This discussion has been archived.
No new comments can be posted.
E ~ mc^2
Related Links Top of the: day, week, month.
And it should be the law: If you use the word `paradigm' without knowing what the dictionary says it means, you go to jail. No exceptions. -- David Jones
E=M*c^2 story. (Score:4, Informative)
December 31, 2002
E and mc2: Equality, It Seems, Is Relative
By DENNIS OVERBYE
Roll over, Einstein.
In science, no truth is forever, not even perhaps Einstein's theory of relativity, the pillar of modernity that gave us E=mc2.
As propounded by Einstein as an audaciously confident young patent clerk in 1905, relativity declares that the laws of physics, and in particular the speed of light -- 186,000 miles per second -- are the same no matter where you are or how fast you are moving.
Generations of students and philosophers have struggled with the paradoxical consequences of Einstein's deceptively simple notion, which underlies all of modern physics and technology, wrestling with clocks that speed up and slow down, yardsticks that contract and expand and bad jokes using the word "relative."
Guided by ambiguous signals from the heavens, and by the beauty of their equations, a few brave -- or perhaps foolhardy -- physicists now say that relativity may have limits and will someday have to be revised.
Some suggest, for example, the rate of the passage of time could depend on a clock's orientation in space, an effect that physicists hope to test on the space station. Or the speed of a light wave could depend slightly on its color, an effect, astronomers say, that could be detected by future observations of gamma ray bursters, enormous explosions on the far side of the universe.
"What makes this worth talking about is the possibility of near-term experimental implications," said Dr. Lee Smolin, a gravitational theorist at the Perimeter Institute for Theoretical Physics in Ontario.
Any hint of breakage of relativity, scientists say, could yield a clue to finding the holy grail of contemporary physics -- a "theory of everything" that would marry Einstein's general theory of relativity, which describes how gravity shapes the universe, to quantum mechanics, the strange rules that govern energy and matter on subatomic scales.
Even Einstein was stumped by this so-called quantum gravity.
For now, any clue would be welcome. There is very little agreement and much confusion about the possible end of relativity. "These are times when theorists are being very adventurous," said Dr. Andreas Albrecht, a physicist at the University of California at Davis. "It's hard to tell where things will go."
The avatars of new relativity have been encouraged by hints that some cosmic rays hitting Earth from outer space have more energy than normal physics can explain. But some scientists doubt that these rays exist or, if they do, that a violation of relativity is the only way to explain them.
The cosmic ray hints are not the only signs making physicists wonder about relativity. They have also been tantalized by evidence, as yet unconfirmed, from distant quasars that a fundamental constant of nature, a measure of the strength of electromagnetism known as the fine-structure constant, might have changed ever so slightly over billions of years, shifting the wavelengths of light emitted by the quasars.
The result has been a minor explosion of interest in strange relativity, with some 70 papers being published this year, said Dr. Giovanni Amelino-Camelia, a theorist at the University of Rome.
The field, while still small, is destined for at least 15 minutes of fame next year with the publication in February of "Faster Than the Speed of Light," by Dr. João Magueijo, a cosmologist at Imperial College London. The book is a racy account of Dr. Magueijo's seemingly heretical effort to modify relativity so that the speed of light is not constant, and he will promote it on a long lecture tour.
"Ruling out special relativity by 2005 is a bit extreme," Dr. Magueijo said in a recent e-mail message, referring to the coming centennial of Einstein's famous paper, "although I would be very surprised if by 2050 nothing beyond relativity has been found."
Most physicists have yet to buy into this presumed revolution. Dr. Edward Witten of the Institute for Advanced Study in Princeton, called recent arguments that some versions of quantum gravity would violate relativity "unimpressive."
Dr. Juan Maldacena of Harvard said he doubted relativity was violated in string theory -- the leading candidate for a theory of everything. "But of course," he noted, "we should always test our theories."
Dr. Carlo Rovelli, a gravitational theorist at the University of the Mediterranean in Marseille, said it was a "risky" hypothesis, "but the prize if it happened to be true is so great that it is worthwhile taking the risk of exploring it in detail."
