I refused to delude myself into thinking I understood special relativity when I read it explained in laymen’s cosmology texts as energy equals mass times the speed of light. I couldn’t find an explanation of why the contant was squared. And 186,000 miles/second squared is much faster than the unexponentiated rate. I couldn’t even get a good answer from physicists. It turned out the answer is simple.
Some people in here must already know.
In the formula, c² is the conversion factor required to convert from units of mass to units of energy, i.e., the energy density. In unit-specific terms, E (joules or kg·m²/s²) = m (kilograms) multiplied by (299,792,458 m/s)2.
It is explained in the link below the Wikipedia article. Interesting that two minute factors in the equation are neglected.
Should I give out the simple answer yet? It’s a geometry problem. We learned it in Grade 10 and forgot it. I found the answer in a exhaustive survey of Mathematics by Jan Gullberg called Mathematics From the Birth of Numbers. About 1100 pages and $43 from Amazon. Great reference book for any serious polymath.
Yes, give the answer.
I’m more concerned how or why he derrived C as the center of his equasion, why is the speed of light the base variable to determine maximum atomic energy within a particle.
the formula E=mc 2 , is virtually identical to the formula used to determine energy of a moving object, E=mv 2, where v=velocity, the reason for this corrilation being that the energy increases exponentually as the velocity is increased.
eg 2kg object traveling 1m/s has 2 jouls of energy (havn’t done physics in a while bear that in mind) meanwhile the same object traveling at 2m/s would have 8 jouls of energy, the scientists who found this out knoticed this corrilation and made the formula to reflect it. not the other way around.
but like I said I’d like to know why he put C as his constant, I would love to see some of his reserch notes so I could determine the origin of this point. that and perhaps touch the mind of one of the greats for a shallow moment before slipping into his maddness.
Peace
The speed of something is dependent on the perspective of the viewer. If the viewer is moving at the same speed as the object he is measuring, then the object will not appear to move.
So, if you’re in you’re car and you look at you’re glasses sitting next to you, they don’t seem to be moving, but they are in fact moving at the speed and direction the car is, but since you’re moving at the speed and direction of the car, you don’t see the glasses move. You only see the world around you move.
Einstein asked what happens if you move at the speed of light, c, and you observe another object moving at the speed of light. He asked whether the object would not appear to be moving as well. His answer was that in this case speed is no longer relative, the object you’re observing will appear to move at the speed of light, unlike the sunglasses which appear to not be moving. He concluded that when you move at the speed of light time slows down for you. Time moves more quickly for the object you’re observing, so it looks like it’s moving faster than you.
I don’t know why this is and I don’t know why c is the constant other than Einstein thought that nothing could ever move faster than light.
You still haven’t answered why c is squared.
I always thought that the main point was E = M. I don’t know why Einstein added the C squared. I think it is regarded as meaningless. The first major test of this theory was the atomic bomb, where matter (uranium/plutonium) being bombarded by other matter at an extremely fast rate, was converted into energy. C squared is meaningless because nothing in this universe can travel that fast. Even in particle accelerators I think the top speed that can be achieved is something like 99% of the speed of light, and I forget what particles these are. Anyway at this rate, they are converted to lighter particles and energy. Maybe Einstein was making the point that if anything could travel that fast, all of it would be converted to pure energy, but I’m not sure.
So if you’re asking what the relevance of C squared is I think there is none. Energy = mass at extremely high velocities, and that’s it.
The speed of light is its velocity times its acceleration. Light travelling through a vacuum accelerates to its velocity. That is, velocity and acceleration are equal. Special relativity deals with nonaccelerated relative motion. If you’re driving at 30 mph and maining that speed, you’re accelerating at 30 mph. Right Ric?
I"m getting confused about these avatars. I get the whole special relativity thing though, that’s nice.
If you’re driving at 30 mph and maintaining 30 mph, your acceleration is 0. Acceleration is a measure of how quickly your getting faster. If you’re not getting faster your acceleration is 0.
