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Television Media Math Science

PBS Features Einstein's Famous Equation 176

Posted by Zonk from the einstein's-party-years dept.
porp writes "On Tuesday, October 11th at 8PM EDT, PBS will feature a docudrama about Einstein's discovery of his famous E=mc^2 equation. The program will include details explaining those who came before him and the development of his miracle year. The pinnacle of which according to the program was his discovery that matter and energy are two sides of the same coin. Yahoo summarizes the program details in length." From the article: "Based on David Bodanis' best-seller 'E=mc2: A Biography of the World's Most Famous Equation,' the program explores the lives of the men and women who helped develop concepts behind each term: E for energy; m for mass; c for the speed of light; and 2 for 'squared,' the multiplication of one number by itself."
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PBS Features Einstein's Famous Equation More

PBS Features Einstein's Famous Equation

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  • Get the formula right. (Score:4, Informative)

    by Pudusplat ( 574705 ) on Sunday October 09, 2005 @01:44AM (#13749257)
    E = [(p2c2) + m2c4]1/2

    • Re:Get the formula right. (Score:5, Informative)

      by pmj ( 527674 ) on Sunday October 09, 2005 @01:57AM (#13749291) Homepage
      If you are going to be pedantic, you should at least put in the right form of the equation.
      E=[(pc)^2 + (mc^2)^2]^(1/2)
      • Could someone please explain the terms of this form to the less physics enlightened of us?

        • Re:Get the formula right. (Score:2, Informative)

          by Anonymous Coward
          p is for momentum, the rest has been defined already.

          Its basically taking E^2 - (pc)^2 = mc^2, and the reason this is chosen is because its an invariant quantity, meaning its the same in all inertial reference frames(Real good thing to have to translate between frames).

        • Re:Get the formula right. (Score:4, Interesting)

          by aktzin ( 882293 ) on Sunday October 09, 2005 @02:22AM (#13749351)

          The anonymous post above already mentioned that p is for momentum and the equation is framed in a way that accounts for quantum mechanics, not just classical (Newtonian) physics. I found a good explanation here:

          http://encyclopedia.laborlawtalk.com/Mass [laborlawtalk.com]

          Scroll about halfway down to the section header "Relativistic relation among mass, energy and momentum".

          By the way, IANAP (I am not a physicist) but I had fun taking physics in college as part of my computer science requirements. And by funny coincidence this post is actually related to my sig. I don't remember where I first saw that (it was in college many moons ago). I always thought it was funny and clever, a good tip of the hat to Mr. Shakespeare, and a good way to describe the universe.

          • Re:Get the formula right. (Score:5, Informative)

            by mako1138 ( 837520 ) on Sunday October 09, 2005 @03:01AM (#13749421)
            Note that the page you mention is a mirror of the Wikipedia article on mass. [wikipedia.org] And it doesn't really have anything to do with quantum mechanics - we are taught non-relativistic (and time-independent) QM in undergrad courses.

            The main things to take from E^2 - (pc)^2 = (mc^2)^2:

            1. Set the mass m equal to 0. We get E = pc, or p = E/c. Thus momentum is defined for massless particles in special relativity. Newtonian mechanics can't handle this correctly.

            2. Set the momentum p equal to 0. We get E = mc^2, popularly known as energy-mass equivalence. There's subtleties to it, though; see Relativistic mass [wikipedia.org].
            • Hrm. On 2, if the universe is expanding then p is never zero. Rather there is always a non-zero velocity. However in some places it might be pretty close to zero considering the cosmological constant is approximately 10^-120. The invariant or rest mass may be more of a limit a particle approachs as it slows down or removes momentum. However because of the nature of a positive cosmological constant there is always energy being applied to a particle's momentum.

        • The relativistic total energy is the sum of the rest energy of a particle and its kinetic energy. The formula for total energy is:
          E = (mc^2)/sqrt(1-v^2/c^2).