Dr. Andrew Strominger of Harvard pointed out that Einstein himself modified relativity in 1915, when he brought gravity into the picture with his general theory of relativity. Special relativity, as the 1905 theory became known, is only strictly valid in flat space without gravity, Dr. Strominger said.
He added, "It is natural to think that Einstein's relativity will in some sense be violated by small corrections, just as Newton's theory of gravity has small corrections." These corrections did not make Newton wrong, he said, they just meant his theory was not always perfectly applicable. Likewise, relativity may give way to a more complete and accurate theory.
How relativity could break down, if it does, depends on how physics might accomplish its grand dream of quantum gravity.
Many physicists are placing their bets on string theory's mathematically imposing edifice in which nature comprises tiny strings vibrating in 10 dimensions of space-time. But this theory may play out in billions of ways, and some physicists complain that it can be made to predict almost anything.
In the late 1980's, Dr. V. Alan Kostelecky, a particle physicist at Indiana University, and his colleagues pointed out that in some of these solutions, the spins of the strings could impart an orientation to empty space, like the lines left by the weave in a fine cloth. In that case, they say, a clock oriented in one direction could tick slightly faster or slower than one oriented differently, in violation of the rules of relativity. That is something Dr. Kostelecky and his colleagues have proposed to test using ultraprecise clocks on the space station.
Dr. Kostelecky and his colleagues have constructed an extension to the standard model of particle physics that catalogs all the possible ways that relativity can be violated. Others, including Dr. Amelino-Camelia, Dr. John Ellis of CERN, Dr. Tsvi Piran of the Hebrew University in Jerusalem and the Harvard theorists Dr. Sheldon Glashow and Dr. Sidney Coleman, have attempted to study the ways that relativity can be violated by quantum gravity or in the high-energy cosmic rays.
Violation is not inevitable, Dr. Kostelecky said. "Is it plausible? Yes. Is it likely? Enough so that I've invested years of my life."
Few physicists would seem to have as much invested in revising relativity as Dr. Magueijo. In his book he describes how beginning in 1996 he cajoled Dr. Albrecht, then at Imperial, into pursuing with him the heretical notion that the speed of light had been much higher in the dim cosmic past as a solution to various cosmological puzzles. Cosmologists did not rally to the idea, which even Dr. Magueijo admitted violated relativity. His co-author, Dr. Albrecht, himself called it an idea that is "not even properly born yet," and said it needed to find roots "in some convincing physics."
In the intervening years, as a sideline to his day job as a conventional cosmologist, he and a growing number of comrades have continued to tinker with modifying relativity in a variety of ways that go under the umbrella name of V.S.L., for variable speed of light theories.
In the science world, the book might attract attention for its jaunty and irreverent style as well as for its content. "What the hell, it's only Einstein going out of the window . .
Asked how he expected his colleagues to react to the book, he answered, "It wasn't written for them; it was written for the public." He called it "a very honest view of how scientists feel," adding, "It's the language I use normally."
The main motivation for considering V.S.L. theories, Dr. Magueijo explained, comes from the as-yet undiscovered quantum gravity. In relativity there is only one special number, the speed of light, but in quantum gravity, he explained, there is another special number, known as the Planck energy, equivalent to 1019 billion electron volts. According to quantum gravity thinking, an elementary particle accelerated to that energy will behave as if space and time themselves are lumpy and discontinuous and all the forces of nature are unified.
According to relativity, however, Dr. Magueijo explained, differently moving observers could disagree on how much energy the particle had and thus whether it was displaying quantum gravity effects or not. In short, they would disagree on what the laws of physics were.
"Perhaps relativity is too restrictive for what we need in quantum gravity," Dr. Magueijo said. "We need to drop a postulate, perhaps the constancy of the speed of light."
The most recent buzz in V.S.L. circles is about something called "doubly special relativity." In 2000, hoping to fix the cosmic ray problem, Dr. Amelino-Camelia proposed modifying the rules of relativity so that there would be a limit to the momentum that any particle could have, just as now there is a limit to the velocity.
Subsequently Dr. Magueijo and Dr. Smolin of the Perimeter Institute proposed their own doubly special version in which there is a limit to the amount of energy that an elementary particle can attain, namely the so-called Planck energy, at which the forces are unified and quantum gravity effects dominate.
