E ~ mc^2 510
Posted
by
michael
from the closeonlycountsinhorseshoes dept.
from the closeonlycountsinhorseshoes dept.
IF I HAD A MINE SHAFT, I don't think I would just abandon it. There's got to be a better way.  Jack Handley, The New Mexican, 1988.
Oh no.... (Score:3, Funny)
Light Speed limits... (Score:2, Funny)
LOL (Score:2)
186,000 Miles per Second. It's not just a good idea. IT'S THE LAW.
The more we learn (Score:2, Insightful)
You misunderstand completely (Score:4, Insightful)
The very thing that shakes your faith in our knowledge is the very thing that *strengthens* our knowledge.
Think about it.
KFG
Re:You misunderstand completely (Score:5, Funny)
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.
Occam's Razor. . . (Score:5, Insightful)
First off, I'm not a creationist. Indeed, I find that whole debate to be entirely infernal, as both sides seem to me quite flawed in their own ways. That being said. .
Occam's Razor bugs me. As a deductive tool, it is a pretty good one; it works for the most part. What I find unsettling, however, is that it seems to have become, thanks to its presentation and treatment in popular media, understood and accepted by many as a de facto scientific law when it is not.
It is a rule of thumb, and only a rule of thumb. It is only a rule of thumb, because it is not always right. Every time something unexpectedly complex turns out to be the reality behind a phenomenon which might otherwise have been explained through simple means, Occam's Razor is blunted.
Example:
When Alexandre Graham Bell first announced to the world that he had discovered a way to send a voice signal over a wire, the world erupted with both excitement and disbelief. One major newspaper even ran a story written by experts which attempted to debunk Bell's claim. They used diagrams demonstrating that sound waves sent down thin metal tubes of the diameter Bell was using for wires, could not possibly travel the kinds of distances he claimed. The experts were engineers well versed in the science and dynamics of sound as employed in the kinds of voice communication pipe systems once used large ocean going vessels. To the writers of the article, they were being entirely reasonable.
"Which is more likely?" they must have asked themselves, "That Bell has created some magical new invention to send sound along miles of very thin tubes? Or that he is lying?"
Occam's Razor is deeply rooted in how one perceives, how much information there is available to work with, and what has been previously accepted by culture as normal and/or outlandish.
Now Bell was, of course, proven to be right. When words crackled out from crude speakers for all to hear, the enthusiastic debunkers, (and there is never any shortage of enthusiastic debunkers or respected, conservative media outlets to give them a voice and print their diagrams), had to quietly go mum and withdraw their objections. But that was in part due to large forces which wanted and allowed Bell to be proven right. If you don't advertise a fact or discovery, facts and discoveries can easily vanish. People have short memories. People have short lives. Without active perseverance, knowledge is a selfburying commodity until it becomes large enough to selfsustain, and even then, it is not so very difficult to forget important turns of history after only a few fickle generations have passed.
Science as a concept, is a pure, wonderful thing, but it does not know everything. Indeed, many institutions are not so pure as the science which they employ; it is well known that individuals with weak morals, and corrupt institution will suppress data, twist data and even make up data on a basis regular enough that the public pool of knowledge has been polluted to the point that the employment of Occam's Razor is by no means reliable in today's arena of public thought.
Just something to consider next time you feel the need to slam a new idea. Remember that Occam gave us a deductive tool, not an irrefutable law.
Fantastic Lad
Re:You misunderstand completely (Score:5, Insightful)
In any case, argument from design doesn't provide any "explanation," much less a better one. How did the designer make the beetle, and all its close genetic relatives, where none had existed before? Why the variety of mechanisms in the close relatives, instead of a single design?
Re:You misunderstand completely (Score:5, Insightful)
Wrong. We also can't see electrons, or stars/galaxies at the edge of the universe. We don't need to see them to observe them though. Evolution has been observed in the fossil record, and even to some extent in the laboratory. Still, the lab observations are fairly new (the last 3040 years) and science is busy debating whether or not it is indeed evolution... after all, as you pointed out, it is a slow effect.
