Is Matter Just Another Form of Energy in E=MC²?

[Bob3141592]

So all we can say is that everything is either matter and energy (which appear to be defined in terms of each other) and that matter can be turned into energy and vice versa.

This is where the whole E=mc^2 thing goes horribly wrong. As has been stated before, the m stands for mass, not matter, and matter is more than just a quantity of mass.

Consider for a moment a cloud of electrons, and nothing but electrons. That bunch of electrons cannot be converted into energy. The matter which is the electrons contains a charge, and that charge is not in any way equivalent to energy. Therefore, the mass of the electrons is not available for conversion into energy. The mass of the electrons in that state is not equivalent to energy. Applying E=mc^2 in that context leads to a philosophical confusion about what the electron is, and by extension, what matter is.

It's almost as if you have to separate the mass from the charge in order to convert it into energy. But I have no idea what charge separated from matter is about. I'm not sure that's even a possible way to think about it. What actually goes on when an electron and a positron annihalate? Surely it's not an instantaneous reaction, is it, but how can it have intermediate steps? Perhaps the answer to that would shed some light on mass-energy equivalnce.

 

[ZapperZ]

I am not sure if you intended to say "matter and mass" or "matter and energy" are "the same". Both raise interesting issues.

It was a typo. I intended to say "matter and energy".

Zz.

 

[Andrew Mason]

This is where the whole E=mc^2 thing goes horribly wrong. As has been stated before, the m stands for mass, not matter, and matter is more than just a quantity of mass.

Consider for a moment a cloud of electrons, and nothing but electrons. That bunch of electrons cannot be converted into energy.

A bunch of electrons can be converted entirely into energy if you have a similar bunch of positrons.

The matter which is the electrons contains a charge, and that charge is not in any way equivalent to energy. Therefore, the mass of the electrons is not available for conversion into energy. The mass of the electrons in that state is not equivalent to energy. Applying E=mc^2 in that context leads to a philosophical confusion about what the electron is, and by extension, what matter is.

What about an electron in a hydrogen atom? If the energy of the electron is increased (by absorbing a photon), the atom actually gains mass. If the energy of the electron decreases by emitting a photon, the mass of the atom decreases. That is mass being converted into energy. Isn't matter being converted into energy? Where does the mass reside? In the electron? In the nucleus? In the 'field' between them?

AM

 

[ZapperZ]

A bunch of electrons can be converted entirely into energy if you have a similar bunch of positrons.

What about an electron in a hydrogen atom? If the energy of the electron is increased (by absorbing a photon), the atom actually gains mass. If the energy of the electron decreases by emitting a photon, the mass of the atom decreases. That is mass being converted into energy. Isn't matter being converted into energy? Where does the mass reside? In the electron? In the nucleus? In the 'field' between them?

AM

But the issue here isn't the "conversion". Since when is a conversion from A to B means A = B?

I convert my money into food. Does that mean the few dollar bills that I "converted" for a sandwich means that those dollar bills are "the same" as the food? Have you tasted a $5 bill before? It isn't pleasent.

Again, F = kx. Have you ever heard of anyone saying displacement and force are "the same thing"? What is "the same" here? What criteria are you using, and what criteria are you ignoring that make them different?

Zz.

 

[Bob3141592]

A bunch of electrons can be converted entirely into energy if you have a similar bunch of positrons.

But what if you don't have a bunch of positrons? Are those isolated electrons equivalent to energy or not?

What about an electron in a hydrogen atom? If the energy of the electron is increased (by absorbing a photon), the atom actually gains mass. If the energy of the electron decreases by emitting a photon, the mass of the atom decreases. That is mass being converted into energy. Isn't matter being converted into energy? Where does the mass reside? In the electron? In the nucleus? In the 'field' between them?

Note that you didn't say the mass of the electron increases, even though you did say that it was the electron that absorbs the photon. It's the mass of the atom that increases. Asking where that mass resides again shows a semantic separation of mass from matter that I don't think is legitimate. Since the electron's energy is only defined in terms of the atomic shell, which is an abstract description of the electron's relationship with the nucleus and not a physical thing itself, perhaps this mass is somewhere between.

And I don't think matter is being converted into energy in the case you described. Both before and after the emission, we have the same protons, neutrons and electrons, just in different relationships with each other. What matter has disappeared? Seems to me in one sense all the bits of matter that were there earlier are still there. You can count them, and nobody's missing.

Maybe the concept of mass is one of those things that everyone thinks they understand until they try to define it. Maybe it has something to do with the Higgs particle, but what that is I don't know. It reminds me of people passionately debating abortion, when neither side can come up with a definition of life that's really at the core of the issue.

