Understanding the importance of E=mc^2

There’s a new book out there, Why Does E=MC2 (and Why Should We Care?), by Brian Cox and Jeff Forshaw. One of Seed’s editors, Elizabeth Cline, took a read through it and wrote about her experiences and what she learned. Is relativity, particle physics, and all the related science really incomprehensible to all except the scientists working on it? Cox and Forshaw don’t think so, and neither do I. So I wrote an article for SEED Magazine here. Here’s an excerpt:

Inside of every atom — every proton, every neutron, every electron, even every neutrino in the Universe — lies the secret of this energy. The idea that we could turn mass into energy brought us an understanding of not only radioactivity, and not just the source of power within Sun, but everything from the bombs of nuclear fission to the hope of clean, pollution-free power from nuclear fusion.

So go read it, and feel free to come back here and discuss!


  1. #1 Mu
    August 25, 2009

    Nice write-up, one quick question so. You say the sun has only converted some 0.03% of it’s mass to energy; how much mass could it theoretically concert if it goes all the way to solid iron (I know, won’t happen, red star, nova etc). And how’s the ratio of mass loss due to energy conversion over mass loss due to solar winds?

  2. #2 CanInternet
    August 25, 2009

    But I have to het this of my chest!

    Yesterday at 9.15 there was ring at the door. The delivery guy from UPS… if it was alright to drop the package at home instead of the internetcafe. (that´s the good thing here, everybody knows were you live, which is handy when you open at 11 or if you´re closed on mondays).
    So I said: YES!!
    He went and came back with a very big box proclaiming: CELESTRON
    I was feeling like a kid after the knock on the door at december the 5th… (dutch santaclaus)

    So there I was alone in the room with a very very large box and two sniffing cats.
    Ordered on thursday in Austria, were it was cheapest, and monday morning at my doorstep.

    So I got a knife and carefully openend the first box. Out came another box with all kinda photo´s of the scope etc. on it.
    So carefully I openend this one only to reveal another box.
    I started to whistle russian folksongs because of the russian doll syndrome setting in and I started to get nervous thinking I would end up with a very very very small telescope.
    But this box was also openend. Revealing a pletora of boxes in various sizes.

    I went for the biggest. Out came the tripod with the mount. Next big one was the telescope itself, which slid into it´s place on the mount.
    Then came the various little boxes, revealing eyepieces (which are junk), a pointerscope, the 2” adapter, the 1,25” adapter and the hand control.
    Then a reversal of putting boxes back into each other and getting my room back for me and the scope and the cats.

    No batteries, so I grabbed a 12V adaptor, plugged it in and switched on.
    Entering place, time etc into the machine and it awoke.

    Next was finding something as far away as possible which I still could make out with the naked eye. A nice very red traffic sign at two miles did the trick.

    Centered it in the scope and then aligned the red dot in the finder. From now on I would see in the centre of the scope whatever I pointed the pointer at. The shape and position gave me a feeling of having a mortar in the house and some evil fantasies wirled for a moment looking to the red dot finder scope.

    The next hours were spend with going through all the menus, settings and getting some feeling of the beast.

    My wife came home at 17:30 and we got a bit overtipsy, so I crashed at midnight into bed… which wasn´t plannend at all!!

    Thank god it was bladder release time at 03:00 and I sneaked outside and saw it was completely clear skies and Jupiter was looking down upon me.
    So out I dragged the scope onto the terras and set it up.

    Then I did a simple allignment on Jupiter and set the scope to tracking. Only some very soft clicking sound told me it did follow Jupiter.

    So there I was first looking with a low magnification. Jupiter nice and blueish with 4 moons. So I switched to the 9mm eyepiece.
    Suddenly Jupiter sat there 72x magnified (which still is a small thing in the eye piece), however, much more detail came into view.
    4 moons became 6 and Jupiter displayed it´s bands when the atmosphere cleared up. Problem is that this is an island, so in summer the warm island pumps up it´s heat during the night surrounded by relative cool seas. Winter will be better.

    So that was how I spend my time till 06:00. Looking at that planet and noting that all that time the scope kept it dead on in the middle of the eyepiece, without any help from me. It tracked perfectly.

