# EM waves in vacuum analogy

• B
• Delta2

#### Delta2

Homework Helper
Gold Member
TL;DR Summary
Is water for water waves (and more generally the fluid for waves in a fluid) what is the vacuum for an EM wave traveling in vacuum?
So, is water for water waves, what is the vacuum for EM waves traveling in vacuum. I know the analogy can't be exactly perfect because water molecules oscillate in the presence of water waves, but in vacuum nothing seems to oscillate? Or the vacuum oscillates in some way?

And no I am not trying to resurrect the ether theory.

Motore

## Answers and Replies

And no I am not trying to resurrect the ether theory.
It seems hard to escape given the question/analogy. The ether was simply the medium light was believed to be carried by and you are asking what medium light is carried by. So you seem to already know the answer, right?

Last edited:
PeroK and Delta2
It is only a paradox if you think of fields as "nothing". If fields are "something" and if the fields oscillate in a vacuum, there is no paradox.

ContrapuntoBrowniano, AveryVDS, andresB and 4 others
Electromagnetic waves are the oscillations of electromagnetic fields and are a kind of energy, but energy and matter can be converted into each other, so although the oscillation of electromagnetic waves looks different from the oscillation of water molecules in water waves, they may be the same thing observed from two different angles.

Also, as far as I know, the motion of water waves is actually extremely complex, so the mathematical equations used to describe water waves are probably much more complicated than electromagnetic waves.

Last edited:
AveryVDS, anorlunda and Delta2
but energy and matter can be transformed into each other,

No they can't. Matter is a 'thing', and energy is a property of things. The same way as apple and red - they can't be transformed into each other.

nasu, berkeman, russ_watters and 1 other person
No they can't. Matter is a 'thing', and energy is a property of things. The same way as apple and red - they can't be transformed into each other.
Correction of expression.
I mean they can be converted to each other by equation ##E=mc^2 ##
Is that correct?

In my opinion matter is a special kind of energy, it is energy of the fermionic fields (e.g electron field). It is just that our human senses perceive this energy different from the energy of the bosonic fields (e.g EM field).

But wait this thread is not about this lol...

Summary: Is water for water waves (and more generally the fluid for waves in a fluid) what is the vacuum for an EM wave traveling in vacuum?

So, is water for water waves, what is the vacuum for EM waves traveling in vacuum
Water has a rest frame. The vacuum does not

PeroK, Hamiltonian, vanhees71 and 1 other person
Is that correct?

This equation states that there is a form of energy connected with mass, namely rest energy. And mass is not the same thing as matter, mass is yet another property of matter.

nasu and vanhees71
This equation states that there is a form of energy connected with mass, namely rest energy. And mass is not the same thing as matter, mass is yet another property of matter.
This is my personal opinion, not a formal scientific statement. Just like when human beings have not yet discovered protons, neutrons and electrons, when they see that one substance can be converted into other substances through chemical reactions, maybe they will imagine that there may be essentially the same thing between these substances

PeroK and weirdoguy
This is my personal opinion, not a formal scientific statement.
Then perhaps it is not appropriate for posting at PF?

DaveE, vanhees71, weirdoguy and 2 others
My conclusion from this thread, is that whether the water molecules oscillate or the EM field oscillates, we have oscillations of fields in both cases but not necessarily the same fields and not oscillation in the same way (for example when water molecules do harmonic oscillation, I don't think that the fermionic fields that correspond to water molecules do simple harmonic oscillation, they do some more complex oscillation, but still an oscillation.)

Everything, whether fermionic or bosonic or both is energy stored in some oscillating field of some type.

Last edited:
ContrapuntoBrowniano
when they see that one substance can be converted into other substances through chemical reactions

But energy is not a substance. Here is a question: do you think that matter can be converted to momentum? Because the full equation that should be considered is:
##E^2=(mc^2)^2+(cp)^2##
This is my personal opinion

Yes, and it's based on a huge minsunderstanding of what energy is.

do you think that matter can be converted to momentum?
Isn't that what is happening inside a nuclear reactor? matter converts to heat energy which rises the temperature of some substance, and we all know that temperature is a measure of microscopic kinetic energy

matter converts to heat energy

Sigh... No. Mass, or other forms of energy. Mass is not a synonym of matter.

