I have been told that energy and mass are the same. What puzzles me is why don't we use the same units of measure for both if they are the same? The unit of mass is kg and the unit of energy is the joule or kg(m/s)² Why the different units of measurement if they are the same thing?
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2$\begingroup$ This is a very bad shortcut. For starters, mass is a Lorentz-invariant, while energy isn't. They are related, but not always identical, and their respective units differ (except in very specific unit systems). You should read about the energy-momentum tensor to refine your question. $\endgroup$– MiyaseCommented Jan 15 at 14:49
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1$\begingroup$ Related: "Is electronvolt a mass or an energy unit?". $\endgroup$– David BaileyCommented Jan 15 at 16:53
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2$\begingroup$ "I have been told that energy and mass are the same." Well, whoever told you that is wrong. $\endgroup$– hftCommented Jan 15 at 17:48
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1$\begingroup$ Voting to reopen. This is a perfectly clear question with some good answers below. It is based on a misunderstanding, but that is not a reason to close a question. $\endgroup$– gandalf61Commented Jan 16 at 10:52
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3$\begingroup$ @Gerry if you want to ask a new question then create a new one, rather than editing the title of your old question $\endgroup$– Eric SmithCommented Jan 17 at 1:22
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8 Answers
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Energy and mass are not the same thing. They are related to each other and the momentum by $$m^2 c^2=E^2/c^2-p^2$$ Both $E$ and $p$ depend on the choice of coordinates, whereas $m$ is invariant. This means specifically that $E$ and $p$ depend on the speed, but $m$ does not.
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$\begingroup$ Now if I write $p_{\mu} = (T+m, \vec p)$ where $T$ is kinetic energy, $p_0$ is ofc not Lorentz invariant, but $m$ still does not depend on frame, so it's kind of invariant (though not manifestly, here)...and it's in the "energy" slot... $\endgroup$– JEBCommented Jan 15 at 15:18
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1$\begingroup$ @JEB Just noting that that should be $p_\mu = (T/c + mc, \vec{p})$ if we're keeping $c$ $\endgroup$ Commented Jan 15 at 15:26
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$\begingroup$ Thank you Dale. I don't have your math background but I can see the distinction conceptually. Mass is a genus of measurement with units of measurement like kg, lb, etc. The phenomenon that goes with that quantitative concept is called matter. One of the things that distinguish matter from non-matter is mass, which is why I get confused when I hear that masscan be covered into energy. It's like saying a pound can be converted into a mile. The better question is can matter be converted into energy? Better yet, if matter is a form of energy, can that form of energy which we call matter be c $\endgroup$– GerryCommented Jan 17 at 0:02
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$\begingroup$ @Gerry Matter is not a form of energy. Energy is a system property. You can more or less take an arbitrary subdivision of the universe and assign an arbitrary amount of energy to it. All you have to do is to pick the "right" observer and the right interaction. Matter and radiation are excitations of the vacuum that you can interact with. You can't interact with energy. Energy is that which describes the interaction. Ontologically these terms are not even in the same category. $\endgroup$ Commented Jan 17 at 0:58
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$\begingroup$ @Gerry regarding the idea of converting mass into energy, I think it is incorrect as explained here: physics.stackexchange.com/questions/518938/… $\endgroup$– DaleCommented Jan 17 at 2:16
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Mass is energy in the rest frame divided by c$^2$. If you use units with c=1 then mass and energy are the same, but only in the rest frame. The now obsolete concept of 'relativistic mass' is energy divided by c$^2$. This may cause confusion hence the concept is no longer used.
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$\begingroup$ What I'm really after is whether matter is energy, not whether mass is energy. Mass refers specifically to one of matter's quantitative properties There's a tendency to use the terms interchangeably (I make this error all the time) because they're so closely connected. I don't know if you are using matter and mass interchangeably, but if you are, you are saying that matter is energy when it is at rest and it's not energy when it's not at rest? More likely, you are saying that the amount of mass is equal to the amount of energy when an object is at rest. $\endgroup$– GerryCommented Jan 15 at 23:39
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It's not true that energy and mass are the same. It's more accurate to say that mass is a form of energy.
As for why they have different units, they don't always (e.g. the masses of elementary particles are usually given in electron volts, a unit of energy). Historically though the units in everyday use were defined before Einstein discovered the connection between energy and mass. We still use them because they are convenient, and because usually the energy due to mass is vastly greater than other energies, to the point that it would be awkward to express mass in terajoules or kinetic energy in picograms.
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$\begingroup$ Thank you for all your answers. People who profess to know physics are always telling me that energy and matter are the same, but I have always suspected that relationship to be a bit more complicated than one of simple identity. I appreciate your confirmation. $\endgroup$– GerryCommented Jan 15 at 20:30
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$\begingroup$ So you're saying we COULD express both energy and mass using the same units, e.g., the eV, in the equation, E = mc². We just don't do that for practical reasons? $\endgroup$– GerryCommented Jan 15 at 21:00
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1$\begingroup$ We can express mass and energy using the same units, and particle physicists do for practical reasons. I have no idea what the mass of an electron is in kg, but I do know it's 511 kilo eV $\endgroup$ Commented Jan 17 at 15:53
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I'm coming in on this after a few answers are already there, but I think nobody has got to grips with it properly. The point about the mass--energy equivalence is that two physical ideas which had been thought to be separate (namely, internal energy and inertia) turn out to be so intimately related that they amount to being two versions of one thing, not two separate physical properties after all.
