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PBS Features Einstein's Famous Equation

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."

128 of 176 comments (clear)

  1. Get the formula right. by Pudusplat · · Score: 4, Informative

    E = [(p2c2) + m2c4]1/2

    --
    "If you put butter and salt on it, it tastes like salty butter." -Terry Pratchet, on Popcorn.
    1. Re:Get the formula right. by pmj · · Score: 5, Informative

      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)

      --
      Are you BioCurious?
    2. Re:Get the formula right. by weilawei · · Score: 1

      Could someone please explain the terms of this form to the less physics enlightened of us?

    3. Re:Get the formula right. by Anonymous Coward · · Score: 2, Informative

      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).

    4. Re:Get the formula right. by aktzin · · Score: 3, Interesting

      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

      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.
      --
      Quantum mechanics: the dreams that stuff is made of.
    5. Re:Get the formula right. by ScriptedReplay · · Score: 1

      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)

    6. Re:Get the formula right. by mako1138 · · Score: 5, Informative

      Note that the page you mention is a mirror of the Wikipedia article on mass. 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.

    7. Re:Get the formula right. by Aglassis · · Score: 2, Insightful

      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 accelerating (inertial reference frames--this also means no rotating, which is accelaration in physics). If you want to deal with acceleration there are much more complicated equations in general relativity.

      --
      Suddenly, the hairy finger of a familiar monkey tapped me on the shoulder. It was time.--G. T.
    8. Re:Get the formula right. by joachimp · · Score: 1

      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-32568ht tp://en.wikipedia.org/>

    9. Re:Get the formula right. by XchristX · · Score: 2, Insightful

      Even more pedantic: p_mu p^mu=1. There.

      --
      l'Homme n'est Rien l'Oeuvre Tout: Gustave Flaubert to George Sand
    10. Re:Get the formula right. by ichin4 · · Score: 1

      Obviously, E=mc^2 is better-known, and you are welcome to view it as the p=0 special case, a formula for the energy content of a mass at rest. (And useful for computing the energy released in a nuclear or particle reaction that changes the mass of the reagents by m.)

      But Einstein himself viewed E=mc^2 as the correct formula even for non-zero p. The reason is that he preferred to define mass via Newton's Law F=ma, which requires m to be velocity-dependent (thus the title of his paper "Does the inertia of a body depend on its energy-content?"). Modern physicists tend to prefer to use m to represent rest-mass, which gives the formula you quote relating energy, momentum, and rest-mass.

    11. Re:Get the formula right. by Stalyn · · Score: 1

      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 best education consists in immunizing people against systematic attempts at education. - Paul Feyerabend
    12. Re:Get the formula right. by Jackmn · · Score: 1
      On 2, if the universe is expanding then p is never zero.
      Velocity is always relative to the measurer (except light, which is always acts the same regardless of your frame of reference).

      There is no absolute velocity.
    13. Re:Get the formula right. by Jackmn · · Score: 1

      "is always"... I'm sorry =(

    14. Re:Get the formula right. by the+morgawr · · Score: 1
      Technically the light is also relative, but because the transform is non-linear (the lorenz transform) light has the same speed in all frames of reference.

      Special Relativity was "just" a modification of Newton's equations to make them invariant under the lorenz trasform, instead of the galilean transform. This resolved the conflict between Maxwell's equations and Newton's equations. Out of Einstein's discoveries, this is by far and away the easiest to explain -- essentially he took into account that it took some finite(non-zero) amount of time between an event's occurance and the observer seeing it, something Newton's laws didn't do.

      --
      The policy of the United States is worse than bad---it is insane. -- Ludwig von Mises, Economic Policy(1959)
    15. Re:Get the formula right. by Captain+Numerica · · Score: 1

      Last I checked that's not the equation that made him famous.

      e = mc^2 says a lot more about the universe than e = ((pc)^2 + (mc^2)^2)^.5

      Before someone rants about how setting p=0 gives you the form blah blah blah... stop. I've been there before. That's still not the equation that made him famous. It is the simplified version which speaks to the direct relationship between energy and mass. It's elegant and simple enough for the wide of public culture to consume.