Furthermore, no evolutionist has ever explained creatures like the Bombardier Beetle and its builtin flame thrower.
Huh? Of course evolutionists don't know everything at once... they don't claim to be omniscient. However, that doesn't mean they are doofuses without a clue. There have already been several possible explanations suggested in the scientific community, and no one disputes that something unknown is going on. You must not be researching this issue very thoroughly, if you believe there are no explanations at all, and that biologists are all sitting around dumbfounded.
Some of the more radical ideas center around the possibility that DNA acts more like a computer than a raw blueprint. That it might "store" a bunch of "mutations", saving them for a rainy day when some threshhold is reached. This "computer" might even span many individuals in the population. So instead of a gradual change into a "bombadier beetle" where there are many transitionary variants doomed to blowing themselves up, evolution simply "skipped over" those and went straight to the version capable of blowing up its enemies, and not itself.
Was it Greg Bear that said "Even evolution is evolving, becoming better at what it does." ?
Besides, lay off Darwinian evolution. Most people today see it as only the crudest approximation of the reality of evolution. Would figure that a bible thumper would be reacting to the scientific community of 100 years ago... you guys are always more than a few steps behind.
Re:You misunderstand completely (Score:3, Insightful)
Re:The more we learn (Score:2)
Well, yes, whenever physics advances and new physics is discovered, the most basic of the equations will change, of course. The same happened when Einstein modified F=mv' of Newton's and the same will always happen, and the more unified physics become, the more "fundamental" an equation will be affected.
What matters as far as "how much we know" is that the changes don't affect almost anything in everyday physics. The currently discussed very minute changes don't affect the physics of almost any known phenomenon observable in any lab that i can think of. E_plank is a very very huge energy and only very huge phenomena involving, say very huge black holes near the birth of the universe will typically have enough energy to attain such energies. In other words, the current changes only affect any calculations in those phenomena.
Re:The more we learn (Score:2)
That's F=ma to you!
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: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:The more we learn (Score:2)
I checked your post history. You don't seem to be a troll, so assuming you just need some reproof, I can't let this one fly. Einstein wrote thousands of pages in his books and lectures, explaining every minute detail of his theories and their foundations. He coined the idea that the framework of basic particle physics is so simple that it is inexcusable not to be able to explain it to anybody.
And your logic statement? Roughly "Because he never explained them, they are flawed." This is a heinous logic fallacy right off the bat, even "pretending" that he never wrote a single book to explain his theories. It just makes no sense.
Even if he was off.. (Score:4, Insightful)
Re:Even if he was off.. (Score:3, Interesting)
Light Speed Relative? (Score:2, Insightful)
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.
Re:Light Speed Relative? (Score:2)
blackhole's don't "suck" anything in. anything with a gravitational field "bends" light, or acts like as a lens because light has mass.
light traveling at c across the void of space and light orbiting a superdense mass at c are still both moving at c. it's just that the latter will never leave the "event horizon" of the black hole. still the same speed.
justin dubs
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: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."
Umm... (Score:2)
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 nearterm 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 socalled 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 finestructure 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 AmelinoCamelia, 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 email 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 spacetime. 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. AmelinoCamelia, 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 highenergy 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 coauthor, 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 asyet 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. AmelinoCamelia 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 socalled 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 email 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. AmelinoCamelia 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.
Re:Of course not.... (Score:3, Informative)
In Your formula E^2=m^2c^4+p^2c^2, your mass is merely the "rest mass".
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: Re:Of course not.... (Score:3, Funny)
Will your bullets have momentum or should I quiver in fear at their rest energy?
No = Registration*link^2 (Score:5, Informative)
can someone explain to me (Score:3, Interesting)
If it's relative to a "given thing" then doesn't that hint toward Ether theory? The further we go in AP Physics the more I realise that my school is imprepared to answer anything that comes up and that modern theories (String theory and the like) seem reminescant of the old ones like Ether theory.
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.
