# Mass Energy Equivalence Equation

• anthonyvigh
In summary: This is how the equation is expressed in particle physics, where ##\Delta E_o## is the change in mass energy of a system and ##\Delta m## is the change in its (rest) mass.In summary, the famous equation e=mc^2 shows the equivalence between energy and mass, with a constant factor of the speed of light squared. Rearranging the equation allows for solving for either energy or mass. The exchange between energy and mass is like an exchange rate, with the net total of mass-energy remaining the same. There is no need for negative signs in the equation. While it is possible to convert

#### anthonyvigh

Hi my question is regarding the famous e=mc^2 equation. Clearly the equation has been proven valid through its various practical applications.

My question is if energy = mass x the constant of the speed of light squared, where energy (e) is total energy release and mass (m) is total mass destroyed multiplied by constant (c) speed of light squared; then if one were to rearrange this equation so that you are solving for the term (m) this would then allow you to solve for the very small amount of mass being destroyed. m = e/c^2 My question is then, what about an equation for going the other way, by this I mean rather than creating energy by destroying mass, creating mass by destroying/consuming energy. By rearranging the mass energy equivalence equation to solve for mass you are still left with a positive value for energy on the RHS, surely if destroying mass releases enormous amounts of energy into the surrounding environment, then creating mass would take away/consume enormous amounts of energy out of the surrounding environment, thus by creating mass you should have a negative value for energy. Are there perhaps some signs missing from the equation somewhere.

Kind Regards
Anthony Vigh

Think of it like an exchange rate. Let's say 1£ = 2$. When I exchange my 1£ I get 2$ and lose 1£. If I rearrange the equation so that 1$= 1$/2 then I hand my 2$back to the exchange I get 1£ back and lose 2$, but my net worth has not changed. There is no need for any signs here or in the mass energy equation.

mass-energy remains the same

so if some mass is annihilated, energy is released, but the net total of mass-energy remains the same, so how much energy would it take to recreate the mass lost in a nuclear reaction, is it possible/is there any catalyst out there to reverse the effects of this annihilation in a nuclear reaction and if so what would it physically look like as opposed to a nuclear bomb being detonated? like what would the reverse reaction look like? energy being converted into matter

anthonyvigh said:
so if some mass is annihilated, energy is released, but the net total of mass-energy remains the same, so how much energy would it take to recreate the mass lost in a nuclear reaction, is it possible/is there any catalyst out there to reverse the effects of this annihilation in a nuclear reaction and if so what would it physically look like as opposed to a nuclear bomb being detonated? like what would the reverse reaction look like? energy being converted into matter

See if this helps http://en.wikipedia.org/wiki/Pair_production

anthonyvigh said:
so if some mass is annihilated, energy is released, but the net total of mass-energy remains the same, so how much energy would it take to recreate the mass lost in a nuclear reaction, is it possible/is there any catalyst out there to reverse the effects of this annihilation in a nuclear reaction and if so what would it physically look like as opposed to a nuclear bomb being detonated? like what would the reverse reaction look like? energy being converted into matter

Energy converts directly to mass as per the equation. If you lost X mass and gained Y energy, then Y energy would turn back into X mass. Unfortunately there is nothing that can do this on a large scale other than supernovas. Well, other than maybe turning uranium into plutonium.

The correct interpretation of the equation is not that energy and mass can be converted into each other. It is that energy and mass are the same thing measure using different units and there is a factor to convert between the units. So, if the mass increases, so does the energy. So, if you want to increase the mass you must increase the energy by providing energy from some energy source.

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dauto said:
The correct interpretation of the equation is not that energy and mass can be converted into each other. It is that energy and mass are the same thing measure using different units and there a factor to convert between the units. So, if the mass increases, so does the energy. So, if you want to increase the mass you must increase the energy by providing energy from some energy source.
This is the way I prefer to look at it also. Although, I wouldn't say that they are the same thing, I would say instead that energy has mass and mass has energy. That probably amounts to the same thing for all practical purposes.