One casualty of this tinkering, the V.S.L. scientists agree, will be everyone's favorite formula, E=mc2, to be replaced by a more complicated, cumbersome equation that Dr. Magueijo reproduces in his book.
A mark of all the doubly special theories, Dr. Magueijo said, is that the speed of light will vary with its color, with higher frequencies and energies going slightly faster than lower ones. That might manifest itself in observations of gamma ray bursters, distant gargantuan outbursts by an upcoming NASA satellite called Glast (gamma ray large area space telescope), scheduled for launching in 2006.
The theory also predicts that light should slow down near massive objects and actually come to a stop at the end of a black hole, preventing anything from entering that dark gate, Dr. Magueijo said in his book. In principle the effect, he said, could be tested by spectroscopic measurements of the light emitted from dense objects like neutron stars.
To some physicists, however, the very idea of variations in the speed of light in a vacuum -- the c in E=mc2 -- is meaningless. The miles and seconds by which speed is measured are human inventions, they point out, defined in fact in terms of lightwaves, so the whole notion of the speed of light varying is circular. In the last analysis, they point out, all physical measurements boil down to a few dimensionless constants like the fine structure constant, alpha. "What we measure objectively is whether alpha varies," said Dr. Michael Duff of the University of Michigan in an e-mail message.
Dr. Magueijo said those criticisms were technically correct but said the speed of light was one factor of several in the formula for alpha. So if alpha varied, as some astronomical measurements have suggested, one could choose to think of it as a variation in the speed of light, of electric charge, or even a variation in another number known as Planck's constant -- or all three -- if that made the math simpler. "It's a matter of convention," he said, adding, "you make the simplest choice."
Despite all the activity, scientists agree that they are mostly in the dark about the deeper consequences of these conjectures. "Some may eventually be developed to the point of being a credible alternative to relativity," conceded Dr. Kostelecky, saying that he suspected that others might not really change relativity or might have already been excluded by existing experiments. Without a systematic analysis it was impossible to know.
Dr. Amelino-Camelia said that the doubly special theories preserve Einstein's principle that all motion is relative, but at an unknown cost to the rest of physics."We paid a dramatic price for relativity: the notion of absolute time," he said. "This time it is not completely sure what is the axiomatic principle we have to give up."
Dr. Albrecht urged caution and said physicists needed guidance from experiments before tossing out beloved principles like relativity. "The most dignified way forward," he said, "is to be forced kicking and screaming to toss them out."
Copyright 2002 The New York Times Company | Permissions | Privacy Policy
Of course not.... (Score:2, Informative)
Unless everything in the universe has zero momentum, that is.
No = Registration*link^2 (Score:5, Informative)
That's the paradox... (Score:5, Informative)
They key thing is that the speed of light is fixed relative to *everything*. This means that if I'm standing by the highway and measure it, I get the same speed as a person in a car going 60 mph away from me. And since the speed of light is fixed, everything ELSE distorts to make up for it. That includes time (time dilation) and space (Lorentz contraction). It leads to some pretty freaky and amazing consequences.
Comment removed (Score:3, Informative)
well, of course... (Score:5, Informative)
Re:gravity effects are instantaneous (Score:5, Informative)
As for magnetism, that travels at the speed of light -- that has been known since Maxwell's time. Basically, that's what electromagnetic radiation is: a changing magnetic field causes a changing electric field, which causes a changing magnetic field, .... The paradox was that Maxwell's equations give you a constant for the speed of light, without reference to the velocity of the observer, so people assumed that they are valid only in the rest frame of a mythical "ether". Einstein showed that Maxwell's equations are correct for all observers, and it is Newton's/Galileo's ideas which are wrong.
Incidentally, just like electromagnetic radiation, GR implies that gravity waves should exist too.
Re:It's been "disproven" for quite a while now... (Score:5, Informative)
Huh? Light *always* goes at c, for every observer--it can't do anything else. I think you've been fooled by the term "speed of light in ". What happens here is the light as it travels is periodically absorbed and then after a brief delay re-emitted by atoms in its path. This produces an apparent average speed that is less than c to an observer on the macro scale. But when the light is actually travelling, it travels at c, and no other speed.
