This is something I thought of about 20 years ago, and no matter who explain it to I seem to get a different response. So first off, I ask on your honour that you not look ahead and copy responses from others who may post here. Post your own answer first - then look at what others have to say.

The idea is to make a "large" wheel, just 1 foot > 1 light minute/pi in diameter (or 1 light minute + a few inches in circumference). Then accelerate the wheel until it's spinning at 1 RPM.

The actual idea behind this is to release a piece of the wheel once it gets up to speed, but that part's optional if you don't think we can get the wheel up to speed in the first place.

Now some say the wheel will shrink to a point-mass. Others say it will expand, even to infinity if we keep trying to accelerate it. I won't go into all the other predictions because I'd like to have those who respond make up their own minds/solve it on their own. To some it might make a difference whether the wheel was simply an empty ring or if it was all one solid piece. If you think this matters, please say so.

Now some say relativity only applies to objects traveling in a straight line, and they have no problem with the wheel getting up to one RPM. But they do have a problem with releasing a piece of the wheel at that speed, since it will have to travel in a straight line.

So what happens when we spin the wheel? I have my own opinion, but I'm not 100% confident that I'm correct. I would really like to know what the mainstream SR/GR predicts, and other solutions are welcome as well.

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That's a sporting offer. And I'm a mainstreamer. So, without looking up relativity for rotating reference frames, my first guess is that you'll never be able to put enough energy into the wheel to get it up to speed, just as you can never get a spaceship (preferably my wonderful starship, used for examples, which can accelerate indefinitely at 1 g) up to the speed of light. Close, yes, but never there. That's the nature of asymptotic functions. In addition, the edges of the wheel will be enormously massive from the viewpoint of the external observer, and my second guess is that frame dragging will be a big issue.

But it’s a clever idea. Ah --- I don’t have the math skills for it, but I think as the edge of the wheel approaches c, weird things happen with the centrifugal force vector (tensor?). Also, to the external observer, the apparent mass of the object will be central. Can it do the gravitational collapse trick due to apparent increase in mass? I have no idea. Maybe a general relativity mainstreamer can help.

* I think you should be more explicit here

This is a fun problem!!

The problem I see is that centrifugal force would overcome the electromagnetic force holding the molecules and atoms together and so the wheel would disintegrate.

If the disintegration were such that only the outermost atoms flew off once their electromagnetic attraction was breached (it eroded from the outside towards the inside) then at what diameter would the wheel stop eroding?

Or at what rpm could the wheel be spun before erosion began?

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I don't believe in the time dilation of relativity but instead I think that the subatomic workings (clocks) of atoms is dilated (slowed).

I also believe that length contraction is a measurement effect caused by using light to do the measurement.

So I do not think the circumference will contract due to length contraction but since the internal workings of the atom are slowed then the bonding power of these workings with adjacent atoms/molecules is affected by the velocity - how this affects the integrity of the structure I can only conjecture.

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If time dilation is true and length contraction is real then I would guess the length contraction would be halted by the electromagnetic forces of the atoms - causing tensile stress around the circumference.

When the tensile stress reaches the limit of the material then it would break apart.

The center portions would be compressed by the circumferential length contraction, also, and whether this force is enough to compress the wheel into a blackhole is up for speculation - but in order for this to happen then the electromagnetic force between the atoms at the circumference would have to be strong enough to be able to crush the matter into blackhole stuff - which I do not think is possible.

Plus centrifugal force would offset the inward compression.

That is about it as far as I can imagine right now but I may be back with more.

I've been reticent to post because it seems somebody gets ticked regardless of your opinion. I don't think I can get in too much trouble here, however.

Because along x prime length only contracts in the direction of motion and that direction is constantly changing, pi and thus infinity are involved in the motion aspect around the circumfrence, but t prime is not affected by the direction of the motion; only the velocity, time would begin to slow for the material around the circumfrence and the direction of the motion would have to begin to approach a straight line eventually...wow...I'm gonna have to give this more thought than I initially thought I would. LOL good one! Are we to suppose that this wheel is constructed from an indestructable material and the piece we are going to let fly is located along the circumfrence?

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Ahhhh...Beer...The cause of and the cure for all the worlds' problems ~Homer Simpson

Generally I prefer indestructible material. Something "hyperspace-age" or with a mechanism like magnetic fields or such could be used. Trouble is: I don't know which problems you have to look out for beyond tensile strength (which is probably an issue).

And for certain we're cutting loose a small piece of the rim. That was my initial goal with this "invention": FTL in a straight line for a sci-fi story I never got around to writing.

What I was taught in high school was that there is lengthwise contraction accompanied by side-to-side expansion (of a lesser magnitude). At least for straight-line travel. If it applies here, this means that the wheel must increase in diameter while simultaneously decreasing in circumference. To me that seems pretty well impossible.

I think the time factor could get interesting in a solid wheel since inner parts are experiencing time closer to normal and outer parts are trying to drag both timewise and masswise (if you buy into the whole thing).

Thanks to everyone who responded so far. I'm rather thrilled to have so much interest in this subject so soon. I haven't time to say more just now, but I'll be back 1st chance I get - prob Saturday.

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Okay. I thought these were the simplest terms to understand, but this amounts to 5901464321 feet in circumference or 18794351694.27 feet in diameter. 1 RPM means the wheel completes one rotation per minute.