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:can someone explain to me (Score:2, Insightful)
Re:can someone explain to me (Score:5, Interesting)
If you are zooming past me at half the speed of light and both of us measure the speed of a particular photon at the same time, we'll both measure it's speed as c. What will be different about our two measurements is that you'll see a higher energy photon (bluer) than me if the photon is moving opposite to your motion relative to me and a lower energy photon (redder) if the photon is moving in the same direction as your motion relative to me.
No particular point in space is special. Once you identify where the observer is located, you can call that point in space an "origin" or "zero" and make all of your measurements from that point in space. The rest of the universe relative to that origin is called an "inertial reference frame", but it's just the same as any other reference frame. There's another trick. Behavior of things in inertial reference frames is time dependent because gravity pulls your frame around and changes everything around it slightly every moment. Besides that, two inertial reference frames may have a relative velocity but for a moment share the same point in space (the example above).
That's when tensor math starts to come in handy. Don't worry, I won't torture you with that.
Relativity, once you grok it, will bend your mind. From a metaphysical perspective, it emphasizes the reality that most of what we call facts are actually just high probability observations.
Remember, there is no spoon.
Regards,
Ross
PLEASE torture me with that! (Score:2)
I've heard the same damn "Just Because" explanations forever! I downloaded a quite lengthy explanation of Tensor Calculus to my Zaurus.
What I was really asking is if anyone knew the basis for these theories.
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.
thx for the links. Here's one for you. (Score:2)
Seriously though, thanks for them.
Re:PLEASE torture me with that! (Score:3, Insightful)
Ah. I'm not going to be able to do more than point you in the right direction in one
At that point, there's enough information to head over to the General Relativity chapter and take a gander. That ought to be enough to blow your mind for a little while as what you thought you knew about the universe resorts itself (don't worry, it happens to almost everyone).
After that, you can finish the book, develop some basic tensor math skills, then come back and explain Special Relativity to all of us! Actually, I do get Special Relativity, but it is mind bending. You really start thinking about the universe on a completely different scale.
I found it incredibly interesting stuff to learn, but because I went to a nontoptwenty school, there were only a few other people in my class with any interest. The hostility from the other undergrad students who hated learning (and especially hated having to rethink the universe) was a bit of a downer for the inclass exchange that the prof was so hoping for.
The graduate level classes were much more fun.
Regards,
Ross
Re:can someone explain to me (Score:5, Insightful)
The speed of light is constant in all possible frames of reference, according to Einstein. Basically what he's saying is that for any two objects at rest relative to each other (regardless of their motion to the rest of the universe, they appear not to be moving to *each other*), time and space behave in the same way. The beauty of his theory is that no one object can be said to be at universal rest to everything else  there is no universal frame to measure against. Therefore, every frame of reference is valid and will behave the same way. This kills Ether theory dead, since Ether theory depends on a universal frame of reference. If it didn't have a universal frame of reference, then space and time would start behaving oddly within your *own* frame of reference depending on your motion. This is not the case  the light on Pluto behaves the same way as the light on Earth, even though the two are moving in different frames.
It's only when you introduce outofframe references (I'm standing still, the train is moving at 60mph away from me) that relativity kicks in and the laws start to behave weirdly.
Not inconsistantly, just weirdly. It's all in shifting your viewpoint.
The trick with light is to realize that although it travels at the same speed in every frame of reference, the *wavelength* is what changes between frame. This is what that whole redshifting/Doppler effect is about. The speed of light is constant; the color, however, changes depnding on your frame of reference. If you shoot a blue light at me while we're both standing still relative to each other, it looks blue to me. If I run away *really fast*, it will still be blue to you, but it will appear red to me because the wavelength alters even though it still travels toward me at a constant rate. Ditto if *you* run away from me  the light is blue to you, but again, it appears red to me, even though it travels at the same speed.
Light does not behave in the Newtonian way  acceleration does not effect its speed, only its wavelength. That's where the question of why light is constant to everything, even moving objects, is answered.
Weird, huh?
For a far, far, better explanation (and a fantastic grounding on String Theory in terms for nonphysicists) check out The Elegant Universe [amazon.com] by Brian Greene. If I could, I'd give this book a Pulitzer every year until the day I died.
only its wavelength? (Score:2)
So with light, velocity!=wavelength*frequency?