    So there it is. My first scope after years of “one day I´ll have a scope

  3. #3 CanInternet
    August 25, 2009

    oh and btw it is an Celestron NexStar 130 SLT Computerized Telescope

  4. #4 Erin
    August 25, 2009


  5. #5 CanInternet
    August 25, 2009

    Ah well, it is only once in a lifetime you´ll get 50 and a birthday present like that from the wife.
    So that´s worth a w00t or two. IMHO

  6. #6 Ethan Siegel
    August 25, 2009

    CanInternet, good for you! It’s kind of an inside joke that a good amateur astronomer knows more about looking through a telescope (i.e., amateur astronomy) than a professional, expert astrophysicist like me. But it’s true, and I’m glad you’re enjoying the wonders of the night sky!

    Erin, thanks for the w00t!

  7. #7 CanInternet
    August 25, 2009

    Thanks Ethan.
    It´s due to people like you, people like me develop the love for all those wonders.
    But now.
    Back to topic.
    I just had to get my little-boy-new-toy-feelings out.

  8. #8 Robert
    August 25, 2009

    I like the way physicists define “everything” to be atoms, elementary particles, radioactivity, nuclear fission and nuclear fusion.

    Chemists know that you convert matter into energy when you drive your car and burn the gasoline. That is the part of “everything” that physicsts don’t seem to care about: the boring molecules that aren’t radioactive and don’t require the temperature of the sun to produce energy.

  9. #9 Peter
    August 26, 2009

    Chemistry??? Oooooh… you mean applied physics (not my joke but I do like it :*)

  10. #10 Robert
    August 26, 2009

    Question: Who won the Nobel Prize in Physics for discovering fission of heavy nuclei?

    Answer: Nobody. The discovery of fission earned the Nobel Prize in Chemistry and went to Otto Hahn, a chemist.

  11. #11 Dunc
    August 26, 2009

    Chemists know that you convert matter into energy when you drive your car and burn the gasoline.

    No they don’t. Mass is conserved in chemical reactions, is it not? All you’re doing is re-arranging the matter, and liberating some energy in the process. For example, the complete combustion of octane is:

    C8H18 + 12.5 O2 -> 9 H2O + 8 CO2

    Notice that there are the same number of atoms of C, H and O on both sides of the equation. Mass is conserved.

  12. #12 rob
    August 26, 2009

    Dunc: mass is not conserved. if there is any energy change in a reaction, then there is an equivalent mass change via e=mc^2.

    however, for chemical reactions the change in mass is very small, and can be ignored. in nuclear reactions the mass change can be large and measurable.

    the difference bwetween chemical and nuclear reactions arises because of the difference in binding energies. nuclear binding energies are on the order of an MeV (million electron volts) while chemical binding energies are on the order of an eV. so the mass changes for nuclear reactions are about a million times larger than for chemical reactions.

  13. #13 Robert
    August 26, 2009

    Can be ignored? Depends on how you look at it.

    The mass change when a 10 kt atomic bomb explodes is the same mass change that results from exploding 10 kt TNT.

  14. #14 Ethan Siegel
    August 26, 2009

    You are all correct, in a way. Whenever you undergo a fusion, fission, or chemical reaction, you are either converting mass into energy or vice versa.

    For the case of a chemical reaction, you’re talking about mass lost via the binding energy of electrons, which is the mass equivalent of about 10^-36 kg per molecule. On the other hand, when you’re talking about a nuclear fusion reaction, you’re talking about the mass equivalent of about 10^-29 kg per proton or neutron. This factor of around 10,000,000 is why nuclear energy is so much more efficient than chemical energy, because a much greater amount (and percentage) of mass gets converted into energy in a nuclear reaction as compared to a chemical one.

  15. #15 Dunc
    August 27, 2009

    I stand corrected. It’s been a long time since I did any chemistry.

  16. #16 SLC
    August 30, 2009

    Re Robert

    It was quite true that Otto Hahn and his group were the first to split the atom experimentally. However, he didn’t understand the results of his experiment and required the expertise of physicist Lise Meitner to provide the explanation.

  17. #17 Jeff
    September 11, 2009

    I was reading, and enjoying, your article in Seed magazine where a link took me to Wikipedia (yeas I am a “layman” who enjoys stumbling though Wikipedia, even though it may not be 100% accurate). I noticed a glaring discrepancy between your article and http://en.wikipedia.org/wiki/Antimatter. In the “Fuel” section (without source) Wikipedia noted “Tsar Bomba . . . reacted an estimated yield of 50 Mt, which required the use of hundreds of kilograms of fissile material.” 47 grams in your article to wiki’s “hundreds of kilograms” is a big difference and I have been unable to find another source on the internet that discusses how much fissile material was used. Does the math work out so that 47 grams of uranium = a 57 Mt of energy?

