# Non-arbitrary units

1. Jan 24, 2004

### davilla

What units in the physical universe are not arbitrary? E.g. time (as measured in seconds and years) is arbitrary since it's based on the changing orbit of this little planet in some odd solar system on the edge of an insignificant galaxy. Atomic mass is arbitrary since it relies on which molecule you pick (why C12 instead of H1 I don't know). Absolute zero is not arbitrary, but the temperature scales are. Pi and e are not arbitrary, but they are unitless.

In contrast the speed of light (c) is constant in the elegant presence of a vacuum. One could define a unit of speed based on this scale, but not for time or distance independently. Similarly the gravitational constant (G) ties together distance, mass, and time. I'm interested in an exhaustive list of all such constants, those that are fundamental rather than, say, used in approximations or a result of poorly understood behavior. Even G is kind of iffy because we don't have a theorem unifying all the forces.

By combining G and c one can produce non-arbitrary values for units of mass/time and mass/distance, whatever that's supposed to mean, and force: c^4/G = 1.2E44 Newtons. Is it possible to arrive at non-arbitrary units for mass, energy, temperature, etc?

2. Jan 24, 2004

### nbo10

The Unit of time is not arbitrary it's based on the tranisition between to states in Cs-133. Units for Mass - eV, Energy - eV, Temp - K. all non-arbitrary.

JMD

Last edited: Jan 24, 2004
3. Jan 24, 2004

### davilla

The measurement of time may be precise, but it's the choice of Cs-133 that's arbitrary. Likewise, 100K is the temperature difference between state changes of water. 0K as absolute zero may not be arbitrary, but the scale relies on the arbitrary choice of water (and the decimal system, for that matter). An electron volt is arbitrary because it relies on the volt, which as related to standard units is arbitrary.

4. Jan 24, 2004

### Hurkyl

Staff Emeritus
Well, that begs the question; why do you think absolute 0 and speed of light are less arbitrary than other things?

5. Jan 24, 2004

### Jimmy

The speed of light isn't arbitrary. The units we use in defining the speed of light is arbitrary. m/s, mi/hr, etc.

6. Jan 24, 2004

### Hurkyl

Staff Emeritus
Ok let me rephrase;

Why do you think using the speed of light or absolute zero as a basis for defining units less arbitrary than any other choice?

7. Jan 24, 2004

Staff Emeritus
The Planck units are not arbitrary. Using the three constants of nature,
c, the speed of light,
h, Planck's constant of action, and
G, Newton's constant of gravity,

you can form units of length, mass and time that do not depend on any other reference.

Then when expressed in terms of Planck length, Planck time, and Planck mass, c, h, and G will all have the value 1.

8. Jan 24, 2004

### Jimmy

Because you are using physical properties that are universally constant. C is the same everywhere just as absolute zero is, no matter what units or number base you are using. I suppose it is an arbitrary decision to use the speed of light as a basis. However, I see it as less arbitrary then just defining, say a yard, as the length of someone's outstretched arm.

Planck units would be the same universally. One planck time, length, or mass would represent the same quantity no matter what units you base them on.

9. Jan 25, 2004

### davilla

What's interesting about Plank length and mass is that it's a lot more than numerology; there are actually some theoretical questions behind it all.

Unfortunately, Plank length and time are too small to be of much benefit for measurements. Plank mass is a nice little chunk, but it could (and might some day) be redefined using "insignificant" factors like pi.

Of course, the manipulation of these constants would be arbitrary if, for instance, spacetime is quantized!

10. Jan 25, 2004

### marcus

you are raising interesting issues and
i'd be happy if you'd be more specific

GR is the classic theory of spacetime
and its main equation employs the force unit belonging to
the Planck system of units, as its central coefficient.

the effort to quantize GR that has made the most progress
lately is probably the Loop/foam approaches where
the quantum operators for area and volume actually turn
out to have descrete spectrums---the possible values of measuring
area and vol turn out to be multiples of planck length and planck vol units.

so when you say "there are some theoretical questions behind it"
that make using Planck units not purely arbitrary
I am inclined to agree and wish you would say what you had in mind
(was it the results of quantizing area and volume or something else)

and also I am puzzled by your saying "of course if spacetime is quantized then [using Planck units] would be arbitrary" since
it seems to me exactly because preliminary results of quantizing
[the Gen Rel picture of] space time actually point to Planck units that one would guess that using those units is not arbitrary.

the only thing that seems arbitrary to me is things like whether or not to include a factor of 2pi in the hbar, or a factor of 8pi in the G. The usual practice is to use hbar, G, and c.
Also when Planck introduced the units around a century ago he set the boltzmann temperature coeff equal to one also so he had a temp scale as well and all the other units, and his stated opinion (whether or not you can consider a straightlaced Prussian gentleman of 1899 as an authority!) was that the units were not arbitrary (that was just his point) they were "natuerliche Maaseinheiten" natural measure-units.

davilla, what in heaven's name is wrong with the planck length unit being short and the time unit being brief, you should know that size does not matter! (uh-oh Planck was a Victorian and probably avoided risque double-entendres)
why cant you just scale them up as needed by powers of ten.
this is what happens to units of all kinds
one always uses power-of-ten scaling to get them into the ballpark of
what you want to measure

10^35 of the length is about one pace
10^45 of the time is about a minute.
so start with pace and minute and scale up or down by tens as desired

11. Jan 25, 2004

### HallsofIvy

I remember reading an article in a physics journal many, many years ago on this. It's quite common to start by asserting that you are working in a system of units in which e= 1. This article was considering the situation in which units are chosen so that c= 1, h (or h/2&pi;)= 1, G= 1, etc. Then the unit of distance is the "diameter" of an electron, the unit of time is the time it takes light to cross the unit distance, etc.

