- #1
michelcolman
- 176
- 2
Suppose you make a big horizontal wheel, put markings at equal distances on the edge and also on the floor just outside the wheel. Now let the wheel spin at relativistic speeds.
If you are standing next to the wheel, the markings on the wheel will be closer together (because they are moving), so you would calculate the circumference to be less. After all, you can count the number of markings, and that is still the same. This means that, assuming the radius is unchanged, the circumference is no longer equal to 2 pi times the radius. How can that be explained?
Meanwhile on the disc, you would measure the circumference of the circle on the floor to be less than that of the disc, since the markers on the floor are closer together. How can that be? The enclosure would appear to be smaller than the disc?
And what about simultaneity? If you do some experiment sending laser beams around the circle and back, and basically checking to see if your own clock is simultaneous with itself seen from a distance, wouldn't you get into contradications with what the outside observer will say? Many straight line thought experiments are solved by considering there is no objective simultaneity, but if you go once around the disc, you have to agree on simultaneity. How do the paradoxes solve themselves then?
For example, what about the twin paradox? Both the observer on the disc, and the observer next to it, will see the other as moving, but there is no turnaround point to shift the reference frames to solve the paradox. Of course there's a different kind of assymmetry in the centripetal force, but how exactly does that solve the problem?
And do both observers agree on the radius of the disc, or does one see it as bigger than the other?
If you can either point me to a good article on this, or answer the questions yourself, I would be very grateful.
Thanks,
Michel Colman
If you are standing next to the wheel, the markings on the wheel will be closer together (because they are moving), so you would calculate the circumference to be less. After all, you can count the number of markings, and that is still the same. This means that, assuming the radius is unchanged, the circumference is no longer equal to 2 pi times the radius. How can that be explained?
Meanwhile on the disc, you would measure the circumference of the circle on the floor to be less than that of the disc, since the markers on the floor are closer together. How can that be? The enclosure would appear to be smaller than the disc?
And what about simultaneity? If you do some experiment sending laser beams around the circle and back, and basically checking to see if your own clock is simultaneous with itself seen from a distance, wouldn't you get into contradications with what the outside observer will say? Many straight line thought experiments are solved by considering there is no objective simultaneity, but if you go once around the disc, you have to agree on simultaneity. How do the paradoxes solve themselves then?
For example, what about the twin paradox? Both the observer on the disc, and the observer next to it, will see the other as moving, but there is no turnaround point to shift the reference frames to solve the paradox. Of course there's a different kind of assymmetry in the centripetal force, but how exactly does that solve the problem?
And do both observers agree on the radius of the disc, or does one see it as bigger than the other?
If you can either point me to a good article on this, or answer the questions yourself, I would be very grateful.
Thanks,
Michel Colman