Why Does E=mc^2? (Synopsis)

“Science is global. Einstein’s equation, E=mc^2, has to reach everywhere. Science is a beautiful gift to humanity, we should not distort it.” -A.P.J. Abdul Kalam

Over 100 years ago, Einstein shook up the physics world with a number of groundbreaking discoveries: special relativity, brownian motion, the photoelectric effect, and his most famous equation, E = mc^2. This mass-energy equivalence underlies everything from antimatter to atomic bombs to the process that powers the Sun.

The longer a photon's wavelength is, the lower in energy it is. But all photons, regardless of wavelength/energy, move at the same speed: the speed of light. Image credit: NASA/Sonoma State University/Aurore Simonnet.

The longer a photon’s wavelength is, the lower in energy it is. But all photons, regardless of wavelength/energy, move at the same speed: the speed of light. Image credit: NASA/Sonoma State University/Aurore Simonnet.

Yet our Universe didn’t have to have this relation; energy could have been equal to any constant times mass times the speed of light squared. Yet if you demand that both energy and momentum are conserved in any interactions, that freedom goes away, and E = mc^2 becomes, once again, your only option.

Mass-energy conversion, with values. Image credit: Wikimedia Commons user JTBarnabas.

Mass-energy conversion, with values. Image credit: Wikimedia Commons user JTBarnabas.

Come get the story on why Einstein’s most famous equation is the way it is, and can’t be otherwise!

Comments

  1. #1 Demetris
    Greece
    May 27, 2016

    first I would like to tell you how much i enjoyed reading your book “Beyond the Galaxy” Although i have a background of studies in Physics and have read many
    popular science books about Cosmology your book help me to put all the pieces of the puzzle together.

    Now i just finished reading your last column ” Why Does E=mc^2?”
    where you write “Conserving energy and momentum both seems to be something our Universe requires, and that’s why E = mc^2”.

    My question is: Do we have an explanation today in Physics of why the Universe “requires” the conservation laws. In other words:

    Why the Universe has the laws it has?

    Greetings from Greece
    (and do come to the Greek islands for holidays some time!)

    Demetris

  2. #2 See Noevo
    May 27, 2016

    If E=mc^2, how can photons have energy if they’re massless?

  3. #3 Narad
    May 27, 2016

    If E=mc^2, how can photons have energy if they’re massless?

    Oh, L-rd, I needed a good laugh.

  4. #4 Narad
    May 27, 2016

    ^ Not that it would be a bad question coming from someone legitimately asking, as opposed to a moronic troll who simultaneously pretends to scientific expertise, e.g.,

    Are you telling me you have the details of stellar evolution worked out?
    That you know *for a fact* how stars and stellar structures came to be?
    Because I’m pretty sure I’ve read cosmologist [sic] accounts of various problems with, and multiple theories of, star formation.

    (Note the failure to even understand the difference. One might also wonder whether S.N. is also obliquely trying to reuse the 45-year-old reference that he attempted to trot out earlier. Then again, “for certain values of” automatically applies to “I’ve read” in this case, anyway.)

  5. #5 Kay Brown
    sillyolme.wordpress.com
    May 27, 2016

    Narad (#2)… I’m not laughing…. this guy is more than clueless, the clue agency won’t let him rent one either…

    photons are NOT “massless” they are “rest-mass-less”

    This equation doesn’t just say that energy can be converted… in fact, that’s the wrong way to think of it… it says that energy and mass are the same STUFF… energy has a mass… photons have a mass. The earth intercepts 2kg of mass every day, in the form of sunlight.

    Another way of thinking of this is that we calculate the kinetic energy of an object in motion in relation to our observer’s reference frame as Ek=MV^2… note the similarity… if we then think of all of the mass M as a photon, then E=Mc^2… because a photon always travels at the speed of light c. Get it?

    Arghhh!!!

  6. #6 Narad
    May 27, 2016

    photons are NOT “massless” they are “rest-mass-less”

    No, they’re massless. S.N. doesn’t understand that the complete formula has a momentum term.