  2. Meaning of "summarises program details in length" by Mostly+a+lurker · · Score: 3, Funny

    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.

  3. Re:Well... by DeafByBeheading · · Score: 1

    I dunno... In the first paragraph, they manage to claim that the formula is--get this--"E mc2". That's right, not squared--just doubled. And who really needs an equal sign in a formula? Go Yahoo! If I had a dog, its blog would have more scientific credibility than this article.

    --
    Telltale Games: Bone, Sam and Max
  4. Re:last part of write-up was great by Anonymous Coward · · Score: 1, Insightful

    Since the program is intended for all audiences, including elementary school students and other non-computer science degree holders, yeah, it is useful.

  5. Re:last part of write-up was great by soft_guy · · Score: 4, Funny

    You geeks are always upset when people explain technical details like "squared". That's why the business majors of the world have to tell you what to do! If you majored in business, you would not have learned useless concepts like "squared" and you would understand why the general public needs this explained to them.

    As to why would someone be interested in E=mc^2 without knowing the concept of "squared", you obviously don't understand business. We can't limit the target audience of our movie to only the few people who know about "squared".

    --
    Avoid Missing Ball for High Score
  6. True origin of the famous equation (Far Side) by macklin01 · · Score: 3, Funny

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

    --
    OpenSource.MathCancer.org: open source comp bio
    1. Re:True origin of the famous equation (Far Side) by Anonymous Coward · · Score: 2, Funny

      Great moments in science: Einstein discovers that time is actually money.

    2. Re:True origin of the famous equation (Far Side) by NanoGator · · Score: 1

      "Great moments in science: Einstein discovers that time is actually money."

      The great Houdini escapes a black hole!

      (Ok, it wasn't about Einstein, but $10 says he would have chuckled.)

      --
      "Derp de derp."
    3. Re:True origin of the famous equation (Far Side) by Destoo · · Score: 1

      Of course he would have..

      However, these hypothetical objects were not the topic of much interest until the late 1960s. Most physicists believed that they were a peculiar feature of the highly symmetric solution found by Schwarzschild, and that objects collapsing in nature would not form black holes.

      Albert Einstein died in 1955.

      Oh.. you meant the other one.. Baby Einstein, right?

      I'll take that 10$ in Sqrt(-1) bills.

      --
      Nouvelles de jeux et technologies en français. TC
    4. Re:True origin of the famous equation (Far Side) by NanoGator · · Score: 1

      "Albert Einstein died in 1955.

      Oh.. you meant the other one.. Baby Einstein, right?"


      Um, no. You see, I used a couple of words in my post that you might have found somewhat interesting. They were would and have.

      --
      "Derp de derp."
  7. Re:Einstein was wrong by biryokumaru · · Score: 1

    Here's the guy (horrendous quality):

    http://www.autodynamics.org/einstein_wrong.html

    --
    When you're afraid to download music illegally in your own home, then the terrorists have won!
  8. Re:last part of write-up was great by Microlith · · Score: 2, Insightful

    The fact that such an explanation is necessary is quite saddening. Knowlege of something so basic as what it means to square a number should be commonplace.

    It shows the willingness of people to remain ignorant of so many things, and concern themselves utterly with the trivial.

  9. WTF @ summary by Sartak · · Score: 5, Insightful

    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?

    1. Re:WTF @ summary by Anonymous Coward · · Score: 2, Insightful

      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.

    2. Re:WTF @ summary by nametaken · · Score: 1

      Around here we're more concerned with the fact that major funding for this production was provided by Google.

      No, really.

    3. Re:WTF @ summary by dos_dude · · Score: 1

      If the program is really based on Bodanis' book, even nerds that presumably "know" the equation will have a chance to learn something new.

      In the book, Bodanis takes each part of the formula and provides background for its origin. While you maybe one heck of a clever nerd, you might not necessarily know about the origins of the equals sign, for instance.

