Tim Goodman
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 Apr 12 answered What force prevents particles from penetrating other particles? Mar 31 comment A list of inconveniences between quantum mechanics and (general) relativity? @juanrga I think this may come down to different interpretations of the OP's question. A lot of times, science articles in the media will talk about "the conflict between quantum mechanics and relativity", and what they really mean is the conflict between Quantum Field Theory and General Relativity. I think that's how I took the question, and I imagine is how Matt Reece took it. So yes, QFT is quite different from non-relativistic QM, but the point is we have a quantum theory (QFT) which is also relativistic in the SR sense (global Lorentz covariance). Mar 19 answered Interactions and scattering length in Feshbach resonances Nov 11 comment What really allows airplanes to fly? The bound vortex moves from front to back above the wing, and back to front below the wing, so the net velocity of the air is greater above the wing than below. See en.wikipedia.org/wiki/Kutta_condition But this doesn't require a particular wing shape (other than the sharp trailing edge). Mostly the reason airplane wings are shaped the way that they are is to minimize drag while still achieving lift - not because the shape is necessary to generate lift. Nov 11 comment What really allows airplanes to fly? @MarkFoskey I think it's misleading to think of the Bernoulli principle as causing the reduction of pressure above the wing. Bernoulli's principle tells us that decreasing pressure occurs simultaneously with increasing velocity - and indeed if we know the velocity we can calculate the pressure - but this is kind of obscuring why the velocity is higher above the wing. For wings with a sharp trailing edge moving with a positive angle of attack, a vortex will initially form at the back of the wing, and produce a corresponding bound vortex of air circulating around the wing. Nov 5 comment Is a non-degenerate wavefunction real or complex? It might be better to say that the wavefunction "can be chosen to be real". For instance in John Rennie's example you could also have $\psi_r = \psi_i$, in which case the state is not degenerate, but instead we have $\psi = (1+i)\psi_r$. You can choose to drop the overall phase factor. Nov 3 comment I have trouble understanding work For example, if you're behind a cart pushing it then you are giving energy to the cart, but if you stand in front of a cart as it moves towards you and push against it then you are taking energy away from the cart. Nov 3 comment I have trouble understanding work Then you want to consider the force that you're exerting. Of course, when you exert a force on something, it exerts a force back on you (Newton's 3rd law), but the direction of the force matters here, because we're taking the dot product of the force with the displacement. So for instance if the force is in the same direction as the movement then you do positive work, whereas if the force is in the opposite direction of the movement then you do negative work. Nov 3 comment I have trouble understanding work That depends whether you're talking about the work done by you or the work done on you. Nov 3 answered I have trouble understanding work Nov 2 comment What makes energy content of a body harder to accelerate it? That step is only necessary if you want to recover the non-relativistic formula for kinetic energy. In relativity, kinetic energy is $\gamma m c^2 - m c^2$ (where $\gamma = \frac{1}{\sqrt{1-v^2/c^2}}$). If Einstein's audience knew that formula, he could have just said "Look, $E$ plays the role of $mc^2$ and skipped the approximation - but he'd only just published his first paper on special relativity 3 months earlier. (Also available online: fourmilab.ch/etexts/einstein/specrel/www ) Nov 2 comment What makes energy content of a body harder to accelerate it? @Weezy Taylor series expansion at $v/c = 0$, keeping the dominant term. Nov 2 answered What makes energy content of a body harder to accelerate it? Nov 2 awarded Yearling Nov 2 answered Will my mass increase in my perspective while approaching near the speed of light? Nov 2 answered Forward-scattering off a potential well Nov 2 answered What does the Hamiltonian do in the Heisenberg picture? Oct 31 awarded Revival Oct 30 comment What really allows airplanes to fly? That said, the wing shape is not so important; it makes some difference, but even perfectly flat wings can produce lift with the right angle of attack. Oct 30 comment What really allows airplanes to fly? @MarkFoskey Yes the air does move faster above the wings than below - in fact, the difference in speed is in general greater than the equal time assumption would imply. And yes, this does correspond to a change in pressure, in accordance with the Bernoulli effect. Given the actual airflow velocities, the Bernoulli effect is consistent with the aerodynamics of flight; the common error is in determining the airflow velocity from the fallacious equal time assumption.