          This can be made more intuitive if we note that momentum is defined as
          p = mv/sqrt(1-v^2/c^2).

          Hence
          E^2 - p^2c^2 = m^2c^4 (remember than 1-v^2/c^2 = (c^2-v^2)/c^2 ).

          Therefore, if v = 0, E = mc^2. In these equations, m is the rest mass of an object, v is the velocity of the object observed from your reference frame. Both the object and you cannot be acc
      • E=[(pc)^2 + (mc^2)^2]^(1/2), yeah, but with the funding cuts, the Corporation for Public Broadcasting just didn't have the *$* momentum to get beyond the rest mass... Do wiki ahref=http://en.wikipedia.org/rel=url2html-32568 [slashdot.org]ht tp://en.wikipedia.org/>
      • Even more pedantic: p_mu p^mu=1. There.
    • the formula is right. E=mc^2 has the mass of the moving object. E=[(pc)^2+(m0c^2)^2]^0.5 has the rest mass m0. The two forms are equivalent (which signifies, geometrically, the invariance of the 4-momentum's contraction with itself)

  • Meaning of "summarises program details in length" (Score:4, Funny)

    by Mostly a lurker ( 634878 ) on Sunday October 09, 2005 @01:45AM (#13749258)
    Does this mean it tells you how long the program lasts? Or does it perhaps indicate that E=mc^2 contains six characters? Surely the editors would have picked up on nonsense implying a lengthy precis of the program.

  • True origin of the famous equation (Far Side) (Score:4, Funny)

    by macklin01 ( 760841 ) on Sunday October 09, 2005 @01:57AM (#13749294) Homepage

    Your desk is all squared away. Yep, all squaaaaaaaaaaaared away. (I couldn't find an image to link to--sorry!

  • WTF @ summary (Score:5, Insightful)

    by Sartak ( 589317 ) on Sunday October 09, 2005 @02:07AM (#13749309) Homepage
    This is, ostensibly, a site which features news for nerds. If you can show me a true nerd who doesn't know what E=mc^2 represents, or even what ^2 means, then I will weep. Couldn't the submitter use something a little more interesting to us?

    • Re:WTF @ summary (Score:2, Insightful)

      by Anonymous Coward
      I submitted the story and the 'From the article' part was not in my submission. It was a Zonk addition. So you complain when the editors edit and complain when they dont. Anyway the other links are pretty informative, and the pbs link has some cool stuff. so stop being a bitch.

      • Re:WTF @ summary (Score:3, Insightful)

        by 1u3hr ( 530656 )
        you complain when the editors edit and complain when they dont.

        As one complains when Bush does nothing, or when he does something stupid.

    • The book in the original article comment is why this is a big deal. In the book, they dissect every point of it, and each points history. It's a fun history book, really. So, if the PBS thing follows the book, even nerds would have something to look forward to...
    • Around here we're more concerned with the fact that major funding for this production was provided by Google.

      No, really.
    • It would somewhat surprise me if knowledge of the general /. public went very much beyond knowing that it means mass and (a lot of!!!) energy are exchangeable, and this idea can lead to nuclear plants, atomic bombs etc. Not _everyone_ is a relativity theory physicist.

      The book is interesting because it offers some 'petite histoire' on the evolution of the formula. Unfortunately you have a point that it is not completely for nerds as it contains fuzzy explanations and crappy analogies here and there. (discla

    • I read Bodanis' book awhile ago. IIRC, he dedicates a whole chapter to each part of the equation and it's history. So while I am aware of what ^2 means, I found the history of the concept of squaring to be interesting. The book isn't a math/physics lesson; it's a history lesson
    • If you can show me a true nerd who doesn't know what E=mc^2 represents, or even what ^2 means, then I will weep.

