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 18 hours ago18 hr 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 17 hours ago17 hr by KJW

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

Edited 13 hours ago13 hr 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 In the UK they were superseded by SI, by the time I got to uni in 1972.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 1 hour ago1 hr by joigus
Brief addition.