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One Hundred Years of E=MC2
Eric Ward writes "To mark the one hundredth anniversary of Einstein's
famous equation, E=mc2, NOVA has gone live this month with a Web site that features exclusive content and podcasts from ten of the worlds top physicists. This once-in-a-lifetime gathering of top scientists such as S. James Gates, Jr., Brian Greene, Neil deGrasse Tyson and Nobel Laureate Sheldon Glashow simplify what the equation means to our world today and the effect it has had on their careers. NOVA online also details how Einstein grappled with the implications of his revolutionary theory of relativity and came to a startling conclusion: that mass and energy are one,
related by the formula E=mc2.
Viewers will also find lesson plans through the
award-winning NOVA Teacher's Guide and a special
library resource kit."
"Plagiarist of the Century" quoth the sensationalist headline; more credit is due, in any case, to certain now-anonymous Italian physicists: Olinto De Pretto comes to mind, et alii.
Its E=MC^2/(1-(V^2/C^2))
There once was a fencer named frisk,
whose movement exceedingly brisk
so quick was his action
the Fitzgerald Contraction
reduced his rapier to a disc
+5, Truth
In response to this momentous occasion...I can only quote the great MC Hawking. :)
"I explode like a bomb. No-one is spared. My power is my mass times the speed of light squared."
#!/usr/bin/perl my $e = (mc * 2); print "$e";
*E=MC^2
This sig is o Unfunny o Funny
Site already slow: Coral cache.
--
Dreamhost superb hosting.
Kunowalls!!! Random sexy wallpapers.
Hosting 20G hd, 1Tb bw! ssh $7.95
Dear Slashdot. NOT A FUCKING PODCAST.
Do your job, editors!
+5, Truth
Einstein's work showed that Newton's equations were a good approximation for low velocities, but not for velocities approaching c. What if Einstein's work is an approximation, too. Perhaps we will discover that the E deviates from mc^2 when temperatures are very high or very low or m is very large or magnetic fields are especially strong.
Newton's 3 laws survived 239 years, I wonder how long Einstein's will last?
Two wrongs don't make a right, but three lefts do.
Richard Stallman created that, not Einstein! And the current release is 21.4, not 2!
... I really have a strange feeling about their web server :(
If you don't fail at least 90 percent of the time, you're not aiming high enough. (Alan Kay)
But m = \gamma m_0, where \gamma = 1/sqrt(1 - \beta^2), and, of course \beta = v/c.
I.e., E = mc^2 = m_0 c^2 / sqrt(1 - (v^2/c^2))
Oh, m_0 is rest mass, in case you didn't know that, and m is the relativistic mass.
Ben Hocking
Need a professional organizer?
I don't know if I fully believe that energy equals mass. The only way that makes sense if something like SuperString theory is true, that we have more than the 4 dimensions (X, Y, Z, and time). To take mass, and BANG, the mass is gone and there is enegery, does not ring true to me. Something more happened than we do not understand. It is like the uncertanty principle. The electron is still there. Or is it? If it is not there, where is it? How many examples are there of the opposite happening. Taking just energy, with no starting mass, and making mass?
What I think is more usefull from E=MC2 is the idea of relativity. It is true, not just for science, but for almost every field of study.
Rosco: "If brains were gunpowder, Enos couldn't blow his nose."
By Peter Norvig.
Don't miss the rest of his site while you're there.
To a Lisp hacker, XML is S-expressions in drag.
I took physics in college and all I got out of it was this cool E=MC2 shirt. :P
Sadly, this comes just days after the anniversaries of the Hiroshima and Nagasaki bombings.
come on mods, time to get a clue.
Fitzgerald suggested that when a body moves through space it experiences a compression in the direction of the motion. Lorentz showed how such an effect might be expected based on electromagnetic theory and the electrical constitution of matter, that is, when a body moves through space its dimension parallel to the line of motion might become less by an amount dependent on its speed. If the speed of the body is v and the speed of light is c, then the contraction is in the ratio
"If Einstein was so smart how come people only call you 'Einstein' when you do something really stupid?" - Brian Regan
So what was E equal to in 1904?
++ Say to Elrond "Hello.".
Elrond says "No.". Elrond gives you some lunch.
It's because you're doing E=MC2, not E=MC^2. Redo your calculations and you'll see everything makes sense now. ;)
:)
Now seriously, I don't get it either.
(Another thing I don't get: why isn't <super> allowed HTML?)
The filesystem is the package manager
Ok everyone, let me proclaim my utter ignorance. I have been trying to understand E=MC^2 for years, and I don't get.
Honestly, I don't even understand many of the basics.
Sure-- it's the formula for "Energy to matter" or something. But why does this matter? How does this relate to Einstein's theories about gravity wells, speed of light, etc.
And I understand the legacy-- E=MC^2 changed how the world was viewed by theoretical physicists. It's different from the Newtonian models of the Universe. I just don't understand why.
Are there any good, visual examples of these ideas?
