Understanding Planck Scale Derivation: Energy, Length, and Uncertainty

[victorvmotti]

I see that Planck scale of mass-energy is related to the corresponding length scale by application of the uncertainty principle.

What is not clear for me is how we find either energy or length scale to compute the other one?

What goes wrong if we assume a higher energy level than the Planck energy scale and then find the corresponding lower length scale via the uncertainty principle.

Is it related to the gravitational constant?

Should we use the concept of a tiny black hole from general relativity?

Also, how we compute the Planck time for given energy and length scales?

 

[jtbell]

Planck units are derived via dimensional analysis so as to make various fundamental constants equal to 1.

http://en.wikipedia.org/wiki/Planck_units

 

[victorvmotti]

So, we get the Planck length by demanding a combination of constants that give a length dimension. And then based on it find other related scales, such as Planck energy scale.

But can you show what goes wrong in general relativity if we consider energy-mass scales larger than Planck energy scale?

 

[victorvmotti]

0 down vote http://physics.stackexchange.com/questions/146046/planck-scale-and-qft#
I see that we use dimensional analysis involving constants of nature to obtain the Planck length and then apply the uncertainty principle to find the corresponding Planck mass-energy.

But the energy and length scales were found by invoking a "particle" interpretation of fundamental entities of nature. Wasn't it?

This is not still clear for me, I mean, where and how we used the notion of particles to obtain Planck scales?

I am not deep into the quantum field theory yet, but if we let go of the notion of particles and introduce the fields (real or complex set of functions of spacetime) instead as the fundamental entities of nature, then can we make sense of arbitrarily large energies or small distances?

But gravity, does not still have any valid QFT, it is now a classical theory, so we say for arbitrarily small distances on space, there should be only quantum fields, and therefore we are waiting for quantum gravity?

Am I right in the above argument?

 

[pmacias]

I can provide some insight into the questions you have raised about the Planck scale derivation. The Planck scale is a fundamental scale in physics that represents the smallest possible units of energy and length. It is derived from the combination of the constants of nature, such as the speed of light, the gravitational constant, and the Planck constant.

To compute the Planck scale, we use the uncertainty principle, which states that there is a limit to how precisely we can know both the position and momentum of a particle. This principle is a fundamental aspect of quantum mechanics and is essential for understanding the Planck scale.

To answer your first question, we do not find one scale to compute the other; instead, both the energy and length scales are derived from the constants of nature. The Planck energy scale is the maximum amount of energy that can exist in a single point in space, while the Planck length is the smallest possible length scale.

If we assume a higher energy level than the Planck energy scale, then the corresponding length scale would be smaller than the Planck length. This is not possible because at the Planck length, the fabric of space-time becomes so distorted that it would create a black hole. This is where the gravitational constant comes into play, as it determines the strength of gravity and ultimately limits the energy and length scales that are physically possible.

The concept of a tiny black hole from general relativity is indeed related to the Planck scale. At the Planck length, the gravitational force becomes so strong that it would collapse any matter into a black hole. This is why the Planck scale is often referred to as the "quantum gravity scale."

Finally, to compute the Planck time for a given energy and length scale, we can use the formula t = ħ / E, where t is the Planck time, ħ is the reduced Planck constant, and E is the energy scale. This formula is derived from the uncertainty principle and is used to determine the minimum amount of time required for a quantum process to occur.

I hope this helps to clarify some of your questions about the Planck scale derivation. It is a complex and fascinating topic that is still being explored by scientists, and there is still much to learn and understand about it.