      Yes. Everyone knows that E=mc^2 means that you're turning on the second least significant bit in the variable mc and assigning that to E. ...wait, it's not?
  • Anybody know off hand how/where I can buy this and other older PBS productions? Much obliged..
  • I seem to remember that a group of physicists disproved the formula. Can anyone remember whom?
    • bah. it's not disproved, but it's only valid for a single unchanging frame of reference dof time. As time bends (due to intense gravity), the equation becomes wrong. So Einstein was right for so long as you're only talking about a single viewpoint. But if you want to use the equation for big bang/big crunch stuff, or for looking at the universe in 4D, it really should be Et=mcg.

      Energy * time = mass * speed of light * gravity .

      Say, at the big crunch, all matter in the universe is heading toward a center

      • Piling on the info, the form of the equation in grandparent is not wrong -- it's a special case. For all the reasons stated by parent it becomes wrong because this form of the equation is a result derived of "Special Relativity". "Special" means your reference frame is not accelerating , etc. "General Relativity" gives you the complete version of this equation in all frames, but my copy of Jackson is in the attic at my folks' house so I can't dig it out for you now -- it's almost time to leave for church.
        • I didn't think Jackson's Classical Electrodynamics got into General Relativity(maybe we are talking about a different book?)

          General Relativity requires LOTS of higher level math (which most /.'ers won't have). Feynman's lectures have a decent non-math description of it, and I think Penrose's book has an explaination.


          • I might be mistaken, but I thing it's the same book -- there's a short optional/supplemental section on it in one of the later chapters, IIRC. At the end of the class, our EM prof gave us a choice between GR (which is of almost no practical use) and wave guides (which you can use to make $$) and we picked GR.

            The funny part is that the math is almost all matrix mechanics, like optics, but to save space and make the equations look less encumbered you write everything out in Einstein notation. Insteaed of w
            • It's been awhile but I though GR requried tensors and manifolds. Am I thinking of something else?

              • Not sure - it's been a while for me too, but I believe the matrix representation of the math is an expression of tensors. I don't remember manifolds being directly involved, but they probably were and he just didn't tell us that. For some reason I think manifolds came afterward, historically, but I might be hallucinating. Maybe they were a latter-day addition to modernize the theory and make it more compact?

                Want to see something hilarious? Two old-school /.'ers up late on a Sunday night arguing about who

  • Animaniacs (Score:5, Funny)

    by thebdj ( 768618 ) on Sunday October 09, 2005 @02:13AM (#13749332) Journal
    Everyone knows that it was the Wacko Brothers and their sister Dot selling kid scout cookies to Einstein [tv.com] that helped him create E=mc^2, by singing the Acme song.

  • If I'm not mistaken, this is the same documentary as here [digitaldistractions.org].

    It's a pretty interesting show.

  • Get it right! (Score:1, Funny)

    by Anonymous Coward
    Pfff, everyone knows how he developed his famous formula: E=mA^2 ....No E=mB^2 ....No E=mC^2 ....Eureka That or he stole it from the patent office
  • Given scientests have managed to make light go slower and indications that some of the universes constants have not been fixed thoughout its lifetime and are constantly changing albeit on such a small scale we dont notice. Could you get a different value for E from the same mass by varying the speed of light, and if light can get slower would that potentialy mean that Energy is being lost or is that touching into relativity.

    --
    If life was simple, there simply wouldn't be any life
    --
    • c refers not only to the speed of light, but specifically, the speed of light in a vacuum. Even our normal atmosphere changes light's speed somewhat.
    • C is the speed of light in a vacuum. It's a constant.

    • "varying" speeds of light (Score:4, Interesting)

      by Quadraginta ( 902985 ) on Sunday October 09, 2005 @03:04AM (#13749425)
      The symbol c in the subject equation, and generally, stands for the speed of light in a vacuum, 299792452 meters/second. In any other medium light travels slower than c, by a factor equal to the inverse of the index of refraction. Id est, for water the index of refraction is about 4/3, so light travels through water 3/4 as fast as it does through vacuum.

