# md65536

Senior Members

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7

1. ## Falling into a black hole "paradox"

Regardless of what happens inside the BH, the original scenario doesn't involve any light from inside the EH whatsoever. It doesn't say anything about what happens after some moment when the astronaut's head is less than a body's length from the EH, still outside, still only receiving light from outside the EH. But, I think you're also wrong about what happens inside the Schwarzschild BH. Light inside can still move in different directions. Draw some light cones on a diagram. Yes, all light cones inside the BH will be tilted so that all light paths head toward the singularity, but the light cone from an event inside the EH can still intersect the worldline of an infalling particle. The lightcones do not instantly tilt an extra 45 degrees or narrow and degenerate into a single line, the instant you cross the EH. Basically. Any observer outside the EH will see the object approach the EH but never appear to cross it. The exact measurements will be different for different observers. My example was basically two observers who both fall in to the BH. But sure, you could make the head and feet two ships arbitrarily far apart, and just make the BH big enough. Actually this thought experiment started from trying to figure out what would happen if two ships at relative rest were flying far from a BH so large that they couldn't detect it, such as J.C.MacSwell suggested, but if one ship ended up inside the EH and one was outside. I think either both ships enter the BH and don't notice, or the ships necessarily separate (head rips off), as the outside ship has to escape the inside ship if it is to escape the EH. It causes problems thinking of the BH as a giant sphere whose event horizon can hover harmlessly between the two ships, or between head and feet. It is a lightlike surface. If the head and feet see each other, or the ships are in communication, the EH between them is moving as fast as they can communicate.
2. ## Falling into a black hole "paradox"

I agree with Halc. When the feet cross the EH, the photons making up the image of that, and directed outward, forever remain at the EH, which is a lightlike surface. It's stationary in the very distant observer's coordinates, but locally moves at the speed of light. The astronaut notices nothing unusual because the EH and image move past its head at the speed of light, just like photons from the feet do in usual circumstances.
3. ## Falling into a black hole "paradox"

An astronaut falls into an extremely large Schwarzschild black hole, so large that they don't notice any spaghettification-like effects. Their head can see their feet the entire time, and their helmet is constantly sending information to Earth, say. At some point, the astronaut sends a message basically saying "My feet are now inside the event horizon", and Earth eventually receives that message. Is there a mistake with this scenario? What prevents the astronaut's head outside the event horizon from seeing their feet inside the horizon, and how does that look to them if they're watching their feet the entire time? I have an answer in mind but I'm curious if there's any room for experts to disagree on a resolution, and also curious if fellow amateurs can resolve it with about a pop-sci level understanding. I'm interested in how different the answers might be, so please share if you have an opinion!
4. ## Why would an athiest not believe in religion?

Yes, I think you're proving your point. If you don't understand something, it can seem god-like. If you read what Einstein wrote and understand even just parts of it, it's easy to see that it's basically a set of assumptions that match observations of reality, and some mathematical consequences of those, whose predictions also match observation. There's nothing god-like about it. But if you don't read it, it's an unknown, and it's already been discussed that people tend to attribute what's unknown to gods. So it sounds like you're assuming that Einstein's work will become an unknown, but that the stories of Him or His work will survive and be passed on (with language, I guess?). But the same can be said about anything that's known. Science can explain lightning, but if everyone ignored and forgot that, then Zeus could regain popularity.
5. ## I want to create a 1 meter BEC

Why do you think it would turn into a BEC if hot? A BEC involves the atoms being in the lowest quantum states, not highly energetic ones. The laser cooling described in the thread is done to take energy away from the atoms. A layman explanation of a BEC (and possibly completely wrong, others please correct me) is that when a particle's speed is very close to zero (ie. very low temperature), you know the momentum of it to high certainty, so due to the uncertainty principle, you can only know the position of it to lower certainty. With a cloud of particles acting as if the particles are each spread out, they overlap each other (their wave functions overlap) and are indistinguishable, and the cloud behaves in ways that are like it's one macroscopic fuzzy particle (for lack of words), instead of behaving like it's made of many microscopic particles. If the atoms are hot (in aggregate), I don't think there's a practical way to force the positional uncertainly that you need for these effects.
6. ## Why would an athiest not believe in religion?

