Was Einstein inconsistent between his theories of Special and General Relativity? In the theory of Special Relativity we learn that energy and mass are interchangeable E = mc^2. In the theory of General Relativity we learn that because of Einstein's equivalence principle (EEP) the mass of a particle is invariant. When a uranium atom undergoes fission, the energy released is only the energy of the system, bound up in the atom, that is being re-allocated; the masses of all the constituent particles making up the atom remain invariant. Are these two theories therefore mutually contradictory?
No. True. The proper mass (aka rest mass) is invariant. That is not a result of relativity. Its a fact of nature which relativity never changed. The energy released is not the only energy of the system. The energy released is the Q of the system and the Q of the system is only part of the energy of the system. See http://www.geocities.com/physics_world/sr/nuclear_energy.htm Not that I've seen. Pete
Your own personal sight is not an independent reference. As always you are spamming for Planck's outdated concept of mass. You are wrong.
So what if it's outdated? That doesn't mean it's wrong. Incidentally, it's not outdated. That concept of mass is still alive and well among those who work in nuclear power.
The mass of a body as measured by an observer depends on the velocity of the the body in the observer's frame of reference.
That is just one convention. We aren't obligated to adopt it, and indeed most physicists don't. The convention adopted by most physicists is that there is only one mass: the invariant mass. That quantity is the norm of the 4-momentum. But as I said before, the concept of mass that says m=γm_{0} isn't wrong, it's just out of style.
That is misleading. The majority of particle physicists don't use it. The majority of GRists and cosmologists do use it. But the way, what are you basing that assumption on? Pete
Misleading? Correct me if I'm wrong, but I think that the community of particle physicists is the majority of physicists who use relativity. Factor in those solid state physicists who use relativisitc quantum mechanics or QED, and it's no contest. Really? Every textbook I have teaches the concept of mass as the invariant norm of the 4-momentum, and they are written by relativists (Taylor and Wheeler, Ohanian and Ruffini, et al). What books do use it? And are there publications in the arxiv that use it? All my undergraduate and graduate coursework.
Hi Tom For my response to be logical it turned out to be too long for a post so I started a new thread. See the new thread Those who use relativistic mass and why Pete
It is outdated whether it is being used or not and it is wrong. It was a guess that just happened to put [tex]\gamma [/tex] in the place that it needed to be in a momentum equation to yield dynamics consistent with special relativity, but the mass term in that equation is NOT where it comes from. It comes from time dilation in the time differential in the velocity term. This missassociation of the factor with the mass is why it is wrong and the modern understanding of where the term comes from in terms of the four vector law is why it is outdated.
What we have here is a conflict of conventions of definition of terms. The question of whether or not the mass of a particle can vary or not ought to be a matter of observation not definition. If we define mass to be invariant then we are blinding ourselves to the fact that it might be otherwise. In the “classical interpretation” of the Einstein’s equivalence principle (EEP) mass is invariant. Therefore we have masses on the one hand and energies on the other, and although energy has a mass equivalent, they cannot transform one into the other. Yet at a fundamental level a particle seems to be a string, or whatever, of vibrating energy, and sufficiently energetic photons can transform into a particle and its anti-particle and vice versa. My original question was to question this convention, is it not inconsistent with the precept of SR? Incidentally SR says nothing about the invariance of mass, that has been read in later. In my theory of self creation I choose to define mass to be able to include potential energy and it leads to some very interesting observational consequences; one of which is a heterodox prediction for geodetic precession, which is about to be measured by the Gravity Probe B satellite.
If dw posted what I think he did then I agree 100%. There are two definitions in common use. Let v = 3-velocity. Then when m is defined such that mv is conserved then this is an implicit definition of m and is commonly refered to as inertial mass (aka relativistic mass). Let U = 4-velocity. Then when m_{0} is defined such that m_{0}U is conserved then this is an implicit definition of m_{0} and is commonly refered to as proper mass (aka rest mass). When people use the term mass, some of them are refering to m while others are refering to m_{0}. And that's the whole story on the concept of mass as it pertains to definition. Please provide a definition of classical interpretation. Thanks Pete
So what? In p=γmv, is γ multiplied by m? Answer: Yes. Does the law of associativity under multiplication still hold? Answer: Yes. Can I associate (γm) together and call it something else? Answer: Yes. Does the quantity have the dimensions of mass? Answer: Yes. Is there anything wrong with giving that mass a name? Answer: No.
Concerning the first question here you are not calling that just "something" else. You are calling it something that it does not mean. Your last question here has a wrong hidden statement. You state that the something you want to name is mass. That is what is wrong.
Classical interpretation of mass: "rest mass", i.e. the mass of an object measured in a co-moving frame of reference in which the object is at rest, is equal to the norm of the 4-momentum vector and is invariant. It is a direct consequence of the EEP (see for example Weinberg) and therefore GR.