      While people may have set up interesting media through which light travels at some odd speed, no one has ever observed light traveling through a vacuum at other than c. Indeed, it's a bedrock principle of relativity that it cannot.

      Interestingly, the eerie blue glow [umr.edu] you see coming from nuclear reactor cores that live at the bottom of pools of water (called Cerenkov radiation) is emitted by particles coming from the core that are traveling faster than the speed of light in water (although of course slower than c). The blue light is a sort of "optic boom" similar in its origin to the "sonic boom" you hear from aircraft exceeding the speed of sound.
      • So if the nuclear reactor core was in a vacuum, would the Cerenkov radiation go faster then C or does it just move through water faster then light?
        • So if the nuclear reactor core was in a vacuum, would the Cerenkov radiation go faster then C or does it just move through water faster then light?

          Cerenkov radiation moves faster than light does in in water (about 2/3 c, IIRC), not in vacuum. There wouldn't be any Cerenkov radiation at all in vacuo, since it's caused by particles hitting water. But more importantly, the "swimming pool reactor" would melt down in vacuum.

    • I think most of the responses to the parent question have missed the intention of the original post.. There is a theory of VSL (variable speed of light) even for c, with the speed of light in a vacuum changing over time (most notably championed by Dr Joao Magueijo [wikipedia.org] of Imperial College London) If you are so inclined you can read the paper yourself here [lanl.gov]

    • Given scientests have managed to make light go slower
      That's not entirely accurate. The speed of actual photons always travels at C. The speed of propogation of a light signal doesn't always travel at C. The difference is that when light travels through a medium it's absorbed, and then re-emitted by atoms. This takes some amount of time that takes more time than it would normally take to cross the distance of an atom. It's kind of like having a bunch of people in a line far apart playing telephone. You

  • Rolling in the grave (Score:2, Insightful)

    by can56 ( 698639 )
    When /. points to Yahoo for "news" about Einstein, and the next item is Y-news is "The Worlds Worst Bathrooms", I hope a few E, M, and C squared smite the editors.

  • I've seen this already I think (Score:4, Interesting)

    by FunkyRat ( 36011 ) <.moc.liamg. .ta. .taryknuf.> on Sunday October 09, 2005 @02:27AM (#13749360) Journal
    If this is the same program as this [channel4.com] Channel4 production, then I highly recommend it. Although undoubtedly it has nothing to offer the Slashdot crowd from a science standpoint, the human face it puts on scientists we all too often only know from their work is excellent.
    • Yes its the same one we had on Channel 4 a while back ... it was certainly interesting from a historical point of view, but as others have said, nothing much to offer from a scientific perspective.

      • I really enjoyed it (Score:3, Informative)

        by FunkyRat ( 36011 )
        I had no idea about Faraday's background in poverty or that Lavoisier was the Paris tax collector and subsequently beheaded in the French Revolution.

        Oh, and as a bonus, it's narrated by Christopher Eccleston. Half expected to hear a metal scream ring out at any moment. "Exterminate!"
  • Is it really that important, or is it because it's popular culture media-friendly?

  • Seen it already (Score:2, Informative)

    by Gabhlan ( 531413 )
    It was on over here in Scotland a few weeks ago. Nothing to get worked up about, it's been hideously dumbed down as you'd expect of anything on TV these days.

  • Rest Mass (Score:4, Informative)

    by Joffy ( 905928 ) on Sunday October 09, 2005 @02:43AM (#13749394)

    People should realize that the M in e=mc^2 is not the widely known idea of mass. Most people think that a bowling ball that weighs 10 pounds has a set mass no matter what. But in Einstein's equation mass is more like inertia. A moving bowling ball has more mass than one at rest. So you can not simply take a 10 kilogram object and multiply it by the speed of light squared to get its energy. This means you must first complete the equation for m first, which I do not know off hand.

