Halc

You're still not reading the posts. Nobody is suggesting light travelling from the interior to the exterior, or for that matter, in any direction that doesn't head steadily in the direction of the sigularity. md65536's picture shows all the light paths and none crosses from in to outside the EH. Typo? Perhaps you meant to say that it cannot. Light cannot orbit (a Schwarzschild BH) any closer than the photon-sphere which is 1.5 times the radius of the EH. It gets more complicated for something like a Kerr-Newman BH which is a more realistic model of actual black holes.

Correct. You could go in spinning for instance, so feet/head worldlines switch sides repeatedly, taking turns being 'in the lead' so to speak. You could have two things orbiting the BH and slowly spinning in with high but opposing relative velocity. The line defining the center of the light cone is frame dependent, so it's always in the center relative to the frame of the falling thing I think. There's not one unique worldline that the one at the center of a given event's light cone, but the BH itself sort of defines an obvious symmetrical frame where the object drops straight in instead of the more likely spiral. Thus there's no worldline of a particle near the speed of light since in the frame of any falling thing, it is stationary with a worldline centered on its (local at least) light cone.

Yes, the worldline would be through the center of a given light cone, not the edge, such as a line connecting A directly through D. I think your head and feet need to be a little closer together to illustrate the light going from one to the other. There are no inertial worldlines in your picture. Neither term means the same thing as 'black hole'. It seems like a black hole is the collection of events enclosed by the event horizon, the event horizon being a boundary between events that can have a causal effect on a distant wordline and events that cannot. As for singularity, there is a coordinate singularity at the event horizon in some coordinate systems (not the one md65536 shows), and there is a physical singularity inside the black hole, the nature of which varies between say Schwarzschild BH, Kerr BH, or other metrics.

This is straight up Einstein's equivalence principle which says that in a small enough box (effectively one where tidal effects are not significant), one cannot tell free-fall in a gravitational field from inertial motion in no gravity. That means there's no obvious effects as you cross the event horizon. You still see your feet, and can go about your business just like before just like anybody falling such as on say the ISS. Nobody is suggesting light traveling from inside the EH to the outside. I never suggested it. Read my first post above and understand what I'm saying. The guy could be broadcasting a video from a head-cam so everybody can watch, and sure enough, the feet are visible in that broadcast, but the feet seen are not yet inside the EH. The light was emitted outside the EH horizon and headed towards the camera. You don't see your feet now, you see them about 6 nanoseconds ago, and nobody seems to realize that, or they're assuming that the head is somehow hovering outside the EH, which would require enough proper acceleration to indeed make your feet invisible, not to mention detached. No, the guy is falling and notices absolutely nothing change as he crosses over. The feet inside the EH also emit light, and that light also reaches the camera, but not before the camera is inside the EH. The broadcast from the head-cam never reaches the outside observer. So the guy falling in notices absolutely nothing amiss as he crosses the EH. The distortion of spacetime will eventually get noticed (arms getting ripped out of shoulders, etc), but we're positing a large BH here with a still reasonably uniform gravitational field at the EH.

No it does not. By the time the photon from the feet meets your eyes (a few nanoseconds later, eye-time), those eyes are long since beyond the horizon. It's not like the head is hovering on the outside. That certainly would kill you, but at least prevent you from seeing your severed feet.

They have videos of this point of view, and the most notable part of it is that nothing particularly weird happens at the event horizon. You can't tell when you cross over. No, you never lose sight of your feet. Everything is pretty normal until the tidal forces start to rip you apart, and for a very large BH, that's well after you cross over. You can still see in all directions in 3D, and you can see the stars in the universe you've left behind, however much you can no longer reach them.

The head cannot have measured the feet having entered the black hole since the head always measures the feet in the past. So sure, he can send that message, meaning the feet are in there 'now' in the falling frame, but he is sensing the part of the feet worldline still outside the horizon.

