# Speed of Light. What is c? Why use the letter c'?

artie
Speed of Light. What is c? Why use the letter "c'?

In the equation E=mc2

E is energy

m
is mass

What is c? I know that c is the speed of light, but why use the letter c? What does c stand for?

nicksauce
Homework Helper
Often in physics a symbol doesn't stand for anything. For example, Momentum=p, Magnetic Field=B... As far as I know, the "c" is completely arbitrary.

artie
Often in physics a symbol doesn't stand for anything. For example, Momentum=p, Magnetic Field=B... As far as I know, the "c" is completely arbitrary.
That's a little strange in this case, because E and m do match up with Energy and mass! The only thing I can think of is c is constant.

Doc Al
Mentor
c for celeritas

I believe that c was chosen for celeritas, Latin for "speed". (But c for "constant" works too.) Read: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html" [Broken]

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'c' is completely arbitrary, probably not having anything to do with 'constant' as there are several constants in the universe. 'c' is just another physical constant, just like a mathematical variable.

I believe that c was chosen for celeritas, Latin for "speed". (But c for "constant" works too.) Read: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html" [Broken]
^^^^^^^^^^^^

or that haha

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Mapes
Homework Helper
Gold Member
I saw a cartoon once of Einstein at a blackboard where he had written E=ma2 and crossed it out, then wrote E=mb2 and crossed that out...

artie
I believe that c was chosen for celeritas, Latin for "speed". (But c for "constant" works too.) Read: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/c.html" [Broken]
Excellent!

Since Einstein was German, I had tried to find a German word for "light" that begins with c but it makes more sense that the word would be rooted either in Latin or Greek.

Thanks

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malawi_glenn
Homework Helper
I saw a cartoon once of Einstein at a blackboard where he had written E=ma2 and crossed it out, then wrote E=mb2 and crossed that out...
that is just a joke.

I saw a cartoon once of Einstein at a blackboard where he had written E=ma2 and crossed it out, then wrote E=mb2 and crossed that out...
wow, i thought i saw that one too, but it had different powers for c. like E=mc0, E=mc1, and finally E=mc2. maybe there was a crossed out E=mc3 on the blackboard.

i guess it's a way to do physics; guess (and see if experiment supports your guess). about E=mc2, no other power would be dimensionally correct if energy and mass are measured in units that do not define c to be one (or dimensionless).

malawi_glenn
Homework Helper
Hmm we have derived E = mc^2 at school, so I dont think Einstein just "guessed" that solution.. ;-)

as we know c is the absoulte speed (speed of light)
and as i think c^2 is the greatest constant in the physics
i dont know exactly how Eisntein found it...

malawi_glenn
Homework Helper
why is not c^88643 bigger?

Just google "derivation of E=mc^2" or search in textbooks about special relativity

why is not c^88643 bigger?

Just google "derivation of E=mc^2" or search in textbooks about special relativity
i said i dont know how Einstein found this equation....
when E=mc^2 apllicated on the particles...it was right
so the scientists has no reason to change c^2 to c^5345345345

why is not c^88643 bigger?

Just google "derivation of E=mc^2" or search in textbooks about special relativity
my own explanation why E=mc^2

E means Energy, measured by Joule
we all now that F=ma and E=Fr =mar(r is the distance)
so Joule=Newton*Meter=Kg*Meter*sec^-2
for E=mc^2 --> Joule=Kg*(Meter*sec^-2)^2
anybody agree with me??

malawi_glenn
Homework Helper
my own explanation why E=mc^2

E means Energy, measured by Joule
we all now that F=ma and E=Fr =mar(r is the distance)
so Joule=Newton*Meter=Kg*Meter*sec^-2
for E=mc^2 --> Joule=Kg*(Meter*sec^-2)^2
anybody agree with me??
That is just an argument from units, why couldn't it be: E = 8*mc^2 ?

You must do the full derivation.

