Let’s say I’ve got two decent-sized weights connected by a spring, and they’re floating in space. Since they’re just sitting there, there’s no tension on the spring, so it’s not at all stretched.
Now, I start them spinning around each other. Due to a phenomenon I call centrifugal force, the spring gets stretched as the weights get further apart.
So far, so good. But now let’s imagine that I put my spinning weights in a universe that contains nothing but these two weights. According to the principle of relativity, there’s no way to tell that the system is spinning, since there’s nothing for it to be spinning relative to. Right?
So can I still stretch the spring by spinning the weights? Or is there no centrifugal force in an empty universe? Or what?
And now, let’s make it even more complicated. Let’s say I have a spaceship designed like a giant version of my weights on springs. I’m inside one of the weights now, and I use the spaceship’s megatronic wormhole generator to spit me out randomly in another universe. I know from my ship’s manual that some of these universes are empty and others aren’t. I look around and see no other matter in the universe I’m in. Can I determine whether this universe is really empty by trying to spin my ship and stretch the spring? And if I can determine the contents of my universe in this way, isn’t that, um, magic? Or at very least very spooky action at a distance?
It seems like the behavior of objects under centrifugal force is dependent on the existence of other material in the universe, even though there’s no force coming from that material actually acting on those objects. Which seems crazy.
I’m sure this problem has a name, but I can’t figure out how to google it. Does anyone know what I’m groping toward here?
No, that is not correct. Relativity says (and I’m paraphrasing here) that you can’t tell your direction or velocity if you are in an interial frame. An inertial frame is a frame of reference that is experiencing no acceleration. This means, for example, that if you are in an elevator, there is no experiment that you can do inside that will tell you whether the elevator is moving at a constant speed up, constant speed down, or not moving at all. However, an object moving in a circle is experiencing an acceleration and is therefore not in an inertial frame. You can tell that you’re spinning. Relativity doesn’t say that you can’t tell if you’re moving, only that you can’t tell if you’re moving with a constant velocity vector.
This is not correct, not sure how you concluded this. Centrifugal force is, roughly, the apparent outward force experienced by an object that is attempting to obey the law of inertia by moving in a straight line, but is pulled into a different direction to move in a curved line. So it requires a moving object, and a force.
The mistake you are making is assuming that your balls and springs are a single point in your otherwise empty universe.
The actual system described contains several objects, each moving relative to the others.
A single object cannot exist alone in the universe. If it is over a Planck Length in diameter, physical laws begin to matter. One end of it is at a distance from the other, and has a different location, proper motion with respect to its own “other end” and resultant interactions.
Our physics do not describe forces or objects less than that size. Whether there could be such physics is a very complicated multidimensional existential problem.
I see where you’re coming from and have a similar example.
That ship from 2001:A Space Odessey. It spun around an axel to create centrifugal force so the guy could jog around in a circle. If it stops spinning he just floats.
So, like you say if the ship is out in the vastness of space with nothing to be realtive to how do you tell if the ship is spinning???
Like Cooking says. In fact, actually doing your experiment with weights and spring would be a tidy demo.
The weights and springs are all stationary in a reference frame chosen in a certain way. This reference frame would be rotating and various common relativistic and other statements would be inapplicable here. However, the centrifugal force would have a sort of magic in this frame, or at least would look that way to people who are conditioned to think only in terms of inertial frames. There is also a coriolis force, and a classic demonstration of the coriolis force involves putting people on a Merry-Go-Round to play catch with a ball while the thing spins. These people witness the ball following trajectories that are horizontally curved.
Tris, where are you going with the Planck length and all?
So in a case of two hollow spheres in space orbiting eachother both making the claim “I’m stationary and you’re orbiting me” the standby by answer of “It’s relative to your location” doesn’t hold? One actually is spinning and can be proven by it’s inhabitants sticking to the inner wall of their sphere?
Yes, you’re right in general: the relative argument does not hold. Straight line motion is relative, but changing speed or direction (acceleration) isn’t. And going in a circle needs constant acceleration, which can be detected.
So if sphere A is orbiting the center of sphere B, you can tell this even if there’s nothing to compare them to, because an object in the center of sphere B will stay there, while an object in the center of sphere A will seem like it moves, if you’re inside the sphere.
