typodupeerror

*E=MC^2
• #### Re:You are missing an operator (Score:2)

NO NO NO. that will never compile. try this:

int getenergy(int mass, int velocity)
{
return mass * (velocity * velocity);
}
• #### Using ints? (Score:2)

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) {

return mass * (c * c);

}

Or:

float getenergy(float mass, float velocity) {

return mass * (speed_of_light_invacuo * speed_of_light_invacuo);

}
if you don't like using "c" for some reason.

• #### What if E = mc^2.0000000001? (Score:3, Interesting)

on Thursday August 18, 2005 @04:12PM (#13350470)
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?
• #### Re:What if E = mc^2.0000000001? (Score:5, Insightful)

on Thursday August 18, 2005 @04:24PM (#13350568)
Newton's 3 laws survived 239 years, I wonder how long Einstein's will last?

Einstein's _theories_ will last until evidence no longer supports them (just like all science).

Newton's _laws_ were and still are wrongly named.

And another pedantic relativity thing. The E=MC^2 was part of the _Special_ Theory of Relativity which says that measurements of time and distance vary as anything moves relative to anything else. This is where the twins where one goes in a rocket near the speed of light and the rocket twin comes back still young and the stationary twin is old (I really hope I didn't embarrass myself by reversing this, but I think this is right).

The other theory of Relativity that Einstein came up with was the _General_ Theory of Relativity that came out in 1915. This is the space-time continuum being bent by gravity.

Einstein was a little upset that he was able to join the two theories into one, but then again that is the goal of many physicists today.

Einstein was a very interesting and good person from everything I have heard and read. RIP.
• #### Re:What if E = mc^2.0000000001? (Score:2, Funny)

You can't get that backwards. However, it depends on which twin you call stationary. If you called the rocket stationary, then it would seem the twin that stayed home would be young.

Relativity, after all...
• #### Re:What if E = mc^2.0000000001? (Score:4, Informative)

on Thursday August 18, 2005 @05:15PM (#13351001)
You can't get that backwards. However, it depends on which twin you call stationary. If you called the rocket stationary, then it would seem the twin that stayed home would be young.

Bzzrt. Wrong answer. Motion is relative, acceleration is not. Rocket Twin accelerates and decellerates to leave and come back. He will always be younger at the end.

• #### Re:What if E = mc^2.0000000001? (Score:3, Interesting)

Bzzrt. Wrong answer. Motion is relative, acceleration is not.

Bzzrt. Everyone who doesn't quite understand relativity gets this one wrong. Right answer, wrong reason. The acceleration isn't important. The velocity is.

Think of it this way. Suppose one twin went to a star 100 light years distant at 0.99995c. Assume he has a magic ship that doesn't accelerate. Just boom and it's moving....

To the twin that stayed behind, he see the ship take 100 years to get to the star and 100 years to get back, (i.e.

• #### Re:What if E = mc^2.0000000001? (Score:5, Informative)

on Thursday August 18, 2005 @09:28PM (#13352400)
Bzzrt. Everyone who doesn't quite understand relativity gets this one wrong. Right answer, wrong reason. The acceleration isn't important. The velocity is.

Velocity causes the time and distance dilation yes, but the accelleration is what breaks the symmetry between the two.

While twin two is heading away from twin one, you can't say who's older - From Twin One's perspective Twin Two is aging slowly, and From Twin Two's perspective Twin One is aging slowly. It's just as legitimate to say that Twin Two is stationary and everything else is moving around him. It's the fact that he _turns around and comes back_ that breaks the symmetry between the two frames of reference and allows you to say that he is in fact the younger one.

You've covered the part about how the second twin is able to see himself covering the distance in that time, but ignored the fact that while he is not accelerating, the frames of reference are relative and that you can just as easily say the _other_ twin is aging slowly. In short, you ignored the principle of relativity. :)

• #### Re:What if E = mc^2.0000000001? (Score:2)

I'm pretty sure that relativity has already been revised a few times after Einstein's initial work.
• #### Re:What if E = mc^2.0000000001? (Score:2, Informative)

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

Interestingly, these conditions provide a good verification of the relationship between energy and mass. High energy photons (no mass) in extremely strong magnetic fields (e.g. near massive stars or in particle accelerators) lead to the creation of electron/positron pairs (with mass).

