E=MC^2: Exploring the Connection Between Matter and Energy

[Universe_Man]

I have read a bit on E=MC^2, and would I be correct in saying that matter and energy are essentially the same thing? I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy? It would make sense to me that energy and matter are essentially two sides of the same coin, that if you were to break an atom down to its most basic particles, then break it down futher, then you would be left with a specified amount of energy. That's how I interpret it anyway. Is there something wrong in my interpretation? Is there something further I need to know? I by no means claim to be a professional (yet).

Thanks

 

[ZapperZ]

I have read a bit on E=MC^2, and would I be correct in saying that matter and energy are essentially the same thing? I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy? It would make sense to me that energy and matter are essentially two sides of the same coin, that if you were to break an atom down to its most basic particles, then break it down futher, then you would be left with a specified amount of energy. That's how I interpret it anyway. Is there something wrong in my interpretation? Is there something further I need to know? I by no means claim to be a professional (yet).

Thanks

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

Zz.

 

[scott1]

I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy?

Are your sure you asked a physics teacher? Einstien said that matter and energy were pretty much the same thing. Which is what $E=mc^2$ says.

 

[pmb_phy]

I have read a bit on E=MC^2, and would I be correct in saying that matter and energy are essentially the same thing? I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy? It would make sense to me that energy and matter are essentially two sides of the same coin, that if you were to break an atom down to its most basic particles, then break it down futher, then you would be left with a specified amount of energy. That's how I interpret it anyway. Is there something wrong in my interpretation? Is there something further I need to know? I by no means claim to be a professional (yet).

Thanks

Einstein said that mass and energy are equivalent. You can hear it online by Einstein himself at

http://www.aip.org/history/einstein/voice1.htm

Pete

 

[Danger]

You're the expert, Zapper, not me, but that seemed a wee bit harsh. Matter, as you well know, is merely energy in a bound state. While a piece of bread is indeed different than a candle flame, it's quite comparable to the wax. When you ignite it, as my ineptitude with a toaster has often demonstrated, the mass is partially converted to energy. Even though the e=mc^2 refers to total conversion, the formula still applies to the part that is converted. My 2 cents worth here is that the teacher didn't properly explain the situation.

 

[Curious3141]

You're the expert, Zapper, not me, but that seemed a wee bit harsh. Matter, as you well know, is merely energy in a bound state. While a piece of bread is indeed different than a candle flame, it's quite comparable to the wax. When you ignite it, as my ineptitude with a toaster has often demonstrated, the mass is partially converted to energy. Even though the e=mc^2 refers to total conversion, the formula still applies to the part that is converted. My 2 cents worth here is that the teacher didn't properly explain the situation.

Hold on a sec. While the general concept is OK, the way you put it can mislead people unfamiliar with mass-energy equivalence.

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.

For more discernible changes, one would look towards reactions releasing a heck of a lot more energy. The obvious choice : nuclear reactions. The same principles apply.

 

[Danger]

I have no argument with you on that, Curious. In fact, it was a nicely presented explanation. The nature of the question led me to assume that the OP is in early high-school or lower, and I was unfortunately in too much of a hurry to formulate a full response, so I elected to keep it simple. My main reason for posting was that it seemed that ZZ's response might be misinterpreted as a 'dismissal' of the question. Those of us who know him (PF-wise, not personally) know that he's an excellent teacher and a brilliant man in his field. I wanted to make sure that the OP wasn't discouraged by what appeared to me to be an uncharacteristically curt response on his part. I'm sure that his intention was to suggest a serious evaluation of the matter, but his wording didn't make that clear.
It was indeed the photonic release, be it visible light or IR, that I was referring too by the part of the mass that truly is converted to energy. My apologies if it created a misunderstanding.

 

[rbj]

Are your sure you asked a physics teacher? Einstien said that matter and energy were pretty much the same thing. Which is what $E=mc^2$ says.

in addition energy density (converted to the same units of mass by multiplying by the conversion factor c^-2) warps space-time in the same manner that mass density does (it is an active source of gravity). also energy get deflected in 3-space by the presence of gravity.

speaking metaphysically, i think at the end of the age when we are all fully enlightened and know all the hidden secrets of the universe, it will be confirmed that energy and mass are two different manifestations of the same thing. sort of like the wave-like properties and particle-like properties of either energy or matter. now, it's like we see in a mirror dimly.

 

[Chaos' lil bro Order]

Curious gave the correct answer and a great one at that.

Zapper berated a good question because the answer was so obvious to him that it would be tedious to properly explain it in lay terms. I really don't see why you answer at all if you aren't going to be nice about it.