      If stories about Einstein's equation make you weep, what about stories about Star Trek/Wars?

    4. Re:WTF @ summary by elgatozorbas · · Score: 1
      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. (disclaimer: I haven't read it completely do far).

    5. Re:WTF @ summary by Anonymous Coward · · Score: 1, Interesting

      So you complain when the editors edit and complain when they dont.

      We complain when they don't edit, and complain when they edit poorly.

    6. Re:WTF @ summary by TrentL · · Score: 1

      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

    7. Re:WTF @ summary by ajpr · · Score: 1

      Most of my professors and lecturers during University did not know what I meant when I used ^ instead of superscript.

    8. Re:WTF @ summary by GrungyLotG · · Score: 1

      That seems rather odd, depending upon when you went to your university. It is common to use "^" for exponents above squared and cubed on the majority of calculators I've handled, and it is extremely common on any HTML page (Apparently the sup element is not well-known.

    9. Re:WTF @ summary by 1u3hr · · Score: 2, Insightful
      you complain when the editors edit and complain when they dont.

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

    10. Re:WTF @ summary by Geoffreyerffoeg · · Score: 1

      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?

  10. Buying my own copy by Douglas+Simmons · · Score: 1

    Anybody know off hand how/where I can buy this and other older PBS productions? Much obliged..

    1. Re:Buying my own copy by TheCarlMau · · Score: 1

      TiVo it. :-)

    2. Re:Buying my own copy by kegwell · · Score: 1

      pbs.org ?

    3. Re:Buying my own copy by Douglas+Simmons · · Score: 1

      thanks .. i was just spamming my sig :). Questions are good bait sometimes, i guess they have to be less stupid.

  11. A little help... by jswalter9 · · Score: 1

    I seem to remember that a group of physicists disproved the formula. Can anyone remember whom?

    --
    Retired from software... maybe. Sort of.
    1. Re:A little help... by larsu · · Score: 1

      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 giant black hole. As it's compacting, the incredible force of gravity from all the matter in the universe over a short distance is trying to compact matter into as small of an area as possible. It is also causing time to be very slow (compared to the your current frame of reference). So, E=mc^2 doesn't quite work to describe the behavior in that system where time is so drastically different. But, how time is measured in the above equation is still undecided. Maybe it should it be a differential from a standing frame of reference?

      I am not a physicist. :)

    2. Re:A little help... by Asprin · · Score: 1


      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.

      --
      "Lawyers are for sucks."
      - Doug McKenzie
    3. Re:A little help... by the+morgawr · · Score: 1
      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.

      --
      The policy of the United States is worse than bad---it is insane. -- Ludwig von Mises, Economic Policy(1959)
    4. Re:A little help... by Asprin · · Score: 1


      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 writting a capital sigma out front of the components to indicate sums, the sums are implied by writing the components with common indices. (E.g. matix M * vector A would be written as Mij*Aj. It's understood that you have to sum over all possible values of j to get the component i you are looking for.)

      --
      "Lawyers are for sucks."
      - Doug McKenzie
    5. Re:A little help... by the+morgawr · · Score: 1

      It's been awhile but I though GR requried tensors and manifolds. Am I thinking of something else?

      --
      The policy of the United States is worse than bad---it is insane. -- Ludwig von Mises, Economic Policy(1959)
    6. Re:A little help... by Asprin · · Score: 1


      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 remembers the least from their grad school E&M class. Snicker!

      --
      "Lawyers are for sucks."
      - Doug McKenzie
  12. Animaniacs by thebdj · · Score: 4, Funny

    Everyone knows that it was the Wacko Brothers and their sister Dot selling kid scout cookies to Einstein that helped him create E=mc^2, by singing the Acme song.

    --
    "Some days you just can't get rid of a bomb."
    1. Re:Animaniacs by thebdj · · Score: 1

      Warner brothers, by goodness this is what happens when I am tired...