• #### What if cows could fly? (Score:3, Interesting)

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.
• #### Re:What if E = mc^2.0000000001? (Score:2)

Well, it sort of does anyway. The factor of 2 in the exponent is exact, but the entire expression mc^2 is only valid when at rest relative to the particle in question. At some relative velocity, the expression is really (gamma)mc^2, where (gamma) is 1/(1-v^2/c^2)^-1/2.
• #### Reaching way back into my memory,but... (Score:2)

If you write Newton's laws with the covariant 4-momentum, don't they still hold (pdot = Force)?

• #### Re:What if E = mc^2.0000000001? (Score:4, Insightful)

<DStaal@usa.net> on Thursday August 18, 2005 @04:46PM (#13350754)
We already know they don't hold under all circumstaces; they have trouble dealing with quantum effects. We have other theories that work there, but they don't work very well on the macro scale.

Which is like Newton's equations. They had known for quite a while that the orbit of Mercury couldn't be accuratly described by his theories, but they were the best avalible.

Einstein's are the best avalible now, for non-quantum events. Someday someone will come up with something that handles both. Then they'll be the genious hailed as the greatest.
• #### Hey! (Score:2)

Richard Stallman created that, not Einstein! And the current release is 21.4, not 2!
• #### What did E=MC2 give us the past 100 years? (Score:2)

I think there would be very different anwsers depending what part of the world you ask. I am sure the people of Nagasaki would have a very different anwser than the people of smalltown, USA. To some, it gave the world a horrible wepon. For others, it gave modern day comforts.

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

• #### Re:What did E=MC2 give us the past 100 years? (Score:5, Informative)

on Thursday August 18, 2005 @04:31PM (#13350616) Journal
I am sure the people of Nagasaki would have a very different anwser than the people of smalltown, USA. To some, it gave the world a horrible wepon.

All this business of E = mc^2 "giving us the nuclear bomb" is another example of newspaper pap-science. There's far more to a nuke than computing the mass defect.

I don't know if I fully believe that energy equals mass.

The whole idea is a staple of Relativistic kinematics which has been verified in collider experiments, etc., etc.

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.

You can define relativistic stuff in less than four dimensions (e.g., one of space and one of time). Take an electron-positron annihilation into two photons. A proper treatment requires quantum field theory, where mass can be understood (in one way) as a parameter constraining the dynamically allowed momentum-energy configurations of the physical ("on-shell") fields. It's [probably] not right to think of electrons as little dots of mass.

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?

Again, you need to consider quantum field theory to [begin to] answer these questions.

• #### Re:What did E=MC2 give us the past 100 years? (Score:2)

How many examples are there of the opposite happening. Taking just energy, with no starting mass, and making mass?

Quite a bunch. IANAP, but it seems to me that the constant forming (and recombining) of virtual electron/positron pairs would be one example of this.

Admittedly, these are rather short-lived, but IIRC, you can turn them into "real" electrons (and positrons) by adding energy to the system from the outside.

• #### Did it in 1932 (Score:3, Informative)

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 [physlink.com] using gamma rays
• #### Re:What did E=MC2 give us the past 100 years? (Score:5, Insightful)

<qaffir@hotmail.com> on Thursday August 18, 2005 @05:04PM (#13350902)
I don't know if I fully believe that energy equals mass... To take mass, and BANG, the mass is gone and there is energy, does not ring true to me.

And Newton's first law of motion didn't ring true to Aristotle—clearly objects in motion tend to come to a stop if nothing is pushing them. Our intuition about how the universe works is based on our limited experience of medium-sized objects moving at low speeds on the earth's surface, with the result that all physics post-Aristotle is more or less counterintuitive. The fact that you can't imagine it doesn't mean it isn't so.
• #### Re:What did E=MC2 give us the past 100 years? (Score:5, Informative)

<qaffir@hotmail.com> on Thursday August 18, 2005 @05:32PM (#13351124)
I realize it's gauche to reply twice to the same comment, but there were a couple things I didn't answer:

What did E=MC2 give us the past 100 years?

It's a fact (approximately) about the nature of the universe. It doesn't need to give us anything. What did the discovery of the planet Neptune do for us? Nothing practical, but I think knowledge is worth seeking for its own sake.

What I think is more useful from E=MC2 is the idea of relativity. It is true, not just for science, but for almost every field of study.