    So the idea of mass that most people know is called rest mass. It took me a while to realize that they meant an object could increase mass but gain no atoms or extra "material". Since most objects we can see and touch don't even go 1% the speed of light, we never notice this increase. For almost all practical cases(even a plan going mach 3) we can consider its mass to be rest mass and still be accurate to within many many decimal places.

    • Suppose m0 is the rest-mass (the mass of an object not moving with respect to the reference frame), and y=gamma=(1/(1-(v/c)^2)) E=y*m0*c^2
    • well, that's exactly the point. The equation is saying that mass and energy are two manifestations of the same reality. So it is harder to change the speed of a 10kg rest mass object if it's moving since the kinetic energy adds inertia (mass) to the object. Just to be the third pedantic one: m=m0/sqrt(1-v^2/c^2)
    • I've always found it odd that in e=mc^2 the c^2 is (probably) a constant, and can be simplified to something else: e=mC. Now, anyone looking at that equation will see that what you are doing is simply converting between units. And units are not part of the physical world, but merely an arbitrary standard we pick to facilitate calculations. So the equation is really just E = M.

      Why have the c^2 part at all? Is the energy contained in an object really variable based upon the speed of light in a particular
      • Why have the c^2 part at all? Is the energy contained in an object really variable based upon the speed of light in a particular material?

        Um, c isn't the speed of a particular beam of light in any sense (which, as you say, changes depending on the medium). c is the speed of light in a vacuum, and is constant.

        So the equation is really just E = M.

        Yes, it is, when you use Planck units [wikipedia.org], which simplify this and other equations by setting certain constants to 1. You are just converting between units, because the
    • My understanding of it, and perhaps I am wrong, but I don't think so this time, is that the m in E=mc^2 is precisely what we all think of it as -- rest mass. The mass of a bowling ball, for example.

      The contribution from motion, that you are referring to, is contained in the second term of the [full] relation:

      E^2 = (mc^2)^2 + (pc)^2, where p is simply the momentum of the object.

      Mike.

                       
    • This means you must first complete the equation for m first, which I do not know off hand.

      You use the conversion factor sqrt(1-v^2/c^2) (let's call that k), where v=velocity and c=speed of light. The relativistic mass of an object is 1/k of its rest mass. The relativistic length of an object in the direction that it's moving shrinks to k times is length. Time also dilates by t=rest t/k, which is how Mazer Rackham got to live for hundreds years by traveling at high speeds and thus having a low k.

      The easy way
  • Is it me, or have the PBS documentaries such as Nova and Nature been dumbed down over the past decade or so. I recently started watching Nova again and the sheer repetition of the main thesis, sometime three or four times in a one hour show, is annoying and pedantic. Nova especially seems to be cranked up on the *gee whiz* factor and less substansive on the actual science.

  • Einstein's Wife (Score:3, Interesting)

    by Donny Smith ( 567043 ) on Sunday October 09, 2005 @03:43AM (#13749507)
    Which one? Second? I'm not sure.

    Anyway, it's a good complementary read:
    http://www.pbs.org/opb/einsteinswife/science/index .htm [pbs.org]

    • Re:Einstein's Wife (Score:3, Interesting)

      by ArcSecond ( 534786 )
      From what I have heard, there is a lot of controversy over Einstein's first wife and her contributions to his early work. I don't believe he ever acknowledged her help publicly, and although her name apparently was attached to his earlier papers, it mysteriously vanished when they were published.

      Not that I am an Einstein hater, but he really was a rotten husband and father.
  • Is this episode of Nova brought to us by a grant by the Chubb Corporation?
  • Wait, now numbers can be multiplied by themselves??? What a wild, fantastic world we live in!!!

    Thank you Einstein for making such a marvelous discovery!!!

    I'm still iffy about the name.. "square"? Is this geometry or astrologics? Get it straight, please.
  • We had it in the UK.
    Its brilliant.
  • So I have a question, in what units do we measure C? The reason I ask, is does the formula still work if C is measured in units of C? Because in that case C^2 == 1.

