XPost: sci.physics
From: ram@zedat.fu-berlin.de
john larkin wrote or quoted:
>>E = mc^2
>Exactly. Mass/energy conversion is one way to create or destroy some
>mass in my cannonball.
"E = mc^2" does not mean, "Mass can be converted to energy and/or
vice versa". It means, "When the momentum of a system is zero,
its energy is its mass (up to a conversation factor of c^2).".
In general, the formula for a non-zero momentum p is (with c=1):
E^2 = m^2 + p^2,
and since E and p are conserved, m must also be conserved. So this
tells us, "Mass is conserved.", exactly the opposite of, "Mass can
be converted . . .".
>Any nonzero effect, no matter how small, would still be real.
Well, I mentioned "Boltzmann brains" here (in
sci.electronics.design) recently, but their energy would not
suddenly come from "nothing" or violations of conservation
but be redistributed from the surrounding equilibrium state.
|It is often said that the uncertainty principle means energy
|is not strictly conserved in quantum mechanics - that you're
|allowed to "borrow" energy delta E, as long as you "pay it
|back" in a time delta t approximately hbar / (2 delta E);
|the greater the violation, the briefer the period over which
|it can occur. Now, there are many legitimate readings of the
|energy-time uncertainty principle, but this is not one of
|them. Nowhere does quantum mechanics license violation of
|energy conservation, and certainly no such authorization
|entered into the derivation of Equation 3.76.
|But the uncertainty principle is extraordinarily robust: It
|can be misused without leading to seriously incorrect
|results, and as a consequence physicists are in the habit of
|applying it rather carelessly.
|
Section "3.5.3 The Energy-Time Uncertainty Principle" in
"Introduction to Quantum Mechanics" (2018) - David J. Griffiths
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