Why Planck's Constant Has Dimensions and a Unit?

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SUMMARY

Planck's Constant is a dimensional constant with both dimensions and a unit, specifically relating energy to frequency. This discussion clarifies that not all constants are dimensionless; for example, the speed of light (c) is another constant that possesses dimensions and units. The confusion arises from conflating mathematical constants, which may be dimensionless, with physical constants that inherently have dimensions. The fine structure constant (alpha) is highlighted as a dimensionless physical constant, contrasting with Planck's constant and the speed of light.

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  • Understanding of physical constants and their classifications
  • Familiarity with units and dimensions in physics
  • Basic knowledge of energy-frequency relationships
  • Concept of dimensionless constants in physics
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Nader AbdlGhani
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Despite being a constant, It has both dimensions and a unit, can someone kindly explain why ?
 
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Planck's Constant is a dimensional constant. Energy= Planck's Constant. * frequency . It is not the only constant that has dimensions , many other physical constants also has dimensions , like gravitational constant.
 
Nader AbdlGhani said:
Despite being a constant, It has both dimensions and a unit, can someone kindly explain why ?

This question is puzzling. Are you saying that the property of a "constant" includes NO dimensions and NO units?

"c", the speed of light in vacuum, is a constant. It has "dimensions and units". Why are you not asking about that as well?

Zz.
 
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ZapperZ said:
This question is puzzling. Are you saying that the property of a "constant" includes NO dimensions and NO units?

"c", the speed of light in vacuum, is a constant. It has "dimensions and units". Why are you not asking about that as well?

Zz.
Actually I intended to ask generally, but then I went for the example spontaneously, I have just studied units and dimensions and they told me that constants don't have dimensions and units, for example, number one itself, angle of measure 60° etc, and what came in my mind are constants which are in many relations in physics
 
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Nader AbdlGhani said:
Actually I intended to ask generally, but then I went for the example spontaneously, I have just studied units and dimensions and they told me that constants don't have dimensions and units, for example, number one itself, angle of measure 60° etc, and what came in my mind are constants which are in many relations in physics

This makes very little sense. Who are these "they" that you are referring to?

The examples you cited are NOT "constants" in physics. These are simply numbers associated with some quantity. Again, look at "c". Do you think this constant has NO dimensions and NO units? This one constant itself falsify any claim that a constant has no dimension and no units.

Zz.
 
Nader AbdlGhani said:
Actually I intended to ask generally, but then I went for the example spontaneously, I have just studied units and dimensions and they told me that constants don't have dimensions and units, for example, number one itself, angle of measure 60° etc, and what came in my mind are constants which are in many relations in physics
As zapperz has pointed out, you are confusing terms. The examples you site are not physical constants, they are just numbers. If used in an equation, they can be called constants as far as math is concerned, but that has nothing to do with physical constants like c
 
Simple answer: A constant may either have dimensions (i.e. units), or it may not.

Examples:
The fine structure constant alpha = 1/137.035... is a dimensionless physical constant.
And, as pointed out already in this thread, Planck's constant and the speed of light are constants that have units.
 

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