      --
      "Some days you just can't get rid of a bomb."
  13. Already out on digitaldistractions by mailman-zero · · Score: 2, Informative

    If I'm not mistaken, this is the same documentary as here.

    It's a pretty interesting show.

    --
    Let's play video games with mailmanZERO
  14. Get it right! by Anonymous Coward · · Score: 1, Funny

    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

  15. Neat but one burning question by zenst · · Score: 2, Interesting

    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
    --

    1. Re:Neat but one burning question by khellendros1984 · · Score: 1

      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.

      --
      It is pitch black. You are likely to be eaten by a grue.
    2. Re:Neat but one burning question by Detritus · · Score: 1

      C is the speed of light in a vacuum. It's a constant.

      --
      Mea navis aericumbens anguillis abundat
    3. Re:Neat but one burning question by orbitalia · · Score: 2, Informative

      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 of Imperial College London) If you are so inclined you can read the paper yourself here

    4. Re:Neat but one burning question by my_haz · · Score: 1

      and this is the documentary on that subject

      Equinox.Einsteins.Biggest.Blunder.DivX511.www.MVGr oup.org.torrent

      You will have to find the actuall link yourself (google it)

    5. Re:Neat but one burning question by Vellmont · · Score: 1


      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 then yell something to the first person, and they repeat it to the next person in line. The speed of sound is still constant in the experiment, but the speed of propogation of your message depends on how many people/meter you have.

      --
      AccountKiller
  16. Rolling in the grave by can56 · · Score: 2, Insightful

    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.

  17. Re:Is this new? by mailman-zero · · Score: 1

    The torrent is here.

    I checked this out a few weeks ago. It's really an interesting show depicting some of the greats that preceeded Einstein as well.

    --
    Let's play video games with mailmanZERO
  18. Re:Is this new? by mailman-zero · · Score: 3, Informative

    The torrent is here.

    I checked this out a few weeks ago. It's really an interesting show depicting some of the greats that preceeded Einstein as well.

    --
    Let's play video games with mailmanZERO
  19. I've seen this already I think by FunkyRat · · Score: 3, Interesting

    If this is the same program as this 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.

    1. Re:I've seen this already I think by Metatron · · Score: 1

      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.

    2. Re:I've seen this already I think by Andrew+Ford · · Score: 1

      I saw it too and while I learned a few historical facts, I thought that the script was poor, the acting was rather wooden, and the program could have conveyed the same information in a third of the time.

  20. The real question is by johansalk · · Score: 1

    Is it really that important, or is it because it's popular culture media-friendly?

  21. Seen it already by Gabhlan · · Score: 2, Informative

    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.

    --
    The wind blew so cold
    The fan won't turn any more
    Files die in the heat
  22. Rest Mass by Joffy · · Score: 4, Informative

    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.

    1. Re:Rest Mass by DirePickle · · Score: 1

      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

    2. Re:Rest Mass by croto · · Score: 1

      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)

    3. Re:Rest Mass by Anonymous Coward · · Score: 1, Informative

      Most people think that a bowling ball that weighs 10 pounds has a set mass no matter what

      And they would be right, to within what they actually can perceive.

      If they were trying to push a bowling ball moving at 99.9999% the speed of light, their concept of mass would still agree with that of Einstein's mass.

    4. Re:Rest Mass by cynical+kane · · Score: 1

      It should be pointed out that, because all frames of reference are equal, rest mass is "real" mass since it's always the same in every frame of reference. Relativistic mass is a derived concept, used because it's easier to understand and because it makes many equations easier.

    5. Re:Rest Mass by DirePickle · · Score: 1

      (1/(1-(v/c)^2))^1/2, that is. Duh.

    6. Re:Rest Mass by mhore · · Score: 1

      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.

      --

      Mmmm......sacrelicious.

    7. Re:Rest Mass by Geoffreyerffoeg · · Score: 1

      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 to remember this is to remember that y=sqrt(1-x^2) is a (semi)circle. In other words, if you are moving some fraction x of the speed of light, then x and k must be points on the unit circle (or alternatively, x^2+k^2=1).