I'm listening to these Physicists. But again, most of these people are talking about the legacy of the equasion-- they talk about how the equasion impacted society. (Although Janet Conrad has a good brief description of why it matters)
94% of Repubs and 21% of Dems voted to renew the Patriot Act
For lazy readers:c id=13279290 (big thread discussing idiocy in calling them "podcasts")c id=13279218 (little thread with wikipedia quote)
http://apple.slashdot.org/comments.pl?sid=158504&
http://apple.slashdot.org/comments.pl?sid=158504&
For even lazier readers:
WIKIPEDIA: Podcasting is a method of publishing audio broadcasts via the Internet, allowing users to subscribe to a feed of new files (usually MP3s). It became popular in late 2004, largely due to automatic downloading of audio onto portable players or personal computers.
+5, Truth
The dilemma is similar to the one posed by Shannon's Capacity Theorem. It indicates the upper bound on the rate at which information can be transmitted but provides no clue as to how to build a device that can transmit at the upper bound. Consider the case of standard copper telephone cable. In the 1950's (?), the theorem told use that we can transmit at 56K baud on the cable, but 30 years elapsed before we actually figured out how to build a modem (with a little help from Viterbi) that can transmit data at that speed.
But only in the rest frame.
I would use floats. And make sure you note the difference between velocity (speed and direction) as opposed to just speed. And it's not just any speed, it's the speed of light in a vacuum. So, this is better:
float getenergy(float mass, float velocity) { }Or:
float getenergy(float mass, float velocity) { }if you don't like using "c" for some reason.
Ben Hocking
Need a professional organizer?
I am not 100 yrs old!
If you have it that the values are irrellevant and only the geometery matters, then for E to be conserved and still change c...
...which only means that as the speed of light changes, mass must change where it does so that E does not change and violate conservation. And if t is related to c then quite possibly as c approaches infinity m drops towards 0 and the distance between any two points drops towards zero and the speed of time climbs towards infinity and at c=infinity everything happens at once and all distances are zero.
E=(m/(n^2))*((n^2)*(c^2))
where n is the factor by which the speed of light changes.
Conversely if c drops toward zero then mass heads for infinity and when c=0 then mass is infinite, nothing happens, and all distances are infinite.
It looks like reverse time dilation and one wonders if you can warp space to create a faster local c, can you accellarate normally at such a rate as to counter it and have dilation=0? It doesn't look so much like Star Trek's integral warp speeds as there being a curve on which normal dilation can match warp dilation. Would be interesting to have a high-speed zero dilation trip to the next system and back to check it out with chronometers.
Just thinking out loud is all...
If my grammar and spelling are off, I am [distracted/tired/careless] (take your pick)
What if Einstein's work is an approximation, too. ..
That's the beauty of science... Science is INQUIRY... it is not static.
Until someone does prove it was an approximation, we'll use it. Once that occurs, we will use the new figure until someone else is able to make it more accurate.
Ignorance is not a crime; neither should it be a way of life
Congress control $ = inmates run the asylum
I don't know the details, but if Newton and Leibinitz can come up with calculus independently of each other (b/c it is true) do not assume Einstein stole the formula without proof.
Except for ending slavery, the Nazis, communism, & securing American independence, war has never solved anything.
...and nothing is faster than the speed of light, how can we square c ???
While we are at giving credit where it is due, why not give Nikola Tesla credit for his work with electricity.
The USA has a bad habit of stealing technology and breakthroughs from other countries and then saying they invented it. There is no way that Benjamin Franklin invented everything from bifocal eyeglasses to a furnace, and still had time to fly kites and discover electricity.
Rosco: "If brains were gunpowder, Enos couldn't blow his nose."
E = mc^2 is Not Einstein's Discovery
...
Robert A. Herrmann
1. Introduction
It appears that some scientists have not received the proper credit for significant discoveries for which they have priority. However, without specific and irrefutable information, it is not possible to give convincing reasons why these individuals have been denied recognition and why others have been given credit for their scientific discoveries. In 1996, I was asked whether certain aspects of General Relativity were originally formulated by Einstein or Hilbert. (Hilbert presented the gravitational equation(s) prior to Einstein.) The questioner said that he knew very little about Einstein's achievements except for such things as "E= mc^2." I answered his question relative to the Hilbert verses Einstein controversy but I neglected to discuss the more easily explained E = mc^2. What follows in this short article shows exactly who developed the idea that "radiation" can be characterized as having an apparent mass and that it was not Einstein in his 1905 paper. Except for the last remarks on Olinto De Pretto, this article is concerned mostly with "radiation" and its relation to E = mc^2.
read more...
Michael.
Linux : Mac
You don't usually hear of a genius physicist named "Chuck Miller"...
Rory Carroll in Rome
Thursday November 11, 1999
Guardian
The mathematical equation that ushered in the atomic age was discovered by an unknown Italian dilettante two years before Albert Einstein used it in developing the theory of relativity, it was claimed yesterday.Olinto De Pretto, an industrialist from Vicenza, published the equation E=mc2 in a scientific magazine, Atte, in 1903, said Umberto Bartocci, a mathematical historian.
Einstein allegedly used De Pretto's insight in a major paper published in 1905, but De Pretto was never acclaimed, said Professor Bartocci of the University of Perugia.
De Pretto had stumbled on the equation, but not the theory of relativity, while speculating about ether in the life of the universe, said Prof Bartocci. It was republished in 1904 by Veneto's Royal Science Institute, but the equation's significance was not understood.
