So, I managed to stump myself with this one. If I am at rest according to my frame of reference (let’s say deep space) and I have a rod one light minute in length, what happens if I pull it? For purposes of this, I am capable of generating force sufficient to move the mass.
I know that the far end of the rod shouldn’t begin moving for one minute. So what happens to the middle bit? Does it stretch, and if so, why? Or is there some relativistic element I’m failing to account for?
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Movement in a solid object only travels at the speed of sound inside that object. If we assume your rod is made of steel, for example, with a speed of sound around 5960 meters / second, it would take about 35 days for your pull to propagate to the other end of the rod.
Someone more clever than me will give you a full answer, but I don’t think your part about “1 minute” is correct. The change in position along the object will move at the speed of sound, not light. And you’re going to lose some of the force to friction as it travels.
If you stretch out a long cord and then snap one end up and down, your motion propagates down the length of the cord, yeah?
Your pull would propagate down the length of the rod.
If you could pull it, it would likely break depending on the material because of the amount of force needed.
If it didn’t break, the elastic response of the the rod material to the force applied at one end would take days to y ears to travel to the other end.
Solid objects are not actually solid at atomic level. You can imagine that all atoms that form your 1 light minute long rod are connected by springs. So when you push on one end the springs contract slightly.
Of course there is a delay before springs further into the rod feel the push as springs before them need to be pushed first. The speed at which this push travels is speed of sound in the material.
For metals it is roughly several kilometers per second. So you will need to wait over 20 days before the the sound wave would travel the entire light minute long rod. Of course as the sound wave travel it dissipates and grows weaker over distance.
Your pull will propagate with the speed of sound. Where the speed of light is the ultimate speed limit, the speed of sound is the speed limit for any mechanical deformation.
A somewhat comparable situation is when you let go of a slincky. The top will start falling before the bottom does.
The pulling action should propagate across the rod even slower at the speed of sound in the material. The rod can stretch and compress on a microscopic level, a bit like it was made of rubber but usually less. So the part that you’re holding will stretch, a moment later the part that is right next to it will feel the force and follow, and so on.
Yep, the rod will stretch. And if you pull too hard, you’ll rip the rod into pieces.
And it’ll take longer than a minute for the other end to begin moving, because you’ve got to wait for the pressure wave to reach the end. The speed of that pressure wave is related to the speed of sound through solid matter, and is slower than the speed of light.
The other end of the rod will be stationary for far more than one minute. When you pull on the rod, you generate a wave that propagates through the molecular lattice, which moves at the speed of sound in that material. Likely on the order of 10^3 or 10^4 m/s. That’s four orders of magnitude slower than the speed of light. The far end of your rod will be sitting idle for a very long time.
And yes- the rod is stretching during that time.
You’re mistaking “seeing the far end of the rod move”
For how long it will take the rod to move.
If you could observe the far end of the rod it will take 1 minute for the light to reach your eyes for you to see it moving, but it’s still moving.
Imagine instead there is a light that turns on when the rod starts moving. It will become visible to you 1 minute after you start pulling the rod, but it turned on the moment you started pulling
It’s my understanding that the movement propagates down the rod.
We’re just used to seeing the “whole rod” move when we move a pencil or something our scale.
In reality, it doesn’t all move at once. The movement propagates. It does “stretch” or it can snap.
I don’t know if any materials would actually be strong enough to allow for this, or what speed. But I believe that’s separate from the core of the question:)
If you have enough hypothetical strength to pull it, then, yes, it will stretch. If you had enough strength to push it, it would compress. But we’re getting into such hypotheticials that you have to cheat the math somewhere. You could add, “What if the rod was made of a magic unstretchable material,” and get to a point where you would break physics and create a situation where information was traveling faster than c, but what’s the point?
The other end actually wouldn’t move in one minute. It would be the speed that sound travels in the material. The motion travels down the bar with all the atoms interacting with the ones next to it.
Alpha Phoenix has a really good video on it where he measures the “speed of motion” using an oscilloscope by running a circuit through a hammer, metal bar, and contact plate.
https://www.youtube.com/watch?v=DqhXsEgLMJ0
At those distances even solid steel kinda acts like a stretchy rubber band. You can pull on one side but the other side remains in place.
The 1 minute would have been right if wave propagation was at speed of light, but wave/motion propagation through a solid is at speed of sound. So you have to take 1 light minute and convert to meters or something then look at speed of sound in meters per time.
One thing I’m not seeing in many of the other answers is consideration for how much mass this rod would have. If it were a 1/2 inch thick steel rod it would mass around 18 million metric tons. So it’s not like you would be able to pull it a foot closer to you instantly.