Thanks Markus! +1 You seem to be the only responder that at least understood the question. So I'm going to ramble a bit, part of which probably isn't worded as precisely as it should. 'Gravitation potential' is a local concept then, relative to say a system that is stationary like Earth, where one can speak meaningfully of the relative potential difference between sea level, geosync orbit, and the hole we've hollowed out in the center, but all potential is relative to some reference (sea level say) and involves whatever components (Earth, sun, galaxy) we decide to include in our calculation. A universe described in its entirety by Minkowski spacetime (infinite uniform distribution of superclusters, not receding from each other, but evolving in place, so gravity wells, but not on the largest scale) would admit this time-like Killing vector field since the matter distribution wouldn't change significantly over time. The density in particular would be fixed, and in such a universe, my argument might be meaningful, but not in this universe.

You're not doing the mathematics at all. Sure, I illustrated infinite potential even with the linear and planar case (even Newton knew this), but the uniform distribution of mass in 3D is even worse. Your -GM/r is for a point mass (or spherical) from which you can distance yourself. Yes, there is finite potential for any one finite mass, but the mass of the universe is not finite and not at some fixed radius. OK, we can do it another way using Newton's shell theorem. At a large enough scale, matter is distributed uniformly in the universe so the shell theorem is valid. Imagine a thin shell of material going from radius r to r+1. Per the formula, it yields a potential of -GM/r where M is the mass contained in that shell. Call this potential X. Consider a different shell that goes from 2r to 2r+1. That shell has 4 times the mass of the first shell and only twice the radius, so it has -G4M/2r potential which is twice the potential. The further away the mass is, the more it's collective influence on our potential, which results in the infinity-squared I suggesting in the OP.

I've not seen this question posed before, and I've approached the question from different perspectives yielding different answers. What is the difference in gravitational potential from here on Earth to zero potential (the hypothetical potential of an empty universe)? From a mathematical standpoint, it seems to be infinitely negative. The escape velocity from a 1D infinite length rod drops off at 1/r, and so if gravity is X at the rod, it is 1/2x at twice the radius of the rod. The series ∑ 1/n does not converge. With a 2D infinite sheet, gravity does not fall off at all with distance, and the series ∑ n certainly does not converge. All these abstract cases have infinite gravitational depth. The universe on the other hand is a 3D uniform distribution of matter at a current density of around 6 protons per cubic meter. Imagine we choose a random orientation for a plane passing through Earth and all mass on one side of that plane is put on the other side where its reflection appears. This does not change the potential at Earth one big since all matter is at the same distance it was before. But now there is infinite gravity (weight) at the plane, and it doesn't drop off with altitude. Hence the absolute depth of anywhere being infinitely negative. There doesn't seem to be an event horizon involved in any of the cases above since there's no altitude where some finite escape velocity exists. Is my argument sound? I can think of a couple different ways to counter it: 1) Gravitational potential is only a function of the mass within the visible universe, a mass that is continuously growing as the visible universe encompasses new material, but a depth that perhaps is lessening due to the reduction in density over time. This approach implies that gravity (as opposed to gravitational waves) 'travels' and therefore the mass outside the visible universe does not contribute to Earth's gravitational potential. 2) I see arguments against the big bang citing that it violates the conservation of energy with all this insane energy density coming from nowhere. But if everything is at -infinite potential, every gram of mass actually has infinitely negative PE and only finite positive energy, so the question becomes: "If energy is conserved, where did all the energy go? Why is it so negative?". If this argument holds water, and I'm not sure it does because we have zero evidence of a different energy level from whatever precipitated the big bang, then the negative potential can probably be computed from whatever is needed to exactly cancel all the positive energy (mostly dark energy I'd imagine) we can find.

The dandelion in my front yard is an atheist. It doesn't believe the Earth is flat either. It's not exactly a remarkable claim to say something lacks a given belief, or for that matter, the capability of any belief.