PeroK and vanhees71
Mass is not a synonym of matter.
Can you expand on this please. What is exactly mass and what is matter?

What is exactly mass and what is matter?

Electron as a thing vs. mass of an electron. Do you see the difference?

ContrapuntoBrowniano and Delta2
But an electron can't exist without it's mass, But ok without its charge also, hmm maybe I see some "light" here..

weirdoguy
So, is water for water waves, what is the vacuum for EM waves traveling in vacuum. I know the analogy can't be exactly perfect because water molecules oscillate in the presence of water waves, but in vacuum nothing seems to oscillate? Or the vacuum oscillates in some way?

I think of a wave as a disturbance that travels through space and time. If one drops a magnet in an evacuated tube near the Earth's surface, one will not be able to see anything material being displaced unless one somehow extends one's imperfect human senses to "see" that disturbance. For example, two pickup coils placed at different heights around the tube would verify that there is an electromagnetic disturbance traveling down the tube. What conclusions can one draw from this? I see two possibilities.
1. This specific disturbance needs no medium to propagate and is, therefore, special in that regard. One then has to develop a theory that describes just that. Maxwell's equations and quantum electrodynamics are such theories. Of course, QED muddles the issue some more because particles are waves and waves are particles. So there is an uncertainty principle at work here since waves need a medium to propagate but particles do not.
2. There is nothing special about this disturbance and, just like all others, it needs something to "disturb". One then has to develop a theory that not only describes that, but also provides a roadmap for extending one's imperfect senses to "see" this hidden medium whatever one chooses to call it.
I am more comfortable with option 1 because I have accepted that that's the way things are.

Delta2
But energy is not a substance. Here is a question: do you think that matter can be converted to momentum? Because the full equation that should be considered is:
EM wave is an oscillation of energy, and water molecule is an oscillation of a substance with mass , so according to Equation ##E=mc^2##, could there be essentially the same thing between them? Can we imagine that they could be the same thing observed from two different angles?

Does this statement violate some kind of physical law?

Delta2
so according to Equation

This equation is a definition of rest energy, that is energy that is asociated with mass of particles and it would be better if you put a ##0## subscript: ##E_0=mc^2##. ##E## does not mean "any form of energy of anything you like". It is a very concrete form energy. General equation for moving particle is ##E^2=(mc^2)^2+(cp)^2##. Just because EM transmit energy (no, they are not "oscillating energy") doesn't mean you can put their energy in any formula you like. Equations have contexts and meanings behind them.

Can we imagine that they could be the same thing observed from two different angles?

We could if we didn't know what ##E=mc^2## means. But we do, and apparently it does not mean what you think it does. But that is ok, pop-culture really played a huge role in spreading misunderstandings about this formula. There are hundreds of threads that talk about that issue, you can check them out.

nasu and Delta2
But an electron can't exist without it's mass

And apple can't exist without being red/green/whatever color it has But still colors and apples are two different things.

Delta2
@weirdoguy I know I am probably mixing up qft, relativity and classical physics, but can we say that mass is the energy stored in some type of oscillating field (fermionic field or Higgs field or I don't know what else I am not an expert on how particles acquire their mass via the Higgs field)?

This equation is a definition of rest energy, that is energy that is asociated with mass of particles and it would be better if you put a 0 subscript: E0=mc2. E does not mean "any form of energy of anything you like". It is a very concrete form energy. General equation for moving particle is E2=(mc2)2+(cp)2. Just because EM transmit energy (no, they are not "oscillating energy") doesn't mean you can put their energy in any formula you like. Equations have contexts and meanings behind them.
I don't quite understand what you mean.

From what I understand ##E=mc^2## does exactly as you say it is rest energy associated with mass, which is best expressed as ##E_0=mc^2##. However, I think ##E=mc^2## can also be understood as the total energy of an object, including its rest mass and the increase in mass caused by the increase in kinetic energy, which is a matter of definition and interpretation. But the point now is that I think mass and energy are convertible one into the other, or at least the equivalence of the mass and energy is described by the equation ##E=mc^2##

Atomic bombs have proved that mass can be converted into enormous amount of energy. I don't know how to convert light energy into matter but I found the following links (Forgive me for not reading the content in detail because it seem more esoteric to me).
https://www.bnl.gov/newsroom/news.php?a=119023
https://www.inverse.com/science/einstein-light-matter
Even if human beings have not been able to turn light into matter, will it be possible in the future?