  7. #7 See Noevo
    May 27, 2016

    To Kay Brown #5:

    “I’m not laughing…. [See Noevo] is more than clueless, the clue agency won’t let him rent one either…
    photons are NOT “massless”…”

    Kay, is Ethan clueless as well?
    In his Forbes article, Ethan writes
    “There are totally massless things in the Universe: light, for instance.”

  8. #8 Kay Brown
    sillyolme.wordpress.com
    May 28, 2016

    OK, lets clear this up… from this link:

    https://profmattstrassler.com/articles-and-posts/particle-physics-basics/mass-energy-matter-etc/more-on-mass/the-two-definitions-of-mass-and-why-i-use-only-one/

    Is a photon (a particle of light) massless? or not?

    If you use “mass” as I do, the answer is YES. A photon is massless, and that’s why its speed is always at the universal speed limit c. Meanwhile an electron is not massless, and that’s why its speed is always below c. All electrons have a mass of 0.000511 GeV/c2.

    But if by “mass” you mean relativistic mass, the answer is NO. A photon ALWAYS has energy, so it always has a mass; no observer will ever see it as massless. The only thing that is zero is its invariant mass, also known as its rest mass. Each electron has its own mass; each photon has its own mass. An electron and a photon with the same energy have (in this definition) the same mass. In fact some photons have larger mass than some electrons, and other electrons have larger mass than other photons. Worse still, one observer might see a certain electron as having a larger mass than a certain photon, but a different observer may see it the other way round! So relativistic mass is a relative mess.

  9. #9 See Noevo
    May 28, 2016

    To Kay Brown #8:

    “Is a photon (a particle of light) massless? or not? If you use “mass” as I do, the answer is YES. A photon is massless… But if by “mass” you mean relativistic mass, the answer is NO… So relativistic mass is a relative mess.”

    You said it, sister.

    “OK, lets clear this up…”

    Well, as the old saying goes,
    ‘If you don’t have something nice to say, don’t say anything at all.’

    So, I won’t say anything at all.

    For now.

  10. #10 Michael Kelsey
    SLAC National Accelerator Laboratory
    May 28, 2016

    @Deceiver #7, #9: Your perennial arguments from ignorance do not “refute” science, they merely reinforce your willful ignorance and deception.

  11. #11 Narad
    May 29, 2016

    Well, as the old saying goes,
    ‘If you don’t have something nice to say, don’t say anything at all.’

    So, I won’t say anything at all.

    Anyone who has followed your comments on SB or Disqustink will immediately recognize the screaming dishonesty of this evasion.

  12. #12 Michael Kelsey
    SLAC National Accelerator Laboratory
    May 29, 2016

    @Narad #11: You know this poor, pathetic servant of the Great Deceiver will always say whatever he needs to say to further his Master’s agenda.

  13. #13 Abel Magwitch
    UK
    May 29, 2016

    What a bunch of pretentious wankers, arguing and bitching at each other. None of you would like to be seen in dispute over the best boy band in Croatia this year, but present a high profile conundrum whereby name dropping Planck or Appleton etc and you are up there condescending and belittling like teenagers on Facebook. Shame on you honey child.

  14. #14 me
    home
    June 1, 2016

    Narad, you are a condescending prick.

  15. #15 Wow
    June 3, 2016

    “My question is: Do we have an explanation today in Physics of why the Universe “requires” the conservation laws. In other words:

    Why the Universe has the laws it has?”

    Two different claims.

    The conservation law of energy is because of time symmeries. If energy was not conserved, you could not reverse a process, and time symmetry would be broken.

    The other symmetries of physics are the reasons for the other conservation laws.

    The other question is too broad and encompasses every law, not the one in discussion here and therefore either irrelevant or misleading.

  16. #16 Wow
    June 3, 2016

    “What a bunch of pretentious wankers, arguing and bitching at each other. ”

    Says someone bitching, arguing and moaning at eveyone here, BOTH SIDES.

    How pretentious a wanker must you be?

