Hi all.

What are the units; is 1 gram times 300,000 Km/s doing joules ? Is it tonnes and metres/second doing watts.hour ? Do not come up with ounces, inches and BTUs, please 🙄

The formula has been everywhere with no grasp of sensing the magnitudes. Light for one gram of mass please ?

Edited February 28Feb 28 by Externet

In SI units:

E is in joules

m is in kilograms

c is in metres per second

There are a number of different systems of units, but as you appear to have discovered, for a formula to make sense, it is necessary for all the units to belong to the same system of units.

Edited February 28Feb 28 by KJW

Same units as for [math]E=\frac{mv^2}2[/math].

Edited February 28Feb 28 by Genady

5 hours ago, Externet said:

Hi all.

What are the units; is 1 gram times 300,000 Km/s doing joules ? Is it tonnes and metres/second doing watts.hour ? Do not come up with ounces, inches and BTUs, please 🙄

The formula has been everywhere with no grasp of sensing the magnitudes. Light for one gram of mass please ?

1g = 10⁻³kg.

c = 3 x 10⁸m/sec

So E = 10⁻³ x (3 x 10⁸)² = 9 x 10¹³ J.

So quite a lot!

You may be aware of the "mass defect" in nuclear physics, by which the mass of a nucleus with several protons and neutrons is less than the mass of the equivalent number of free protons and neutrons that make it up. This is because of the extra stability (i.e. lower total energy) they have when bound together than they have separately. So when protons and neutrons fuse together to form a larger nucleus, this energy difference is released, powering the sun - and H bombs.

I'm not sure if it's still a 'thing', but back when I was in school, the metric system had two dedicated systems of measuring units for science.
The CGS ( centimeter-gram-second ) system, and the MKS ( meter-kilogram-second ) system.

They are interchangeable, and fully consistent.
The important thing to keep in mind is that Energy has units of ( Mass x Distance² / Time² ).

14 minutes ago, MigL said:

I'm not sure if it's still a 'thing', but back when I was in school, the metric system had two dedicated systems of measuring units for science.
The CGS ( centimeter-gram-second ) system, and the MKS ( meter-kilogram-second ) system.

They are interchangeable, and fully consistent.
The important thing to keep in mind is that Energy has units of ( Mass x Distance² / Time² ).

Yes I remember that too. In the UK they were superseded by SI, by the time I got to uni in 1972.

37 minutes ago, MigL said:

I'm not sure if it's still a 'thing', but back when I was in school, the metric system had two dedicated systems of measuring units for science.

CGS with rationalised units for charge (Heaviside-Lorentz) are my favourite.

I once won a bet that you could reduce units of charge to mass-length-time units (something which should be obvious) against a student of electronics. The MKS system introduces the crazy fiction that units of charge are (for some mysterious reason) independent of mass, length, and time. They aren't.

IMO, there are foggy hints of this in the Klein-Gordon equation and the Dirac equation. (statCoulombs are proportional to the square root of grams). The KG equation is the square of the Dirac equation. And in the KG eq. mass occurs naturally, while in the Dirac eq. it has to be forced into it.

I'm still waiting for that person to pay me.

1 hour ago, exchemist said:

Yes I remember that too. In the UK they were superseded by SI, by the time I got to uni in 1972.

It's OT, but I can't ignore the coincidence that this is the same year I got to uni.

33 minutes ago, Genady said:

It's OT, but I can't ignore the coincidence that this is the same year I got to uni.

Well SNAP!, then. Er, or something. The following summer was the summer of Lou Reed Walk on the Wild Side and Floyd Dark Side of the Moon, heard through open windows everywhere.🙂

2 hours ago, joigus said:

I once won a bet that you could reduce units of charge to mass-length-time units (something which should be obvious) against a student of electronics. The MKS system introduces the crazy fiction that units of charge are (for some mysterious reason) independent of mass, length, and time. They aren't.

Do elaborate, please.

2 hours ago, exchemist said:

  3 hours ago, Genady said:

It's OT, but I can't ignore the coincidence that this is the same year I got to uni.

Well SNAP!, then. Er, or something. The following summer was the summer of Lou Reed Walk on the Wild Side and Floyd Dark Side of the Moon, heard through open windows everywhere.🙂

I was still in Gr 8 in 72-73.
However the following year ( Gr 9 in 73-74 ) the Canadian band Rush, played in our school gymnasium.
If you knew what I looked like back then, you could find me in the audience near the beginning of their documentary 'Beyond the Lighted Stage'.

Didn't get to Uni until 5 years later, old timers 😄 .

