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Scale of Universe Tool

Aepervius said:
They have an error inside, they cite 2.5 mm for human egg, it is actually 0.25 mm (2.5*10^-4 m). You can compare with the other items around it.

IMO 1/4 of a millimeter is not exactly viewable with naked eye, unless you count a dot as "viewable".
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I'd count a viewable dot as viewable!

It seems to have a diameter bigger than a human hair, so probably just about viewable.
 
dogjones said:
I'd count a viewable dot as viewable!

It seems to have a diameter bigger than a human hair, so probably just about viewable.
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I would rather count it as "perceivable" under the correct condition, and only viewable (to see its form or details) under a magnification. But that's probably only me.
 
Lots of fun.

Only a few flaws such as their assertion that Uranus is pronounced (YER uh niss)
 
sol invictus said:
The "wavelength" of an electron at rest or slowly moving is h/(mc), where m is the mass of the electron, h is Planck's constant, and c is the speed of light in vacuum. That's more or less its size - it's the approximate radius of the region where you might find the electron if you look.

If the electron is moving very fast, so its kinetic energy is larger than its rest mass energy mc2, then its wavelength is h/p, where p=γmv is its momentum. If you like, you can think of the difference when γ is big and v~c as due to Lorentz contraction (that's why there's a γ factor).

Photons are always moving very fast, and their wavelength is therefore always just h/p, where p is the photon's momentum.
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Isn't there an equation that can give the electron's wavelength at any v? I can't see how h/mc can change to h/γmv as v goes to c, so it doesn't look like h/mc is just an approximation of a relativistic h/p. I can't imagine that nature has some arbitrary threshold where you change equations, rather one must be an approximation for low velocities, so can we apply h/p at low velocities as well? Or are both approximations and there is another more complicated equation that works in both high and low velocities?

HELP :boxedin:

edit: by the way "If you like, you can think of the difference when γ is big and v~c as due to Lorentz contraction (that's why there's a γ factor)" seems like it should be an answer to my question, but I don't see it...
 
Roboramma said:
Isn't there an equation that can give the electron's wavelength at any v?
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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.
 
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sol invictus said:
The "wavelength" of an electron at rest or slowly moving is h/(mc), where m is the mass of the electron, h is Planck's constant, and c is the speed of light in vacuum. That's more or less its size - it's the approximate radius of the region where you might find the electron if you look.

If the electron is moving very fast, so its kinetic energy is larger than its rest mass energy mc2, then its wavelength is h/p, where p=γmv is its momentum. If you like, you can think of the difference when γ is big and v~c as due to Lorentz contraction (that's why there's a γ factor).

Photons are always moving very fast, and their wavelength is therefore always just h/p, where p is the photon's momentum.
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Trying to get this. What is "γ" and what does v~c mean?

Also this

sol invictus said:
That's more or less its size - it's the approximate radius of the region where you might find the electron if you look.
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doesn't seem to tell me anything about the 'size' of the electron, rather the location. Is it even correct to think of it in terms of 'size' then?
 
dogjones said:
Trying to get this. What is "γ" and what does v~c mean?
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http://scienceworld.wolfram.com/physics/RelativisticGamma.html

v~c means the speed v is close to c, the speed of light.

doesn't seem to tell me anything about the 'size' of the electron, rather the location. Is it even correct to think of it in terms of 'size' then?
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Well... the radius of the probability cloud is the closest thing to a "size" you can really make sense of in quantum mechanics. You can think of that cloud as really being the electron, not just an uncertainty about its location, in which case an electron in that state really is that big.

Of course if you then go and measure where it is, you might change its state so it's much better localized - but that's because you changed the state by your measurement, not because it actually had a better defined location to begin with.
 
sol invictus said:
Of course if you then go and measure where it is, you might change its state so it's much better localized - but that's because you changed the state by your measurement, not because it actually had a better defined location to begin with.
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Ah, so measuring it would 'shrink' it, in a sense?
 
dogjones said:
Ah, so measuring it would 'shrink' it, in a sense?
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A very accurate measurement of its position would shrink it, yes - but it would also impart a large amount of momentum to it and strongly affect its state. For instance, it might require ionizing the hydrogen atom (i.e. removing the electron from its bound state with the proton). A not-very-accurate measurement might or might not shrink it depending on how it was done.
 
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? And likewise h/p = 2 pm?
 
mike3 said:
Does this mean there could exist a vast layer of reality which we may never be able to explore?
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There is already such a layer. It is called "the mind of Woman".

(OK that was a crp joke.)
 
mike3 said:
Does this mean there could exist a vast layer of reality which we may never be able to explore?
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No, all we need is a good, solid theory to predict how photons behave, which accounts for the two ways we tend to measure them. We can then develop other methods of testing predictions made by that theory.

Some interpretations of Quantum Theory attempt to do this.

At a basic, fundamental level, String Theory also tries to do this. Though, its ideas are not exactly testable, yet.

Dessi said:
I was half expecting the large end of the diagram to include a label saying "yo mama"
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Sounds like XKCD should do its own version of this thing.
 
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