Chris Mattern
Comment removed (Score:4, Informative)
Re:Light Speed Relative? (Score:4, Informative)
The light itself does not speed up or slow down. From outside the blackhole, light is moving away from an observer at the speed of light. From inside the blackhole, light is moving towards you at the speed of light.
You have to remember that "speed" is a function of distance and time. Time is not constant, but from any frame of reference (you for instance) however, the "speed" of light is.
I'm sorry, but this is entirely incorrect. (Score:4, Informative)
Light is not Newtonian. It dosn't "speed up" as it falls, or "slow down" as it rises. That's kind of the point. Try working some simple Lorentz Transformations to begin to get a feel for this.
KFG
Re:PLEASE torture me with that! (Score:4, Informative)
Here are three (of many) links that I've found in the past that deal with relativity and provide varying degrees of rigor and completeness in the explanations.
How stuff works! Talking about special relativity:
http://www.howstuffworks.com/relativ
A pretty interesting and more rigorous explanation:
http://physics.syr.edu/courses/modu
And finally, a question and answer format explanation
http://www.sciencenet.org.uk/database/Physic
This should get you a good set of basic coverage about relativity.
No, what this is saying is that. . . (Score:3, Informative)
Please note that most physicists are of a mind that the physicist who are seeing these things are, ummmmm, seeing things.
So far it's all still a lot of waving of hands in the air and ignoring the part where "a miracle happens."
Not to say that it might not all work out in the end, but to imply that Relativity has been disproven, or even that certain limits have been found, is, ummmmm, premature.
KFG
Re:so if two objects are traveling toward the same (Score:4, Informative)
Nope. Drop all your newtonian physics assumptions out the window. Speed is relative as well, and doesn't add in such a straightforward fashion. An observer on one object will actually measure the velocity of the other as something less than c. (pardon me if I don't go look up the exact equations right now). That's where relativistic time dialation comes from- time has to slow down to make up for the non-additive properties of velocity.
By that same argument if I am traveling at c toward Earth, Earth gains infinite mass and the gravitational pull drags me toward it even faster!
Wrong again. You can't travel at c toward earth, so the question is meaningless. It takes infinite energy for a massive to reach that velocity, so it's impossible.
No offense, but this makes no sense. Either none of us understand it, or the emporor has no theory.
Quite a bit of offense taken, actually. You missed the third possibility, that *you personally* don't understand it, and that physicists do. Do you really think that points as obvious as yours would have been missed in all the years that Relativity has been under close scrutiny?
Oh, well. People who argue "I don't get it, therefore it's wrong" annoy me.
Einstein knew he was wrong (Score:5, Informative)
Of course, the rest of the world was busy experimenting with his theories of relativity, but after he published them he quickly lost interest in their progress. He spent the rest of his life searching for what he referred to as the "unified field theory," a single theory that could properly explain quantum physics and relativity at the same time.
I'm not a physicist by any stretch of the imagination, but theoretical science does interest me. Brian Greene's book, The Elegant Universe [amazon.com] does a great job of explaining the background on this. It's worth a look.
Comment removed (Score:3, Informative)
Wait a sec: Kinetic energy is relative too! (Score:2, Informative)
Actually, it's E = m * c^2, where m is the rest mass times the Lorenz transform.
If you then subtract the rest energy from the energy when in motion (m*c^2 - m0*c^2), you get the kinetic energy, which at low speeds is approximately equal to 1/2*m*v^2, which we all recognize as the formula for kinetic energy in Newtonian physics.
That is to say, relativistic kinetic energy is not exactly equal to newtonian kinetic energy.
Re:gravity effects are instantaneous (Score:2, Informative)
Please try to use EM instead of just light, some people get confused
Re:only its wavelength? (Score:3, Informative)
For light velocity DOES wavelength*frequency.
But different people will see the same photon as having different wavelenths and different frequencies. When you travel very fast you get time dilation and time slows down for you. When your clock runs slow more "waves" will occure in one second. The frequency appears to increase. High speed also cause distortions in apparent distances.
EVERYONE will see the volocity as C. It doesn't matter if you are standing still or moving towards the light at 500 million miles per hour or moving away from the light at 500 million miles per hour. The light always looks to you like it is moving at speed C.