I'm not seeing your point at all. Maybe you can explain, why would a religious person not believe in atheism? Is that similar to what you're asking? Can you describe the analogous point to the one you're making from that perspective, or if it's not analogous, what's the difference?
7. ## Why would an athiest not believe in religion?

Most? Do you have data on that? Why would we not believe what neanderthals believed? We could try to understand what they did in the context of the world they lived in, but does that mean we should share their beliefs? I lot of the beliefs of a religion have a god as their core. If ancient people ate raw pigs and got sick, but they didn't know why, they may explain it as "God does not want us to eat raw pork!" Now we understand why you would get sick, and don't need the concept of a god to explain it. It's not like atheists say "I don't believe in god, so I won't believe there's anything wrong with eating raw pork!" Atheists and religious people and neanderthals share a lot of the same beliefs. However, if you believe in something, and can't separate the concept of god from it, but are an atheist, I think that means there's a contradiction in your beliefs. As it is, there is nothing in reality that is inconsistent with the belief that no supernatural god exists.
8. ## I want to create a 1 meter BEC

A laser is practical for other reasons, like being single wavelength, high intensity, easy to direct, and needing a small window into the vacuum chamber. If you had some other setup and a single-wavelength light source that directed photons into the atom cloud, but the photons came from different directions, that would work too. I think all that's needed is enough photons with a) right wavelength b) aimed at the atoms c) symmetric or balanced distribution of directions. If you're talking about fredreload's ideas, I don't agree that any of them improve on what's already been done. If you had a way to scatter light into the cloud to get a distribution of directions, that's great, but using mirrors and multiple laser beams seems much easier. Scattering after the impact is basically how the atoms are cooled. As per the quote provided earlier by fredreload, from https://www.sciencedirect.com/topics/chemical-engineering/laser-cooling So to recap, "in the direction of absorption" is why you need photons coming from multiple directions, and you need a wavelength slightly longer than the atom's resonant frequency so that the photons are only absorbed by atoms moving toward the light source (blue-shifted to the resonant frequency). Contrary to what fredreload seems to suggest (I may be misinterpreting), you need the atoms to release that energy to get them to a lower quantum state. If they only absorb, I suppose you could still cool them, but they won't form a BEC by being in their lowest quantum state.
9. ## I want to create a 1 meter BEC

Which two are irrelevant? Do you mean when you wrote, "Do you not realise the basic mechanics that momentum directed along 2 of those 6 directions cannot affect spin?" I'm not talking about affecting spin, I'm talking about slowing of atoms that are moving toward the laser, ie. laser cooling. If you have 4 lasers aimed at +x, -x, +y, and -y, then atoms with movement in the z direction will not be cooled effectively. I think you don't need lasers aimed in opposite directions, but merely a symmetric distribution of photon directions, to avoid propelling the cloud. 4 lasers arranged like a triangular pyramid might work, but probably not as well. Maybe it's better to use more than 6 lasers, surely with diminishing return. 6 is not "magic", but probably the simplest arrangement needed to get good results. Sorry, I (and fredreload it seems) thought you meant the photons had to have parallel directions, not just that they're lined up with the target.
10. ## I want to create a 1 meter BEC

Scattering seems fine to me. You want photons coming from different directions, because the atoms are moving in all different directions. As long as the wavelength is right, it can slow an atom moving in the opposite direction of the photon. Is that wrong? Why do you want it collimated? Scattering would be less efficient if the photons aren't going through enough of the cloud. You'd use lasers for the single wavelength, focus, and high output. The light being collimated is actually a problem---you need the light coming from different directions---which is solved by using 6 lasers.
11. ## I want to create a 1 meter BEC

The spontaneous emission implies there's a lower limit to the average velocity of an atom that you can achieve, so a limit to the cooling. Even if absorption brought an atom to complete rest, re-emission would propel it in a random direction. Why might a laser be preferred over a flashlight? What are some problems you might run into using a flashlight? By the way, how many atoms are you cooling? How dense is this cloud? You could also try a microwave oven, to bombard it with microwaves. You could add a toaster, and let it absorb infrared. But will that cause spontaneous emission like in what you quoted? And how do you get the atoms moving toward these heat sources to preferentially absorb the light? Why does resonance matter, in what gets absorbed and what is emitted, if the atoms can simply absorb light of many different wavelengths?
12. ## I want to create a 1 meter BEC

