I Real life example of the energy contained at E=γmc^2

[Foruer]

We've just begun studying about relativity, and I find it amazing that bodies have the energy of E=γmc^2. Even at rest they have E=mc^2.
But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

 

[Orodruin]

But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy,

Most of that energy is due to the rest mass of the constituents.

but how is it usable?

Why does it have to be usable for anything?

 

[Foruer]

Because it's a big amount of energy in small mass bodies, so you'd think that if it was really usable somehow, you would could provide energy to the entire world by using small amount of matter. I just wonder if it can be expressed somehow in real life?

 

[jbriggs444]

Because it's a big amount of energy in small mass bodies, so you'd think that if it was really usable somehow, you would could provide energy to the entire world by using small amount of matter. I just wonder if it can be expressed somehow in real life?

If you throw a baseball toward home plate, the difference, $\gamma mc^2 - mc^2$ gives the kinetic energy of the baseball.

 

[russ_watters]

For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

Well, you could collide it with an anti-keyboard...

In reality, this isn't usable energy, but rather an energy equivalence. However, if you've studied nuclear energy yet, you'll see that there are small differences in the starting and ending mass that you can evaluate.

 

[pervect]

Aside from colliding your keyboard with an anti-keyboard, you could extract energy from it by lowering it into a black hole. You could extract this energy in principle the same way as you could extract energy from a dropping weight, by having it turn a gearshaft that cranks a generator or whatever.

If you had a strong enough cable, you could in theory extract the entire amount of energy from it, but any sort of realistic cable would break.

 

[PAllen]

A quarter teaspoon of water plus a quarter teaspoon of anti water would yield an explosion approximately twice the energy of the atomic bomb dropped on Nagasaki in WW II.

 

[Nugatory]

But where exactly is this energy present in real life?

If you look closely at any reaction that releases energy, you will find that the mass of the material coming out is very slightly less than the mass of the material that went in (and the other way around for a reaction that consumes energy, like charging a battery). For example, if I burn a chunk of wood... the weight of the wood plus the weight of the oxygen from the air will be very slightly more than the weight of the ashes and the gases released by combustion. The difference is exactly what you'd calculate from the energy change using the $E=\gamma{m}c^2$ formula (easiest if everything is at rest so $\gamma=1$, of course).

So the best answer for where the energy is will be something along the lines of "the mass is the energy, just in a different form".

As a practical matter, only nuclear reactions involve enough energy for the effect to be detectable; $c^2$ is a very big number. For example, a lead-acid automobile battery weighs only a few nanograms more when charged than discharged.

 

[Herman Trivilino]

Because it's a big amount of energy in small mass bodies,

No, it's not. The rest energy is equivalent to the mass, so it doesn't make sense to say that one is larger than the other.

 

[nitsuj]

No, it's not. The rest energy is equivalent to the mass, so it doesn't make sense to say that one is larger than the other.

I found it clear that they were referring to energy density, not a stress energy tensor

 

[nitsuj]

But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

Read about the constituents of an atom. It's really neat, allot of it (mass in "real life") is kinetic energy of quarks (things that form protons neutrons) bound by gluons; this is the strong nuclear force.

there's also such a thing as a nuclear battery, weak nuclear not strong...using tritium beta decay! That's hydrogen turning into helium "exactly" over time.

with both fission and fusion we can (potentially) do work.

there was allot of added info in the replies.

Yes to "power the world"; interesting political topic regarding nuclear power...far to complicated for discussion in a physics thread :D

 

[Sorcerer]

I found it clear that they were referring to energy density, not a stress energy tensor

May I ask how that matters with respect to the equation in question? If the rest energy is equivalent to the mass, then they are one and the same. It's not like the left side of the equation takes up more volume than the right side, or something like that. I mean, does it make sense to ask if mass*acceleration is larger than force? So yeah, your response has confused me somewhat. Would you care to elaborate why Mr. T is wrong?

 

[stevendaryl]

A pet peeve of mine about $E = mc^2$ is that people often say that nuclear reactions are demonstrations of that formula, that the reason that so much energy is produced in an atomic explosion is because matter is being turned into energy. I consider that both true and misleading.