    Or does C have to be in units relative to the resting state of the observer? And in that case does the energy in a given mass by another observer change . And still what is to say that an observer doesn't go around talking in stellar units rather than anything smaller than that (again c^2 1)?

    • Think about it this way: if you measure c the way you'd normally measure velocties, say in meters / second, then you get c^2 in units of meters^2/seconds^2. (IIRC, c ~= 3 * 10^8 m/s, so c^2 ~= 9 * 10^16 m^2/s^2). But let's say you want to measure velocity in units such that c = 1 -- say, measure it in light-seconds/second. Then c^2 = 1 ls^2/s^2, this is true.

      But a light-second is huge, and a light-second squared is even huger. In fact, of course, 1 ls ~= 3 * 10^8 m, and thus 1 ls^2 ~= 9 * 10^16 m^2. (
  • I've always wondered why the constant term is the square of the speed of light (in a vacuum). A square is almost like the "++" operator, indicating that the value is the same, but in "the next higher dimension". So the amount of energy is thereby exactly equivalent to the amount of matter, but in "the next higher dimension" of space, scaled up by a velocity of the very phenomenon that seems to straddle our matter/energy distinction. What is the geometric root of that enigmatic relationship?
  • What if Einstein discovered that the Universe is hourglass shaped [imdb.com]?
  • A theory... that you only tell your relatives. ;)
  • and 2 for 'squared,' the multiplication of one number by itself."

    Thanks Yahoo, and Slashdot (or is it Sesame Street?)

  • Heaviside's Equation (Score:3, Interesting)

    by radtea ( 464814 ) on Sunday October 09, 2005 @11:11AM (#13750575)

    As I've pointed out before on /., Oliver Heaviside was the first person to write down E = mc^2, in 1892 or thereabouts. He did so based on an electro-mechanical model of the electron, where the mass of the electron was due to the resistance of the electric field to motion as the electron travelled through the aether. The same approach is what let Lorentz and Poincare' write down the full expression of what would eventually be known as Special Relativity several years before Einstein.

    Einstein's contribution was to show that what these others derived from a dynamical theory could be understood in kinematic terms. Dynamics is the study of the causes of motion, and kinematics is the description of motion. In the pre-Einstein theory the resistance of the electron to motion--and the contraction of moving electrons in the direction of motion--was understood as due to electro-magnetic forces acting on it due to the aether. What Einstein showed was that the same phenomena could be understood in purely kinematic terms, as a consequence of the way motion must be described if the laws of physics are to be the same for all observers.

    To get a sense of how profound this is, imagine that at one time the inverse-square law for light had been understood in terms of an absorbing medium. That is, the fact that lights appeared dimmer as the square of the distance to the observer was explained by empty space being filled with a substance that absorbed light. There would be many difficulties with such a theory, but I'm sure with sufficient mathematical prowess one could make it work. Then someone like Einstein comes along and points out that one can explain the phenomenon in purely geometric terms, as a consequence of the way the light is spreading out over the surface of a larger sphere as it gets further from the source. What previously required a complex, difficult mathematical description now becomes so trivial that even a philosopher can understand it.

    That was Einstein's contribution, but it shouldn't completely eclipse the work of those who came before.

  • This program has already been on tv in either the UK or Canada (i'm not sure which). Anyway you can get the torrent of it right here:

    http://www2.digitaldistractions.org:8080/torrents/ E=mc2%20-%20Einstein%20And%20The%20Worlds%20Most%2 0Famous%20Equation.torrent [digitaldistractions.org]

    if the link doesn't work go to http://www2.digitaldistractions.org:8080/ [digitaldistractions.org] and search for e=
  • E = ma^2 ... nah

    E = mb^2 ... feh!

    E = mc^2 !!!!!
  • A few years back there was a controversial suggestion [pbs.org] that Einsteins first wife- fellow student Mileva- had made substantial contributions to his papers. Some even said they saw her handwriting in the paper drafts.

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