Why is Planck time scaled by c^5?

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Discussion Overview

The discussion revolves around the scaling of Planck time by c^5 in its formulation, exploring the relationships between fundamental constants and their implications in theoretical physics. Participants examine the derivation of Planck time and its connection to Planck length, as well as the dimensional analysis involved in these concepts.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that the Planck time is derived from the Planck length divided by c, which introduces two powers of c due to the square root operation.
  • Others suggest that the combination of constants leading to Planck time is unique in yielding a quantity with time units.
  • A participant questions the intuition behind the power of 3/2 in the Planck length and highlights the Planck volume's scaling with c^9/2, suggesting a lack of naturalness in SI units.
  • Another participant discusses the implications of Newton's law in natural units, indicating that G behaves as a length squared, which is a unique relationship when incorporating c and hbar.
  • One participant raises a question about the assumption of three spatial dimensions at the Planck scale, suggesting that the dimensional analysis may not be straightforward.

Areas of Agreement / Disagreement

Participants express various viewpoints on the scaling of Planck time and its derivation, with no clear consensus reached on the intuitive understanding of the powers of c involved or the implications of dimensional analysis at the Planck scale.

Contextual Notes

Some assumptions about the nature of space at the Planck scale remain unresolved, and the discussion highlights the complexity of relating physical constants to characteristic quantities.

apeiron
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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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The Planck time is just the Planck length divided by c. This adds two powers of c because they are inside the square root.
 
apeiron said:
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
 
phyzguy said:
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.
 
apeiron said:
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.
 
Newton said Gmm'/r=energy. In natural units, that means G is a (length)^2.
The hbar and c are just put into get G in cm^2. This is always unique.
 
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 (G, c, \hbar) and you want to build characteristic quantities out of them ... So for everything, you just write:
[X]= [c]^{a} [\hbar]^{b} [G]^{d}
and you solve for a,b,d
 

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