# Heard from a particle physics lecture

1. Dec 14, 2005

### jet10

I heard from a particle physics lecture that no one (till now) knows what charge is. We know the interactions of things with charges and more or less its connections with other things, e.g. through electrodynamics, but no one can say what charge is. It is the same with time.
I think something is described by its characteristics and its connections with other things. Without these connections, we won't be able to describe anything. So, what do phycisists really mean, when they say they don't know what charge or time is, and what requirements have to be fulfilled in order to say that we know what something IS?

Last edited: Dec 14, 2005
2. Dec 15, 2005

### rbj

i think we're talking about fundamental dimensions of physical quantity. usually we think that [L]ength, [T]ime, and [M]ass, are completely different species of animal and consider their measure as measuring completely different stuff. Feet and meters are different units, but they measure the same thing, and with appropriate conversion factors, we can ascribe physical meaning to the concept of adding 1 ft to 1 meter. but we cannot ascribe meaning to adding 1 ft to 1 kg. it's like comparing "apples to oranges" (see cavaet below.) physical quantities must be of the same dimension to be compared or added.

then come the derived units. a Newton of force is exactly the force required to accelerate one kilogram of mass at the rate of one meter per second per second. so we don't just say that force is proportional to the time rate of change of momentum, we say it is equal to the time rate of change of momentum and define our unit of force to make it so. so [v]elocity, [p]Momentum, [F]orce, [E]nergy, [P]ower are all secondary or derived dimensions of physical quantity because their units are fully derived from these 3 fundamental dimensions of physical quantity.

the thing about the fundamental dimensions is that the units associated with them are not derived from other units as are the "derived" units and the "secondary" dimensions of physical stuff. so the second was originally defined to be 1/86400 of a day, the meter was defined to be 10-7 of the distance from the North Pole to equator going through Paris, and the gram was the mass of one cubic centimeter of water. those are totally anthropocentric (unnatural) definition.

so far we have:

time [T]
length [L]
mass [M]

velocity [v] = [L]/[T]
momentum [p] = [M][v] = [M][L]/[T]
force [F] = [p]/[T] = [M][L][T]-2
energy [E] = [F][L] = [M][L]2[T]-2
power [P] = [E]/[T] = [M][L]2[T]-3
intensity = [P]/[L]2= [M][T]-3

i do not consider temperature, $[\Theta]$, to be a fundamental dimension of quantity. absolute temperature is just a measure of the amount of energy per particle per degree of freedom of matter. heat is just mechanical energy (in a random sense) and is not some other trancendent phenomenon. the Boltzmann Constant is totally man-made and depends completely on the Advogadro's Number, which is also pretty arbitrary, not fundamental.

then (finally) comes E&M and charge. now the cgs folks defined charge completely in terms of the big 3, by defining the unit charge to be whatever it has to be to make the Coulomb Force Constant precisely equal to the dimensionless 1. so for the cgs guys, the Coulomb electrostatic force is:

$$F = \frac{Q q}{r^2}$$

that means that the dimension of electric charge (for the cgs guys) is

charge [Q] = ( [F][L]2 )1/2 = [M]1/2[L]3/2[T]-1

but that is entirely unsatisfying to me. Electric Charge is another fundamentaly physical quantity (that happens to have some physical properties measurable with existing physical quantities), so like Time, Length, and Mass, i would assign Charge its own independent and fundamental dimension, [Q] (which means, unless your doing Planck Units, that the Coulomb constant or permitivity of space is not dimensionless).

(caveat): then along comes relativity to suggest that energy and mass are the same thing (normalizing c to 1) and later along comes quantum mechanics to suggest that energy and the reciprocal of time are the same thing (normalizing $\hbar$ to 1), but if you continue that logic and normalize G to 1, then you get to weird conclusions that time is the same as its own reciprocal (and similar goofiness regarding the other dimensions of quantity) and by that point i give up and say there is no such thing as dimensions of quantity or that these 4 physical constants (c, G, $\hbar$, and $\epsilon_0$) cannot be considered to be dimensionless, i don't care what your unit system is.

note that the number of fundamental dimensions of quantity (that is four, [T], [L], [M], and [Q]) is the same as the number of fundamental universal constants (that is four, c, G, $\hbar$, and $\epsilon_0$) describing how things interact (without identifying any particular "thing" like electrons or cucumbers or dandruff, that is they are properties solely of the vacuum and take on the numbers that they do, solely because of the anthropocentric units that humans have come up with to measure them). i do not think that that is an accident. the fact that there are both four fundamental dimesions and four fundamental universal constants of the vacuum, tell us unambiguously that there are a set of four natural units of time, length, mass, and charge to make those four fundamental constants go away (they become 1).