In an anhillation reaction the system before anhillation and after anhillation has the same mass and the same energy. Same with a pair production reaction. It isn't that mass is being destroyed and energy created (or vice versa), it is that particles are being destroyed and created but the new system has the same mass and energy as the old system and the mass and energy of each system is related by E=mc².

e=mc2
Divide left and right by c2, we get e/c2=m
Choose another unit for e by multiplying it by c2 so we get e=m
I think the equivalence is as profound as it looks.
This is not all. There is just such an equivalence between energy and information.

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anthonyvigh said:
like what would the reverse reaction look like? energy being converted into matter

Mass and energy are properties, and as such are not in the same category as matter. Matter occurs naturally, properties are invented. There are reactions that create matter, and there are reactions that destroy matter. But in all those reactions it's simply a transformation of what one chooses to call mass into what one chooses to call rest energy, or vice-versa. Mass and rest energy are two different names for the same thing.

To address the ideas you presented in your question about negative signs, you could look at the relation in the form ##\Delta E_o=\Delta mc^2##. If the left side of the equation is negative, so is the right side.

DaleSpam said:
I would say instead that energy has mass and mass has energy.

Careful... does the phrase that I boldfaced mean that in a particle or object moving freely through space, its kinetic energy contributes to its mass? That would take us back to the notion of "relativistic mass" which is generally disparaged here.

If you have a bunch of gas molecules confined in a box, their kinetic energy does indeed contribute to the mass of the system of box plus molecules. However, it doesn't contribute to the masses of the individual molecules!

In fact, it gets even more subtle than this. The statement above applies only if the system of box + molecules is at rest (total momentum = 0). If the box (along with the molecules inside it) is moving through space, only part of the KE of the molecules (the part associated with the random motion of the molecules inside the box) contributes to the mass of the system. The rest contributes to the kinetic energy of the system.

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PeroK
BertMorrien said:
There is just such an equivalence between energy and information.

Have a reliable reference for this?

Drakkith said:
Have a reliable reference for this?
The next link may be appropriate.
http://physicsworld.com/cws/article/news/2010/nov/19/information-converted-to-energy
This relation is intuitively more challenging than e=m, because a photon can be thought of as pure kinetic energy while an electron in rest as pure kinetic energy in the form of spinning energy, although this is my own untested idea. Hovever, I am not alone, see e.g. the following link. [Unacceptable link removed by mentor]

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BertMorrien said:
The next link may be appropriate.
http://physicsworld.com/cws/article/news/2010/nov/19/information-converted-to-energy
This relation is intuitively more challenging than e=m, because a photon can be thought of as pure kinetic energy while an electron in rest as pure kinetic energy in the form of spinning energy, although this is my own untested idea. Hovever, I am not alone, see e.g. the following link. [Unacceptable link removed by moderator]

I'll allow your first link, but the 2nd goes against PF rules and has been removed. In addition, please see PF rules regarding personal theories and speculation. https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

As for energy-information equivalency, I'll let others more knowledgeable in that area decide on the validity of that. I've always thought that information was a propagation of cause-effect within a system, but I don't know much beyond that.

jtbell said:
Careful... does the phrase that I boldfaced mean that in a particle or object moving freely through space, its kinetic energy contributes to its mass?
You are correct. This quote was from 2013, I would delete the part in bold if I were to write it today. All mass has energy, but not all energy has mass. Mass and energy are equivalent only if the momentum is 0.

DaleSpam said:
This quote was from 2013, I would delete the part in bold if I were to write it today.

Arggghhh, I've been necro'd!

@BertMorrien, this is one reason why we discourage "necroposting" (reawakening long-dormant threads). You may have been aware that you were responding to very old posts, but it's easy for other people to overlook the dates and think that those old posts are part of a currently ongoing conversation.

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jtbell said:
Arggghhh, I've been necro'd!