The facts for nuclear fusion is that there is a transformation that looks like this (yes, I know, that is not the way that fusion happens, directly, but I'm just simplifying for illustration)

$4H \Rightarrow He + 2 \bar{\nu_e}$

The fact that this reaction is exothermic (the total energy of the right-hand side is less than the total energy of the left hand side) is what makes it possible for fusion to produce energy. I don't see that it essentially involves $E = mc^2$ any more than the chemical reaction

$2H + O \Rightarrow H_2 O$

The relevance of $E = mc^2$ is that if you measure the total mass of the products on the right-hand side, it will be slightly less than the total mass of the constituents on the left-hand side. But that's as true for the chemical reaction as it is for the nuclear reaction: Water has slightly less mass than the hydrogen and oxygen atoms it was made of. I don't see why the nuclear process is an example of matter being turned into energy any more than the chemical process is.

 

[Orodruin]

I don't see why the nuclear process is an example of matter being turned into energy any more than the chemical process is.

A pet peeve of mine is that matter is not being turned into energy. It is converted from one form of energy (mass energy) to another (kinetic energy in the products that in the end goes to heat).

 

[stevendaryl]

A pet peeve of mine is that matter is not being turned into energy. It is converted from one form of energy (mass energy) to another (kinetic energy in the products that in the end goes to heat).

But I would say that it's not really doing that, either. I would say that in both nuclear and chemical processes, it's a matter of binding energy, rather than mass energy. If you have a nucleus with N protons and M neutrons, in some cases a neutron can transform to a proton + electron + anti-neutrino + kinetic energy, and sometimes a proton can transform to a neutron + positron + neutrino + kinetic energy. The reason one or the other is favored is because of the binding energy for nucleons (which involves both strong forces and electromagnetic forces). So it's really a matter of converting potential energy into kinetic energy, just like chemical processes.

 

[nitsuj]

May I ask how that matters with respect to the equation in question? If the rest energy is equivalent to the mass, then they are one and the same. It's not like the left side of the equation takes up more volume than the right side, or something like that. I mean, does it make sense to ask if mass*acceleration is larger than force? So yeah, your response has confused me somewhat. Would you care to elaborate why Mr. T is wrong?

their statement wasn't wrong at all, the interpretation of the question was. Mister T has allot of great replies to questions and has enlightened me a number of times.

To be even more clear, surely the OP is, like the vast majority of people, used to "chemical energy", and in turn the concept of energy density.

They are not "one and the same", they are equivalent...clearly on opposite sides of the equation.

 

[nitsuj]

But I would say that it's not really doing that, either. I would say that in both nuclear and chemical processes, it's a matter of binding energy, rather than mass energy. If you have a nucleus with N protons and M neutrons, in some cases a neutron can transform to a proton + electron + anti-neutrino + kinetic energy, and sometimes a proton can transform to a neutron + positron + neutrino + kinetic energy. The reason one or the other is favored is because of the binding energy for nucleons (which involves both strong forces and electromagnetic forces). So it's really a matter of converting potential energy into kinetic energy, just like chemical processes.

So the distinction between one being a nuclear force and the other being em force is moot, because with either we use the work in the same way ?

 

[stevendaryl]

So the distinction between one being a nuclear force and the other being em force is moot, because with either we use the work in the same way ?

The big distinction that I see between common nuclear reactions and chemical reactions is that in the case of chemical reactions, you can think of the transformation as a rearrangement of constituent particles. In contrast, when a neutron transforms into a proton + electron + anti-neutrino, it's not literally the case that it's just a rearrangement of constituent particles. (There is no proton or electron or neutrino inside a neutron).

That's something new with nuclear physics: transformations that are not just rearrangements of constituents. But I would still say that in nuclear reactions, it's the binding energy that makes the reaction go, rather than converting rest mass energy into kinetic energy.

Let's take two different nuclear reactions:

1. $^{14}C \Rightarrow ^{14}N + e + \bar{\nu_e}$: Carbon 14 decays into Nitrogen
2. $^{23}Mg \Rightarrow ^{23}Na + e^+ + \nu_e$. Magnesium 23 decays into Sodium

Now, let's combine the two reactions into one:

$^{14}C +\ ^{23}Mg \Rightarrow\ ^{14}N +\ ^{23}Na$

That's a nuclear reaction which is possible (though extremely unlikely) that is simply a rearrangement of protons and neutrons. In this case, it's much more like a chemical reaction: A rearrangement of constituent particles results in a lower total energy, so it releases some kinetic energy. But to me, it doesn't make sense to say that the first two reactions involve transmuting rest mass energy into kinetic energy, but the last one does not. But if you say that the latter illustrates converting rest mass energy into kinetic energy, then I don't see how that description wouldn't apply equally well to chemical reactions.