  18. #18 Ethan Siegel
    September 11, 2009

    Jeff, although it took over 100 kg of Uranium to make the Tsar Bomba, much less than 1% of that Uranium’s mass was actually converted into energy via E=mc^2. That accounts for the discrepancy between my article (which is right) and the wikipedia page (which is also right).

    Even in nuclear fusion, when the Sun burns 4 atoms of hydrogen into 1 of helium, the amount of mass converted into energy via E=mc^2 is less than 1%! Pretty neat, hmm?

  19. #19 Robert
    September 11, 2009


    It’s true Hahn didn’t “understand” fission in 1938. He only discovered its existence. But that in itself was a really big deal at the time.

  20. #20 Hush
    November 17, 2009

    Three words – Stephen J. Crothers
    Disprove his rigorous proofs or assign meaningful physical interpretations to math done correctly. GRT & SRT’s math is incorrect.


  21. #21 Ethan Siegel
    November 17, 2009


    I don’t think you understand what Stephen J. Crothers’ work means for actual black holes in space. Perhaps I should clarify in a future post.

  22. #22 Hush
    November 18, 2009


    Alright. Feel free to clarify what I don’t understand what Stephen J. Crothers work means.

    Yes, you should clarify in a future post what Crothers’ work means for actual(!) black holes in space.

    Crothers’ work needed to be addressed yesterday, though.

    I look forward to your future post with anticipation.


  23. #23 Michael Varney
    November 19, 2009

    Oops… I replied to Ethan’s post on singularities as treated in GR. Then I did a quick search on Stephen J. Crothers. I should have done the search first, because his web page make it absolutely clear that he is nothing but a petulant crackpot! 8(

    So, by equivalency, and in three words:

    Stephen J. Crothers = insanely disturbed crank

  24. #24 Jim Jones
    March 8, 2010


    Thats great about your telescope but you must be aged or something beacuse any internt savvy person or young child knows that an “OFF TOPIC ALERT” doent make you immune to posting an irrelevant “rant” on the blog. This is surley within the top 10 rules of the internet. You = FAIL my friend…. and if it were written in all caps with bad grammar it would of been an EPIC FAIL. Next time just look for an outdated blog about new telescopes and you can put it in there…

  25. #25 Uncrackpotted
    July 24, 2010

    “…his web page make it absolutely clear that he is nothing but a petulant crackpot,” is a statement which clearly shows the whole world that you do not have the faintest idea what you’re talking about. Stephen J. Crothers is absolutely right. The BB is just another creationist myth, but you’re free to believe what you want.

  26. #26 video games
    November 8, 2010

    7 grams in your article to wiki’s “hundreds of kilograms” is a big difference and I have been unable to find another source on the internet that discusses how much fissile material was used. Does the math work out so that 47 grams of uranium = a 57 Mt of energy?

  27. #27 Harser
    November 11, 2010

    You’ve definitely got to respect the geniuses that came up with these theories. Albert Einstein and also Niels Bohr. The world has never been the same, it’s just how we use the information that makes the difference.

  28. #28 jocuri cu hannah montana
    November 14, 2010

    Mass is conserved in chemical reactions, is it not? All you’re doing is re-arranging the matter, and liberating some energy in the process.Ok

  29. #29 forex demo
    January 12, 2011

    It’s a hugely well known equation, but frighteningly few people actually understand what it means or it’s uses. we should propbably just use this explanation on the Simpsons or something and watch understanding skyrocket!

  30. #30 florida mortgage rates
    January 12, 2011

    the amount of engery contained in even a small amount of matter is pretty astonishing. when you see how much plutonium is actually used to create a nuclear device and the effect when it’s released into raw energy you get to understand a lot more about the true potential energy contained in even simple substances.

  31. #31 Ron Beck
    May 29, 2015

    All of Stephen Crothers’ mathematics is riddled with errors, as shown in the following papers:

    1) “The Mathematics of Black Hole Denialism” – Dr. William D. Clinger (PhD in Mathematics from MIT)


    2) “Coordinate Transformations and Metric Extension: a Rebuttal to the Relativistic Claims of Stephen J. Crothers” – Dr. Jason J. Sharples (PhD in pure Mathematics and Mathematical Physics from the University of Canberra, Australia)


    3) “A clarification on the debate on the original Schwarzschild solution” – Dr. Christian Corda (PhD in Physics from Pisa University, Italy)


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