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

• artie
In summary, the symbol "c" is used to represent the speed of light in the equation E=mc^2. While it may seem arbitrary, it is likely derived from the Latin word "celeritas," meaning "speed." This symbol has been used by scientists before Einstein's famous equation was derived, such as in Maxwell's equations. It is not the only constant in physics and its numerical value can vary depending on the units used.
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?

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.

nicksauce said:
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.

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"

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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.

Doc Al said:
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"

^^^^^^^^^^^^

or that haha

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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...

Doc Al said:
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"

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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Mapes said:
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.

Mapes said:
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).

Hmm we have derived E = mc^2 at school, so I don't 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 don't know exactly how Eisntein found it...

why is not c^88643 bigger?

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

malawi_glenn said:
why is not c^88643 bigger?

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

i said i don't 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

malawi_glenn said:
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??

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.

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".

HallsofIvy said:
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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malawi_glenn said:
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)

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.

malawi_glenn said:

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 I am from Syria

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

malawi_glenn said:

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 got to 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 into get the body moving (relative to our frame or reference).

i'll get back to this later.

This is the question:

artie said:
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?

Doc Al said:
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"

Einstein began by using an upper-case V for the speed of light [9]. At that time he was also writing papers about the thermodynamics of radiation, and in those he used up upper-case L

L would have been the German root for the English word "Light". It was later changed to C. The word for Light begins with an L in German and in Greek:

Light (n.) - "brightness," O.E. leht, earlier leoht, from W.Gmc. *leukhtam (cf. O.Fris. liacht, M.Du. lucht, Ger. Licht), from PIE *leuk- "light, brightness" (cf. Skt. rocate "shines;" Arm. lois "light," lusin "moon;" Gk. leukos "bright, shining, white;" L. lucere "to shine," lux "light," lucidus "clear;" O.C.S. luci "light;" Lith. laukas "pale;" Welsh llug "gleam, glimmer;" O.Ir. loche "lightning," luchair "brightness;" Hittite lukezi "is bright"). The -gh- was an Anglo-Fr. scribal attempt to render the O.E. hard -h- sound, which has since disappeared.

It would seem that since, according to the Theory, the speed of light is absolute speed, that he would change it to a word for "speed" - C for celeritis (which must be the root of the word "acceleration"?) The theory allows for the Speed of Light not Light itself.

Thanks for every one who posted here. I still must review all of your posts and since I have no understanding of physics jargon, that may take me some months.

In the meantime, I have another question that I offer, and I hope that it is not a stoopid one, but here goes:

If the speed of light is absolute, then how can the speed of light be squared? How can E=mc2 be possible?

Thanks
artie

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artie said:
In the meantime, I have another question that I offer, and I hope that it is not a stoopid one, but here goes:

If the speed of light is absolute, then how can the speed of light be squared? How can E=mc2 be possible?
What does the speed of light being "absolute" (a better term would be invariant) have to do with it being squared in that expression?

Doc Al said:
What does the speed of light being "absolute" (a better term would be invariant) have to do with it being squared in that expression?

What I think I understand is that the speed of light can not be increased. This must be true if it is invariant. Therefore, I am led to ask, "How can it be squared?" If the speed of light is squared, then the speed of light varies and is not absolute speed.

artie said:
If the speed of light is squared, then the speed of light varies and is not absolute speed.
I don't understand the logic of that sentence. Just because a quantity is squared in some expression, does not mean that the quantity varies.

Trivial example: A car of mass "m" moves at constant speed "v". Its (non-relativistic) kinetic energy is 1/2mv^2--the speed is squared in that expression--yet its speed remains constant.

I suspect you are getting messed up with the apparent implications of English grammar. Just because the speed of light appears squared in some expression, does not mean that we did something to physically change the speed of light.

malawi_glenn said:
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
Can you cite a specific formula that involves the speed of light to the 6th power? I'm not doubting you but I would like to see it.

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.
That I agree with completely.

Doc Al said:
I don't understand the logic of that sentence. Just because a quantity is squared in some expression, does not mean that the quantity varies.

Trivial example: A car of mass "m" moves at constant speed "v". Its (non-relativistic) kinetic energy is 1/2mv^2--the speed is squared in that expression--yet its speed remains constant.

I suspect you are getting messed up with the apparent implications of English grammar. Just because the speed of light appears squared in some expression, does not mean that we did something to physically change the speed of light.

I guess that you are right. The expression is only trying to illuminate the nature of energy and the relation of energy to mass. It tells us that if we could speed up a given mass that the energy would equal mc2. Still, in order to demonstrate that E=mc2, isn't is necessary to speed up a given mass to c2, and release it's energy? Isn't that what we do in an atomic explosion? And isn't that the evidence that E=mc2 is a correct assessment of the nature of energy? I was under the impression that the atom bomb was proof that E=mc2 was correct.

You're still making the same mistake. The fact that it is squared in the equation doesn't imply anything like what you are suggesting - just like the regular kinetic energy equation. It's just how the calculation works. Ie, you plug the actual speed of a car into the equation to calculate the kinetic energy of the car, right...?

E=m(c*c)

There, no more pesky 2.

artie said:
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?

C is a conversion factor, an artifact of defining separate, supposedly incompatible, units for space and time before we understood the relevant physics. We now know that space and time form a single entity (space-time) so we should simply put c = 1. The equation E = M c^2 simply expresses the relation between mass and rest energy: The mass of an object is the rest energy (up to a factor c^2, which should be set equal to 1).

The proper way to derive classical physics from relativity is to rescale time relative to space by inserting c back into the equations (which is to be interpreted as a dimensionless rescaling parameter) and to consider the limit c ---> infinity. When taking this limit you must redefine your physical quantities such that they stay finite in this limit (so, in general, they will scale with c as well). The classical equations are relations between these quantities that are valid (and nonsingular) in this limit.

What happens is that you get more independent equations and more independent physical equations than you started out with. This is caused by the fact that in the limit c ---> infinity, the equations must be nonsingular. So, loosely speaking, since c is formally infinite, certain quanties involving c cannot be compared to each other anymore and they become "independent quantities".

E.g. mass and energy become physically independent quanties and we get an extra physical equation that expresses conservation of mass.

I think I'm beginning to understand and I must have understood when I read The Special and General Theory a year or so ago. mc2 is a measurement for E. This equation measures the energy in a given mass. I must have let my imagination run away since that first reading.

Now what is energy? Are we talking about light and heat only? Or are there other kinds of energy? And does E=mc2 account for all types of energy?

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