so guess what? i don't have an answer to your question (what, exactly, is electric charge). whatever it is, it seems to be quantized with the Elementary Charge, it has polarity (unlike mass), like gravity it interacts with an inverse-square law, and also like gravity the speed of propagation of this interaction is "c" (which we can set to 1, if we choose the units just so). but whatever it is, it is not Time, nor Length, nor Mass, nor the square root of Mass times the square root of Length cubed divided by Time (as the cgs people would have us believe). whatever it is, it is different, just as Time is different from Mass which is different from Length.

Last edited: Dec 15, 2005
3. Dec 15, 2005

### Dmstifik8ion

Given the scope of the question, I don't know of a better way to say, "I don't know". I am truly humbled by your 'ignorance'. Thank You!

Last edited: Dec 15, 2005
4. Dec 16, 2005

### Mk

Jeez man, you don't have to be so impolite. You can learn a lot from that post, and how we can arrive at the answer.

5. Dec 16, 2005

### jet10

thanks for the reply... i think i will need some time to think about it.

6. Dec 17, 2005

### debeng

charge is just a hypothesis?

we dont have to afriad for now, that we only know charge is atlesat not a matter. it is just a attractive and repulsive notation.what if we would have given photon the -ve, and electron the +ve, i dont think it would have bought about difference in our study. what really matters is we conied an electron to have one -ve charge like there is no any fundamental entity that would carry smaller charges.

Last edited: Dec 17, 2005
7. Dec 17, 2005

### debeng

mass is not fundamental

fundamental quatity, we mean to be an independent quantiy. scalar quantiy, or actually of constant properties. they were assumed fundamental only to describe the motion of matters in our surrounding, precisely in earth's atmosphere.mass is not anymore fundamental quantity since it has proved to change into energy. i do not know wat time is? but i can only say it is not a fundamental at all in the higher physics. einstein actually mentined that time can be shortened. perhaps it could also be transformed to energy. i dont mean mechanical or electromagnetic forms of energy, but perhaps a differnt form of energy.

8. Dec 17, 2005

### rbj

it might be the "pot calling the kettle black" but your posts are hard to read. try spell checking.

anyway, if mass cannot be considered a fundamental dimension of quantity because it's the same as energy, that begs the question, what is energy? (we classically defined energy, or work, in terms of mass, time, and length).

also, if you're gonna equate the two physical quantities (mass and energy), then that effectively defines c to be 1 (or at least dimensionless). but then that means that length and time are the same thing and there is a lot in the relativity lit that says that (they put time on a fourth axis and attach the imaginary unit i to it. so time is imaginary length. fine, but that is still qualitatively different.

the x-axis is not qualitatively different from the y-axis or z-axis, but is qualitatively different from the t-axis. also, except maybe within the event horizon of a black hole, i am not aware of any concept of the "arrow of space" or "arrow of length" as there is an "arrow of time". we can (usually) freely move back and forth on the x, y, and z-axes, but not on the t-axis.

again, to make mass and energy the same thing (so they can't both be fundamental quantities of physical stuff), you have to set c to 1. but you can make the same argument for $\hbar$ (making mass and energy the same thing as reciprocal time) and G (making [M] = [L]3[T]-2). but then since [L] = [T], then [M] = [L] = [T]. but because [M] = [E] = [T]-1, that mean time is the same as its reciprocal or you could say the same that length is its reciprocal or anything else has the same dimension as its reciprocal. that pretty well leads either to madness or (more likely) the conclusion that there is no such thing as dimensions of physical quantity. that everything is dimensionless. while that may very well be true (who knows?), it isn't a particularly classical POV.

9. Dec 18, 2005

### erickalle

rbj:

Next quote is from James Clerk Maxwell.

Much more satisfying is it to convert electromechanical units into mechanical units and we will end up with our usual units of mass, length and time without fractional powers. This will also yield some surprising results.

