KJW

One thing that is not generally recognised is when you see an image representing a black hole, the outer edge of the black disc is not the event horizon. In fact, it is the photon sphere at [math]r = \dfrac{3r_s}{2}[/math], where [math]r_s[/math] is the Schwarzschild radius (the radius of the event horizon). Note that the photon sphere is the minimum radius for light to escape transversely away from a black hole.

Because this would provide a way to locally test whether you’re in free fall in a gravitational field, or just in an “ordinary” inertial frame - which is a violation of the equivalence principle. Either way, I think the answer to this has been worked out mathematically by different authors, for example here. Actually, my question was semi-rhetorical because I knew you had to answer the way you did. But there is the possibility that radiation from a charge is a non-local phenomenon, in which case the equivalence principle doesn't apply. Not if the detector is comoving wrt to it. However, if the detector is in a locally inertial frame (ie freely falling past the charge), then radiation is detected. One argument against the notion that a charged object sitting on a table doesn't radiate is the absence of a magnetic field. A locally inertial detector can be at instantaneous rest relative to the accelerated charge, so that even though they have different accelerations, there is no magnetic field detected from the charge. That can’t be the case, since the electromagnetic field is a tensorial quantity. The electromagnetic field is a tensor, but this is about the splitting of the electromagnetic field into the radiation field and the Coulomb field, and it is this splitting that might not be covariant. So far in this discussion, I've not seen any explanations that are covariant. This is the first time I've seen the Rindler horizon invoked to resolve this issue. At present, I don't accept the Rindler horizon explanation for two reasons: 1: What is happening in the spacetime region between the accelerating charge and its Rindler horizon? Note that the proper distance between a constantly accelerating charge and its Rindler horizon is [math]\dfrac{c^2}{\alpha}[/math]. 2: Rindler horizons don't exist in reality. A Rindler horizon in Minkowskian spacetime occurs as a result of an object outrunning a pulse of light after being given a head start. This requires that the object asymptotically approach the speed of light, the head start given corresponding to the proper distance to the Rindler horizon. But in reality, the object will eventually stop accelerating, the pulse of light will inevitably catch up, and there was no Rindler horizon after all.

In the topic I'm remembering, the person was claiming to be the victim of a targeted attack with electromagnetic radiation.

The OP evokes in me a sense of déjà vu. But this was from the other forum, so maybe @exchemist or @geordief could weigh in on this topic.

The way I see it, if one expresses the electromagnetic energy-momentum tensor in terms of the electromagnetic field tensor, then the divergence of this quadratic expression, which gives the Lorentz force, should also be the source of this quadratic expression similar to the way the charge current is the source of the electromagnetic field. That is, instead of considering the divergence of the energy-momentum tensor itself, which is a force, one considers the divergence of a particular quadratic expression of the electromagnetic field, which should be part of Maxwell's equations rather than requiring the Lorentz force explicitly.

But when a charge accelerates, there has to be a back-reaction on the electromagnetic field causing it to accelerate. So, I don't think it is as straightforward as invoking derivatives of the acceleration. On the other hand, radiation from a charge can be obtained from the solution to Maxwell's equations.

I fully agree with this. One possibility that I'm currently unwilling to accept is that radiation from a charge is not covariant, that it does depend on the frame of reference from which it is observed.

What are you talking about? Changing your IP address that external world sees, or changing your IP address within your local network? What you've written above seems to be about your local network. Not long ago, I had a problem in this area so I do have some experience, although it did take a change of modem to completely fix the problem. Your IP address that the external world sees is allocated to you by your ISP, and if you want to present a different IP address to the websites you visit, you could use a VPN.

Why do you say that freely falling charges do not radiate? A charged object sitting on a table doesn't radiate even though it is accelerating. I think the circumstances under which a charge radiates is not straightforward. This is a topic that interests me a lot and I've even been considering this issue quite recently. Part of the difficulty as I see it is that the mathematics that says an accelerated charge radiates is limited to the Minkowskian metric and needs to be generalised to arbitrary metrics. Another difficulty as I see it is how the Lorentz force relates to Maxwell's equations. I'll discuss this in more detail in the hopefully-not-too-distant future.

I think many websites are adopting this as their business model for ads:

What is a water wave without the water? In the case of an electromagnetic wave, without the medium, one still has the electromagnetic wave.

I knew this (that the distinction between x-rays and gamma radiation is how they are produced and not their wavelength, frequency, or energy), but had forgotten this (that the kinetic energy alone of the electron striking the nucleus could provide gamma radiation).

Hmmm. I'm actually somewhat surprised that in the fusion from hydrogen to iron, the first step to helium provides about 80% of the energy (or am I interpreting the diagram incorrectly?).

Do beta processes (any type) emit gamma radiation?

Thank you for your effort, but I was hoping for something I didn't already know (although a clarification of the distinction between global and local symmetries pertaining to Noether's theorem would be helpful). My particular difficulty is about the connection between a wavefunction, which describes probability of general objects, and electromagnetism, which is a more specific notion than the objects to which wavefunctions apply. And of course, there are the weak and strong forces, with their own symmetries. The symmetries of the electromagnetic, weak, and strong forces are often described as "internal symmetries", but I find this term unsatisfying. Another thing: How does [math]A'_{\mu} = A_{\mu} + \partial_{\mu} \phi[/math] from classical electrodynamics relate to [math]\psi\, ' = e^{i \phi} \psi[/math] from quantum mechanics?

What I meant was: to what symmetry does charge conservation correspond?

[My bold] To be fair, relatively few people are aware that charge is the result of a symmetry. Perhaps you could explain what that symmetry is.

You could use the endothermic reaction as the cold sink of a heat engine, with room temperature being the hot source.

I have to admit that the inclusion of the "exergonic" choice seems odd among the other four choices. But I'm not convinced that any of the other four choices are correct anyway. You say that tert-butoxide is a sterically hindered base, but I don't think it qualifies as a sterically hindered base. A sterically hindered base is one where the lone pair(s) are sterically crowded to the extent that the base is totally non-nucleophilic and is stronger due to the steric relief provided by protonation. Tert-butoxide is definitely nucleophilic. One other thing: In the question, the reaction is conducted in ethanol, which is a somewhat stronger acid than tert-butyl alcohol. Therefore, the base is predominantly ethoxide rather than tert-butoxide. This opens up the possibility of an SN2 reaction forming the ethyl ether product instead of an elimination reaction. This is stereospecific although no mention was made in the question that the starting material is anything but racemic.

Actually, it does because if the reaction was stereoselective then there would be two correct answers in contradiction of the given statement that there is only one (the reaction is exergonic). Ok, I was probably mistaken in my view that stereospecific excludes stereoselective, though I am perfectly aware that these two notions are conceptually distinct (as indicated by the textbook figure you presented).

No. There is only one answer allowed, and the reaction is most definitely exergonic, thus eliminating the other four choices as the answer. (BTW, E2 reactions are stereospecific.)

It seems to me that the new definition of AI is better than the old definition because it basically says that an AI system is intelligent, whereas the old definition can be satisfied by any old computer, intelligent or not.

An ideal clock always ticks at the same intrinsic rate regardless of its location and motion. Time dilation is always about the comparison of the length of a trajectory in four-dimensional spacetime of one ideal clock to the length of a trajectory in four-dimensional spacetime of another ideal clock. An important part of this is how the two ends of each of the two trajectories relate to each other.

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E. Exergonic Let's just say that this reaction will proceed irreversibly to the products.