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Re: Science and Astronomy Questions

07 May 2023 02:58

This is an interesting read and topic!
I think you're asking though if a slower than light ship using a warp bubble could escape by having some effect on the horizon.
Yes.  It's not really about speed, either, but if given the ability to warp whether you can manipulate the event horizon.  What you write makes sense.  A better question is whether through warping you can dodge the singularity.
That upward distortion isn't like a region of antigravity or a white hole though -- we can see the arrows still point towards the black hole through this region, and have very high magnitude. A test particle released in this region would quickly fall into the merged black holes. But the warping of spacetime is obviously very different from normal. If the usual downward curve means that there is more distance between nearby points in space than you expected, an upward curve means there is less.
My thinking was that since the distant observer sees things slow down the more downward the distortion is, the opposite would be observed where the distortion is upward, things would appear to speed up, and since the speed is already near light speed, it would give apparent FTL by this thinking.
At a distance of 1000km (just outside of the final orbit they made), the waves carried a strain of about 1 part in 100. That would stretch and squeeze your body in alternating directions by several centimeters, multiple times in much less than a second. I'm not sure what that would feel like, but I doubt it would be pleasant, or even survivable!
What it takes for a gravitational wave to become lethal sounds a bit like what it takes neutrino radiation to be lethal.  It's not difficult to picture what a steep gravity gradient would do to the body, but a steep spacetime gradient?  Since this would happen so fast, I'm not sure if there will be effects at the macro level.
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Re: Science and Astronomy Questions

16 May 2023 14:48

What if Pluto was truly the last object out there? Like if it was the only thing out beyond neptune along with it's moons.
Do you mean the last object in existence or just our solar system? If we didn’t find Pluto’s siblings and the Kuiper Belt, nothing would’ve changed. It still would’ve been an oddball, but now we know it has a family of other planets it orbits with.
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Re: Science and Astronomy Questions

01 Jun 2023 19:08

The forums are so silent these days, so here's a challenge question, something I certainly struggle to wrap my head around.  For a distant observer it will take an infinite time to see an astronaut fall into a black hole.  But it will take a finite time for the same observer to see the black hole evaporate due to Hawking radiation, i.e. before the astronaut crosses the event horizon.  Black hole information paradox solved?  But how then explain the paradox that the astronaut will experience Hawking radiation at a normal rate and not experience that the event horizon slips away?
I think the black hole information paradox has already been solved, although the "solution" is still being investigated.  What it boils down to is that black holes don't evaporate because that would violate quantum mechanics central tenet that information cannot be destroyed-- it just gets scrambled and an extra copy is made, so a black hole is like a quantum copier.

The information isn't destroyed, it's just extremely difficult to unentangle it!  The information cannot be destroyed because that violates a central theorem of quantum mechanics.

I also like the idea of being swept up into another universe, especially with a Kerr black hole.
 
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Re: Science and Astronomy Questions

01 Jun 2023 19:20

The slowness of black hole evaporation really is astonishing. Even though I already understood stood as much, I was still taken aback by how small the correction to the event horizon size because of it turns out to be. I figured it would at least be, like, a micrometer or something, which you could say is significant enough to be real but still small enough to ignore. Less than a Planck length is ridiculous. :P

Aside: a similar thing happens with how solar wind modifies planetary orbits. The wind constantly pushes outwards, so shouldn't the orbits expand? Again it's one of those things that turns out to be negligible. Since it pushes radially outward, it doesn't give the planet orbital energy. Instead, the pressure from solar wind acts like a constant centrifugal force, which is like slightly decreasing the Sun's effective gravitational force. This makes the circular orbit at a given orbital speed slightly larger than you'd expect, but it does not grow over time. For Earth, it raises the orbit by about 1 micrometer. 

Let's say that Alcubierre drive shipships are possible.  Could they go through a black hole by bending away the event horizon?
If the ship could go faster than light, absolutely. Not by bending the horizon away, but by following a spacelike path, which exits its own future light cone. At the event horizon, the outgoing edge of the light cone is parallel to the horizon, and tilted more inward the further in you go, so a greater FTL speed is needed to get closer to the center and emerge again. When would the ship emerge, according to an external observer, I'm not sure has an invariant answer. But this scenario of course introduces all sorts of paradoxes even without a black hole involved.

