How can we derive the value of energy in rest mass and the relationship to c^2?

[alba]

I have read different version/interpretations of Einstein derivation of the formula, no one is logically satisfying.

But my question is more general: the value of energy in rest mass is a scalar, which is not related to anything, how can we use logic or math to derive such a value? Stretching it a bit to make myself clear, how can you derive the number of fingers in a human being? There is sure anarcane reason, but that is the way Nature decided and has it, how can you prove/derive it if you have no direct acces to it?

Because of annihilation we knew that it is in the region of c^2, but many coefficients have been suggested and they are all right or wrong, depending on the init of energy we choose. They choose to adopt that value to honour him, but I read that he himself had suggested the factor of 1/2, and when he was accused of plagiarism, he changed it to 1. If there were a compelling reason or rationale, you do not change it overnight.

 

[Let'sthink]

Due to relativistic considerartion the whole kinematics and dynamics changes. Three is nothing like this that there is annihilation region where it works and for ordinary events it does not. It works but the difference is too very small. When you apply force on a a particle it increases its speed and also its mass.. F = dP/dt with P = mv and m is a function of time and not constant; and not F = m*(dv/dt). We are not adding fingers to our hand but just stating that mass and energy are equivalent and if a particles energy is increasing then its mass is also increasing such that the total energy = mc^2 where m is the instantaneous mass.

 

[mfb]

Proofs are something in mathematics. Physics does not have proofs, it has theories.

E=mc² as rest energy is consistent with literally tens of thousands of experiments, and it fits to the framework of special relativity. A prefactor of 1/2 would be completely inconsistent with experiments. A prefactor like 1.0000000000001 would not directly be in disagreement with observations, but it would not fit into special relativity - which has been tested extremely well. There is no consistent theory that would have a different prefactor.

but I read that he himself had suggested the factor of 1/2, and when he was accused of plagiarism, he changed it to 1.

This is pure nonsense.@Let'sthink: The concept of a "relativistic mass" (velocity-dependent mass) is not used in physics any more.

 

[alba]

Proofs are something in mathematics. Physics does not have proofs, it has theories.
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Thanks for refuting let'sthink
No proof, what is a derivation, then? They all talk of Einstain derivation of the formula, don't they?
You ignored my post, if they had chosen the joule as twice its current value, then the factor is 1/2, right?

 

[Ibix]

No proof, what is a derivation, then? They all talk of Einstain derivation of the formula, don't they?

You can derive it from certain assumptions. The fact that nuclear reactors work strongly suggests that those assumptions are valid.

You ignored my post, if they had chosen the joule as twice its current value, then the factor is 1/2, right?

No. One way to decrease the value of the Joule would be to decrease the value of the kilogram. Then no factor of two is needed.

If you only change the Joule then you no longer have an equation because the units don't match. So you need to add a factor of (1/2)J'/J (where J' is your new unit), not just a half.

There's no way to make a dimensionless 1/2 just appear in the equation.

 

[alba]

Y

If you only change the Joule then you no longer have an equation because the units don't match. So you need to add a factor of (1/2)J'/J (where J' is your new unit), not just a half.

There's no way to make a dimensionless 1/2 just appear in the equation.

1/2 joule is the Ke of 1 Kg at 1m/s. You can have the joule with the Ke of 1 Kg at any velocity, you can have any value of the factor. The same applies if you refer the joule to gravity

 

[mfb]

No proof, what is a derivation, then? They all talk of Einstain derivation of the formula, don't they?

You can use mathematics to derive things within a given physical theory: "If assumptions A,B,C are true, then [calculation] we predict XYZ". You cannot prove that A, B and C are true. You can only observe that this assumption leads to great predictions.

if they had chosen the joule as twice its current value, then the factor is 1/2, right?

The formula is independent of any unit system.

You can replace all occurrences of "E" in all formulas by "E/2" or "2E", but where is the point? You would not change physics at all, but you would make many formulas more complicated than necessary. You can do the same independently for the definition of a Joule, but again, there is no point. The current Joule definition is convenient.

There was an actual discussion about that at the time the concept of energy was introduced, because kinetic energy in nonrelativistic mechanic has this 1/2 prefactor in E=1/2 m v². You could change this, if you also change all other formulas - it is purely a convention to use the current energy concept. This was centuries before special relativity was developed.

 

[Ibix]

1/2 joule is the Ke of 1 Kg at 1m/s. You can have the joule with the Ke of 1 Kg at any velocity, you can have any value of the factor. The same applies if you refer the joule to gravity

But, as I said in the post you quoted, many equations will then be invalid unless you add a conversion factor with units. You are essentially making a daft choice of units then undoing the daftness. You aren't multiplying by an arbitrary constant which is what you were accusing Einstein of.