  17. #17 Michael Kelsey
    SLAC National Accelerator Laboratory
    June 3, 2016

    @Demetris #1: What you want to look up is “Noether’s Theorem” a mathematical (i.e., not just physics!) theorem which shows that when the Lagrangian (technically, the action, which is the integral of the Lagrangian) of a system has a symmetry, that symmetric has an associated conserved quantity.

    Time-translation symmetry (not time reversal) has energy as the associated conserved quantity. Spatial-translation symmetry has momentum as the associated conserved quantity. Rotational symmetry has angular momentum as the associated conserved quantity.

    All of this is a consequence that our Universe can be described by mathematical equations.

  18. #18 Narad
    June 3, 2016

    I take it that both “Abel Magwitch” and “me” are Philip Hills, Hope Osteopathic Clinic Essex.

  19. #19 Narad
    June 3, 2016

    All of this is a consequence that our Universe can be described by mathematical equations.

    Thanks for that, Michael; I went though several drafts that were all ultimately premised on “this might sound like a non-answer…” (OK, where do these symmetries come from?) and then devolved into SR vs. GR, CPT, etc.*

    If Demetris is still around, John Baez has a gentler introduction than the W—dia entry.

    * “Hey, maybe charge conserva…. Oh, wait.”

  20. #20 Demetris
    Greece
    June 4, 2016

    Yes I am still around but my comments don’t pass through (don’t know why) Thanks for your replies They were all helpful but my main question remains:

    Why the Laws of the Universe are time-symmetrical (same in all ages) and space-symmetrical (same in all places)?
    In other words why Noerther’s theorem is valid?
    (Although there are physicists like Lee Smolin who speculate that this might be not so and that the Laws of Nature might evolve with time).

    Do we have an explanation for why the Laws are as they are? This is still not clear to me.

    Only John Weeler’s saying that they are as they are because they were given at the Big Bang makes some sense to me but I don’t think it is a satisfying explanation.

    Thanks again
    Demetris

  21. #21 Michael Kelsey
    SLAC National Accelerator Laboratory
    June 4, 2016

    @Demetris #20: Your first two questions are _not_ the same!

    Your second one, “Why is Noether’s theorem valid?” is a question of pure mathematics. It’s called a “theorem” in English because it can be proven mathematically, and is therefore always and forever valid.

    Now maybe, you meant your second question to be “Why does Noether’s theorem apply to our physical universe?” That is a special case of the more general question, “Why can we use mathematics (in particular, continuous partial differential equations) to describe our physical universe?” We don’t know, but we _do_ _know_ that we can. It is certainly possible to imagine a random, capricious universe controlled by magic, where gravity works one day and not the next, where rainbows are sometimes colored and sometimes black and white. But that’s not the Universe we live in. So the answer to your second question is basically what I said before — we can describe our Universe with mathematics, therefore Noether’s theorem applies to our Universe.

    As to why we observe time and spatial symmetry — well, that’s an observation. We see the universe behave that way — if we apply the laws of gravity we have deduced here on Earth, and calculate the orbits of some distant binary stars, then we see our observations of those stars match our calculation. That tells us gravity works the same there as here.

    Lee Smolin’s physics does _NOT_ violate time symmetry. What he is exploring is the possibility that some of our physical _constants_ (the numbers that we plug into the laws to get predictions out) might vary in time. That doesn’t change the underlying symmetry, it just means that some of those parameters, instead of being fixed values, have some (measurable) variation.

  22. #22 Narad
    June 4, 2016

    It’s called a “theorem” in English because it can be proven mathematically, and is therefore always and forever valid.

    I’d add “given its premises.” This brings things back to the Lagrangian, which might bear some clarification. In introductory mechanics, one’s mainly talking about masses and their velocities, right?

    It’s possible to reformulate this Newtonian stuff into a more abstract sense, the cool part of which is that it’s amenable to Fermat’s principle from classical optics: light just plain seems to want to get from point A to point B in as little time as possible.

    Why do apples fall down rather than up? As Michael said, “well, that’s an observation.” It turns out that the physical world seems to be lazy that way; it’s not just light, but the action* that’s down with being minimized, too.