And WHY is c^2 the biggest constant in physics?

i) There are formulas which have c^6 .. aren't that a bigger constant?

ii) c is the constant, c^2 = c*c, i.e the constant c is multiplied with another constant c ...

iii) c is not a real constant, it also have a unit: Lenght/time, so c^2 has units lenght^2/time^2

iv) How can we compare e.g G with c? They have different nummerical values, but they have also different units. Also, you can easy come up with a unit system where G has a bigger nummerical value than c. It is like comparing colour with sound.

/Glenn - 1 term from Masters degree in physics.

HallsofIvy
Homework Helper
I'm still unclear as to what the question is! You say you know that "E" is "energy" and "m" is "mass" and understand that "c" represents the speed of light. Are you really only asking why the letter "c" is used for "speed of light?

That was not original with Einstein. Maxwell had already used "c" for the speed of light in his derivation of the wave equation from his equations for the Electric and Magnetic fields and I suspect it had been used that way before. My understanding is that it is from "celerity" which is Latin for "speed".

I'm still unclear as to what the question is! You say you know that "E" is "energy" and "m" is "mass" and understand that "c" represents the speed of light. Are you really only asking why the letter "c" is used for "speed of light?

That was not original with Einstein. Maxwell had already used "c" for the speed of light in his derivation of the wave equation from his equations for the Electric and Magnetic fields and I suspect it had been used that way before. My understanding is that it is from "celeritas" which is Latin for "speed".
yes that's right

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That is just an argument from units, why couldn't it be: E = 8*mc^2 ?

You must do the full derivation.

And WHY is c^2 the biggest constant in physics?

i) There are formulas which have c^6 .. aren't that a bigger constant?

ii) c is the constant, c^2 = c*c, i.e the constant c is multiplied with another constant c ...

iii) c is not a real constant, it also have a unit: Lenght/time, so c^2 has units lenght^2/time^2

iv) How can we compare e.g G with c? They have different nummerical values, but they have also different units. Also, you can easy come up with a unit system where G has a bigger nummerical value than c. It is like comparing colour with sound.

/Glenn - 1 term from Masters degree in physics.
i said first....im not sure of it...but maybe c^2 is the
biggest physical constant
and tell me about these formulas which have c^6... i hav no idea abt them...
about c is not a real constant?? i didnt understand
...it is a unit thats right.... so wheres the problem???
c is specified unit (at least in caccum)

malawi_glenn
Homework Helper
i said first....im not sure of it...but maybe c^2 is the
biggest physical constant
and tell me about these formulas which have c^6... i hav no idea abt them...
about c is not a real constant?? i didnt understand
...it is a unit thats right.... so wheres the problem???
c is specified unit (at least in caccum)

The thing is that we can only compare things that have equal units. For example 3Joules - 1 Joule = 2 Joule. But what is 3Joules - 5m/s ? And what is biggest between 300 000 000m/s and 1.626*10^-34 J*s ?

Using your argument, why is not h^-1 bigger than c^2? If we only look at the figures, using SI-units, h^-1 = 1.51*10^33 ...

It is only meaningful to compare quantities with the same units. c.f. pi vs. natural number e, or 2000m/s with 10m/s.

The thing is that we can only compare things that have equal units. For example 3Joules - 1 Joule = 2 Joule. But what is 3Joules - 5m/s ? And what is biggest between 300 000 000m/s and 1.626*10^-34 J*s ?

Using your argument, why is not h^-1 bigger than c^2? If we only look at the figures, using SI-units, h^-1 = 1.51*10^33 ...