Tallying these numbers, I realized that it isn't really all that big as extra-terrestrial things go (it's only .12 parsecs around the thing). There are certainly stars reported to be bigger. So I started investigating spinning stars.

The best star I've found a report of so far is PSR J1748-2446ad, a pulsar with an equatorial surface speed thought to be 40% of c. It's a millisecond pulsar. (little, but really fast)

They expect pulsars with periods of less than .001 seconds to be unable to hold together - so it looks like my wheel will need to be made of something even more indestructible or with much stronger magnetism + gravity / whatever to hold it together. Why oh why must matter always be too wimpy for fun experiments!

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Signatures? We don't need no stinking signatures!

I think you swapped the circumference and the diameter.

(5.90 x 10^9)*(3.14 x 10^0) = (18.53 x 10^9)

Hmm, still something wrong. I'll be back later.

What I meant was, how you plan to accelerate it up to 1rpm There ya go!

The professor's diameter is correct because if it is rotating at 1 rpm then the circumference is traveling at light speed - which is the point of the problem.

The fact that the professor wants the wheel diameter to be a little larger, by a foot or several inches, means that an attempt is being made to create a faster-than-light (ftl) propulsion device because any diameter larger than 1 light minute/pi spinning at 1 rpm causes the circumference to travel at ftl speeds.

Faster-than-light speeds, of course, is impossible but it is interesting to consider the relativistic effects of such a "miracle" device.

Here are my calculations:

c in miles per second 186,282.40

seconds 60.00

circumference in miles 11,176,943.82

circumference in feet 59,014,263,369.60

pi 3.14

diameter in miles 3,557,732.46

diameter in feet 18,784,827,364.47

radius in miles 1,778,866.23


Professor Illwill’s figure, 5901464321 feet, or, easier to see, 5,901,464,321 feet, is off by an order of magnitude, due to dropping a 3.

Which doesn't change the fact that this is one fun idea. Cm'on, folks, more posts.

It looks like I'm right and you're right which makes somebody wrong - we'll have to have our lawyers get involved so that we can truly know the truth (after about 20-30 years and millions in cash).

Knowing next to nothing about relativity, and in response to the OP, here were my thoughts, more or less in the order they came to me.

1. It would fly apart before it ever got up to speed.
2. But if it didn't, how would any one section of the wheel be any different than a car racing around the inside edge of it? The car would be following a circular path at 1 RPM, but since it's not connected to itself on both ends, the distortion would affect it.
3. Shut up cat. (That was mainly in my own frame)
4. What if the "drive" section was located at about 50% of the radius of the wheel and only accelerated to 0.5c? It would not have the infinite energy requirement (would it?) that 1c would, but it would still allow the outr edge to break 1c (or not).

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A Nerd can figure out how long it will take the original Enterprise traveling at warp 6.5 to travel from Regulus to Antares.
A Geek will think he can use that to pick up a girl in a bar.
A Dork knows he can't pick up the girl with it, but will hang around for hours anyway, just in case she asks.
She might. You never know.

Feed the cat!!


I think if the wheel had gaps in it then it would still have to contract because relativity requires not just matter to contract but also space between matter. So if length contraction affected the entire circumference of a solid wheel then length contraction would likewise affect the entire circumference of a discontinuous wheel.

Let the cat out.

1. True, but that takes all the fun out of it.

2. I think you're right.

3. I assume this is Schroedinger's cat. I'm glad to know it's alive.

4. I think it still has the infinite energy requirement. The wheel is accelerating as one piece (at least until it comes apart).

I think there is a way around the flying apart problem, but we'll save it until the thread bogs down.

Also, this is not really an ATM thread, it is more of a 'what if' using mainstream special and (hopefully, I can't do it) general relativity.

I suspect that this wheel may shrink --- without internal stress --- but it's going to be difficult to demonstrate it.

i can see why you chose the name Professor ILLWILL because your little problem is going to trouble me now for the rest of my life!
I love it! Thank you!

Assuming that your "indestructable material" is immune Even on the Quantum Level....
I'm still wondering about 1/)the ENERGY required to get it up to speed and 2.) the TIME required to get it up to speed.

Sidewise expansion is a common misconception, and yes, it has gotten into some references. I know, because I had it wrong for years, on the basis of misinformation supplied to me. It doesn't happen. The contraction is in the direction of motion, and that's it. The rocket ship, atomic particle, piece of the wheel, whatever, doesn't get any wider. Reference 'Space and Time in Special Relativity' by Mermin for a good discussion.

Also, before we go off on a tangent (pun on the piece of the wheel intended) about relativity, let's keep in mind that special relativity is demonstrably correct to 1 part in 10^20th. If you want to argue about relativity, this isn't the place for it.

It just occurred to me that a circular particle accelerator is similar to the proposed wheel. The particles circle the accelerator at 99% plus of the speed of light. One of the side effects is profuse synchrotron radiation from the accelerator's magnetic field. Even in a weak interstellar magnetic field, I think the wheel is going to glow in the dark--at least at some frequencies.

By the way, Dr. Illwill, did you do some studies of hand launched free flying oblate spheroids for the Denver Broncos?

Actually, this is the place to argue about relativity because this is the ATM section.

I don't think there is a space requirement. Everything comoving in a moving reference frame, for example a frame with two physical objects separated by some distance, is contracted in the direction of motion, including the distance between the objects, and the distance between the atoms of the objects, and the distance between the air molecules being transported with the frame (assuming the usual rocket ship example) to a stationary observer.