# You don't need all that junk.

#### Tyger

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=ml2t-2= energy
p=ml1t-1=momentum
L or h=ml2t-1=angular momentum or action

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
&omega;=E/h=frequency

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

&Omega;/l=k
&Omega;/t=&omega;

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

If we let &theta; represent plane angle then

h-bar=&Omega;/&theta;=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.

Vgroup=kC2/&omega;

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 &omega;/C2 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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#### Integral

Staff Emeritus
Gold Member
Of what use will your units be to the man on the street? Irregardless of their fundamental nature and the beauty of simplicity the idea has to one trained in Physics, they will have no meaning or use in daily life. I would rather be able to use units which are tied to my daily life and activities rather then some estoteric meaningless dimension to which I cannot relate.

#### Tyger

The man on the street

Originally posted by Integral
Of what use will your units be to the man on the street? Irregardless of their fundamental nature and the beauty of simplicity the idea has to one trained in Physics, they will have no meaning or use in daily life. I would rather be able to use units which are tied to my daily life and activities rather then some estoteric meaningless dimension to which I cannot relate.
will have better toasters and television sets and CD players because we understand the world better when we look at it in more elegant ways. And he can still talk in miles per gallon and pounds and watt-hours. If you've ever been to an antique bookshop and picked up an old book on systems of units you'll know that the system we use in our everyday life is tremendously simplified.

#### Integral

Staff Emeritus
Gold Member
If you've ever been to an antique bookshop and picked up an old book on systems of units you'll know that the system we use in our everyday life is tremendously simplified.
It is not clear what this means?

Very little engineering work is done near the quantum limit, why does introducing QM into the non QM world help?

#### Tyger

Originally posted by Integral
If you've ever been to an antique bookshop and picked up an old book on systems of units you'll know that the system we use in our everyday life is tremendously simplified.

It is not clear what this means?

People used to think it was important to know all kinds of units, When was the last time you heard peck refered to as anything but a kiss on the cheeks?

Very little engineering work is done near the quantum limit, why does introducing QM into the non QM world help?
Metals and plastics and semiconductors are designed on the atomic level.

This post is about helping people picture the world and think in a QM way. Maybe someday we'll all be able to see the world that way?

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#### Integral

Staff Emeritus
Gold Member
So you are attempting to create yet another set of units to replace the archaic units???? This is simplifing? Why not let the archiac units go, daily life can and will be measured in feet or meters, and meters ain't all its cracked up to be.

In my daily work I deal in microns and even nanometers, While the quantum limit in looming for semiconductors we are not quite there yet. Your units may be an interesting curiosity but what is the real value.

#### marcus

Gold Member
Dearly Missed
Originally posted by Integral
So you are attempting to create yet another set of units...Your units may be an interesting curiosity but what is the real value.
A possible use for streamlined units might be as an alternative to metric in general physics courses. Not to replace but to use in alternate problems. Assign some of each kind of problem for homework (some problems in Tyger units, some in SI)

If you look in older editions of the classic freshman physics texts, like Halliday Resnick, you see that students up thru Seventies learned to use more than one system and knew how to convert and this may seem like a useless skill but actually represents a kind of sophistication like being bilingual teaches you some sophistication about language----in getting comfortable with converting units you absorb something about physical quantities and scales and dimensional reasoning.

So I dont think this kind of sophistication (of using more than one system) is bad. Also metrology (and how units are defined) is an interesting applied physics area.

I think Tyger is probably talking about something like the Planck units----since he says h-bar = 1. And units like them get used in upperdivision/graduate level courses. At least c=G=1 gets used in relativity courses and h-bar=c=1 gets used in some quantum courses.

So I would not see any harm in introducing students to some streamlined system of units with the natural constant equal to 1 or some easy numbers to work with like that---actually as they are working Halliday/Resnick type examples and homework problems.

#### HallsofIvy

Homework Helper
This is not a new idea. I recall reading a physics journal article about 25 years ago which discussed using units based on
physical constants: h, c, G for example. One interesting aspect was that what we tend to think of as "elementary" units, distance, time would be "derived" units. Instead of speed being a derived unit- it would be an elementary unit since the unit of speed would be defined as the speed of light.

The unit distance turns out to be the "diameter" of an electron. The unit time is the time it would take for light to cross the diameter of an electron. Those would be very small for use even in laboratory work!

Actually many physics books and journal articles specify that they are using units such that c= 1 or h/2pi= 1.

