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
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.
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.
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.
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.
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.
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?
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.
**IF** you could spin fast enough, yes.
**BUT**. The laws of physics as we understand them are consistent, and you’re looking at things from the wrong end (as it were) – if your rod is obeying physical laws, you **can’t** spin that fast, precisely **BECAUSE** it would make the other end surpass the limits.
As you speed up it will get harder and harder to rotate “a little faster” – and however strong you are, there’s a limit to your rotational speed that you’ll never reach. And if the rod is several light-years long, it’s a rather small limit.
*(As I work it out, the limiting period of rotation – in YEARS – is simply the length of the rod in light-years x 2 Pi. You can’t spin it faster than that without breaking known physical laws.)*
*(So if your rod is 1 light-year long, and you can somehow get the far end moving at a speed very close to that of light, it’s still going to take you over 6 years to spin it round you once. It will take about 7 days to turn by 1 degree. And you can’t spin faster – that’s an upper limit you can never quite reach, let alone exceed. You’re going to start out WAY slower. I hope you’re got a lot of time to spare.)*
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
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.
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