# md65536

Senior Members

1973

3

1. ## Modification of twin "paradox" with a wormhole.

Can you have a multiply connected flat spacetime with a bridge between two locations? I didn't specify that, so one could add other curvature if they want, but with a flat spacetime, SR describes time dilation while outside the wormhole. But traversing the wormhole itself involves a singularity? Because of that, the time dilation factor is indeterminate? So it doesn't matter if it takes a negligible time to traverse the wormhole, because another clock might elapse an indeterminate amount of time in that instant? I think that SR is not needed to describe the time dilation that occurs while traversing the wormhole, because I've given that information in the specification of the wormhole. I could post what I calculated for one of the scenarios to see specifically where this reasoning might go wrong, but I was hoping someone would have their own answer to discuss first. What is your quick answer? Maybe we could discuss it and fill it in more, and perhaps end up in agreement or learn about something we're both missing!
2. ## Modification of twin "paradox" with a wormhole.

I think it can be resolved with SR. Yes, the rules of SR still apply even if there are other aspects involved that it doesn't resolve, and even when there are aspects that modify the rules. Eg. if there's spacetime curvature involved, you don't throw out the results of SR, but neither does SR give you the complete answer. It's highly possible that my question is ill-posed! My intention was to describe the wormhole so that doesn't add aging effects that can't be described in the domain of SR. SR can deal with faster than light particles, but shouldn't work for accelerating between faster and slower than light. However the wormhole is just a shortcut through spacetime. Basically it involves taking a shorter path between two events, shorter say than a straight path through flat spacetime that a beam of light might travel along, but it doesn't actually involve moving relative to something else at a speed higher than that of light. The situation above can break some physical laws, eg. it allows being in 2 places at once, but I think that on its own it's set up so that causal paradoxes aren't possible. The events here that an object can pass through "simultaneously" are outside of each other's light cones. I guess "the time experienced by the twin travelling through the wormhole" would depend on the metric, and that would typically involve things outside of SR, but I tried to specify (not clearly?) that the proper time taken to traverse the wormhole is negligible. You should also be able to calculate some things based on being consistent with what some other observer sees. I may have missed something (ill-posed question) or reasoned wrong, but I came up with unambiguous answers that are consistent between observers. Yes, I'm curious about the intuitive answers! But more along the lines of intuitive reasoning, where you can convince yourself that you have an answer that the maths agree with, not just a guess. Also if you only have a guess, are there results from SR that can fill in the missing information?
3. ## Modification of twin "paradox" with a wormhole.

Does ds^2 = 0 make sense as a metric, describing a wormhole with negligible interior length and no other specifications? Or is it the external length (which I doubt because there's no requirement of external connections for general wormholes), something like $ds^2 = -c^2 dt^2 + dx^2 = 0 + (1 LY)^2$? I think that enough information is given, with the assumption that we start with the basic twin paradox and nothing more (so assume flat spacetime, no gravity etc.), then add just the wormhole information given (is that even possible while keeping external spacetime flat?). Wormhole traversal events are described; an object enters one location at time t and exits at the other 1 LY away at time t in Earth's frame. All other information can be determined because there is also the 1LY external connection, I think. Any other complications could be added if you want, and you get a different answer, but the same it true for the basic twin paradox setup. Have I oversimplified things to the point of nonsense?
4. ## Modification of twin "paradox" with a wormhole.

Is it not possible to describe a simple bridge between the two locations, assuming the simplest configuration without additional complications if they're not specified? Eg. no gravitational properties given, so assume no additional gravitational effects? No discontinuity given so assume it's continuous? The proper time needed to traverse the wormhole is negligible because its length is specified as negligible, right? This of course is a mathematical problem and not a physically possible experiment or anything. What other information is needed? Is it a case where there are eg. gravitational effects that contribute to the answer and can change it by a lot, or is it that there are multiple possible wormholes that equally fit the inadequate description above, but have opposite answers to the question?
5. ## Modification of twin "paradox" with a wormhole.

Consider a stationary Earth, with one end of a wormhole fixed nearby, and the other end fixed one light year away. The wormhole is a shortcut of negligible length connecting pairs of events, one at (0, t) and one at (1 LY, t). There are two twins, one on Earth and one in a rocket that travels at a relativistic speed relative to Earth (say 0.6 c or choose a convenient number). Who ages more in these 4 scenarios?: 1. The rocket leaves Earth, travels to and enters the far end of the wormhole, and ends up back at Earth, having been inertial the whole time. 2. The rocket leaves Earth through the near end, exits at the far end, and travels back to Earth, inertial the whole time. (How do these appear different, in terms of Doppler effect? Is there something here that you would say is "equivalent to acceleration" of the basic twin paradox?) 3. Suppose the same as (2), except that when the rocket exits the far end of the wormhole, it's moving in the opposite direction, and turns around (in negligible time) before travelling back to Earth. (How is this different from (2) in terms of measurements and/or what an observer sees?) 4. The rocket leaves Earth, travels to the far end of the wormhole, but it is the Earth that goes through the wormhole, and meets the rocket at the far end. (Is there an "equivalent to acceleration" here?) I have guesses and explanations I can post later, but like before I'm curious about other people's answers and how intuitive relativity is.
6. ## Falling into a black hole "paradox"