A Swiss Italian named Michele Besso alerted Einstein to the research and in 1905 Einstein published his own work, said Prof Bartocci. It took years for his breakthrough to be grasped. When the penny finally dropped, De Pretto's contribution was overlooked while Einstein went on to become the century's most famous scientist. De Pretto died in 1921.
"De Pretto did not discover relativity but there is no doubt that he was the first to use the equation. That is hugely significant. I also believe, though it's impossible to prove, that Einstein used De Pretto's research," said Prof Bartocci, who has written a book on the subject....
Seastead this.
But I have a few nagging question about this famous equation. People just tend to explain c^2 by saying something like "a little matter represents a lot of energy, and c is a big number and so c squared is even bigger". Well, that certainly is true if c is measured in meters per second or any other common unit. But it's all about the units. If c is expressed in light-seconds/second rather than meters per second, or worse yet light-years/second then the "logic" of that argument is exposed as just hype. So the real issue comes down not to the equation e=mc^2 itself, but the selection of the units that e, m and c are expressed in. Use a different unit and, as I try to show above, the whole thing breaks down.
Al himself made a pretty famous point of saying that c was a constant. So c^2 is also a constant. So the equation boils down to expressing an important relation between e and m. But it all depends on the units of measure. So here's the question:
Is there some science behind the selection of the units involved that allows this equation to be so simple, or are we to believe that some serendipitous magic just allows this to be an exact equation and the units somehow just happen to match up? After all, I certainly don't know of any reason why a meter is any more of a valid unit to do this calculation with than a furlong, or a foot, or a parsec. And I am under the impression that the units of both mass and energy were determined before the equation, not as a result of it. So should I believe that this equation is just a serendipitous chance match up of units, that Einstein made some sort of deal with God, or that the equation just might be a bit over simplified?
If a meter were and inch shorter or an inch larger, there would still be an equation that could show the relation between e and m, but a conversion number would have to be added to the equation to make up for the slight difference in the size of the meter. How is it that this equation works out with the current rather arbitrary length of a meter to such whole numbers?
I'm an American. I love this country and the freedoms that we used to have.
As my mass has gone up, my energy has gone down. What more proof do you need?
That's near boston mass., isn't it?
How many examples are there of the opposite happening. Taking just energy, with no starting mass, and making mass?
Here's the link you need to CD Anderson's 1932 experiment using gamma rays
Ignorance is not a crime; neither should it be a way of life
Congress control $ = inmates run the asylum
Another interesting fact, derived from empirical analysis : in a Windows field, light speed is negative.This explain the interesting "expanding copy time" (aka "30 seconds left... 4 centuries left...") experienced by most Windows users.Another explaination would be a schrödinger-like effect induced by closed source.
I'm jack's useless sig
If you write Newton's laws with the covariant 4-momentum, don't they still hold (pdot = Force)?
Helium balloons want to be free.
Why do they get all the hacks with books to explain these things? The real people doing the real work are never on these shows. I guess Michio Kaku, Alan Guth, and Brian Greene are all more suitable for public consumption even though their work sucks.
100th anniversary? Yeah, but it's all relative
It doesn't explain quantum effects, so the theory of relativity (both of them) is already known to be lacking for many years...
Thank you, thank you, I'll be here all week.
This guy sounds like another nutbar. Check his home page for proof.
(geeks+intelectuals)-(1st posters+flamebaiters)*(low bandwidth)= "/.effect" ...somebody better be able to do way better than this BTW....
Don't ya hate it when the correct spelling of your favorite screen name is taken?
To begin: Wolfgang Pauli postulated the neutrino, not Einstein.
Next: Whatever one concludes about the validity of Eddington's solar eclipse experiment, the predictions of General Relativity have been tested and proved out in hundreds, if not thousands, of repeatable and rigorous experiments since then.
And Next:
This quote falls somewhere between the irrelevant and a non-sequitur. Thanks for sharing man--but what does it mean? No physicist takes cold fusion seriously, and autodynamics is a competing theory to General Relativity, for which Richard Moody, Jr. is clearly a shill.
At the end of the day, it doesn't matter whom it was that provided the first, or the first accurate, derivation of e=mc^2. It could have been Einstein, Poincare', or William goddamn Shakespeare, for all I care. What matters is that both Special and General Relativity have withstood an awful lot of testing over the last century, and stood up well under that onslaught.
The autodynamics camp also seems to believe that Special Relativity is used in radioactive decay calculations, and I could have sworn that Quantum/Statistical Mechanics holds sway there....
I'm the mc squared, at the speed of light
My rhythm is loose, but my rhymes are tight
From the heart of the Sun, into your eye
Call me irrational, I'm easy - as pi
(C) 1988, 2005 mc squared
--
make install -not war
Is Brian Greene a top scientist, or just a famous one?
Errr, n^2 cancels out on the right hand side, no?
-mkb
http://en.wikipedia.org/wiki/Oliver_Heaviside
Oliver Heaviside is one of the forgotten men of science, much like Philo T. Farnsworth (inventor of the electronic television) is one of the forgotten men of engineering.
As well as casting Maxwell's equations in their modern (vector) form, he contributed to work in relativity, and if memory serves first wrote down E=mc^2 in 1892. David Bohm's book on special relativity covers this in considerable detail.
This is not to diminish the contribution of Einstein, who worked mostly independently of previously known results, but to make it clear that there were others who set the stage for Einstein's great performance.
