Lightspeed - Spaceship on a lever theory.

[GideonRey]

I've been thinking about the speed of light, and if it is possible to exceed it.

So, I came up with my spaceship on a lever theory.

Essentially, you have a long lever with a fulcrum near one end. At the other end, you attach a spaceship. Next, you apply pressure at the short end of the lever.

Given a large enough ratio of difference between the two sides of the lever, I would think it would be possible to accelerate the spaceship beyond the speed of light.

I am, of course, assuming that the fulcrum is firmly fixed at one point in space, that I have an unlimited energy source, and that the lever will not bend or break.

Am I missing something here, or, given the above conditions, would it be possible to exceed the speed of light?

 

[Vorde]

https://www.physicsforums.com/showthread.php?t=536289

Not quite the exact same thing, but this should get the point across.

Also I'd note it's impossible to have an infinite amount of energy, so you're asking if you can do something impossible by doing something impossible.

 

[phinds]

... so you're asking if you can do something impossible by doing something impossible.

Well put !

 

[Lsos]

I am, of course, assuming that the fulcrum is firmly fixed at one point in space, that I have an unlimited energy source, and that the lever will not bend or break.

It should also be noted that "a fulcrum fixed in one point in space" and a lever that "will not bend" are also impossible.

And of course the impossibility of an unlimited energy source is, indeed, a very often cited reason as to why achieving the speed of light is impossible.

 

[BobG]

https://www.physicsforums.com/showthread.php?t=536289

Not quite the exact same thing, but this should get the point across.

Also I'd note it's impossible to have an infinite amount of energy, so you're asking if you can do something impossible by doing something impossible.

This is not the same thing. Certainly, the information that the lever is being pushed can't instantaneously reach the other end of the lever, but the information will get there eventually, and when the information does get there, something should happen. The link is related; but doesn't really address the original poster's problem.

However, you can do this a lot easier if Einstein's theory of relativity is not true. Simply bounce a light back and forth between two mirrors that are mounted on a moving train (preferably a very, very long train, traveling very fast since it would be hard to make precise measurements on a normal train).

Since the train is moving, light traveling in the direction of the train should take longer to reach the forward mirror than it takes for light traveling the opposite direction of the train to reach the rear mirror.

And, yes, one would expect there to be a difference.

However, even though the set-up is different (since a real experiment requires that you come up with a way to take some measurements), the experiment is basically the Michelson-Morley experiment and the expected is not what happened.

Nor would the expected happen in the original poster's experiment. Granted, the original poster's experiment would be virtually impossible to carry out, which makes it no more than a "what if" thought experiment with no real answers unless you're deriving the answers from an experiment that actually was carried out.

Not really a criticism of your post (or any others). I just think it would be more fruitful to direct him to an experiment that was really carried out.

 

[HallsofIvy]

This is a variation on another old "paradox". Imagine a rigid pole extending from the Earth to the nearest star. I can send a "morse code" message to the other star by pushing on this end- a long push being a "dash", a short push a "dot". Although no physical object moves faster than light, I am sending a message faster than the speed of light!

The error in that is that, for exactly this reason, there can't be "perfectly rigid" poles- there is always some "give" which means that the speed of sound in the pole is less than the speed of light and the push is transmitted at the speed of sound. Similarly, you cannot have a lever bar that will turn without bending.

 

[Vorde]

The reason I linked to the post I did was because I thought the error in the OP's logic was what HallsofIvy just said - that the fulcrum could be perfectly rigid. In that sense I thought it was the same mental problem as the rigid pole thought experiment.

 

[russ_watters]

Because of the infinite energy requirement, the pole would still have to be infinitely rigid. So while not quite the same, there are some similarities. The need for the infinite rigidity just doesn't manifest at first glance.

 

[VantagePoint72]

This is not the same thing. Certainly, the information that the lever is being pushed can't instantaneously reach the other end of the lever, but the information will get there eventually, and when the information does get there, something should happen. The link is related; but doesn't really address the original poster's problem.

I disagree, I think the link answers the question completely. If I understand your objection correctly, you're saying that the FAQ post only demonstrates that the far end will not begin move instantaneously, but that this does not imply that when it does start to move, the motion couldn't be FTL. In fact, it does imply this.

Imagine that enough time has passed that the information that the end of the lever near the fulcrum is moving has reached the far end so it begins to move. As the lever is pushed, the far the end will trace out some kind of curved path (a perfect circle if the shape of the rod stays fixed—ie it settles into some kind of stable curved shape after the far end starts moving—and a more general path otherwise), which means the end of the rod is accelerating. This requires a force, provided by the tension in the rod, and other restorative forces like from the rod flexing. Tension, etc., is the result of stretching molecular bonds and so, by the same arguments as the FAQ post, is limited by the speed of light—i.e. if I pull on one end of a fixed rod, I won't feel it "pull back" until the disturbance I create by tugging on it has had time to propagate down to the fixed end and then back to me. Hence, even after the end of the rod starts moving it can't move faster than light because (1) it's accelerating, (2) the force for acceleration along each infinitesimal segment of the end's path is provided by the tension in the rod, (3) that tension arises from mechanical disturbances propagated between the ends of the rod, and (4) the speed of those mechanical disturbances are limited by the speed of light.

Maybe a concrete experimental example like you've suggested helps make the point better, but the original response does fully address it.

 

[soothsayer]

The idea of a rigid object breaks down in special relativity, so at a certain point, your level could no longer accelerate the ship. It would basically cease to be a lever
.