-
That's not exactly true... (Score:4, Informative)
On one hand, the formulations of string theory are Very Hard (TM). I'm sure you think youv'e seen hard math, but there's hard math and there's string theory math. Classic standard model quantum mechanics and general relativity is hard math, nice hard partial differential equations to solve. String theory math makes this look easy though. It's so hard that nobody has yet even formulated the exact equations - everybody's working with approximations. So the predictions that people are making with string theory may not be completely accurate, as they aren't working from the real threory, just an approximation of it. Nice, eh?
On the other hand, most of the quantitative predictions that string theory does generate are mindboggling hard to test anyway, since in almost all respects string theory agrees with classic quantum mechanics (there's an oxymoron...) until you get to some pretty insane energies (think plank energy).
Fortunately, recently a few physicists have come up with some more subtle qualitative predictions that should prove feasible to test (for example, string theory predicts that cosmic microwave background radiation should be pixelated - the big bang didn't do antialiasing:).
-1, Disbeliever (Score:3, Informative)
It is actually not that much of a stretch. After all, when Einstein published his findings about ninety-eight years ago (I think), physicists abandoned the notion of absolute time (you have to spend a moment sometime to really appreciate what that means, most of the time, we really are Newtonians through and through). Today, some theoreticians and experimenters are considering to do the same with c, the speed of light.
The idea that c varies, however, is not all that new, it has already been conjectured to be a function of time, c -> c(t), to make sense of some odd stuff in cosmology. What's new in Dr. Magueijo and other's work is that they play with the idea of c varying in much more complex scenarios, having to do with with position, wavelength, momentum, etc.
It's worth mentioning that the latest shift in the literature tends to go to a varying alpha, the fine structure "constant", from which c can be seen to be derived from. For more info, check out this article [lanl.gov], co-authored by Magueijo (full text in pdf, on windows you have to add ".pdf" to the filename).
Needlessly to say, there's dozens of scientific articles about this issue, some quite readable (I have a couple of links at home, writing this from a party I'm supposed to enjoy).
The real news in all of this, it seems to me, is how almost esoteric science (in a good sense) has made its way into mainstream journalism. And with the publishing of Magueijo's book, which will be among the more readable ones of its kind, being scheduled for 2003, there's certainly a hot issue to watch as it unfolds. Last, unlike with superstring theory (you know, the little elastics swinging in 10 or so dimensions, and whose detection is so many orders of magnitude away from current technology, it ain't funny anymore), VSL is going to get some experimental underpinnings in 2006 from NASA's GLAST (Gamma Ray Large Area Space Telescope) satellite.
Hey, with a little luck, who knows what the limit is going to be. It would be fucking amazing if we arrived at a correct Theory Of Everything within our lifetimes. Boy, what better issue for today.
Massless particles CAN travel at light speed (Score:5, Informative)
WRONG, only objects with mass cannot travel at c. Photons exploit a diverging gamma by having zero mass, and hence having a finite momentum Thus, light in a vacuum will travel exactly at c (provided the laws of physics as we know them are correct). It's 3:45 AM and I'm not yet sober, but while my girlfriend is calling her family in El Salvador, I may as well explain a few things, hopefully they're coherent.
For those rusty on their special relativity, gamma is basically a factor of speed, which can run from 1 to infinity, defined as gamma=1/(1-beta^2) where beta is the velocity relative to the speed of light (ie, beta=v/c). This factor of gamma prevails throughout special relativity, and measures the factor of time-dilation or Lorentz length contraction.
Regarding momentum, classically it is defined as p=mv but v can never exceed c. However, a relativistic momentum can be defined as p=gamma*mv instead. Recall that at ordinary everyday velocities, v is much less than c, so gamma is very close to 1, and the classical equation holds. This is the proper way to describe the apparent "increase of mass" of an object at relativistic speeds.
Any object traveling at c will have an infinite gamma, and hence infinite momentum and infinite energy (Relativistic energy for a particle is E=gamma*mc^2. Einstein's equation E=mc^2 is the rest energy, and doesn't include kinetic energy, which is accounted for by the gamma factor.) So, a photon, travelling at c, has an infinite gamma, but it also has zero mass thus demonstrating finite momentum and finite energy.