The fundamental contribution of Einstein was his ability to show that results that had previously been derived by people like Heaviside and Lorentz with great difficulty from an electro-mechanical dynamical model of the electron could be generalized and proven very simply as a result of a purely kinematic invariance.
Blasphemy is a human right. Blasphemophobia kills.
FWIW, E=mc^2 was a pretty good book on the subject and a very enjoyable read.
Have fun: Join D.N.A. (National Dyslexics Association)
If we are getting pedantic...
[PEDANTIC]
For things like photons that have zero rest mass
E = m0*c^2 / sqrt (1-(v/c)^2)
Doesn't work so well... By using the following:
(E^2) = (m0^2)*(c^4) + (p^2)*(c^2)
Now photons (which by definition are moving and have momentum) can have kinetic energy associated with them without having to divide zero by zero (since photons travel the speed of light v/c = 1 and the denominator is zero in your equation).
[/PEDANTIC]
E=mc2 is a "sexed equation". Newton's Principia (a "rape manual"):
p osts
http://www.freerepublic.com/focus/f-news/1076200/
Thanks God I went to college a long time ago.
Give a man a fish and you have fed him for today. Teach a man to fish, and he'll say "WHERE'S MY FISH, YOU IDIOT?"
I mean why does it seem that anytime someone mentions challenging theories like E=MC^2, other scientists distance themselves from the poor sap proposing such sacrilege?
I am just curious if people doing real science think similarly...
Disclaimer: I am not a physicist nor do I play one on the internet.
-----
Among the names given in the summary, there is no doubt that Sheldon Glashow was a top scientist - twenty years ago. As for Brian Greene, Neil deGrasse Tyson and S. James Gates, they are good science popularizers, and competent physicists in all likelihood. However, I think they would be the first ones to pooh-pooh the notion that they are top physicists in a world ranking.
The paper seems to be basically saying that Special Relativity is a special case of General Relativity, which IIRC is true. But then you see the context in the author's homepage, and, well, yes, he does appear to be a little goofy.
Which all points to the dangers of mixing science with politics and religion. You can piss away a lot of credibility that way, and luckily Einstein never claimed to be an expert at either.
Give a man a fish and you have fed him for today. Teach a man to fish, and he'll say "WHERE'S MY FISH, YOU IDIOT?"
"E=mc^2 is crankin'!"
"We are fortunately not bathed in that level of energy because we would first get sterilized, then it would mess with our DNA, then we would die."
We raise our slide-rules high.
According to many current theories, photons have zero rest mass, but still have momentum (another mysterious conservation book-keeping number like energy except it has the ability to describe the movement of energy from one place to another using massless photons or electromagnetic waves).
When this photon with a certain momentum strikes your solar sail, depending on the precise interaction with the matter in the sail, transfers some of it's momentum to the sail.
Which is why this whole thing makes more sense when you talk about with this type of formula...
E^2 = (m0^c^2)^2 + (p*c)^2
Assuming we aren't converting any "rest mass" to energy in the interaction, conservation of energy implies that we are going to conserve relativistic momentum and we don't get no perpetual motion machine (unless you count motion as drifting in mostly the same direction as the original photon)
Some of you people are waaaay to quick to latch onto these conspiracy theories that einstein stole other people's theories, etc...
Almost every well known scientist and scientific discovery was built upon a foundation of prior knowledge, often without "proper" citation of others contributions, be it newton, copernicus, whoever. They all "stole" many of the ideas that were "discovered" in the past or even by their contemporaries. What set these guys apart, was the CONCLUSIONS they drew, and putting the whole picture together that made sense. Every physicist is aware of the fact that Einstein's papers were not his research or "discovery" alone... the whole concept of that is preposterous... but the idea that his work in its entirety and all his conclusions and effort had already been done is equally preposterous. It does NOT diminish the value of what he did, just because:
1. All the ideas and concepts were not his own.
2. Ignorant people interpet them as being his own.
Heck someone had already "discovered" the idea of swatting flies with a branch long ago... but that doesn't take away from the guy that "produced" the modern fly swatter. Ya maybe the other guy deserves more credit than he gets... but the guy responsible for what i'm actually using deserves more, because he made it more practical and effective for ME.
If speeding up Mass gets us Energy, does slowing down Energy get us Mass?
For example, if we slowed down photons enough, would they accumulate into something of serious Mass?
DEAD DEAD DEAD DELETE ME
I feel sorry for Lise Meitner; never receiving the recognitiopn she deserved. F**king Nazis.
My web domain.
Regularly updated text source == blog
Technique for doing something == hack
Audio file available from a website == podcast
That's somewhat backwards. In math, someone usually calls a result a lemma to indicate it is a preliminary result being used to prove a more important result. What you are describing would usually be called a corollary.
No if anyone "observed" that time was relative it was Michelson-Morley. Einstein postulated this observation as the basis of a formal system which yielded new testable hypotheses.
Seastead this.
Yeah, slashdot won't allow the tag for this posting. But for crying out loud, how about E=mc^2, at least?
Damn. Self-proclaimed "nerds", unite! Or something.
