The Saga of Light, Part 2: The Hardest Fall in the Universe and How Hot Pockets can Fell Telescopes… And Some Stuff on the EM Spectrum

ALL the Colours of the Rainbow

Welcome to the second part of this series on light and electromagnetic radiation. In this part, we’re going to talk about – as the title suggests – cooking hot-pockets, befuddling telescopes and the worst free-fall in the universe. Well, at least that’ll be part of it. But really what we want to talk about is the different “kinds” of light, and those topics are going to fit nicely into that.

In part 1, we learned that light is an electromagnetic wave; an electromagnetic wave that *radiates* away whenever an electric charge undergoes acceleration (or deceleration). So we also call it electromagnetic radiation. I’ll re-iterate that point because it is super important: When electrical charges accelerate or decelerate there is an emission of electromagnetic waves/light, this doesn’t happen for stationary charges or charges that are moving with a constant velocity or wires with a constant electrical current. Their velocity must be changing. That’s all we really need to know here, but if you’re not okay with any of these concepts I’d recommend going back and reading Part 1.

In light of (yay, puns!) this discovery about light, I’m going to start to get pretty loose with my language. So from now on, as far as we’re concerned, the terms EM wave, electromagnetic wave, electromagnetic radiation and light all mean the same thing, and I will use the terms interchangeably.

Some people might be annoyed by me blurring these terms. They may turn their nose up at me saying things like “radio light” or “visible EM radiation”. This is because, for historical and humanocentric reasons, there is a set of terminology surrounding EM waves that tries to draw lines in the proverbial sand and group EM waves into different categories – force them into different bins – in order to manufacture a sense that these groups are in some way wholly different from one another. Humans love labels. And I think it’s important we discuss some of these artificial labels now to maybe touch base with a lot of terms you’ve heard before.

Anatomy of an Electromagnetic Wave

To start out, how can one EM wave be different than another? For that matter, how can one EM wave be the same? I mean, if you’re going to subdivide and categorize something, you need a way to discriminate one from the other, and based on what we’ve learned so far this might seem hard to do.

What I mean by this is that in Part 1 I introduced the notion of electromagnetic radiation by considering what happens to the electric and magnetic fields that surround an electrical charge when I give it a brief acceleration, or “flick”, like this:

GIF_Pulse

A crucial discussion we had was that the speed with which that flick traveled was universal; it was the speed of light. However, the general *shape* of that pulse is arbitrary and relates to the specific way I flicked the charge. To demonstrate this, let me do a different flick that involves different speeds and accelerations, a different “flick-of-the-wrist”, if you will:

Alt_Pulse

We see that the pulse changes shape. In fact, the thing need not be pulse-like at all. Rather than “flicking”, I could also simply endlessly oscillate a charge back and forth – because apparently I have nothing else better to do today – in order to produce a continuous wave-shape, like this:

Sine_Pulse

This is the light “shape” we might expect from something like a dipole antenna, which we discussed in Part 1.

All of these pulses seem pretty different, and it’s pretty clear that with the right kind of flick I could probably make most any shape under the sun. So what does it even mean to categorize light?

Well, it turns out that *all* wave shapes have a common building block. I’m going to hold off discussing in-depth what I mean by a “building block” until a bit later, however, the basic idea is that it turns out that you can assemble any pulse shape you like simply by adding up a bunch of these “base” EM wave-shapes – these wave-building-blocks – I’m about to introduce. Conversely, *any* complicated wave pulse can really be “disassembled” into its component base waves. If what I mean isn’t clear, don’t worry. Let’s introduce what these base waves are first then return to this idea of decomposing a complicated wave into these basic blocks.

The “base”, “prototypical” or “paradigmatic” wave-shape, which can be added together to build up any other complicated electromagnetic wave-shape, is the “sine” or “plane” wave:

EM_Wave2[Adapted from: https://pixabay.com/en/electromagnetic-waves-wave-length-1526374/]

It has an electric field (indicated by “E”) that is sinusoidally varying in a direction perpendicular to the direction of motion (indicated by “c”), and as we’ve already discussed, in any EM ripple the electric field must be accompanied by a magnetic field (indicated by “B”) that is oscillating in a direction that is perpendicular to both the electric field and the direction of motion. Now, take a minute to study that diagram as it’s fairly important to understand: A sine-wave moving in the direction “c” with an oscillating electric field “E” 90 degrees to the direction of motion and a magnetic field “B” 90 degrees to both “E” and “c”. To help you visualize better here’s another animation:

