Halc

Great. A cartoon eye. No, an electron microscope can only see things sitting still since it works effectively by touch, not light as implied by the eye. What they're probably detecting for electrons is some kind of charge detector like is used by a ground-fault detector in your bathroom outlet. Not sure if you can turn it on and off since it is a passive device. If the device takes no measurement (has no effect on the electron) 50% of the time, then 50% of the time the electron will reach the target with a simple pattern and the other times with an interference pattern. If the electrons are coming continuously, you'd see the pattern change from one to the other as the sensing device is function or not for whole seconds at a time. If they're using photons, I know a diagonal polarizing filter at the slits is enough to eliminate the interference pattern. You can't turn a polarizing filter on and off either, unless there is some really weird gadget that does this.

The 'device' can be the far wall on which the interference pattern appears, which isn't something that can be 'turned on and off' 50% of the time. Perhaps you have a specific device in mind that can meaningfully be turned on and off, and thus allowing a more specific answer. And yes, there being a human involved anywhere or not makes no difference. The vast majority of quantum measurements/collapses take place without any human being immediately aware of them. This is true even with experiments set up in labs by humans.

How about a galaxy 50 BLY that-away? Definitely mathematically expressible, but so is a perfect square. Neither is physically observable, at least not by us. It would be measurable ('observable' makes it sound like a life form is necessary) by something in that galaxy. Does that make a difference? A relativist would say it doesn't exist relative to Earth and v-v. Existence is a relation (not an objective property) in such a view, which is precisely the attraction of it. If you accept the principle of locality (no faster-than-light information transfer) in quantum physics, then it is a mistake to assert the specific distant galaxy exists at all. It leads to contradictions per Bell's theorem. That throws quite the wrench into the idea of objective existence. Side note: I agree that a route doesn't require my existence. My sister doesn't exist, and yet the route does. Of course, expressed as a relation, the route to the Milky Way doesn't exist to my sister, so go figure.

I can actually think of epistemological cases. The Egyptians of old were known for stamping out all mention of certain prior Pharaohs from the records. These were rarely entirely successful, but when they were, they did very much make them 'cease to having ever existed', at least from an epistemological standpoint. They very much have an ontological existence in history, but nobody can remember them anymore. Your memory (of this and that) very much once existed, and cannot cease to have ever existed. It just doesn't exist now. Same with history or Earth and our respective fathers, which have been erased from existence, but with no implication of having never existed. Nowhere did I say that any of these things might no longer exist. More explicitly, I meant that nothing that once existed can subsequently cease to have ever existed. Area54 seems to get my gist. Yes, it's a verb tense thing, not a deep point.

This is very much a philosophical topic which needs proper definitions to communicate clearly. If a brain is changed while being formed, it's still the same brain, just altered from some prior state. Putting a scratch in my car doesn't make it not-my-car. You change ever second of every day, and yet you're still you. A static unchanging thing cannot be alive. By definition, nothing can cease to ever exist. If it ever existed, then that’s that. It’s not something that can be ‘changed’. I can bring about a premature cessation to the duration of its existence, but that doesn’t make it having never existed. You’re asking what changes the identity of the consciousness? That, being essentially a process, doesn’t necessarily have an identity. You having consciousness is like a candle having a flame. Combustion doesn’t really have identity. I can use a candle to light another one. Is it the same combustion, or a different one? What if I blow out the original candle and relight it from the 2nd one. Now is it the same combustion or a new one? The Olympic torch is about the only example I can think of where humans worry about the identity of the combustion. In other words, you need to backtrack and spell out what you think defines your identity. If it’s stream of consciousness (one that is interrupted every night?), then the ‘memory’ answer (see Bufofrog’s reply) works for a while, but then what if that memory can be duplicated or replaced? It’s only the lack of our witnessing that sort of thing going on that allows us to function with such a definition. Again, if it was made, in the womb or otherwise, then it exists and cannot be in a state of not-ever-going-to-exist. The process mostly goes on there, but a brain without the rest of the body is about as unconscious as can be, so I’d be reluctant to box it in that tightly. I’d say that my consciousness extends well beyond my body into the world that is part of my experience. Now this isn’t a case of altering an existing thing. It’s like saying that if my Honda was instead a Lexus, it would still be the same car (because it’s mine?). Small change, same ‘parents’, but different factory. Hard to argue that it’s the same car, as opposed to the same car being painted blue or green near the end of the assembly line. It seems completely implausible that a non-existent entity can experience somebody else. There’d be no you to experience this other person. They’d experience themselves by definition. I think you envision an immaterial entity that experiences your body. That’s pretty much a religious stance, sorely in need of clarification, such as what role is played by the various parts. What holds memory, the experiencer or the brain? What makes the decisions? Who’s in control? Without such elementary designations, there are too many permutations to comment on them all.