Indeed. A pair of plumb bobs will not be parallel on Earth, but will be in an accelerating ship. In the inertial case, a plumb-bob in the no-gravity case will not point anywhere, but off-center in an orbiting space station, they will. So there are very much differences. The most basic test: Create a 3D arrangement with 4 balls (stationary relative to our small orbiting lab) arranged in a tetrahedron (in a vacuum so air currents don't move them around). The movement of the balls will show the direction of the source of gravity, or at least the axis of it.

There are still tidal effects with acceleration. An accelerometer at the front of a rockets reads less than one at the rear. The difference is negligible for the tiny acceleration of our rockets, but if you really jacked the g forces and made the rocket long (and strong) enough, the figures would be very different. Yes, the air moves to the rear, just like helium balloons tend to move to the front of a car when it is accelerating. If the accleration acts on all particles of the ship (say due to a large mass passing in front of it), then the passengers will feel no acceleration at all, only tidal effects at best. Alternatively one could put the people in a weighless situation like under water. That makes you weightless on Earth despite the 1g acceleration, and thus you'd be fairly weightless under this insane acceleration as well. The danger then would be from the bends, and not so much from being bent.

I was speaking of the first trial where the vote went straight down party lines.

The question doesn't seem to be a scientific one on the surface, but rather a philosophical one. He's asking the wrong people. It is akin to asking if the combustion of a candle can continue after the candle goes out. Can a process continue after the cessation of the process? Bufofrog gave a great reply to that. If 'human consciousness' is defined/modeled in a way outside of methodological naturalism, then it outside of the methodology of modern science. Still, I am of the opinion that it can be treated as a black box and essentially reduced to the candle case.

Like the last impeachment trial, there seemed to be a complete lack of correlation between the outcome and the evidence presented. The crime upon which the vote was based was the crime of belonging to the minority party, and Trump was rightfully acquitted of that. They've threatened, before the inauguration even, to impeach Biden as soon as they could, not for any crime other than again, being a member of the minority party. Those plans have been sidelined since Biden is no longer guilty of that crime, at least not for the next 2 years. I am crushed by the fact that such matters are not decided by fact or evidence at all. Not a single member on either side seems to have based their vote on evidence. The country seems rightfully doomed as long as this path continues. Impeachment trials should be judged by impartial people without biased ties to one side or the other. Such people are pretty much impossible to find these days.

Even as a pre-teen I wondered these questions about the six million dollar man. Here he can lift a truck with this bionic arm, but no explanation as to how that force gets transferred through his torso to the bionic legs below. He'd need an I-beam from shoulder to hips to do that, and said beam would prevent any ability to move like a normal human. The arm wrestling thing (6 vs. 7 million dollar man) had similar issues. From where comes the reaction force to this theoretical insane pressure/torque between the two guys? I was a kid and couldn't handle the blatant disregard for physics suggested. Point is, you can make the arm as fictionally strong as you want and the flesh shoulder connection is still going to limit what you can do with it. A pro weight lifter can exert incredible stress on those shoulders, and his bones are not appreciably stronger than mine, but the muscles and tendons and such are, so the answer lies there, as described by the prior posters.

But the sister cells are just as old. Excepting cells that are manufactured (*), all bad (damaged, stressed) cells are replaced by mitosis of the remaining ones, all of which are essentially as old as you are. Maybe I'm wrong about that. Hardly an expert here. The DNA is also replicated this way, not manufactured from scratch, so all the DNA is effectively as old as you are,. Neurons can't just split since their connections cannot be reproduced, so they're intended to exist without replacement after their initial allotment is complete some months after birth. * Blood is a nice example of manufactured cells. Red blood contains no DNA and cannot reproduce by mitosis. They're short lived (1/3 year?) and manufactured continuously by non-blood cells.