Electromagneticwave3D
[Source: https://commons.wikimedia.org/wiki/File:Electromagneticwave3D.gif]

Now, it’s very important that you interpret diagrams like these correctly as they’re a little complicated. It’s a very common misconception, when looking at stuff like this, to forget that, if the z-axis is the direction of movement, the x- and y-axes are showing the strength and direction of the electric and magnetic fields at that point along z. I think it’s easy to get confused and think that those axes are somehow representing actual movement in space, like light doesn’t fly straight but is instead wobbling back and forth like a crazy person. That’s NOT what is being shown. The entire diagram is meant to tell you what is happening along a single line in space, and the other axes tell you what your handy “electric-field-o-meter” and “magnetic-field-o-meter” would read if you were standing at that point.

It’s also important to understand, as I said, that such diagrams are really only showing what the electric and magnetic fields are doing along one line. Unless you’re dealing with a single ray of light, you’re generally going to have what is called a “plane” wave like this:

Plane_Wave1
[Source: https://en.wikipedia.org/wiki/File:Linear_Polarization_Linearly_Polarized_Light_plane_wave.svg]

Again, take a good look at that diagram to make sure you understand what’s going on. Basically we have a sorting of marching wave-front, like this:

Plane_Wave_GIF
[Source: https://en.wikipedia.org/wiki/File:Plane_Wave_3D_Animation_300x216_255Colors.gif]

And our sinusoidal diagrams above are meant to show what we’d see if we took a single 1-dimensional slice (i.e. a line) out of such a plane wave and looked at what is going on with the electric and magnetic fields.

This “basic” or “fundamental” EM wave also has a number of well-defined properties. Specifically, it has what are called a wavelength, frequency, amplitude, speed and polarization. All of these properties can be easily understood in terms of what the “crest” and “troughs” of the EM waves are doing. By “crest” I mean the *positive* maximum of the electric (or magnetic field), and by “trough” I mean the *negative* maximum. Remember, electric and magnetic fields have a direction so as an EM wave passes by, like in the animation above, the electric field goes from a maximum in the “up”/positive direction to zero to a maximum in the “down”/negative direction. Then it repeats.

With these terms in mind, the wavelength is indicated in the diagrams above with the symbol λ and is the physical distance from “crest-to-crest” or “trough-to-trough”, which are the same distances. It’s the important number that tells us how a wave changes in space. The natural partner of wavelength is then the frequency of a wave, which tells us how the wave changes in time. If I camped out at a given spot with my “electric-field-o-meter”, the frequency of a plane wave would basically be how many times per second a crest was detected. Looking at the animations above will probably help if you don’t get what I’m saying; it’s “crests past a given point per second”, if you like. In waves, not just electromagnetic waves but all wave phenomena (sound, ocean, etc.), wavelength and frequency are NOT independent degrees of freedom. They are in fact directly determined relative to each other by the speed of the wave.

Let’s say you picked a specific crest of a wave that you wanted to follow; I don’t know why, maybe you’re just into that. The speed of a wave tells you how far, let’s say in meters, that particular crest will move along the direction of propagation in a given second, which is why speed is in meters per second. Wavelength tells you how many meters there are between crests. So let’s say I’m standing at a specific point and there’s a plane wave with a speed of, say, 8 meters/second and a wavelength of 2 meters that is passing right by me. That means that every second, as I watch motionless, 8 meters of wave pass me by, OR 8/2 = 4 crests pass me by. The speed divided by the wavelength is the numbers of crests per second… otherwise known as the frequency.

Don’t worry if that was a little dense. The key point is that if a wave has a certain speed (like light) and if I state the wavelength, the frequency is also then exactly determined (it’s the speed divided by the wavelength), or, similarly, if I state a frequency, then the wavelength is uniquely determined. So frequency and wavelength CANNOT vary independently, and if I know one, assuming I know the speed of the wave, I know the other. Thus, frequency and wavelength don’t hold different information, and I can use the terms fairly interchangeably.

So wavelength, frequency and speed are all interrelated and tied to one another. That leads us to our last two properties: amplitude and polarization. Amplitude is simply what the magnitude of the maximum of the crests actually is, like as a value:

Amplitude_Diagram2

Basically, the amplitude (A) simply amounts to: “When the electric (or magnetic) field has its maximum strength, how strong is that field?”. That’s all it is.

