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

[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.

 

[rewebster]

for post 47

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.

I remembered seeing something about that on NOVA:



http://www.pbs.org/wgbh/nova/einstein/ance-sq.html



The 'science' behind the c^2 isn't exactly a 'eureka' moment the way it's explained in the two paragraphs (at the bottom of that page). In fact, it seems rather un-scientific. I like their terminology, " did suddenly appear " for the explanation--- .

 

[rbj]

I didn't invent the concept of mass-energy equivalence. When you add energy to an electron traveling at 0.9999999999999c the energy goes almost entirely into increasing the mass of the electron.

from the POV of the observer that the electron is whizzing past at 0.9999999999999c.

Andrew, for some reason it has become out of vogue to think in terms of relativistic mass.

$$E = m c^2 = E_0 + T$$

makes sense when $m$ is relativistic mass and

$$E_0 = m_0 c^2$$

is rest energy (i think this is the equation most people mean when they say " E = mc² " and $T$ is kinetic energy (energy which depends on who is watching).

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.

this equating of dimensions can, in my opinion, eventually lead to madness. so if we equate space and time (there's an arrow of time, but there is no arrow of space outside the event horizon of a black hole) that is effectively setting $c = 1$. that means (besides that length is the same thing as time), that

$$E = m c^2$$

becomes

$$E = m$$

and energy is the same thing (or same dimension) as mass.

why stop there? let's do like Planck and set $\hbar = 1$ and $G = 1$. so

$$E = \hbar \omega$$

becomes

$$E = \omega$$

and energy (which is the same as mass) is the same thing as frequency or 1/time. and since time is length, then mass is the same as 1/length. now

$$E = G \frac{M m}{r}$$

becomes

$$E = \frac{M m}{r}$$

so now energy (the same thing as mass) is the same as mass² x length^-1. that says the same thing that mass is the same as length.

so length = 1/length? or time = 1/time? or mass = 1/mass? all this would be true if we say that length (or space), time, or mass are all dimensionless.

so, for my money, either:

1. there is such a thing as different dimensions of physical quantity and mass is not the same as length nor is the same as time. (so energy is not dimensionally the same thing as mass.) i would also view electric charge as a fundamental dimension, but the cgs people might not.

or

2. there is no such meaningful thing as dimension of physical quantity and they are just human constructions which no deep physical correspondence.

that's my story and I'm stickin' to it.

 

[rewebster]

I'm really (really) surprized that there isn't some one making a comment on the origins of the c^2 (from the NOVA link-post 61).


Is the c^2 just 'accepted' ? as 'the' maximum speed possible transposed? justified from a ball in clay?

 

[Universe_Man]

Hey everyone, thanks for the input, I really apppreciate it. It would seem that I have much more to learn on the subject.

 

[russ_watters]

I'm really (really) surprized that there isn't some one making a comment on the origins of the c^2 (from the NOVA link-post 61).


Is the c^2 just 'accepted' ? as 'the' maximum speed possible transposed? justified from a ball in clay?

That's an interesting story on the origin of the concept of energy, but it isn't all that relevant here. It seems like you think that is the entire basis for squaring velocity in any equation, including Einstein's. It is nowhere near as trivial as you are implying. It was derived mathematically for its application in E=mc^2. And it isn't "just 'accepted'", it is accepted because it is well supported by the evidence available.

Part of the mathematical derivation, on a basic level, Blahness, is that the units have to work out. Energy has the units mV^2, so that's what it has to be, whether Newtonian or relativistic. If Einstein had come up with anything else, it wouldn't have been consistent with the definition of "energy".

 

[rewebster]

It seems like you think that is the entire basis for squaring velocity in any equation

no, I didn't mean that or mean to imply that

Energy has the units mV^2, so that's what it has to be, whether Newtonian or relativistic.

yes

If Einstein had come up with anything else, it wouldn't have been consistent with the definition of "energy".

This is the part of his idea of his theory that I have trouble with.

And it isn't "just 'accepted'", it is accepted because it is well supported by the evidence available.

the evidence supports his theory as long as you go "by his theory"

 

[DaveC426913]

the evidence supports his theory as long as you go "by his theory"

You've got the cart before the horse.

If there is a theory out there that better describes the evidence, we're all ears.

 

[Kalouste]

The answer to your question can be found on this book: http://www.davidbodanis.com/books/emc2/" .

6th chapter, «2»

The post's question is why c is squared. The author, after a brief introduction about Emile du Châtelet and Voltaire introduces few reasons for c being squared. You should look up.

Good Luck.

Edit: Thanks for the correction rewebster.

You can also watch a video presentation with David Bodanis himself to learn more about the book: http://www.meettheauthor.com/bookbites/397.html

 

[rewebster]

The big question is why c is squared.

Well, I don't think that's the big question. The BIG question is rather it's right or not.



Is there a 'published' theory out there?

Not that I've read that I (me, personally) discern to be 'correct' as that they (those theories) can't answer all (everyone's/most people's) concerns (from my knowledge --which would not be as great as 'x'% of the people on this forum--where 'x' is an unknown); and, of course, I haven't read them all---and someone could spend time^2 reading all (everything relating to and about physics and/or philosophy) that's out there (published, unpublished, on the web, written on napkins hidden in books).


And if you're asking the question that I (may, can) assume (induct,deduct) you're asking---that's the reason I initially found the Physics Forum.

Did that answer your question?

PS:
I guess you really didn't state it as a question, though, so...

 

[Andrew Mason]

Well, I don't think that's the big question. The BIG question is rather it's right or not.

It is not whether it is right or wrong in the sense of being a true description of physical reality. Science does not work that way. Any theory is 'correct' so long as it is consistent with all the evidence. Theories can only be disproven. They can never be proven absolutely true. One fact will destroy the most elegant theory. A gazillion facts will not make it 'absolutely true'.

All Einstein did was derive, from very few simple principles, a mathematical and conceptual model of matter and energy that, to date, is completely consistent with all physical observation. In a hundred years, no one has been able to find a fact that is inconsistent Einstein's theory.

You don't have to believe that Einstein's theory of relativity represents 'truth' or 'reality'. But it is irrational to think there is something wrong with it if you are unable to identify a fact that it is inconsistent with.

AM