Can E=mc^2 Be Derived Without Special Relativity?

[journeytospace]

Einstein derived E=mc2 using his SR in 1905...My question is

1. can E=mc2 be derived only using SR?
2. Even before einstein some(poincare,de pretto) have arrived at mass - energy equivalence relation... does this mean E=mc2 can also be derived without SR?

 

[Shooting Star]

Lorentz's theory of electron predicted the mass increase, as did the theories of some other scientists like Poincare and De Pretto. But they all assumed some kind of aether or the other. Some of them assumed the aether to be a kind of gas or fluid, and even tried to derive its pressure.

Einstein's contribution was deriving the equations using relativity.

Actually, Einstein didn't even use this particular form of the formula in his initial papers. He simply derived the decrease in the mass of the body due to energy loss by radiation. I don't know who wrote this in its modern form.

 

[journeytospace]

Thank you...

 

[Jwink3101]

As mentioned by Shooting Star, What made einstein's work on relativity so great is that it took a lot of what other people had done and did it without ether. Poincare had similar length contraction stuff but it depended still on Ether.

What is also amazing to me is Lorentz made his equations before relativity. They weren't designed to apply to relativity but it ended up, that they were the same thing.

Another thing of note, how SR is thought now is different from Einstein's way of looking at it. The biggest example is Minkowski space. Einstein has been quotes as saying something along the lines of "now that the mathematicians got their hands on relativity, i am not sure i even understand it anymore" (Not a direct quote by any means). Minkowski (who was Einstein's old professor in math) created a lot of the math that goes along with relativity. He combined energy and momentum into a four-vector of momentum and position was combined with time.

If you are interested, private message me and i can send you a lot of readings and links on this stuff. In addition to my normal science courses, for a humanities course, i am taking a course on the history and development of everything Einstein did in 1905 so i have a lot of stuff on this.

 

[robphy]

Jwink3101,

I'm interested to see your reading list,
and I think others may be interested.

By the way, the centenary of Minkowski's contributions to Relativity is approaching.

Along these lines, I have a question concerning Einstein and Minkowski's spacetime diagram... but I'll post that soon in another thread.

 

[pmb_phy]

Lorentz's theory of electron predicted the mass increase, as did the theories of some other scientists like Poincare and De Pretto. But they all assumed some kind of aether or the other. Some of them assumed the aether to be a kind of gas or fluid, and even tried to derive its pressure.

Einstein's contribution was deriving the equations using relativity.

Actually, Einstein didn't even use this particular form of the formula in his initial papers. He simply derived the decrease in the mass of the body due to energy loss by radiation. I don't know who wrote this in its modern form.

Einstein wrote several papers after 1915 on this topic.

Pete

 

[timur]

In the original 1905 paper Einstein has exactly the same formula, E=mc^2, only he wrote it as m=L/c^2.

 

[Shooting Star]

"If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes."
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This is what Einstein had written in his 1905 paper. Compare with what I have given in my post. He says E=mc^2 in words, but not using the equation.

 

[JesseM]

"If a body gives off the energy L in the form of radiation, its mass diminishes by L/c². The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes."
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This is what Einstein had written in his 1905 paper. Compare with what I have given in my post. He says E=mc^2 in words, but not using the equation.

Also, his statement above is not quite as general as the later understanding of E=mc^2, which doesn't exclusively deal with changes in mass due to giving off radiation...for example, a solid object weighs more when heated than when cold, due to the increased kinetic energy of its molecules, see this later quote from Einstein:

In his 1938 book, The Evolution of Physics, 1 Einstein writes:

Energy, at any rate kinetic energy, resists motion in the same way as ponderable masses. Is this also true of all kinds of energy?

The theory of [special] relativity deduces, from its fundamental assumption, a clear and convincing answer to this question, an answer again of a quantitative character: all energy resists change of motion; all energy behaves like matter; a piece of iron weighs more when red-hot than when cool; radiation traveling through space and emitted from the sun contains energy and therefore has mass, the sun and all radiating stars lose mass by emitting radiation. This conclusion, quite general in character, is an important achievement of the theory of relativity and fits all facts upon which it has been tested.

Classical physics introduced two substances: matter and energy. The first had weight, but the second was weightless. In classical physics we had two conservation laws: one for matter, the other for energy.7

 

[FireBones]

Lorentz's theory of electron predicted the mass increase, as did the theories of some other scientists like Poincare and De Pretto. But they all assumed some kind of aether or the other. Some of them assumed the aether to be a kind of gas or fluid, and even tried to derive its pressure.

Einstein's contribution was deriving the equations using relativity.

Actually, Einstein didn't even use this particular form of the formula in his initial papers. He simply derived the decrease in the mass of the body due to energy loss by radiation. I don't know who wrote this in its modern form.

I have a question... could you explain where the constancy of the speed of light for all observers is used in the derivation of E=mc^2 indicated here: http://www.adamauton.com/warp/emc2.html

The reason I ask is that the derivation on that page does not appear to use anything other than conservation of momentum and other basic laws.

Thanks.

 

[bcrowell]

I have a question... could you explain where the constancy of the speed of light for all observers is used in the derivation of E=mc^2 indicated here: http://www.adamauton.com/warp/emc2.html

The reason I ask is that the derivation on that page does not appear to use anything other than conservation of momentum and other basic laws.

Interesting question!

I would rather rephrase your question: where in this derivation is special relativity assumed? The reason I want to do that is that from a modern point of view, it really doesn't make sense to state special relativity using Einstein's 1905 postulates, in which light is given a special role.

But anyway, to answer your question, the derivation assumes that light has momentum. How do we know that light has momentum? Basically we know that because of Maxwell's equations, which say that light is an electromagnetic wave. But Maxwell's equations are not mathematically self-consistent if you use Galilean relativity; they require special relativity instead. So by assuming that light has momentum, we have effectively assumed special relativity. The thing is that people in 1900 didn't understand that Maxwell's equations implicitly required SR.