Finally, we have the polarization. We talked about the polarization in Part 1. Basically, the “rules” are that if I have an EM wave moving in a given direction, then the electric field must be perpendicular to that direction and the magnetic field must be perpendicular to both the electric field and the direction of motion. That might seem like some pretty rigid rules, but in reality it means that really the electric and magnetic fields could point in any direction within the plane perpendicular to the direction of motion. There’s 360 degrees of freedom for how the electric field and magnetic fields can point and still obey those “rules”. For example, here are two “options” with a “polarization angle” between them:

Polarization_Angle2

If polarization is confusing, don’t worry. I won’t be talking about it further in these posts. (Although I may talk about it extensively in a future set!)

Sorting Light

When we talk about electromagnetic radiation, we talk about it in terms of these “building block” plane waves. In general, however, a given source of light won’t give off a pristine wave like this but rather will give off a complicated shape, like the pulses I showed earlier, or maybe like the following resulting wave:

Different_Waves2

But as I’ve shown in that diagram, I can actually construct (or deconstruct, depending on perspective I guess) that wave by adding up a bunch of sine/plane waves. We will have a LOT more to say about this in future posts when we talk about things like optical spectrometry, but for now it’s enough to simply understand that I can take any complicated electromagnetic “ripple” and conceptualize it as simply an additive mixture of our plane waves with different wavelengths and amplitudes.

Thus, we now understand how we can categorize light: By these properties of our plane waves. Most specifically, the labeling system we use is based on wavelength only (or frequency only, remember since the speed of light is fixed, in a vacuum at least, these quantities hold the same information).

Binning Light: Radio

So the way we can label, group and discriminate between light is based on its wavelength (or frequency!). If an EM wave has a very, very long wavelength, which is to say a wave whose wavelength is anywhere from about a meter long at its shortest (about 3 feet for you Americans) or any amount longer, we conceptually group them all together. We call them radio waves. The term “radio” is the catch-all for all EM waves with wavelengths longer than a meter so. It has no “far end”: 1 meter wavelength, 1 kilometer wavelength, 1 lightyear wavelength, doesn’t matter, all “radio”.

That’s all the word radio means; it’s light, which is to say EM radiation, whose wavelength is a meter or longer.

Now, we can talk about radio and radio waves and the important role they play in modern technology maybe another time. (Would people be interested? Vote here!) But for today the key thing we care about is that it is light with the longest wavelength (or lowest frequency).

FM radio wavelengths are about 3 meters, AM radio wavelengths are about 3 kilometers, which is about a thousand times longer. Both are still radio signals.

Because these wavelengths are meters, kilometers, 100,000 kilometers, whatever, if you want to collect radio waves, like to build a telescope, you’re looking at something very different than an optical telescope. To understand why one needs to think in terms of resolution. There’s a very simple relation for telescopes that roughly says that if I have a telescope of size or width D, and it’s taking in light of wavelength λ, then the angular resolution of the telescope is proportional to λ/D.

Angular_Resolution2

Angular resolution (see above) is basically just the ability to recognize two objects, which from my view are separated by an angle, θ, as indeed being separate and distinct and not simply blurred together into one object. If two objects in the night sky appear to you closer in angle than your angular resolution, then you will just see one big blurred blob. If they’re much farther than your angular resolution, then you can see all their detail and clearly tell they’re different objects and collect separate information from each. This is very important in something like astronomy because you’d like to collect radio data from ONE object, not an assorted hodge-podge of many objects that happen to fall approximately along a line (i.e. only slightly different view angles) from your telescope’s perspective.

When we think of telescopes we often think of something like this:

Optical_Telescope

But because of this simple reality of angular resolution, if the wavelength of the light I’m interested in is very, very long and I want decent resolution, I need to have a very, very wide telescope. This is why radio telescopes look like this:

Radio_Telescope1
[Source: https://en.wikipedia.org/wiki/File:CSIRO_ScienceImage_4350_CSIROs_Parkes_Radio_Telescope_with_moon_in_the_background.jpg]

Or this:

Arecibo_Observatory
[Source: https://en.wikipedia.org/wiki/File:The_Arecibo_Observatory_20151101114231-0_8e7cc_c7a44aca_orig.jpg]

Yes, by the way, that last one is where the final battle in the James Bond movie Goldeneye took place, and I did show it in the last post. Actually, I feel bad for the guys who worked there when they were shooting that. Probably had to shut down their science-ing for like a week so that Sean Bean could die in yet another movie.