 

[russ_watters]

...the value of energy in rest mass is a scalar, which is not related to anything, how can we use logic or math to derive such a value?

Just because something is scalar doesn't mean it is "not related to anything" - otherwise, you could never find a scalar in an equation!

 

[alba]

Just because something is scalar doesn't mean it is "not related to anything" - otherwise, you could never find a scalar in an equation!

It is not the fact of just being a scalar. To what theory/cause is it related ? what determines the fact that an electron has energy of .511 MeV? from what assumptions do you derive that?

 

[alba]

You can replace all occurrences of "E" in all formulas by "E/2" or "2E", but where is the point? You would not change physics at all, but you would make many formulas more complicated than necessary. You can do the same independently for the definition of a Joule, but again, there is no point. The current Joule definition is convenient.

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That is not the purpose of my question, mfb.
The point I am making is that observation showed that energy is in the range of (k) c^2. They suggested various factors:1/2. 3/8 etc, then Einstein suggested 1, and everybody say he derived the formula. I am trying to say that any factor is right if you base your unit on that asssumption.

I am asking you to show evidence that the other factors are wrong, and that there are objective reason to prefer, or from which you derive that value. Did I make myself clear?

 

[alba]

You are essentially making a daft choice of units then undoing the daftness. You aren't multiplying by an arbitrary constant which is what you were accusing Einstein of.

I made no daft choice since I made no choice, and I amnot accusing Einstein, either.You are accusingme without ground.
If you read the historical accounts, probably you understand what I am saying.

But my question is :
How do you derive that?
Can you derive that in the first place?

Can you address the specific questions?

 

[mfb]

It is not the fact of just being a scalar. To what theory/cause is it related ? what determines the fact that an electron has energy of .511 MeV? from what assumptions do you derive that?

From (a) the laws of physics are the same in every reference frame and (b) the speed of light is the same for all observers. Everything else follows from that, plus quantum field theory if you want to study things like annihilation reactions, and general relativity if you want to study gravity.

Why don't you start learning the basics of special relativity before you start threads like this one?

The point I ammaking is that observation showed that energy is in the range of (k) c^2. They suggested various factors:1/2. 3/8 etc, then Einstain suggest 1 and everybody say he derived the formula.

This is just nonsense.
Feel free to ask questions, but don't make up nonsense.

 

[Ibix]

I made no daft choice since I made no choice

You were proposing a daft choice of units then.

I amnot accusing Einstein, either.You are accusingme without ground.

You said in your OP that I read that [Einstein] himself had suggested the factor of 1/2, and when he was accused of plagiarism, he changed it to 1, suggesting that Einstein had intellectual property problems, rather than that E=mc²/2 is wrong.

But my question is :how do you derive that?

Here is a derivation that vanhees71 posted earlier today.

 

[alba]

Feel free to ask questions, but don't make up nonsense.

Forget what you consider nonsense, my question remains:
how do you derive that formula

 

[martinbn]

Forget what you consider nonsense, my question remains:
how do you derive that formula

I suppose it boils down to what is meant by a derivation. But since most textbooks on relativity have a derivation, I think you need to say what you don't understand/like/accept/(or whatever reason you have for this question) about the standard derivations.

 

[vanhees71]

http://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[Drakkith]

how do you derive that formula

Here's Einstein's paper where he derives it himself: https://www.fourmilab.ch/etexts/einstein/E_mc2/www/

Note that the units are not in kilograms and joules, but in ergs and grams. Also note the remark at the bottom of the page : the italicised sentence in the conclusion may be written as the equation "m = L/c²" which, using the more modern E instead of L to denote energy, may be trivially rewritten as "E = mc²".

 

[ChrisVer]

I have read different version/interpretations of Einstein derivation of the formula, no one is logically satisfying.

Then either the "different versions" you've seen are incomplete or you are not yet able to understand it... Especially the impressions you leave by the rest of your posts, I tend to doubt your references [and since it's about Einstein and such a basic equation, the probability that you found yourself reading some crackpot's article is high]...

 

[Dale]

I have read different version/interpretations of Einstein derivation of the formula, no one is logically satisfying.

This thread is closed until a specific reference can be produced which meets PF standards but is not "logically satisfying".

E=mc^2 is correct (no factor of 1/2 etc) in any system of units in which the units of mass, length, and time are consistent with Newton's laws.