# Why is Planck time scaled by c^5?

• apeiron
In summary, the Planck length and Planck time are both very small and elusive numbers. They are difficult to understand and comprehend because they involve math that is not common in everyday life. However, the Planck volume has c9/2 and this is a physical constant that is always unique.
apeiron
Gold Member
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?

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 $a,b,d$

## 1. Why is Planck time scaled by c^5?

Planck time is scaled by c^5 because it is the unit of time derived from the fundamental constants of nature, including the speed of light (c). This scaling allows for a consistent and universal measurement of time in the context of the laws of physics.

## 2. How does c^5 affect Planck time?

The scaling factor of c^5 in Planck time is a result of the principle of relativity, which states that the laws of physics should appear the same to all observers regardless of their relative motion. By incorporating c^5, Planck time remains consistent and invariant in all reference frames.

## 3. What is the relationship between c^5 and the Planck time unit?

The relationship between c^5 and Planck time is that c^5 is used as a scaling factor to convert between the two units. This scaling allows for a more precise and universal measurement of time in the context of quantum physics.

## 4. Why is c^5 used in the Planck time formula?

C^5 is used in the Planck time formula because it is a fundamental constant that represents the speed of light in a vacuum. This constant is essential for understanding the behavior of the universe at a very small scale and is incorporated into the Planck time unit to maintain consistency with other fundamental constants.

## 5. How does the scaling factor of c^5 impact our understanding of time?

The scaling factor of c^5 in Planck time has a significant impact on our understanding of time, particularly in the context of quantum mechanics. It allows us to measure time consistently at a very small scale and provides a fundamental unit for understanding the behavior of the universe. Without this scaling factor, our understanding of time would be limited and inconsistent with the laws of physics.

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