Now, about real life, all materials will have permittivities (epsilon) and permeabilities (mu) at least somewhat different from vacuum, and thus the speed of light in that material (v=1/sqrt(epsilon*mu)) will be somewhat less than the speed of light in vacuum (c=1/sqrt(epsilon_0*mu_0)) where epsilon_0 and mu_0 are permittivity and permeability of free space respectively.
Recall, those constants of free space are the constants of proportionality in Maxwell's equations which you can determine by measuring electrostatic and magnetostatic attraction/repulsion in a standard laboratory. But they yield the speed of light when taken as above. That, IMHO, was one of the coolest things about E&M, when you realize how intertwined electric/magnetic phenomena are with light. And even more so when you realize you can write magnetostatic phenomena strictly as relativistic corrections to electrostatics!!!
Also, FYI, it is possible to travel faster than light, that has been known for at least the past 50 years. Not faster than light in vacuum, of course, only faster than light in a particular medium. Radioactive sources can spew out particles at high-speeds, which just might be faster than the speed of light in another material (eg, water). This produces somewhat of an equivalent of a sonic boom, but optically, and sends out so-called Cerenkov radiation. This is why nuclear-rods glow underwater, and is the basis of how most neutrino observatories work.
Re:so if two objects are traveling toward the same (Score:3, Informative)
NO, you cannot look at a relative velocity in a simple Newtonian method, as others have described above.
You can realize this easily by looking at the Lorentz transform of an object in a moving frame as observed from the rest frame, to determine the relative velocity. Or from the moving frame.
Just to get you started, because it looks like you're rather confused, here are the Lorentz transforms. I hope you understand what the Lorentz transforms are. Basically, they let you convert an event occuring at a specific time/place in one frame to the time/place in another frame. We'll assume 1-D systems here, which is essentially true because only the direction of motion is Lorentz-contracted. Note, these formulae convert a moving frame to the rest frame (where the moving frame is moving at velocity v in positive coordinate number relative to the rest frame).
x'=gamma(x+v*t)
t'=gamma(t+v*x/c^2)
Okay, now the fun part. Assume an object moves distance dx in time dt in the moving frame. how far does it move in the rest frame? Plug in, and then divide and we get our relativistic velocity.
dx'/dt'=(dx+v*dt)/(dt+v*dx/c^2)= (dx/dt+v)/(1+v*dx/dt/c^2)
The object in the moving frame moves at velocity dx/dt, so we'll call that velocity u. Thus, we want the speed u as measured in the rest frame.
u'=(u+v)/(1+uv/c^2)
That is the formula you should be using. Note that at very small relative velocity between frames, uv/c^2 is practically zero, and hence you can use the Newtonian relative velocity formula u'=u+v. But at appreciable speeds, it's not valid. And plugging in numbers for your v=c/2 example, from one of the incoming reference frames you would see the other frame moving at v=(4/5)c, which is CLOSE to c but definitely LESS THAN c.
Happy New Year to all you other folks on slashdot, It's 4am here, and i'm not sober yet, but my girlfriend is still talking to her family in El Salvador so I'm still browsing /. yay...
Re:The more we learn (Score:4, Informative)
F = dp/dt = d(mv)/dt = m * dv/dt + dm/dt * v.
You must remember to use the product rule, and that the derivative of a constant is zero.
F = ma only in a system of constant mass.
Re:That's the paradox... (Score:5, Informative)
There's also some very nice mpegs floating around the net of tram cars and flashing lamp posts in a world where the speed of light is slowed to a couple of meters per second. Now if only I could dig up the URL...
Re:The more we learn (Score:3, Informative)
We don't replace a theory with one that is better. We replace it with one that is slightly less wrong.
-- Prof. Stephen Hawking
Re:You misunderstand completely (Score:5, Informative)
Well, I don't know if it's really the case that evolutionists consider their views to be a "truth that is impossible to disprove" etc. (at least not the scientfically minded ones, for any theory there are supporters that one could do without).