It's a different state of matter, but the meaning (according to wikipedia) comes from, "Einstein proposed that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state". But even if it's analogous to condensing from gas to liquid to solid, those are typically going from higher energy states to lower energy states. Eg. water releases energy when it freezes, it doesn't absorb it. Anyway, a BEC involves atoms being in their lowest quantum state; they must get rid of that energy to form a BEC.
13. ## I want to create a 1 meter BEC

As a toy model just to describe where the energy's going, is the following a reasonable description? Say you start with one million photons moving to the right, and one atom moving to the left. After absorption and re-emitting, you end up with one million photons, scattered in a spherically uniform distribution of directions. The re-emitted photons would have variance in Doppler shift (because they're not necessarily immediately re-emitted?), but the photons re-emitted to the left would be blue-shifted on average, and the photons directly to the right would have no shift on average (basically, if a photon enters the atom from the left, and is re-emitted to the right, that photon hasn't changed the atom's final speed). Also you end up with an atom with near zero velocity. The total energy of the system is the same. I would guess that nearly all of the kinetic energy of the atom at the start, goes into the scattered direction of the photons in the end, and a tiny portion of it goes into the Doppler shift of those photons?
14. ## I want to create a 1 meter BEC

I assume it doesn't. If it did how would it do that? Atoms in a higher energy state? Even if it were possible, it couldn't be done forever. That would mean the more time spent cooling the cloud, the more energetic it would get.
15. ## I want to create a 1 meter BEC

Sure, but what is meant by "use"? The energy is not reduced through use. Naively I can think of it like, photons are absorbed by atoms moving toward the laser, and the kinetic energy of the two partially cancel each other out. But really I think it's more like, an atom absorbs a photon with energy E in the atom's rest frame, changes speed in the process, then emits the same energy E (as one photon? or several over time?) in its new rest frame. In the lab frame, the energy absorbed is less (on average???) than the energy emitted due to the atom's change in speed. --- However, if the light is re-emitted in a random direction, I'm not sure this idea makes any sense. The issue is, the real cooling corresponds with energy coming out of the cloud, not energy going in.
16. ## I want to create a 1 meter BEC

So basically, if you can start cooling the edges of the cloud, more laser light penetrates further into the cloud, but the further in, the less chance the re-emitted light has of escaping the cloud? The cooling effect occurs because of absorption, but it still requires the energy being put into the cloud to escape? The initial absorption reduces heat energy, but since you can't just increase the non-thermal energy of the atoms indefinitely, it's going to have to escape the cloud or end up increasing the heat. Does this mean that the laser cooling process is effectively using light to "poke" the atoms just right so that they emit more light energy than they absorb, so that more light energy goes out of the cloud than what goes in? PS. as a spectator up till now, I appreciate the patient informative responses. Replies that focus on discouraging amateurs don't help others who are reading.
17. ## A Simple Arithmetic Teaser !

It's a bit confusing because it's not a valid sentence with all of those question marks, but if they're changed to commas, one solution is Is this the easier solution? Oh I see, just by trying some things out:
18. ## A Simple Arithmetic Teaser !

I was curious about how many answers there might be, so I wrote code. I gave up before trying to deal with parentheses, but got the following: (11 - 17) * 13 + 2 + 19 + 101 = 44 (11 - 13) * 19 - 17 - 2 + 101 = 44 (13 + 101) / 2 - 11 - 19 + 17 = 44 (11 - 13 - 17) * 2 - 19 + 101 = 44 (13 - 17 - 19) * 2 - 11 + 101 = 44 (17 - 19 - 2) * 11 - 13 + 101 = 44 (17 - 19) * 11 * 2 - 13 + 101 = 44 (13 - 11 + 19 + 101) / 2 - 17 = 44 (11 - 17 + 19 + 101) / 2 - 13 = 44 (my answer) ((17 - 19 + 101) / 11 + 13) * 2 = 44 ((13 * 17 - 19) / 101 + 2) * 11 = 44 ((19 - 11) * 17 - 13 - 101) * 2 = 44 (13 * 17 - 19) / 101 * 2 * 11 = 44 (Commander's answer, ignoring order) Sensei's answer isn't here because it's not left-to-right order of operations. I wouldn't doubt this is a small fraction of the possible answers, but neither would I bet that it is. (I also manually culled duplicates so I may have removed too many.)
19. ## A Simple Arithmetic Teaser !

