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Education Science

100 Years of Special Relativity 299

phrotoma writes "Wikipedia notes in their Selected Anniversaries section that today marks the 100th anniversary of Albert Eintein's publication of the third of his four Annus Mirabilis Papers entitled On the Electrodynamics of Moving Bodies; the seminal work that introduced the concepts which would come to be known as Special Relativity. This event is also being commemorated in a UN endorsed celebration of physics: World Physics Year 2005 with talks and events at public schools, museums, and universities the world over."
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100 Years of Special Relativity

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  • 100 Years (Score:5, Funny)

    by Inkieminstrel ( 812132 ) on Thursday June 30, 2005 @10:45AM (#12950681) Homepage
    100 years according to which observer?
    • 100 years according to which observer?

      The first five posts are all riffs on the same theme -- dilation of time. Does that say more about the level of education among Slashdotters, or about our lack of creativity, or both? I guess it's all relative.
      • by Black Parrot ( 19622 ) on Thursday June 30, 2005 @11:21AM (#12951069)


        > The first five posts are all riffs on the same theme -- dilation of time. Does that say more about the level of education among Slashdotters, or about our lack of creativity, or both?

        Maybe it's just one post arriving via gravitational lensing.

      • Re:100 Years (Score:4, Insightful)

        by drsquare ( 530038 ) on Thursday June 30, 2005 @01:50PM (#12952336)
        It happens with all vaguely-science related articles. Most Slashdotters are just kids who've managed to install Linux, they don't know much about science and technology. So when an article like this comes up, they've nothing informed to say. But they treat Slashdot as a chatroom, the social life they don't get in the real world. And they're desperate for attention, so they HAVE to post. Even if they have nothing to say. Especially if they have nothing to say.

        So we have kids, desperate to get a +5 funny to validate themselves, on an article they know nothing about. So what do they do? They try posting something 'hilarious', like a play on words of something in the article, or something starting with 'Did anyone else read this as...', or a reference to one of the tired slashdot memes, as if quoting Douglas Adams makes them one of the Slashdot 'in crowd'.

        It ruins it for the rest of us, as on any science article, we have to scroll half way down the page to get to the first person who actually says something relevent to the article.
    • Re:100 Years (Score:3, Interesting)

      by RWerp ( 798951 )
      Each object in the Universe has its own coordinate system (a thing equivalent to an observer), in which it is always at rest. To put it shortly, it's observing itself. The time measured in this coordinate system is called a proper time. I guess we can say that it's been ca 100 years of proper time of the manuscript of Einstein's article...
      • Re:100 Years (Score:3, Interesting)

        by AKAImBatman ( 238306 ) *
        Arguably, space-time warping can be accounted for in a calendar as long as some sort of reference point is given. For example, if I left on a rocket ship at .95C, bound for Alpha-Centauri and returned 10 years later (Earth time), I could still say that ten years have passed on the Sol calendar based on the current positions of the bodies inside the solar system. The fact that the movement of those bodies occurred inside a period of only 8 years my time is irrelevant. 10 years has still passed according to t
    • by millennial ( 830897 ) on Thursday June 30, 2005 @11:10AM (#12950960) Journal
      Due to special relativity, I accuse you of stealing my joke and posting it before I could.
  • Pffft (Score:5, Funny)

    by kaellinn18 ( 707759 ) on Thursday June 30, 2005 @10:45AM (#12950688) Homepage Journal
    I already read about this tomorrow.
  • 100 years? I don't understand. That paper was published just two years ago, right before I embarked on my intersteller voyage travelling near the speed of light. I've only been gone two years, so clearly one of us has calendar issues.
  • by RealProgrammer ( 723725 ) on Thursday June 30, 2005 @10:48AM (#12950717) Homepage Journal
    Leif Ericson discovered it hundreds of years earlier, and the Native Relativians were already there anyway. Their boats were just to slow to test the theory.