 

[Andrew Mason]

But what if you don't have a bunch of positrons? Are those isolated electrons equivalent to energy or not?

The electrons represent stored or potential energy. Would you say that potential energy is equivalent to other forms of energy?

And I don't think matter is being converted into energy in the case you described. Both before and after the emission, we have the same protons, neutrons and electrons, just in different relationships with each other. What matter has disappeared? Seems to me in one sense all the bits of matter that were there earlier are still there. You can count them, and nobody's missing.

The bits of matter are still there. But the atom has less mass. So I guest that the bits of matter must have lost part of what it is that makes them matter.

AM

 

[ZapperZ]

The electrons represent stored or potential energy. Would you say that potential energy is equivalent to other forms of energy?

I can write T = V. Can you write E = M? Is it even dimensionally correct? (and don't give me the high energy physicists shorthand of M having units of energy).

Again, you seem to ignore my question to you as when "conversion" always means "equal".

Zz.

 

[Mk]

But what if you don't have a bunch of positrons? Are those isolated electrons equivalent to energy or not?

The electrons are tiny little pieces of matter, as we understand them today. Not energy, although it holds an amount of energy. E=mc².

 

[Andrew Mason]

I can write T = V. Can you write E = M? Is it even dimensionally correct? (and don't give me the high energy physicists shorthand of M having units of energy).

Again, you seem to ignore my question to you as when "conversion" always means "equal".

If we were to use Planck units, one could write: E = M

If quantities can be converted to one another, are they not equivalent - different physical forms of the same fundamental physical entity?

AM

 

[ZapperZ]

If we were to use Planck units, one could write: E = M

Er.. no. Again, I said to not use the shortcut of h=k=c=1. And it IS a shortcut, thank you. Dimensionally, E and M are not identical.

If quantities can be converted to one another, are they not equivalent - different physical forms of the same fundamental physical entity?

AM

So you DO explain Hooke's Law by saying Force is equivalent to displacement? How often do you see the puzzled look on the faces of those you explain to?

Zz.

 

[rewebster]

In a way, I find this post amusing it that it represents one of the 'problems' with discussions and interpretations.

E=mc2


The equation is a representation of an idea. Does E "equal" mc2 , or does E "have similar qualities of" mc2 ? or does/can E "be converted into" mc2 ?

(I forgot the big one: Is E "the same as" mc2 ? )

What exactly is 'the proper' interpretation of "=" , as someone translates the terminology from math to the 'real world' ?


Personally, I prefer the 'language' of the 'idea' to mean more that any equation.

 

[ZapperZ]

To me, it is actually simpler than that. If I have a clump of mass m, and IF (big IF) that mass were to be converted completely into energy (of WHATEVER form - binding energy, kinetic energy, photons, gluons...), then I will have an amount of energy equal to mc^2. Done!

People may add all their cultural, sociological, psychological, philosophical, neurological, etc. to make that mean whatever they wish on top of that, but at the simplest case, that is all it means.

Zz.

 

[rewebster]

There you go----I like it---language with a touch (of math)

 

[rewebster]

For my 2c worth (c=cents) here, I still think that the idea behind the equation E=mc^2 is still off (not quite right) though.

 

[Curious3141]

To me, it is actually simpler than that. If I have a clump of mass m, and IF (big IF) that mass were to be converted completely into energy (of WHATEVER form - binding energy, kinetic energy, photons, gluons...), then I will have an amount of energy equal to mc^2. Done!

People may add all their cultural, sociological, psychological, philosophical, neurological, etc. to make that mean whatever they wish on top of that, but at the simplest case, that is all it means.

Zz.

Which is why I stated my opinion early on in this thread that the equation adds no interpretive value as far as "understanding" or "insight" go. These are very subjective things, and arguing about them can become a waste of time and effort. The one thing we can all agree upon is the phenomenological predictions the math makes, and that's all that really matters.

I guess in a sense, I'm more a "Greek" sort of scientist than a "Babylonian" - that's how Feynman would've labelled me. The math is the most important thing to me, I find it less important to gain a fuzzy warm intuition about stuff.

 

[Andrew Mason]

Er.. no. Again, I said to not use the shortcut of h=k=c=1. And it IS a shortcut, thank you. Dimensionally, E and M are not identical.

We define E as mass x velocity^2. So, obviously, we have to divide Energy by a velocity^2 to get conventional units of mass. But that does not mean they cannot be different manifestations of the same physical phenomenon.

If we defined E not as a mass x velocity^2 but as a number of a certain type of photon, we could define a unit of mass or energy in the same units. (The concept of mass would be the inertia carried by that number of those photons). Then E would be in the same units as m and you could write E=M.