A few years ago the National Library in Canberra had an extremely popular exihbition called "National Treasures" or something like that. It was a collection of many historical and influential works like ancient maps, the original lyrics to "Yesterday" by Paul McCartney, and other incredible things I've forgotten about. Included amongst them was Einstein's original paper on relativity open at the famous equation E=mc^2.
A German friend of mine went and saw it, and when he read that page he laughed because Einstein had written (in German) a long explanation concluded by 'this can be aproximated by the equation E=mc^2'.
We both hoped that all the physicists around the world knew that the equation wasn't acurate :)
http://physicsmathforums.com/showthread.php?t=60
Moving Dimensions Theory
By Dr. E
http://physicsmathforums.com/
Questions Addressed by MDT:
Why is the speed of light constant in all frames?
Why are light and energy quantized?
How can matter display both wave and particle properties?
Why are there non-local effects in quantum mechanics?
Why does time stop at the speed of light?
How come a photon does not age?
Why are inertial mass and gravitational mass the same thing?
Why do moving bodies exhibit length contraction?
Why are mass and energy equivalent?
Why does time's arrow point in the direction it points in? Why entropy?
Why do photons appear as spherically-symmetric wavefronts traveling with the velocity c?
Why is there a minus sign in the following metric? x^2+y^2+z^2-c^2t^2=s^2
What deeper reality underlies Einstein's postulates of relativity?
What deeper reality underlies Newton's laws?
What underlies the laws of Inertia?
Why does general relativity fail at short distances? Why does quantum mechanics dominate at short distances?
Why have so many great minds, Einestin, Godel, Wheeler, Hawking, and Penrose called for a new conception of time?
If at first the idea is not absurd, then there is no hope for it.
--Albert Einstein
If I have seen further it is by standing on the shoulders of giants.
--Isaac Newton
Max Planck, the father of quantum theory, felt that the pioneer scientist must have "a vivid intuitive imagination, for new ideas are not generated by deduction, but by artistically creative imagination."
An important scientific innovation rarely makes its way by gradually winning over and converting its opponents: What does happen is that the opponents gradually die out.
--Max Planck
Moving Dimensions Theory (MDT) Today I am writing regarding Moving Dimensions Theory--a deeper model for explaining diverse phenomena in both quantum mechanics and relativity.
The General Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial dimensions.
The Specific Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial dimensions at the rate of c in quantized units of the Planck length.
Relativistic, classical, and quantum mechanical phenomena, as well as time itself, are emergent properties of this fundamental principle. Newton's laws, the principle of Inertia, Einstein's postulates, and the inherent wave-particle duality of QM may be explained with this model.
A few years back, while surfing a towering wave on the Outer Banks of North Carolina, a beautiful thought occurred to me. Suppose the wave I was riding represented a coordinate in a dimension. Then although I was approaching shore, I was not moving in this dimension.
The dimension itself was moving with me--I was surfing the dimension. In a flash I saw that that is why photons never age--they are moving along with the fourth dimension, and thus stationary relative to it. In another flash I saw that that is why a photon's space-time interval is represented by a null vector, or a 0, no matter how far it travels. Indeed Einstein stated that an object's velocity through space-time was always c--even stationary objects are traveling at the velocity c through time! How could this be, were it not for a fourth expanding dimension, which matter could surf as photons, giving rise to our notion of time? And so it is that Moving Dimensions Theory was born as the wave crested and crashed about me, thundering on down, as I fought to remain surfing amidst the foam, facing the setting sun silhouetting the Hatteras light. And the waves kept on crash
NOVA podcasts - well, it's more enlightening than the 50 or more sex talk podcasts...
... of iPods!
Billions and Billions and Billions
Einstein was awarded the Nobel in 1921 for contributions to physics, and especially the photoelectric effect which demonstrated the quantization of photons.
E = hf
where E is energy, h if Planck's constant, and f is frequency. The energy of light is limited to a multiples of a constant (h) and determines the color (frequency) of the light.
Without this, Bohr doesn't develop his electron model and a lot of twentieth century physics doesn't get discovered.
When m is converted into E, ...
all the little bundles of energy making up m are unbundled, and are released in all directions
I thought we had space/time up to 11 or 15 dimentions?
(And if you watch ST:TNG - 26 or 27 dimentions...)
Sorry but parent was more insigtful by far. In *real* physics there is no "m0" and "m" since you ALWAYS have m0=m. Someone invented the m0 and relativistic m to use old, classical physics. Same thing goes for t0 and t, as well as v and v0.
In *real* physics, m is always the rest mass, v is always relative, and t is always relative. Relative to what, you ask? To the measurement frame of course!! (Physics is about measurement after all).
Furthermore, in high energy physics E=m, c=1 so...
It is Lorentz, but not the same Lorenz (as it's usually spelled) of "Lorenz attractor." Lorentz was a contemporary of Einstein. Lorenz is a meteorologist and mathematician who discovered the Lorenz attractor from weather research in the 1960s.
Pick your E and m units right and c=1, so E=m.
We are talking about e-mc^2 here. Not the Special theory of Relativity. Not the General theory of Relativity. Not relativity at all. I'm just asking (and still not quite convinced) how it happens that a formula based on joules, kilograms and meters can just happen to work out in nice round numbers. I do understand the relationship between mass and energy; I don't yet accept what links joules, killograms and meters so serendipitously in this simple equation.
I'm an American. I love this country and the freedoms that we used to have.