    Eurocentric insensitive clods!
  • by Doc Ruby ( 173196 ) on Thursday June 30, 2005 @10:48AM (#12950718) Homepage Journal
    Although he's a hero of mine, I've found only Einstein's "photoelectric effect" insights to be a work of genius - a "quantum leap", if you will (or even if you won't, how will I know? It's all the same to me...) Relativity is brilliant, and changed science and culture forever. But it's really an ingenious refinement of Maxwell's field equations, even more than extra precision added to Newton's formulas.
    • [ ] You understand relativity :)
    • by wass ( 72082 ) on Thursday June 30, 2005 @11:18AM (#12951036)
      Relativity is brilliant, and changed science and culture forever. But it's really an ingenious refinement of Maxwell's field equations, even more than extra precision added to Newton's formulas.

      First of all you're only referring to special relativity here, which ignores acceleration and gravity. Secondly, there were still some leaps of faith to be made, such as assuming c is constant in all frames of reference, which Lorentz showed non-Newtonian transformations that would allow this for Maxwell's equations. And expanding the new energy definition and concluding the zeroth-order term (mc^2) is the rest energy of mass also took another leap of faith (although that paper wasn't published until a few months after this first relativistic one).

      But even so, discovering the connection between relativity and E&M is still amazing, in my opinion. For examle, the permittivity (epsilon_0) and permeability (mu_0) of free space are two constants that can be measured in the laboratory rather easily. Yet Maxwell's equations in vacuum describe waves travelling at speeds 1/sqrt(epsilon_0*mu_0), which is exactly the speed of light in vacuum (although in Gaussian units this connection is far more obvious). It's pretty amazing to think how these are related. But you still need to make some assumptions to get the Lorentz transforms between reference frames.

      Additionally, even simple special relativity was extremely controversial, it rejected many assumed notions of space/time. There were also many paradoxes that took awhile to get ironed out. Many scientists didn't believe in relativity until it was shown in experiment. And in fact the theories of relativity were so controversial that the Nobel committee didn't want to award Einstein the prize based on these, so went for the safer 'Photoelectric Effect' instead.

      And thirdly, general relativity, although again not included in this 100 year anniversary, is total genius, and it took Einstein 10 years to come up with the theory. So don't wave off relativity as just a 'refinement of Maxwell's field equations' because it really is much more than that.

      • Well, we are discussing special (not general) relativity. General is a magnum opus. But we might have a merely semantic disagreement, which does reflect in different standards for "genius". I mean it quite literally, "the origin or source". Special relativity was an evolution of Maxell's fields, and General relativity was an evolution of Special. Even the equivalence of gravity and EM was implications of those progressive developments. Often it is a novel implication that is more valuable, and even a greate
      • (BTW, nice .sig ;)

        Well, we are discussing special (not general) relativity. General is a magnum opus. But we might have a merely semantic disagreement, which does reflect in different standards for "genius". I mean it quite literally, "the origin or source". Special relativity was an evolution of Maxell's fields, and General relativity was an evolution of Special. Even the equivalence of gravity and EM was implications of those progressive developments. Often it is a novel implication that is more valuable
        • Firstly, it took decades after Maxwell's equations were known to get the Lorentz transformations. Lorentz merely idenfitied them as those required to keep the equations the same in all reference frames. Einstein took it further to postulate that laws of physics ARE the same in all reference frames, with speed of light the maximum possible speed. And furthermore that time and space REALLY ARE non-Newtonian. that's quite a proclomation to make.

          If SR was just a tippy-toes extension of maxwell's laws, as

          • This disagreement really is a question of semantics, of degree of "innovation" required of "genius". Did SR contradict Maxwell in any way, as it did Newton? If so, I'd have to call Einstein's jump "genius". Just as I call his radical reformulation of light, from "either corpuscles or waves", to packets of momentum somehow equivalent to photons, "genius". Which showed up later in the matter-energy equivalence in General Relativity.

            I consider Einstein himself a genius. Because his vision of the universe, fro
            • Einstein basically came up with SR because he was troubled by some apparent (and well known at the time) contradictions between Maxwell's equations and Newtonian time frames. SR was his method of resolving these contradictions.

              Regarding the photoelectric effect, Planck had already proposed the notion of discrete quanta of radiation a few years prior in order to get a consistent statistical-mechanical description of blackbody radiation that wasn't susceptible to the 'ultraviolet catastrophe'. Einstein ex

          • Einstein took it further to postulate that laws of physics ARE the same in all reference frames

            Nope, that was already postulated by Newton. The laws of Newtonian mechanics are the same in all frames of reference and they are transformed by the Galilei-transformations. I guess this was also the drive for Lorentz to look for transformations which do the same on Maxwell's equations.
            What Einstein managed was to bring these two contradictory theories into a consistent one, the Special Relativity.