If by "the idea of relativity" you mean, roughly, "there are no privileged inertial frames of reference", then I have a hard time imagining what bearing that idea has on, say, art history, or comparative religion. If you just mean that "everything is relative", then I'd say that your idea of relativity has very little to do with Einstein, and is probably too vague to be much use in any other field, either.

• #### Albert Einstein's performance review, 1905 (Score:5, Funny)

<bane&gst,com> on Thursday August 18, 2005 @04:13PM (#13350484) Journal
By Peter Norvig [norvig.com].

Don't miss the rest of his site [norvig.com] while you're there.
• #### Theory Of Relatively... (Score:2)

I took physics in college and all I got out of it was this cool E=MC2 shirt. :P
• #### Timing (Score:3, Insightful)

on Thursday August 18, 2005 @04:14PM (#13350495)
Sadly, this comes just days after the anniversaries of the Hiroshima and Nagasaki bombings.
• #### If Einstein Was So Smart... (Score:5, Funny)

by Anonymous Coward on Thursday August 18, 2005 @04:16PM (#13350513)
"If Einstein was so smart how come people only call you 'Einstein' when you do something really stupid?" - Brian Regan
• #### One Hundred Years of E=MC2 (Score:4, Funny)

on Thursday August 18, 2005 @04:17PM (#13350516) Homepage
So what was E equal to in 1904?
• #### From the i-still-don't-get-it dept. (Score:2)

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?)
• #### Re:From the i-still-don't-get-it dept. (Score:2)

It's because you're doing E=MC2, not E=MC^2.

That's dimensionally inconsistent.

• #### Ok guys... educumacate me (Score:2)

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 und
• #### Re:Ok guys... educumacate me (Score:3, Interesting)

Well, one example of where Netwon fails is explaining the rotation of the planet Mercury around the Sun. Since the gravity is so strong that close, Netwon fails, and we must use General Relativity. I believe the planet's orbit (someone correct me) actually spirals.
• #### Re:Ok guys... educumacate me (Score:2)

But e=mc^2 is special relativity, and you can derive it with high school math (they still teach math in high school, right?). Historically, it broke down the wall of separation between matter and energy, and was a major conceptual hurdle that we had to get over to proceed into modern physics.

• #### Re:Ok guys... educumacate me (Score:2, Insightful)

Ummm - a good visual example? Ever seen photographs of the ruins of Hiroshima? I don't think it gets much more visual then that! A few grams of matter (Ok, not sure exactly how much) converted to enough energy to level a city.
• #### Re:Ok guys... educumacate me (Score:2)

Well, there's your problem....you're watching PBS...you're probably falling asleep halfway thru....
• #### Re:Ok guys... educumacate me (Score:2, Informative)

Relativity : The Special and the General Theory
By Albert Einstein

This is written for the technically inclined layman. I read it and since then I've been life of the party. It really did make things much more clear - like what does flexible of spacetime have to do with the speed of light? It's all in there!
• #### Re:Ok guys... educumacate me (Score:3, Interesting)

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.

First thing to realise is that there are two theories of relativity - special and general. Special came first, is much easier to get your head around, and concerns motion, energy and that equation. The second, general theory came after, concerns gravity and is a complete pig to work with (Riemann curvature tensors [wikipedia.org] anyone?)

As to why do

• #### Re:Ok guys... educumacate me (Score:3, Insightful)

E=mc^2 is the most famous part of the theory of special relativity, but I can tell you what's the most amazing part, IMO.

Einstein noticed that there's a discrepancy between Newton's laws and Maxwell's laws of electricity and magnetism (E&M). To patch this, most physicists assumed special treatments for E&M like ether. Einstein went backwards and decided Newton must be wrong.

The most amazing conclusion he reached was that the speed of light is a constant in any reference frame. ANY reference frame.

• #### Of course, a minor change points to warp physics (Score:2, Interesting)

If you have it that the values are irrellevant and only the geometery matters, then for E to be conserved and still change c...

E=(m/(n^2))*((n^2)*(c^2))

where n is the factor by which the speed of light changes.