    The Feynman Lectures are open-access; perhaps this one might help a bit: h[]tp://www.feynmanlectures.caltech.edu/II_19.html (I’m out of links; replace the brackets with the obvious).

    * Rant about undergraduate physics pedagogy would go here if it weren’t so ancient.

  23. #23 Wow
    June 6, 2016

    They were all helpful but my main question remains:

    Why the Laws of the Universe are time-symmetrical (same in all ages) and space-symmetrical (same in all places)?

    Except that your first claim is wrong: the question you are NOW asking is YET AGAIN different from any of the previous ones.

    Given that as soon as anyone answers your damn question, you go “ta, but you didn’t answer this question!”, I feel that either you take what you’ve been given or work out what the fuck you want answered BEFORE you ask the frigging question.

  24. #24 Wow
    June 6, 2016

    If you’re digging to the “Well, obviously it must be GAWD that made the laws!!!!” bullshit, please explain WHY there is a god.

    What the hell is the POINT of one? What does IT get to take as the meaning of ITS existence?

    Religion inherently dead ends EVERY question, leading to intellectual stagnation and really does nothing to answer any of the questions, merely pretending to be one.

  25. #25 Ragtag Media
    June 6, 2016

    “Religion inherently dead ends EVERY question”
    Wrong dummy. We can give attributes of God but as the Bible says “Who can know the mind of the Lord”

  26. #26 Demetris
    Greece
    June 6, 2016

    Hi all and thanks for all the newer replies.
    Perhaps I have not expressed my basic question clearly.
    It is this:

    The Universe is governed by Laws. I accept that these Laws are objective (i.e. they are “out there” in the Universe and that they are not “constructions of the human mind” as some postmodernists are claiming.

    So, why are the Laws of the Universe these ones and not others?

    One answer is: they happened to be like that by accident, maybe there are other Universes with different sets of Laws (Multiverse)

    Another answer is: A Creator/God gave these Laws to the Universe (Deism)

    I am obviously not satisfied with either of them and I am asking if we have a physical theory that answers the question by not finding an easy cop-out either to Multiverse or Deism.

    My readings so far tell me that we don’t have such a theory and that’s why I wanted to ask some experts with a much deeper knowledge of Physics in one of the best scientific blogs in the Internet.

    Thanks again for all your answers.

  27. #27 Michael Kelsey
    SLAC National Accelerator Laboratory
    June 6, 2016

    @Demetris #26: Thank you; you hadn’t (at least, for us other readers) expressed your basic question clearly.

    “Why is physical law the way it is, and not some other way?” is a legitimate question, but it is NOT, at least today, a physics question. It’s philosophy, and not particularly useful (in the sense of answerable) philosophy either.

    The problem is, we don’t have, and in our current state of science, cannot even expect to have, any way to _test_ a putative answer!

    That is, we could go to the bar, have a few beers, and probably come up with half a dozen different plausible “explanations” of why physical law is the way it is. But we cannot possibly measure any of those “explanations,” or come up with a physical way to either confirm or refute them, which makes them (and the question itself) Not Science.

  28. #28 Demetris
    Greece
    June 6, 2016

    @Michael Kelsey #27

    Thanks Michael.
    I think now we can understand each other better 🙂

    Since unfortunately we can’t meet in a bar would you mind to tell me here what is your (as a working phycisist) position on this philosophical question?

  29. #29 eric
    June 6, 2016

    RM:

    Wrong dummy. We can give attributes of God but as the Bible says “Who can know the mind of the Lord

    That’s funny, I’d estimate that 90% of public religious speech I hear about is people telling me the mind of the Lord on some issue. Gay rights, abortion, poverty, US exceptionalism….people go to great lengths to tell me the Lord’s opinion on all of these issues.

  30. #30 eric
    June 6, 2016

    So, why are the Laws of the Universe these ones and not others?