I think you're asking though if a slower than light ship using a warp bubble could escape by having some effect on the horizon. My current thinking leans against it, for probably an unintuitive reason. The reason is that the curvature of spacetime near the horizon is small, and unrelated to the existence of the horizon. If we imagine an arbitrarily large black hole and a ship a small distance inside it, the local environment of the ship is no different than being in flat spacetime far from any black hole at all. But the horizon now behaves the same way as a receding flash of light. Even if you accelerate to arbitrarily large fractions of the speed of light, whether by using rockets or by a slower than light warp bubble, that horizon remains ahead of you (even getting further away), in the same way as if you were trying to catch up to a light flash.

That answer might be confusing, because isn't curvature the very thing that "causes gravity" by "telling matter how to move" in the first place? That's right, but in the sense of telling how nearby particles will accelerate relative to one another (tidal forces). Otherwise, the only thing any particle does at the local level is "move straight", i.e. along a geodesic, in spacetime. It is the global geometry rather than local curvature that constrains geodesics to move more inward.

at 0:50 we see an extreme opposite warping.  Does this imply that it's possible to ride these waves for a split second to achieve faster-than-light travel as seen for a distant observer?

This is pretty neat. The short answer is no, but there's a lot of information to digest here, so let's cover each part of what the video is showing.

The colors represent the magnitude of time dilation. Arrows represent the direction and magnitude of acceleration (as seen by a stationary observer at that location). The height of the sheet represents a measure of the warping of space. What measure, exactly? I'm pretty sure it is the spatial part of the metric, which is the most common way to create this visual (also called an embedding diagram) for a black hole. 

The Schwarzchild metric for a static, non-spinning black hole in the time and radial directions is 

Image

The first term in parentheses gives you the time dilation, while the second term tells you how much the space has been distorted. This is not the curvature in the sense of tidal forces, but rather in the sense of how much the proper distance (which you would measure with a ruler) between two points in the radial direction is different from what you would expect if you were in flat spacetime. See my earlier post here for more explanation and a thought experiment you could imagine doing around the Earth, in order to interpret this type of spatial distortion.

For a single, non-spinning black hole, this distortion changes with distance in the same way as the time dilation does (those two metric components are just negative inverses of each other), and the spatial distortion is typically plotted with a minus sign so that it looks like a funnel. For a black hole merger, some regions get the spatial component distorted the other way (upwards in the diagram), even while the time dilation is still very strong so the colors are red. That upward distortion isn't like a region of antigravity or a white hole though -- we can see the arrows still point towards the black hole through this region, and have very high magnitude. A test particle released in this region would quickly fall into the merged black holes. But the warping of spacetime is obviously very different from normal. If the usual downward curve means that there is more distance between nearby points in space than you expected, an upward curve means there is less. Space is, in a sense, more compressed in the radial direction than you would have expected. (I expect it is more stretched out in the perpendicular directions.) The large magnitude also implies large tidal forces -- this is where the gravitational waves have the greatest effect.

It's fun to do a quick calculation to see how violent the gravitational waves are this close to a merger. The fractional amount something is stretched and squeezed by the wave (called the strain) is inversely proportional to the distance from the wave source (whereas the energy of the wave drops off with the inverse square law.) At Earth, the strain was about 1 part in 10^21, and the source was about 400 Mpc away (give or take about 150 Mpc.) Each black hole was about 30 solar masses, or about 180 km in diameter. 

If we ignore the fact that the regular tidal forces are already lethal this close to black holes of this size, the gravitational waves are probably lethal, as well. At a distance of 1000km (just outside of the final orbit they made), the waves carried a strain of about 1 part in 100. That would stretch and squeeze your body in alternating directions by several centimeters, multiple times in much less than a second. I'm not sure what that would feel like, but I doubt it would be pleasant, or even survivable!
Question Wat, for a spinning Kerr black hole with a ring singularity, would it be less lethal and perhaps even navigable because of that spinning motion?
 
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Re: Science and Astronomy Questions

02 Jun 2023 15:28

I think the black hole information paradox has already been solved, although the "solution" is still being investigated.  What it boils down to is that black holes don't evaporate because that would violate quantum mechanics central tenet that information cannot be destroyed
No, black holes do evaporate. They have both energy and entropy, and any object with both properties will have an effective temperature and therefore radiate. (See my post here for a walkthrough of why this is true and how to derive the temperature and emission rate.) If they didn't evaporate this would violate statistical mechanics.