To me, the lesson from $E=mc^2$ is that if you have a reaction that releases kinetic energy, then the rest mass of the products will be less than the rest mass of the original ingredients. That's true of chemical reactions as well as nuclear reactions.

 

[martinbn]

Since we are talking about peeves, I have this one. It bothers me that people say things like "matter is turned in this or that" or "matter is equivalent/equal to so and so". The $m$ in the equation stands for mass, matter is not mentioned at all.

 

[stevendaryl]

Since we are talking about peeves, I have this one. It bothers me that people say things like "matter is turned in this or that" or "matter is equivalent/equal to so and so". The $m$ in the equation stands for mass, matter is not mentioned at all.

Matter is just an informal word meaning stuff that has mass, isn't it?

 

[martinbn]

Matter is just an informal word meaning stuff that has mass, isn't it?

If that is the case, then matter can have energy but cannot be energy.

 

[Orodruin]

I would say that in both nuclear and chemical processes, it's a matter of binding energy, rather than mass energy.

That depends on what you mean by "mass energy". As the mass of the original systems it is certainly a mass energy of, e.g., the incoming O2 molecule. If you further subdivide that you can say that the mass energy of the molecule has several contributions. It is all a question of what level you do your bookkeeping at.

If that is the case, then matter can have energy but cannot be energy.

Nothing can be energy. Energy is a property, not a substance.

 

[stevendaryl]

That depends on what you mean by "mass energy". As the mass of the original systems it is certainly a mass energy of, e.g., the incoming O2 molecule. If you further subdivide that you can say that the mass energy of the molecule has several contributions. It is all a question of what level you do your bookkeeping at.

My point is to dispute that nuclear reactions involve transforming mass energy into kinetic energy any more than chemical reactions do.

 

[martinbn]

Nothing can be energy. Energy is a property, not a substance.

That is exactly my point.

 

[SiennaTheGr8]

That depends on what you mean by "mass energy". As the mass of the original systems it is certainly a mass energy of, e.g., the incoming O2 molecule. If you further subdivide that you can say that the mass energy of the molecule has several contributions. It is all a question of what level you do your bookkeeping at.

"Bookkeeping" is a great word to use here.

I don't view the mass of a composite system as a form of energy, per se. Rather, it's the total energy of the system as measured in its rest frame, equal to the sum of the kinetic, potential, and rest energies (masses) of the system's constituents (as measured in that frame)—and the same applies to the masses of the constituents, and to the masses of the constituents' constituents, and so on, until you get to the elementary particles, whose mass is fundamental and certainly a "form" of energy.

So yes, I'd say that the mass of a composite system is more a "bookkeeping" device than a "form" of energy. But it's also convenient when taking an "outside" view to speak of a system's mass as energy that can be converted to other types of energy. For this purpose, I think "type" is a better word than "form."

My take on the pet peeves:

-"Mass is converted to energy." No, mass already is energy (rest energy). Rest energy can be converted to other types of energy. In matter/antimatter annihilation, for example, the mass of elementary particles is converted to kinetic/electromagnetic energy (and the elementary particles cease to exist). In chemical and nuclear reactions, we can take an "outside" view and say that mass of the composite system is converted to kinetic energy, or we can take an "inside" view and say that potential energy is converted to kinetic energy.

-"Matter is converted to energy." No, the energy in question was already a property of the "matter." Closer to the mark is "matter is converted to radiation," but even then one needs to carefully define both "matter" and "radiation."

 

[jbriggs444]

"Bookkeeping" is a great word to use here.

Feynman's metaphor for energy as blocks resonates with me.
http://www.feynmanlectures.caltech.edu/I_04.html
Especially the punch line: "The most remarkable aspect that must be abstracted from this picture is that there are no blocks."

 

[ZapperZ]

My take on the pet peeves:

-"Mass is converted to energy." No, mass already is energy (rest energy). Rest energy can be converted to other types of energy. In matter/antimatter annihilation, for example, the mass of elementary particles is converted to kinetic/electromagnetic energy (and the elementary particles cease to exist). In chemical and nuclear reactions, we can take an "outside" view and say that mass of the composite system is converted to kinetic energy, or we can take an "inside" view and say that potential energy is converted to kinetic energy.

