There’s no problem with solving the Klein-Gordon Equation. It’s just that some of the solutions have a form for which [math]H\Psi=i\frac{d\Psi}{dt}=E\Psi[/math] with arbitrarily large negative values of [math]E[/math]. If we were to try to interpret the solution as a quantum wavefunction this would correspond to having no lower bound on the energy – which is physically unstable.
Author: alan
Entanglement
Entanglement is just a word we can use to describe a situation where knowledge of some property of one object gives us information about some (possibly different) property of another.
The term is rarely used in the classical case, because we take it for granted. If we separate a pair of gloves for example and pack them up in identical boxes and then choose by a coin toss to send each in one of two opposite directions, then we are not surprised by the fact that if someone who knows how they started out but does not know the result of the coin toss opens one box and sees a left glove, he or she knows immediately that whoever opens the other box will see a right glove.
There is often similar classical chance-based uncertainty in our knowledge of quantum systems; but for such systems, even in the most precisely prepared “pure” states the knowledge of some properties makes it impossible for us to know others. This residual uncertainty is expressed by representing the state of the system by a “state vector” in a Hilbert space and the “mystery” of quantum entanglement is that the correlations between systems (like the gloves) that were once together but are now far apart can sometimes be greater than would be possible for any way of randomly assigning the properties at the outset.
The reason this extra correlation is sometimes considered “spooky action at a distance” is because the change of state vector (often called “collapse”) that occurs when we open one box seems to trigger a simultaneous collapse at the other box – and in a way that can change what the remote observer will see when looking at different properties from the one that obviously has to be opposite. At first sight it may seem that this effect might be used to send a signal where what the second observer sees might depend on what the first one chose to measure, but that turns out not to be the case.
Whether or not this bothers you may depend on whether you consider the state vector to be a property of the system itself or rather of the way it appears to a particular class of observers.
Is special relativistic time dilation a real effect or just an illusion? Given two inertial frames each observer finds that the clock of the other runs slower than that observer’s own clock. So who is right?
This is a pretty good answer except that I wouldn’t say either of them is right if they think that their perception of relative slowness represents something that is objectively true for all observers.
Time dilation is a real effect on the perceptions of observers (with regard to the rates at which one another’s clocks are ticking). Neither of them is “right” if they think there is any real sense in which the other’s clock is objectively slower. But neither of them is wrong about how it appears to them, so it’s not really an illusion any more than the fact that if they are looking at one another then their ideas of the “forward” direction are opposite to one another. What turns out to be more of an illusion is the sense we all have that there is some absolute standard of time which determines which of two spatially separated events occurs before the other.
(3) Alan Cooper’s answer to How can a moving/faster observer see a ‘stationary’ clock running slower, when it doesn’t, e/specially when his really does? All the YouTube videos about the Twin Paradox say so. In what sort of universe is that possible? – Quora
The relativity principle does NOT say that all frames are equivalent, just the inertial (unaccelerated) ones. In the twin “paradox” situation, the traveler and stay-at-home both figure that the other is ageing more slowly while their relative velocity is constant but when the traveler turns around he or she figures that the stay-at-home suddenly ages much more rapidly. The two may have different explanations in mind for the effect, but when they get back together they agree on the result.
(3) Alan Cooper’s answer to How does the twin (clock) paradox (in SR) really work? Please see the comment for the specific case. – Quora
According to the comment, what this question is really asking us to address is something completely different from “How does the twin (clock) paradox (in SR) really work?”
What the comment asks us to explain is as follows: “A clock flies around the equator eastwards, it ages slightly less. A clock flies around the equator westwards, it ages slightly more. Than a clock which stayed, at home.”
The explanation for this (in the context of either Special OR General Relativity) is that the alleged effect exists only for motion relative to the Earth’s surface (which is already rotating). So if I stand still on the Earth’s surface I will age more slowly than a twin who stands still relative to the Earth’s centre (which entails flying Westwards at a rate of about 1000mph) and more quickly than a twin who flies Eastwards and so is actually moving more quickly relative to the Earth’s centre.