#### Tyger

Originally posted by HallsofIvy
This is not a new idea. I recall reading a physics journal article about 25 years ago which discussed using units based on
physical constants: h, c, G for example. One interesting aspect was that what we tend to think of as "elementary" units, distance, time would be "derived" units. Instead of speed being a derived unit- it would be an elementary unit since the unit of speed would be defined as the speed of light.

The unit distance turns out to be the "diameter" of an electron. The unit time is the time it would take for light to cross the diameter of an electron. Those would be very small for use even in laboratory work!

Actually many physics books and journal articles specify that they are using units such that c= 1 or h/2pi= 1.
Well the cat isn't entirely out of the bag yet and when it is you'll find than it's a bit different than what you and Marcus describe. And I'm not claiming that no one else has thought of some of this too, if it's a good idea there's a good chance that more than one person has thought of it. And don't forget that any system involves two things, a choice of units and a system of quantities, both have to be chosen to make the scheme work.

#### chroot

Staff Emeritus
Gold Member
Originally posted by Tyger
And don't forget that any system involves two things, a choice of units and a system of quantities, both have to be chosen to make the scheme work.
Actually, marcus rather surprised me when he started doing most of his computations in natural units. I was at first miffed that he wasn't indicating whether a quantity was a length, time difference, or other such 'fundamental' quantity.

When I really started to think about it, though, I came to what was then an incredible revelation. As you begin setting constants (c, G, h-bar, etc.) to 1, you start losing degrees of freedom.

c is in units of length time-1
G is in units of mass3 kg-1 s-2
h-bar is in units of energy time
k is in units of energy kelvin-1

When you're done, something remarkable has happened -- the universe has selected all of your units for you, and, further, the universe has decided that all of your units are congruent, and it is no longer necessary to say a measurement is a length, time, or mass... or energy, or temperature, or anything else. There is actually only one.. single.. universal.. unit.

Although I've becoming a bit more comfortable using dimensionless natural numbers, my mind is still boggled by the concept.

marcus, do you have anything to add?

- Warren

#### marcus

Gold Member
Dearly Missed
Originally posted by chroot
Actually, marcus rather surprised me when he started doing most of his computations in natural units. I was at first miffed that he wasn't indicating whether a quantity was a length, time difference, or other such 'fundamental' quantity.

When I really started to think about it, though, I came to what was then an incredible revelation. As you begin setting constants (c, G, h-bar, etc.) to 1, you start losing degrees of freedom.

c is in units of length time-1
G is in units of mass3 kg-1 s-2
h-bar is in units of energy time
k is in units of energy kelvin-1

When you're done, something remarkable has happened -- the universe has selected all of your units for you, and, further, the universe has decided that all of your units are congruent, and it is no longer necessary to say a measurement is a length, time, or mass... or energy, or temperature, or anything else. There is actually only one.. single.. universal.. unit.

Although I've becoming a bit more comfortable using dimensionless natural numbers, my mind is still boggled by the concept.

marcus, do you have anything to add?

- Warren
you said it
setting c = G = hbar = k = 1 works pretty well for many sorts of calculations
we haven't specified electric charge--various ways to do that
Labguy promises an unexpected angle, perhaps it will involve the electric units

#### Tyger

The new system.

The basic elements of the new system of units are a length=l (which can also be used as a time=t), plane angle=&theta; and quantum mechanical phase=&Omega;.

Some quantities expressed in these units.

wavenumber=k=&Omega;/l

frequency=&omega;=&Omega;/t

angular momentum=h-bar=&Omega;/&theta;

force=f=&Omega;/lt

square of electric charge=e2=&Omega;l/&theta;t

mass or inertia=m=&Omega;t/l2

To get the new units from the old just factor any quantity that has a mass factor with h/&Omega; where h is Plancks Constant. To get the new physical canonical to a quantity just factor it into &Omega;.

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#### KillaMarcilla

My professors can never remember where all the "c"s go when they're writing out relativistic equations, because they all work in their day-to-day lives in a system of units where c, m0, e0, h, and many other constants are 1

I think that to anyone these units would be useful, they'll use them and convert when necessary whether there's a name for the units or not,

But natural units wouldn't be any more convenient in day-to-day life at all

Take an obnoxious unit like kilowatt-hours, for example. Although it's ugly and plugging it into introductory Physics formulae is a pain, it's exceptionally convenient for day-to-day use

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