-"Matter is converted to energy." No, the energy in question was already a property of the "matter." Closer to the mark is "matter is converted to radiation," but even then one needs to carefully define both "matter" and "radiation."

Mass is NOT "already energy". The dimensions are wrong! Not only that, a "mass" may carry charge, while energy can't! You are looking at it simply from ONE characteristic (energy equivalent) and then making wholesale conclusion that they are one of the same thing while ignoring other differences between mass and energy. There are OTHER things involved in the "bookkeeping", not just amount of energy.

To the OP and the original question, the "missing mass" that we get when we measure the mass of atoms is our everyday illustration of energy-mass conversion. Take the individual mass of an electron, a proton, a neutron, and then add them all together in the appropriate amount to form all the various elements in the periodic table. Then compare those masses that you have added to the actual masses of each individual element. They are not identical!

Zz.

 

[Orodruin]

Mass is NOT "already energy". The dimensions are wrong! Not only that, a "mass" may carry charge, while energy can't! You are looking at it simply from ONE characteristic (energy equivalent) and then making wholesale conclusion that they are one of the same thing while ignoring other differences between mass and energy. There are OTHER things involved in the "bookkeeping", not just amount of energy.

I strongly disagree with essentially everything in this paragraph. First of all, ”mass” is not a thing and does not in any sense relate to being able to carry charge. It is a property of a system, just as energy is. Second, it does have the correct dimensions as long as you stick to a reasonable system of dimensions where spacetime coordinates all share the same dimension such that speeds are dimensionless. That it happens to be convenient for everyday use to use a different unit for it such that the conversion factor is c^2 is a different matter. I agree that there are more things to bookkeep, but the mass goes into the energy bookkeeping and nowhere else. Charge is a separate property. Both mass and energy are properties of a system, not anything that in itself can carry other properties.

 

[ZapperZ]

I strongly disagree with essentially everything in this paragraph. First of all, ”mass” is not a thing and does not in any sense relate to being able to carry charge. It is a property of a system, just as energy is. Second, it does have the correct dimensions as long as you stick to a reasonable system of dimensions where spacetime coordinates all share the same dimension such that speeds are dimensionless. That it happens to be convenient for everyday use to use a different unit for it such that the conversion factor is c^2 is a different matter. I agree that there are more things to bookkeep, but the mass goes into the energy bookkeeping and nowhere else. Charge is a separate property. Both mass and energy are properties of a system, not anything that in itself can carry other properties.

And I disagree with your assessment that they are. That's like saying water in liquid form is identical to water in ice form, while ignoring the phase transition between them. The mass of an electron is more than just an energy content. It's presence in itself immediately puts a limit to how fast it can move in any frame. It is not a merely a superficial difference.

Because of that (i.e. they are not identical), it should not be wrong or even be someone's pet peeve to say that there is a form of "conversion" when it goes from one form to another, especially when now, it is a matter of semantics! And that was what I was addressing.

Zz.

 

[SiennaTheGr8]

Mass is NOT "already energy".

Do you agree that "rest energy" $E_0$ is "already energy"?

 

[ZapperZ]

Do you agree that "rest energy" $E_0$ is "already energy"?

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

 

[Orodruin]

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

No. It is just a matter of unit conversion in terms of the actual SR definitions, which defines mass as the rest energy up to the unit conversion factor $c^2$. That the rest mass then happens to be the inertia in the rest frame is the mass-energy equivalence.

 

[SiennaTheGr8]

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

Yes, but the $c^2$ in the equation $E_0 = mc^2$ is no more than a unit-conversion factor, which we're free to set equal to $1$. The distinction between mass and rest energy is merely an artifact of unnecessarily using different units for energy and mass in the first place. There is no conceptual difference between the quantities at all. They are one and the same property, measured in different units.

 

[Orodruin]

The mass of an electron is more than just an energy content.

It really isn't in terms of how mass is defined in SR.

 

[ZapperZ]

No. It is just a matter of unit conversion in terms of the actual SR definitions, which defines mass as the rest energy up to the unit conversion factor $c^2$. That the rest mass then happens to be the inertia in the rest frame is the mass-energy equivalence.

Yes, but the $c^2$ in the equation $E_0 = mc^2$ is no more than a unit-conversion factor, which we're free to set equal to $1$. The distinction between mass and rest energy is merely an artifact of unnecessarily using different units for energy and mass in the first place. There is no conceptual difference between the quantities at all. They are one and the same property, measured in different units.

