md65536

I don't know! Is it all/only electromagnetic radiation, ie. photons? I see references to "radiation field", but it's described separately from the electromagnetic field? I assume that if electromagnetic radiation is detected, that means a photon is emitted at one event and absorbed at another event. That seems at odds with the quote from the paper, "the detection of radiation has no absolute meaning", so I'd already concluded my assumption of EMR was wrong. Then I (mis?)interpreted the quote as a description of what the radiation is, as something that remains when things like EMR are separated out. Doesn't EMR drop off as 1/R2? It's all very confusing...

I read https://arxiv.org/abs/physics/0506049 [1] from swansont's earlier link, and it clears up some of my misconceptions. The basic conclusion, in the case of a comoving observer and a uniformly accelerated charge, is that there is only a certain region of spacetime that "would allow us to detect unambiguously the radiation emitted by the charge," and that region is outside the light cone of any event on the particle's world line, meaning that no radiation is detectable at all. Within the light cones, "the detection of radiation has no absolute meaning because the detection depends both on the radiation field and the state of motion of the observer." So I guess if you wanted to argue that any radiation could be detectable, you'd have to be really creative with definitions in order support that conclusion. Also it is not electromagnetic radiation as I'd assumed. "The radiation content can be extracted by separating the components that drop off as 1/R from the usual Coulomb 1/R2 fields." 1. The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation Camila de Almeida, Alberto Saa

Oh, right. I see that was already resolved earlier. The frame where no light (of any wavelength) is radiated is an accelerating frame.

What does this mean? Wouldn't it radiate as light? If so, what frame wouldn't it radiate in? Isn't the problem that if there was radiation, the expected energy would be undetectably low?

Yes, what I described, at the limit where the BH can be removed leaving just the photon sphere, fits the definition of a geon. I can't imagine that such a spherically symmetric shape wouldn't work, and that a geon needs a different shape.* It would be unstable because if any photon deviated slightly outward, its orbit would be wider and it would escape, leaving less energy, reducing the photon sphere radius and letting other photons escape. I imagine a photon deviating inward, without a central BH, would cross the photon sphere again and escape, but I'm not sure (maybe it could collapse the geon?). * Actually, I see Wheeler's 1955 paper "Geons" describes this and interesting complications I hadn't thought of. PDF: https://blackholes.tecnico.ulisboa.pt/gritting/pdf/gravity_and_general_relativity/Wheeler_Geons.pdf To make it stable, it would have to be a quantum geon. Those are theoretical only and seem to require quantum gravity. I guess the basic idea is that if energy can only leak in specific amounts, one could be coherent enough to prevent that. There are papers on them but I haven't yet found anything I can make sense of.

I'm interested in any situation or metric, or any simplification (or complication) involving a system of trapped light and a minimum of anything else. (Now that I say that, I have a vague memory of well known physicists speculating on astronomical objects made of light itself, gravitationally bound to itself but not collapsed, but I can't remember what they're called and I think that might be harder to reason about.) It does seem like if you think of the system of a black hole and a photon at 1.5 rs with at least as much energy as the black hole, and consider it inside a sphere of size 2 rs, it should collapse, but that assumes all the energy is contained within that radius, but it is not spherically symmetric, and it should have angular momentum (unless you contrived it not to by giving the BH itself the right angular momentum, but that just further complicates things), and like you say Markus, the Schwarzschild metric can’t be used. It also seems like all these complications are just more "stress" than a Schwarzschild case, and more certain to collapse. But are there ways to remove stress from the system so you could increase energy without collapse. eg. a cosmological constant. What might happen if the original photon was moved farther away to avoid collapse, such as at the photon sphere of the new black hole you describe? Or to make it symmetric, many uniformly distributed photons in a photon sphere. It seems like in general, for a real black hole photon sphere of a given size, if you add more energy to the photon sphere, you could get away with a smaller black hole, to the point that you don't need the black hole at all (which sounds reasonable now that I remember the idea of objects made of gravitationally bound light).

I shouldn't have used the word "stable", what I meant was just "circular orbit" for some time (several orbits or so) because apparently circular already implies it's on the photon sphere. A bit of a digression on this: I see in https://en.wikipedia.org/wiki/Photon_sphere , "all circular orbits have the same radius". At the event horizon, light aimed directly outward will have a constant r, and at the photon sphere, light aimed tangentially will have a constant r. Is that correct? Then, everywhere in between, there is some direction that will let light have a constant r. These photons would circle the black hole, but they're not called circular orbits?

I figure they would because their orbits should have an effect on the electromagnetic field detectable at a distance?

Is it possible trap light in a stable circular orbit around a tiny Schwarzschild black hole such that the energy of the light is greater than that of the black hole?

You should still be able to model a universe with an absence of light without removing the rules for it, such as a universe made up only of dark matter, or maybe including uncharged black holes. You'd have to make assumptions, but in accepted models, energy/mass equivalence holds for dark matter on its own.

I'm struggling to figure out your meaning relating to previous posts. This represents the timing of events along the length of say a train, in a particular inertial reference frame? But the rate is slower than c, which would mean those events cannot be simultaneous in any frame. Are you using the composition of velocity calculation to figure out the velocities or at least check that they make sense? It seems like you should be doing that here.

I looked elsewhere and it looks like "coordinate velocity" and coordinate speed are terms that are used and understood. Yes there's no flaw in relativity here. Alice and Bob, using their different respective local coordinates, disagree on the coordinate speed of light in empty space, just as GR predicts they should.

For example, in Schwarzschild coordinates, the rate at which light propagates at the event horizon is zero, but still the local speed of light at the horizon is c. Obviously both things can't be referred to as "the speed of light" and be used interchangeably. I used "rate" instead of "speed" because I don't think the latter is the right word to use here. What's the correct term for what you're describing (or for what Bjarne-7 is having a problem with?). I wouldn't use "speed of light" when talking about curved spaces unless whatever d/t that's referred to is the same as the local speed of light over d. Anything else I think needs to be described more specifically than just "speed of light."