It's not a waste of time for the reasons posted above. You must realize the reason for the stance, which might be (as mentioned above) to promote critical thinking as opposed to just assuming the answer you've been taught. It also might just be to push people's buttons, in which case engaging is considered 'feeding the troll'. The moon thing seem unnecessarily complicated and dependent on how one orients a camera. How about the fact that I can be talking to somebody and one of us in in daylight (or can see the moon at all) and the other not. If Earth were flat, it would be daylight everywhere or nowhere. Dusk would be simultaneous everywhere. The sun would shine as much at the poles in winter as at the equator. Still, it is an interesting exercise. Suppose it is the year 1400 and you cannot get to the poles to show how dark it is there, and cannot talk to somebody on another continent to compare daylight. But you do have sextants and surveying equipment and such. How do you demonstrate the Earth is round? How do you measure it? Columbus was a BS artist and convinced the science advisors to the king of Portugal that the Earth was smaller than everybody knew it was. He had a hard time funding his venture not because nobody believed the Earth was round, but rather because everybody knew it was too large to make the trip. Columbus knew that, but wasn't really looking for the Indies.

Entanglement conveys no information. The sources of this pop article seem not to know that. Saplakoglu writes: It just doesn't work like this. A pair of particles unmeasured are not meaningfully in any state at all. If measured, they're not entangled. Some logical fails follow: No, it is not at all like placing 100 coins with 50/50 mix. That implies a measurement already taken. It's more like having 100 unknown coins and measuring 99 of them gives zero clue as to what the last one will be. Entanglement is like slicing 100 coins in half and sending the 100 halves to Pluto. Now if you count the halves here on Earth, you know what the Pluto guy will count if he ever looks at them. Nevertheless, the Pluto guy will have no idea what the last one will be if he hasn't received a message from Earth about the expected totals. I'm saying that either this 'Vuletić and his team' are complete fools, or their suggestions are being completely misrepresented by this Saplakoglu pop-science article writer. What I suspect is going on is having 50 coins split in half and all put on the table. Then, without measuring any of them, you know ahead of time that it's a 50/50 split. Nobody is carrying any of the coins elsewhere, and somehow having them entangled in pairs like that makes some kind of measurement more stable on average, thus allowing construction of a better clock. I'm guessing. The author of the article doesn't seem to comprehend the concepts involved.

Sounds like a stroboscopic effect. Have you tried it in natural or incandescent light? A spinning ring/disk will not reverse direction, but the spin goes anti-clockwise and the precession of the primary axis turns clockwise and the latter becomes more noticeable as the spin flattens.

If the cube is floating (not resting on anything), then it must displace its mass in water (just like a floating boat displaces its mass in water). When it melts, it still displaces its mass in water so no change in water level. All floating ice has about 10% of its volume above the surface since that's the density difference. If it is resting on the bottom of the glass, some of the weight is supported by the glass and not water, so the water level would be low and would rise as the ice melts. This rise ends once the ice stops resting on anything. If the ice is held under the water (by a lid on the glass say), then the water level will lower as it melts until the ice stops touching the lid.

To correct myself, it would depend on if the ice is floating or resting on the bottom or sides of the container. I had assumed floating.

Archimedes says it stays the same. So when the Titanic sinks, does the level of water increase or decrease? At what point in the process does this occur?

There's eternal inflation theory in all its variants which suggest that inflation never ends but forms fractal regions where inflation ceases thus forming bubbles that can be described as 'universes' with varying properties (different physical laws, constants, numbers of dimensions, etc.). In such a model, the universes don't 'disappear' since they're all bounded by inflation still going on. The model does not posit an initial condition for the inflation itself, so an infinite 'past' (if such a word is meaningful there) is not off the table. The 'theory' is an excellent counter to the fine-tuning argument since these bubbles of every conceivable tuning are all inevitable. I put 'theory' in quotes because lacking any empirical predictions (the fine-tuning thing isn't one??), it can be argued that it doesn't meet the definition of a theory.