EM transmit energy (no, they are not "oscillating energy") doesn't
I just understand it very simply. A wave (including EM waves and mechanical wave, etc.) is a continuous oscillation of energy in space time. The frequency of each wave is determined by measuring the number of repetitions an event occurred within a given time period then dividing the number of repetitions by the length of the time period. The amplitude of a wave is maximum or minimum magnitude of an oscillation...

We could if we didn't know what E=mc2 means. But we do, and apparently it does not mean what you think it does. But that is ok, pop-culture really played a huge role in spreading misunderstandings about this formula. There are hundreds of threads that talk about that issue, you can check them out.
Anyway, I respect what you said and try to understand it better.

PeroK, weirdoguy and Delta2
Thread closed temporarily for Moderation...

Edit -- Thread is reopened.

Last edited:
Delta2
I think mass and energy are convertible one into the other
If that were a correct interpretation then energy would not be conserved. In other words, if you convert mass into energy then you have decreased the amount of mass and increased the amount of energy. This is not possible for a conserved quantity like energy, it can neither increase nor decrease, so it cannot be converted to or from mass.

Last edited:
jbriggs444, weirdoguy and Delta2
If that were a correct interpretation then energy would not be conserved. In other words, if you convert mass into energy then you have decreased the amount of mass and increased the amount of energy. This is not possible for a conserved quantity like energy, it can neither increase nor decrease, so it cannot be converted to or from mass.
This holds only if you view mass as something different from energy and maybe that holds in the classical or relativity point of view, but according to the QFT point of view, isn't everything corresponding to energy in some type of (oscillating) field? (We might need an expert with the Higgs field here...).

I am inspired for this by the typical example of QFT with photons, a photon is the quanta of EM field that carries energy ##E=hf##. Ok probably mass of a particle isn't exactly the quanta of the Higgs field, which is the Higgs boson but my guess is that somehow is related to the energy of the Higgs field.

Atomic bombs have proved that mass can be converted into enormous amount of energy.
Nothing is being converted into energy. Mass energy is being converted to other energy forms. This is conceptually not very different from potential energy being converted into kinetic energy when a ball rolls down a slope. You cannot say that mass is converted into energy, mass already has energy. What is going on in an atomic bomb is that energy being changed into other forms of energy - hence energy conservation.

Energy is not a thing that something can be converted into. It is a property of physical systems.

PeroK, vanhees71, alan123hk and 1 other person
This holds only if you view mass as something different from energy and maybe that holds in the classical or relativity point of view, but according to the QFT point of view, isn't everything corresponding to energy in some type of (oscillating) field? (We might need an expert with the Higgs field here...).

I am inspired for this by the typical example of QFT with photons, a photon is the quanta of EM field that carries energy ##E=hf##. Ok probably mass of a particle isn't exactly the quanta of the Higgs field, which is the Higgs boson but my guess is that somehow is related to the energy of the Higgs field.
You can convert one form of energy into other forms of energy, thus the total energy is constant. But the idea that you can convert mass into energy is simply wrong, for the reason I stated.

In relativity energy and momentum form a four vector called the four-momentum ##(E/c,\vec p)##. Mass is the invariant norm of the four momentum ##m^2 c^2= E^2/c^2-p^2##. For a system at rest ##\vec p=0## and we get the famous ##E=mc^2##. So the famous equation is a special case of the general relation and describes a system with 0 momentum. Such a system still has energy, and that energy is proportional to its mass. For a system with nonzero momentum the energy ##E=c\sqrt{m^2 c^2+p^2}## is no longer proportional to the mass. This is why a single photon can have non-zero energy with zero mass.

The four-momentum is conserved so energy is conserved and each component of momentum is conserved. Since the invariant mass is a function only of conserved quantities it is also a conserved quantity. Mass is therefore particularly important being both conserved and invariant. Energy is conserved but not invariant, so mass (in the standard usage of the term) is in fact different from energy.