We're celebrating Einstein's work on relativity, brownian motion, and the photoelectric effect.
World Year of Physics 2005
...the greatest physics jokes collection. Lots of other science jokes there as well.
Tag lost or not installed.
n/t
Ben Hocking
Need a professional organizer?
Actually it is more correct to write it as:
E^2 = p^2c^2 + m^2c^4
"relativistic mass" is a very bad concept to learn (something which even Einstein pointed out). A far better way to think about it is that our classical definition of momentum is just a low energy approximation of true momentum. The mass of a particle, just like its charge, is something that does not change.
Actually this is not consistent with special relativity. Special relativity allows me to convert mass into energy so suppose I start with a neutral pion. This can be travelling at a constant velocity when it decays into two photons. Suddenly I have now have no mass and my speed is that of light...and no external forces acted. Ooops!
Newton's Second Law: that the change in motion is proportional its change in momentum
First that is NOT Newton's second law since Newton actually defined momentum as "motion" and the above is just that definition - no physics involved. The correct law is:
The rate of change of momentum of a body is proportional to the external force applied.
This is only correct if you use the 4-vector definitions for force and momentum and not Newton's. Thus, the law as Newton wrote it is wrong.
Newton's Third law, Every reaction is met by an equal and opposite reaction is simply conservation of energy and is not violated in any classical theory, of which relativity both General and Special are.
Ok lets fix this one...first a minor point: relativity is NOT classical physics. Now consider trying to stop a relativistic cricket ball (or baseball for you Canadians out there). The distance moved by the ball while you stop it will vary depending on whether you look at it from the balls point of view or the cricket pitch's point of view. Since, as you point out energy is force times distance the ball and the catcher will both observe different forces. Thus NIII is not correct either...unless you use 4-vector definitions for force.
What Newton was wrong about (and it's not really fair to call him wrong since ......)....and the nature of light as a particle.
Oh boy this is so utterly wrong it is even funny! One of Newton's most amazing ideas that turned out to be CORRECT was the particle nature of light, although the lacked the means to prove it. What is so ironic about your statement is that Einstein was the one who showed that light behaved as a particle in the same year as his relativity paper. Thus the one time you would be correct in saying that Einstein showed Newton to be correct you instead say he is wrong!
As for calling Newton wrong I think you have got confused between cause and effect. Newton was wrong BECAUSE he lacked the means to discover relativity. This does not make him any less wrong. His achievements were amazing given his resources and the previous state of physics and no amount of time will alter that...but he is still wrong! Even at everyday energies Newton's laws are only approximatations and are not correct. However they are such good approximations and so much simpler to understand that we still teach them to school kids. Newton was an amazing genius, arguably even more so that Einstein: he also made huge contributions to maths [~invented calculus] and anti-counterfeiting measures [as master of the royal mint]. His contributions to physics were incredible, but still in the end his laws were proven wrong just, as I am sure, we will find a lot of our current understanding will not quite be correct in a hundred years from now.
I have not read every last comment, but it seems nobody understands, including the people who mentioned that others wrote and published "E=mc^2" up to ten years before Einstein, what its true significance is, or why Einstein gets credit.
It is somewhat straightforward to derive E=mc^2 from Maxwell's equations, just as Fitzgerald derived the correct equations for the contraction of a moving object in its direction of motion. But the key, the big thing, that Einstein did was not just derive by rote an equation, but assign consistent physical interpetations to those equations and make some pretty bold predictions. He put the thing together.
For instance, many people keep saying "E=mc^2" means that matter and energy can be "converted" from one to another. THat is actually incorrect - the MEANING of the equation is that the TOTAL ENERGY CONTENT of a system can be derived by noting its resistance to changes in motion as a result of applied force; i.e. its mass. In other words, the MASS of an object, as measured objectively, describes the TOTAL ENERGY CONTENT of that object as per E=mc^2. Or, put more simply, a boiling pot of water has slightly more mass than the exact same pot at room temperature. E=mc^2 can be shown to be a consequence of Maxwell's laws; Einstein's boldness was in asserting that ALL forms of energy, not just electromagnetic, are imbued with mass (a resistance to changes in motion) in proportion to the amount of energy within. His general theory of relativity tied this idea of inertial mass with gravitaional mass, by again boldly asserting that they are the same thing; this is by no means obvious (Eotovs experiments back it up to 10 significant figures, tho). And neither gives a clue about how to extract nuclear energy; all it says is that objects have an internal energy as evidenced by the fact they have mass; accessing that energy is a completely different matter.
Concisely put, the relationship is the same nomatter what units you use. For example, "E" in this case is energy, defined in Joules, where a Joule is (approximately for comparison) the amount of force required to lift 1 kilogram of mass up by 10 centimeters
In Imperial measurements, the relation would be identical, except for semantic differences. The closets unit of measurement in the Imperial system to the Joule the foot-pound, which is the amount of force required to lift 1 pound of material up by 1 foot (a Joule is equal to 0.737 foot-pounds).
If you expressed E=mc^2 in terms of Imperial terms, it would be the same except that E would be in foot-pounds, m would be in pounds, and C would be in feet per second. So the numbers would change, but not the relationship.
---- I'll take you in a Hunt deathmatch any day.
I admit it, I am crazy and my mind entertains me.
