# Einstein's equation

Einstein's equation ....

E = MC2

if energy and mass are equivalent, is that if it's moving at the speed of light?

or does that mean if you shot a beam or photon of light at a piece of matter you get that energy amount, and how much is that amount?

tiny-tim
Homework Helper
Hi Xyooj!

No, it's for any speed except the speed of light.

M is the "relativistic mass", = m0/√(1 - v2/c2).

For photons, the rule is different: E = Planck's constant times frequency.

That equation gives you the amount of energy any object you know the mass of, contains.

And apple weighing 200 grams (0.2 kg) contains 1.8*10^16 Joules.
That's enough energy to melt 4.3*10^10 kg of ice, and then raise its temperature to boiling temp.

By the way ,it should be called ' De Pretto equation' since he discovered it before Einstein :)

- Principle of Relativity : Poincare

- Mass Energy equivalence : De Pretto

- Lorentz Tranformation : Lorentz

then , why is it called Einstein's Relativity ??

JesseM

One way of thinking about the physical meaning of the equation is by thinking of some bound system which contains various forms of energy--the rest mass energies of all the particles in the system plus the kinetic energy of the particles, and the binding energy (i.e. the difference in potential energy between the bound state and the potential energy they'd have if all the particles were far apart from one another). If you try to accelerate the system and see how much energy is needed, or you put the system on a scale and weigh it while in an accelerating room (or weigh it in Earth's gravity since inertial mass and gravitational mass are the same), you'll find that this is proportional to the total energy, not just the sum of the rest mass energies. So, for example, a hot brick would weigh slightly more than a cold brick because the heat gives the particles extra kinetic energy, and an atomic nucleus weighs slightly less than the sum of the rest masses of the protons and neutrons that make it up because the potential energy is less in the bound state than when they're far apart.

JesseM

By the way ,it should be called ' De Pretto equation' since he discovered it before Einstein :)

- Principle of Relativity : Poincare

- Mass Energy equivalence : De Pretto

- Lorentz Tranformation : Lorentz
Of course, most physicists would see Einstein's big achievement as general relativity, not special relativity. But on the subject of De Pretto, something I wrote a while ago on this:

In Olinto De Pretto's case, he did write down the equation E=mc^2 before Einstein, but instead of deriving it from basic principles as Einstein did, De Pretto just made a guess made on incorrect assumptions. An italian speaker who read the original article summarized here:
I had the opportunity to read the original paper by De Pretto (I have a copy of it). I am italian (born and living in Italy) and, moreover, I have a degree in Mathematics and a further education in Mathematical Physics. I think that it would be clear to anyone who is not looking for a sensational story that De Pretto's paper has no connection with relativity. It is quite clear that by mv^2 he meant "forza viva" which is the way (twice the) kinetic energy was (also) called at that time in Italian books. His considerations revolve about the idea that the particles of "ether" with small mass but great velocity (like the speed of light) would acquire a huge kinetic energy. The whole paper has almost no equations or precisely defined concepts and it is clear that the framework of special relativity is entirely missing.

I think that this whole story would be forgotten if more people could actually read De Pretto's paper. As for the very few Italian supporters of this idea I noticed that they never present precisely De Pretto's ideas (or the few things one can get from them) but just cite this formula which, by itself, doesn't mean much, out of context. The reason is that this whole story "holds no water".
The equation for kinetic energy is E=1/2*mv^2, so it sounds like De Pretto decided to consider the case of v=c (v=velocity, c=speed of light) and remove the factor of 1/2 for some reason, which isn't anything like the derivation of E=mc^2 in relativity, and it also suggests De Pretto would have thought of the equation as only applying to things moving at the speed of light, as opposed to relativity where the equation gives the relation between mass and energy for all objects regardless of their velocity.

A bad deduction of a correct fact or equation should also be considered

Look at Ramanujan, many of his formula were deduced incorrectly, the same is valid for Euler.

JesseM

A bad deduction of a correct fact or equation should also be considered

Look at Ramanujan, many of his formula were deduced incorrectly, the same is valid for Euler.
At least with Ramanujan we can speculate that he must have had some kind of correct understanding on an intuitive or subconscious level, with De Pretto we know that his reasoning was completely misguided and that it was nothing but a lucky guess (of a very short formula).

