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Why is Planck time scaled by c^5? 
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#1
Mar114, 04:45 PM

PF Gold
P: 2,432

Just curious.
The Planck length is lpl = (hG/c^{3})^{1/2} = 10^{33}cm And it seems intuitive that it's c cube because space has three dimensions for the action. But the Planck time is tpl = (hG/c^{5})^{1/2} = 10^{43}s So is there some obvious physical reason why c is to the power of five here? 


#2
Mar114, 05:09 PM

P: 2,179

The Planck time is just the Planck length divided by c. This adds two powers of c because they are inside the square root.



#3
Mar114, 05:30 PM

Thanks
P: 1,948




#5
Mar214, 04:55 AM

Mentor
P: 11,831

The planck volume has c^{9/2}. Those odd factors just show how "unnatural" the SIunits (where c, h, G, k are not nice numbers) are in terms of fundamental physics. 


#6
Mar214, 04:27 PM

Sci Advisor
HW Helper
PF Gold
P: 2,010

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. 


#7
Mar214, 08:24 PM

P: 872

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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