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c² "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Please keep in mind that you're talking to someone who is very familiar with calling "ω" or "1/k" as "binding energy". So I get it! But how this fits into the thread at the level that the OP is asking is puzzling, and invoking advanced ideas of mass and energy into something like this is very confusing.

Zz.

 

[SiennaTheGr8]

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c² "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Then are $v$ and $\beta=v/c$ physically different quantities? Are $t$ and $ct$? $p$ and $pc$?

But how this fits into the thread at the level that the OP is asking is puzzling, and invoking advanced ideas of mass and energy into something like this is very confusing.

Yes, this conversation might be better suited for another thread. Cheers.

 

[Orodruin]

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c2 "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Do you also consider time and length to have different dimension? In that case you are missing out on one of the greatest insights of SR. The entire point is that length and time depend on perspective and intrinsically are just a matter of defining directions in a Lorentzian manifold.

To me $c$ in relativity is nothing but a unit conversion factor between things that have the same dimension, just as $k = 2.54$ cm/inch is a conversion factor between different length units.

 

[PeterDonis]

there is a physical difference between "energy" and "mass" from my perspective.

I'm not sure what you think the difference is. For example, when you say:

Take the individual mass of an electron, a proton, a neutron, and then add them all together in the appropriate amount to form all the various elements in the periodic table. Then compare those masses that you have added to the actual masses of each individual element. They are not identical!

This is true, but it leaves out something: where did the difference in mass go? There is still a conservation law involved, so it couldn't just disappear.

In a typical process of this sort--individual constituents coming together to form a bound system--the difference ends up in radiation that is emitted by the system. But "energy" is not synonymous with "radiation": it's a property of radiation (for example, a bunch of photons) just as much as it's a property of "matter" (stuff like electrons, protons, and neutrons). So what is the difference?

The mass of an electron is more than just an energy content. It's presence in itself immediately puts a limit to how fast it can move in any frame.

Here it seems like the key difference is that the electron has nonzero rest mass, while the photon has zero rest mass. (Or, to put it in more fundamental terms, an electron has a timelike 4-momentum, while a photon has a null 4-momentum.) I'll agree that this is a physical difference, but I'm not sure it lines up with the difference between "mass" and "energy".

 

[ZapperZ]

This is true, but it leaves out something: where did the difference in mass go? There is still a conservation law involved, so it couldn't just disappear.

In a typical process of this sort--individual constituents coming together to form a bound system--the difference ends up in radiation that is emitted by the system. But "energy" is not synonymous with "radiation": it's a property of radiation (for example, a bunch of photons) just as much as it's a property of "matter" (stuff like electrons, protons, and neutrons). So what is the difference?

I didn't say there isn't a conservation law here. The "mass difference" is the example I was giving the OP that the missing mass goes into the nuclear binding energy of the atom, i.e. a "real life example" (remember the original title?).

I'm surprised I'm being given a lesson in this. This is a standard General Physics material in an undergraduate textbook.

Zz.

 

[PeterDonis]

The "mass difference" is the example I was giving the OP that the missing mass goes into the nuclear binding energy of the atom.

But it doesn't; the binding energy is negative* (because the mass of the nucleus is less than the sum of the masses of the constituents). So, heuristically, the binding energy gets "taken out" of the constituents, and has to go somewhere else. Where does it go? That's the question I asked (and answered for a typical process), and which has to be answered to see how conservation laws are satisfied.

[*Edit: Negative if we're using the implicit sign convention we've been using, which is different from the sign convention that is often used for binding energy in textbooks.]

I'm surprised I'm being given a lesson in this. This is a standard General Physics material in an undergraduate textbook.

The process itself is, yes. But I'm trying to understand what, specifically, you think the physical difference between "energy" and "mass" is. I don't think that specific question is treated in undergraduate textbooks (and as you can see, I'm not the only one in this thread who is asking it).

 

[ZapperZ]

But it doesn't; the binding energy is negative* (because the mass of the nucleus is less than the sum of the masses of the constituents). So, heuristically, the binding energy gets "taken out" of the constituents, and has to go somewhere else. Where does it go? That's the question I asked (and answered for a typical process), and which has to be answered to see how conservation laws are satisfied.

