My understanding is that for extremely large black holes the tidal forces are negligible near the event horizon. So things should function pretty much the same other than you can't move in reverse and get out.
If two rockets fall past the horizon at the same time, one accelerating forward towards the singularity, and the other accelerating backwards away from the singularity, then shouldn't the distance between the rockets increase, even though they are both moving inexorably forward?
If the tidal forces are low, I'd assume that my muscles are still strong enough to "slow down my hand enough" to move it above my head.
The relevant quantities are the curvature scalars near the horizon, and for a sizable black hole they are small there. As an example, consider the Kretschmann scalar (KS). The KS is the sum of the squares of all components of a tensor. In Schwarzschild spacetime KS looks like R_{\mu\nu\lambda\rho}R^{\mu\nu\lambda\rho} = (48 G^2M^2)/(c^4r^6), where R is the Riemann curvature tensor, and we can safely set G=1 and c=1 so (48 M^2)/r^6. In this setting, KS is proportional to the spacetime curvature. At r = 2M, the Schwarzschild radius, the number becomes very small as we increase M, the black hole's mass. However, for any M at r = 0, the Kretschmann scalar diverges.
For a large-M black hole, there is "no drama" for a free-faller crossing the event horizon, as the KS gradient is tiny.
Since the crosser is in "no drama" free-fall he can raise his hands, toss a ball between his hands, throw things upwards above his head, and so forth. The important thing though is that all these motions are most easily thought of in his own local self-centred freely-falling frame of reference, and not against the global Schwarzschild coordinates. His local frame of coordinates is inexorably falling inwards. Objects moving outwards in his local frame are still moving inwards against the Schwarzschild coordinates.
You might compare with a non-freely-falling frame of reference. Your local East-North-Up (ENU) coordinates let you throw things upwards or eastwards, but in less-local coordinates your ENU frame of reference is on a spinning planet in free-fall through the solar system (and the solar system is in free-fall through the Milky Way, and the galaxy is in free-fall through the local group). That your local ENU is not a freely-falling set of coordinates does not change that the planet is in free-fall, and your local patch of coordinates is along for the ride.
A comparison here would be a long-running rocket engine imparting a ~ 10 m s^-1 acceleration to a plate you stand on. In space far from the black hole, you and the rocket engine would tend to move away from the black hole, but you'd be able to do things like juggle or jump up and down, and it'd feel like doing it on Earth's surface. This is a manifestation of the equivalence principle. Inside the horizon the rocket would still be accelerating the plate and you at ~ 10 m s^-1, but you, the plate, and the rocket would all be falling inwards.
Tidal forces are not the constraining factor - the transformation of space into a timeline property is. There is no out, no away direction. All paths lead to singularity. No particle can travel away from singularity .
Two rockets can diverge in distance, because one is slowing itself along the timeline space dimension toward singularity. If you are moving 1 m/s toward singularity, the fastest your hand can raise above your head is 1 m/s with infinite energy expenditure. The same goes for blood pumping to your head, electrical impulses to your brain, etc.
You can move away from a singularity once you are inside the event horizon. You just can’t achieve escape velocity anymore once you’re inside the event horizon.
After you pass the event horizon, all your possible paths become elliptical. That doesn’t mean all possible paths instantly point directly at the center.
This is not true. There are some special exceptions (rotating kerr ring singularities) but in general there is no 'upward' direction away from the singularity. Space becomes timelike. There is only forward, toward the singularity. You can expend energy and accelerate toward the singularity slower, but every particle within the event horizon can move only closer to the singularity. There is absolutely no moving away from the singularity. Full stop. If you think there is, you are misunderstanding something fundamental about the model.
> Space becomes timelike. There is only forward ...
No. It's a fanciful analogy on a particular family of coordinate charts, particuarly systems of coordinates which do not smoothly/regularly cross the horizon. The black hole interior is still part of a Lorentzian manifold, there is no change of the SO+(1,3) proper orthochronous Lorentz group symmetry at every point (other than spacetime points on the singularity). One can certainly draw worldlines on a variety of coordinate charts and add light-cones to them, and observe that the cones interior to the horizon all have their null surfaces intercept the singularity. However, there's lots of volume inside the interior light cones (and on the null surfaces) and nothing really constrains an arbitrary infaller's worldline, especially a timelike infaller, to a Schwarzschild-chart radial line (just as nothing requires arbitrary infallers to be confined to geodesic motion).
The interior segment of a Schwarzschild worldline in general can't backtrack in the r direction, but there are of course an infinity of elliptical trajectories which don't. (That is to say that all orbits across the horizon are plunging orbits; but one can also say that of large families of orbits that cross ISCO, which is outside the horizon).