6 minutes ago, swansont said:

Do elaborate, please.

Gladly. We do need to step back a bit to before quantum mechanics was invented. The reason is once you introduce Planck's constant, electric charge becomes dimensionless, as you know very well and I've read you talk about in these forums several times.

Before one knows anything about quantum mechanics, one can use Coulomb's law to define units of charge by,

\[ F=\frac{q²}{r²} \]

where electric charge is expressed in statCoulombs or, Franklins. Also,

\[ F=\frac{1}{4\pi}\frac{q²}{r²} \]

In Heaviside-Lorentz units.

As dimensions of force are,

\[ [F]=MLT^{-2} \]

\[ \left[Q\right]^{2}=MLT^{-2}L^{2} \]

and therefore,

\[ \left[Q\right]=M^{1/2}L^{3/2}T^{-1} \]

Now, the question is, does this have any significance at all by way of the physical laws? Let me state clearly: I'm totally clueless about this. The closest one can get to this purely dimensional fact having any significance at all is what I mentioned about the KG and Dirac equations.

As, once we introduce Planck's constant, electric charge becomes dimensionless, that means mass can be made dimensionless too and, at least in principle, a function of charge and perhaps other (dimensionless) quantum numbers. Or maybe just as an artifice.

As I've remarked over and over to other people in countless discussions, there is the possibility that physics units might be ultimately be overdetermined. Why not?

Edit: I've removed one comment as it's just too speculative and not really necessary. I striked it through to keep it visible.

Edited February 28Feb 28 by joigus
Brief addition.

1 hour ago, joigus said:

Gladly. We do need to step back a bit to before quantum mechanics was invented. The reason is once you introduce Planck's constant, electric charge becomes dimensionless, as you know very well and I've read you talk about in these forums several times.

Before one knows anything about quantum mechanics, one can use Coulomb's law to define units of charge by,

F=q²r²

where electric charge is expressed in statCoulombs or, Franklins. Also,

F=14πq²r²

In Heaviside-Lorentz units.

As dimensions of force are,

[F]=MLT−2

[Q]2=MLT−2L2

and therefore,

[Q]=M1/2L3/2T−1

Now, the question is, does this have any significance at all by way of the physical laws? Let me state clearly: I'm totally clueless about this. The closest one can get to this purely dimensional fact having any significance at all is what I mentioned about the KG and Dirac equations.

As, once we introduce Planck's constant, electric charge becomes dimensionless, that means mass can be made dimensionless too and, at least in principle, a function of charge and perhaps other (dimensionless) quantum numbers. Or maybe just as an artifice.

As I've remarked over and over to other people in countless discussions, there is the possibility that physics units might be ultimately be overdetermined. Why not?

Edit: I've removed one comment as it's just too speculative and not really necessary. I striked it through to keep it visible.

Well I have a problem with this definition of the coulomb, which is surely independent of mass.

Faraday showed that the amount (ie number) of ions liberated in an electrolysis is proportional to the strength of current flowing and the time for whixh it flows.

From this we may draw the connclusion that the number of ions liberated is proportional to the amount od electricity which has passed throught the elecrrolyte since the current is the rate of flow of charge.

But each different ion has a different mass hence the proportionality is independent of the mass liberated.

Nowadays we use current density as easier to tie in with EM theory as the base electric unit, but you cannot do without one.

Here are some comparison tables and definitions from older systems and Si. Not this was SI before 'count' or number was admitted as a valid dimension.

3 minutes ago, studiot said:

Well I have a problem with this definition of the coulomb, which is surely independent of mass.

But I didn't mention the Coulomb. I mentioned the Franklin (Fr, AKA statCoulomb or statC).

Many, many people wrongly believe the so-called electric permitivity of the vacuum \[ \varepsilon_{0} \] to be an actual physical property. It's rather a part of the definition of electrostatic charge.

I'm sorry that I'm not familiar with Faraday's (independent?) convention. But it sounds to me very much like it is made to depend on current rather than on electrostatic charge. Fair enough.

This of course is always possible. Don't forget Maxwell's equations contain the term \( \mu_{0}j \) with \( \mu_{0} \) being the magnetic permeability of the vacuum.

One could define the "permitivity of the vacuum" to be anything one wants. And then the "magnetic part of the overall EM machinery" react to varying electric fields with much more "inertia" (bigger \( \mu_{0} \) ). Every game you want to play with E and M definitions is OK as long as,

\[ \varepsilon_{0} \mu_{0} = \varepsilon_{0}\mu_{0}=\frac{1}{c^{2}}\]

It's not the first time that the French have made other people disagree. 😅

In matters of units, and just this once if you will, we should all have stuck with British units (Heaviside's). Much more sensible.