      An interesting side note of this is that a photon, traveling at the speed of light, has k=0. Since it has energy, and energy is proportional to relativistic mass, it must have relativistic mass. But mk=m0, so its rest mass is zero. This is how a photon can have zero (rest) mass yet be influenced by gravity.

      (I think that physicists prefer gamma=1/k as the conversion factor, but k is easier to visualize in my opinion, because it avoids the reciprocal.)

  23. Read the book by 1ad · · Score: 1

    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...

  24. "varying" speeds of light by Quadraginta · · Score: 4, Interesting

    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 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.

    1. Re:"varying" speeds of light by bjbyrne · · Score: 1

      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?

    2. Re:"varying" speeds of light by poopdeville · · Score: 1

      Yeah. I spent quite a bit of time at Reed's TRIGA Mk1. Cerenkov radiation is purty.

      --
      After all, I am strangely colored.
    3. Re:"varying" speeds of light by 1u3hr · · Score: 1
      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.

  25. Re:last part of write-up was great by Beavbo · · Score: 1

    It shows the willingness of people to remain ignorant of so many things, and concern themselves utterly with the trivial.

    Well thank goodness slashdot is here to educate us all, otherwise I would be off doing something completely trivial! Where's that link to the "Intelligent Door Handle" thread... Oh wait....

  26. PBS Scientific Documentaries by crumbz · · Score: 1

    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.

  27. I really enjoyed it by FunkyRat · · Score: 2, Informative

    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!"

    1. Re:I really enjoyed it by Metatron · · Score: 1

      By the looks of it, the narration has been redone for the US, seems like they're going to have John Lithgow instead.

  28. It's a semantics, the formula WAS right by Newton+IV · · Score: 5, Interesting

    Nah, the formula is right E=mc^2, except the mass m is the RELATIVISTIC mass, defined as m_0/sqrt(1-(v/c)^2). m_0 here is the mass of the body at rest. But indeed, the rest mass m_0 is a better quantity to use. See for example http://math.ucr.edu/home/baez/physics/Relativity/S R/mass.html

    1. Re:It's a semantics, the formula WAS right by Aglassis · · Score: 1

      I was responding to "Could someone please explain the terms of this form to the less physics enlightened of us?" I did that and I explicitly stated that m was the rest mass (I don't like writing m_0 unless I have to). I'm not sure why you think that I believe the formula was wrong.

      --
      Suddenly, the hairy finger of a familiar monkey tapped me on the shoulder. It was time.--G. T.
    2. Re:It's a semantics, the formula WAS right by XchristX · · Score: 1

      There's no such thing as relativistic mass. It's an unnecessary concept invented by Bergmann, Einstein's student. We can formulate all of STR without even mentioning this odd thing. It leads to the misconception that mass depends on velocity, which it does NOT. There is only the rest mass, which is the mass of the particle, a lorentz invariant since it equals a lorentz covariant term if you express it in 4-vector notation.

      --
      l'Homme n'est Rien l'Oeuvre Tout: Gustave Flaubert to George Sand
    3. Re:It's a semantics, the formula WAS right by Jesus+2.0 · · Score: 1

      It leads to the misconception that mass depends on velocity, which it does NOT. There is only the rest mass

      Are you not, then, more gravitationally attracted to a moving object than you would be were it stationary (all relative to you, of course)?

    4. Re:It's a semantics, the formula WAS right by XchristX · · Score: 1

      I said STR, NOT GTR. In GTR, matter tells space how to curve (through Einstein's Field equations), and space tells matter how to move. In the case mentioned above, the metric depends on relative velocity, that's all. You do not need any 'relativistic mass' crap to figure that out.

      --
      l'Homme n'est Rien l'Oeuvre Tout: Gustave Flaubert to George Sand
  29. clarification... by Quadraginta · · Score: 1

    The Cerenkov radiation itself is just light. The light comes from particles moving faster than light moves in water.

