If I swing a hammer, I rotate the pole upon which the hammer is mounted a certain distance. Because of the distance from the point of rotation, the hammerhead must move faster in order to keep up. This is why a hammer is more effective than simply pounding a nail with a rock.
So, if I had a hammer mounted on a long enough, unbreakable pole, the hammerhead would eventually have to move at the speed of light to keep up, right? What happens if at this point I make the pole longer? Would the hammerhead be forced past the speed of light?
This is a classic question - and the answer is that special relativity implies that there is no such thing as an unbreakable, unbendable pole. See here for more The Superluminal Scissors
As the hammerhead approaches the speed of light its mass increases. This makes it harder to swing. Eventually either the force required to swing it becomes greater than whatever is providing the force can manage, or the pole will break.
An absolutely rigid stick violates causality - because when you move part of it, the rest has to move not as a resulting effect of the causal force, but at exactly the same time.
And any nearly-absolutely rigid stick, no matter how closely it approximates absolute rigidity, will bend to any degree you like - given that the force necessary approaches infinity as the tip speed approaches c.
…And if there was an infinitely rigid, strong stick, you still couldn’t get the hammerhead to exceed the speed of light. Time itself would slow down around the hammer in order to prevent this, if I correctly interpret the Time Travel episode of Stephen Hawking’s Into the Universe I watched last night.
This is a neat visual example of a change in force taking time to propagate through an object. A man holds a stretched slinky with a tennis ball on the bottom and lets go. The tennis ball sits and hovers there, Wile Coyote style, until the top end of the slinky reaches down and notifies the ball that there is no longer any force holding it up, and now it’s time to fall.
I think this is analogous to the interstellar pole communication device. From what I remember from a professor at college, the idea was that you would mount a long rod between our solar system and another star system several light years away. When you wanted to communicate with people in the other system, you would push or pull the rod (e.g. you could use a binary code, or perhaps morse (pull - dot, push - dash ) or something. Then, you could send messages faster than the speed of light.
The problem was that the rod is not actually fully rigid. When you push on it, a compression wave goes through it at the speed of light or less. After a few years, the wave reaches the other side and it pops out. So, what you might think was a solid rod is, in fact, a slinky.
The hammer, I think, would do a similar thing. Assuming you swung it overhand, the handle would bend backwards and the head would lag, and end up traveling at the speed of light or less.
Bollocks. Babale, that hammer head would totally exceed the speed of light. Sure that handle will flex, but the hammer will catch up eventually because the handle wont flex indefinitely. Theoretical physicists think they’re so smart, but they don’t spend much time with hammers.
Ignoring Einstein, how long would the handle have to be in order for a regular carpenter to get the head to the speed of light?
Isn’t there a quantum effect, IIRC entanglement, that will allow exactly the above to happen, a effect on one ‘particle’ having a instant corresponding effect on another regardless of the distance or the speed of light?
No. There is such a thing as quantum entanglement, but even though the particles can be instantaneously correlated across an arbitrary distance, there is no way to use this setup to send any matter or information at faster than c. The mere act of confirming your correlations requires boring old c-speed (or slower) communications.
In a similar exercise, you can swing a laser beam, but in this case you CAN make the spot where it hits a wall travel faster than c. The beam will be curved, but only to a certain degree. In a similar sense, you can spray a hose nozzle around in a circle and make the spot where it hits a circular wall travel faster than the water is traveling. If you use slow motion photography to watch more closely from above, you will see a very slanted stream of water traveling almost sideways relative to its length, and hitting a wall, and the point of collision moves much faster than the water in the stream does. This isn’t quite the same because there is no significant Einsteinian relativistic effect in the water, and there would be with the laser beam, but still the important principles are the same.
Note, you can’t get much utility out of that laser spot moving faster than c. It is not as if somebody at one point on the wall can change the spot somehow so that somebody further along the wall can find out about it at faster than c.
In principle, there’s no reason that even the point of collision of the water couldn’t move at faster than c. Though of course there’d be significant engineering challenges to setting that one up.
In the same way, the point of intersection of scissor blades can.move at any speed, because the intersection is not an actual object.
(In fact, a pair of scissors could be contrived with inward-curved blades so the tips meet before the rest, and the intersection moves back toward the handles - which, if it were an object, would violate several physical laws
“This is the base of the handle, and you can just make out the hammer head 500 metres away. In the experiment, we will accelerate the hammer to 100,000 revolutions per second. Then, this device will fire a coconut into its path.
You might expect the coconut to be smashed, but at this point the hammer head has imaginary mass, so there’s considerable debate among theorists about what the result will be…”