    One partial answer is to point out that, over time, science has found many seemingly disconnected rules and phenomena are really connected and explained by a smaller subset of general rules. So the group of rules for which the question “why these and not others” applies, keeps getting smaller. The rules we used to think were arbitrary turn out to be logically or mathematically dependent on other, more fundamental rules. Do I think we will eventually find that every law of physics, every constant value, is deductively dependent on some single first principle, that no conditions are free? No; there are probably some laws or constants for which the question will always make sense. But do I think our current set of “fundamental” laws and constants are really fundamental, with no deeper dependency or explanation to be found? No there too; I think it’s very likely that some of things for which you ask “why this way and not some other way” today, will get the answer “because all those things depend on this more fundamental principle” sometime in the future.

  31. #31 Michael Keley
    SLAC National Accelerator Laboratory
    June 6, 2016

    @Demetris #28: You wrote, “what is your (as a working phycisist) position on this philosophical question?” Now that’s a fair question 🙂 This is just my opinion, mind you. On this kind of issue, I tend toward the weak anthropic principle.

    If the universe were NOT governed by laws which are consistent across space and time (on scales comparable to the size of the universe itself), then I think it would be very unlikely that complex chemistry or macroscopic structures could evolve or survive for long periods.

    So, in order for us to be here observing our universe, it “needs” to have consistent uniform laws of some kind. This is NOT the same as a fine tuning argument, or an argument from design. There’s no reason why the Universe “has” to be the way it is, we just would be around to argue in the alternative 🙂

  32. #32 Ragtag Media
    United States
    June 6, 2016

    “That’s funny, I’d estimate that 90% of public religious speech I hear about is people telling me the mind of the Lord on some issue”

    eric, you should thank God then for that 10% who doesn’t.

    eric are you Gay (Or Have A Queer family Member Like Dean)?
    You do realize that Gay individuals have the same “rights” in America as everyone else.
    The whole Gay rights should be removed from any religious discourse because from a pure scientific one it is a FAILURE.
    Two dudes (same sex) can’t procreate so the species dies out. So SCIENCE FACT would lead to homosexual behaviour unnatural and a not scientific.
    No need for a preacher or Bible to tell ya that. Just comman scientific facts.
    Same with a Tranny. They simply have a mental disorder that should be handled by a physiatrist and treated as a mental medical issue.
    Not condoned via political correctness as a “Normal” Condition.

  33. #33 Ragtag Media
    June 6, 2016

    I meant a “Psychiatrist” for those head cases where people of one sex “think” they are of another.
    No Bible need, just a head doctor.

  34. #34 Ragtag Media
    United States
    June 6, 2016

    “The Universe is governed by Laws”
    Yes Demetris it is. However, there is an element of the universe (People In It) that perverts laws. religious folks have their own views of human nature and reasons for perverting those laws.

  35. #35 See Noevo
    June 6, 2016

    To Demetris #26:

    “One answer is: they happened to be like that by accident, maybe there are other Universes with different sets of Laws (Multiverse)
    Another answer is: A Creator/God gave these Laws to the Universe (Deism)
    I am obviously not satisfied with either of them and I am asking if we have a physical theory that answers the question by not finding an easy cop-out either to Multiverse or Deism.”

    I’m not satisfied with the “Multiverse” “explanation” either, to put it mildly.

    But as to the alternative (“Deism”), if you maintain your current stance, then you’ll be “not satisfied” till the day you die.

  36. #36 See Noevo
    June 6, 2016

    Mikey the SLACer writes to Demetris:
    “That is, we could go to the bar, have a few beers, and probably come up with half a dozen different plausible “explanations” of why physical law is the way it is.”

    A “few beers” must mean about dozen.
    Because only a really hammered person could come up with JUST ONE alternative explanation, and even then it would be plausible only to him in his inebriated state.

  37. #37 dean
    United States
    June 6, 2016

    “Another answer is: A Creator/God gave these Laws to the Universe (Deism)
    I am obviously not satisfied with either of them and I am asking if we have a physical theory that answers the question by not finding an easy cop-out either to Multiverse or Deism.””
    Liar – you push the creator crap every chance you get. You can’t even be honest about your science denial.

