The Connection Between Planck Units and the Uncertainty Principle

[Temporarily Blah]

I know that Planck Time is the amount of time it takes light to cross Planck Length, but how did they figure out Planck Length?

What are all the Planck units, how large are they, and how were they figured out?

 

[Fallaciousmiles]

If i am not wrong Planck units are calculation constants, of which part of the constant is Planck constant itself. like h/2pi, is what they call h bar. with a small diagonial stroke at the top left of "h"

Like Light year, the value of the constant is pretty much suggested in the name itself

 

[arivero]

Planck length is the square root of Planck Area, which in turn is extracted from Newton gravitational constant. I think that the units were first suggested by Planck himself in 1899.

 

[Hans de Vries]

I know that Planck Time is the amount of time it takes light to cross Planck Length, but how did they figure out Planck Length?

What are all the Planck units, how large are they, and how were they figured out?

The Planck scale is there where Quantum Mechanics and Gravity collide and
where their predictions are expected to fail one way or the other.

Quantum Mechanics:

Heisenbergh's uncertainty relation connects mass and scale.
To be confined into a smaller and smaller area the mass of a particle needs to
be higher and higher. The radius of the confinement area is the Compton
radius of the particle.

Gravity:

When an object (say a star) is compressed more and more there will be a
radius when it will collapse under it's own gravity an become a black hole.
This radius is called the Schwarzschild radius. This radius becomes larger
when the mass increases.

Planks Scale:

Going back to particles. We have a radius which increases with mass
(Schwarzschild) and a radius which decreases with mass (Compton). The two
meet at the Planck scale. Particles with Plancks mass are so heavy and so
confined that they would collapse under their own gravity.


Planck mass _________ 2.17645e-8 kg
Planck length _______ 1.61624e-35 m
Planck time _________ 5.39121e-44 s
Planck temperature __ 1.41679e32 K



Regards, Hans

For the math, see for instance: http://math.ucr.edu/home/baez/planck/node2.html

 

[Temporarily Blah]

Thank you all. ^_^

 

[DaTario]

To Hans:

How does one get the uncertainty relation between mass and scale ?
Is it derivable from time-energy, position-momentum or number-phase UR´s ?

 

[Hans de Vries]

To Hans:

How does one get the uncertainty relation between mass and scale ?
Is it derivable from time-energy, position-momentum or number-phase UR´s ?

There's no really "correct" way of doing this, but mostly a relation like E=pc
is used to connect $\Delta E \Delta t$ and $\Delta p \Delta x$. This then also leads to the relation of
Plancks length and Planks time ($l_P = c\ t_P$ )

For an estimated radius of the proton of 10^-15m this leads to an energy
of ~ 200 MeV which was once used by Yukawa as an estimate of the mass
for his hypothetical carrier of the strong nuclear force.

You see it sometimes used as an argument to estimate the mass of the proton
at at least 600 meV (= 3x the mass of a (quark) confined to 10^-15m )


Regards, Hans