Re:only its wavelength? (Score:2)
No.
>So with light, velocity!=wavelength*frequency?
No.
Speed is always c, and does not depend on wavelength. OTOH, Energy of the photons, does depend on wavelength.
E = h nu , where nu is the frequency nu = c/l
where l is the wavelength.
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.

And just a stupid quibbling footnote (Score:3, Interesting)
String Theory, in part, seeks to explain the structure of the universe in such a way as to accomodate both gravitation and quantum effects. It does this by shifting the understanding of particles from a family of points that all have different properties (protons, electrons, quarks, what have you) toward a *truly* fundamental form of matter  a string  that displays different properties depending on its orientation and motion in space. One (and ONLY one) type of string, many configurations, all leading up to families of particles.
It's elegant, unproven, pretty damn keen, and possibly wrong, but worth a look. The math involved makes *predictions* about the fundamental properties of matter, rather than being built off of measurements of those properties (as quantum theory and relativity are). That's an important step that cannot be underscored enough.
String Theory doesn't posit that there's a universal medium that everything travels through, as Ether theory does. Instead, it describes a configuration of space that strings wiggle around in to produce the world that we're used to looking at.
String Theory rocks. I hope it's right.
GMFTatsujin
Re:And just a stupid quibbling footnote (Score:2)
Yeah, except we have basicly zero clue what the predictions are. Pretty interesting definition of "prediction"

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:).
I hate to say this... (Score:4, Funny)
But why do you think that your brain is capable of understanding the basic forces of the universe?
Your brain evolved to keep you away from things that want to eat you, find things you want to eat, and basically preserve you until you could insure that you have spread your genes. Last time I checked, understanding the basic rules of reality wasn't needed to ensure that you live long enough to breed.
Hell, we'er just lucky that the same math that works on our scale also seems to work when we look at how the universe works.
Even now, logic has begun to fail us when we ask the deep questions. Consider this: What made this reality? Oh sure, I know the theories that suggest that this universe might have been created by another universe, and at this level, cause and effect goes out the window, leading to the possibility that this universe can create the ancestor of the universe that created it, but what allowed this gestalt to exist?
There's an Heinleinian phrase that occasionally gets said on slashdot: There ain't no such thing as a free lunch (TANSTAAFL). Too bad that its wrong, since the universe is the biggest example of a free lunch in action.
[ Don't feel so bad  my brain also seems hellbent to make me survive long enough to ensure my genes are passed on. Damn thing is that my body agrees with it and is planning to expire in half a century in order to free up resources for my future offspring. Its a comspiracy, I tell you... ]
Just my $.02
Examine your assumptions (Score:4, Interesting)
Re:I hate to say this... (Score:3, Insightful)
You can write down music, but the written music is just a description, not the actual music. In the same way, math is a handy, concise, notation used to write down descriptions of the universe.
What is C relative to? (Score:4, Funny)
so if two objects are traveling toward the same (Score:2)
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!
No offense, but this makes no sense. Either none of us understand it, or the emporor has no theory.
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 nonadditive 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.
Re:so if two objects are traveling toward the same (Score:2)
no, because their relative velocity is not c as you might think. IT is merely
> 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!
you (or any other material body), being a mere mortal with a finite mass, will never be able to attain a speed of c relative to earth.
>No offense, but this makes no sense. Either none of us understand it, or the emporor has no theory.
No offense, but physicists are not foolish. Almost any possible theoretical or mathematical objection you are likely to raise is very likely to be a mere first paragraph in a course on the subject. You really aren't in a position to judge a theory unless you atleast understand the math, the physics, the experimental results and then see using the cherished Occam's Razor why a theory is the one proposed.
Re:so if two objects are traveling toward the same (Score:2)
The problem is that you think 30mph + 30mph is 60mph, but it isn't.
30mph + 30mph is really 59.99999999999999999mph
Is is so close to 60mph that you can't measure the difference. 30mph is extremely close to zero c so the "missing speed" is close to zero. As you get closer to the speed of light the "missing speed" gets closer to one.