And how about this one from the movie Contact:

VLA
[Source: https://en.wikipedia.org/wiki/File:USA.NM.VeryLargeArray.02.jpg]

That one dish isn’t the telescope. No, all of those dishes, all 27 of them, make one telescope. It’s an array of dishes that is very large. It’s like a very large array. Yep, very large array. VLA. No seriously that’s actually what it’s called, it’s called the VLA. If you want dumb-yet-undeniably-charming-and-overly-forced acronyms, go talk to an astronomer. Maybe one at CANGAROO. At least until he gets a job at GADZOOKS to look at DONUTs.

The VLA is actually a different type of telescope to the previous ones I’ve showed. It’s what is called an astronomical interferometer that behaves like one huge telescope (the entire array) by comparing the signal of a bunch of smaller telescopes (each individual dish) against one other in a very special way.

Binning Light: Microwave

Alright, moving on from this aside on radio telescopes in movies, chop chop. So if light has a wavelength of any length up to about a meter, we call it radio. If it’s shorter than that, from about a meter to a tenth of a centimeter (or about 1/25th of an inch in Freedom Units), then we call it something else, we call it a microwave. Actually some people still call these radio waves also, because humans really aren’t great on agreeing on things, especially when nerds get involved. But we’re going to call them microwaves, and you Radio Frequency engineers out there can just sit there and stew silently. I mean you can yell at your screen if you want, but I can’t hear you.

EM waves in the microwave range have wavelengths of about a few centimeters. This is actually something you can partially see in a microwave oven, which is just a box (the fancy word is “electromagnetic cavity”) for holding and reflecting microwaves that are produced by the oven’s “magnetron”. To see the size of the microwaves, take something that is really melty, like cheese or chocolate or marshmallows, then take the little rotating table on the bottom of the microwave out and lay these things out thin on a plate so they evenly cover the plate’s surface. Then put them in the microwave and turn it on. What you’ll see is that the cheese/chocolate/marshmallows melts in certain spots more than others, and in general the distance between these spots will be related to the wavelength of the microwaves.

Melting_Microwave2
[WARNING! Unrealistic Diagram!]

The reason is because inside your microwave you have EM waves, and there are points where their electric fields are always at a maximum, which is where the melting is happening, and points where they’re always zero, where no melting happens. In general, an EM wave is travelling, at the speed of light, but if you have waves constantly bouncing around and reflecting off the walls of the cavity, you can (and I stress can) end up with spots where the electric field always ends up being at a minimum or maximum when it hits that spot.

The energy in an EM wave (much more on this to come) depends only on its magnitude, not whether it’s positive or negative, so for one full wavelength you’ll have two points of maximum energy (see the diagram). Thus, the melted-spot-to-melted-spot distance is related to half the wavelength (i.e. the wavelength is twice the distance between spots). The fact that there are points where no melting is happening is a design flaw, and that’s why your microwave has the rotating table to begin with, so no part of your tasty Hot Pocket spends the whole time in a “cold spot” but rather rotates through hot and cold spots and thus cooks more evenly.

Now, right away I want to warn you that if you do this experiment on your microwave, it may not work very well. You can see an excellent YouTube video from “The Engineering Guy” (click here) where he does this. But there are a few engineering realities of microwave oven design that may well stop your experiment from working as well as I’ve described on your particular microwave. The first is that, precisely to reduce the effect of these hot and cold spots, many microwaves have a little metal fan-looking-thing, called a “stirrer”, that basically jumbles up the trajectories of the microwaves leaving the magnetron, causing their pattern to be somewhat randomized. Secondly, you may have noticed that in my little drawing, I’m actually assuming that the wavelength of the microwaves is some very nice multiple of the size of the microwave cavity (i.e. the inside of the microwave) so that you can have a nice, what is called, “standing wave” shape. In general, the dimensions of the inside of the microwave will not have any such special relationship. The wavelength of microwave ovens is fairly universal (I’ll tell you the value in a second), but the size of microwaves is entirely up to a manufacturer and has more to do with what fits in a typical “microwave cubby” in cupboards than any crazy physics relationship. So you can try the experiment if you like, but depending on the design of your microwave, results may vary in terms of how nice and regular the pattern of spots you get is.