However, mass is not additive as energy and momentum are. Suppose you have a system composed of an electron and a positron at rest. In units where ##c=1## and both mass and energy are measured in ##\mathrm{keV}## then the system has a four-momentum of ##(511,\vec 0)+(511,\vec 0)=(1022,\vec 0)## and therefore a mass of ##1022 \mathrm{\ keV}##. When the electron and positron annihilate two photons are produced with opposite momentum as ##(511,511,0,0)+(511,-511,0,0)=(1022,\vec 0)##. The post annihilation system has the same conserved four momentum and the same mass as the pre annihilation system. The resultant photons are each individually massless but the system composed of both of them together has the same mass as the original system of the electron and positron.

A nuclear reaction does not convert mass into energy. It converts a system of particles with low KE into a system of particles with high KE. The invariant mass of the system is unchanged, but sum of the masses of the resulting particles is less than the sum of the masses of the original particles.

vanhees71, nasu, Delta2 and 2 others
You can convert one form of energy into other forms of energy, thus the total energy is constant. But the idea that you can convert mass into energy is simply wrong, for the reason I stated.
So you do not consider mass as a form of energy. But I *think* the QFT view is exactly that, that it views mass as a form of energy. But ok I am not an expert in Higgs Boson and Higgs field so I might be wrong here.

I will not quote the rest of your post since I think it is the relativity point of view and I am a total scrub in relativity, special and general.

But I *think* the QFT view is exactly that, that it views mass as a form of energy.
Well, with QFT there is the bare mass, the pole mass, the running mass, and the invariant mass, so QFT is simply more complicated. None of those correspond to the energy, although the running mass at least changes with changing energy scale.

vanhees71 and Delta2
Well, with QFT there is the bare mass, the pole mass, the running mass, and the invariant mass, so QFT is simply more complicated. None of those correspond to the energy, although the running mass at least changes with changing energy scale.
Ok well I am sad that the QFT point of view doesn't see mass as a form of energy. I thought somehow that the energy of the Higgs field relates to mass.

In both classical and quantum field theory the "mass terms" are of course contributing to the total field energy. It's just as any other contribution to the energy, including the "kinetic term" and "interaction energy" between different fields.

In the Standard Model of elementary particle physics indeed all the fundamental mass terms in the description of the underlying quantum field theory are due to the coupling of the various fields with the socalled Higgs field. Due to the mathematical structure of this theory (a socalled gauge theory) you cannot simply write down "mass terms" for all the particles, because that would spoil the underlying mathematical structure (the socalled local gauge symmetry), which would destroy entirely destroy it. It would become mathematically inconsistent and couldn't be used to calculate anything reliably to describe the observed properties of the elementary particles and their interactions. That's why you have to introduce the Higgs field, and to tailor the theory in such a way that this Higgs field takes a non-vanishing "vacuum expectation value". The coupling of the other fields to this part of the Higgs field results in mass terms for all these fields and the particles described by them (i.e., the quarks, leptons, W- and Z-bosons; only the Higgs boson's own mass stems from its own generic mass term, which is allowed by the gauge symmetry).

One should, however, note that most of the mass of the matter around us is not due to this "Higgs mechanism" but "dynamically generated" by the strong interaction. Most of the mass is in the nucleons (protons and neutrons), which are bound states of quarks and gluons. Most of the mass of the nucleons (around ##938 \; \text{MeV}/c^2##).

PeroK, Dale, Delta2 and 1 other person
One should, however, note that most of the mass of the matter around us is not due to this "Higgs mechanism" but "dynamically generated" by the strong interaction. Most of the mass is in the nucleons (protons and neutrons), which are bound states of quarks and gluons. Most of the mass of the nucleons (around 938MeV/c2).
So can we say that mass is energy in the strong nuclear field? I know you probably tell me it is an oversimplification...

I know you probably tell me it is an oversimplification...
It is an oversimplification.

What is rest energy really depends on how you draw the limits of your system that is at rest. To draw a classical analogy, consider gas in a container. If you heat the gas the total mass of the container goes up. If you look at the molecular level, the increase in energy is due to the increase in kinetic energy of individual molecules.

The great realisation of ##E=mc^2## in my opinion is that a system’s rest frame inertia is equal to its rest frame energy.

Last edited:
Dale, vanhees71 and Delta2