# E =mc{squared} How Did He Arrive At This ?

E =mc{squared}
How Did He Arrive At This ?
What Was The Guy Thinking When He Cooked Up This Mess .

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He guessed. :)

Try the search you'll find alot of stuff on this.

SpaceTiger
Staff Emeritus
Gold Member
I think it's fair to say that most ground-breaking theories are little more than educated guesses.

Don't you think it's kind of a coincidence that the formula is that small, and it just uses our units O.O perfectly, like meters, second, joule, kilograms......
am I missing something here?

SpaceTiger
Staff Emeritus
Gold Member
moose said:
Don't you think it's kind of a coincidence that the formula is that small, and it just uses our units O.O perfectly, like meters, second, joule, kilograms......
am I missing something here?
Units are a human invention, so their consistency has no physical meaning. The real key thing here is that the physical concept of energy is related to that of mass, things which had been considered separately prior to Einstein.

SpaceTiger said:
Units are a human invention, so their consistency has no physical meaning. The real key thing here is that the physical concept of energy is related to that of mass, things which had been considered separately prior to Einstein.
Does this mean units of the "meter" and "kilogram" were invented to have a relationship too?

dextercioby
Homework Helper
Nope.Physics (menaing experiments and theories) "cooked" up relations between quantities which automatically mean relations between units.

Daniel.

SpaceTiger
Staff Emeritus
Gold Member
eNathan said:
Does this mean units of the "meter" and "kilogram" were invented to have a relationship too?
Not sure what you mean. The units of meters and kilograms are arbitrary scalings to two different kinds of quantities. Nobody writes an equation with one side having units of meters and the other with units of kilograms. That would imply "inconsistent" units.

SpaceTiger
Staff Emeritus
Gold Member
A small amendment to my previous statements. There ought to be some correlation between our choice of units for different quantities, but only a very rough one (noticable on a logarithmic scale). In other words, the units will usually be chosen so that "1 unit of x" will be typical on the scales of interest. For example, mks units are mostly chosen to be relevant on a human scale, while astronomers will often express things in terms of much larger units (like solar masses and AU).

yerz

SpaceTiger said:
Not sure what you mean. The units of meters and kilograms are arbitrary scalings to two different kinds of quantities. Nobody writes an equation with one side having units of meters and the other with units of kilograms. That would imply "inconsistent" units.
We are talking about e=mc^2 here, what this means is that the energy that could come from mass (in joules) is equavilant to the product of the mass (in KG) and the speed of light, c (in meters/second).

So what I am saying is this. What if we re-arranged the equation to this.

e=mc^2 where "m" is in pounds, and "c" is in miles per hour, and "e" is still in joules. Would this equation work? no, the units have a relationship. The American Standard Units are terrible :rofl:

chroot
Staff Emeritus
Gold Member
eNathan said:
e=mc^2 where "m" is in pounds, and "c" is in miles per hour, and "e" is still in joules. Would this equation work? no, the units have a relationship. The American Standard Units are terrible :rofl:
Of course it would still work:

The units (meters, kilograms, etc.) are meaningless. The dimensions (length, mass, etc.) are quite significant, however you can choose any units you wish to represent those dimensions.

- Warren

dextercioby
Homework Helper
Yes,but it would not be that simple

$$1 \ J=1\ Kg\cdot 1ms^{-2}\cdot 1m=\frac{1}{0.453}\mbox{pounds}\cdot \frac{1}{1609}mi\cdot \left(\frac{1}{3600}hr\right)^{-2}\cdot \frac{1}{1609} mi$$

It's not pretty anymore.

Daniel.

russ_watters
Mentor
SpaceTiger said:
Not sure what you mean. The units of meters and kilograms are arbitrary scalings to two different kinds of quantities.
I wouldn't quite say "arbitrary". Unlike the English system, SI was designed specifically to be easy to use. I don't know the specifics of how it was done, but it is very convenient that (for example) water has a mass of 1g/cc and a heat capacity of 1cal/g*C.

dextercioby
Homework Helper
Well,Russ,trust me,SI-cgs (or cgs-gauss for electrodynamics) is as difficult as the Anglo-Saxon system,at least for someone like me who's worked with SI-mKs all his short life...