@BertMorrien, this is one reason why we discourage "necroposting" (reawakening long-dormant threads). You may have been aware that you were responding to very old posts, but it's easy for other people to overlook the dates and think that those old posts are part of a currently ongoing conversation.
I was not immediately aware of that, but this blog was still open. Sorry for my reference, at least I was explicitely talking about untested ideas.
FYI there are several articles on the same subject available at arXiv. The article I was referring to was probably about an idea that was ruled out. I apologise for that, I was too quick.

I was angry at myself for not looking at the date on Dale's post, not with you. We do cut newcomers some slack.

If you see an old thread like this one and want to comment on it, it's probably better to start a new thread and include a link to the old one, with a comment/warning about it being an old thread. "I have a question/comment about something that I saw in this old thread..."

We used to close regularly all threads older than a certain period. However, a year or two ago, we moved to different forum software which apparently doesn't have this feature.

jtbell said:
Arggghhh, I've been necro'd!

Me, too. But at least I learned that it has a name! :-)

"The correct interpretation of the equation is not that energy and mass can be converted into each other. It is that energy and mass are the same thing measure using different units and there a factor to convert between the units..."

Seems like energy and mass are NOT quite 'the same thing': Electromagnetic waves travel at 'c', mass does not, for one. Mass has an energy equivalent; and energy has a mass equivalent, which seems to me to be a different concept.

alw34 said:
Seems like energy and mass are NOT quite 'the same thing': Electromagnetic waves travel at 'c', mass does not, for one.

Electromagnetic waves are a model for light. Light and matter are naturally-occurring phenomena. Waves, mass, and energy are part of the modelling process that is science.

It's true that light travels at speed c, and massive particles (as opposed to massless particles) travel at speeds less than c.

Mass has an energy equivalent; and energy has a mass equivalent, which seems to me to be a different concept.

It is a different concept, but it's mass and rest energy that are equivalent. Total energy is not equivalent to mass. A single photon has energy, but it has no mass. In a reference frame where a single particle of mass ##m## is in motion it has a total energy that is greater than ##mc^2##. In a reference frame where that same particle is at rest, it has a total energy that is equal to ##mc^2##.

Mister T said:
Electromagnetic waves are a model for light. Light and matter are naturally-occurring phenomena. Waves, mass, and energy are part of the modelling process that is science.

It's true that light travels at speed c, and massive particles (as opposed to massless particles) travel at speeds less than c.
It is a different concept, but it's mass and rest energy that are equivalent. Total energy is not equivalent to mass. A single photon has energy, but it has no mass. In a reference frame where a single particle of mass ##m## is in motion it has a total energy that is greater than ##mc^2##. In a reference frame where that same particle is at rest, it has a total energy that is equal to ##mc^2##.
This is not accordingly to what I understand from special relativity. When matter gains speed, it's mass increases, so it is always equal to ##mc^2##. This is the reason why the speed cannot become c, the energy would become infinite. The energy is never greater than ##mc^2##. What you mean is that the energy of matter in motion is greater than the energy of that matter in rest.
See also https://www.physicsforums.com/threads/what-is-the-massenergy-equivalence.763067/ where the contribution of motion to the total energy of a moving mass is mentioned.

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BertMorrien said:
This is not accordingly to what I understand from special relativity. When matter gains speed, it's mass increases, so it is always equal to ##mc^2##. This is the reason why the speed cannot become c, the energy would become infinite. The energy is never greater than ##mc^2##.
This is using a concept called "relativistic mass" which has largely fallen out of fashion. The ##m## you are using is not the same as the one Mister T is referencing. In the notation you are using ##m=\gamma m_0##, so the total energy of a moving body is ##\gamma m_0c^2##. Mister T is referring to ##m_0## as the mass.

This is the more modern way of doing it. Relativistic mass isn't a particularly useful concept outside this application (it works for 3-momentum and force perpendicular to the direction of motion, but that's about it), so isn't much used anymore.

