# Read a bit on E=MC^2

1. Apr 30, 2006

### 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

2. Apr 30, 2006

### ZapperZ

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

Zz.

3. Apr 30, 2006

### scott1

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.

4. Apr 30, 2006

### pmb_phy

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

Last edited: Apr 30, 2006
5. Apr 30, 2006

### 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.

6. Apr 30, 2006

### Curious3141

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 occuring 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.

7. Apr 30, 2006

### Danger

I have no arguement 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.

8. Apr 30, 2006

### rbj

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. sorta like the wave-like properties and particle-like properties of either energy or matter. now, it's like we see in a mirror dimly.

9. Apr 30, 2006

### 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.

10. May 1, 2006

### ZapperZ

Staff Emeritus
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.

11. May 1, 2006

### Andrew Mason

?? 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

12. May 1, 2006

### ZapperZ

Staff Emeritus
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.

13. May 1, 2006

### Curious3141

At the end of the day, one must realise 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 travelling 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.

Last edited: May 1, 2006
14. May 1, 2006

### nrqed

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

15. May 1, 2006

### 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.

16. May 1, 2006

### Hootenanny

Staff Emeritus
Pair production.

~H

17. May 1, 2006

### 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.

18. May 1, 2006

### 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.

19. May 1, 2006

### 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.

20. May 1, 2006

### Curious3141

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.