    If the core were in vacuum, there would be no Cerenkov radiation, because however fast the particles came out, they could not exceed the speed of light in a vacuum. Nothing can.

  30. Einstein's Wife by Donny+Smith · · Score: 2, Interesting

    Which one? Second? I'm not sure.

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

    1. Re:Einstein's Wife by ArcSecond · · Score: 2, Interesting

      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.

      --

      I've got a bad attitude and karma to burn. Go ahead. Mod me down.

  31. But the real question... by servognome · · Score: 1

    Is this episode of Nova brought to us by a grant by the Chubb Corporation?

    --
    D6 63 0D 70 89 81 BB 8E 7B 7C 5F 5D 54 EA AB 73
  32. Re:last part of write-up was great by NanoGator · · Score: 2, Funny

    "It shows the willingness of people to remain ignorant of so many things, and concern themselves utterly with the trivial."

    ... said the guy bitching on Slashdot.

    --
    "Derp de derp."
  33. Multiplication by itself?!?!? by brian0918 · · Score: 1

    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.

  34. WATCH IT! by carldot67 · · Score: 1

    We had it in the UK.
    Its brilliant.

    --
    I wish at was Friday, but I dont want to wish my life away. So I wish it was last Friday.
  35. -1 Pseudoscience by cynical+kane · · Score: 2, Interesting

    Have you read that web site? It reads like cult propaganda with math added. Not to mention the horrible grammar, constantly misspelled words, gross misuse of math, horrible website design... we obviously aren't dealing with very smart people here.

    They claim that frames of reference don't actually exist. I don't see why not, but that leaves you with a theory that is completely unable to meaningfully describe any phenomenon that is not standing still. Try to calculate the orbits of a moving Bohr atom, using Autodynamics... whoops, you can't, because the atom is moving, and you can't use the atom's frame of reference because it "does not exist".

    I get the feeling they just can't wrap their puny brains around the concept of a frame of reference, so they outright deny it.

    1. Re:-1 Pseudoscience by biryokumaru · · Score: 1

      I know it's silly pseudoscience, I was just providing a link relevant to that movie =]

      --
      When you're afraid to download music illegally in your own home, then the terrorists have won!
  36. Re: more clarification... by pbhj · · Score: 1

    >>> "they could not exceed the speed of light in a vacuum. Nothing can."

    I think you'll find that the theories show nothing can traverse the s.o.l boundary, that still allows for superluminal particles but makes them hard/impossible to detect.

    http://scienceworld.wolfram.com/physics/Superlumin al.html

    Tachyons aren't just a plot tool for StarTrek script writers!

  37. Measurement Units? by barfy · · Score: 1

    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)?

    1. Re:Measurement Units? by Jamu · · Score: 1

      The c is only there because of the different units. If you don't mind measuring energy and mass in the same units (and any unit of mass or energy will do, provided you stick to just one) then Einstein's equation becomes even simpler and its meaning clearer.

      E = m

      c is normally defined as 299792458 m/s. But people also define it more simply as 1. As you've noticed, doing it this way is much more natural to relativistic domains (but obviously not to everyday experience).

      --
      Who ordered that?
    2. Re:Measurement Units? by fgb · · Score: 1

      If I remember correctly, if you express c in meters/second and m in grams you will get E in joules.

    3. Re:Measurement Units? by Daniel+Dvorkin · · Score: 2, Informative

      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. (Again, IIRC.) Try translating that into units that make sense on an earthly scale: if I throw a 1 kg weight at you at 1 m/s, you're going to feel the impact when you catch it. Now think about that scaled up by almost 17 orders of magnitude.

