What in the world does E =mc2 mean?

What in the world does E =mc2 mean? (Einstein's equation.)

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The amount of energy that could be obtained by completely annihilating a mass m Kg is equal to m Kg multiplied by $$9X10^{16} meters^2/second^2$$. The units come out right for an energy.

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SA, you mean ~9 times 10 to the power of 16, right? :uhh:

Daniel.

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dextercioby said:
SA, you mean ~9 times 10 to the power of 16, right? :uhh:

Daniel.

Eek! I put in the value for the wrong length! It's changed now.

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You had put the number for "cgs", instead of "mKs" but left out the all important "centi".

Daniel.

ok, thanks for the anwser.

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Matthias765 said:
What in the world does E =mc2 mean? (Einstein's equation.)

mass and energy are two sides of the same coin
you can convert one to the other
the conversion factor is c-squared
a little matter is made of a lot of energy

Ratzinger
But what's energy here? The energy of gamma rays (high energy photons). Correct?

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Ratzinger said:
But what's energy here? The energy of gamma rays (high energy photons). Correct?

hehehe

Gamma rays.. x-rays.. visible light... all sortsa fun stuff.

eNathan
Ratzinger said:
But what's energy here? The energy of gamma rays (high energy photons). Correct?

My understanding is that there's only one type of energy (AFAK). This energy can come in many different forms, including gamma rays. m=mc^2 obviously uses the SI unit of joules.

whats whe speed of light have to do with the deveration of energy from mass nanyway :yuck:

Ratzinger
energy comes in form of photons when E=mc^2 is involved

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Ratzinger said:
energy comes in form of photons when E=mc^2 is involved

No. This doesn't have to be.

For example... if you heat up a pot of water... its mass will increase, and the increase in mass = $$E/c^2$$ where E is the amount of heat added.

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learningphysics said:
For example... if you heat up a pot of water... its mass will increase, and the increased mass = $$E/c^2$$ where E is the amount of heat added.

... no. The mass will not increase at all.

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Pengwuino said:
... no. The mass will not increase at all.

Yes it does. It may not be measurable. But it's a consequence of special relativity that the mass increases.

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learningphysics said:
Yes it does. It may not be measurable. But it's a consequence of special relativity that the mass increases.

Well if it does, news to me. Someone else should be along soon enough to tell me off.

The rest mass of a system of particles is generally bigger than the sum of the rest masses. The reason is that you can´t find a frame where all particles are at rest - the residual movement wrt the center of mass increases the mass of the system.
The most common form of residual movement is called temperature.

pmb_phy
Matthias765 said:
What in the world does E =mc2 mean? (Einstein's equation.)
By definition the mass, m, of an object is associated with the momentum, p, of the same object. The sum of the kinetic energy, K, and the rest energy, E0, equals the inertial energy of the object. Therefore E = K + E0. If the object is free of all external influences, or the object is a particle, then it can be shown that E = mc2.

Phobos said:
mass and energy are two sides of the same coin. etc
[/quote]Not quite right. That expression is limited in form. In general it is incorrect. When you have an object of finite extent and there are forces being exerted on it then that equation is incorrect.

If you have Shutz's new text Gravity from the Ground up then you can read about an example he gives about how the inertia of a body increases with an increase in the body's pressure.

Pete

pmb_phy
Pengwuino said:
Well if it does, news to me. Someone else should be along soon enough to tell me off.
This depends on what you mean by the term "mass." learningphysics is thinking of p = mv as the expression defining m. Others define mass as follows; p = M(v)v, m = M(0).

Pete

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Yah but if you heat up bunch of copper molecules or whatever, there's still the same # of molecules if its at 100K or 200K.

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pmb_phy said:
This depends on what you mean by the term "mass." learningphysics is thinking of p = mv as the expression defining m. Others define mass as follows; p = M(v)v, m = M(0).

Pete

Pete, but in this example (heating the water up... assuming the center of mass of the water is motionless in the frame of interest)... the inertial mass = invariant mass. So regardless of either definition, mass increases right? You clarified this for me in a thread a few months back.

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pmb_phy
learningphysics said:
Pete, but in this example (heating the water up... assuming the center of mass of the water is motionless)... the inertial mass = invariant mass. So regardless of either definition, mass increases right?
Yes.

Pete

εllipse
Pengwuino said:
Yah but if you heat up bunch of copper molecules or whatever, there's still the same # of molecules if its at 100K or 200K.

But the molecules move faster if they're heated up, so their relativistic mass increases.

pmb_phy
εllipse said:
But the molecules move faster if they're heated up, so their relativistic mass increases.
Yes. That's quite true. Its also part of the mechanism of why the mass of the object increases with the addition of heat. Take the simple case of a box of particles whose velocity has only an xy-component and no z component. Let the mass of the containment walls be insignificant when compared to the mass of the gas. Then as the gas is heated the particles move faster. The faster they move the greater the weight. Let the total momentum of the gas be zero. With all this in mind its rather easy to see why the mass of the gas increases when its heated up.

See details at http://www.geocities.com/physics_world/gr/weight_move.htm

Pete

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pmb_phy said:

Interesting, but a bit questionable. For instance, in your second derivation, if you take the result dead seriously, the weight would depend on the height 'z'.