However, just to be clear, spinning is independent of moving in a circle. You can spin in place without moving, or you can walk in a circle while always facing north (walking sideways and backwards), so that you’re moving but not spinning. Or you can walk in a circle while always facing the center of the circle (moving and spinning at the same rate), or spin as fast as you want while moving in a circle (the Earth spins about 365 times for every orbit it does). So even if sphere A is orbiting sphere B, either or both could be spinning.
If a hollow sphere is spinning, then an object near the axis won’t move, but farther away will seem to be pushed against the wall. If the sphere is also moving in a circle, you’ll get the two imaginary forces added to each other.
Others have mentioned Newton’s bucket. But also, if you’re thinking about ‘the rest of the universe determining the results of rotational motion’, that’s called Mach’s principle. Have a butchers at that. I’m actually reading Einstein’s “Relativity: The Special and the General Theory” at the moment, in an attempt to understand what I was not really able to back when I finished my physics degree six years ago. I think it’s available online for free, check it out too.
I just ( 6 mts ago) participated in a discussion at (a scientific forum I don’t know if I can mention here) forum regarding whether or not centrifugal force actually exists. There is an arm of science that currently claims it is nothing but a false force (the pseudo force people) while others claim it has been removed from elementary physics books as beginning students need be concerned only with straight line accelerations. Others still use the term and understand the forces involved. I’m not touching this because my understanding of Newton’s 3 laws isn’t as strong as it should be, but it the subject makes for an excellent discussion.
Centrifugal force is not a fundamental, real force in the same way that gravity or EM forces are. It is the simply the force (composed of real forces, coming from somewhere) that’s needed in order to keep an object moving in a circle. The natural tendency of objects is to move in a straight line at a constant speed, of course.
Both the centrifugal and Coriolis forces are “fictitious”, in that you wouldn’t observe them to exist if you tracked everything relative to an inertial reference frame. But, if you insist on pinning your coordinate system to a rotating object — like the Earth, as we often do, or the wheel-like space station in 2001 — then within that reference frame, you’ll observe objects acting as if they’re experiencing this extra force.
As **hobscrk777 **said, any force that keeps an object moving is a real force (it can be any kind of force from gravity, to the normal force) and called the centripetal force. The centrifugal force is what I like to think of as an apparent force. It is caused by the acceleration, but it feels just like a force and acts just like a force, if you change to an accelerating frame of reference.
I always thought the actual Einstein analogy was comparing the acceleration in the elevator to the acceleration due to gravity (i.e. you couldn’t tell the difference between being in an elevator accelerating upwards at 1g and sitting motionless on the surface of the Earth. However, if that is the case, it would seem false to me. The gravitational field lines will always be curved when sitting on the surface of the Earth (and would vary in strength from the bottom of the elevator to the top). Both of these would be different in an elevator accelerating at 1g.
My analogy of the elevator isn’t related to Einstein’s notion of comparing an accelerating frame of reference to one under the influence of gravity, even if Einstein also talked about an elevator. I stand by my example of things moving with a constant velocity vector.
I’ll discuss this anyway. Even though you may have a point, I suspect that the forces in an accelerating elevator also vary from the bottom to the top, although I don’t know enough physics and math to work out the details rigorously. After all, the accelerating force has to be applied somewhere, like pushing from the bottom, in which case the transmittal of that force through the elevator takes time.
I don’t know what you mean by curved gravitational field lines. The gravitational field lines all point straight towards the center of mass, when considering gravity idealized for a single spherical body. I would agree that the force lines for the elevator would be parallel pointing towards the floor, which is indeed different in principle.
I think that the Einstein example was to illustrate a point rather than to be rigorously correct mathematically down to the gnat’s eyeball. I don’t know if the force gradient and direction differences could even be measured for an object the size of an elevator car.
>However, if that is the case, it would seem false to me. The gravitational field lines will always be curved
Flex, I think you’re right, and never thought of this.
I hope that Einstein, whenever he needed to be sufficiently clear and correct ahd thorough, would have further constrained the problem, saying there’s no experiment you could do in the center of the elevator once everything was in a steady state, etc etc. But however he spoke about it, his picture was correct in its most surprising sense, about the equivalence of resistance-to-velocity-change and weight.
Even though you may have a point, I suspect that the forces in an accelerating elevator also vary from the bottom to the top, although I don’t know enough physics and math to work out the details rigorously. After all, the accelerating force has to be applied somewhere, like pushing from the bottom, in which case the transmittal of that force through the elevator takes time.