0.99c + 0.99c = 0.99995c
1c + 1c = 1c
Speeds never add up to a value above c.
Either none of us understand it, or the emporor has no theory.
No, things just get really wierd at high speeds and you don't understand it.

Re:so if two objects are traveling toward the same (Score:2)
Re:so if two objects are traveling toward the same (Score:3, Funny)
No, I doubt the geeks had any trouble with it. It was a perfectly logical system. It was the nongeeks who didn't get it.
2+2=0 (mod 4 arithmetic)
2+2=1 (mod 3 arithmetic)
2+2=1.9999999 (relativity)
2+2=2 (bitwise OR)
2+2=3 (karma cap at 3).
2+2=5 (2 is really 2.4 rounded down and 5 is really 4.8 rounded up)
2+2=10 (base 3 arithmetic)
2+2=22 (string concatenation)
2+2=44 (sum of ascii characters, hexidecimal)
2+2=100 (sum of ascii characters, decimal)
Geeks "get it". Nongeeks don't understand anything other than 2+2=4.
Cross refference this post. [slashdot.org]

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 1D systems here, which is essentially true because only the direction of motion is Lorentzcontracted. 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...
similar.. (Score:3, Insightful)
viz:
Einstein's modification:
P=mv/(1+v^2/c^2, the denominator being the new addition.
Now:
E= mc^2/(1+mc^2/E_p).
the denominator being the new addition.
Quantum voodoo (Score:5, Funny)
E != mc^2 (Score:5, Insightful)
Re:E != mc^2 (Score:3, Interesting)
Well, what matters is the energy not be equal but just be very close to mc^2 in our usual "everyday" phenomena, and here, by everyday we mean almost every known situation in physics, except when you are right very close to the very very very large Plank energies.
well, of course... (Score:5, Informative)
Re:well, of course... (Score:4, Informative)
Though I suspect they have gone back to (the nowunfashionable) convention of letting m refer to the relativistic mass.
Thus, in their formula, m probably refers to m0/(sqrt(1v^2/c^2)) both when it occurs in the numerator as well as in the denominator.
Quick review (Score:4, Interesting)
Please don't forget your subscripts! As everyone learns in basic special relativity, total energy, which is kinetic + potential, is
where gamma = 1 / sqrt( 1v^2/c^2 ) and m0 is the rest mass.At v = 0, gamma = 1 and E = m0 c^2, Einstein's famous formula for rest energy. Kinetic energy is given by KE = E  m0 c^2, or
To see any appreciable effect of velocity, consider the situation where you are going fast enough to double your effective mass (gamma = 2). Solving for velocity gives v = c sqrt(3/4) = 86.6% of the speed of light. Not gonna happen with current technology (outside of atom smashers).As v > c, gamma > infinity and this is Einstein's rationale for saying it's impossible to accelerate any matter up to the speed of light, since doing so would require an infinite amount of kinetic energy. On the other hand, the formula for photons is
where p is momentum, h is Planck's constant, lambda is wavelength, and c / lambda = nu is the frequency. Since photons are never at rest (remember the constant speed of light?), you won't see any m's make an appearance here. And just for the record, this last formula explains the photoelectric effect, which is what won Einstein his Nobel, not E = m c^2.Re:well, of course... (Score:2)
Re:well, of course... (Score:2)
Re:well, of course... (Score:3, Informative)
I think you're thinking of the expansion of E=mc^2/sqrt(1v^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.
Bad Memories (Score:2)
Coincidence...? (Score:5, Funny)
186,000 Miles per Second. It's not just a good idea. IT'S THE LAW.
Re:Coincidence...? (Score:2)
If you're in a car that's going at the speed of light, what happens when you turn on the headlights?
Re:Coincidence...? (Score:4, Funny)
I just thought of the funniest joke (Score:2, Funny)
IN SOVIET RUSSIA,
mc**2 = e
Heheee. +5 FUnny,.