I think I could be friends with anyone who made this statement...
Now... are you and your mind two different things and if you are not your mind, who/what are you?
While I do have a BS in Physics/Math, I lost interest in these when I became more interested in HOW it is that I solved physics problems. How do I do it? To learn about this process I study Buddhist meditation.
But, to those who still want to study physical reality, please, please, please, read the following and tell me what you think. I did read this and I think it makes Einstein almost look like an amature, but I would rather spend my energy into studying the nature of thought than alternate views on reality.
Autodynamics
How can the icon of modern Physics be wrong? Well believe it or not, tens of thousands of physicists, engineers, scientists, and students around the world believe very strongly that Einstein is not correct. This does not Diminish Einstein in any way. His equation E=mc^2 and his Nobel Prize work on the Photo-Electric effect are still brilliant. It is simply time to move onto a greater truth.
Autodynamics
Ok, I'm double-posting this, but I really want to know what you smart physics Slashdotters think. I even got this turned down down as a "Ask Slashdot" question a couple of times!
The modernized version of the formula is as follows: The amount of electronic commerce is money times speed of light to the power of two So the more money you throw at it, the more "E" you get into your business. I just love wireless networking, as I can post to Slashdot even in a seminaar!
He wrote something like E^2 = m^2c^4 + p^2c^2. Hazy memories of university physics lectures 15 years ago... Outgeeked a lot of you with that one!
...therefore it cannot break symmetry between twins.
Besides, what happens if the second "twin" never accelerates, but merely passes its clock readings between several already "moving" ships (from the point of view of the general relativity)?
Now this one I can answer, cos I've just fought my way through a term of quantum dynamics. The electron isn't in any one place, it's splurged out. It gets fluffier and fluffier until something "detects" it, at which point it coalesces. Or doesn't. That's what the "detection" process does - it decides (on a probabilistic basis) whether the electron is currently in that area of space. Of course, once it's been detected and "decayed" to a point particle, it starts getting fuzzy again.
That's the classical version anyway. The problem with it is that it's not time-independent, which messes up all those nice Einsteinian symmetries (i.e. you'd probably never be able to mesh the two theories). The more confusing version, Quantum Electrodynamics, uses a rather weird "sum over paths" approach which, by a roundabout route, suggests that our universe is predestined, but we don't know which of many many similar universes we're in (the whole "Many Worlds" thing).
Oh, and your "idea of relativity" is fluffy to the point that a real physicist would probably lose his lunch. The fact that the phrase "everything is relative" strikes a chord with you does not mean that that's what Einsteinian relativity is all about.
For the love of God, please learn to spell "ridiculous"!!!
At the Large Electron Positron Collider, electrons and positrons have smashed together at energies of 200 GeV. That means that each particle has an energy of 100 GeV. Using m = \gamma m_0, and the rest mass (m_0) of an electron being 511 MeV, we find that \gamma^2 = 1/(1-\beta^2) \approx 38,300. This makes \beta^2 \approx 0.99997, or \beta \approx 0.99999.
What all this math boils down to is that the electrons at CERN-LEP are traveling at 99.999% the speed of light, which is quite a bit above 0.4!
Ben Hocking
Need a professional organizer?
Sigh. Now everything's a "podcast".
There's no subscription. There's no RSS feed. They're audio files with talking. I have a 2 hour car ride today, and I would have loved it if this were an actual "podcast" and I could have clicked one link to sync all of the audio commentary to my iPod.
Are audio files with music "podcasts" also? How about audio files with video attached?
Sorry. "You must be less than this pedantic to read Slashdot." Moving along now.
Special relativity deals with acceleration all the time. It just doesn't deal with gravity. (Even if you want to claim that accelerating reference frames are GR, not SR -- which was true under the original definitions but not under modern definitions -- SR has always been able to handle accelerating bodies as viewed from an inertial (non-accelerating) reference frame.
Special relativity allows me to convert mass into energy so suppose I start with a neutral pion. This can be travelling at a constant velocity when it decays into two photons. Suddenly I have now have no mass and my speed is that of light...and no external forces acted. Ooops!
Atomic decay is governed by a force in this case the electromagnetic, and thus the first law does not apply. However, because Newton defined momentum as Mass*velocity a massless photon can't carry momentum according to Newtonian theory. This is because Newton's definition of momentum was wrong due to his misunderstanding about the nature of light, not because the law was incorrectly stated. When the proper expression for momentum is used, namely the four vector of relativity Newton's second law is consistent.
First that is NOT Newton's second law...The correct law is:
The rate of change of momentum of a body is proportional to the external force applied.
This is only correct if you use the 4-vector definitions for force and momentum and not Newton's. Thus, the law as Newton wrote it is wrong.
I forgot a clause in my original statement, the phrase due to an applied force should follow change in motion. Thanks for the catch. The idea of momentum as a 4 vector only makes sense when motivated by the invariance of the velocity of light with respect to comoving observers. Newton had no reason to believe in that invariance and thus it's unsurprising he came up with a definition of momentum which is only approximately true when velocities do not approach that of light. However as you note when written with a 4 vector for momentum (which leads to the issue of which time to use to express the derivative as I noted earlier) Newton's second law is correct. Like his force law for gravity, his formula for momentum is incorrect due to his ignorance, but the law itself is fine when the correct expression for momentum is used.
first a minor point: relativity is NOT classical physics.