  38. #38 Ragtag Media
    United States
    June 6, 2016

    “Because only a really hammered person could come up with JUST ONE alternative explanation, and even then it would be plausible only to him in his inebriated state.”

    Nope.. A hammered person would be more imaginative and creative vs a sober staunch liberal progressive who is clueless.

  39. #39 Ragtag Media
    June 6, 2016

    “Liar – you push the creator crap every chance you get. You can’t even be honest about your science denial.”

    Deano, ever occur to ya that the “Creator” created “Science”?

  40. #40 Ragtag Media
    June 6, 2016

    @ Dean the “Dope”. Did you actually read the previous post in this thread?
    I think not. You just bloviate bull shiit from your weak mind to your keyboard.

  41. #41 Narad
    June 6, 2016

    I’m not satisfied with the “Multiverse” “explanation” either, to put it mildly.

    Actually, you seem to be quite comfortable with it as a moronic, go-to straw man that you’re too stupid to competently argue against. You might as well just be wandering to and fro with your fly unzipped.

  42. #42 Dean
    June 7, 2016

    As usual rag your comments are worthless.

    Every science denial post by an is based on the fact that it isn’t his lack of intelligence that makes him disagree with science, it is his religion and his belief that it explains everything there is about the universe. His comment here that he isn’t satisfied withh a creator explanation is, as I stated, as blatant a lie about his beliefs as there could possibly be.

    And yes I have read all of the items. Sadly, that means I’ve read your substsnce free blatherings.

  43. #43 eric
    June 7, 2016

    Ragtag:

    Two dudes (same sex) can’t procreate so the species dies out. So SCIENCE FACT would lead to homosexual behaviour unnatural and a not scientific.

    If we were all male the species dies out too, so I guess you oppose the concept of male people?

    I don’t think anyone is advocating for any public policy which contradicts the ‘facts of life.’ Things like inheritance, child custody, etc., however, are not biological facts of life. They are social arrangements. We can change them regardless of biology.

    Same with a Tranny. They simply have a mental disorder that should be handled by a physiatrist and treated as a mental medical issue.

    LOL next you’ll be telling me all Scottish men are mentally discordered – they wear skirts, after all. Oh I forgot, the pleats make them not skirts. 😉

    In grad school one of my Uni’s dorms had both-sex bathrooms. The showers and toilets each had their own stalls, but both men and women used the same big room and set of sinks. It wierded me out all of the first time. After that…[shrug]. This was literally decades ago. That men can pee standing up more easily than women is biology. Where and in what company humans pee is a social convention, easily changed, and frankly is far less momentous than most puritanical Americans think. We make a mountain out of this particular privacy molehill. The Roman civilization that Jesus lived and peed under, for example, didn’t separate public toilets by gender, nor did they even have stalls. Just a big long bench with holes in it that everyone (regardless of race or gender or mode of dress) used. So the next time you get theologically upset at the thought of a transgender person in the stall next to you, just ask yourself, how would Jesus pee?

  44. #44 Narad
    June 7, 2016

    A “few beers” must mean about dozen.
    Because only a really hammered person could come up with JUST ONE alternative explanation, and even then it would be plausible only to him in his inebriated state.

    Let’s see, who’s more persuasive, the Caltech Ph.D. or the slobberingly ignorant misogynist throwing a tantrum? Decisions, decisions.

  45. #45 Ragtag Media
    United States
    June 7, 2016

    “The Roman civilization that Jesus lived and peed under, for example, didn’t separate public toilets by gender, nor did they even have stalls.”

    LOL next you will be telling me that it’s ok to crucify people and feed Christians to lions, what’s the harm the Romans did it.
    Or rather Pederasty is all good as well..

    “In grad school”
    Now I understand how your mind became polluted.

  46. #46 eric
    June 7, 2016

    “In grad school”
    Now I understand how your mind became polluted.

    Well, that about says it all.

  47. #47 Ragtag Media
    United States
    June 8, 2016

    “Well, that about says it all.”
    Does it?
    eric tell me, how much Student debt do you still have from College or a total with “grad school”?

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