It is only meaningful to compare quantities with the same units. c.f. pi vs. natural number e, or 2000m/s with 10m/s.
excuse me.....i learned myself the english
if u know arabic....maybe we can communicate better :D
coz im from Syria

malawi_glenn
Homework Helper
I hope you understand what I wrote.

it may be simple if we calculate energy in special relativity by the relation
W= T2-T1= integral F.dr
W Work
T kenitic energy
F force
dr deplacement element
this formula is generalisation of the case in classical mechanics
the force is rate of change of momentum in time
the component // to r is
F//=G(v)m(dv/dt)
m rest mass
G Gamma factor = 1/sqrt(1-v²/c²)
then F.dr=F//.dr
and dr=vdt
W= integrale m G(v) v.dv
the bound of velocity 0"rest" and v
W= T2-T1=G(v)mc²-mc²
like we know in this case E=T=G(v)mc²
rest energy =mc²
in presence of interaction the effect must be take into account in enrgy's formula

The thing is that we can only compare things that have equal units. For example 3Joules - 1 Joule = 2 Joule. But what is 3Joules - 5m/s ? And what is biggest between 300 000 000m/s and 1.626*10^-34 J*s ?

Using your argument, why is not h^-1 bigger than c^2? If we only look at the figures, using SI-units, h^-1 = 1.51*10^33 ...

It is only meaningful to compare quantities with the same units. c.f. pi vs. natural number e, or 2000m/s with 10m/s.
I think that i understand your viewpoint
in classiccal mechanics the kenitic energy is T=(1/2)mv²
but if we take the expression of energy in relativity for free particule
E=mc²/sqrt[1-(v²/c²)]
and make a taylor development for v very smaller than c we find
E=mc²+ (1/2)mv²+... =T
this is not a physical problem because the principle of consevation energy is not broken if we add a constant , because the interising is the amount of change make by the interaction of physical systems in this case representing by the work W= T2-T1 =(1/2)mv2²-(1/2)mv1²

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i haven't (since college 3 decades ago) looked at Einstein's original derivation, but the simplest derivation i have seen is in my first Modern Physics text (Beiser) from about the same era 3 decades ago. but we use the concept of "relativistic mass" which seems to be deprecated here. whether it's classical or relative, we start with a body of (rest) mass m0, apply a force of F to it over an interval of distance x0 and see how much velocity comes out.

work done: $$T = \int_0^{x_0} F \ dx$$

the force F is: $$F = \frac{dp}{dt} = \frac{d(m_0 v)}{dt} = m_0\frac{dv}{dt} = m_0 a$$

in the classical case. we can pull the mass m0 out of the derivative because Newton had no concept of it changing, and thus we get the familiar F=ma for Newton's 2nd law.

so this work integral comes out as:

$$T = \int_0^{x_0} F \ dx = \int_0^{x_0} \frac{d(m_0 v)}{dt} \ dx$$

with two substitutions of variable (that we learn in calculus):

$$T = \int_0^{m_0 v_0} v d(m_0 v) = m_0 \int_0^{v_0} v dv$$

where v0 is the velocity of the body when it gets to the place x0. that last integral comes out to be:

$$T = m_0 \int_0^{v_0} v dv = \frac{1}{2} m_0 v_0^2$$

the familiar kinetic energy formula for classic mechanics. we had to do T amount of work to bring the body of mass m0 from a velocity of 0 to a velocity of v0, so that work we needed to do is somehow transferred into the moving body (from our perspective) and "stored" as kinetic energy as long as it continues to move at velocity v0.

hey guys, i just realized i gotta get going before i finish this. i'll come back to it tonight. you can kinda see how it will go. in the relativistic case, the mass is not constant, the integral will come out different and the kinetic energy will come out to be

$$T = m c^2 - m_0 c^2$$

where $$m = m_0 \frac{1}{\sqrt{1 - \frac{v_0^2}{c^2}}}$$

the relativistic mass. the interpretation of the kinetic energy in the above equation is

$$T = m c^2 - m_0 c^2 = E - E_0$$

where E=mc2 is the "total energy" of the body (from our perspective with it whizzing past us) which is proportional to the relativistic mass and E0 is the "rest energy" and is proportional (with the same constant of proportionality) to the rest mass. so total energy is equal to rest energy plus the extra kinetic energy you kick in to get the body moving (relative to our frame or reference).

i'll get back to this later.