location”.
However, an electron is not a point, but rather a wavefunction which has a wide extent in space. If you were to examine the electron at the tip of my pinky finger, there is in fact a non-zero (but very, very small) part of that electron that can be found at the base of the flag which Neil Armstrong planted on the moon (n.b. I’m not looking up whether it was actually Armstrong who did that), or even all the way out in the core of Alpha Centauri.
We could still try to talk about the size of an electron (and the size of an atom, which is a similar question) by considering the volume that contains 99% of the electron (and likewise a volume that contains 99% of a proton or neutron).
Considering this volume, the largest part of any given atom would be an electron, with the nuclear particles occupying a much larger volume (something something strong force). In this sense, the size of the atom is in fact coextensive with the size of its “largest” electron, and that electron is by no means smaller than the atom. There are of course in many atoms multiple electrons, and some of these may be “smaller” than the largest electron. However, I do not think the survey had this in mind as the justification for the answer it considered “correct” for the question.
I think the appropriate next step for Scott Alexander is to retract the relevant sentence from his post.
The question is not comparing electrons to protons or neutrons, or even to atomic nuclei (in which case the electron has less mass but spread over a wider area, and you’re right that the answer seems likely to be that the electron is bigger).
It is comparing electrons to atoms, which contain multiple electrons as well as protons and neutrons.
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.
Yeah, I also found this question weird.
Like, I’m sure the survey respondents weren’t thinking about Compton wavelength. But neither answer is good because it’s a confused/confusing question, so if the respondents were confused and didn’t remember being taught an answer in school, I would consider this a victory for their ability to be more confused by fiction than reality.
(The mentioned ACX post is https://www.astralcodexten.com/p/a-theoretical-case-against-education )