[*Edit: Negative if we're using the implicit sign convention we've been using, which is different from the sign convention that is often used for binding energy in textbooks.]

OK... I do not see why this is an issue. This is the reason why the mass of the atom is less than the mass of the individual constituents added together. Isn't this a clear example of E=mc² that the OP was asking waaaaaaaay back in Post #1? I gave that example not to show the difference between mass and energy, but to provide a simple example that the OP might be able to understand.

The process itself is, yes. But I'm trying to understand what, specifically, you think the physical difference between "energy" and "mass" is. I don't think that specific question is treated in undergraduate textbooks (and as you can see, I'm not the only one in this thread who is asking it).

But I've already stated earlier about the specific limits to speed in mass, etc., which Orodruin disagreed. But go back to why I got into this in the first place. It was because of the semantic reason that somehow describing the process that energy and mass can be converted into another becomes a "pet peeve"! Considering the level of this thread, I argued that it should not be! Trying to get e-p pair out of gamma photons is a painful "conversion"! And in the back of my mind, I'm reminded of all the threads that we've had on this forum of people claiming that electrons, etc. are nothing more than just clumps of energy, while ignoring all the other attributes associated with these particles beyond just the energy content. Maybe it is silly to think about what someone could use this thread for later on, but it won't be the first time that someone misunderstands a thread on here.

Zz.

 

[PeterDonis]

Trying to get e-p pair out of gamma photons is a painful "conversion"!

Sure. But is it a conversion of "mass" to "energy"? Or is it a conversion of, well, an e-p pair into a pair of gamma photons? The latter description seems to me to be much less subjective, as well as less likely to be misunderstood.

 

[ZapperZ]

Sure. But is it a conversion of "mass" to "energy"? Or is it a conversion of, well, an e-p pair into a pair of gamma photons? The latter description seems to me to be much less subjective, as well as less likely to be misunderstood.

But that plays right into what I said earlier that the conservation laws with these "mass-energy conversion" process involves more than just mass-energy conservation. Certainly, for e-p to gamma, you have charge and momentum conservations to take care of as well. I know that these are external issues to the mass-energy equivalent, but I'm looking at the entire process and consider that, semantically, I do not see why calling this a "conversion" is wrong or make it someone's pet peeve. I mean, I don't go around and announcing that it is my pet peeve when someone claims that photon energy less than a work function cannot emit a photoelectron, even though I have done it numerous times! At some point, the level of the discussion (and the OP) requires us to hold back the whole, advanced picture.

Zz.

 

[SiennaTheGr8]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

 

[ZapperZ]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

 

[Orodruin]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

The big problem is that "energy" in many layman conversations refer to "usable energy" in the sense of energy available to do work on something I need to do work on. This often translates into laymen thinking that energy is some sort of substance that can be produced.

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

I do not think it is to be overly picky. The misconception that energy is some form of substance is a something that it takes years to pull out of many university students.

 

[SiennaTheGr8]

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

Please do! It might help someone who's struggling to understand this stuff.

 

[Sorcerer]

their statement wasn't wrong at all, the interpretation of the question was. Mister T has allot of great replies to questions and has enlightened me a number of times.

To be even more clear, surely the OP is, like the vast majority of people, used to "chemical energy", and in turn the concept of energy density.

They are not "one and the same", they are equivalent...clearly on opposite sides of the equation.

Well, in terms of the equation. What is mass? Energy ultimately is just a concept, but so is mass. It's mostly space, made up of little sub-atomic particles, and of course, energy, and what are those exactly? What are they made of? Quarks, etc?

Obviously that's unanswered at the moment. But I mean, point is, why and how could one be larger than the other? What does "larger" even mean in that context? Magnitude? (mc²)² literally IS the magnitude of the energy-momentum equation, isn't it?
E² - (pc)² = (mc²)², right?

 

[nitsuj]

Well, in terms of the equation. What is mass? Energy ultimately is just a concept, but so is mass. It's mostly space, made up of little sub-atomic particles, and of course, energy, and what are those exactly? What are they made of? Quarks, etc?

Obviously that's unanswered at the moment. But I mean, point is, why and how could one be larger than the other? What does "larger" even mean in that context? Magnitude? (mc²)² literally IS the magnitude of the energy-momentum equation, isn't it?
E² - (pc)² = (mc²)², right?

 

[sweet springs]

As a real life example nuclear fuel get lighter after spent in power station.