So you DO explain Hooke's Law by saying Force is equivalent to displacement? How often do you see the puzzled look on the faces of those you explain to?

In a spring-mass system, displacement is equivalent to force. If we grew up in a spring mass world we might very well have equated force to a distance and measured it in the same units.

We live in a world in which the underlying structure of things is not obvious or intuitive. It is not obvious that water and O + 2H are equivalent. They are just structurally different (different spatial arrangements of the same atoms). Mass and energy are equivalent in the sense that they amount to different structures of the same underlying phenomena - not much different than saying that a mole of water is equivalent to a mole of oxygen and 2 moles of hydrogen: H₂O = 2H + 0

AM

 

[Blahness]

Okay, so energy and mass are equivalent, just different forms of the same thing. I think most of us got that.

However, I came to this thread, not to hijack it, but to not make a new thread(keeps the board cleaner), since someone is already talking about this:

Why C^2? E=MC^2, but why is it the speed of light squared?

Just wondering.

 

[ZapperZ]

We define E as mass x velocity^2. So, obviously, we have to divide Energy by a velocity^2 to get conventional units of mass. But that does not mean they cannot be different manifestations of the same physical phenomenon.

If we defined E not as a mass x velocity^2 but as a number of a certain type of photon, we could define a unit of mass or energy in the same units. (The concept of mass would be the inertia carried by that number of those photons). Then E would be in the same units as m and you could write E=M.

Sorry, but you have to go through several contortions to be able to spit out something like that. I don't buy it. Since WHEN are we using self-defined units? You HAD to go back to the concept of inertia and dig up some really weird point of view to justify your postion. I'm sure if I look at an elephant upside down when the moon is full, it will resemble an ice-cream cone too.

In a spring-mass system, displacement is equivalent to force. If we grew up in a spring mass world we might very well have equated force to a distance and measured it in the same units.

But the point is, when was the last time you sold the spring-mass system using THIS point of view? I asked you how many strange looks did you get back when you tried this before.

We live in a world in which the underlying structure of things is not obvious or intuitive. It is not obvious that water and O + 2H are equivalent. They are just structurally different (different spatial arrangements of the same atoms). Mass and energy are equivalent in the sense that they amount to different structures of the same underlying phenomena - not much different than saying that a mole of water is equivalent to a mole of oxygen and 2 moles of hydrogen: H₂O = 2H + 0

AM

By the same token, if you obey your own advice, you won't be so quick to say they are equal. It seems to me that I was the one who is being conservative in making that leap, not you. So if you truly believe that ".. the underlying structure of things are not obvious...", you wouldn't be so quick to jump on the "equal" bandwagon, because you don't know that much either! So what you say here is inconsistent with your insistence that they are "the same thing".

Zz.

 

[Curious3141]

I'm sure if I look at an elephant upside down when the moon is full, it will resemble an ice-cream cone too.

I'm sleep deprived, but *that* woke me up!

 

[PRodQuanta]

(The concept of mass would be the inertia carried by that number of those photons).

Your keyboard you are typing on is massive. I would like to see you define your keyboard as the inertia carried by n photons.

*Sorry for budging*

Paden Roder

 

[Andrew Mason]

So what you say here is inconsistent with your insistence that they are "the same thing".

I didn't invent the concept of mass-energy equivalence. When you add energy to an electron traveling at .9999999999999c the energy goes almost entirely into increasing the mass of the electron.

The root of the apparent difference between mass and energy is the distinction that we make between space and time. Einstein showed that space and time are observer dependent and not absolute. So if time and space are equivalent, space^2/time^2 cancel each other and mass=energy.

AM

 

[Mk]

You can convert one into the other

Its been said many times, and do not let it be asked again!

Would you say that a piece of bread is the same as the flame coming out of a candle?

Einstein said that mass and energy are equivalent.

When a piece of bread burns to a crisp and shrivels up, it loses mass. But most of the lost mass goes to solid flakes that come off the bread and to combusted carbon that gets released as carbon dioxide gas. This is essentially a chemical transformation and does little to exemplify mass-energy equivalence.

Of course, let's say you set the bread on fire (or set a wax candle on fire) and drop it into a container containing air on a very precisely calibrated weighing balance and seal the container completely. No mass can escape the sealed container, only energy can leave it.

By classical physics (Lavoisier attempted something like this), the reading on the balance should not change since the masses of the burnt residue and all the released gases etc should total the initial mass. But in fact, a very precise measurement would show the container losing mass. This exemplifies Einstein's mass-energy equivalence : the exothermic reaction occurring in the container releases chemical binding energy that then gets radiated off as photons that pass through the container into the external Universe or heat up the walls of the container (which will then radiate off that energy to the exterior). For the small quantity of chemical energy that is released, the decrease in mass will be really miniscule, which is why this setup would only work as a thought experiment.

