Windmills and the Speed of Light

[audiomatic]

An acquaintance (my boss, actually, so please be nice) has suggested that, if a windmill could be made large enough, the tips of the blades could travel at the speed of light. Notwithstanding the impracticalities (there's no wind up there; the blades would surely strike the planets; where would the raw materials come from?), I'm intrigued by the prospect of traveling along one of the blades until I achieve the speed of light. Not me personally, although I could be pursuaded to go part-way.

What are the theoretical limitations? The only rule is that the blades must remain ridgid and "straight." I added this rule because my next question is: Would the limitations on the tips of the blades traveling at the speed of light in turn limit the rate of rotation of the hub?

We might also not place the windmill within a planetary system or anchor it to a massive object so as to avoid undue gravitational forces. As impressed as I may be with any formulae you may provide, lay responses would likely be of most interest to me. Also, if anyone has actually tried this, please post pictures. Oh yeah: I am not in the business of manufacturing or selling windmills, and this is not a Homework Question.

Thanks in advance for any thought-provoking responses. The most concise yet informative response will win this contest.

 

[Dale]

What are the theoretical limitations? The only rule is that the blades must remain ridgid and "straight."

The problem is that this rule is impossible; perfectly rigid materials are incompatible with relativity. As the blade tips approach c the stresses in the blade become infinite, so, regardless of how strong the material, it will deform and it will break.

 

[n4n0b0y]

This question has been voiced to Albert Einstein himself, back when he was still formulating the principles of relativity. It is one of the mind experiments which brought on the space-time revolution.
However, back then, the question was posed with a mary-go-round ;)
Anyway, the material will NOT break, nor will they remain straight, though. Due to the curvature of space, and the cosmic speed limit (c), the windmill's arms will slowly begin to curve inward as the speed of the endpoints approaches c (→c).
Hope this helped.

 

[yuiop]

Even if you could have perfectly rigid blades (which as Pervect pointed out, is impossible according to the rules of relativity) you would still require infinite energy to get even one atom at the tip of one blade to travel at light speed, so impossible.

 

[AdrianMay]

We'd need GR for this cos nothing is moving in a straight line.

 

[Dale]

That is not necessary.

EDIT: actually, I thought more about this and I think that it is necessary, see post #8

 

[AdrianMay]

Ohhhh yes it is.

Fancy meeting you here ;-)

 

[Dale]

We'd need GR for this cos nothing is moving in a straight line.

Actually, I have thought a bit more about this. GR is required for a complete analysis of this problem, but not for the reason given, i.e. not because things are moving in curved lines.

GR is not required to analyze acceleration nor even accelerating reference frames. GR is only required to analyze gravitation, i.e. curved spacetime.

The curvature of spacetime is governed by the Einstein field equations which state that the curvature depends on the stress-energy tensor. Since the stress in the windmill becomes infinite as the tips of the blades approach c the stress-energy tensor becomes non-negligible and GR is needed.

 

[audiomatic]

Thanks all,

So . . . the Special Relativity factors that may prevent an object from achieving C (increased mass, elongation in the direction of travel, time slowing down) would not control in the case of windmill blades (or “objects” rotating around an axis). General Relativity (the curvature of space), not stresses on the blades, would “cause” the blades to curve before Special Relativity considerations become relevant. Am I interpreting this correctly?

To the second question: If the blades cannot remain straight due to the curvature of space (rather than stresses imposed due to the blade tips being unable to achieve C), would there be any reason for the rate of rotation at the hub to slow, or is rotation at the hub unaffected by the curvature of the blades?

Thanks for indulging us and not citing formulae. I will certainly pass along n4n0b0y’s suggestion that the inability of the blade tips to achieve C can be equally accomplished with a merry-go-round; somehow this seems more practical than the windmill idea.

 

[Dale]

Thanks all,

So . . . the Special Relativity factors that may prevent an object from achieving C (increased mass, elongation in the direction of travel, time slowing down) would not control in the case of windmill blades (or “objects” rotating around an axis). General Relativity (the curvature of space), not stresses on the blades, would “cause” the blades to curve before Special Relativity considerations become relevant. Am I interpreting this correctly?

To the second question: If the blades cannot remain straight due to the curvature of space (rather than stresses imposed due to the blade tips being unable to achieve C), would there be any reason for the rate of rotation at the hub to slow, or is rotation at the hub unaffected by the curvature of the blades?

Thanks for indulging us and not citing formulae. I will certainly pass along n4n0b0y’s suggestion that the inability of the blade tips to achieve C can be equally accomplished with a merry-go-round; somehow this seems more practical than the windmill idea.

AFAIK n4n0b0y's comments are completely incorrect and totally unsubstantiated. The blades will not curve inwards, like any material they will stretch outwards under the radial stress and according to GR they will break no matter how strong the material. His/her comment would be the worst one to pass along.

 

[AdrianMay]

I'll agree that you only need SR to conclude that the tips are not going to exceed c. I strongly disagree that you can treat a rotating system like this with anything less than GR. For instance Mercury's orbit was adjusted by both SR and then again by GR, and its speed is nowhere near c.

In fact, there has been work done on rotating black holes, which I think is more or less what were are talking about. Just by supposing that the dilemma arises, we are postulating a black-hole-like centripetal force.

As for acceleration in SR, well, you can talk of an inertial mass adjusted by gamma, but that's about it. GR gets started by considering an astronaut floating about weightlessly in a tin can. It points out that he wouldn't really know if he was moving inertially in a region of no gravity, or falling towards a mild gravitator (mild meaning that we can ignore tidal forces (at least until page 2.)) Similarly, if he was standing on one wall, he wouldn't know whether he'd landed on a planet or had his engines on. It would feel the same. (You also know that Issac Asimov liked his space stations doughnut shaped so he could spin them to make artificial gravity.) A deep connection between gravitation and acceleration is thus established on page one of GR. Persuing that line of thought, he dispenses with the "force" of gravity altogether and formulates gravity as a kind of acceleration that's instrinsic in the spacetime itself.

So I wasn't trying to say that SR banishes the concept of acceleration from the universe, or that you can't do any naive calculations to first order. But a FULL treatment of systems involving lots of acceleration (including rotation) does indeed call for GR. It is not the case that SR can handle anything at all that happens in deep space where there are no stars and planets around.

 

[Dale]

I strongly disagree that you can treat a rotating system like this with anything less than GR. ...

So I wasn't trying to say that SR banishes the concept of acceleration from the universe, or that you can't do any naive calculations to first order. But a FULL treatment of systems involving lots of acceleration (including rotation) does indeed call for GR. It is not the case that SR can handle anything at all that happens in deep space where there are no stars and planets around.

This is incorrect, see my full rebuttal at:
https://www.physicsforums.com/showpost.php?p=3788733&postcount=30