            </nit
      • First of all you're only referring to special relativity here, which ignores acceleration and gravity.

        I agree with the central message in your post. However, SR does include acceleration, jerk (the third derivative of position with time), and in principle all orders of positional change with time. You can also apply gravity as "just another force" in Newton's Second Law F=dp/dt, where F is the net force and dp/dt is the instantaneous rate of change of the momentum in time. Relativistically, p=gamma*m

    • I don't think I agree with you. It is true that after Michelson-Morley's experiment there was all data available to everybody to put forward Einstein's theory. However, it took Einstein to pluck up the courage and propose it.
      • I'm not sure it was "courage" that produced Einstein's "frames of reference" thought experiments. Or that "genius" is defined by courage. Though there is some of that in working as the source of a new idea. But Einstein's new idea of Special Relativity was a refinement of Maxwell's fields - as Einstein himself claimed. Einstein's source for Relativity was Maxwell.
      • The proposed experiments to detect gravity waves almost exactly replicate the Michelson-Morley experiment (to a *much* greater precision), and researchers expect the opposite result. Funny how that works.
    • Actually, it is not really a refinement. Maxwell's equation are the same. Maxwell's brilliance was in determining that the equations for electrical and magnetic phenomena were inconsistent. He fixed the inconsistency by modifying one equation with a drift current term. The net result was showing that electricity and magnetism were inter-related and demonstrating the equations governing time-harmonic electromagnetic fields. This gave rise to concepts such as Lorentz contraction, which is based on how an
      • True, it's not really a refinement of Maxwell's equations - just their application to other phenomena. Even less a "radical departure" than Einstein's extra terms on Newton's equations, which were more like a "refinement". Einstein, like most geniuses, had a new vision - unlike many geniuses, he could communicate it to others who could recognize it, and help articulate it.
  • by Citizen of Earth ( 569446 ) on Thursday June 30, 2005 @10:52AM (#12950754)
    You'd think it wouldn't be considered quite so Special any more.
    • > You'd think it wouldn't be considered quite so Special any more.

      Please use those equations to calculate the path of this ball I'm going to throw deep. You'll understand what I mean. It just is plain neglibile in a general physics perspective.

      But it does come into play while designing gigahertz circuits for sattelites or when calculating gravity pull of celestial bodies. Nothing an average man needs to know to calculate anything on earth (unless he works at CERN or something). Hence special .

  • Remember though. . . (Score:4, Informative)

    by smooth wombat ( 796938 ) on Thursday June 30, 2005 @10:52AM (#12950759) Journal
    it's only a theory, not a fact. As such I demand that schools teach that it is tiny demons which are causing the effects we are seeing.

    My theory is just as credible as yours since it's only a theory and not a fact.

    Ok, now that that diatribe is over, what's truly interesting is not that what Einstein proposed 100 years ago is still being studied and restudied, it's that one portion of it was recently confirmed. Frame dragging was only confirmed last year [universetoday.com].

    Certainly other parts have been verified (relative time for example) but this portion, frame dragging, puts things in a whole new light. We're not just bodies in space. Instead, are bodies are changing the space around us!

    • You mean Maxwell's Daemon?
    • by Cheeko ( 165493 )
      Well more accuratly Frame dragging was proposed 97 years ago ;) as a part of General Relativity. As opposed to Special Relativity :)
      • OK, I just heard about this, it's bad enough that I have to drag around a separate PDA, phone, and laptop - now I find out I'm dragging space and time around with me as well?
      • Actually, one could argue that frame dragging predates general relativity. Frame dragging grew out of Mach's Principle. Essentially Mach was worrying about relativity pretty early on. Although Einstein asserted that velocity relative to empty space was meaningless, Mach wanted to argue that so was acceleration. The only way he could make sense of it was if acceleration was relative to the distant stars. This is the very first version of frame dragging - that somehow our local coordinate frame follows the ma
    • by Decaff ( 42676 )
      it's only a theory, not a fact. As such I demand that schools teach that it is tiny demons which are causing the effects we are seeing.

