I Discover the Relationship Between Mass and Energy in Electromagnetic Fields

[Bobski]

TL;DR Summary

Are fundamental particles made up of electromagnetic waves or fields or oscillations?

When E=mc^2 is rearranged using the substitution c=1/√ε₀μ₀
, and making mass the subject we get m=Eε₀μ₀

This equation basically says that mass is directly proportional to the energy contained in
an electromagnetic field. Does it not? Does this equation tell us that mass particles are made up
of electromagnetic oscillations or fields?

 

[PeterDonis]

When E=mc^2 is rearranged using the substitution c=1/√ε₀μ₀
, and making mass the subject we get m=Eε₀μ₀

Since this depends on a particular choice of units (SI units), it can't be telling you anything useful about physics.

This equation basically says that mass is directly proportional to the energy contained in
an electromagnetic field. Does it not?

No. It's just an artifact of a particular choice of units. The energy contained in an electromagnetic field is given by a different formula that has nothing to do with $E = mc^2$. Any good textbook on electromagnetism will discuss this.

$E = mc^2$ (which is actually a special case of more general equations) tells you, heuristically, that mass is a form of energy. But it's not the only form of energy, nor does it have to be "made of" some particular kind of energy.

Does this equation tell us that mass particles are made up
of electromagnetic oscillations or fields?

No. See above.

 

[Vanadium 50]

TL;DR Summary: Are fundamental particles made up of electromagnetic waves or fields or oscillations?

basically says that mass is directly proportional to the energy contained in
an electromagnetic field

Not really. The energy density in an EM field goes as E² + B² which appears nowhere in what you wrote down.

 

[Dale]

TL;DR Summary: Are fundamental particles made up of electromagnetic waves or fields or oscillations?

This equation basically says that mass is directly proportional to the energy contained in
an electromagnetic field. Does it not?

No. It does not. The $E$ in $E/c^2$ is not specifically the electromagnetic energy, it is the total energy.

 

[dsaun777]

Since this depends on a particular choice of units (SI units), it can't be telling you anything useful about physics.No. It's just an artifact of a particular choice of units. The energy contained in an electromagnetic field is given by a different formula that has nothing to do with $E = mc^2$. Any good textbook on electromagnetism will discuss this.

$E = mc^2$ (which is actually a special case of more general equations) tells you, heuristically, that mass is a form of energy. But it's not the only form of energy, nor does it have to be "made of" some particular kind of energy.No. See above.

I wouldn't say it has nothing to do with it. Isn't the E, in the most general use, supposed to represent all of the energy including its electromagnetic energy?

 

[Ibix]

I wouldn't say it has nothing to do with it. Isn't the E, in the most general use, supposed to represent all of the energy including its electromagnetic energy?

Yes, the binding energy of the electrons and the nuclei contributes to the mass of a body, but no, it does not mean that the mass of some arbitrary object is proportional to the energy of any electromagnetic field (which is what the OP was asking).

 

[PeterDonis]

Isn't the E, in the most general use, supposed to represent all of the energy including its electromagnetic energy?

Yes. But that's not what the OP was asking about. He was asking about the formula $E = m \varepsilon_0 \mu_0$. That's what I said was an artifact of a particular choice of units.

It's also worth pointing out that $E = mc^2$ is only valid in the rest frame of the object. In any other frame that formula does not work. So the formula the OP asked about is frame dependent as well as choice of units dependent.

 

[Herman Trivilino]

TL;DR Summary: Are fundamental particles made up of electromagnetic waves or fields or oscillations?

Fundamental particles don't have a composition. That's what makes them fundamental.

 

[vanhees71]

I think a lot is mixed up here. First of all we must be clear, whether we discuss the problem of "electromagnetic mass" on a classical or a quantum level. The former is in some sense the more difficult question, because there is no consistent solution on the "point-particle level". The problem of the diverging mass in classical "electron theory" is infamous. It was discovered by Lorentz and Abraham around 1900. It results from the fact that when trying to calculate the influence of the electromagnetic field of an accelerated particle on itself, this leads to an infinite self-energy. Already for a point particle at rest the Coulomb field's energy diverges. On the other hand it's clear that the electron's measured mass always refers to an electron with its own electromagnetic field around it. So when calculating the "self-force" on the accelerated electron after regularizing this self-field somehow (e.g., by making the electron a little extended object with a charge distribution rather than a point-charge-$\delta$ distribution) you can subtract the divergent part of the self-force in the point-particle limit, by lumping it into the mass and declaring the total resulting mass as the measured mass of the electron. Unfortunately this doesn't solve the problem completely, because the resulting equation of motion is a third-order differential equation, the Lorentz-Abraham equation, which shows a-causal behavior. Extending these ideas to relativistic dynamics also doesn't help. Then you have the Lorentz-Abraham-Dirac (LAD) equation. The best you can do is to use the first-order perturbation theory in the self-force, which leads to the Landau-Lifshitz approximation of the LAD equation.

In the quantum-field theoretical description these (UV-)divergences presist, i.e., if you start with the "bare electron" interacting with the electromagnetic field and calculate the electron's self-energy you also get a divergent result, but you can, order-by-order in perturbation theory, do the trick of lumping these infinities into the constants of the theory, i.e., the wave-function normalization factors, the mass of the electron/positron, and the electromagnetic coupling constant, i.e., you get order-by-order in perturbation theory well-defined results for the coupled dynamics of the em. field with the charged particles, and this "renormalized" QED is among the most accurate theories ever, predicting some properties to 12 or more digits of accuracy (e.g., the anomalous magnetic moment of the electron, the Lamb shift of hydrogen-energy levels).