Of course, if you’re not one for wasting cheese or chocolate (I’m with you there!) you could also just have looked on the back of your microwave, where there’s often a sticker with a lot of technical information. If you look at that sticker, somewhere it likely says 2,450 MHz (a megahertz is a million Hertz) or 2.45 GHz (a gigahertz is a billion Hertz), which is typical for microwave ovens. Those are frequencies and, remember, this means that if you stood at one of those maximas of the electric field with your little electric field detector then it would go from positive maximum to negative maximum and back at a rate of 2,450,000 times a second (one Hertz is “once per second”). Based on our direct relationship between the speed of light (in a vacuum) and its wavelength and frequency, that means that the wavelength of the light it’s generating is 12 centimeters long.

The fact that the wavelength of the light produced by your microwave is about 12 cm also answers a question you might have had: Why do microwaves have that little mesh full of holes in their doors? Of course, the point of it is so you can look in and check on your Hot Pocket, but why is it a mesh of holes? Well, it’s a little result of the physics of electromagnetism that electromagnetic waves can only really react or respond to physical features that are about the size of their wavelength or bigger. Thus, if you have a metal sheet full of holes, but those holes are much smaller than the wavelength of the light (like the holes in that mesh, which are ~0.1 cm, or 100x smaller than the wavelength of the microwaves), then the light will treat it as if there were no holes at all. So microwaves just see the door as a solid metal sheet, just like the other walls, and are thus reflected by it. But visible light, as we’ll see, has wavelengths of ~0.00001 cm – much, much smaller than the holes – and thus sees holes. So that way you don’t get cooked by the microwave when checking on your dinner.

This is also why you can use a cell phone in a car but your AM radio antenna needs to be on the outside. Your cell phone works because the wavelength of light it is transmitting on are about 40 cm long and thus can get out through the car windows. However, AM radio has wavelengths in the kilometers and thus has a wavelength that is much, much longer than the windows and thus just sees a big metal box and can’t get in, like the microwave door. At least that’s the traditional reason, nowadays cars are increasingly plastic and have things like glass-embedded antennas and dammit, Jim, I’m a physicist not a radio engineer, so I’ll leave it to someone else to give a more up-to-date discussion.

Perytons: Felling Telescopes

By the way, your internet router is communicating using light whose wavelength is about 10 centimeters. These are close enough to the 12 cm of microwave ovens that having microwaves leak out of your microwave oven can interfere with your WiFi signal. This is something you may have already known. However, there’s also a true story related to this that I just love. In the late 1990s, a radio telescope in Australia, called the Parkes radio telescope, made an amazing and strange discovery of intermittent radio/microwave pulses that only lasted a fraction of a second. They dubbed these mysterious signals “Perytons” after a mythical creature that was part stag, part bird. What were they? Signals from another world? Mysterious astronomical phenomenon? But only the Parkes telescope, and no other facility, seemed to detect them. Such strange! So mystery!

Let me copy an excerpt from the abstract of a 2015 paper in the “Monthly Notices of the Royal Astronomical Society” (Vol. 451, 3933–3940 (2015)), which you can read the full thing of here

Subsequent tests revealed that a peryton can be generated at 1.4 GHz when a microwave oven door is opened prematurely and the telescope is at an appropriate relative angle. Radio emission escaping from microwave ovens during the magnetron shut-down phase neatly explains all of the observed properties of the peryton signals.

The pulses were literally coming from people pressing the “open door” button on a microwave oven within the facility before the cook cycle was finished. When they did this there was the briefest fraction of a second where the magnetron was still on but the seal around the microwave door was slightly open allowing microwaves to spill out until the magnetron shut itself off. Totally harmless, but it was a brief enough pulse that the powerful radio telescope could detect it. So the mythical “Perytons” were Steve the intern (you just know his name was “Steve”) getting impatient and not waiting the full 2:00 minutes for his popcorn to finish microwaving. (Classic Steve.)

