Scale of Universe Tool

[Tubbythin]

Sounds like XKCD should do its own version of this thing.

Dark Flow.

 

[Wowbagger]

There are (at least) two relevant XKCD cartoons:
Height and Powers of 1, but nothing exactly equivalent.

Dark Flow.

These are exactly the cartoons that inspired my comment.

 

[sol invictus]

OK. So back to the scale website. It shows the electron itself at 1 attometer, and the electron (straight outta) compton wavelength at 2 picometers. How/why do they make this distinction? Does h/(mc) = 1 am?

No. h/(mc) is the Compton wavelength, which is about 2 picometers.

There is no (known) attometer scale associated with the electron, so that part is just wrong. My best guess is they've put that in because approximately attometer scales are the smallest we've probed in any experiment (in those experiments, h/p is about an attometer), so that's an upper bound on the size of any putative electron sub-structure. But to the best of our knowledge now, there is no such sub-structure and there's nothing special about attometer.

 

[dogjones]

Right. I also remembered recent reports of the electron being spherical. Are they talking about the electron's probability cloud here rather than the electron itself?

 

[Roboramma]

Actually, no. That's the problem - these formulas are really just rules of thumb, because in fact the electron can be in infinitely many possible states, and even if you know the state, it doesn't actually have a perfectly definite wavelength or size.

For example, think of a hydrogen atom in the ground state. The electron probability cloud is spread fairly uniformly over a spherical region with radius the Bohr radius, which is very roughly 20 times bigger than the electron's Compton wavelength. By the same token the momentum of the electron is very low in that state - it's much smaller than the mass (and in fact the product of momentum and position uncertainties for that state comes close to saturating the Heisenberg uncertainty principle).

One way to think about the relation between the de Broglie and Compton wavelengths is to note that the "size" of a slow (p<mc) electron cannot be smaller than its Compton wavelength - because if it was, that state would violate the uncertainty principle. So the Compton wavelength is a kind of minimum size for a slow electron. But slow electrons can be spread over much larger regions than that, depending on the circumstances.

For fast (p>mc) electrons relativity comes in, and then you should use the de Broglie wavelength - which again is more or less a lower bound on the size.

Thanks sol.

This sort of thing is why it seems to me that the idea of wave/particle duality, while somewhat useful, is basically only a tool for understanding phenomena that can't be encapsulated by both or either. Ie. An electron doesn't have a "wavelength", rather it behaves in a way that can sometimes be usefully modeled as a wave with a wavelength that can be calculated from one of those formulas.

Is that reasonable?

 

[dasmiller]

This sort of thing is why it seems to me that the idea of wave/particle duality, while somewhat useful, is basically only a tool for understanding phenomena that can't be encapsulated by both or either. Ie. An electron doesn't have a "wavelength", rather it behaves in a way that can sometimes be usefully modeled as a wave with a wavelength that can be calculated from one of those formulas.

Actually, I look at all of physics this way. The formulas, models, etc, don't necessarily describe the "true" underlying reality, they're just models that provide very accurate and usable results. In that view, an electron isn't "really" a particle or a wave or even something in-between, it's just a thing that can be accurately modeled in the manner that Sol and others have described.

Is that reasonable?

Obviously, I should think so.

 

[dogjones]

Yes, and of course it's fun to extend that out to normal experience, a la Kant. The manifold of perception that we experience (phenomena) doesn't describe the 'true' underlying reality (noumena) either; again it is just a model that provides useable results.

I'll stop before the mods move this post to philosophy.

 

[Roboramma]

Yes, and of course it's fun to extend that out to normal experience, a la Kant. The manifold of perception that we experience (phenomena) doesn't describe the 'true' underlying reality (noumena) either; again it is just a model that provides useable results.

I'll accept that as long as it's stressed that our perception is related to that underlying reality. If it weren't, it wouldn't be able to provide useable results.

 

[sol invictus]

Ie. An electron doesn't have a "wavelength", rather it behaves in a way that can sometimes be usefully modeled as a wave with a wavelength that can be calculated from one of those formulas.

Is that reasonable?

According to current theories, all particles are "wave-packets" - which simply means they are partially localized collections of waves all travelling coherently together. They (particles) are localized excitations of a field that exists everywhere in space and time. They behave like the kind of particles we're used to thinking about because they are (somewhat) localized, and because the field is a quantum field, which means its excitations are quantized and cannot have arbitrarily small amplitude.

Wavepackets even classically don't have perfectly well-defined wavelengths or sizes. And a given particle can correspond to a number of different types of wavepacket depending on its state.

So particles really are always waves, but not all waves have a well-defined wavelength, and not all electron-waves look the same.

ETA - wavepackets: http://www.st-andrews.ac.uk/~bds2/ltsn/Edinburgh/wave/

 

[dogjones]

According to current theories, all particles are "wave-packets" - which simply means they are partially localized collections of waves all travelling coherently together. They (particles) are localized excitations of a field that exists everywhere in space and time. They behave like the kind of particles we're used to thinking about because they are (somewhat) localized, and because the field is a quantum field, which means its excitations are quantized and cannot have arbitrarily small amplitude.

Wavepackets even classically don't have perfectly well-defined wavelengths or sizes. And a given particle can correspond to a number of different types of wavepacket depending on its state.

So particles really are always waves, but not all waves have a well-defined wavelength, and not all electron-waves look the same.

ETA - wavepackets: http://www.st-andrews.ac.uk/~bds2/ltsn/Edinburgh/wave/

Cool. And where does the "spherical" description come in then? Is it that the waves in the wavepackets don't have a well defined wavelength, but nonetheless can be guaranteed a certain proportion to each other, namely that which creates a spherical-shaped excitation?

 

[sol invictus]

Cool. And where does the "spherical" description come in then? Is it that the waves in the wavepackets don't have a well defined wavelength, but nonetheless can be guaranteed a certain proportion to each other, namely that which creates a spherical-shaped excitation?

Yes - although if the electron is moving fast Lorentz contraction will turn a sphere into an oblate ellipsoid (i.e. a pancake).