Planck Units: Mass and Length

[Dmitry67]

I was always puzzled by the fact that while almost all Planck units are extreme (very high or very low), Mass and Energy are exception from that rule. Planck mass is in the ‘middle’ of the spectrum, and it divides the mass spectrum into 2 parts:

• For small masses/energies m << Mplanck we can define a wavelength corresponding to the energy (E=hv). The higher energy – the shorter wavelength.
• For big masses we can define Schwarzschild radius Rs which is proportional to mass (and as I noticed in Black Hole physics scientists think in Rs units, substituting R with M). So, the higher energy – the longer wavelength.

So the same length corresponds (in Planck’s sense) to 2 masses: one light and one heavy. And there is also a correspondence (mapping) of heavy masses into light masses and vice versa. Assuming that Planck units are natural such mappings must be important, but so far I haven’t heard anything about it.
This is really weird. Any thoughts? (or URLs?)

 

[Finbar]

I was always puzzled by the fact that while almost all Planck units are extreme (very high or very low), Mass and Energy are exception from that rule. Planck mass is in the ‘middle’ of the spectrum, and it divides the mass spectrum into 2 parts:

• For small masses/energies m << Mplanck we can define a wavelength corresponding to the energy (E=hv). The higher energy – the shorter wavelength.
• For big masses we can define Schwarzschild radius Rs which is proportional to mass (and as I noticed in Black Hole physics scientists think in Rs units, substituting R with M). So, the higher energy – the longer wavelength.

So the same length corresponds (in Planck’s sense) to 2 masses: one light and one heavy. And there is also a correspondence (mapping) of heavy masses into light masses and vice versa. Assuming that Planck units are natural such mappings must be important, but so far I haven’t heard anything about it.
This is really weird. Any thoughts? (or URLs?)

This is confusing but you really just need to think about what different physical mass/length scales are. You need to differentiate between the A) total energy of the system B) the typical energy scale of the system. Its only when B) is approaches the Planck scale that we need to start caring about Planck scale physics. In terms of black holes you can think of A) as the mass of the black hole M and B) as the temperature T of the black hole. Large Black holes M>>m_p have T<<m_p where small black holes M~m_p will have a temperature T~m_p.

 

[Entropia]

The concept of Planck units can definitely be confusing at first, especially when it comes to the exceptions of mass and energy. However, there is a logical explanation for why these units seem to contradict the extreme nature of other Planck units.

First, it's important to understand that Planck units are based on fundamental physical constants, such as the speed of light, the gravitational constant, and the Planck constant. These units represent the smallest possible scales at which our current understanding of physics breaks down. This means that they are essentially the building blocks of the universe.

Now, when it comes to mass and energy, they are not considered as extreme in the Planck scale because they are already on a scale that we can comprehend and measure. The Planck mass, for example, is about 0.00002 grams, which is still within the range of our everyday experiences. Similarly, the energy associated with a Planck mass is also within our understanding.

But as you mentioned, there is a correspondence between mass and energy in the Planck scale. This is because they are fundamentally connected through the famous equation E=mc^2. This means that a certain amount of energy can be converted into an equivalent amount of mass, and vice versa. This is why the same length can correspond to both a light and a heavy mass in the Planck scale.

In terms of the mapping of heavy masses into light masses and vice versa, this is likely due to the fact that in the Planck scale, all mass and energy are essentially the same thing. They are all just different manifestations of the underlying fundamental constants. So while it may seem strange, it is actually a natural consequence of the way our universe is structured.

I hope this helps to clarify the concept of Planck units and their relationship to mass and energy. As for further reading, I would suggest looking into quantum mechanics and general relativity, as these are the theories that underpin the concept of Planck units. You can also check out the work of Max Planck, who first proposed the idea of these fundamental units.