Alternative definition of constants

[carllacan]

Hi.

First off, sorry about the title, its not very descriptive but I had no clue on how to sum my question.

I'm reading Sakurais' Modern Quantum Mechanics. In the discussion of the K operators (p47) he compares it to the classical momentum operator, states that K = p/(some constant) , and mentions that if microphysics had been discovered before macrophysics the conversion constant would had been 1. My question is what does this exactly mean?

If we had discovered quantum physics first we would have defined K first, and then we would have discovered p and tried to relate both: wouldn't we have neede a constant there, too?

Thanks.

 

[UltrafastPED]

The suggestion is that "life is simpler" if you choose units of measurement where h-bar (reduced Planck's constant) is equal to 1.

This if fine for simplifying the mathematical theory, but is very inconvenient for engineering work!

 

[dauto]

Hi.

First off, sorry about the title, its not very descriptive but I had no clue on how to sum my question.

I'm reading Sakurais' Modern Quantum Mechanics. In the discussion of the K operators (p47) he compares it to the classical momentum operator, states that K = p/(some constant) , and mentions that if microphysics had been discovered before macrophysics the conversion constant would had been 1. My question is what does this exactly mean?

If we had discovered quantum physics first we would have defined K first, and then we would have discovered p and tried to relate both: wouldn't we have neede a constant there, too?

Thanks.

Not necessarily. That depends on some arbitrary choices that have to be made for every system of units. To give an example: Originally resistance Voltage and Current were defined independently and Ohm's law had an arbitrary constant V=c RI. nowadays those quantities are not defined independently. We actually use Ohm's law to define the resistance, hence no need for an arbitrary constant. The constant c was set to c=1 (no units) and just like that, it's gone from the equation.

 

[dauto]

The suggestion is that "life is simpler" if you choose units of measurement where h-bar (reduced Planck's constant) is equal to 1.

This if fine for simplifying the mathematical theory, but is very inconvenient for engineering work!

Why is that? can't engineers deal with a few powers of 10?

 

[carllacan]

But even if the numerical value is 1 K has units of length^-1, so we would still need either a constant to relate K and p, wouldn't we?

 

[Nugatory]

Why is that? can't engineers deal with a few powers of 10?

Powers of ten... No problem.
But when you're calculating the deflection of a steel beam under a working load, and then developing the material specifications and attachment points for that beam prior to handing the design off to the fabricators... Geometric units won't get you very far.

 

[dauto]

But even if the numerical value is 1 K has units of length^-1, so we would still need either a constant to relate K and p, wouldn't we?

Any physical constant can be made unitless by definition if we chose to include that definition as part of the defining set of procedures used to establish the system of units.