In the sense that relativity is not a quantum theory, and that General Relativity allows for infinite energy densities just like Newtonian physics, relativity is a classical theory. Note that when I got my first degree in physics, using Schrodinger's equation in which potential fields are also treated as fully continuous and thus allow for infinite potentials technique is referred to as semi-classical, since it bears that resemblance to other classical theories. Thus in the sense that any physical theory that allows infinite energy densities to occur is classical, relativity is classical. Or to use another common definition, any non-quantum theory of which both Newtonian physics and relativity are examples, is classical. If you want to draw the classical/nonclassical boundary elsewhere that's your perogative but since in physics the latter definition is most common I doubt you'd find many people who understand you.
One of Newton's most amazing ideas that turned out to be CORRECT was the particle nature of light
Light exhibits self interference which no reasonable definition of the word particle as used in everyday experience allows. Einstein's paper on the photoelectric effect was strong evidence of the quantization of energy of light, and quantized energy is a property of particles as commonly understood, however the reconcilliation of self interference and quantized energy is ultimately what led to quantum theory not relativity. Newton's conception of light as a particle was explicitly the idea of light as little billiard balls which is simply wrong.
Even at everyday energies Newton's laws are only approximatations and are not correct
I have no idea what your every day energy level is, but even if your total energy was 1/100th greater than your rest energy (equivalent to kinetic energy gained from moving at 14% of the speed of light, wh
Please note that the formula E=mc^2 resembles very much Leibniz's vis viva which is mv^2. He introduced this concept somewhere between 1676 and 1689.
If anyone's interested, Richard Feynman's lectures on Einstein's special, and general relativity - for me - made its effects v.clear, and understandable [um, I think!].
... he said something like "why things tend to move in a straight line ... until a force acts ... well, no one knows" - but's that's the same as saying - 'given that motion is relative ... 'why things tend to stand still [instead of jiggling around], no onew knows!' Ok, it's common-sense *and* experience that things don't go and move about unless *forces act*, but what the heck!!!
Maybe the lack of understanding is just one manifestation of how a mind that's been subjected to 'common sense' doesn't question things. We're all *corrupt* in many ways!!
However, why it's all *just so*, neither Feynman, Einstein or Newton [or anyone?] [really] knows [no 'mechanism' is given: which was enough the Newton] - Maybe that's how it should really be???
However, one thing that Feynman said that did puzzle me
@peetm
Firstly pion decay is not atomic decay - no nucleus is involved. Secondly you don't understand what an external force is, which you really should do if you do have a physics degree. This force is internal to the system and thus Newton's first law does apply as long as you consider the entire system i.e. both photons.
The idea of momentum as a 4-vector only makes sense when motivated by the invariance of the velocity of light with respect to comoving observers.
I'm sorry but this is absolutely wrong. Momentum is fundamentally a 4-vector. For "everyday" energy levels i.e. processes that typical people encounter in an average day an excellent approximation is Newton's 3-momentum. The motivation for using 4-vector momentum is that you have to at high energy levels (bodies with K.E. > ~10% of the rest mass energy) otherwise you get experimental results inconsistent with conservation of momentum. It was historically discovered through the path you describe but there is no requirement that be the case. Had Einstein not been born accurate measurements of high energy electron momenta would also lead to Special Relativity. Einstein's genius was that with a tiny amount of data he lept to the right conclusions. But realtivity is way more important than just talking about the speed of light in two intertial frames.
In the sense that relativity is not a quantum theory...
Depends on your definition of "classical" physics. The one I use, and I believe is the most common one, is physics based on Newtonian mechanics. SR is non-Newtonian and therefore non-classical. It is possible that my definition is not as common as I think but you'll have to excuse me if I don't take your word for it.
Light exhibits self interference which no reasonable definition of the word particle as used in everyday experience allows.
That is where quantum physics comes in. Light is indeed made of "particles" or quanta called photons. These do not behave like ordinary everyday particles but nevertheless are referred to as particles because of their localised nature.
Given that few people have ready access to equipment that measures time or distance to better than six significant figures the relativistic correction is indistinguishable from measurement error.
I'm glad you agree, that is PRECISELY my point! They are approximations. I'll grant you they are very good approximations (which is why they held so long) but approximations nonetheless.
Which leads to my point that Newton was correct for what he was capable of knowing.
What exactly does this mean? He was "correct" because he didn't know he was wrong? So does that mean the only time you are ever wrong is when you are capable of knowing you are? If so perhaps you'd better brush up on the meaning of the word "wrong".
Neither was there any reason to suppose that they were true. He certainly had no experimental evidence to that effect. That was a mistake, an easily forgivable one but still a mistake....and mistakes lead to being wrong!
Newton's formulas, which are to be distinguished from his laws...
Why exactly? What you are saying here is that if you take Newton's words, redefine the physical quantities to the SR expressions and keep calling them the same thing then he is still correct. i.e. if we redefine the bits that Newton got wrong the rest still works! All you have done is said that instead of getting the laws wrong Newton got the definitions of momentum, acceleration and force wrong.
This is pure semantics either I redefine 'F' and 'p' to keep F=dp/dt or I keep 'F' an