      My theory is just as credible as yours since it's only a theory and not a fact.


      It is an extremely well tested theory. For example particle accelerators would not work unless it were true.

      Ok, now that that diatribe is over, what's truly interesting is not that what Einstein proposed 100 years ago is still being studied and restudied, it's that one portion of it was recen
      • My diatribe was aimed at those who want to consider Intelligent Design/Creationism alongside Darwins theory of Natural Selection. Apparently the part about testing what a theory proposes escapes them.

        Yes, you are correct. I confused General and Special Relativity. My apologies. Good thing I don't have a geek card or it would be taken away for such an oversight.

        Regardless, I still think it's cool that bodies in space can change space itself. Opens up interesting possibilities.
      • Ah ha, but have you have seen a so-called 'particle accelerator' actually 'working' or are you just taking the fact that they exist and work on FAITH from someone else.

        Ah ha, ha ha. Another soul saved for the good Lord's work.
    • You're exactly right, special relativity, as originally proposed by Einstein, isn't the full because it ignores quantum mechanics. It's QED, the quantizing of the electromagnetic field in a way consistent with both traditional quantum mechanics and special relativity, that supersedes it.

      And of course even QED ignores QCD and whatever quantum gravity turns out to be too.

  • [Church Lady]
    Well, isn't that special.
    [/Church Lady]
  • by DanielMarkham ( 765899 ) on Thursday June 30, 2005 @10:54AM (#12950788) Homepage
    The guiness of Einstein was that he synthesized some more arcane work into some fairly simple equations, continuing to refine what we knew about the universe
    But it's already common knowledge that we don't have a GUT yet, and everything we do have seems very complex and overdone, much the same as it was before E=mc2
    I can't help but wonder if someone will come along in the next decade or so and synthesize these more complex equations into another step forward for mankind. Who knows? Maybe the answer is something like "42"

    Was Worf A Programmer? [whattofix.com]
    • > The guiness of Einstein was that he synthesized some more arcane work into some fairly simple equations, continuing to refine what we knew about the universe [...] I can't help but wonder if someone will come along in the next decade or so and synthesize these more complex equations into another step forward for mankind.

      I'm sure more guiness [wikipedia.org] will help.

      > But it's already common knowledge that we don't have a GUT yet, and everything we do have seems very complex and overdone, much the same as it w

      • In a way, he did make things simpler too - most of the transformations arising from SR had already beeen derived elsewhere (e.g. when trying to explain the Michleson-Mosley experiment), but Einstein produced a simple rule (i.e. that physical constants are invariant) which led directly to those results - and several other interesting ones, too
    • is not 42, it's the fine structure constant [wikipedia.org], which basically ties E&M to quantum mechanics. As Richard Feynmann said, it is "one of the greatest damn mysteries of physics: a magic number that comes to use with no understanding by man". It's interesting because it's dimensionaless, meaning it's the same in any system of units, so physicists and mathematicians have tried to figure out special properties of this number, or simple ways to derive it via numerology.

      It's also possible this number may have

  • This is an incredible time to be alive and watching the strides made by physics. Recent developments in the creation of new forms of matter [slashdot.org], and the coming experimental fusion reactor in France make the future hopefully brighter for man and mankind.

    Lets hope we don't end up with a "Black Mesa" incident...
    • What are you on man!? That would be SO FREAKING COOL.

      Shotgun City 17!

    • This is an incredible time to be alive and watching the strides made by physics.

      My view is that things are rather tedious at the moment. Physics has become mired in a swamp of obscure mathematics and possibly permanently untestable hypotheses (such as String theories). Any attempt to find out 'what is really going on' seems to have been forgotten in the race to publish indecipherable papers and come up with yet another 'how many dimensions this time?' idea. It is definitely Vroomfondel and Magikthise t
  • by YetAnotherName ( 168064 ) on Thursday June 30, 2005 @10:59AM (#12950841) Homepage
    ... and being ONLY a "theory," won't be taught in Kansas public schools.
  • by Anonymous Coward on Thursday June 30, 2005 @11:04AM (#12950892)
    And just think -- under today's copyright laws of life+70, these papers would still be under copyright until 2025. Wikipedia is able to publish these today because copyright law was more sane a century ago.