Dale correctly points out that rest mass does not depend on inertial frame, whereas energy does, and one can write: $$ (m c^2)^2 = E^2 - p^2 c^2 . $$ When $p=0$ we get $E = m c^2$. The equivalence is between rest energy and rest mass (up to a factor of $c^2$). This does amount to a profound equivalence, because it means that if we provide energy to a body (e.g. by heating it up, or by compressing a spring) then the resulting body will have a larger inertia. That was entirely unexpected from classical physics and it is a profound insight. It leads to the suggestion that the mass of ordinary objects might be entirely from the energies in the fields associated with massless particles. It turns out that that is not quite true, but it almost is: if one invokes a kind of 'QCD light' field theory with zero rest mass for quarks then the rest masses of protons and neutrons don't change by much.
The central point about mass--energy equivalence is, then, that things with more internal energy are heavier, and if they give up internal energy they get lighter. This affects the mass of a molecule compared to the constituent atoms, and (a bigger effect) the mass of an atomic nucleus compared to the constituent nucleons. This is the ordinary mass, which is a measure of response to force, which is why I have written about inertia in the above.
answered Jan 17 at 16:21
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Units are somewhat arbitrary--I mean just look at the stat-Coloumb.
They have to make sense, ofc, but there is still a lot of leeway.
I think it's not too difficult to figure out why we measure time differently from length, since Les Metric System predates relativity, but you don't have to, so you can choose $c=1$, et voila:
$$ E = mc^2 \rightarrow E = m1^2$$
or $$ E = m $$
which is why we say mass and energy are equivalent.
Basically, $mc^2$ is the minimum energy required to make a particle of mass $m$ at rest, and that $m$, the inertia associated with is not "stuff" resisting motion...it's the energy, but since it's energy with zero momentum we kind of think of differently from other types of energy--but it's not.
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1$\begingroup$ I think setting $c=1$ is the source of the confusion. Rigorously, it should be $c = 1\ \text{m/s}$, or whatever units, and the units need to be carried through. Then, it can be seen that they aren't equivalent but are scaled to be numerically the same. $\endgroup$– Dr. NateCommented Jan 15 at 19:55
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$\begingroup$ If I set c to 1, I get the amounts would be equivalent, but that wouldn't mean the units are equivalent, so we still need to carry the units thru as Dr Nate is saying. If I were to ask the same question about speed and distance, I would think the reason we use different units is because they aren't the same even though they have quantitative relationships, that the difference is a result of something qualitative. That's not alway true. I could say that x kilograms = y pounds without there being any qualitative differences in what is being measured. $\endgroup$– GerryCommented Jan 15 at 20:54
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$\begingroup$ @gerry It's called natural units. there is nothing wrong with $c=1$ and measuring time in feet. One foot is a nanosecond. $\endgroup$– JEBCommented Jan 16 at 7:11
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The confusion between energy and mass is common because $E=mc^2$ is the most famous equation in physics, and special relativity chapters in high-school level physics textbooks often only talk about relativistic mass, which actually is essentially equivalent to energy:
$$m_{\mathrm{rel}}\equiv E/c^2= \frac{m_0}{\sqrt{1 - \dfrac{v^2}{c^2}}}$$
When professional physicists refer to "mass", however, we pretty much always are referring to the invariant/rest mass:
$$m_0\equiv \sqrt{E^2-p^2c^2}/c^2$$
The values of energy $E$ and momentum $p$ depend on the reference frame in which they are measured, but this invariant mass is the same in all reference frames.
So invariant mass and energy are not the same, but they do have the same units in systems of natural units where it is defined that $c=1$. For example, except in pedagogical or formal contexts, particle physicists pretty much always use electron volts as the unit for both energy and (invariant) mass.
It is perhaps worth noting that you are in good company in your confusion. There has been philosophical disagreement about whether mass and energy are distinct properties, and eminent thinkers such as Arthur Eddington and Roberto Torretti have argued that mass and energy actually are the same and should be measured in the same units.
answered Jan 15 at 20:47
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$\begingroup$ Who takes the action to update the high school books? $\endgroup$– my2ctsCommented Jan 17 at 12:06
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1$\begingroup$ @my2cts Somewhat to my surprise, the Texas State Board of Education (which traditionally has an outsize impact on school textbooks) might be doing this for you. Their current learning objectives include requiring students to be able to "Explain why the only mass it makes sense to talk about is rest mass". $\endgroup$ Commented Jan 17 at 16:16
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Since the title of the question was changed after I submitted my answer, here is my new answer to the new title, which no longer agrees with the body of the post.
Matter is not the same as energy. Energy is a property of matter, but so is mass, momentum, angular momentum, spin, charge, lepton/baryon number, strangeness etc. These properties are conserved which limits the possibilities to convert one form matter to another. A proton cannot decay to an electron because charge, baryon number and lepton number are conserved. Alternatively put, physicists put forward these properties to describe a world in which this reaction is prohibited.
Still a good question, though.
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First of all you should know what is mass? Previously before the formulation of Higgs field into the known quantum fields, it was not known, it was thought to be as a fundamental thing like electric charge is a fundamental thing. But in the equations we only had massless particles, to give them mass Professor Higgs assumed an existence of scalar doublet field called Higgs field, which allows extra terms in the theory to account for masses of elementary particles. And as we go into the details of physics of these masses we can find that these masses are just interaction energy packets associated with the Higgs and elementary particle fields. So it turns out to be a form of energy which is a property of the particles. These masses can be converted to equivalence energy by the famous E = mc^2. Einstein's realisation of this mass energy equivalence was independent of how i explained you here. More examples include decay processes where the parent particle can be changed to other doughter particles, here some of the mass can convert into released energy.