 

[ZapperZ]

What the?

All I asked the OP was to think about how one categorized something as being EQUAL or EQUIVALENT!

I asked if a flame is equivalent to a piece of bread? In other words, what CRITERIA does one use to say something is equal? An apple is equivalent to an orange IF you only use the criteria of something being a FRUIT. If you are using "flavor" as a criteria, would you say an apple is equivalent to an orange? NO!

How is this "berating"?

It illustrates very clearly the SHORTCOMMING of using ordinary language in trying to tie things in physics! One is trying to put into words what a mathematical description is saying. If you say "yes, a piece of bread is the SAME as the flame from a candle", then your criteria of considering something to be the SAME is very broad. Most high energy physicists would consider the same thing.

But if you tell me, no, they are not the same, then your criteria of indicating what are equal now is different. People are TOO QUICK to answer a question like this without considering the "frame of reference" that the OP is using. What is meant by "the same thing" or "different things"? An electron is NOT the same thing as a photon if you use a set of criteria (charge, spin, mass, etc), but yet, everyone here is saying it is a mass-equivalent with energy via that equation.

Just because you guys are TOO QUICK to answer this question without seeking exactly what the OP considers to be "different" or "the same" does not mean my ONE LINE question to the OP was a means of "berating" him! It wasn't even close! If you want to see "berating", THIS post is what I called berating!

And Chaos, you should follow your own advice next time. Your post also contains nothing nice and nothing to add to answer the OP. So next time, if you have zero content relevant to the OP to post, don't!

Oy vey! Such a nice way to start the day!

Zz.

 

[Andrew Mason]

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

Zz.

?? This does not exactly help answer the question. Both the bread and the flame coming out of the candle consist of matter. Both emit energy due to internal molecular activity.

AM

 

[ZapperZ]

?? This does not exactly help answer the question.
AM

It wasn't meant to. It was meant to get the OP to figure out what is the criteria used in distinguishing what is "different" and what is "the same". 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.

What I find to be more outrageous (except that I didn't express my displeasure till now since I've been accused of "berating" the OP) is to be able to somehow make all kinds of assumption of what is being used as the criteria, AND the irresponsibility of not considering the consequences of imparting such an answer. I'd rather NOT answer a question than giving such an impression, in which some poor instructor later on would have to do the dirty work of correcting, while we sit here gloating in our fine effort of imparting our wisdow!

.. and yes, I'm still miffed at this whole thing.

Zz.

 

[Curious3141]

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.

The thing is, I believe I understand mass-energy "equivalence", but that's just a way of saying I understand the math behind the equation and the phenomenological consequences in certain special instances. In my mind, I view a certain mass as being "associated" with a certain amount of energy. There are ways to measure (observe) changes in mass and changes in energy in a defined closed system, and my understanding tells me that when one observed parameter changes, the other is sure to change in a definite way. In simple terms, I view mass and energy as two separately measurable parameters of a system that are always linked by the equation.

So I think of simple chemical exothermy (observation of energy being given off as heat) being associated with a miniscule decrement in mass. A nuclear reaction as being associated with a rather more easily observable decrement in mass. An object traveling at a high speed (and therefore being observed to have a high kinetic energy) apparently gaining mass compared to when it's at rest.

Now, those are all simply phemenological instances where mass-energy "equivalence" applies, but the principle or equation did not really give me any deeper insight into how to view (or rationalise) the "meaning" of the equivalence.

I don't think there's a single right answer as to how to interpret the equivalence. Some might prefer to think as I do, of mass and energy being related objective parameters of a system. Others might prefer to think in terms of a "conversion" of sorts. Which interpretation seems more relevant also depends on the phenomena under consideration.

(Note that there are other areas of modern physics where theory gives a definite mathematical formalism, but personal physical interpretation is largely subjective and variable [and perhaps, really not that important]. Wave-particle duality, the many-worlds interpretation of QM, these are some obvious examples that spring to mind. An even simpler example that nearly everyone should be familiar with is the apparent equivalence between "inertial" mass and "gravitational" mass; again, theory doesn't give concrete answers why this should be so, it is really up to us to come to terms with it and imagine that we have an intuitive understanding of the concept.)

At the end of the day, it is largely a personal choice how we want to conceptualise the relationship implied by the equation. What's more important is being able to predict accurately what happens in various diverse phenomena where the equation applies.