I got (101+11+19-17)/2-13=44.
20. ## Norm Square of the Four Acceleration Vector

Okay, but I'm trying to understand a statement that you made, because it makes no sense to me and I'm trying to figure out where the misunderstanding is. You wrote, "He’s essentially using an inertial coordinate system to show that there is no acceleration - which is trivially true." That makes NO sense to me, because you can describe a particle that's accelerating, using an inertial coordinate system. The coordinate system has nothing to do with whether the particle is properly accelerating or not. Eg. Consider an inertial observer on a train bank. A train accelerates from rest at a rate of 1 m/s^2, relative to the observer. The observer's coordinate system doesn't trivially show that there is no acceleration. Am I using the term "coordinate system" incorrectly? What I don't understand is if one can refer to a particle, and its own coordinate system, as the same thing, or if you and Anamitra are talking about different things. If I have an inertial observer and a train accelerates, I don't think I can sensibly describe it as "an accelerating coordinate system". I'm trying to find out what you're saying is trivially true.
21. ## Norm Square of the Four Acceleration Vector

No acceleration of what? It originally mentions and later clarifies that the acceleration of "particles" is being discussed, and that's not trivially true. If you're assuming it's reference frames being accelerated, where is that stated? This topic is confusing from the start, with seemingly some explanation or details missing?? It's difficult for me to follow if I first have to guess at the same assumptions being made, even if they're reasonable. Yes, that seems to explain what is going on, thanks. I did not get that from the discussion so far. Basically is it: specify a particle that has no acceleration, conclude that it cannot be changing speed? (I'm guessing then the main flaw in reasoning is that OP starts with equations of inertial motion, but is treating them as "the equations of general motion in SR"?)
22. ## Norm Square of the Four Acceleration Vector

Then I still don't understand. Particles *can* accelerate, and their motion can be described in the coordinates of an inertial observer. Why do you need an accelerating observer to describe accelerating particles? It can be described in Minkowski coordinates, why suggest Rindler? Not all particles are observers; to me it looks like where OP is talking about particles, you're describing observers. "in this article we see that the particle cannot accelerate." (emphasis mine) I understand to mean that we're talking about the case of constant gamma, ie. we're limiting ourselves to particles that don't accelerate. If you two are really on the same page and understanding each other, then I apologize. (Besides all that, a particle can accelerate and maintain constant speed relative to an inertial observer, thus constant gamma in that observer's inertial frame but only changing direction, while the particle undergoes proper acceleration, so I think I disagree with both of you however your statements are understood!)
23. ## Norm Square of the Four Acceleration Vector

That's not what OP literally said, and you've interpreted what OP wrote as nonsense, but still I don't know what OP really meant because it could be interpreted different ways. I don't think you two are talking about the same thing, at least in some cases like this, and I don't see how the problems can possibly be resolved if you're not even talking about the same things. I think OP needs to clarify first. Eg. in this case, Anamitra were you talking about general particles, as they are measured in various inertial frames of reference? Or particles in their own rest frames, being inertial in some inertial frames of reference and accelerating in other inertial frames of reference? Or something else? I think some consider a particle being "in" a given frame to mean that the frame is its rest frame, but I take it to mean the particle "as measured in" a given frame. Eg. a train can have a positive speed in the bank's frame. The train is in all the different frames, not just its rest frame. Is that at odds with your interpretation of OP's statement?
24. ## Norm Square of the Four Acceleration Vector

I'm not following this. An accelerometer that is measuring proper acceleration can be described in the coordinates of an inertial observer. My reading of what you replied to, is "An inertial observer remains inertial as measured in any other inertial reference frame, but a particle can (properly) accelerate as measured in an inertial reference frame." It only mentions particles being able to accelerate. What are you referring to when you say "there is no proper acceleration"?
25. ## Insight on the Matrix

Actually humans create water. How much more you'd weigh depends on what part of it you keep. Plants consume water but they don't generally hold on to the oxygen.
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