Weird thought experiment

If you had an infinitely long bar and you set it attached at one end so it could rotate around that end. Would it appear to have a finite length to an outside observer when it’s spinning?


if it’s infinitely long, doesn’t that mean that it doesn’t have an end to attach a rotation point to it in the first place?


Extends to infinity from the rotation point. Also infinite tensile strength.


For an outside observer, the bar can only spin about its own axis, because finite c. I wonder if there are any weird effects on space-time if it does spin about its axis?


The unfortunately boring answer is well, you can’t do that. I get the idea is that you’re trying to ignore specific physical limitations to explore what would happen with others in the limit, but here they add up to much.

Regardless of tensile strength, what keeps an object solid is interaction between its atoms, and those only propagate outward so fast. If you ignore this and imagine an infinite bar rotating around one endpoint, other parts of the bar are going to go arbitrarily fast, past the speed of light on to infinity – they’re not even moving along time-type intervals any more. You can’t describe what that looks like to an observer if it’s breaking all the rules we use to describe observers.

Better to come up with some other model that reflects what you’re trying to consider, without reaching quite so far past what physics can tolerate.


Thank you. You said what I wanted to say, but better. :slight_smile:


ok. your thought experiment, your rules.


Not really. To make such a thought experiment possible, you’d need a fairly complete set of rules for a universe where mass can exceed the speed of light (and the bar will be moving much more quickly over most of its infinite length), partly because, as @chenille has noted, the weak, strong and electromagnetic forces that hold mass together only propagate at light speed, and because, as Einstein noted, as the velocity of matter tends toward c, its apparent mass tends toward infinity, and the force required to accelerate it further also tends toward infinity. Frankly, I doubt that it would be possible to even start spinning such a bar.


Agree; it’s like the old puzzle of an irresistible force meeting an immovable object. Neither can actually exist, and certainly not in the same universe.

But even if you could somehow set up those conditions, the infinite bar doesn’t have an “end” that can come into view. That would seem to violate the definition of infinite.


I briefly thought this was about the time travel thought experiment until I realized the question had the bar spinning around one end rather than rotating around its length.


A Tipler cylinder with one end is the only version of the described setup which avoids exceeding c.


I think that, as a hypothetical, @Daveb’s single-ended bar can be infinite (but it would have to be single-ended). It would be analogous to {Ɐx ∈ ℝ, x ≥ 0: ƒ(x) = x}. That defines an infinite line with start at the origin.

However, if it extends infinitely away from the observer, and assuming it instantaneously came into being not long in the past, then a) the observer will only be able to see a very small portion of the bar, the portion that equals the distance light can travel in the period since the bar came into being (i.e., its visible length will increase at a rate of a light year per year), and b) an infinite portion will never become observable, because the damned thing will extend past the observable universe’s event horizon and keep going.