Despite the wording above, I agree that dark energy isn't an actual force, but dark energy will begin to increase the proper separation between two relatively stationary objects, and that translates to a sort of kinetic energy which could hypothetically be harnessed to do work (imagine a seriously long thin string between them). Gravity will also separate the pair of objects when placed in the deep void * (regions of negative mass density relative to the mean), and gravity isn't an actual force either, at least not under relativity. Like gravity, I think dark energy can be expressed as a force only when considered in Newtonian terms, and it doesn't make much sense there since Newtonian physics has no concept of expanding space. From a geometric standpoint, spacetime with expansion but without gravity and without dark energy is effectively indistinguishable from Minkowskian spacetime. There would be no event horizon since light would eventually reach us from galaxies of any distance and any recession speed. That horizon is only there because of the effects of dark energy. * One of the nearest such regions is the Dipole Repeller which seems to expel all the galaxies in its vicinity. This shows that in an otherwise uniform distribution of matter, the absence of matter in an isolated pocket of that distribution will have a repulsive gravitational effect on all the nearby surrounding masses. Right. The CMB would not appear isotropic from Y's PoV, and from this Y could measure his peculiar velocity of 70 km/sec towards X. I couldn't quite parse that, but by stationary relative to each other, I explicitly qualified that to mean 'constant proper separation', meaning a string between the two would not break or stretch.

The question is, why do you think they do? 'Space' isn't something that can apply a friction-like force and begin accelerating an object. Assume we have two pebbles X and Y that are a megaparsec apart, and they're way out in the void between galaxies. Now a megaparsec is a long way. You can fit at least a couple dozen galaxies like ours side by side on one. Nearby galaxies are going to exert tidal forces on our pebbles drawing them apart, so we're going to ignore gravity and also dark energy and just concentrate on the expansion. Pebble X is stationary relative to the cosmological frame, that is, the CMB appears isotropic from X's PoV. It is said to have a peculiar velocity of zero. Y is stationary relative to X, that is, the proper separation between X and Y is constant at 1 megaparsec. Since 'space' is expanding at a rate of 70 m/sec/mpc, Y must have a peculiar velocity of 70 m/sec towards X which exactly cancels the space expansion. There's no reason to think it will lose this velocity per Newtons first law. If expansion exerted a force on it, that would be akin to friction with some kind of aether, and that would drag any peculiar motion down to zero over time, which would have all orbiting things (going around a galaxy especially) lose their orbital motion and spiral into the centers. Angular momentum would not be preserved.

Earth is not moving in some direction due to expansion. It is moving in some direction (relative to say the cosmological frame) because net forces on Earth or the materials from which it is composed have cumulated in its present velocity/momentum. Our velocity (relative to the frame of your choice) has changed by over 400 km/sec since the Spinosaurus was around, so those external forces are not insignificant. In other words, if I put two objects in space separated by say a megaparsec, that are stationary relative to each other and not subject to external forces like gravity from nearby objects, then under just expansion alone, they will remain forever the same distance apart. Dark energy is probably the only actual force (that is not expansion itself) that will push the two objects apart over time. This is not expansion, but the acceleration of expansion, and yes, that does require force and energy and would affect said mutually stationary things.