...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 sp
• #### E = mc^2 is Not Einstein's Discovery (Score:3, Informative)

on Thursday August 18, 2005 @04:39PM (#13350687) Homepage Journal
E = mc^2 is Not Einstein's Discovery

Robert A. Herrmann

1. Introduction

Michael. [michael-forman.com]
• #### 2 years too late (Score:2, Informative)

Einstein's E=mc2 'was Italian's idea' [guardian.co.uk]

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 Pre

• #### serious question (Score:4, Insightful)

on Thursday August 18, 2005 @04:40PM (#13350698)
I, of course, learned this famous equation back in grade school. And I understand the relationship between matter and energy (at least as well as most physics students do and better than most lay people, if anyone really understands it).

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?

• #### Re:serious question (Score:3, Informative)

Energy is a derived unit.
it is in m^2kgs^-2
Speed is also a derived unit.
it is in ms^-1
So when you pick a definition for time and distance, everything matches up.
• #### Re:serious question (Score:5, Informative)

on Thursday August 18, 2005 @05:07PM (#13350944)
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.

I think you are making the mistake that, for example, a 4-slice pizza is smaller than an 8-slice pizza, because, as everyone knows, 4 is less than 8. However, the pizzas are exactly the same size, it is just that the slices are larger in a 4-slice pizza.

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?

Yes, there is a very challenging derivation of this simple relationship. It is just math, and it is not magic. I won't do the derivation, but I will show that the units do, indeed, make sense:

Energy is a force acting through a distance: F x d
Force is a mass undergoing an acceleration: F = m x a
Acceleration is a change in velocity over a change in time: A = deltaV/deltaT, whose units are length/time x 1/time. Let's use metric. That would be m/s x 1/s.
Substituting the units back into the general energy equation, we get:
E = F x d = m x A x d = kg x (m/s x 1/s) x m. If we pair the 1/s with the meter from "Force acting over a distance" The units are:
E = kg x (m/s) x (m/s), which are the same units as Einstein's famous relation. So, yes, the units do make sense, it is not serendipitous that this works out, and the reason it is so famous is because it is so simple.

• #### Re:serious question (Score:5, Informative)

on Thursday August 18, 2005 @05:09PM (#13350953)

E = mc^2 holds true no matter what units c is expressed in - as long as the units for energy, mass, and c are consistent.

If you say c is expressed in meters/second, and m in kilograms, then energy must have the units of [kg*m^2/s^2] which we also call Newton-meters or Joules.

Just to confuse you further: sometimes we choose our units such that c=1! In this case, E = mc^2 becomes just E = m. Energy is mass.

Numbers in physics are just convenient ways to express a measurement; they are not of numerological significance (well, maybe the fine structure constant...).

Check out http://en.wikipedia.org/wiki/Physical_unit [wikipedia.org] if you have more questions on the units.
• #### Re:serious question (Score:3, Informative)

Apparently the teacher was advanced enough to teach you E=mc^2, but skipped over dimensional analysis.

If E is in Joules and m is in kg, c would have to be in m/s for the equation to work. Otherwise you'd need a conversion factor. That's all units are, attached labels that assume you're being consistent throughout the equation.
• #### Einstein was so wrong (Score:5, Funny)

on Thursday August 18, 2005 @04:40PM (#13350699)
As my mass has gone up, my energy has gone down. What more proof do you need?
• #### Quantum debugging (Score:3, Funny)

on Thursday August 18, 2005 @04:41PM (#13350717)
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.
• #### Obligatory lame physics joke: (Score:4, Funny)

on Thursday August 18, 2005 @04:43PM (#13350726)
100th anniversary? Yeah, but it's all relative
• #### Re:Obligatory lame physics joke: (Score:3, Funny)

Exactly. It's only 100 years in this frame of reference.
• #### Plagiarism is at least better than bullshit (Score:4, Informative)

on Thursday August 18, 2005 @05:09PM (#13350958) Journal
Hate to point this out, but that article is flawed, flawed, flawed.

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:

The physics community is also supported by a three-legged stool. The first leg is Einstein's physics. The second leg is cold fusion. The third leg is autodynamics. The overriding problem with a three-legged stool is that if only one leg is sawed off, the stool collapses. There are at least three very serious disciplines where it is predictable that physics may collapse.

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....

• #### Heaviside's Equation (Score:3, Interesting)

on Thursday August 18, 2005 @05:26PM (#13351079)
http://en.wikipedia.org/wiki/Oliver_Heaviside [wikipedia.org]

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.

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