A black hole with horizon angular momentum and general charges offer up different possibilities, as does the presence of any matter near (including interior to) the horizon (all of these also split the ISCO radius, move the apparent horizon, and may split the apparent and event horizons). The Schwarzschild solution of course is a non-spinning, chargeless, vacuum solution everywhere, and is maximally symmetrical, and is usually probed with a test particle. An astrophysical system like a magnetic black hole formed that passes through a jet from a companion pulsar, for example, does not neatly admit the Schwarzschild chart (and has no known exact analytical solution to the field equations). At least one such astrophysical binary is known (in NGC 1851 from TRAPUM/MeerKAT) (and if you don't immediately run away from A. Loeb papers like you should, he added his name to one that argues there are thousands of such systems in the galaxy centre near Sgr A*, which itself is now known to have strong magnetic fields (thanks to EHT's study of the polarized ring)).
No, not really. To boil it down to thinner text, and to focus on your "Space becomes timelike", I think you are stuck on (a) a particular system of coordinates that (b) are not regular across the horizon and (c) thinking that either of these does anything physical to free-falling infalling test particle.
The huge flashing red warning sign on (a) & (c) is that you drop in the words "'upward' direction", "{toward, closer to, away from} the singularity" and most especially "slower": you are clearly implicitly slicing spacetime into space and time.
From a product standpoint, we're beginning to look at lot more like Europe did to us in the last few decades. The EU couldn't manufacture a cheap consumer item no matter how hard it tried and no matter how much the EU subsidized things. Just too much government/societal bloat. Seems to be the direction we're heading unless we can recapture the "get it done" spirit of old. I don't think we can do that while we're continually focusing on making sure everything is always fair to everyone all the time.
I'd definitely buy one! Back in around 2007 I went to the Chevy dealer and said "What's the cheapest car you got" and he said you want a Cavalier... I got it with air conditioning and an automatic for around $12k.
It was a great car at a great price, zero problems.
I don't understand why cars have gotten so much more expensive in the last 20 years. There is definitely room at the bottom for entry level vehicles.
I suspect the problem may be the increasingly strict emissions laws that push the OEMs into preferring certain segments at the expense of others. It might be that it doesn't make sense for the OEMs to pursue the low end market, it's not worth the trouble.
On that page, I clicked on the "Build and Price" button. All that page contains is their SUV models.
I then checked the 5 dealers closest to me. At these 5 dealers, there are only a total of 3 base model cars in inventory, all last years' model: 18k, 18k, and 20.6k
The explanation is obviously the chicken tax and fat profit margins on their larger SUVs.
Sam Altman complaining about mercenary behavior from competitors... Talk about the pot calling the kettle black. Guess he's unhappy he's not the one being mercenary in this situation.
In many ways Chris is ending things just as his dream is about to come to fruition. His vision was just 40 years ahead of the technology. If only he could stay engaged another 10 years. The best times are ahead of us
A few months ago someone here reported on making text adventures with language models. If I remember correctly, a problem is that it is not trivial to control the AI in a way that players can't cheat on puzzles.
This doesn't surprise me. Here's my hot take, having worked building these kinds of ecosystems in automotive and related industries (RV), and also working with German automotive/caravan companies in those spaces.
1) They don't want to invest in building vehicle software ecosystems as it's expensive, time consuming, and not exactly in their wheel house. Wireless and cloud connectivity just aren't their language.
2) They don't want to work with existing proprietary off the shelf ecosystem solutions -- they feel that because it's "their vehicles" they should "own" the technology and IP. They don't want vendor lock in, so they avoid existing proprietary solutions they can't "take over". And by "take over" I mean "have the vendor give their proprietary stack to them for free, so they can then share it with their other suppliers".
3) They expect the vendor base to "partner" to develop "open" software stacks for free -- which most vendors aren't keen on doing as there is little upside for the vendor to spend their own internal NRE building a system that their competitors benefit from and can quickly undercut them on. They generally refuse to pay for the development of a stack that they can own and build upon.
The root cause seems to be magical thinking from the higher ups - "Hey connectivity stuff is everywhere, it can't be hard, why should we pay for this?"
They don't want to build it. They don't see the value in paying for it. So of course open source is the obvious solution. Hey, just have the nerds build it! They love doing that kind of work for free.
My understanding is that for extremely large black holes the tidal forces are negligible near the event horizon. So things should function pretty much the same other than you can't move in reverse and get out.
If two rockets fall past the horizon at the same time, one accelerating forward towards the singularity, and the other accelerating backwards away from the singularity, then shouldn't the distance between the rockets increase, even though they are both moving inexorably forward?
If the tidal forces are low, I'd assume that my muscles are still strong enough to "slow down my hand enough" to move it above my head.