Once you put the trash out, and realize you’re spinning, will you get dizzy? (suddenly start experiencing centrifugal forces?)
Special relativity can handle acceleration just fine, too. It just means that you have to use high school calculus instead of just high school algebra.
Grin! You should see some of my trash! It’d disorient an orc!
But, of course, less obviously and more seriously, if you’re talking about becoming dizzy inside the spaceship – then there are already two objects: you and the spaceship. You could also say that, in feeling dizziness, this already implies multiple objects, or a system of objects: the internal structure of your body, your blood vessels, your inner ear, etc.
The “one object in the universe” concept has to be very, very limited, or else the object’s internal structure begins to contradict the premise.
Yeah. You can even predict gravitational time dilation with SR and the equivalence principle - you don’t need the full machinery of GR.
True enough. Unless I’m mistaken, though, SR is still treating acceleration as a series of inertial frames, while in GR it’s handled more “naturally” (acceleration is built into the coordinate system from the start).
I think that’s right.
You can use the same conceptual machinery (metrics, tensors, etc.) usually used for GR to do SR, too, and in fact it often works out simpler than trying to do it the more naive way. Whether you call that “doing SR” or “doing GR in the special case where it’s SR” is I suppose a matter of taste.
OK, I got the special and general mixed up…
IIRC from years ago - you will feel the centrifugal force. By GR, you can’t tell acceleration from gravity. You can test for coriolis and similar effects, but if you do not detect them it simply means that you could be accelerating, experiencing gravity; or the lack of detectable coriolis effect puts a lower limit on possible radius and speed of rotation of your frame of reference, depending on the resolution of your experiment.
Stop worrying about whether you’re moving or not, and start working on the more immediate problem that you’re going to freeze to death. If the engines are dead and there’s no star shining a warming light on you, the ships going to radiate all your heat away. You can work on the motion question later.
Oh, I switched on the heaters running on radioisotope batteries, and things are pretty warm and cosy right now, thank you.
Back to my real problem:
Centrifugal force. If my ship were moving at 300 miles/sec, I would hesitate to fire a sideway thruster that would change my ship’s course by even 1 degree. At an appreciable fraction of lightspeed, it would be disastrous to fire the side thrusters at all.
(Using the usual analogy of a car: it makes a difference you take a turn at 30 mph or 100 mph. The inertial forces are much larger the faster you take the turn. Same goes for a spaceship and its occupants.)
I left Earth and accelerated at a constant 1g/s until I reached 30% of lightspeed. Then I went into hypersleep and woke up 500 million years later to find myself in a giant intergalactic void. I have no way to calibrate my motion sensors, but my ship is still travelling at 0.3c (wrt Earth). If I attempt to change course at this speed, I will be subject to a centrifugal force proportional to my velocity of 0.3c. Or not?
Regardless of the presence or absence of external frames of reference - and regardless of the conflicting information arising from using different reference frames to measure my velocity - my ship is still moving, and an attempt to change course should produce forces proportional to… what? The centrifugal force would be proportional to velocity measured using which frame of reference?
Sorry if I sound hopelessly confused. Appreciate if someone can explain what happens, in layman’s terms.
This is wrong. The force you’d feel depends on how much thrust your thrusters generate. That’s it. There’s no dependence on your frame of reference.
It’s not like turning a car. Turning when traveling faster, and assuming the tires don’t slip, just means there’s more force from friction. When you turn your car’s wheel some amount, the force comes from friction between the wheels and the road. If you were to try to turn using thrusters, they’d have to provide more thrust to make a faster turn in a circle of some size than a slower turn in that same circle.
If you used the same thrust, when you were going faster, you’d just make a bigger circle. The same would happen in space. If you were going slowly in some frame of reference, and had a small sideways thrust, you could make a small circle. If you were going 0.3C in that frame of reference, you’d make an enormous circle. But the force on the ship would be the same.
Except you wouldn’t go in a circle by just applying sideways thrust. If we designate our original direction of travel as north and you apply thrust in line with the ship’s center mass directed east, all that will happen is that your direction travel will change a bit towards the east, but you will still retain all northward velocity.
If you want to go in a circle you need change the direction of the thrust, eg start the main engines and turn the ship at a constant rate. And even then, depending on thrust from the main engines and the turn rate you can end up with that would look like a series of loops heading north at 0.3C to the outside observer.
You would if the sideways thrust lasts long enough.
Once you’ve turned even a little bit, there’s a southerly component to the sideways thrust that is decreasing your northward velocity. At the point where you’ve completed 90 degrees of turn, all the thrust is southerly.
Only if you turn that the ship as well, something that doesn’t happen if you apply the thrust in line with the ship’s center mass like I said.
Assuming he and his ship have no rotation, mandala could slowly rotate the ship by standing in the middle and spinning the other way.
If you can see stars, you should be able to get a fix on your position. Then do the same after a day or two. This will give you your average velocity which sounds like what you want. Can ypu do me a favor: have them nanobots rig up something that can measure Planck’s Distance in iron atoms at 10 billion light-years away … I’m curious if it’s the same as in your space ship.
True enough, but at some point we need to bring out the spherical cows or we could end up anywhere. 
Anyway, upon rereading what you said earlier I think I agree with what you were trying so say. So just to clarify, by “sideways thrust” you essentially meant ‘thrust that is perpendicular to the current direction of travel, regardless of the orientation of the ship’, correct?
We can’t do that, because we don’t know what the current direction of travel (if any) is, and in fact, without a specified reference frame, it’s undefined.
I was referring to what ZenBeam said in post 31, about the thrust needed to go in a circle.
And I was careful to specify “some frame of reference”.