Planck's Unit and universal constants

[shounakbhatta]

Hello,

I am reading Planck's Unit. What I understand is that what is the need for Planck's unit. Kilogram, meter and second are measurement, rather arbitrary measurement, which humans have done in the past. The question is what do we know that is constant throught the universe? We know (1) The gravitational constant (2) Planck's constant and (3) The speed of light. So if we could measure, say mass M, in terms of gravitational constant and Planck's constant and speed of light, then we can get something which is fundamental.

My question is what is fundamental? G,c and h bar, how can they be called universal constants if they are again measured by us, human beings?

Thanks.

 

[mfb]

They are fundamental in the sense that a perfect length prototype for a light-second (=distance light travels in a second) and a perfect clock will always keep synchronized - light will need one second to travel along that length. In the same way, an atom will always the same fraction of the Planck mass, and the acceleration between two objects with the same mass will always stay the same - assuming those 3 constants do not change.

In the Standard Model of particle physics, they are not considered as fundamental constants - it is assumed that they are constant (and this has been measured with incredible precision, using the idea described above), and then they can be set to 1.
Fundamental parameters are always dimensionless - they are real (or complex) numbers, and independent of the measurement system.

 

[HallsofIvy]

The numerical value of "G", "h", and "c", etc. depend upon choice of measuring system (which is what I presume you mean by "measured by us, human beings") but the fact that they are constant, not changing from place to place or time to time, does not.

Some texts do, as mfb suggests, choose units of measurement to make those constants equal to 1. If I remember correctly, the unit of length is the diameter of an electron, the unit of time is the time it takes light to cross the diameter of an electron, etc.

 

[mfb]

If I remember correctly, the unit of length is the diameter of an electron, the unit of time is the time it takes light to cross the diameter of an electron, etc.

?
There is no (known) diameter of an electron, it is probably a point-particle.

The second is defined in terms of the frequency of radiation emitted in a specific atomic transition, together with the fixed numerical value for the speed of light this fixes the length as multiple of that wavelength as well.

 

[shounakbhatta]

Thank you for the details.

 

[dauto]

Think about it. If something is fundamental than measuring it is the only way we can know its value. It cannot be stipulated, it must be measured.