E = MC2

if energy and mass are equivalent, is that if it's moving at the speed of light?

or does that mean if you shot a beam or photon of light at a piece of matter you get that energy amount, and how much is that amount?
A more complete formula is: $E^2 = (m c^2)^2 + (pc)^2$

No, [E=mc2]'s for any speed except the speed of light.

M is the "relativistic mass", = m0/√(1 - v2/c2).

For photons, the rule is different: E = Planck's constant times frequency.

Uh.. if you're going to use relativistic mass, you should pick one set of rules that all work for both "massive" and "massless" particles:
E = hf = mrc2 = m0c2+KE,
p = mrv = h / de Broglie wavelength.

One way of thinking about the physical meaning of the equation is by thinking of some bound system which contains various forms of energy--the rest mass energies of all the particles in the system plus the kinetic energy of the particles, and the binding energy (i.e. the difference in potential energy between the bound state and the potential energy they'd have if all the particles were far apart from one another). If you try to accelerate the system and see how much energy is needed, or you put the system on a scale and weigh it while in an accelerating room (or weigh it in Earth's gravity since inertial mass and gravitational mass are the same), you'll find that this is proportional to the total energy, not just the sum of the rest mass energies. So, for example, a hot brick would weigh slightly more than a cold brick because the heat gives the particles extra kinetic energy, and an atomic nucleus weighs slightly less than the sum of the rest masses of the protons and neutrons that make it up because the potential energy is less in the bound state than when they're far apart.

hmmm......is that correct?
ever since elementary school, we have been taught that hot air raise, while cold air stay down the floor, due to their difference in weight. Why is that a hot brick would weight more? would it not weight less as the the molecules/atoms within it are moving and does not exert on the weighing scale? isn't kinetic energy just potential energy that is moving due to external force exertion?

anyways, the original question is that E = M only at the square of speed of light C?

JesseM

ever since elementary school, we have been taught that hot air raise, while cold air stay down the floor, due to their difference in weight.
This is because hot air is less dense, so in a given volume of hot air there are fewer molecules. I'm talking about some confined system with a set number of molecules, like a brick or a closed box filled with air. If you heat up the air in a closed box, it can't become less dense, instead the pressure just increases. The box will weigh a tiny bit more when heated, because the extra kinetic energy of the molecules adds to the weight.

The fact that heated objects weigh slightly more has been tested experimentally, see this paper:

http://arxiv.org/pdf/gr-qc/9909014

I actually originally got the example of a heated brick from this paper:

The principle of equivalence—the exact equality of inertial and gravitational mass—is a cornerstone of general relativity, and experimental tests of the universality of free fall provide a large set of data that must be explained by any theory of gravitation. But the implication that energy contributes to gravitational mass can be rather counterintuitive. Students are often willing to accept the idea that potential energy has weight—after all, potential energy is a rather mysterious quantity to begin with—but many balk at the application to kinetic energy. Can it really be true that a hot brick weighs more than a cold brick?

General relativity offers a definite answer to this question, but the matter is ultimately one for experiment. Surprisingly, while observational evidence for the equivalence principle has been discussed for a variety of potential energies, the literature appears to contain no analysis of kinetic energy. The purpose of this paper is to rectify this omission, by reanalyzing existing experimental data to look for the “weight” of the kinetic energy of electrons in atoms. I will then try to reconcile the results with the occasional (and not completely unreasonable) claim that “objects traveling at the speed of light fall with twice the acceleration of ordinary matter.”
Xyooj said:
Why is that a hot brick would weight more?
Because all forms of energy add to inertial mass, and the average kinetic energy of atoms in an object will be greater when it's heated, assuming no atoms are lost.
Xyooj said:
isn't kinetic energy just potential energy that is moving due to external force exertion?
No, kinetic energy and potential energy are separate, although decreases in potential will normally be balanced by increases in kinetic and vice versa.
Xyooj said:
anyways, the original question is that E = M only at the square of speed of light C?
The speed of light squared is just a conversion factor, I don't understand what you mean by "at the square of speed of light" (the square of the speed of light is not itself a speed, if that's what you mean)