Yes, it would violate the principle that information cannot be destroyed if black holes evaporated but the information didn't get back out somehow. The solution is not that they don't radiate, but that the information is encoded into the radiation -- just in a highly scrambled way. It was known for a while that the solution should be some form of this (because the proof for black hole evaporation is very strong), but it took a very long time for physicists to work out the details of how the information is encoded.

it just gets scrambled and an extra copy is made, so a black hole is like a quantum copier.

Not correct, either. That would violate the no-cloning theorem. There is no sense in which a copy is being made because no observer could measure them. If it helps, remember that for outside observers, the interior of a black hole doesn't exist (no events in the interior can be known to them). Likewise for observers who fall into the hole, the evaporation is not accelerated, nor do they experience themselves evaporating.
 
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Re: Science and Astronomy Questions

02 Jun 2023 16:26

Question Wat, for a spinning Kerr black hole with a ring singularity, would it be less lethal and perhaps even navigable because of that spinning motion?
In the idealized mathematical extension for a Kerr black hole, sure, but in reality, no. You would be destroyed by the mass inflation singularity near the inner event horizon before meeting the ring singularity, but in nature there is no ring singularity, anyway.
 
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Re: Science and Astronomy Questions

02 Jun 2023 18:44

I think the black hole information paradox has already been solved, although the "solution" is still being investigated.  What it boils down to is that black holes don't evaporate because that would violate quantum mechanics central tenet that information cannot be destroyed
No, black holes do evaporate. They have both energy and entropy, and any object with both properties will have an effective temperature and therefore radiate. (See my post here for a walkthrough of why this is true and how to derive the temperature and emission rate.) If they didn't evaporate this would violate statistical mechanics.

Yes, it would violate the principle that information cannot be destroyed if black holes evaporated but the information didn't get back out somehow. The solution is not that they don't radiate, but that the information is encoded into the radiation -- just in a highly scrambled way. It was known for a while that the solution should be some form of this (because the proof for black hole evaporation is very strong), but it took a very long time for physicists to work out the details of how the information is encoded.

it just gets scrambled and an extra copy is made, so a black hole is like a quantum copier.

Not correct, either. That would violate the no-cloning theorem. There is no sense in which a copy is being made because no observer could measure them. If it helps, remember that for outside observers, the interior of a black hole doesn't exist (no events in the interior can be known to them). Likewise for observers who fall into the hole, the evaporation is not accelerated, nor do they experience themselves evaporating.
Wow this is very interesting-- from your other post I think you implied that it would be possible to unscramble the information but it's very impractical to do so, Wat?  Is there a way to calculate how much energy it would take to unscramble a given amount of information?

Also, can black holes be looked at as "recorders"-- that is they record the entire history of the universe and given enough time (the whole lifetime of a universe) they will contain all the information of the universe?
 
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Re: Science and Astronomy Questions

02 Jun 2023 18:46

Question Wat, for a spinning Kerr black hole with a ring singularity, would it be less lethal and perhaps even navigable because of that spinning motion?
In the idealized mathematical extension for a Kerr black hole, sure, but in reality, no. You would be destroyed by the mass inflation singularity near the inner event horizon before meeting the ring singularity, but in nature there is no ring singularity, anyway.
Wat, I think we discussed this before-- there not being a ring singularity in nature, is that because of the infalling matter and energy  into the black hole disrupting what could only exist under "perfect" conditions?
 
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Re: Science and Astronomy Questions

02 Jun 2023 23:05

Wow this is very interesting-- from your other post I think you implied that it would be possible to unscramble the information but it's very impractical to do so, Wat?  Is there a way to calculate how much energy it would take to unscramble a given amount of information?
Very impractical, indeed. The key idea is that any process (even an artificial one) must increase the entropy of the universe (the system + its environment), or at least keep it the same. A black hole is the maximal entropy state of any system of particles, so to decode the information that created the black hole, you would need an amount of processing that would collapse the system into a new black hole. In other words, you can't do it. 

The best you can do is get a sort of "partial information" from the statistical correlations between different photons of the radiation. If you analyze, for example, the polarization directions of a very large number of those photons, you may be able to tell that there are correlations between them that you would not expect to occur by random chance from a purely thermal blackbody radiation. But you would not be able to say "aha, this black hole was created from a collapsing star, but that black hole over there was created by collapsing a bunch of apples."

Also, can black holes be looked at as "recorders"-- that is they record the entire history of the universe and given enough time (the whole lifetime of a universe) they will contain all the information of the universe?