Even if his theories are improved (Score:4, Insightful)
I dont see the big deal in "disproving" him. It's sad that people will take some sort of glee in thinking "Ha! Einstein was wrong!" Einstein himself would be glad to see people come closer in figuring out the natuer of the universe.
Given the knowledge and tools available to him at the time, its amazing he came up with something in 1904 that people nearly 100 years later are still trying to figure out how to improve or disprove. Today we have the advantage of knowing how to look at things the way he did.
Einstein's abilities, creativity, and ideas will have a permanent influence on humanity's acheivements.
What I want to know is... (Score:2)
So the new equation is... (Score:2)
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.
Re:Einstein knew he was wrong (Score:3)
In fact, Einstein was one of the unwilling architects of modern quantum theory. Because his challenges to it shaped the developing theory. And THIS was probably the actually most important thing he was doing.
The QOTD I had (Score:2)
Well, I thought it was a funy coincidence.
Physics is nothing by a model (Score:2)
By the way are all the comment posters the one who answered "I would be reading slashdot" for what would be doing during the new year
1, Disbeliever (Score:3, Informative)
It is actually not that much of a stretch. After all, when Einstein published his findings about ninetyeight 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], coauthored 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.
Doubly Special Relativity (Score:2)
(read the article before modding)
Extra Special Relativity
Relatively Special Relativity
Double Secret Relativity
Not Ready for Prime Time Relativity
Britney Spears Nude !!!
Bummer (Score:3, Funny)
E=mc^1.99999923850927642081748272
is just not quite as catchy. Harder to fit on Tshirts also.
Oldie but goodie revised! (Score:2)
E=mc2 but only for large values of E
FTL == Time Travel ? (Score:3, Interesting)
I do understand why you cannot ever reach or exceed the speed of light through normal acceleration. The closer you get to the speed of light, the more aparrent mass you get, and thus the more energy it takes to accelerate you. To hit the speed of light would take infinite energy (and you would have infinite mass when you hit it). Infinite energy and mass aren't really available, so you can't have a speeed >= C by accelerating, no matter how hard you try.
The part I don't understand:
I have been told that theory forbids any travel faster than light, no matter what the means ("warp drive", "hyperspace", "teleporter", whatever). My understanding is that if you could, some observers would see you traveling back in time, and this is forbidden.
I would appreciate any explanation of this, or even just a pointer to a reference I can understand. Thanks.
steveha
Re:FTL == Time Travel ? (Score:5, Interesting)
Yes. One of the hypotheses of relativity is causality, that is, one event can possibly cause another only if the latter occurs at a later time than the former, and this must hold true for all possible observers whatever their frame of reference.
Now, as you know, the passing of time for an observer varies with his frame of reference (his speed, to put it simply). Hence, given two events, the interval of time from one to the other will not be the same for all observers. But if one is to cause another, it must always remain in its past; the sign of the time difference "t2t1" must not change whatever the observer.
Unfortunately, my memories of relativity are too scarce to put this into equations, but if you could travel faster than light, you could, say, watch an asteroid smash into the Earth and warn your friend on the Centauri stock market to sell shares of all Terran businesses before anyone could "see" the flash of the impact.
And in a given frame of reference (maybe that of a traveler aboard a STL ship inbetween), it would look as if you knew about it before it happened; stretching it further, it would be possible for the traveler (maybe through another FTL "jump") to warn Earth before the impact. Byebye causality.
If these situations are not to happen, information must not travel FTL.
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 lightyears away and at rest relative to X. S is a ship traveling along the (XY) line at 0.866c, which yields a gammafactor of 2. Times are measured in years, distances in lightyears. t, t', t" are the times for X, Y and S.
Here are the events of interest in Earth's and Centauri's timeframe:
Now, to understand that it does not merely look like timetravel, 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 lightyears away in the timeframe of S, and receding at 0.866c). In the timeframe of S:
Now, if you are not convinced, then I think you're thinking either:
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 lightyears apart. In Earth's timeframe:
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 timetravellike paradoxes are eliminated altogether.
Re:It's been "disproven" for quite a while now... (Score:3, Informative)
?? It does go at c.