 

[nrqed]

I have read a bit on E=MC^2, and would I be correct in saying that matter and energy are essentially the same thing? I was wondering about this because I asked my Physics teacher and she said that matter and energy are two separate entities. but can't matter be converted into energy? It would make sense to me that energy and matter are essentially two sides of the same coin, that if you were to break an atom down to its most basic particles, then break it down futher, then you would be left with a specified amount of energy. That's how I interpret it anyway. Is there something wrong in my interpretation? Is there something further I need to know? I by no means claim to be a professional (yet).

Thanks

Hi there.

I would say that it is a matter of what one means by "two separate entities" or "being the same thing".

Consider throwing a ball upward. It has both kinetic and gravitational potential energy, right? Are these "the same"? I think that most people would say that there are different things (in the sense that if an object has 10 Joules of kinetic energy or 10 Joules of Gravitational potential energy, the situation is not necessarily the same. In one case the object is moving wheras in the other case, it could be at rest!). Now, kinetic energy can be transformed into gravitational potential energy and vice versa...but this is not necessarily the same as saying that they are identical things, right? Same for mass and Energy (in the sense of kinetci energy, say). 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...

Pat

 

[DaveC426913]

In direct answer (as opposed to analogy) to the OP's original question:

I suspect that your teacher is oversimplifying the answer. She may not realize that you are as knowledgeable as you are about E=mc^2.

If you look at them right, matter and energy are indeed two sides of the same coin.

You can convert one into the other. For example: you can combine a proton and an antiproton, you will be left with a lot of energy (in the form of gamma rays and a whole bunch of heat) and no matter.

Nuclear reactors and nuclear bombs exploit this fact - converting matter into energy - but they do so with a much lower efficiency than matter-antimatter. Nuclear reactions convert only a tiny fraction of their mass into energy, leaving most of the mass as waste products.

It is much harder to convert energy into matter. I can't think of any common examples off-hand.

 

[Hootenanny]

It is much harder to convert energy into matter. I can't think of any common examples off-hand.

Pair production.

~H

 

[Chaos' lil bro Order]

Zapper

Didn't want to ruin your day, but your 500 word response in defence of what I said really helps to confirm my comments (and you know it but will never admit it on PF, so there's really no point in us playing 'prosecutor-plaintiff' anymore).

As for the original question, I think we can all agree that matter and energy are equivalent. I mean heck, if they were not equivalent then any time a physical process like pair-production, combustion, or particle collisions occured, to name a few, conservation of energy would be violated.
Yes a piece of bread is the same as a candle flame in this sense. Given great enough heat, bread could be turned completely into energy, even the smoke coming off of it could be further converted into energy at high enough temperatures. The shortcoming of this equivalency being that you could never turn the candle flame into bread due to entropy and combustion being an irreversible process.

Everything in the Universe started out as energy after all, its matter that has slowly formed since the BB. EVERYTHING IS ENERGY.

 

[Chaos' lil bro Order]

Curious is the new SpaceTiger of General Physics. Welcome Curious, you are really an impressive poster, keep up the genius posts.

 

[Chaos' lil bro Order]

Curious is the new SpaceTiger of General Physics. Welcome Curious, you are really an impressive poster, keep up the genius posts.

 

[Curious3141]

Curious is the new SpaceTiger of General Physics. Welcome Curious, you are really an impressive poster, keep up the genius posts.

I really appreciate the kind words, but I don't think I'm anywhere near that impressive. There are people here (Zapper included) who are far more knowledgeable than me in Physics, in fact Zapper is an expert in the field.

At the end of the day, we're all here to learn, and have fun doing it, let's not let petty differences stand in the way.

 

[Andrew Mason]

The shortcoming of this equivalency being that you could never turn the candle flame into bread due to entropy and combustion being an irreversible process.

Not quite. Irreversible processes can be reversed if you add energy. So you can turn the candle flame into bread. In fact, wheat plants take carbon dioxide from combustion and convert it into wheat.

Everything in the Universe started out as energy after all, its matter that has slowly formed since the BB. EVERYTHING IS ENERGY.

I don't think it is settled that the universe started out as energy. Or matter. It may have started out as a singularity, which may have been neither mass nor energy but something which out of which the laws of physics - and our forms of energy and matter - emerged.

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.

AM

 

[ZapperZ]

Zapper

Didn't want to ruin your day, but your 500 word response in defence of what I said really helps to confirm my comments (and you know it but will never admit it on PF, so there's really no point in us playing 'prosecutor-plaintiff' anymore).

HA! Please don't start taking the high road, because you know perfectly well that your post was meant to incite me. You got what you ASKED for. That post of yours had ZERO content other than to insult me.