Note: As with the usual out-and-back twin “paradox” what makes the travelers different from the stay-at-homes is that they are not in fixed inertial frames but are accelerated. And in the case of this scenario the twin flying West at 1000mph is basically staying stationary wrt the Earth’s axis which (if we neglect the curvature of the Earth’s orbit) is pretty close to being in an inertial frame. But the one standing still is actually rotating with the Earth and so is accelerating (centripetally) towards the axis. And the one flying East is actually accelerating even more. According to SR, an observer who is accelerated figures that stationary clocks towards which she is accelerating are speeded up by an amount that more than counterbalances the fact that if the speed was fixed she would figure that they were slowed down. And if you do all the calculations it turns out that when they get back together they all agree on their relative ages (with Eastflier younger than Standstill and Standstill younger than poor old Westflier(who is actually the only one who is really standing still)).
(3) Alan Cooper’s answer to What is the Calabi-Yau manifold? Are we ‘inside’ it right now or is it just a mathematical concept? – Quora
Calabi-Yau manifolds (there’s not just one) are a type of mathematical concept, but they’re not “just” that as they do have applications in certain attempts to describe physics. The role they usually play in physics is to help us formalize the relationships that we postulate between the various internal variables that describe what particles are likely to show up at a point in space time. As such the theory often combines the six dimensions of a Calabi-Yau manifold with the four dimensions of the space-time that we are ‘inside’ to get a total of ten dimensions. But the extra dimensions are often either considered to be very small in some sense, or to have the part that contributes to the physics we see be just a slice through the whole thing. In the first case it makes more sense to say (as in James Bridgeman’s answer) that there’s a C-Y manifold at every point inside us (rather than vice versa), and in the second case that the entire space-time we live in is just a (4d) slice through the extended C-Y manifold (with other slices or “branes” perhaps corresponding to “alternate universes” of some kind). But neither of these cases is in any sense known to be true. So far it’s all just speculative construction of mathematical models that might eventually be shown to describe our actual physics.
(3) Alan Cooper’s answer to Why is the Raman effect’s classical interpretation not adequate? – Quora
The classical theory of the Raman effect is not adequate for determining the actual spectrum because it allows the molecule to have arbitrary amounts of vibrational (or rotational) energy and in fact the possible energy levels are quantized (just like everything else in physics).
Source: (3) Alan Cooper’s answer to Why is the Raman effect’s classical interpretation not adequate? – Quora
(3) Alan Cooper’s answer to Does any physicist truly understand wave function collapse? – Quora
There are certainly many physicists who use the term “wave function collapse” to refer to something that they understand well enough for their own purposes. Whether or not that means they “truly understand” it depends on what you mean by that (in my opinion rather silly) expression.
Source: (3) Alan Cooper’s answer to Does any physicist truly understand wave function collapse? – Quora
(3) Alan Cooper’s answer to Will the unresolved philosophical issues behind quantum theory ever be fully resolved? – Quora
There are no “unresolved philosophical issues behind quantum theory” that have been identified in this question. So it’s kind of like asking when will all the dinosaurs on the moon be dead.
(3) Alan Cooper’s answer to How come quantum mechanics hasn’t been fully replaced by quantum field theory in the physics community? – Quora
On the one hand, Quantum Field Theory is just a special case of quantum mechanics. It’s just the quantum mechanics of fields (corresponding to situations whose classical analogues involve an infinite number of degrees of freedom). So replacing quantum mechanics with QFT is like replacing dogs with dobermans. Yes, we could replace all other dogs with dobermans, but they’d still be dogs (and for some purposes less useful than the ones they replaced). On the other hand, in a situation with only a limited number of degrees of freedom (such as where there are only low energy interactions between a fixed number of particles – in the analysis of a chemical bond formation for example), the use of quantum field theory would be like keeping track of the motions of all the engine components in a car when all we are interested in is the effect of a collision on a crash test dummy (or replacing a dachshund with a doberman for flushing rabbits out of their burrows).