You can use the formula g=4π/3 Gρ*r to calculate the surface gravity of a homogenous sphere with density ρ and radius r. G is the gravitational constant.
With r=50 m and ρ=1000 kg/m[sup]3[/sup] you get g=1.40E-5 m/s[sup]2[/sup], which would make a 75 kg human weigh about the same as 0.1 gram on Earth.
IIRC they’ve demonstrated immersing lab rats in oxygenated Freon liquids; I don’t believe they’ve tried it with actual humans. It’s been a suggestion, too, for space - humans immersed in a dense liquid could tolerate much higher acceleration perhaps.
That of course does not address the problem of getting the air out of other body cavities, such as the inner ears.
For the OP, a balloon maintains its shape (if it does) by having the same or slightly higher pressure than its surroundings. For every 100 feet you go down, that’s another 3 atmospheres, give or take. So beyond 300 feet, or about 9 times normal concentration of oxygen and nitrogen - our bodies were not meant to take that, it’s not within our normal range of experience so biochemistry can’t handle it.
I remember reading about the use of oxygenated fluorocarbons for diving years before Cameron’s The Abyss came out. What I read said that they had done the tests with small animals*, but that the furthest they got with humans was to fill one lung – evidently they were leaving the other available for backup. That was decades ago. I’m sure they’ve gone farther with testing, but I haven’t been following it. The Wikipedia article on Liwuid Breathing says that they have certainly gone further: Liquid breathing - Wikipedia
SF writer Hal Clement has people living in a fluorocarbon environment at the bottom of the sea in his novel Ocean on Top (1973). They have to medically stifle coughing and gag responses, because it would hurt to have the body trying to rapidly move that dense fluid instead of air.
*They reportedly really did use a rat breathing fluorofluids for The Abyss, something that supposedly cost them a “no animals were harmed during the filming…” certification. I haven’t followed up on these claims, but they sound believable.
Having Pina Colada as much as I do, I’d better live under a coconut shell, but there are mammals living at altitudes -3000m so what makes the difference?
Evolutionary adaption to the environment. Gas saturation of myelin sheaths was given as answer to my above question of critical point of system failure. It’s probably not a coincidence that giant squids and octopuses lack those sheaths. As for mammals, yes, sperm whales might be able to go that deep, but not for very long (and they certainly have some evolved mechanisms too, to be able to cope with the pressure!)
A Google search for “deepest whale dive” turned up this National Geographic article about Cuvier’s beaked whales, which can dive to ~10,000 feet (3000m).
I believe I read it in a 1960s-era Nat’l Geo magazine, perhaps a Cousteau article. The article was remarkably similar to The Abyss, and remarked that “one day soon” humans could do it. But it appears human liquid breathing, like cheap fusion power, is always going to be “one day soon”. (Perpetually ten years in the future).
The sub-ocean floor super train was supposed to run from North America to Europe via tunnel. It has been proposed numerous times by serious engineers (and maybe not-so-serious engineers).
Forgetting about the astronomical cost, what if the train breaks down? You can’t just leave folks below the ocean to die, can you?
So there would have to be an entire emergency and rescue infrastructure all along the way. And you would need to worry about air pressure and geological hazards…and from there, why bother? You could fix all the up-here world’s problems for that kinda scratch!
One would assume that a train breakdown would still leave the train accessible via the tunnel. So you just send along a repair crew on another train. The Chunnel simply provides three interlinked tunnels. One each direction, and a third smaller tunnel between them for access.
If the problem is failure of the tunnel itself, it comes in two forms. A collapse that doesn’t breach the seafloor - you are going to have to dig them out. The presence of the sea above makes no difference. It would be the same as a tunnel collapse of part of a tunnel through a mountain. If on the other hand the collapse breaches the seafloor, rescue isn’t an option. Everyone died before you even found out about the problem.
Under normal operations the air pressure in the tunnel is not materially different to that at sea level. Any idea of a pressurised tunnel balancing the water pressure at the deepest part of the tunnel is not going to work for a host of reasons. No existing tunnels are so pressurised, so no reason to start now.