Daniel.

Integral
Staff Emeritus
Gold Member
Why are we getting into unit bashing? It really doesn't make any difference which units are used as long as you are consistent.

Just for the record, Einstein did not just "guess" this relationship. It is a derived result of aplying the Lorentz transforms to the kinematics equations of physics.

DaveC426913
Gold Member
Consider a slightly different example (because that's the one I know).

$$F = \frac{m_1.m_2}{r^2}$$
This is the formula that shows the relationship to between two masses and gravity. It tells us that the gravitational attraction is directly proportional to the masses of the two bodies and inversely proportional to the square of their distances. Note that there are no units, and that you cannot use this formula to calculate actual values. you can only show relationships (double the mass to double the force, halve the distance to quadruple the force).

To use it to provide actual figures, we need to provide some units. We will measure the mass in grams and the radius in meters. But now our formula needs a constant: G.

$$F = G.\frac{m_1.m_2}{r^2}$$

The constant G is equal to $$6.672.10^-11 N m^2 kg^-2$$. Note the units.

If you plug all these together into the formula, including some mass and distance units, you will end up with a number and a unit of measurement:m.a - as in F=m.a. Hey! That's a unit of force!

Note that you could plug inches and stones into the equation, but to do that, your G constant would have to be converted to those units too.

The law itself is universal. The application of that law, is man-made.

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dextercioby
Homework Helper
You can't do that,it's illogical.You know that in the LHS you must have a force,since that's what you're measuring (along with mass & distance),so the units for G are obtained as a consequence,not as a premise...

Daniel.

DaveC426913
Gold Member
When all is washed and dried, does that make a difference?

I was merely pointing out the difference between proportionality and equality.

E=mc^2 is a proportionality.

Or am I completely wrong?

Integral said:
Why are we getting into unit bashing? It really doesn't make any difference which units are used as long as you are consistent.

Just for the record, Einstein did not just "guess" this relationship. It is a derived result of aplying the Lorentz transforms to the kinematics equations of physics.

I was joking.

E = mc^2 is a proportionality and an equality.

For every unit mass m multiplied by the square of the speed of light in any unit, will result in energy released with units composed of those m and c are made of. Its redundant, I dont know why you would want to toy with the units, but the relationship holds anway.

Changing the units will just require a scalar conversion factor, such as G in gravitation or K in electrics to get an answer in joules.

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HallsofIvy
Homework Helper
Yes, you are wrong. E= mc^2 does NOT say "E is proportional to mc^2" with some constant of proportionality. It says that, as long as E, m and c are all given in the same system of units (Joule, kilogram, meter/sec or erg, g, cm/sec, or slug {also called "poundal"}, foot, foot/sec) then E is exactly mc^2.

dextercioby
Homework Helper
DaveC426913 said:
When all is washed and dried, does that make a difference?

I was merely pointing out the difference between proportionality and equality.

E=mc^2 is a proportionality.

Or am I completely wrong?
No,you're partly right/wrong.You need both experiments and theory to confirm to you that:

$$E\sim mc^{2}\Rightarrow E=k\cdot mc^{2} \ \mbox{with} \ k=1$$

Oh,and logics usually makes a difference.If it hadn't been for logics,science would have been different,to say the least.

Daniel.

DaveC426913
Gold Member
So, as Moose said "Don't you think it's kind of a coincidence that the formula ... uses our units O.O perfectly, like meters, second, joule, kilograms......"

The units for energy, mass and speed were in existence before Einstein found this formula.

dextercioby
Homework Helper
Yeah,ever since the works of Leibniz,who defined the concept pf KE and saw the proportionality between and the square of velocity.

It's nothing new...

Daniel.

SpaceTiger
Staff Emeritus