"what is the velocity of the energy....so I have my amplifier, I fire a laser at it...some light comes out? Is it from my laser or my amplifier? Energy is fungible. Energy is energy."...
"No the energy that was already stored in the amplified as the inverted two-level atoms leaks out..."
If you assume there is no superluminal information as energy ...but how do you prove that is correct - how do you prove where the energy came from...
There are better ways of talking about the energy velocity ....
the propagation of the wave - a ripple and a wave packet envelope have two different velocities - the ripple is the phase velocity but don't worry about it.... the group velocity tells you where the energy is on average...
when the phase velocity is superluminal physicists said "don't worry about it."....
But when the group velocity was superluminal - physicists said "we must be missing something" and so... the information velocity is still slower than light - so causality is not violated....So then the energy velocity is also typically slower than light...
It turns out by their definition - in the case of a tunnel barrier or an absorbing medium where very little is transmitted, the group velocity maybe faster than C, the information velocity is never faster than C and the energy velocity is much slower than C since most it is absorbed or reflected back...
Can we make the energy velocity high? In the transparent case of an "on resonance" - the energy velocity turns out to be superluminal - faster than light!!
So now we need a better definition for the actual propagating energy to maintain causality....
"We know it can't be faster than light" but there are different ways of defining it...
four velocities - a technique of "constant fraction discrimination" as 1/2 of the maximum amplitude...that's the definition of information velocity. Then there's the "front velocity" - the speed of light as the ultimate information velocity of d/c
It's the difference between physics and math - physics is based on precise experiments.... and the story behind it is not rigorous....
If in mine reference frame if it is superluminal than in another reference frame it is backwards in time - violating causality.
https://www.youtube.com/watch?v=cOZ3Kto6NIc
The dwell time or excitation time - the amount of time the atoms spend in the excited state - was also in negative time as "on resonance."
there are "several times" not just "a time."
Operators correspond to observables... the limit corresponds to position classically...
Measuring time has different definitions...a "time scale" can be negative but not "time itself" ...
Time measurement is not an operator... the things we measure are a function of time... so we can't measure time itself... so measuring time is always indirect... time itself is not an "observable property."
so we have to define what is the "constant" as the "unit" - a "click of the cesium" is a second...
there's an "intrinsic uncertainty" - not just a measurement disturbance... in quantum physics...
It is time-frequency uncertainty.... that is less than Heisenberg's uncertainty principle...
the more you "open the aperture" the more you disturb the momentum (mass direction and speed) but you get precise position and vice versa and the limit is inherent to the measurement process (not what you are measuring with)... Heisenberg Uncertainty:
the smaller a particle is, the lighter it is (with less weight) and therefore the WORSE the position resolution - that does not exist classically.
Yakir Aharonov emphasizes time symmetry. So in weak measurements can go backwards in time and the future informs the past. Steinberg says "he finds this difficult to believe."
"the uncertainty principle can't help you with negative time"
the "wave theory" - de Broglie-Bohm quantum physics - as a nonlocal "hidden variable" does explain negative time....
Bohmian mechanics ADDS something because it takes about the "hidden trajectories" along the way...
and the weak measurements corroborate that the trajectories are real - and not just probabilities.
1/2 spin is a mathematical law but we don't understand the physics underlying the nonlocality of it....
except it is noncommutativity!!
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