The author admits in the intro that an observer does not see the history of the universe. That question is discussed on stack exchange here which admittedly discusses the simplified case of a Schwarzschild black hole. This image from there: This clearly shows a finite history of some outside object (dotted worldline) seen by the blue worldline of our infalling observer, Cauchy horizon or not. Kino's Kruskal diagram shows the same sort of thing. The Cauchy horizon for a charged or rotating BH seems to have special treatment in that the spacetime beyond it isn't 'smooth', but I still don't know how the history of the universe could be in the causal path of that region. The wiki page on a charged black hole makes references to the 2nd horizon. No nice diagrams like above ☹️ and the ones in the paper don't seem to demonstrate the claim to my untrained understanding. It seems that sufficient charge can prevent any mass from collapsing into a black hole (layman guess: because the EM repulsion is greater than the gravity attraction?), and perhaps below said Cauchy horizon, it prevents the singularity from forming, resulting in a chaotic fixed 'density' with no actual singularity? Just guessing here, but such a construct could be maintained indefinitely. This does not seem to be what the author above is saying, since he talks of a point p where the observer crosses this horizon (an event) that has the whole universe in its causal history, not the collective set of events inside this horizon. I'm obviously out of my depth here. Still, Reissner-Nordström and Kerr black holes (and Schwarzschild) are not models of real black holes since none of those solutions include Hawking radiation. Any BH has a finite life, and any events outside the past light cone of the final evaporation event will not be in the causal past of any event within the black hole.

I was going to jump on that. +1 for catching it. In my reply above your post, I mentioned the other companions all around you falling with you. They don't disappear from your sight. They're not 'below' you, they trace a worldline near your worldline and there is no way light from one nearby worldline doesn't reach the other, regardless of the direction in which this companion appears in relation to you. The usual local laws of SR very much do apply here per the equivalence principle. The falling observer is very much stationary in his own reference frame. That frame simply doesn't correspond to any inertial reference frame relative to a distant outside frame of reference, say the inertial frame in which the center of mass of the BH is stationary. This is not a contradiction, just an abstract consequence that no outside inertial coordinate system foliates the events inside a black hole. That in no way implies that the events inside a black hole cannot be locally mapped with an inertial coordinate system. The falling observer is stationary in his own frame and sees the objects all around him in any direction. If not, he'd not see his feet or hands.

That was the question in the OP, yes, and it has been answered. The feet that he sees are the feet from a few nanoseconds ago (falling frame), same as the feet you see now are not the present feet, but the feet in the past. Those feet were outside the EH when the light was emitted from them. I've said as much since my first reply in this thread. A body does not experience itself in the present since it takes time for any information to travel from say feet to head. So there's no anomaly in spacetime from the PoV of the falling guy. It's all normal physics to him, and he has no awareness of having crossed over unless he has a computer with him that informed him of the situation, since it is a calculable thing. The view outside the window also doesn't change appreciably. There is a section of the normal universe that occupies a percentage of his view, with the rest of the view black except for other sources of light falling in with him, such as his feet. If 50 guys all fell in sort of with each other, not all at the same time or place, they'd all still be able to see each other at all times, but tidal effects would eventually alter their distribution. It is red shifted only from the perspective of something hovering outside. Our infalling guy is in a completely different frame of reference in which no red-shift is observed at all, at least not until the spaghettification begins to occur. Per the equivalence principle, he cannot perform a test that demonstrates when the EH is crossed. GR rests on that principle and would collapse if the descriptions you paint actually occurred. My feet appear to me to be more red shifted here at my desk than would be seen by our guy falling in. This is because the falling guy is inertial and I am not.

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.