> ... > > 1=1/2*2*v_net^2 > > v_net=0.707

You missed the extra factor of "*2" at the end and took the square root of 1/2 by mistake. Had you taken the square root of "1/2*2" you would have gotten v_net=1, i.e. the speed of the two balls together is the same as each ball separately. But that's because, as other commenters pointed out, you used conservation of energy for a perfectly-elastic collision. Using conservation of momentum in a perfectly-inelastic collision v_net will be zero and all the kinetic energy will be destroyed (converted into thermal energy of the atoms inside the ball bouncing around randomly).

This is exactly why Newton's laws were revolutionary and why it took humanity until 1687 to discover them! Until then, it was perfectly reasonable to believe everything naturally slows down and stops, unless someone is working hard to keep it moving. That's because everything we could see around us did just that! We know now that everything that we see slowing down does so because of friction and air resistance, but it was not obvious if you've never seen anything different. It took Galileo's physics experiments with carefully constructed artificial conditions to inspire an alternate explanation.

Maybe the closest everyday example of a self-moving object they had at the time was a runaway horse cart. Later on it was an easier idea to swallow when we had trains around. Trains have such low friction that you have to work hard to slow them down. It's more natural to believe that an object in motion remains in motion if you've seen trains your whole life!

Everything inside the event horizon must travel towards the singularity, but the speed at which they travel inwards can still be different. This allows things like "blood" or "nerve impulses" to subjectively travel "upwards", such that from your perspective you will feel physically normal, even as you cross the horizon.

Here's an example using fake units: you are falling through the horizon, at t=0 your head is 1m above it, your legs 1m below it. Your toe sends a nerve signal. At t=1, your head enters the horizon, your leg is 2m below, and the nerve signal is 1.75m below. The signal is "deeper" into the black hole than when it started, but it still travels up your leg. At t=8, your leg is 9m below, your head is 7m below, and the nerve signal finally reaches your head. You can feel you toe!

You could even have two spaceships fall in separated by 1km (a rope linking them together optional!) and you could see your buddy on the front spaceship fall in past the event horizon and wave at them and then see them wave back in response. Of course, by the time you see the response, you yourself will already be inside the event horizon and way past the point where they were when they waved back.

If the black hole is large enough (like the 4 million solar mass at our galaxy center), the point where tidal forces become unbearable lies way inside the event horizon. You could fall through the event horizon and not even notice unless paying attention to your navigation instruments. You'd continue to fall for the next 30 seconds blissfully unaware that there is now no chance to escape. You WILL get spaghettified in the last second before impact with the singularity though.

Wikipedia says variable speed of light hypothesis is an alternative to the cosmic inflation theory, not a feature of it! I agree with the other commenters, saying something like:

> in the first very very tiny fraction of a second at the birth of the universe, during which the universe expanded faster than the speed of light

makes you look very suspect, since the Hubble parameter is completely separate from the speed of light. It is measured in units of "per second" (though for convenience usually expressed as (km/s)/Mpc). If you check far enough in our present-time universe, you'll find parts of it that are moving away from us faster than the speed of light even now. The first 10^-32 seconds of the inflationary era is not special in that respect.

If the purpose of proposing cosmic inflation (not to be confused with cosmic expansion itself!) is to explain the smoothness of cosmic microwave background (matter could have reached thermal equilibrium before the inflation happened), then it makes sense that proposing a higher speed of light would be an alternative explanation to that!

> But a person on ISS will tell you the same thing about earth!

You can only say that about spaceships flying past Earth in a straight line. The ISS goes in circles, i.e. always changes directions. Only the Earth reference frame is "inertial". As Duros001 said above, this creates not just a perceptual but an actual measurable difference between the clocks on Earth and ISS - the clock on ISS will tick slower and all observers will agree on that.

Not to mention the blood still needs to circulate in your body. Trying to pump blood up to your head 0.5m above your heart at 100G is equivalent to your neck being 50m long. Your heart is not as strong as a giraffe's! Not gonna happen without some form of suspended animation.

This is why everyone thinking that water suspension will allow humongous accelerations is deadly mistaken. Being underwater at 1km IS NOT THE SAME as accelerating at 100G in a water bath. Not the same! At 1km you have 100atm of pressure on all sides. You can probably scuba dive at 1km just fine if you descend slowly and prebreathe the right gas mixture. Sitting in a 1m tall chair in a water tank at 100G, your head is at 1atm and your feet are at 100atm. This is different! You'll be crushed like a bug. Filling your lungs and other body cavities with water or perfluorocarbons or whatever will not help!

A water tank should instead be thought of as the most comfortable acceleration couch possible, that supports every part of your body with the highest softness possible and no pinch points. You'll also do best if you lie perfectly flat horizontally, instead of sitting or standing.

The egg cells will have already acquired copying errors when they were created inside the fetus still in the womb. They will accumulate additional DNA errors from random chemical/radiation damage during their dormant lifetime. It is nearly impossible for human offspring to contain no mutations on top of the parents.

OP did say discounting light pollution. Technically, the night sky is brightest today because of light pollution.

Other galaxies would not have made the sky brighter, at least not 4 billion years ago. Andromeda is the closest galaxy and it is barely visible to the naked eye as is. Cosmic expansion means other galaxies would have been closer to us in the past, but not as close as Andromeda. Maybe if you go back like 13 billion years to when galaxies were being first formed, the cosmic neighborhood would have been 8 times denser back then, and maybe multiple galaxies would have been visible in the sky, including some that Milky Way has since collided with.

What would have been visible 4 billion years ago is more brighter stars. The brightest stars are the heaviest but also the most short-lived. They are only visible for a few million years after they are formed, but make up most of the starlight reaching us. The number of heavy bright stars is proportional to number of new stars formed, but star formation in galaxies is always slowing down... There were more bright stars in the past, and there will never be as many bright stars as there are in the sky today, except for a short period of time in 5 billion years when Andromeda crashes into the Milky Way, causing a temporary burst in new star formation.