Now let me start by saying that I'm not really an expert on evolution, since I'm european I've never had to be. There are no creationists here to speak of, and hence I'm not well versed in their way of thinking. I am a "scientist" however, so I'm somewhat qualified to speak about that.
Now, not to write an essay answering your question, but much of it boils down to what we mean by "wrong." First some preliminaries though. The strength of any scientific theory rests on its predictive powers, how well does it foresay and explain the outcome of experiments or observations (past of future). Any good scientific theory then is very specific (or strong), what we like to call "easily falsifiable", i.e. it is simple to detect when its predictive powers are failing. (Hence many of them in the natural sciences are formulated in some form of logic; "mathematics" since that provides for a stronger statement to be made). So, strong theory equals "easy to prove wrong" given contradictory evidence.
Now, then what does it mean to be "wrong" in the scientific sense? In short it's when there are observations made that cannot fit into the current theory. A prime example would be Newton's law of kinetic energy E=1/2mv^2. For a long time that was thought to be all there is to it, and all the experiments and observations that could be made corroborated that. Today we know that it's not "true". It's OK for lower speeds, but it completely fails to take relativistic effects into account (see previous posts in this thread), and hence has been relegated to the scrap heap of scientific theories, right?
Well, not quite. It's still a very good approximation for most macroscopic real world phenomena. It still explains them very well, and even post Einstein, it hasn't really lost any of it's predictive powers in the domain in which it was thought up. So even though it may now be thought "wrong" in the strictest sense of the word; it may not tell all of the truth to all people, it's still a pretty darn good theory if you're a bit more careful with it's application.
This is also true of Darwinian evolution. It's a very well tested theory (or "fact" if you will) by now, with wast predictive and explanatory powers. Any later theory that superseeds it must still explain all the observations with the same (or better) accuracy as Darwinistic evolution has to date. So even though evolution as a theory may be proven "wrong" at a later date, it'll still be mostly "right." As Newtons' laws still are.
Now, in order to completely close the sack, we also need Occam's razor. I.e. given two equally predictive theories, we prefer the simpler one. It's really a common sense argument. Why make things harder than they have to be. It's also the only scientific loophole that creationists can exploit. By invoking a "deus ex machina" in the form of an omnipotent God, that stacks the deck so that scientists cannot make correct observations (or make them correctly), you can of course invalidate any and every theory. And that's why science doesn't deal with that. If someone stacks the deck, we won't play! (Then we can continue various philosophical arguments, and in doing so rapidly leaving the natural sciences.)
And that's incidentally why science isn't "just another religion", science specifically is about absolutely minimising the things that have to be taken on faith (such as the existence of the rest of the world etc), while religion(s) are about systematising the things you take on faith. Often that means that science cannot say very much on a subject, and people having a natural tendency towards taking things on faith, often over interprets scientific statements (it takes practice to so thoroughly disiplining your subjectiveness as the scientist must do). This leads to "scientific" statements or belif in the general public, that really aren't. But that's not the fault of science, more a fault of the schooling system.
If you're specifically interested in evolution, I have it on good authority that you could do worse than studying talk origins [talkorigins.org]. I haven't got any good references on the philosophy of science in english for you, but I'm sure that a few minutes of googling will turn up a multitude.
Re:well, of course... (Score:3, Informative)
I think you're thinking of the expansion of E=mc^2/sqrt(1-v^2/c^2), which produces
E=m c^2 + 0.5 m v^2 + ...
where m is the rest mass. This is a beautiful piece of math. It shows that the kinetic energy that we already knew about (0.5 m v^2) is actually an artefact of the relativistic change in mass.
The rest of the terms are negligible for low v, which is why we never noticed it in the lab before Einstein.
Re:FTL == Time Travel ? (Score:3, Informative)
The PostScript version might be more comfortable.
In your example, if X and Y share the same frame of reference, G and L may not be aware of anything, but the problem is that you don't take into account the point of view of someone traveling between X and Y, who will effectively see G going back in time, even if he takes the information travel time into account. (I shouldn't have mentioned seeing a "flash" in my previous message, it sent you off the wrong path...)
The document will have told you all about it, but let's try. X is Earth, Y is Alpha Centauri, four light-years away and at rest relative to X. S is a ship traveling along the (XY) line at 0.866c, which yields a gamma-factor of 2. Times are measured in years, distances in light-years. t, t', t" are the times for X, Y and S.
