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When Physics as we know it started, in Galileo's and Newton's time, people used systems of measurement based on Mass, Length and Time because those were quantities that could be easily measured. As it progressed more units were added, such as Temperature, and more quantities were expresssed in the basic units, such as Energy or Action. And Relativity and Quantum Mechanics have changed our view of systems of dimensional units.

Over the last couple of centuries our system of dimensional units has begun to look more like a garage that is cluttered with junk and needs to be cleaned out. And here is how we develop a system which does that based on "modern" units.

You might think that because h and h-bar are "modern" quantities we should use them in our system but in fact, as we know them, they will be completely eliminated because they are nothing more than conversion factors from the old to the new.

The Old

m=Mass

t=Time

l=Length

E=ml

p=ml

L or h=ml

We won't mention Force, Pressure, etc, because they are derivitive, and can be derived from either system.

On to the New

First I'm going to make a comment about Mass (inertia) and say that it is not in any sense a fundamental quantity, that it can be derived by very simple reasoning from Quantum Mechanics and Relativity. The reason why I'm stating this now is because there has been a lot of misinformed hype about the nature of inertia and we will try to clear some of it up as we proceed.

k=p/h=wavenumber

ω=E/h=frequency

These two equations express the conversion of two important quantities, Momentum and Energy, to the new system. But if we let Ω represend quantum mechanical phase we can express them another way.

Ω/l=k

Ω/t=ω

So that h is just a conversion factor from classical action to quantum mechanical phase.

If we let θ represent plane angle then

h-bar=Ω/θ=angular momentum.

So that we retain h-bar as a symbol but it now represents one radian of QM phase per radian of plane angle, and of course in any sensible system of units it can be assigned the value of one.

So the basic elements in our new system are quantum mechanical phase, a length (which can also be used for a time) and plane angle. There is no energy, only quantum mechanical frequency, no momentum, only QM wavenumber, but all the rules and laws that obtain for energy are applied to frequency, ect., so that we can talk about the potential and kinetic parts of the frequency just as we did the classical concept of energy. And the same global rules apply, such as the total frequency in a closed system is conserved.

And temperature is frequency too, for it represents the mean available energy per unit quantum in a system of states.

You may wonder what units mass (inertia) will have. Consider that a wave group or "wavelet" made by superposing wavefronts with different wavenumbers moves at the group velocity and not the phase velocity, which is.

V

This expression is linear in k (wavenumber) so if we add more k it behaves just like Newton's equation for impulse. Classicaly V=p/m

So the expression for inertia is ω/C

Using this system will help you to think in quantum mechanical terms.

Go to the eleventh reply for the new system.

Over the last couple of centuries our system of dimensional units has begun to look more like a garage that is cluttered with junk and needs to be cleaned out. And here is how we develop a system which does that based on "modern" units.

You might think that because h and h-bar are "modern" quantities we should use them in our system but in fact, as we know them, they will be completely eliminated because they are nothing more than conversion factors from the old to the new.

The Old

m=Mass

t=Time

l=Length

E=ml

^{2}t^{-2}= energyp=ml

^{1}t^{-1}=momentumL or h=ml

^{2}t^{-1}=angular momentum or actionWe won't mention Force, Pressure, etc, because they are derivitive, and can be derived from either system.

On to the New

First I'm going to make a comment about Mass (inertia) and say that it is not in any sense a fundamental quantity, that it can be derived by very simple reasoning from Quantum Mechanics and Relativity. The reason why I'm stating this now is because there has been a lot of misinformed hype about the nature of inertia and we will try to clear some of it up as we proceed.

k=p/h=wavenumber

ω=E/h=frequency

These two equations express the conversion of two important quantities, Momentum and Energy, to the new system. But if we let Ω represend quantum mechanical phase we can express them another way.

Ω/l=k

Ω/t=ω

So that h is just a conversion factor from classical action to quantum mechanical phase.

If we let θ represent plane angle then

h-bar=Ω/θ=angular momentum.

So that we retain h-bar as a symbol but it now represents one radian of QM phase per radian of plane angle, and of course in any sensible system of units it can be assigned the value of one.

So the basic elements in our new system are quantum mechanical phase, a length (which can also be used for a time) and plane angle. There is no energy, only quantum mechanical frequency, no momentum, only QM wavenumber, but all the rules and laws that obtain for energy are applied to frequency, ect., so that we can talk about the potential and kinetic parts of the frequency just as we did the classical concept of energy. And the same global rules apply, such as the total frequency in a closed system is conserved.

And temperature is frequency too, for it represents the mean available energy per unit quantum in a system of states.

You may wonder what units mass (inertia) will have. Consider that a wave group or "wavelet" made by superposing wavefronts with different wavenumbers moves at the group velocity and not the phase velocity, which is.

V

_{group}=kC^{2}/ωThis expression is linear in k (wavenumber) so if we add more k it behaves just like Newton's equation for impulse. Classicaly V=p/m

So the expression for inertia is ω/C

^{2}and we have derived this mysterious property of matter from simple facts about QM and Relativity without any appeal to Mach's Principle or Gravity.Using this system will help you to think in quantum mechanical terms.

Go to the eleventh reply for the new system.

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