10. Dec 18, 2005

### rbj

i do not disagree with you or Maxwell that all energy is, ultimately, mechanical. you somehow have to mechanically move these charges around (in the transmitting device or antenna) to make an electromagnetic radiative field that will have a mechanical effect on the (free) charges at some remote location (the receiving antenna).

but, not all (mechanical) forces or actions are the same thing. even though there is a common model for 3 of the 4 big interactions, the source of the mechanical "push" or "pull" (that might result in work or energy being transfered somehow) between electrical charges is not the same mechanical action that gravity is (the non-GR perspective, for argument).

it still doesn't speak to my issue with bogusly defining electric charge purely from [T]ime, [L]ength, and [M]ass, by defining its unit in such a way to set the Coulomb Force Constant to the dimensionless 1. it's hard to totally quantify the objection, but i'll try by using the example of how force is defined.

i suppose we could say that [F]orce is a completely different and independent species of animal than anything we could construct from [T]ime, [L]ength, and [M]ass. then we would observe, experimentally, and codify in a "law" that force is proportional to the time derivative of momentum (where momentum is defined to be the dimensional product of mass and velocity). So then we would say, that force measured in some completely arbitrarily defined unit we'll call a "farg" to be

$$F \propto \frac{dp}{dt}$$

or

$$F = K \frac{dp}{dt}$$

where $K$ is whatever constant or proportionality that we need to convert (kg m/s2) to fargs.

so suppose there was some prototype spring somewhere and the force required to compress it by 1 cm is defined to be 1 farg (note that this definition has something to do with the definition of length, but nothing to do with time or mass), then because that definition of the unit force is pre-existing, after observing that 1 farg accelerates a kg mass 3 m/s2 and 2 fargs accelerates a kg by 6 m/s2, we would then need a a constant $K$ = 1/3 farg s2/(kg m) to express Newton's 2nd law. but there is no natural motivation to define force in that way. whatever Force is, when there is a non-zero net amount of it acting on any body, it always manifests itself as a time rate of change of momentum. there need be no difference between the concept of force and the time rate of change of momentum, so we may as well define and understand them to be the same thing, just as we understand velocity to be the time rate of change of position or power to be the time rate of transfer of energy.

now, we have observed that this stuff we call "charge" exerts forces on each other, that the force between a pair of charges is proportional to either charge (and thus proportional to its product) and inversely proportional to the square of distance between the two.

so we say:

$$F \propto \frac{q_1 q_2}{r^2}$$

or

$$F = k \frac{q_1 q_2}{r^2}$$

then the cgs guys make the same kind of argument (but it's not so natural, this time) as with the Newton of force definition, to define the unit electric charge in such a way that causes the the $k$ factor to disappear. to become exactly the dimensionless 1. but then, for the cgs guys, the units on charge have to be:

dyne = statC2/cm2

or

g cm/s2 = statC2/cm2

or

statC2 = g cm3/s2

or

statC = g1/2 cm3/2 s-1

that is what the cgs people say a statcoulomb is. but to that, admittedly without a rigorous refutation, i'm simply saying that identifying electric charge to be

[Q] = [M]1/2 [L]3/2 [T]-1

simply seems more unbelievable than saying that electric charge is something else. some other completely different property or dimension of physical quantity than that contrived expression above. i didn't declare that it's salient physics, only than that it is completely "unsatisfying to me." but then that means that there is a dimensionful conversion factor $k$ that converts the computed quantity of [Q]2/[L]2 to [F]orce. we can still choose units to set the numerical value of $k$ to 1, but unless we go all the way to describe everything in terms of Planck Units (where all physical measure is dimensionless), i don't accept that conversion factor to be dimensionless. it's like saying G is dimensionless (and we can do that, but not if we define [T], [L], and [M] independently).

11. Dec 19, 2005

### jet10

So, is it right to say (in scientific language) that we know what something is, if we can describe something in the fundamental units? and we can't say we know what something is, if it is fundamental? we can only describe the fundamentals by describing them in the context of secondary units or dimensions? What about length and mass - do we "know" what they are?

I think it works more or less the same way in logic: we have to assume that certain things are true and build our reasoning upon it to deduce new knowledge. What we know, is what we can describe by what we know, or what we assume to be always true. So somehow we go around in circles until we define what fundamental is and describe everything by these fundamentals and satisfactorily say "we know what it IS".

Perhaps one of the most fundamental things we know is movement, which we observe daily - mechanics (Maxwell). So I suppose many would be satisfied, if things can be described through movement - like temperature, virtual particles. But movement involves change and change involves time. So time is something more fundamental which we cannot describe, so we don't know what it is...

What do you think of this?