When we talk about acceleration iwe usually talk about how fast something goes from 0 to 60 mph. So if a Ferrari does it in 10 seconds and a Mustang in 20, the acceleration is higher in the Ferrari. It changed from speed 0 to speed 60 faster than the Mustang.
I wouda thunked the c^2 was to balance out the J to Kgm^2s^2. Also, most of us think that all objects have potential energy, and since the speed of light is the fastest we have seen anything go, that leads to thinking that plugging the speed of light in for V in the equation (1/2)MV^2, would be the maximum energy the object could achieve. 
yes , no? how did I do?
-Guy6870
To maintain C, accelerate to maintain V. ie . unaccelerated motion
The c^2 is just a constant. Energy is proportional to mass, meaning, mass times something is energy.
Bilby, Einstein didn’t arbitrarily add the c^2. C^2 isnot a measure of how fast something is going its a number. E does not equal M, that wouldn’t make any sense.
I still don’t know why the constant is c^2… it seems so simple a number and yet it seems so fundamental.
That’s kinetic energy. PE = mgh, KE = 1/2mv^2.
And for some reason, which I cannot remember exactly how to put it into words, E = mc^2 explains why no object, with mass, can accelerate to or even obtain the speed of light, c.
If you want to know exactly, read Simply Einstein: Relativity Demystified by Richard Wolfson. It’s not that long, and, for a physics book, you don’t have to have much, if any, mathematical…expertise…to read it.
Lorentz transformation. Say an object is nearing the speed of light, all the energy henceforth applied increases it’s mass, not it’s velocity.
To understand why its c squared first you need to know what Energy and Mass are in physics terms.
We’ll start with eneregy. If we start with newtons equation F=mass x acceleration then an easy way to understand it is that energy is equal to the force applied to a body times the distance it travels (strictly this is the defination of work but work an is an energy).
So basically we have E= mass x acceleration x distance
now acceleration is a change in velocity per unit time (v/t) and veloctity is a change in distance per unit time (d/t). Therefore aceleration is a change in distance per unit time per unit time (d/t^2)
So
E = mass x distance/time squared x distance
= mass x distance squared/time squared
as velocity is distance/time
E= mass x veloctiy squared
This is just a general equation(defination) for an energy. In any equation, be it newtonian kinetic energy or relativistic energy, energy must always be equal to a mass times a velocity squared.
Now to further understand why its E= mc^2 we need to understand what mass is. Mass is somethings resistance to acceleration. As you can see if we again look at F=ma i.e. a= F/m basically the more mass a body has the less it will accelerate (this is intertial mass as supposed to gravitational mass). Now if you know anything about relativity you’ll know things can’t go faster than light. This means that as a particle(with a rest mass ie not a photon) reaches the speed of light its mass (resistance to accelertion) must equal infinity so it can’t go any faster. Its not hard to see then (with a bit of maths I can’t be bothered to show) that the more energy a particle has the more mass it has ie Energy = mass x (some constant). As Energy in any equation must be equal to mass times a velocity squared and the speed of light is the only constant velocity in relativity(all others being relative) its clear to see the equation must be( again its a case of maths to show it properly)
Energy = mass x the speed of light squared
So yeah thats why…
one more thing the true equation for relativistic energy is
E= rest mass/(1-(v^2/c^2)) x c^2
so when v = c the “rest mass/(1-(v^2/c^2))” which is the relativistic mass goes to infinity as i said it should.
If v=0
E=mc^2 which is the equation for rest mass.
Anyway thats my best effort on explaining it off the top of my head
Yes.
Now all you have to do is derive that equation and you’ll really know what’s going on.
Also note that whoever said c^2 was arbitrary and a conversion factor…well, they’re kinda right…if you make a unit system where c = 1, then E = mc^2 becomes E = m. Energy is mass and mass energy, our unit systems just make it look a little more involved.
As for RicDemian’s geometric answer, I have no idea. You weren’t talking about a conservation of momentum problem, were you?
…bit patronizing me thinks.