If Bob made no mistake then he or she understands that a local clock is ticking at a different rate than a clock in empty space, and that light traveling through empty space at a speed of c according to a clock in empty space, is not going to give the same result when using clocks that are ticking at different rates. You measure the time of light's journey according to conditions all along the journey, not just those at the end. (In SR this would be different, because with everything assumed to be empty space, the conditions at the end are the same as conditions throughout the journey.)

It sounds like the question is only about gravitational time dilation, not about inertial frames or relativity of simultaneity. Bob and Alice agree that the local speed of light is c. They don't say "I can measure the speed of light in empty space using measurements I'm making locally in a gravitational well." Bob errs in doing so. Another way to say it is, "the coordinate speed of light isn't always c", however I don't know if "coordinate speed" (as in, measuring d and t using a distant observer's coordinates) is a standard term.

c is a universal constant that refers to the speed of light in a vacuum. It's not shorthand for "speed of light" in all possible contexts or coordinates. In a medium, light generally propagates at a rate lower than c, it doesn't change its value.

Look up those things and let me know what you want to discuss. I can't teach it.

I came to that same conclusion a decade ago. In figuring out that it's wrong, I learned the definitions of speed, time, and c. The speed of light doesn't have to be measured, because it is defined. There are other measures of rate of motion where the rate of (or approaching) light is infinite, such as rapidity and celerity. These also have definitions.

Right, which means that it's in the sun more than someone on the ground is. How much more is what I'm wondering. At 400km high, the ISS can be seen from 2300km away. That's more than a timezone at the equator, and more than 2 at the highest latitude the ISS passes over (51.6 degrees). So for example, the sun may have set for you an hour or two ago while the ISS above you is still lit by the sun. Or to think of it another way, if you were on the ground and had 12 hours of daylight, someone in a 400km-tall tower would get in the ballpark of 2 to 4 more hours of sunlight that day, which means 4 to 8 more hours of light than dark (very rough estimate). That's 58% to 67% of the time in sunlight, rather than 50%. I'm leaving out some important details, but how different is the correct answer from this estimate?

All the sources I see, repeat that the ISS spends on average about 45 minutes of a 90 minute orbit in darkness. I can't fathom why and I can't find any more accurate numbers. Only at equinox, would half of every orbit be above night on Earth. In summer and winter the orbits can vary over the day, as some orbits are in longer days and some in longer nights. However I'd like to ignore that variation and consider only the average times. First, the ISS is raised above the surface of the Earth, so it is in the sun more than the surface is. The higher a satellite is, the less it will be in the Earth's shadow. For example, the moon is in sunlight about 100% of the time. Second, the ISS orbit is tilted off the ecliptic. If a satellite is in a polar orbit (or better, orbiting over the edge of the polar circles in an optimal way), it can spend 100% of the time in sunlight for part of the year. Combined, using one very rough measure using a satellite tracking website, the ISS can spend about 5.25 minutes in the sun while the point on Earth below it is in darkness, on every sunset and sunrise. I think this measure must vary? But if this were the correct average measure, in a 93-minute orbit the ISS would spend 57 minutes in daylight and 36 minutes in darkness, or 61% of the time in light. This seems like an important difference from "about 50%" that I see quoted everywhere. Am I getting something wrong? Is there a more accurate calculation available? To me it seems like the 50% estimate is more misleading than a useful simplification. Why wouldn't they use a more accurate number, even if it's too complicated to explain?

Because you are. Drop down one dimension and the problem is similar to finding the area under a curve. Your questions about the "instantaneous fuel consumption" might be equivalent to asking what is the area of an infinitesimally wide line under the curve. I believe it was thinking along these lines that lead Newton to develop calculus, and that if you look into Newton's reasoning, it might help make sense of the fuel consumption idea without apparent paradoxes.

What is the cross section of a pipe filled with fuel, that you consume by moving along it instead of moving the fuel through the pipe?

However, the sand's momentum is gained while in free-fall, not contributing to the weight of the hourglass. As the sand builds up, the falling sand has less momentum, but there's also less sand falling. When the hourglass is started, there is sand falling weightlessly, and no sand hitting the bottom, and the hourglass briefly weighs less. At the end, there is sand hitting the bottom but no more of it falling, and it is briefly heavier. The start and end are similar to standing on a scale holding some mass, letting go of it, and then catching it lower down. https://demoweb.physics.ucla.edu/content/110-weight-hourglass But I see other links claiming experimental verification of different results.

That's not how SR works. The observations are reciprocal, not absolute. If the planet observes the cosmic ray's clock ticking slowly relative to its own due to relative motion, the cosmic ray observes the planet's clock also ticking slowly relative to its own.

Earlier in the thread, it was used like this: Given a set of events, the velocity of non-simultaneity is the distance between pairs of subsequent events divided by the time between those events. So for example if you have a train at rest with a bunch of synchronized clocks along its length, the events "noon" at each clock are all simultaneous and the "velocity of non-simultaneity" is undefined. In other frames, the events would propagate along the length of the train at a rate greater than c (the pairs of events are space-like). SR can handle particle velocities greater than c just fine, you just can't accelerate something from slower than c to c or faster, or vice versa. I guess a frame of reference moving relative to another at v>c doesn't make sense? So a composition of velocity formula for v>c doesn't make sense? Anyway, DimaMazin didn't you already calculate the rate at which events would propagate along the x-axis for a given reference frame velocity? You would just use the existing composition formula for that velocity, which is less than c, and find the "velocity of non-simultaneity" using that.