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
No it would take years for the other end of the rod to move. Just like when you pick up a long stick here on earth, there’s a delay between your input and the reaction.
Vsauce did a good video on this if you wanted to search it up.
Far from. The kinetic energy you impart on the rod travels through the rod at the speed of sound in whatever material it is made of.
So it’s going to bend, then twist, all at the speed of sound in the material, which is less that light speed by orders.
The rod would be like a piece of spaghetti.
You’d basically start to reel in the rod around you, much like winding a wire into a spool, just it would take a lot more effort. At first it would feel like the rod was rigidly tied off, and it is – anchored to millions of tons of rod behind it. After pulling for some time the length of the rod under tension would start to be many miles long as the pull propagates down the rod at the speed of sound in its material, this would appear to give your some slack, because you’re basically stretching mile upon mile of the rod, so would get noticeable elongation at your end and the appearance of having freed up the attached end somewhat.
The other end of the rod wouldn’t feel anything until many years later as the first movement finally propagated to the end at the speed of sound in the rod material.
You would be limited by what we call “The speed of sound” – but that’s because the speed of sound is just the speed at which molecules (basically) vibrate against one another
Your initial movement (or impulse, or vibration) would travel at the speed of sound down the length of the rod, so the other end of your several light-years long rod would take a long time before noticing your initial movement.
This is such a good question and it made me do some googling to figure out the answer.
When you exert a force on the end you’re holding, it doesn’t instantly exert a force on the other end. The atoms have to transmit that force down the length one by one, and that happens at a finite speed. So, even with the most rigid material possible, over a huge distance the rod would kind of look like a palm tree or a bamboo stick being swung – the far end would take some amount of time to “catch up” to where a perfectly straight line would be.
There’s a lot of answers here about how long it takes for the act of you pulling on the rod to travel down the length of it before it fully starts to react, and that’s fine, but if, in this scenario, you were willing to wait, that wouldn’t be the main issue.
The main issue is the acceleration. In Newtonian mechanics even that wouldn’t be an issue and you’d be able to, albeit slowly, accelerate the end of the rod past the speed of light. But we’re not talking about Newtonian mechanics, we’re talking Einstein’s relativity. And with that on mind, even if you could get the force to be applied to the whole thing at once, and you were somehow strong enough to move a light year’s worth of rod, you still wouldn’t be able to get the end moving faster than light because no matter how much torque you put on that rod, no matter how hard you try to spin it, it’s other end will only ever get closer to the speed of light, but will never surpass it. It’s hard to wrap your head around but it’s diminishing returns – if eating one hamburger gave you enough strength to spin the rod a certain amount, get it to a certain speed, if it’s close to the speed of light then you might have to eat two hamburgers to go make the end speed up the same numerical amount. Then 3-4, then more. By the time you’re at 99.99999% the speed of light you could build a machine that would turn the entire universe into energy for the purpose of spinning up that rod and you’d only get maybe one more extra decimal place with a nine in it. It gets harder and harder to do as you get closer and to actually get to the speed of light you would need infinite energy, which is impossible.
Might this idea be related to the pull of a black hole on the space around it? The line extending from the black hole would be pulled beyond the event horizon such that the space itself would be bent including the line with it, such that the line would rotate about the black hole so inside the event horizon it is an ever tightening circular spiral?
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.
Stephen Hawking explains this brilliantly here through the concept of a near light speed train:
The speed of light is a cosmic speed limit. You simply cannot break it. Time actually dilates around these speeds to prevent it.
The simple answer is that anything with mass can’t exceed the speed of light because the energy required to do so becomes Infinite so you may get it moving fast but not even close to a good percentage of C
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