See Next Page…

10 thoughts on “The Saga of Light, Part 2: The Hardest Fall in the Universe and How Hot Pockets can Fell Telescopes… And Some Stuff on the EM Spectrum

    1. Wow, great question! There’s actually a lot to unpack in your question and some of the specifics actually take things to the fringes of physics, specifically by talking about absolute zero. In fact, talking about temperature and accelerating reference frames is an extremely difficult (and often ill-defined) topic. I’ll maybe talk a little bit about why saying absolute zero in this scenario is actually opening up a Pandora’s Box, but first let’s just talk about the finite-temperature case.

      In the finite-temperature case if I have a “Box O’ Charge” sitting on the surface of a neutral rotating sphere we can kind of simplify our thinking to really just a charge confined to make loops around a circular track. In this case, as it is accelerating, it will emit light in the forward-ish direction and as a result of what’s call a “recoil reaction” it will slow down as it does this until it eventually comes to a stop. If we bring the planet into this then the box – through the frictional interaction between the bottom of the box and the surface of the planet – would act to essentially slow down the rotation of the planet. So in principle, if we assume that the planet is rigidly attached to the box, then this deceleration of the box will also bring the planet’s spin to a halt.

      Now, I haven’t said anything about the thermal system and that’s because generally we conceptually separate the, so-called, “center-of-mass” motion of an object from the random thermal motion. Thus, the temperature of the box doesn’t come into it as it is its center-of-mass acceleration that is driving EM emission and that emission is in turn stealing energy resulting in a reduction of center-of-mass velocity. So the entire story rises and falls on the behaviour of the center-of-mass motion.

      Now for just a little bit about the “can of worms”. Temperature is a somewhat nebulous concept when we start talking about both non-accelerating or accelerating frames of reference. It’s generally the case that even if different observers measure an object as having a different CONSTANT (i.e. no accelerating) speed they still agree on the temperature of the object, which relates back to what we’ve talked about (center-of-mass motion and random thermal motion being distinct). For reference frames that aren’t accelerating, temperature is not frame dependent. However, I’ll get back to that in a second because let’s consider a simpler question: “can an object, through black-body emissions, reduce its temperature to absolute zero”. The answer here is “no” because a thermal system is always in thermal contact with another system, even in a vacuum of space it must trade heat with the vacuum of space through our thermal radiation/black-body emission. Thus, you can’t get colder than the thermal “reservoir” you’re in contact with. From this you might say “but space has no temperature”. It actually does, there’s a couple ways of defining it, either in terms of the temperature of particles (there’s still about 1 hydrogen atom per cubic centimeter in interstellar space) or – more commonly – in terms of the Cosmic Microwave Background Radiation (CMB) that permeates the universe. This CMB sets a hard floor throughout the universe of about 3 degrees above absolute zero for any object cooling itself through thermal radiation. However, let’s say there was no CMB, then what? Well, here’s where we reach the fringe of physics and what is called the “Unruh effect” (google it if you’re curious). This Unruh effect is an unverified and somewhat controversial prediction of general relativity which basically says: “an accelerating observer will observe blackbody radiation where an inertial observer would observe none”. Put another way, it predicts that an accelerating observer sees the universe as HOTTER than a non-accelerating one. So by the way you’ve set up the problem, our “Box O’ Charge”, if the Unruh effect is true, would see the vacuum of the universe as being hotter than absolute zero, even ignoring dilute hydrogen atoms and the CMB and thus could not be at absolute zero.
      Anyways, that was maybe a bigger trek to the frontier of physics than you were looking for but hopefully that helps clarify things, or at least made things very confusing, but in an interesting way.

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      1. That’s quite interesting to read, but it’s actually not what I was intending to get at. If I understand general relativity correctly, there’s no difference between an accelerating frame of reference and a non-accelerating frame of reference that’s in a gravitational field. If that’s correct, wouldn’t it imply that a charged particle on the surface of a non-rotating planet would also emit Bremsstrahlung radiation, since it’s undergoing proper acceleration?

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      2. Ah, I see. That’s actually a well known paradox of GR/E&M and one that took quite a while to pick apart, you can see a wikipedia about it here:

        https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field

        The key point is that radiation is defined as energy transfer, via the EM field, at infinity and the “supported observer” (i.e. someone sitting beside the box on the planet) and an “unsupported observer” (someone watching in space far from a gravitational field) have frames that don’t have the same “at infinities”. Thus, the unsupported observer observes radiation but the supported does not, which is fine because the infinity of the unsupported observer is outside the observable horizon.

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      3. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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      4. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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      5. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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  1. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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