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jbar18

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In summary: Lp is the maximal length for photons - the first problem can be explained by the fact that the electron has a much higher energy than the photons and so its wave-length is much smaller.- the second problem is still a mystery and has to do with the fact that the electron has a much higher mass than the photons and so its wave-length is much smaller. In summary, the units are based on the assumption that the size of an object is proportional to its energy.

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jbar18

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MathematicalPhysicist

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In case of Planck length we know that the maximum barrier over the speeds of particles is c, so we know it should be included, we also know that at the tiny scales there's a parameter of h cause at the macro h=0, and we also look for gravity effects in this scale, which means G should be there.

Obviously this is a rough estimate of the smallest length, if there something like that.

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jbar18

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Bill_K

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It's more than just dimensional analysis, there's actually a reason behind it. It's the scale at which the Compton wavelength is equal (ignoring a factor of two) to the Schwarzschild radius.

GM/c^{2} = ħ/Mc

Solving for M you get M = √ħc/G, the Planck mass. The Planck length is then

GM/c^{2} = √ħG/c^{3}

Significance:

The Compton wavelength is the distance scale at which the zero-point energy of a confined quantum particle is equal to its rest mass.

The Schwarzschild radius is the distance at which the gravitational potential energy of a particle is equal to its rest mass.

All three (zero-point energy, gravitational potential and rest mass) become equal at the Planck scale.

GM/c

Solving for M you get M = √ħc/G, the Planck mass. The Planck length is then

GM/c

Significance:

The Compton wavelength is the distance scale at which the zero-point energy of a confined quantum particle is equal to its rest mass.

The Schwarzschild radius is the distance at which the gravitational potential energy of a particle is equal to its rest mass.

All three (zero-point energy, gravitational potential and rest mass) become equal at the Planck scale.

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bobie

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Hi, could anyone please clarify these points:Bill_K said:It's the scale at which the Compton wavelength isequal(ignoringa factor of two) to the Schwarzschild radius.

[2]GM/c^{2}=ħ/Mc

Solving for M you get M =√ħc/G, the Planck mass.

The Planck length isthen

GM/c^{2}, L=√ħG/c^{3}

- why are we allowed to ignore the factor of two?

- isn't the formula

- why should the unit of length L be equal to

- is that the real genesis of the units? In 1900 the Schwartzschild radius was not known.

- one last problem : the r

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Planck units are a set of fundamental units of measurement that are based on natural constants, such as the speed of light and the gravitational constant. They are important because they provide a universal scale for understanding physical phenomena and can help bridge the gap between theories in different branches of science.

The Planck length is the smallest possible length that can exist in our universe, and it is the scale at which quantum effects become significant. It is also thought to be the length scale at which the fabric of space-time becomes discrete and grainy, according to some theories of quantum gravity.

Planck units are useful in understanding the origins of the universe because they provide a way to study the universe at its most fundamental level. By using these units, scientists can explore the earliest moments of the universe, when the laws of physics were still being formed. They can also be used to study extreme phenomena, such as black holes and the Big Bang.

No, Planck units cannot be measured directly because they are extremely small and beyond the capabilities of our current technology. However, they can be used in theoretical calculations and predictions, and some scientists are working on ways to indirectly observe and test these units.

Yes, there are alternative theories and criticisms of Planck units. Some scientists argue that they are arbitrary and do not have any physical meaning, while others propose alternative fundamental units. Additionally, some theories, such as string theory, suggest that the Planck length may not be the fundamental length scale of the universe.

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