Yes, exactly, so we can discuss what would happen or be seen in a particular model of a black hole, but must be careful not to make the same claim for just "a black hole" in general. Having the universe's entire history in your causal past would describe a particle that is stuck on (or asymptotically approaching) some horizon, with a proper time that approaches infinitely slower than the rest of the clocks in the universe. That would be similar to an observer who could hover infinitely close to a Schwarzschild BH event horizon. So, EM repulsion exceeding gravity would make sense... it would be like the BH itself is causing you to hover (but this is inside the EH, so I don't think infinite energy would be needed?). I think the singularity still exists in those types of BHs, but with different geometry.
7. ## Falling into a black hole "paradox"

Looking for more details, I came across this: Falling into the Schwarzschild black hole. Important details S. Krasnikov https://arxiv.org/abs/0804.3619 which is surprising, but is a reminder that the details describing a Schwarzschild BH can be vastly different for BHs in general. The Kruskal diagrams are of Schwarzschild spacetimes.
8. ## Falling into a black hole "paradox"

This is wrong, as Kino wrote and the diagram shows. It seems you never lose sight of your feet, even if you dropped them in ages before the rest of you went in, but you'd also never see them hit the singularity (of course). You just see older images from when they were above where you are now, and there'd be a last possible image of them which depends on how long ago they entered, so I suppose they'd have to appear increasingly red-shifted.

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

But the future light cone interior is in the direction of the BH interior, that doesn't matter? Is it that the EH is a null surface, but also a light-like surface, yet the latter does not give you enough information to define the horizon? My main argument in this thread is basically that you can see what is below you, because it doesn't involve a photon increasing its r-coordinate, but rather the observer decreasing its r-coordinate to reach that light. Is that argument wrong? Inside the horizon, the r-coordinate of all photons must decrease over time. Near the horizon, the photons aimed "upward" decrease r very slowly. By necessity, an infalling object must decrease in r faster than some of its photons could---the object can't leave the future light cone of a past event on its own world line, and fall slower into the singularity than all of its light. This implies that an infalling particle can decrease in r faster than the "upward"-directed photons from events on the world line of an object below it. Thus, the infalling observer must be able to see objects that are always below where it is now, but were above where it is now when they emitted the light the observer is now seeing, which appears to come from below. In Schwarszchild coordinates (I think???) those photons are decreasing r very slowly, but in the observer's local coordinates they are moving upward at the speed of light. Just like the EH has a fixed r coordinate but locally moves past the infalling observer at the speed of light. If this is wrong, I don't see how the astronaut could see their own feet, because their feet are at a lower r coordinate.

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

I agree, that would be better. Wouldn't the shape and orientation of the light cones be independent of the motion of the light source?, while the shape of the source's world line would be entirely dependent on it. So not all world lines would be pointed locally along the axis of the cone. I think the image is a fair representation of the world lines of inertial particles entering the BH at near the speed of light, which is not at all what I wanted to show.
13. ## Falling into a black hole "paradox"

I've attached an image showing light cones inside the horizon. The labelled events are: A - Feet pass the EH. B - Head passes the EH. C - Astronaut twitches her feet D - Astronaut sees her feet twitch E - Photons from twitched feet reach the singularity. The scale of this is out, the astronaut twitches her feet in the short time before the head has entered the BH. More realistically, the head's world line would be very close to the feet's. The light cones inside the BH show that light from a single event does not take the same amount of time to reach the singularity, in all directions. Also... I think I made a mistake, the lines I'm using as the head and feet worldlines appear to be light-like. Can you see from the diagram as-is how it should look, or should I post a correction? Also, if you still think the head can't see the feet inside a BH, please show how this would look with light cones.
14. ## Falling into a black hole "paradox"

The slowing of time is only relative. An external observer measures the infalling clock slowing relative to its own, but the infalling observer measures their own local clock's proper time ticking at a rate of 1s/s. Their own clock does not stop as they fall into a BH. If an infalling astronaut would lose sight of their feet, and smaller distances, this would imply that a light clock would stop functioning, or at least would stop depending on its orientation. Theory doesn't predict that. I really didn't expect there to be debate after a resolution was posted. You still have light cones inside the EH, outside of the singularity. The cones do not become lines, where there is only one path for light from an event to the singularity. The path of light that goes from feet to head also leads to the singularity. "Light beams aimed directly outward from just outside the horizon don't escape to large distances until late values of t." -- https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html but they do escape.
15. ## Falling into a black hole "paradox"

Isn't that the same thing? Yes, but if both ships fell in, they could remain close enough to relative rest to not notice, for some time. Just like a person falling into a large enough black hole doesn't feel themselves being pulled apart for some time, even if tidal forces are always present (though negligible here). I'm talking about a black hole so immense that the gravitational effects are very weak at r_s, like an r_s of tens of billions of lightyears. If that's too small, maybe a billion times that! If you make it big enough, you should be able to continue falling toward the singularity for a lifetime without ever noticing you're trapped in a black hole. All the rules still apply, you can't communicate with anyone outside the EH, but the EH has expanded beyond you at the speed of light, and anyone you try to communicate with who hasn't escaped, is inside with you. I can't say what would be observed on the inside of a BH, but my understanding is that accepted theory does not predict any strange local effects of crossing the event horizon, like suddenly being unable to communicate with or see "nearby" infalling particles. By "paradox" I meant it's not a real paradox, just a conceptual problem to resolve.
16. ## 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.
17. ## 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.
18. ## 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!
19. ## 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.
20. ## 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.
21. ## 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?
22. ## 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.
23. ## 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.
24. ## 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.
25. ## 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.
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