12. Jan 25, 2004

### Nereid

Staff Emeritus
If you've got length, mass, and time, do you need any other (fundamental) units to 'do' all of physics (many convenient units to be constructed from these three of course)? I'm thinking of things like charge, isospin, etc.

13. Jan 25, 2004

### Chrisc

Davilla, great question.
Thinking through these kinds of questions reveals more about the nature of physics than most care to know.
It is much easier to accept as true the things we learn early on in life than to risk getting bogged down in the philosophy that reveals what we know is fundamentally a function of what we ARE as apposed to finite realities we discover independent of our nature and fundamental to the universe regardless of human existence.

The concept of unit is that we take ARBITRARY values and set them to UNITY in order to avoid endless and complicated conversion from one cultural or disciplinary convention to another.
Your question implies that there are fundamental values that are universally finite regardless of human observation.
The single largest quest in physics over the last hundred years has been to decide if the universe is as Einstein suggested- of a continuous nature (continuum field) or as Planck suggested -of a finite nature (quantum field).
If it is as Einstein suggests, we must accept that the only UNITY or UNIVERSAL FINITENESS will be in the constancy of translation between all measures of all dimensions (mass, space[length] and time) but all will be a continuum with infinitesimal and infinite values (arbitrarily determined by position).
If it is as Planck (more accurately Bohr) suggests, then we must accept that the universe has a FINITE dimension of scale, the value of which we can set as fundamental, non arbitrary units of each dimension (mass, space[length] and time).And below such units the universe has no physical reality.
Although such units will still be subject to the principle of relativity they will be finite within arbitrarily determined inertial frames.
Both are presently correct in their own domains (macro and micro respectively) and each uses the other in mischievous and necessary fashion.

Is the UNIT of quantum action (h) the magnitude below which our universe disappears or our theory fails us?
In which case we find the only non- arbitrary UNITS of dimension are those fundamental to either the existence of the universe or our ability to describe it.
It is in our pursuit of the finite nature of the universe that we discover the infinite nature of our minds. Whereupon we must decide to revamp our expectations of the universe or decide whether we will accept it to be greater than, equal to, or lessor than our minds ability to describe it. Of course this is an endless circular process that will continue until we give up the desire to learn.

14. Jan 25, 2004

### davilla

For one, I wasn't aware that G shows up in relativity formulas, although it makes perfect sense in retrospect. Also there's the question of how to unify relativity (big things) and quantum mechanics (little things). Somewhere I read that a Plank mass concentrated in a Plank radius would have similar critical radii used by both theories. I can't be too much more specific without being inaccurate.

I wasn't aware of that. I was going to include a proviso--"unless, of course, a quantum leap magically turned out to be the Plank length"--but I thought it would have been more of a distraction.

When someone comes up with a theory of everything and discovers that most wave-particle-loop-string-whatevers have certain properties that correspond with G over 8pi, then it won't be so arbitrary any more.

Because the power of ten is arbitrary. It makes more sense, in the advent of computer technology, to use a binary number system. (I've actually gone as far as to invent new characters base 16 where the top and bottom portions are indicitive of the base 4 representation.) But anyways, that choice is also arbitrary. Wouldn't you think the proper scaling is more properly arrived through exponentiation and natural logarithms?

I had initially requested an exhaustive list of all such constants, thinking that certain combinations might produce more usable results. After all, the combinations are themselves somewhat arbitrary if there are no meaningful equations behind them (and one should check that there are).

Good question. I don't know much about particle physics. Is there a common denominator?

Last edited: Jan 25, 2004
15. Jan 25, 2004

### marcus

Hello davilla, I'll try to reply to some of the comments in your post and anyone (Nereid selfAdj etc) is welcome to jump in.

Last edited: Jan 26, 2004
16. Jan 25, 2004

### Nereid

Staff Emeritus
units and forces

To follow on from my earlier comment about anything else (than mass, length and time), and davilla's question.

In physics we have GR, QM, and the Standard Model; waiting in the wings are LQG, SMT, and maybe more.

In high school physics we are told that time and length are physical dimensions; in GR we learn there is 'spacetime', a four-dimensional thing.

In the Standard Model we have four forces - strong, weak, electromagnetism, and gravity (OK, gravity isn't part of the Standard Model).

As we've been discussing in another couple of threads, you need 26 'numbers' to define the universe. Several of these 26 fundamental constants are masses, and since we've got a unit of mass, we don't need 26 (more) units to 'do' all of physics. Further, mass ties us to GR, so we're done there.

Here's a guess: 'charge' gives us all we need for electromagnetism.

What about the strong and weak forces?

BTW marcus, you made some very good points in your last post, but I found the presentation (embedded [[ ]] in a quote, which itself is bold) somewhat difficult to follow; would you consider editing it? perhaps use color?

BTW davilla, if you want a 'non-arbitrary' base for your counting system, you need to find an integer (other than 1 or 0). Maybe there's a ratio among the 26 constants which is an integer? Perhaps the number of dimensions in spacetime (4)?

17. Jan 26, 2004

### marcus

Re: units and forces

Adopted yr suggestion and tried italics as the distinguishing "color"

18. Jan 26, 2004

### davilla

Re: units and forces

Hmmm... I wasn't suggesting using e as a base. I seriously doubt any choice of base would be other than arbitrary.

What a "strange" color, er... flavor?