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1

To reach the Lienard-Wiechert potentials or to prove Feynman's equation (exposed in his Lectures without proof) it's necessary to begin with the so called retarded potentials expressed here conveniently by the following \begin{equation} \phi\left(\mathbf{r},t\right)=\dfrac{1}{4\pi\varepsilon_{o}}\iiint ...


3

To add to ACuriousMind's answer on the Liénard-Weichert potentials. You can put these formulas into an even more wonderfully descriptive form since you can derive Feynman's formula for the radiation from a moving charge: $$\vec{E} = ...


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The force does not change instantaneously, the correct way the electromagnetic field of (and thus the force exerted by) a moving electric charge is given by the Liénard-Wiechert potential, where one can see that the effect of the charge does not travel faster than light.


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The force is not propagated instantly, it takes time for the information to get from one point to another. You can treat that as istant if you are working with small enough distances and velocities but it's not. If you'll ever study field theory you'll meet retarded potentials, that are just this: the field propagates at the speed of light and it's no longer ...


4

To know what a closed timelike curve looks like, you just do like every spacetime metric. You compute geodesics and field equations and all of that. Unfortunately, things start getting complicated. Closed timelike curves have a lot of weird behaviours, especially when it comes to matter fields upon them. They may not have a properly defined Cauchy problem, ...


0

A closed timelike curve wouldn't actually "look" like anything because it's an abstract thing. You can't actually see any lightcones or worldlines. A metric is an abstract thing too, to do with your measurements of distance and time, typically made using the motion of light. And the crucial point is this: you don't travel along your worldline. You move ...


1

There are a few misconceptions in your scenario that cause the misunderstanding. First of all, by definition, causality means that if the time interval between two events is positive in one reference frame, then it is positive in any other reference frame of your choice and viceversa, provided the velocity the events propagate to be smaller than $c$. If, on ...


0

The very useful solutions of the Shrodinger equation that are usually taught in beginning quantum mechanics are not Lorenz invariant and therefore paradoxes with respect to special relativity may be constructed. The relativistic equations of Dirac: the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its ...


1

Comment on the answer of @Michael: The short answer is that you need antiparticles is false. In Quantum Field Theory you have perfectly working solutions also without antiparticles, i. e. for real fields. Even if you do want to consider antiparticles, always have in mind that despite the misleading name they are in fact different particles from the ...


1

In the entangled system we do not have two separate particles. Instead we have a single wavefunction describing a single system. When you interact with the wavefunction you are not interacting with particle $A$ or with particle $B$, you are interacting with a single wavefunction and causing it to change as a result. So the statement measuring $A$ affects ...


2

There exists no "spooky action at a distance" except in the mind of the bemused. Correlation is not causation, correlation is not causation, correlation is not causation .... I have read the article about entanglement and EPR paradox. The spin of two particles is measured when they are very far apart, and they always make opposite choices. It seems that ...


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The MWI explains the EPR experiment without invoking any non-local influences. Each observer measures one particle. The measurement affects only the particle being measured and the measurement device. Each measurement device differentiates into two versions, one for each measurement outcome. The correlations are established only after the results are ...


1

What the author means is as follows. Consider the (un-normalized) vector field $\partial_r$ where $r$ is the radial coordinate; $\partial_r$ is thus just the vector field orthogonal to the level sets $r = \text{const.}$ or, equivalently, it is the vector field foliating said level sets. As an aside, note that Schwarzschild coordinates are perfectly valid ...


-1

He says that there is nothing funny going around for r < rs because both dt² and dr² term changes sign. I'm perfectly fine with this You shouldn't be. When you aren't happy with some conclusion you should go back over everything with a fine tooth comb. Examine your assumptions, check your postulates, look closely at the things you've taken for granted. ...


2

The Schwarzschild metric as you've written it is only one particular coordinate system and the fact that $r$ and $t$ switch roles at the evnt horizon is an artifact of that coordinate system. There are other coordinate systems which make certain properties of the metric more intuitive. The ones that might be most useful for you are ones which can be drawn as ...


1

If you plot a continuous curve in spacetime, it could be a path of a body if the tangent to the curve exists and has positive squared interval. General relativity is a geometrical theory, so everything is written in a geometrical way and the geometrical generalization is the predictions the theory makes. So outside the event horizon your curve has to have ...


0

Let $|\Omega\rangle$ be the quantum state that describes the whole universe. Certainly it doesn't make sense to talk about the entanglement of $|\Omega\rangle$ with something else, since $|\Omega\rangle$ describes everything. However, we can meaningfully discuss the entanglement of the marginals of $|\Omega\rangle$: \begin{equation} ...


0

A particle can only be maximally entangled with exactly one other particle. If it helps, you can think of being maximally entangled as having a perfect relationship between two particles rather than either particle having a perfect property in the slightest. If you had a perfect spin up (in a particular direction) then obviously you could have some (that ...


3

It might help to cite your source: I found this one here - is this what you speak of? Anyhow, actually this kind of idea has had considerable, if not mainstream attention over the years. Many people who have worked with quantum mechanics will have at least heard of the following: it's just that it doesn't make it into many QM courses (being an equivalent ...


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According to the relativistic doppler effect light shifts into blue or red depending on the relative velocity of object and observer. Thus, looking at a redshifted light ray which source is close to the event horizon of a SMBH it must be possible to shift its light back into blue just by accelerating the speed of the observer by the relative amount. ...


2

For a non-rotating uncharged black hole (the Schwarzschild metric) once you have crossed the event horizon there is no timelike trajectory that will increase the distance between you and the singularity. By this I mean that to increase your distance from the singularity would require you to be moving faster than light, which is of course impossible. So all ...


2

In most introductions to Special Relativity, students learn a special procedure for setting up coordinates which involves synchronizing clocks with light pulses. This leads to a natural definition of simultaneous events as events which occur at the same coordinate time. The notion of simultaneity basically stems from a preference for a particular set of ...


3

Here's the original comment: @docscience: IMO, simultaneity has no real meaning in SR, either. It is only used for pedagogical purposes - basically, to explain SR to someone who is used to thinking in Newtonian terms. By the time you get to explaining GR, the student is expected to be knowledgeable enough to cope without it. – Harry Johnston What ...


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While I'm not a relativist I think that the notion is perfectly well defined (if frame dependent). After all, Einstein told us how to synchronize space-like separated clocks presuming that they are mutually at rest and that these clocks define the time coordinate for that frame. Thus I don't see how you can avoid the conclusion that simultaneity is defined. ...



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