If the universal speed limit is 299,792,458m/s. And you had a rod several light-years long, and began spinning while holding the rod, wouldn’t the other end of the rod surpass the limits?
In: Physics
Alright, one of my all time favorite physics questions.
So… Lets start off by understanding that the rod you are imagining cannot physically exist. And actually violates the rules about traveling faster than the speed of light from concept.
What you are proposing is a system where you push on the base, and instantly the tip – several light years long – moves. That’s transmission of information faster than the speed of light right there. The force you apply to the rod will move through it at the speed of sound in the object. That means after you start to twist the base it will take hundreds of years for the tip of the rod to even start to move. Make sense? No. Ok but so lets say we had a rod several light years long that was infinitely rigid (violate laws of Physics 1) and absurdly light (say it only weighted a thousand tons).
What happens when you start to spin it?
Well the first thing you will notice is that the engine you have hooked up to spin this thousand ton rod is drawing WAY more power than you predicted it would. You know its going to take some time to get the rod “up to speed” but right from the start your power draw is massively more than you expected. Why? It is taking WAY more energy than anticipated (under your normal non relativistic physics) to accelerate the tip of the rod even at relatively low %’s of the speed of light.
Ok, but what are we? Wimps? You expected you would need 1 massive space based nuclear reactor complex to power this machine, but call up your investors because we are going to actually need 20 of those bad boys. No problem.
But now something REALLY weird starts to happen – shit starts melting. The engine is melting, the metal rod is melting, the connections are melting. There is no such thing as a 100% efficient transfer of energy. Even just moving something that you already are holding in your hand leaks energy as your hand flexes from imparting the energy into the object you hold. Even if you are 99.999% efficient in your transfer of energy you still have 0.02% of the entire output of one of those massive nuclear complexes that is JUST going into heating up this engine and rod. That doesn’t sound like a lot, but these are really big reactors remember.
Ok, so cooling system. But the closer you get to the speed of light the worse all of this gets. You finally come to the point where the heat being generated by this system is impossible to remove and the materials heat beyond what anything is willing to remain a solid at. This will be the first time in this experiment where you scratch your head and ask “is what I’m seeing here an engineering challenge or is this part of the laws of physics messing with me?” And the answer is that its the laws of physics.
Ok but lets ignore that (violate laws of Physics 2).
Alright now we hit another problem. The rod is pulling away from you MUCH harder than you anticipated. Again, the end of that rod is becoming more and more massive (relitivistically) and that is dramatically increasing the forces at play.
At this point we get into an odd question about when the strength of material might be part of the universe’s upper limitations. Like if I took a loaf of bread and crushed it into a small enough dot I would make a microscopic black hole. So just how tightly will the universe permit me to squish a loaf of bread? Same thing here, just how much tension is the universe willing to permit physical particles to bear before ripping apart? Those are the kinds of numbers we are going to get to VERY quickly in this system.
Alright but lets make the rod infinitely strong (violate laws of physics 3).
So again… What happens? Two things:
1) As the tip of that rod gets ever closer to the speed of light the energy needed to spin the rod, the forces the rod is under, the waste heat generated by the system, all race up towards infinity. You will simply never be able to put enough power into that system to get the tip of that rod faster than the speed of light.; and
2) Time shear. The tip of that rod experiences time moving at a much slower rate than the base of the rod (time slows as you approach the speed of light). “So what, its a rod, it doesn’t get old, or bored,” That’s true, but forces and energy travel through it based on time. Simply put the base of that rod is going to have forces flowing through it in a wave (based on the speed of sound in the material) that build up like a whip as they move down towards the end of the rod. The wave’s length is shortened which means forces are more concentrated in it. No matter how strong your rod is it WILL bend because the forces pulling the end of it will not reach the end before they move the base. This is a different but related problem to the first one we faced. Remember how I said the basic setup of this question violates the laws of physics? (see violate laws of physics 1) Well now that same problem is being compounded a thousand times over, a billion times over. So I think its fair to call it a completely different problem. But just the time dilation involved is going to bend your rod like wet spaghettis.
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