In GR, mass is founded on asymptotic flatness, which is nowhere mentioned in your webpage. A standard method would be to use the energy pseudotensors in an asymptotically Minkowskian coordinate system.

Igor_S
pmb_phy said:
Then as the gas is heated the particles move faster. The faster they move the greater the weight. Let the total momentum of the gas be zero. With all this in mind its rather easy to see why the mass of the gas increases when its heated up.

See details at http://www.geocities.com/physics_world/gr/weight_move.htm

How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.

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Igor_S said:
How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.

The invariant mass of each particle remains the same. The invariant mass of the system of particles changes. Pete's page here explains this well:

http://www.geocities.com/physics_world/sr/invariant_mass.htm

pmb_phy
Igor_S said:
How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.
It's only the proper mass that is invariant. Not the relativistic mass.

Pete

Aer
pmb_phy said:
Take the simple case of a box of particles whose velocity has only an xy-component and no z component. Let the mass of the containment walls be insignificant when compared to the mass of the gas. Then as the gas is heated the particles move faster. The faster they move the greater the weight.
Is this an experimental result or something derived based on certain postulates? If it is the latter, what are the postulates used to derive this result?

εllipse
Aer said:
Is this an experimental result or something derived based on certain postulates? If it is the latter, what are the postulates used to derive this result?

It was originally derived from the postulates of the special theory of relativity (that all inertial reference frames are equivalent for the description of the laws of nature and that the speed of light is the same in all inertial reference frames), by Einstein himself. The original publishing was Does the Inertia of a Body Depend Upon its Energy-Content which was a follow-up to On the Electrodynamics of Moving Bodies.

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.

It has, of course, been proven since by experiment.

Aer
εllipse said:
It was originally derived from the postulates of the special theory of relativity (that all inertial reference frames are equivalent for the description of the laws of nature and that the speed of light is the same in all inertial reference frames), by Einstein himself. The original publishing was Does the Inertia of a Body Depend Upon its Energy-Content which was a follow-up to On the Electrodynamics of Moving Bodies.

It has, of course, been proven since by experiment.
You are reiterating the concepts since abandoned by physicists. I am very aware that Einstein proposed relativistic mass long ago. However, regardless of an objects speed relative to some other abitrary reference frame (I could say the Earth is moving at .9c relative to a ship's reference frame) does that neccessarily mean that an object on our fast moving Earth has a larger mass and takes more energy to accelerate? No. Why? Because you measure accelerate with respect to the object which is accelerating. If an object is said to accelerate constantly, it is assumed that the object is accelerating constantly with respect to the instantaneous velocity's inertial reference frame at any given instance. It is not a physical concept to assume that an object is accelerating constantly in a single inertial reference frame because eventually the object will have to reach a speed greater than c. And it is this situation (measuring acceleration in a single inertial reference frame) in which relativistic mass has any relevance. And since the notion itself is not physical, it is not too much to say that relativistic mass is not physical either.

In summary, if you wish to use relativistic mass, you must add extra rules such that you don't lead to a non-physical situation. I believe Occam would have something to say about this.

εllipse
Aer said:
You are reiterating the concepts since abandoned by physicists. I am very aware that Einstein proposed relativistic mass long ago.
You asked for a reference; I provided one. No need to be so harsh.

Aer said:
And it is this situation (measuring acceleration in a single inertial reference frame) in which relativistic mass has any relevance.
You seem to be assuming that the only thing we care about is how the world looks to us as we accelerate. But what about how things look to us as we accelerate them, while we remain inertial? For instance, when we get particles moving close to the speed of light in particle accelerators, the concept of relativistic mass does have use to us then because we do have a single inertial reference frame with which to make the measurement. Why can't we put a charged particle in a strong enough magnetic field to accelerate it faster than the speed of light? A very simple explanation is that its relativistic mass increases as we accelerate it, so its inertia/resistance to acceleration increases as well.

Aer
εllipse said:
You asked for a reference; I provided one. No need to be so harsh.

You seem to be assuming that the only thing we care about is how the world looks to us as we accelerate. But what about how things look to us as we accelerate them, while we remain inertial? For instance, when we get particles moving close to the speed of light in particle accelerators, the concept of relativistic mass does have use to us then because we do have a single inertial reference frame with which to make the measurement. Why can't we put a charged particle in a strong enough magnetic field to accelerate it faster than the speed of light? A very simple explanation is that its relativistic mass increases as we accelerate it, so its inertia/resistance to acceleration increases as well.
I've never said you cannot do this to obtain a correct result. However, it is not necessary to use relativistic mass to get the same thing, that is all I am saying. Relativistic mass is mearly a perception in other frames - however, too many people equate this perception to be actual mass accumulation to the object in the objects rest frame. This point of view is very wrong. It is just as easy to not use relativistic mass, but I'm not going to prohibit you from doing so.

Aer
pmb_phy said:
Then as the gas is heated the particles move faster. The faster they move the greater the weight.
What is the weight of a particle (you may choose any particle you wish) moving .9999c through the atmosphere?