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Matthias765
What in the world does E =mc2 mean? (Einstein's equation.)
dextercioby said:SA, you mean ~9 times 10 to the power of 16, right?
Daniel.
Matthias765 said:What in the world does E =mc2 mean? (Einstein's equation.)
Ratzinger said:But what's energy here? The energy of gamma rays (high energy photons). Correct?
Ratzinger said:But what's energy here? The energy of gamma rays (high energy photons). Correct?
Ratzinger said:energy comes in form of photons when E=mc^2 is involved
learningphysics said:For example... if you heat up a pot of water... its mass will increase, and the increased mass = [tex]E/c^2[/tex] where E is the amount of heat added.
Pengwuino said:... no. The mass will not increase at all.
learningphysics said:Yes it does. It may not be measurable. But it's a consequence of special relativity that the mass increases.
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.Matthias765 said:What in the world does E =mc2 mean? (Einstein's equation.)
[/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.Phobos said:mass and energy are two sides of the same coin. etc
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).Pengwuino said:Well if it does, news to me. Someone else should be along soon enough to tell me off.
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
Yes.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?
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.
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.εllipse said:But the molecules move faster if they're heated up, so their relativistic mass increases.
pmb_phy said:
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
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.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.
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?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.
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?
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.
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.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 asked for a reference; I provided one. No need to be so harsh.Aer said:You are reiterating the concepts since abandoned by physicists. I am very aware that Einstein proposed relativistic mass long ago.
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 said:And it is this situation (measuring acceleration in a single inertial reference frame) in which relativistic mass has any relevance.
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.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.
What is the weight of a particle (you may choose any particle you wish) moving .9999c through the atmosphere?pmb_phy said:Then as the gas is heated the particles move faster. The faster they move the greater the weight.
E = mc2 is a famous equation in physics that stands for energy equals mass times the speed of light squared. It was developed by Albert Einstein as part of his theory of special relativity.
The equation shows that energy and mass are interchangeable and are essentially different forms of the same thing. It also demonstrates that even a small amount of mass can produce a large amount of energy.
The speed of light, which is represented by the letter "c" in the equation, is a constant that is equal to approximately 299,792,458 meters per second. Squaring this value makes it a very large number, which is why even small amounts of mass can produce a large amount of energy when multiplied by it.
One example of how E = mc2 is used in real life is in nuclear reactions, such as in nuclear power plants or nuclear weapons. In these reactions, a small amount of mass is converted into a large amount of energy, as predicted by the equation.
E = mc2 is often considered one of the most famous equations in science, along with other well-known equations such as Newton's law of universal gravitation and the Pythagorean theorem. However, its fame may also be attributed to its connection to Albert Einstein and his groundbreaking theories.