The equations of relativity are such that that the relative speed between a ray of light and ANYTHING ELSE turns out to be always c. No matter whether that other thing is you standing in Chicago or a car moving. That relative speed "c" is the "constant".
Re:It's been "disproven" for quite a while now... (Score:2, Insightful)
Your post is *exactly* the reason why. . . (Score:2)
Thank you for trying out, but I'm afraid you're just not "Jeopardy" material yet. We have a lovely parting gift for you though, this boxed of set of the Feynman Lectures.
Read them. Work the problems. Try again next year.
KFG
Re:It's been "disproven" for quite a while now... (Score:5, Informative)
Huh? Light *always* goes at c, for every observerit 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 reemitted 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
Re:It's been "disproven" for quite a while now... (Score:3, Funny)
Don't worry about it too much; everyone expects the civil engineering students to be stupid.
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/(1beta^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 timedilation 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 highspeeds, 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 socalled Cerenkov radiation. This is why nuclearrods glow underwater, and is the basis of how most neutrino observatories work.
Re:It's been "disproven" for quite a while now... (Score:3, Insightful)
I've read many things and heard many things that supposedly came from Einstein's theories. Examples are that time travel is impossible, faster than light (or even fast as light) travel is impossible, and others. Many of these simply are not true.
Einstein himself said that in order to understand the theories, you need to be able to think in the abstract. There are few that can, even those who have been well trained in the areas of physics that take Eistein's theories into account.
As for the speed of light itself, I submit that it may not be the speed of light that is changed, but the nature of the universe around it that has. The reason that light bends in a gravitational field is not because light is slowed, or even that it bends, it's because space itself is different. Our space is curved and warped, moreso around massive objects, and like an object traveling along a bumpy, uneven path, light too will change apparent direction and speed. Change other properties of the physical space through which light travels, and that too will appear to affect the speed of light (and possibly its direction). But is the speed of light really changing, or is it just our relativistic perception of it?
PGA
Re:It's been "disproven" for quite a while now... (Score:2)
Let's say there is a solar system 10 light years away.
You build a very fast space ship and you go there and back in 5 years.
Huh?
That's 5 of *your* years. Everybody else back home has gone through 25 years.
Re:gravity effects are instantaneous (Score:2, Interesting)
Since it is impossible to "transport" an object in that sence, no one has yet to be able to say that it is instantanius.. and Magnatism is definitely not the same way.. I believe its logical to assume that Gravity is Not Instantanious.. Example.. The stars as we see them in the universe are not actually where we see them.. we see them as they were several to hundreds to Thousands of years ago.. Yet if we calculate where gravity is interacting, its where we see it..
There is a study being done now I believe that is designed to find out if gravity travels instantaniously or if its trackable.. but as a logical person, I find it much more likely that at best it travels faster than we can track, not instantaniously. Much the way Light was thought to travel instantaniously before it was clocked at really really fast.
Slashdot, Add spell check!:)
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:gravity effects are instantaneous (Score:2)
This is how we have things like electromagnetic waves and gravitational waves. If time (speed) did not factor in to magnetism or gravity, there would be no such thing as a wave based on either of these things.
Re:gravity effects are instantaneous (Score:2, Informative)
Please try to use EM instead of just light, some people get confused
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:No, what this is saying is that. . . (Score:3, Insightful)
Wow. You really have taken an advanced physics class! (not being sarcastic at all) In my brief experience with quantum mechanics, that's pretty much all it is. Sure, there's math to back up most of it, but a lot is just "classical parallels".
some physicists believe they may be seeing things at the macro level that are unexplainable by Relativitly theory
Something like when you examine a classical system of a partical moving in a onedimensional region of definite length (the 1D infinite square well), you can see that it is equally probable to find the particle at any distance from the sides. However, quantum mechanically, the particle has a definite probability of being in the centre and said probability decreases like a gaussian distribution as it approaches either boundary. However, this is only for the ground state. As you get to higher and higher energy levels, you start to notice that the QM probability begins to resemble the classical one. But I'll leave with the best quote ever, which means my sig is finally applicable: