# Does E really = MC squared?

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*bump*

ha ha ha ha

man, this thread is so off the wall

There's a guy who has no clue, and a guy who has no clue as to how to grant the other guy a clue

You oughtta explain what energy and mass are, since most people think in terms of "Energy", "Power", "Mass" and "Force" being the same thing, roughly

marcus
Gold Member
Dearly Missed

Originally posted by ando
Ok Warren. Thanks for the post, but I'm not sure this really settles the bet. Would object X, consume more, less, or the same ammount of energy when travelling from point A (let's assume these objects are moving through a vacuum - drag was not intended to be part of the equation), to point B than object Z if object Z travelled twice as fast?
Sometimes you get clarity by changing a word in the question.
You are focused very hard on the idea of CONSUME energy, use up energy.
Suppose you think about how much energy is INVESTED in something, like matter or motion or whatever----tied up in the existence of it for as long as it exists.

Now you said "drag was not intended" so I am going to take you seriously and imagine no friction or air-drag or losses of any kind.
and have the motion on level ground too.

Pretend your object X and object Z have the same kilograms or tons of mass---two cars of the same make, weighing the same.

If Z goes twice as fast then it has 4 times as much energy tied up in its motion, as X has invested in its motion.

If Z goes three times as fast than it has 9 times as much energy tied up in its motion as X has in its.

[Integral already told you this but maybe you didnt think about it]

Something has to happen to this energy in order for Z to stop!!!
It has to go into heating the brake pads or the disk-brakes.

Or Z has to crash into a wall and expend the energy in bending its front end.

So if it is going 3 times as fast the crash will be 9 times as bad.
Or there will be 9 times as much heat dissipated in the brakes----when it comes time to stop.

The work energy it took to get the car rolling becomes the heat energy that has to be gotten rid of when its time for it to stop.
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The famous cee-squared equation talks about the energy invested in the sheer existence of a thing.

If an electron is sitting there then at some point in the history of the universe some type of energy was invested in causing it to come into existence. That energy is tied up in that things being.
And the really amazing thing is that if that electron should ever go out of existence nature would get the SAME AMOUNT back again----in some form: heat, light, gammarays. Even if it lasted for a billion years and then went poof. Nothing is consumed. Nothing is lost. It is only temporarily tied up in what exists----like the motion of car X and car Z----and the energy will be recovered when that motion or that existence ceases.

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This too shall pass. hmmm. and yield back the energy of which it was made
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does it strike you as mathematically nice that in both
cases----the case of motion and the case of material existence---
a SQUARE of a velocity is involved. Physicists are complete children when it comes to algebra----show them a square or a square root and they immediately stop squabbling and come to attention. Normal people, I regret to say, are not so in love with algebra. But perhaps it was the square of some velocity that intrigued your friend you had the bet with.

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E=mc2 where m is relativistic mass represents the Total Internal Energy of any mass m, so pmb is right, it wouldn't change with combustion unless the energy source were in the air. Myyy mistake.

Can one still get away with talking about relativistic mass?
I thought the current generation of physics custodians give one the back of the handle for saying that.
I hope the answer is YES.

well that's what the "m" is in the equation, OK. m=mo&gamma;

pmb
First off regarding the comment
E=mc2 where m is relativistic mass represents the Total Internal Energy of any mass m,..
This isn't quite right. The internal energy is the energy inherent to the particle itself - i.e. E_o = m_o*c^2 = rest energy.

Note: The quantity gamma*m_o*c^2 is not the total energy of a moving particle of proper mass m_o. It's the kinetic energy plus the rest energy. The total energy is the kinetic + rest + potential.

See --- www.geocities.com/physics_world/relativistic_energy.htm

Regarding the comment
Can one still get away with talking about relativistic mass?
I thought the current generation of physics custodians give one the back of the handle for saying that.
I hope the answer is YES.
Sure. You can always talk about relativistic mass. Many physicists still do. Even recent GR books do. There are no "custodians" in physics. There is an entire spectrum of ideas and opinions. It just so happens that the con-relativistic mass people are more apt to try to force their ideas on others. The pro-relativistic mass people know that it's a matter of definition and use it was they see fit.

Don't let them fool you though. Relativistic mass is the closest thing you'll get to the having the all the properties one normaly associates with mass.

Pete

Thanks, Pete. I feel better already.

pmb
Originally posted by quartodeciman
Thanks, Pete. I feel better already.
Glad to help. If you'd like I can scan a few articles in and e-mail them to you. One is a response by Wolfgang Rindler (a well known relativist) who wrote and article for Physics today defending relativistic mass. There is another one from the American Journal of Physics called "In defense of relativistic mass" that you might enjoy.

Just e-mail me at peter.brown46@verizon.net

I can also send you the paper I'm writing on this very concept. It's in a good enough stage that I don't mind letting someone read it at this point.

Pete