Sort of but also not really. Think of how telescopes work -- if you want to make an image of a distant planet, your telescope has to have a sufficient aperture size. The larger the aperture, the better the resolution of the image you get. A black hole is an extremely compact object for its mass -- the most compact possible. It's only intersecting an extremely small portion of the wave fronts from any object or event in the universe. So most of the information does not go into the black holes. (The formation of a black hole does, however, maximize the entropy of everything that directly went into creating it.)

So there are essentially two main components to the information and entropy content of the universe. The first is in the arrangement of particles of matter, and the second is in the arrangement and energy distribution of particles of radiation (mostly photons and neutrinos). As the universe ages, supermassive black holes become the most significant contribution to the entropy of the former, while the CMB is the most significant contribution for the latter.
 
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Re: Science and Astronomy Questions

03 Jun 2023 03:37

If there is no way to unscramble the information, how is that different from information not lost?

Like, the idiot's super efficient compression algorithm for a binary stream would be to count the number of 1's and 0's, and leave it to the decoder to arrange them back in the proper order.  In a sense, nothing is lost, every 1 and 0 is accounted for, but clearly all information is truly forever lost.
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Re: Science and Astronomy Questions

03 Jun 2023 05:55

If there is no way to unscramble the information, how is that different from information not lost?
The paradox was that if Hawking radiation is purely thermal/blackbody radiation, there would be no information about what went into the black hole hidden in that radiation at all. But the information does go into the Hawking radiation, in theory it is all accounted for, while in practice you can unscramble different portions of it depending on what you choose to measure. This is quite different from the information being trapped on or in the black hole or being destroyed.
 
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Re: Science and Astronomy Questions

03 Jun 2023 17:38

Wow this is very interesting-- from your other post I think you implied that it would be possible to unscramble the information but it's very impractical to do so, Wat?  Is there a way to calculate how much energy it would take to unscramble a given amount of information?
Very impractical, indeed. The key idea is that any process (even an artificial one) must increase the entropy of the universe (the system + its environment), or at least keep it the same. A black hole is the maximal entropy state of any system of particles, so to decode the information that created the black hole, you would need an amount of processing that would collapse the system into a new black hole. In other words, you can't do it. 

The best you can do is get a sort of "partial information" from the statistical correlations between different photons of the radiation. If you analyze, for example, the polarization directions of a very large number of those photons, you may be able to tell that there are correlations between them that you would not expect to occur by random chance from a purely thermal blackbody radiation. But you would not be able to say "aha, this black hole was created from a collapsing star, but that black hole over there was created by collapsing a bunch of apples."

Also, can black holes be looked at as "recorders"-- that is they record the entire history of the universe and given enough time (the whole lifetime of a universe) they will contain all the information of the universe?

Sort of but also not really. Think of how telescopes work -- if you want to make an image of a distant planet, your telescope has to have a sufficient aperture size. The larger the aperture, the better the resolution of the image you get. A black hole is an extremely compact object for its mass -- the most compact possible. It's only intersecting an extremely small portion of the wave fronts from any object or event in the universe. So most of the information does not go into the black holes. (The formation of a black hole does, however, maximize the entropy of everything that directly went into creating it.)

So there are essentially two main components to the information and entropy content of the universe. The first is in the arrangement of particles of matter, and the second is in the arrangement and energy distribution of particles of radiation (mostly photons and neutrinos). As the universe ages, supermassive black holes become the most significant contribution to the entropy of the former, while the CMB is the most significant contribution for the latter.
Thanks Wat-- so the idea of being able to reproduce some of the information that fell into a black hole into its original form sounds like it would be extremely unlikely, the most we can do is perhaps be able to say what might have fallen into it?  Could we ever achieve a level of precision where we could tell if a person (or a spaceship) fell into a black hole, even if we could not recreate that person or space ship?

Thanks for mentioning supermassive black holes-- my other question to you would be about the least lethal black holes, which would be supermassive black holes from what I have read?  Is that because smaller black holes do a much steeper warping of spacetime while supermassive black holes do a much "gentler" warping of spacetime so that an infalling astronaut can survive for much longer inside a supermassive black hole?
 
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Re: Science and Astronomy Questions

04 Jun 2023 01:54



Thanks Wat-- so the idea of being able to reproduce some of the information that fell into a black hole into its original form sounds like it would be extremely unlikely, the most we can do is perhaps be able to say what might have fallen into it?  Could we ever achieve a level of precision where we could tell if a person (or a spaceship) fell into a black hole, even if we could not recreate that person or space ship?
In practical terms, reconstructing a specific object that fell into the black hole is not much easier. The problem is really that the information has been scrambled to the highest degree possible. The information about a person or spaceship that fell into it is encoded into all of the Hawking radiation that will ever be emitted by the black hole (which will also be in all directions), so you still have to gather and analyze a very large quantity of data over a very long period of time even if you only want to learn details about a specific object that fell into it.