As for the original question, I think we can all agree that matter and energy are equivalent. I mean heck, if they were not equivalent then any time a physical process like pair-production, combustion, or particle collisions occured, to name a few, conservation of energy would be violated.

And this is where you have put your blinders on. The FACT that for matter to be CONVERTED into energy, or energy to be converted into mass require a whole bunch of things to occur means that it isn't a simple issue of "equivalence"! Pair production requires a nearby massive object for conservation of momentum. It also requires that the product being produce conserve angular momentum. An electron just simply doesn't turn itself into pure energy because it violates a whole zoo of conservation laws. It requires its antiparticle partner for that to occur!

In other words, it isn't THAT easy and requires a whole set of circumstances for such a conversation to occur. Why? Because "matter" isn't just defined by simply its mass! That's like saying a person is only defined by what his/her face looks like and ignoring other properties. This is absurd! And yet people say that matter and energy are "the same"? Fine. A leaf is the same as an elephant. If the OP have mentioned that in the very beginning, we could have easily said everything in the universe are the same and we can all go home.

Chaos: I've tried to not involve myself with your post and the thread you've created, letting others deal with those (I'll keep my opinion to myself in what I think of them, unlike you). However, if you keep trying to incite me with such comments, then please don't play the dump part of being the innocent party. You are more then welcome to ignore and skip everything that I wrote because I am sure none of what I have to say is of any value to you.

Zz.

 

[Mk]

Hey guys, keep it down! We can hear you all the way over from in the PF lounge!

I can't resist, sorry, I must say something about the Zz-Chaos conflict.

Although Zz's first post in this thread was not near as an in depth reply as Curious's (Comparable to SpaceTiger's or Zz's own posts) posts, I did not think it to be a full answer. It may or may not have been intended as, but I thought it was a very clever post meant to invoke thought to the original poster, Universe_Man, and see if he could figure it out on his own. Kind of a Socratic answer, that was a very good one in fact. Many of the mentors' posts that are first replies to questions as common as this are exactly like this. Doc Al and Integral do the same.

I can understand how Chaos may have seen it as a bit rash, but by all means not a "bad" post!

 

[ZapperZ]

Hey guys, keep it down! We can hear you all the way over from in the PF lounge!

Sorry, I won't use the bullhorn next time.

I can't resist, sorry, I must say something about the Zz-Chaos conflict.

Be careful you don't get trampled.

Although Zz's first post in this thread was not near as an in depth reply as Curious's (Comparable to SpaceTiger's or Zz's own posts) posts, I did not think it to be a full answer. It may or may not have been intended as, but I thought it was a very clever post meant to invoke thought to the original poster, Universe_Man, and see if he could figure it out on his own. Kind of a Socratic answer, that was a very good one in fact. Many of the mentors' posts that are first replies to questions as common as this are exactly like this. Doc Al and Integral do the same.

I can understand how Chaos may have seen it as a bit rash, but by all means not a "bad" post!

As I have explained earlier, the OP did not indicate what is meant by "the same". I suppose I could have asked him directly by asking that. But my philosphy has ALWAYS been that one learns more effectively by discovering the answer oneself by thinking something through. The BEST thing that the rest of us can do is act as GUIDE!

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!

Most of us, under ordinary circumstances, would NOT consider an apple and an orange to be "the same thing". In fact, we often use the phrase "well, you're talking about apples and oranges here" to signify that someone is talking about DIFFERENT things! Yet, we are going to leave the impression that everything in this universe is "the same", whatever THAT means. As with the issue of "relativistic mass", we simply cannot just spew things to satisfy our egos out without regards to the consequences of what we have said. You'd be surprised how many things that are read here are taken seriously, for better or worse. The teacher was absolutely right in having a hesitation in answering this kind of question. I would too, because those who feel such responsibility would think 2, 3, or even 4 steps ahead of how the students will absorb such an information. Anyone who have had to stand in front of a class and teach impressionable young minds would be aware of this!

Again, no one here has somehow justified the consequences of saying that energy and matter are "the same thing". I could easily ask "Well, if they're the same thing, then how come I have to use the boson picture to describe photons, and the fermionic picture to describe electrons? How come they behave in such different manner?" And then what? We retract and say "Oh, but you were just using that equation which says energy and mass are the same. That's all we were basing it on when we say they're the same thing". Well, this is balony! That's like saying just because the tail of two animals look similar, they're the same animal! You are then ignoring a whole bunch of characteristics that describe the animal! An electron isn't JUST defined by its mass, thankyouverymuch! But to simply use JUST that property and proclaim that it is "the same" as the stupid photon that just passed by my eye is utterly ridiculous.

