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Why is Planck time scaled by c^5?

by apeiron
Tags: planck, scaled, time
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apeiron
#1
Mar1-14, 04:45 PM
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Just curious.

The Planck length is lpl = (hG/c3)1/2 = 10-33cm

And it seems intuitive that it's c cube because space has three dimensions for the action.

But the Planck time is tpl = (hG/c5)1/2 = 10-43s

So is there some obvious physical reason why c is to the power of five here?
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phyzguy
#2
Mar1-14, 05:09 PM
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The Planck time is just the Planck length divided by c. This adds two powers of c because they are inside the square root.
dauto
#3
Mar1-14, 05:30 PM
Thanks
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Quote Quote by apeiron View Post
Just curious.

The Planck length is lpl = (hG/c3)1/2 = 10-33cm

And it seems intuitive that it's c cube because space has three dimensions for the action.

But the Planck time is tpl = (hG/c5)1/2 = 10-43s

So is there some obvious physical reason why c is to the power of five here?
Yes, that's the only combination of physical constants that gives you a constant with time units

apeiron
#4
Mar1-14, 05:49 PM
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Why is Planck time scaled by c^5?

Quote Quote by phyzguy View Post
The Planck time is just the Planck length divided by c. This adds two powers of c because they are inside the square root.
Thanks. Beautifully simple.
mfb
#5
Mar2-14, 04:55 AM
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Quote Quote by apeiron View Post
Just curious.

The Planck length is lpl = (hG/c3)1/2 = 10-33cm

And it seems intuitive that it's c cube because space has three dimensions for the action.
I don't see how a power of 3/2 looks natural.
The planck volume has c9/2.

Those odd factors just show how "unnatural" the SI-units (where c, h, G, k are not nice numbers) are in terms of fundamental physics.
Meir Achuz
#6
Mar2-14, 04:27 PM
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Newton said Gmm'/r=energy. In natural units, that means G is a (length)^2.
The hbar and c are just put in to get G in cm^2. This is always unique.
ChrisVer
#7
Mar2-14, 08:24 PM
P: 754
what does "space has 3 dimensions for the action"? I mean that it's kind of weird, we don't know whether at Planck scale you need more than 3 spatial dimensions, so it's not so intuitive...
On the other hand, everything seems normal under what is called dimensional analysis... So you have some constants ([itex]G, c, \hbar [/itex]) and you want to build characteristic quantities out of them .... So for everything, you just write:
[itex] [X]= [c]^{a} [\hbar]^{b} [G]^{d} [/itex]
and you solve for [itex]a,b,d[/itex]


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