Here are the events of interest in Earth's and Centauri's timeframe:
- S passes X: t=t'=0, t"=0.
- X sends a distress call to Y thanks to a "10c" device (so that it is not instantaneous): t=t'=4 (t"=2).
- Y receives call: t=t'=4.4 (t"=2.2).
- S passes Y: t=t'=4.6, t"=2.3; it is after Y got the message, so Y breaks the news.
Now, in the timeframe of S, things are slightly different; X and Y are seen as moving at 0.866c, and the distance between the two is only two light-years due to length contraction. Two events are easy:- S passes X: t"=0, t=0 (t'=4.45).
- S passes Y: t"=2.3, t=1.15 (t'=4.6 because they say so).
See? From the point of view of S, not only you cannot consider that the time is the same at X and Y, but if a message from X bears the date t=4 but has already arrived at Y at t=1.15, it looks like it has come from the future.Now, to understand that it does not merely look like time-travel, suppose Y tells S that X sent a distress call; S has the same kind of FTL device, which can reach X in about 0.22 years (it is two light-years away in the timeframe of S, and receding at 0.866c). In the timeframe of S:
- S sends inquiry to X: t"=2.3, t=1.15.
- X receives inquiry: t"=2.52, t=1.26.
so X receives a message at t=1.26 which contains information about something about to happen at t=4, time enough to send Bruce Willis. As you can see, there really is a paradox, which never appears without FTL devices.Now, if you are not convinced, then I think you're thinking either:
- S is moving but not X or Y, so the FTL device won't work the same, or:
- when S passes Y and learns about X, it merely thinks that t=1.15, whereas it really is 4.6, or:
- X does not move with respect to Y, whereas S is moving with respect to X, so the FTL communications won't work the same.
Item 3 could be valid, but you can always suppose that another ship S2 follows S and passes Earth at the right time; it won't be moving with respect to S, so FTL communications must work. For the other cases, you have to violate relativity in some way.To settle it down, try to reverse the situation: A is Earth (time t), and two spaceships B and C (time t',t") are coming up on it at 0.866c, two light-years apart. In Earth's timeframe:
- B passes A: t=t'=0.
- C passes A: t=2.3, t'=1.15.
and in B's timeframe:- B passes A: t'=t"=t=0.
- B sends out a distress call to C: t'=t"=4 (t=2).
- C is four light-years away in this timeframe, the message will reach it at t'=t"=4.4 if it travels at 10c.
- At t'=t"=4.6, C passes A (four light-years distance, still 0.866c) and tells them about B's problem.
When C passes A, in A's timeframe, t=2.3, t'=1.15; A sends a message to B at 10c, which arrives at t=2.52, t'=1.26...If you object, remember, the situation has to be the same when you exchange A, B, C for S, X, Y, if no single frame of reference is to be privileged, so the objection has to work both ways.
If you single out a given frame of reference, however, and state that you believe that causality must only hold there, then you can build a consistent theory of FTL travel - the FAQ I pointed to does just that, by the way, when trying to reconcile Star Trek with relativity in part four. But I'm not too convinced by the postulated physics of subspace, and not sure that time-travel-like paradoxes are eliminated altogether.
Re:I'm sorry, but this is entirely incorrect. (Score:3, Informative)
Lorentz transformations might be "normal math" to you, but to a lot of people (even the average slashdotter) they probably aren't. Think about it. If the poster that you're replying to could *do* Lorentz transformations then he wouldn't be having this mental roadblock...because by learning how to do them, he would have figured out the concepts involved.
It might be more helpful in the future to say something like "here is a cool little Java applet that visually (and interactively) explains a Lorentz transformation [qmul.ac.uk]. It's not a thorough mathematical explanation, but it should give you some clues to what I'm talking about. Simple Lorentz transformations can be done easily with the skills that you (hopefully) learned in high school algebra. I know that most papers explaining Lorentz transformation are written in mathematicese, but, hey, it's just like learning Perl. Take it slowly, one step at a time, and work all of the examples out yourself. Good luck."
Re:That's the paradox... (Score:2, Informative)