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

[nu_paradigm]

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

 

[whozum]

He guessed. :)

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

 

[SpaceTiger]

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

 

[moose]

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]

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.

 

[eNathan]

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]

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

Daniel.

 

[SpaceTiger]

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]

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).

 

[eNathan]

yerz

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

 

[chroot]

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

Of course it would still work:

http://www.google.com/search?hl=en&lr=&safe=off&q=5+pounds+*+(670616629+miles/hour)^2&btnG=Search

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]

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]

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]

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]

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]

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.

 

[dextercioby]

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]

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?

 

[whozum]

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.

 

[whozum]

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 don't 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.

 

[HallsofIvy]

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]

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]

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]

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]

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.

I would still say that's pretty arbitrary from the physical standpoint. You don't have to convince me that metric units are easier to use, though. English units drive me nuts.

 

[SpaceTiger]

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.

Einstein had to "guess" several things in order to derive relativity, but they were very educated guesses. There was no reason to assume a priori that the laws of physics would be the same in all inertial frames at speeds near that of light. It was clear from the measurements that classical theory was wrong, but the question was which part? He had to guess which aspects of classical theory to keep and which to trash.

 

[whozum]

Is it true Einstein sucked at algebra, and that he handed his theories to some mathematician friends of his to derive an equation (gamma) that would model his relativity theories?

 

[dextercioby]

I dunno.Personally,I doubt it.He definitely wasn't a mathematician and if he were,he would have gotten all credit for GR.So,he shared it with David Hilbert.

Daniel.

 

[eNathan]

Einstein had a lot of trouble with the mathematics of his theory. Einstein was not a mathematician, he was a physicist was an imagination, with which he revolutionized the world :)

 

[whozum]

I remember he rejected a major part of his discoveries, but I don't remember which. He refused to believe, I think that the universe was expanding. Why is this? Science is absolute is it not? Once you prove something, its proven and should be accepted?