    I am sorry, nothing deserves 120 years of copyright protection. I doubt almost anything needs even 28 years. I weep for those who will be looking back 100 years from now.
    • > And just think -- under today's copyright laws of life+70, these papers would still be under copyright until 2025. Wikipedia is able to publish these today because copyright law was more sane a century ago.

      > I am sorry, nothing deserves 120 years of copyright protection. I doubt almost anything needs even 28 years. I weep for those who will be looking back 100 years from now.

      Nobody will be looking back, because there won't be anything for them to see without a fee.

    • Yeah, and Einstein would have been a billionaire if it weren't for everone being able to pirate his work.
  • by hubie ( 108345 ) on Thursday June 30, 2005 @11:06AM (#12950908)
    The World Year of Physics is celebrating the year that Einstein put out three of his best papers [aip.org]: Special Relativity, brownian motion, and the photoelectric effect. In addition to the importance of relativity, he also confirmed the existence of atoms with the brownian motion paper, and the existence of quantized energy with the photoelectric effect.

    That was one hell of a year. Any one of those would have established his reputation, but all three, and in the same year!!

  • by everphilski ( 877346 ) on Thursday June 30, 2005 @11:10AM (#12950947) Journal
    Einstein is working in a patent office
    Smith: I'd like to patent this. I call it "Smith's Theory of Relativity"
    Einstein browses through Smith's work, nods approvingly and then kills Smith with the overhead window door
    -everphilski-
  • by RedLaggedTeut ( 216304 ) on Thursday June 30, 2005 @11:13AM (#12950992) Homepage Journal
    Since it seemed to me 5 minutes ago that people where reluctant to answer to this topic, I went to read the intro of Einsteins paper. I found one line that is memorable and that might help you to answer the quiz-question "What are the two postulates of The theory of special relativity?" The answer is in this quote:

    .. the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity") to the status of a, postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice ..

    The thing that needs explaining to me would be "frames of reference". A difference between two frames can be that they are in motion with respect to each other. For example, take a spaceship accelerating to half the speed of light, starting from our resting position. The 2nd postulate explains that the speed of light can be a constant velocity c, both with respect to the frame of the resting observer and the frame(view) of the spaceship. This leads to the question: if you shoot a light ray(velocity c=the speed of light) from the spaceship moving with half= 0.5 c, how come the light ray moves with 1.0 c from the view of both observers, not with 1.5 c from the resting observer?

    As Einstein states, he then proceeds to reconcile the two seemingly paradox postulates by formulating laws of electrodynamics that will work.

    • In the simplest possible terms, "frames of reference for which the equations of mechanics hold good" means that both observers can move at different speeds, but that neither one can accelerate or decelerate while the observation is made.

      This is important because you can always tell by mechanical means if you are accelerating, but without a point of reference, you are unable to tell if you are moving at constant speed. (Gravity and circular motions are just accelerations)

      • you can always tell by mechanical means if you are accelerating

        Are you sure?

        What's the mechanical means to tell if I am floating in deep space or falling down a liftshaft (in a vacuum, obviously ;-).

        J.

    • by aug24 ( 38229 )
      The thing that needs explaining to me would be "frames of reference".

      Let me help: A frame of reference is anywhere from which you can observe anything. Really!

      You sat in a chair is a frame of reference from which you observe the telly which is not moving much relative to you. You in a car moving across the surface of the earth is a FoR from which you observe roadsigns whipping past you at 70mph. You in a space ship is a FoR from which you observe stars and planets zooming past you at half the speed

    • by Decaff ( 42676 )
      This leads to the question: if you shoot a light ray(velocity c=the speed of light) from the spaceship moving with half= 0.5 c, how come the light ray moves with 1.0 c from the view of both observers, not with 1.5 c from the resting observer?

      Maxwell's equations of electromagnetism predicted that an electromagnetic wave (such as light) would travel through space at a certain speed (c). This light is not travelling relative to any physical medium (such as the hypothetical 'aether'). The speed of light is
  • Half of the native residents of West Virginia are filing a lawsuit against the Einstein estate for his use of the phrase "It's all relative" when he was traveling through the state and asked what he thought of the state compared to New Jersey.

