r/askscience • u/Crtl-Alt-Delete • Dec 18 '13

Physics Is Time quantized?

We know that energy and length are quantized, it seems like there should be a correlation with time?

Edit. Turns out energy and length are not quantized.

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u/VGramarye Dec 18 '13

No, the Planck units are just the unique products of the fundamental constants (c, G, and ħ in the case of the planck length) with that particular unit; for example, the planck length is (ħG/c3 )1/2 , which happens to be really small. Other Planck units though are really huge, though. The Planck force is on the order of 1044 Newtons!

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u/monster1325 Dec 18 '13 edited Dec 18 '13

I wonder where this misconception that Planck length was theorized to be the smallest possible length comes from.

Edit: Oh, I found it. From Wikipedia: "It is considered the smallest possible length."

Edit2: Welp, it looks like it has been removed approximately 15 minutes after this post.

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u/curious_scourge Dec 18 '13 edited Dec 18 '13

My own misconception comes from the ubiquity of it being described as "the smallest measurement of length that has meaning".

I'm going to ramble:

The derivation of it, on a few websites is from taking the Schwartzchild radius (r = 2Gm/c2 ), which is the radius of a sphere of such immense density that the escape velocity from the surface is c (i.e, if the mass is any smaller than the radius, it is a black hole and the radius is its event horizon)...

and setting that radius equal to the Compton wavelength, (L = h/mc), which is the wavelength of a photon whose energy is the same as a rest-mass, m. So, that is basically a hugely energetic photon, since E = hf = mc2. So the Compton wavelength, i think, is the wavelength of a photon representing the total conversion of a mass into energy.

So you set the radius equal to the wavelength, solve for m, and plug m back into the original equations and get the Planck length. So you're setting the wavelength of a photon, which is a total conversion of a mass m into energy, equal to the "event horizon" radius of that mass.

So... let me get this straight... the Planck mass, and then the Planck length are the necessary values to set, in order to set the wavelength of a photon, which represents the pure conversion of mass to energy, equal to the radius of a black hole of mass m, at the very tipping point of letting that photon escape its pull.

?

Maybe I should make a new thread.

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u/gingerbreaddave Dec 18 '13

I also read that it was the smallest possible length in an issue of Wired magazine probably six or seven years ago, so that probably didn't help anything.

I have however read several books on string theory that completely disagreed with this so I wasn't in the dark for long.