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ftr
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I mean is the formula taken as a postulate or can we derive it from QFT at least?
SteamKing said:The mass-energy equivalence equation is definitely not a postulate. It is derived using special relativity.
See: http://en.wikipedia.org/wiki/Mass–energy_equivalence
SteamKing said:Einstein derived it from SR first because he discovered/developed SR before QFT was developed.
There is a certain historical order in which discoveries have been made, which is separate from what we may consider to be the logical order in which things should be developed.
For instance, Archimedes played around with the concepts of the infinitesimal calculus centuries before number systems and algebra were developed, when only arithmetic was crudely understood.
This is not to say that energy-mass equivalence may not be developed using QFT (I can't say because I am not a quantum mechanic), but that's not how it happened first.
dauto said:QFT is usually started by postulating some field Lagrangian which is assured to be relativistic by design. So we cannot really be surprised when we find out that the particles obtained by quantizing the fields also turn out to obey fully relativistic relations, can we. In other words, we feed our knowledge that the world is relativistic into the theory from the get go.
Special relativity is nothing that is tied to classical physics. And quantum field theory doesn't need to be relativistic either. It's wrong to think about special relativity as something classical that has to be carried over to QFT. Instead, it is a basic insight about space and time that applies equally to classical physics and to quantum physics.ftr said:Exactly. Usually newer theories include the older ones as a limit. But in this case it is curious that supposedly QFT our most advanced tool that probes nature depend on a semi-classical theory for its survival. You would expect the opposite wouldn't you?
rubi said:Special relativity is nothing that is tied to classical physics. And quantum field theory doesn't need to be relativistic either. It's wrong to think about special relativity as something classical that has to be carried over to QFT. Instead, it is a basic insight about space and time that applies equally to classical physics and to quantum physics.
ftr said:... we cannot apply GR to QFT even so GR is considered to be the generalization of SR.
is not correct. Yes, many theories (all candidates I have listed above) try to quantize GR. But the conclusion that this quantization results in SR (in some limit) is not correct. SR is already present in classical GR, but only as a local (instead of a global) symmetry. Spacetime in GR need not have any global symmetry at all, but is always has local Lorentz invariance by construction. This is nothing else but the famous equivalence principle. A free-falling observer cannot detect spacetime curvature locally; to her spacetime always looks flat. So for local experiments a free-falling observer can always use SR calculations.ftr said:... many theories of QG try to consider GR as a quantum theory which implies that the origin of SR is indeed in QM system somehow.
E=mc^2 is a fundamental equation in QM/QFT that relates energy (E) and mass (m) to the speed of light (c). It is significant because it explains the relationship between matter and energy and is the basis for understanding the behavior of particles at the atomic and subatomic level.
E=mc^2 is a key component of the theory of quantum mechanics and quantum field theory. It helps to explain the behavior of particles and their interactions by incorporating the concept of mass-energy equivalence.
Yes, E=mc^2 is still valid in QM/QFT. It has been extensively tested and confirmed through numerous experiments and observations. However, it is important to note that in certain situations, such as at the quantum level, the equation may need to be modified to account for other factors.
Yes, E=mc^2 can be derived from the principles of QM/QFT. It is a natural consequence of the theory and has been shown to be consistent with other fundamental equations, such as the Schrödinger equation and the relativistic energy-momentum equation.
While E=mc^2 is a powerful equation that has been successfully applied in many areas of physics, it does have limitations. It is most accurate when applied to particles with very small masses and high speeds, and may not fully account for certain phenomena, such as the effects of gravity or quantum entanglement.