  • I guess today is the day to finally listen to these...

    http://www.teach12.com/ttc/EinsteinLectures.asp?ai =18990 [teach12.com]
  • Moving backwards (Score:4, Insightful)

    by ggambett ( 611421 ) on Thursday June 30, 2005 @11:23AM (#12951093) Homepage
    100 years ago Einstein was publishing his theory. Today we're discussing intelligent design and how the dinosaurs attacked Noah's ark [livejournal.com]. Why do I feel we're going backwards? (low res images because of Slashdotting, I guess... can't find a high res version)
    • Yes, I think you could include stuff like ID and Noah's ark under a general phenomenon of anti-science but it's really nothing new. There has always been plenty of anti-science nuts around and they are, well... mostly harmless. As long as no-one tampers with the scientific method, it's ok.

      What's more worrying is the increasingly extensive politicization of science (yes, it's always been political but it's getting even more so), the concomitant drop in the general education levels and the rise of anti-scie

    • While it may seem we are moving backwards, within 20 years of "100 years ago", we had the Scopes Monkey trial, and physicists are still doing research now. We've had backwards people and forwards people the entire time. The only issue now is who is making policy.
    • Today we're...

      When you say we you use a pronoun that includes me. So that's me you're talking about there. I'm not discussing how dinosaurs attacked the ark. So you're offending me buddy. Watch what you're saying. You really mean "Today there's this crackpot talking about how dinsoaur's attacked the Ark...". And you see, when you phrase it correctly, it has nothing to do with Einstein but is just a statement about a crackpot. Crackpots existed in Einstein's time too.

  • As long as we are on the topics there has been some major innovations in the last generation in terms of relativity in the area of optics. That is what would you see if you were going near the speed of light. Turns out is is much more interesting than the typical "everything is shorter in the direction of motion" view of a generation ago. click here for movies with explination [anu.edu.au].

  • Gravity Probe B (Score:4, Interesting)

    by mknewman ( 557587 ) * on Thursday June 30, 2005 @12:05PM (#12951445)
    It's worthy of note that one of the more obscure aspects of Einstein's theorum of Relativity is Frame Dragging, which predicts that time and space will be dragged around a spinning object's mass. This is being tested to an extremely high level of accuracy by the 4 most perfect spheres ever created in the Gravity Probe B (http://www.gravityprobeb.com/ [gravityprobeb.com] experiment going on currently. The project is a 1 year flight with NASA and Stanford as the sponsors, and they are keeping mum as to interim results of the test. Supposedly the results will be announced in the near future after the 1 year test period is complete.
    • It's worthy of note that one of the more obscure aspects of Einstein's theorum of Relativity is Frame Dragging, which predicts that time and space will be dragged around a spinning object's mass.

      Um... actually this is a result of general, not special, relativity. The centenial of that paper isn't for another decade or so.

      The difference is that (in broad terms) general relativity concerns gravity and special relativity concerns objects moving at high speeds.

      --Jeff
  • If only the fans of sci-fi would learn about special relativity, they would quickly learn that their dreams of intergalactic travel would quickly shrivel up. Consider the so-called "twin paradox" that would have a space traveler age quite differently than the people left behind. Here is a link http://theory.uwinnipeg.ca/mod_tech/node141.html [uwinnipeg.ca] with a brief explanation. Better ones can probably be found.
    • What are you talking about? Sci-Fi with integalactic travel almost never (never in my experience, but I'm sure there are some) has ships that go faster than light by just accelerating conventionally. They usually have some explanation for how they get around relativity (wormholes, shifting to diminsions with different rules etc).

      It's rarely good science, but almost all Sci-Fi authors and fans do know about it.

  • "Any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments."

    Galileo was trying to explain why its difficult to tell the earth is moving: when everything moves in unison its like relatively no motion at all. Thats why we dont have thousand mile winds at the equation, the soup doesnt pool to the east in its bowl, etc. The other image Galileo used was things and activities inside a moving ship.

    Einstein amplified this
  • by Forget4it ( 530598 ) on Thursday June 30, 2005 @01:23PM (#12952113) Homepage
    Theories of Relativity
    Five specially commissioned short stories to mark the centenary of Einstein's discovery. Listen to them for next few days only here [bbc.co.uk].
    Share and Enjoy!




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