BertMorrien said:
See also https://www.physicsforums.com/threads/what-is-the-massenergy-equivalence.763067/ where the contribution of motion to the total energy of a moving mass is mentioned.

Note this statement at the top of that FAQ post:
Confusion can arise due to multiple definitions of mass (see our https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/ [Broken]), but using the modern convention of identifying the word "mass" with the "invariant mass" (also known as "rest mass") it is clear that mass and energy are not equivalent.

This "modern convention" is at least 40 years old among working physicists who actually deal with relativistic objects. When I was a graduate student in experimental high-energy particle physics in the late 1970s and early 1980s, none of us graduate students and professors talked about "relativistic mass." There was no rule against using it. The concept simply never came up because it wasn't useful for anything.

The only place I remember ever seeing "relativistic mass" during that time was in a textbook about accelerator design which was originally written in the early 1950s by someone who had probably learned relativity in the 1920s.

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vanhees71
BertMorrien said:
This is not accordingly to what I understand from special relativity. When matter gains speed, it's mass increases, so it is always equal to ##mc^2##.

That's not a consequence of the postulates, rather it's an argument based on an arbitrary definition of the term "mass".
This is the reason why the speed cannot become c, the energy would become infinite.

This falsity appeared in the vast majority of introductory physics textbooks up until about 20 years ago or so. Likely this is the reason authors were persuaded by reviewers to remove it from those textbooks, and for a number of other good reasons the best and easiest way to do that is to remove the notion of relativistic mass from the lexicon.
What you mean is that the energy of matter in motion is greater than the energy of that matter in rest.
But note that in the case of a single particle, for example, that's not due to any property of the object, but rather a result of measuring the total energy in different frames of reference. The same object, when viewed from various different reference frames will have different amounts of total energy. It's the rest energy, energy measured in the object's rest frame, that is the same for all observers. This is the quantity called the mass.

To understand the equivalence of mass and rest energy one doesn't look at an object from various different reference frames. Instead, one looks at composite objects, that is, objects that consist of a collection of at least two particles. The energy of those particles contributes to the rest energy (mass) of the composite body.

Suppose you have a box of mass ##M## containing a marble of much smaller mass ##m## bouncing around inside the box. The total mass of the composite body is ##M+\gamma m##, which is not in general equal to ##M+m##. Note that this is something all observers will agree on, regardless of their motion relative to the box.

Perhaps another reason the concept of relativistic mass was removed from those textbooks is that authors became convinced that referring to ##\gamma m## as the mass obscured the true meaning of the mass-energy equivalence. It leads to the misconception that the equivalence is due to the state of motion of the observer.

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## 1. What is the Mass Energy Equivalence Equation and who developed it?

The Mass Energy Equivalence Equation, also known as the famous formula E=mc^2, was developed by Albert Einstein in 1905 as part of his Special Theory of Relativity.

## 2. What does the equation E=mc^2 mean?

The equation states that energy (E) is equal to the mass (m) of an object multiplied by the speed of light squared (c^2). This means that a small amount of mass can be converted into a large amount of energy.

## 3. How does the Mass Energy Equivalence Equation relate to nuclear energy?

The Mass Energy Equivalence Equation explains the principle behind nuclear energy, as it shows that a small amount of mass is converted into a large amount of energy during a nuclear reaction. This is the basis for nuclear power plants and nuclear weapons.

## 4. Can the Mass Energy Equivalence Equation be applied to everyday objects?

Yes, the Mass Energy Equivalence Equation applies to all objects, no matter how small or large. However, the amount of energy produced from converting mass into energy is usually only significant in nuclear reactions or in objects traveling at extremely high speeds.

## 5. What are some real-world applications of the Mass Energy Equivalence Equation?

The Mass Energy Equivalence Equation has many practical applications, including in nuclear power plants, nuclear medicine, and nuclear weapons. It is also used in particle accelerators to create high-speed collisions, which can help scientists study the fundamental building blocks of matter.