I have never, ever seen anyone mistaking that a Force is "the same thing" as a Displacement (F = kx). Yet, these two can be formulated into the SAME form as that energy-mass equation. So notice the inconsistency here. Two separate mathematical equations having an identical form. Yet, people are so happy to intermingle one, where they never do that with the other. I have never seen anyone explaining Hooke's Law by saying "Well, you see, displacement and force are the same thing, just in different forms and disguises." This is silly!

Moral of the story: Never tell me that I'm berating someone when all I did was ask a straightforward question that I was hoping to help the OP think something through.

 

[DaveC426913]

ZapperZ is harsh? berating?

This is a classic case of reading too much between the electronic lines. ZZ's initial response was:

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

That is not "harsh" or "berating" unless the reader read that into it.

What I read in this was an attempt to mentor the OP by drawing critical thought out of him, rather than handing him the answer on a plate.

What is all the more surprising is that anyone misunderstood ZZ's intention; afterall, encouraging critical thought rather than handing answer on a plate is what PF is all about, isn't it?

 

[Andrew Mason]

And this is where you have put your blinders on. The FACT that for matter to be CONVERTED into energy, or energy to be converted into mass require a whole bunch of things to occur means that it isn't a simple issue of "equivalence"!

Not true! Let's not confuse the OP by suggesting that the creation of discrete particles of matter is the only way mass can be created from energy.

Converting energy into mass, and vice versa, occurs all the time all around us. Every time a photon with energy $E=h\nu$ is absorbed by an atom the mass, or inertia, of the atom increases by the amount $E/c^2$. Hence the title of Einstein's original paper: "Does the Inertia of a Body Depend on its Energy Content?" This is the essence of $E=mc^2$.

Particle creation is a special case, but by no means the only case. After all, Einstein developed his equation long before it was even known that new particles of matter could be created.

AM

 

[ZapperZ]

Not true! Let's not confuse the OP by suggesting that the creation of discrete particles matter is the only way mass can be created from energy.

Converting energy into mass, and vice versa, occurs all the time all around us. Every time a photon with energy $E=h\nu$ is absorbed by an atom the mass, or inertia, of the atom increases by the amount E/c^2. Hence the title of Einstein's original paper: "Does the Interia of a Body Depend on its Energy Content?" This is the essence of $E=mc^2$.

AM

But even then, there are rules for that to occur. For an atom to absorb a photon, a specific dipole transition must occur, and whole set of conservation laws on why the atom much change an orbital angular momentum by 1. In other words, there are more stuff than meets the eye here. It isn't just a simple "energy becomes matter and let's all go home".

But I still don't see how you can argue that due to such an absorption, matter and mass are "the same". Your illustration is a perfect example here, that it requires a series of things to occur for a "conversion", and one has to consider several conservation laws to kick in, not just conservation of mass-energy. The extra mass that atom has gained via absorption of the photon is not "the same" as the original photon.

Zz.

 

[rewebster]

I agree with #25----And if I "have to" use math here, it seems like the argument is from two sides of thought.

one: 1=1

or

two: 1=x+y

Which goes back to the basic question----what EXACTLY is 'x' and what EXACTLY is 'y' ?

 

[liucibegemoc]

Energy can be converted from mass and vice versa - mass can be converted from energy. That's theory of big bang. A lot of mass was created from a lot of energy.

 

[Andrew Mason]

Distinction between matter and mass

But I still don't see how you can argue that due to such an absorption, matter and mass are "the same". Your illustration is a perfect example here, that it requires a series of things to occur for a "conversion", and one has to consider several conservation laws to kick in, not just conservation of mass-energy. The extra mass that atom has gained via absorption of the photon is not "the same" as the original photon.

Zz.

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

The distinction between 'matter' and 'mass' is subtle - more subtle than the distinction between weight and mass, which always troubles young physics students. The OP's science books probably define 'mass' as 'quantity of matter'.

So perhaps the more illuminating question is not: "are matter and energy the same?" but is: "how are matter and mass fundamentally different?"

Here are a few thoughts that come to mind:

1. Matter defines an inertial frame of reference (ie. there is a frame of reference in which the matter body is stopped). Mass is a measure of inertia (momentum/speed or force/acceleration) carried by a body.

2. Some non-matter objects cannot define an inertial frame of reference (eg. photon) but can carry momentum and transport mass from one matter object to another. One could say that such objects carry mass but do not possesses it themselves. Or one could make the distinction between rest mass and non-rest (relativistic) mass and say that matter particles have rest mass but energy particles have only non-rest mass.

AM

 

[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.