Thanks for mentioning supermassive black holes-- my other question to you would be about the least lethal black holes, which would be supermassive black holes from what I have read?  Is that because smaller black holes do a much steeper warping of spacetime while supermassive black holes do a much "gentler" warping of spacetime so that an infalling astronaut can survive for much longer inside a supermassive black hole?
Basically, yes. The thing that's lethal about gravity near a black hole is how quickly its strength changes between nearby locations (say your feet and head). This is called tidal force and it is exactly equivalent to spacetime curvature. A bigger black hole has more mass and more gravity, and the lethal range of its tidal forces is larger, too. But the size of the event horizon grows even more rapidly with mass. For stellar mass black holes the lethal range is much larger than the event horizon, while for supermassive black holes it is the horizon that is much larger.

An interesting fact is that if you fall into a black hole, the death by tidal forces happens at the same amount of time before meeting the singularity, regardless of how big the black hole is. It is approximately one tenth of a second. But the time you can experience between the horizon and singularity increases with the mass of the black hole. It's about a minute for SgrA*. About a day for M87*.
 
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Re: Science and Astronomy Questions

04 Jun 2023 04:44

So in a sense the information that is emitted from the black hole is also "spaghettified" in that it's emitted over a very long period of time and in all directions.  So this isn't like a geological fossil record where you look at a specific layer to analyze  like, say, the dinosaurs that existed in the Late Cretaceous right before they were exterminated by the K-T asteroid.

Thanks Wat, that explanation helped me to visualize how and why smaller black holes' lethal range extends beyond the event horizon because of how steep the spacetime curvature is around them.

This might get a little complicated, but if you have a spinning Kerr black hole with two horizons (the event horizon and the Cauchy horizon) does that change anything as far as how long you could survive before hitting the singularity?  Would you make it to the Cauchy horizon or would you die before that second horizon was reached?  Does it depend on the size of the Kerr black hole too?  I also wonder if an astronaut could make it to that second horizon before dying, would they know and would they experience any changes at the Cauchy horizon or just after they crossed it?
 
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Re: Science and Astronomy Questions

04 Jun 2023 07:37


This might get a little complicated, but if you have a spinning Kerr black hole with two horizons (the event horizon and the Cauchy horizon) does that change anything as far as how long you could survive before hitting the singularity?  Would you make it to the Cauchy horizon or would you die before that second horizon was reached?  Does it depend on the size of the Kerr black hole too?  I also wonder if an astronaut could make it to that second horizon before dying, would they know and would they experience any changes at the Cauchy horizon or just after they crossed it?
A little complicated, but still calculable. :) You might be surprised to learn that for the spinning Kerr black hole, the amount of time you experience in freefall from the horizon to the central singularity (or the Cauchy horizon, or whatever else happens to be lethal in the interior) is shorter than it is from the horizon to central singularity for a non-spinning Schwarzschild black hole. 

Part of the reason for this is simple: the size of the event horizon for a Kerr black hole is smaller, by up to a factor of 2 in the limit of maximum spin. But another part is more surprising: even if we imagine two astronauts jump into a spinning and a nonspinning black hole from the same distance away, the trip to the center of the spinning one is shorter.  If we imagine the two fall into their respective black holes from very far away, and they each start their watches when they pass within the radius 2GM/c^2 (this is the event horizon for the Schwarzchild black hole and the static limit for the Kerr black hole), then the one falling into the Kerr black hole will experience about 29% less time before reaching the center than the one falling into the Schwarzchild black hole.

There are a few ways to see why this is true. For a brute force method you could calculate the metric along a freefalling geodesic, to relate the change in radial coordinate to the change in proper time along the path. Another way is to look at the effective potential which describes the radial acceleration (again in terms of proper time). The potential becomes steeper near a spinning black hole for a freefalling plunge with no angular momentum. A third way requires no math at all: the spin of the black hole twists your trajectory in spacetime away from purely radial motion, and you gain angular motion even though you had no angular momentum. Your freefall path traverses more space, but ends at the same inevitable singularity event, and in relativity, a longer path in space between two events is a shorter path in spacetime, which means a shorter proper time experienced along the path.

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