I didn't intend to leave it at that, but rather have a systematic progress in developing the idea of why something can be "the same" and "different" at the same time, depending on what criteria one is using. So his teacher CAN be correct in saying that we cannot simply put on blinders and say matter is equal to energy simply based on that equation.

At the end of the day, one must realize that E=mc^2 is merely a mathematical formalism. It makes predictions that we can verify experimentally if we know what to look for. It does not give us an intuitive understanding of the nature of the relationship between mass and energy.

They can be transformed into one other but it is not the same as saying that they are "the same". I would not say that it is the same to have an unexploded atomic bomb resting on my desk as to have an atomic explosion in my office...

The electrons are tiny little pieces of matter, as we understand them today. Not energy, although it holds an amount of energy. E=mc².

 

[Mk]

I've gone through years and years of schooling, and if there is one thing that I have learned, it is THAT. I know that personally, I find such satisfaction when it is a problem that I solved myself. A student, especially, need that kind of self-esteem, especially when the road ahead into graduate school and employment can be bumpy.

So how does one guide things through? I learn this from the BEST instructors that I've ever had in college. You instead ask the student to think of something similar, or ask what he/she meant, or figure out what he/she knows and START from that. That was my intention in asking that question - to get the originator to think about the question itself and see if by looking at it closely, he can figure out "Ah ha! It depends on what I use to say something to be "the same"! Holy cow! My question, and how I ask it, can some time dictates the answer that I could get!" This is the FIRST step in becoming a physicist - being aware of what question you should ask of Nature and how that question can some time effect the type of answer that you get!

Erm, well, that's what I meant.

Einstein showed that space and time are observer dependent and not absolute. So if time and space are equivalent, space^2/time^2 cancel each other and mass=energy.

Uhm, what? How did you go from time and space being equivalent to mass equalling energy? The relation between space and time are kind of like matter and energy, although I don't know how to explain.

 

[Andrew Mason]

Your keyboard you are typing on is massive. I would like to see you define your keyboard as the inertia carried by n photons.

Ok. Let's define the unit of energy and mass as a Gork which is 5.5x10^24 photons emitted by Hydrogen when its electron undergoes the n=2 to n=1 energy transition (\nu = 2.47\cdot 10^{15} sec^{-1}.

My laptop has a mass of about 2x10^10 Gorks or 20 gigaGorks (written 20 gG). It also has an energy of 20 gG.

AM

 

[Curious3141]

Ok. Let's define the unit of energy and mass as a Gork which is 5.5x10^24 photons emitted by Hydrogen when its electron undergoes the n=2 to n=1 energy transition (\nu = 2.47\cdot 10^{15} sec^{-1}.

My laptop has a mass of about 2x10^10 Gorks or 20 gigaGorks (written 20 gG). It also has an energy of 20 gG.

AM

"Gork" ! This is becoming more entertaining than most episodes of Seinfeld !

 

[Andrew Mason]

Uhm, what? How did you go from time and space being equivalent to mass equalling energy? The relation between space and time are kind of like matter and energy, although I don't know how to explain.

E = mc^2 Since c = distance/time, if distance and time were in the same units, E would have the same units as m.

AM

 

[Mk]

E = mc^2 Since c = distance/time, if distance and time were in the same units, E would have the same units as m.

But distance and time aren't in the same units. They're in meters and seconds respectively. Are meters and seconds the same? Space and time aren't the same! Just like matter and energy, they are only very closely related, and not quite the same thing.

I like the Gork thing.

 

[ZapperZ]

I didn't invent the concept of mass-energy equivalence. When you add energy to an electron traveling at .9999999999999c the energy goes almost entirely into increasing the mass of the electron.

The root of the apparent difference between mass and energy is the distinction that we make between space and time. Einstein showed that space and time are observer dependent and not absolute. So if time and space are equivalent, space^2/time^2 cancel each other and mass=energy.

AM

IF time and space are equivalent??! Hello? Which parallel universe are you living in right now?

You are being very sloppy in this whole debacle. You want to tell me that we know nothing about the structure of things, and yet, you go against THAT advice yourself by insisting that you know E = M, while IGNORING other properties of M that are not contained in E. All you care about is "conversion" automatically means "equal". It is YOU who is making this blatant assumption of things. You contradict yourself.

Zz.

 

[Mk]

Jeez Zz, keep your cool. Don't use caps, it has the effect of yelling, even if you are. Smart people don't yell.

 

[ZapperZ]

Jeez Zz, keep your cool. Don't use caps, it has the effect of yelling, even if you are. Smart people don't yell.

But I'm not smart. So I YELL!

Zz.