Edited February 28Feb 28 by joigus
Latex editing

2 hours ago, joigus said:

Gladly. We do need to step back a bit to before quantum mechanics was invented. The reason is once you introduce Planck's constant, electric charge becomes dimensionless, as you know very well and I've read you talk about in these forums several times.

Before one knows anything about quantum mechanics, one can use Coulomb's law to define units of charge by,

F=q²r²

where electric charge is expressed in statCoulombs or, Franklins. Also,

F=14πq²r²

In Heaviside-Lorentz units.

As dimensions of force are,

[F]=MLT−2

[Q]2=MLT−2L2

and therefore,

[Q]=M1/2L3/2T−1

Now, the question is, does this have any significance at all by way of the physical laws? Let me state clearly: I'm totally clueless about this. The closest one can get to this purely dimensional fact having any significance at all is what I mentioned about the KG and Dirac equations.

As, once we introduce Planck's constant, electric charge becomes dimensionless, that means mass can be made dimensionless too and, at least in principle, a function of charge and perhaps other (dimensionless) quantum numbers. Or maybe just as an artifice.

As I've remarked over and over to other people in countless discussions, there is the possibility that physics units might be ultimately be overdetermined. Why not?

Edit: I've removed one comment as it's just too speculative and not really necessary. I striked it through to keep it visible.

OK, but the MKS system didn’t “introduce” a fiction; it’s true in the MKS/SI system. You are using a different unit system; what you mean by charge in that system is not what is meant in the MKS system. IOW, you’ve incorporated the constant k into the charge, and redefined it.

IOW, conversion requires other units, unlike converting e.g. ergs to joules to BTU, or newtons to dynes to pounds

So how do you regard the status of the Faraday constant, F ?

F = N_Ae = 96485 coulombs / mol

where N_A is Avogardo's number and e is the charge on the electron

4 minutes ago, swansont said:

OK, but the MKS system didn’t “introduce” a fiction; it’s true in the MKS/SI system. You are using a different unit system; what you mean by charge in that system is not what is meant in the MKS system. IOW, you’ve incorporated the constant k into the charge, and redefined it.

Ok. Let me rephrase it this way, which may be more honest-to-goodness: You can define units of charge in terms of mass, length, and time, without ever appealing to any "properties of the vacuum". Once you learn about magnetism, you end up realising why space-time had been involved from the very beginning.

2 minutes ago, studiot said:

So how do you regard the status of the Faraday constant, F ?

F = N_Ae = 96485 coulombs / mol

where N_A is Avogardo's number and e is the charge on the electron

F has the mole involved in it ( \( F=N_{A}e \) ). And Avogadro's number has the value it has only because grams are grams, and the mass of a proton in grams, once stripped of its units, is roughly an inverse amount of Avogadro's number.

You are not addressing my concerns.

It doesn't matter how long or short your wires are, or what their cross sectional area is.
Nor does it matter how long it takes to pass a given number of units of charge .
All that matters is that each unit liberates one ion with one unit of charge. so counting the number of ions liberated equals the number of unit charges passing.
That gives the total charge.
No forces, vacuums, permeabilities, permitivities, etc are involved.
Counting over a particular time period connects this as a curent to an existing dimensions (time)
Avogadro's number connects it to another existing dimension (mass)

Connection to length appears if you change from current to current density.

But you cannot derive a basic unit of charge from these connections.

45 minutes ago, studiot said:

All that matters is that each unit liberates one ion with one unit of charge.

Yes, but according to this definition, your unit of charge is \( .6\times10^{-19} \) Coulombs, or 1 Fr (or statC), so any ion could be nothing but an integer number of this elementary charge. There's nothing special about the Coulomb, or the Franklin, or the Heaviside-Lorentz unit of charge. There is however, something very special about the elementary charge of the electron or the positron. You could say the charge of an elementary ion is one.

As to \( N_A \), as you well know, it's not a fundamental unit of "number of elementary things" that plays any central role in the laws of Nature. It's been fixed to that value only because you can translate, by means of molecular numbers, numbers of entities into numbers of grams. Had the mass of the proton been around \( 10^{-70} \) of our preferred units of mass, I'm in no doubt Avogadro's number would have been named (perhaps) Arline's number and defined to be in the ballpark of \( 10^{70} \).

Edited March 1Mar 1 by joigus
minor correction