Scientists have been telling us for some time that it is impossible to achieve the speed of light. The formula says that mass goes to infinity as you approach C so the amount of power to go faster also rises to infinity. The theory also says that time is displaced (slows) as we go faster. We have proven this by tiny fractions of variations in the orbits of some of our satellites and in the orbit of Mercury. For an issue within physics that is seen as such a barrier to further research, shouldnt we see a more dramatic demonstration of this theory? I think it should so I made up one.
Let us suppose we have a weight on the end of a string. The string is 10 feet long and we hook it up to a motor that can spin at 20,000. The end of the string will travel 62.8 feet per revolution or 1,256,637 feet per minute. That is 3.97 miles per second or an incredible 14,280 miles per hour. OK so that is only .0021% of C but for only ten feet of string and a motor that we can easily create, that is not bad.
There are motors that can easily get to 250,000 RPM and there are some turbines that can spin up to 500,000 RPM. If we can explore the limits of this experimental design, we might find something interesting. Now lets get serious.
Lets move this experiment into space. With no gravity and no air resistance, the apparatus can function very differently. It could use string or wire or even thin metal tubes. If we control the speed of the motor so that we do not exceed the limitations imposed by momentum, we should be able to spin something pretty fast.
Imagine a motor that can spin 50,000 RPM with a sting mechanism that can let out the string from the center as the speed slowly increases. Now lets, over time, let out 1 mile of string while increasing the speed of rotation to 50,000 RPM. The end will not be traveling at nearly 19 thousand miles per hour or 2.82% of C.
If we boost the speed up to 100,000 RPM and can get the length out to 5 miles, the end of the string will be doing an incredible 188,495,520 miles per hour. That is more that 28% the speed of light.
What will that look like? If we have spun this up correctly, the string (wire, tubes, ?) will be pulled taunt by the centrifugal force of the spinning. With no air for resistance and no gravity, the string should be a nearly perfect vector outward from the axis of rotation. The only force that might distort this perfect line is momentum but if we have spun this setup slowly so that the weight at the end of the string is pulling the string out of the center hub, then it should be straight.
I have not addressed the issue of the strength of the wire to withstand the centrifugal force of the spinning weight. Not that it is trivial but for the purposes of this thought experiment, I am assuming that the string can handle whatever the weight size we use.
Let us further suppose that we have placed a camera exactly on the center of the spinning axis facing outward along the string. What will it see? If the theory is correct, then despite the string being pulled straight by the centrifugal force, I believe we will see the string curve backward and at some point it will disappear from view. The reason is that as you move out on the string, its speed is going faster and faster and closer to the C. This will cause the relative time at each increasing distance from the center to be slower and appear to lag behind. When viewed from the center-mounted camera, the string will curve.
If we could use some method to make the string visible for its entire length, its spin would cause it to eventually fade from view when the time at the end of the string is so far behind the present time at the camera that it can no longer be seen. It is possible that it might appear to spiral around the camera, even making concentric overlapping spiral rings.
If synchronized clocks were places at the center and at the end of the string, and then we placed a camera at both ends but could view the two images side-by-side at the hub. Each one would view a clock that started out synchronized and the only difference would be that one is now traveling at some percentage of C faster than the other. I believe they would read different times as the spin rate increased.
But now here is a thought puzzle. Suppose there is an electronic clock at the end of the string as described by the above paragraph but now instead of sending its camera image back to the hub, we send its actual reading by wires embedded in the string back to the hub where it is read side-by-side with a clock that has been left at the hub. What will it read now? Will the time distortion alter the speed of the electrons so that they do NOT show a time distortion at the hub? Or will the speed of the electricity be constant and thus show two different times? I dont know.