      --
      The correlation between ignorance of statistics and using "correlation is not causation" as an argument is close to 1.
    4. Re:Measurement Units? by stevelinton · · Score: 1

      c in meters/second, m in KILOgrams gives e in Joules
      c in centimeters/second, m in grams, gives e in Ergs

      This is not a coincidence or anything. A Joule is by definition the work done by a force of 1 Newton pushing something 1 meter. Meanwhile a Newton is the force which, applied to 1 kilogram body will accelerate it at 1 meter/second/second, so a Joule is a kilogram meter^2/second^2. A similar story holds for centimeters, grams and ergs.

      So, you can get a truly unit free formulation: the energy equivalent of a certain amount of mass is the work done by a force sufficient to accelerate it to the speed of light in one time period, pushing an object as far as light travels in that time period. This gives the same answer, no matter what time period you take.

  38. UKTV by BeCre8iv · · Score: 1

    This was on UK terrestrial a few weeks back - well worth watching

    --
    This perpetual motion machine Lisa made is a joke, it just keeps getting faster and faster. - Homer
  39. Re:Is this new? by Destoo · · Score: 1

    Is this the nova episode that's going be broadcast on tuesday?

    Thanks for the link.

    --
    Nouvelles de jeux et technologies en français. TC
  40. Re:Well... by Destoo · · Score: 1

    Of course, get it wrong at just the right time.

    E^(Pi * i)+1=0

    (plus, not minus)

    I always though E^(iPi)=-1 fit more tightly, or even E^(iPi)=i^2.

    --
    Nouvelles de jeux et technologies en français. TC
  41. Squares With Geometry by Doc+Ruby · · Score: 1

    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?

    --

    --
    make install -not war

    1. Re:Squares With Geometry by Doc+Ruby · · Score: 1

      OK, Anonymous stoner Coward, what is the enigmatic weed that you are having too close a relationship with? And why do you find it more interesting than the real geometric implications of Einsteins spacetime equivalence algebra?

      --

      --
      make install -not war

  42. Curved Spaceballs by Doc+Ruby · · Score: 1

    What if Einstein discovered that the Universe is hourglass shaped?

    --

    --
    make install -not war

  43. 'Simple' is right by 26199 · · Score: 1

    That page is full of nonsense, and the derivation is nonsense as well. Where does 'p = E/c' come from?

    Looks like that whole page is one big troll... someone has too much time on their hands.

    1. Re:'Simple' is right by 26199 · · Score: 1

      Actually, looking at that page again, they're selling something... their book on how everything in modern science is wrong. Heh. Not a good place to go for scientific information, then :p

  44. Not very Intelligently Designed... by FatSean · · Score: 1

    Cheezy website and questionable gobbledy-gook. WOuld not be surpirsed to find some wack-job fundamentalist religious half-wit behind this 'production'.

    'Cause it sure doesn't seem to be toungue-in-cheek...

    --
    Blar.
  45. Re:Simple derivation of this equation by ZombieWomble · · Score: 1

    That website makes me want to cry :( For example: As we all know, perpetual motion machines are impossible, and claims of such devices are a clear sign of bad science. No device (or natural phenomenon) can operate endlessly without draining a power source, and certainly no device can operate without a power source at all. Yet, our science states that an object dropped into a tunnel cut through the Earth would oscillate back and forth endlessly from one end of the planet to the other. Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy... And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light). And this is just in the first couple of blurbs from that page you linked. And not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light. Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.

  46. Re:Simple derivation of this equation by ZombieWomble · · Score: 1
    D'oh... I sorta forgot paragraph breaks. Well doesn't taht look like a complete mess? Here it is with proper formatting, if the above hurts your eyes: That website makes me want to cry :(

    For example: As we all know, perpetual motion machines are impossible, and claims of such devices are a clear sign of bad science. No device (or natural phenomenon) can operate endlessly without draining a power source, and certainly no device can operate without a power source at all. Yet, our science states that an object dropped into a tunnel cut through the Earth would oscillate back and forth endlessly from one end of the planet to the other.

    Pretty much anything can sustain perpetual motion if you neglect forces like friction which remove energy... And he doesn't seem to understand the difference between force and energy, or even the basic CONCEPT of a black hole (he explains the fact that light can't escape in terms of the fact that the black hole doesn't produce it's own light...) And this is just in the first couple of blurbs from that page you linked.

