Cees Alons
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- Cees Alons
Energy is equal to the mass of an object times the speed of light squared.
....
It really has nothing to do with why we cannot exceed the speed of lightOh, but it does.
Physicists had noted before that, as Brian already said, light in an absolute vacuum always travels at exactly the same speed - even if the object transmitting it moves relatively to the observer (when Earth moves towards, say, Jupiter, the light coming from Jupiter doesn't appear to have a higher speed than if we travel away from that planet).
Difficult assumptions about the nature of the 'ether' were necessary to explain that.
Einstein started a new theory (and another one later), simply taking the fact that light always has the same speed to any observer as an axiom.
One result of that axiom was that we cannot go faster than light. Another delivered the equation E = m . c^2.
It mainly works out like this: when a mass already has a certain speed, and you apply energy to accelerate it with a certain new amount of speed, the resultant speed will not be the sum of the initial and the added speed, but less.
The interesting part is this: from the view of an observer who happens to be at the initial speed of the mass (to whom it looked in rest), it now does have the intended new (added part of the) speed!
If something moves at a certain speed, the mass of it and the speed represent a certain energy that's stored in that object, its momentum. It's exactly the energy that was put into it to give it that speed (losses, e.g. friction warmth, are discarded here for simplicity). And it is the same amount of energy you get back when you slow the object down again.
Energy and mass are never lost or added. Old theories believed that in a closed system both energy never increased or decreased and mass never increased or decreased. This is where Einstein comes in.
If something accelerates towards the speed of light and (according to the above axiom) its actual speed appears to be less than you'd expect according to the 'old' energy-applied-to-mass rule, it behaves as if it has gotten more mass. You push, but it doesn't' go that much faster: apparently it is now heavier.
So the energy put into an object to accelerate it, doesn't just speed it up (as the old theory used to assume): that energy is also partly converted to mass.
When he computed the energy needed to add that amount of mass, Einstein got his famous formula.
So now we believe that in a closed system energy as well as mass can change, but the amount of energy + mass can never be increased or decreased, when you apply Einstein's formula to compute the sum (you have to convert one of them to avoid adding apples to oranges).
When the object slows down again, you get all that energy back, the converted-to-mass part too.
But the bottom line is: energy ("push") applied to a moving object will almost exclusively speed it up when it moves slowly, but gradually it will be exploited less to just speed it up, but also to increase its mass. Close to the lightspeed, such energy will almost totally be used to create more mass and it won't speed that mass up so much any more.
At the light speed (impossible to reach) all energy added will become mass and it won't accelerate any more: so the mass would become infinite (because the energy needed to move that huge amount would be infinite) and yet it will not go any faster.
So, both outcomes have indeed everything to do with each other!
We cannot go faster than light: in fact nothing that has a non-zero mass at a speed lesser than light can ever go as fast as light.
Cees