    Not to mention, his 'simple' derivation is based entirely on conclusions which arise from relativity (i.e. Einstein's own derivation, which he also gleefully 'debunks' in many places) and is only applicable to light.

    Once again: If an 'earth-shaking'/'revolutionary' theory is first published in a book, it's usually best to laugh and walk away.

  47. Ah. the theory of relativity by David+Horn · · Score: 1

    A theory... that you only tell your relatives. ;)

    --
    PocketGamer.org - For the gamer on the go!
  48. 2 for 'squared' by 1u3hr · · Score: 1
    and 2 for 'squared,' the multiplication of one number by itself."

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

    1. Re:2 for 'squared' by RealOldGuy · · Score: 1

      Yeah, now I know why I could never find the footnote.

      -- rog

  49. Heaviside's Equation by radtea · · Score: 2, Interesting


    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.

    --
    Blasphemy is a human right. Blasphemophobia kills.
  50. Re:Simple derivation of this equation by RichardX · · Score: 1

    Well, the page you linked to appear to be a pile of steaming woo-woo crap, but on the up side, we're sig buddies!
    Glad to see some other slashdotters have been Saved here. Praise spaghetti!

    --
    Curiosity was framed. Ignorance killed the cat.
  51. Re:last part of write-up was great by IchNiSan · · Score: 1

    If you business majors didn't learn about ^2 (squared) in middle school, or at least by freshman year of high school, how the fuck did you graduate?

  52. here's the torrent of the show, already been on tv by Squeezer · · Score: 1

    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

    if the link doesn't work go to http://www2.digitaldistractions.org:8080/ and search for e=

    --
    Does the name Pavlov ring a bell?
  53. c^2 unnecessary? by cgenman · · Score: 1

    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 material? Or is it just there to show school children that the energy contained is really, really big? Is there something that I'm missing?

    1. Re:c^2 unnecessary? by Geoffreyerffoeg · · Score: 1

      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, which simplify this and other equations by setting certain constants to 1. You are just converting between units, because the constant C becomes just 1 (length/time)^2. And you get a definition of units that's based on the universe's physical constants, not just some bar of metal in Paris*.

      Or is it just there to show school children that the energy contained is really, really big?

      No, the energy is not really big. It's exactly the same as the mass. It just seems big because we're used to large masses, small energies, and slow velocities in everyday life (in terms of Planck units). As the Wikipedia article quotes an article in Physics Today, "We see that the question is not, 'Why is gravity so feeble?' but rather, 'Why is the proton's mass so small?' For in [Planck] Units, the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number."

      *Yes, I know they redefined the meter based on some 12345.67 wavelengths of some random isotope's emission. But they got that number by measuring the bar of metal in Paris. What's more, they got the bar of metal by taking some fraction of the Earth's circumference, and they got the second by taking a fraction of the Earth's day, which is a really non-sequitur way of getting units to measure the speed of light.

  54. SPOILER: Here's the drama... by finelinebob · · Score: 1

    E = ma^2 ... nah

    E = mb^2 ... feh!

    E = mc^2 !!!!!

  55. how much did wife Mileva help him? by peter303 · · Score: 1

    A few years back there was a controversial suggestion 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.

  56. Re:Well... by Rubyflame · · Score: 1

    Of course, the more general form, exp(x) = cos(x) + i sin(x), is much more useful.

    --

    All it takes is nukes and nerves.
  57. To put it simply, by arun_s · · Score: 1

    just as 1 mile = 1.6 x 1 km approximately,
    E = (c^2) x m
    Its just a conversion from one unit to another, the beautiful thing here being that it relates a unit of energy to a unit of mass (not energy to energy or mass to mass), showing that energy and mass are effectively two sides of the same coin.
    If he were alive today, Einstein woulda got a +5 Insightful at /.

    --
    I can explain it for you, but I can't understand it for you.