Couldn't the outer part of a ring travel faster than light?

[Floridian]

If you created a gigantic ring in space. Lets just say its the size of our solar system. Couldn't you pump energy from the outside into the outside parts of the ring to increase its spin speed indefinently, also, lets say you couldn't get the outer part of the ring to spin faster than the speed of light, isn't the inner part of the ring spinning faster than the outer part, couldn't this part pass the speed of light?

I guess I don't understand all the physical laws of "spinning" an object in space. Lets just say the ring was surrounded on all sides by lasers that hit it at an angle to give it spin.

*****EDITED TO SAY OUTER PART INSTEAD OF INNER PART*****

Other edit -

Instead of bombarding the outer part of the object with photons or a laser or something (it would be impossible to reach light speed this way), what if there were an axis in the inner part that was spinning. If the outer part was moving 2x as fast as the inner part. My question is if you accelerated the inner part to .6c the outer part would be 1.2c correct? Barring whatever problems there are with that. Lets say you had the energy source.

 

[theridane]

Re: Couldn't the inner part of a ring travel faster than light?

Nah. If the outside of the ring is spinning at a velocity v, then the inside of it is going to spin at a velocity lower than v.

The thing with accelerating near the speed of light is that the closer you get to it, the larger your relativistic mass is. So if the ring is spinning at an angular velocity so that the outside-most layer of it is going nearly c, then this layer will have its relativistic mass nearing infinity. And since acceleration is equal to force divided by mass, dividing any force by near infinity yields near zero. That's why you're not gonna reach it - close to the speed of light your forces don't do squat.

 

[Astro_Robert]

Re: Couldn't the inner part of a ring travel faster than light?

For rotating things, linear velocity is related to angular velocity times radius. If you take a string with a weight on the end and whirl it about, the entire string will be taught and complete a rotation at the same rate, say 1 per second. The speed any portion of the string is travelling at is then related to how far it is away from your hand.

Circumference = 2 * pi * r. Angular Speed = 1 rotation per sec. Linear speed = 2 * pi * r / # rotations per sec in whatever units of length you are using. Its just: Rate * Time = Distance, or Rate = Distance / Time.

This is why theridane stated that the inner part of the ring would necessarily be rotating more slowly than the outer part of the ring, the inner part by definition has a lower radius than the outer part, which is why it is called 'inner'.

 

[ramparts]

Re: Couldn't the inner part of a ring travel faster than light?

All of these things are true, but there's another reason the idea wouldn't work. Actually, two. First of all, due to relativistic effects, length contraction and time dilation and all that good stuff would happen along a ring traveling near c, and that would serve to make sure the rest of the thing can't move faster than c. But there's one other thing which I especially want to talk about, which is that there's no such thing as a pure solid. A ring or any other solid is a collection of atoms held together by electromagnetic forces, and those by definition can never provide a force which moves anything faster than c. So the fact that a ring is solid wouldn't get you around the restriction on c, since you actually wouldn't be able to drag the ring's particles along to travel at those speeds.

 

[BurgerB75]

Re: Couldn't the inner part of a ring travel faster than light?

Plus I would imagine that the forces involved, especially as the outer edge gets closer and closer to c that the whole ring would just rip itself apart.

 

[theridane]

Re: Couldn't the inner part of a ring travel faster than light?

Well if we're talking realistic materials here, the whole thing would fall apart ages before it would even touch relativistic speeds.

Let's say the ring is about 60 AU in radius, roughly 2 Neptune's orbits. In an equlibrium, it would be rotating at the orbital speed at that distance, which would be around 3.8 km/s or about 465 years for one orbit.

Now if this speed were to increase, the inertia would try to inflate the ring, i.e. it would start feeling a centrifugal force.

Every material known (and unknown) to man has some kind of tensile strengt. If this force (or more technically, negative pressure) is exceeded, the material breaks. The absolutely super-best material known (carbon nanotubes) has a theoretical breaking strength of 300 GPa (realistic values are orders of magnitude lower, and materials like steel reach values of only 0.5 GPa and less).

Assuming material density of 100 kg/m³ and ring diameter of 1 meter, the whole ring would weigh approximately 4500 gigatonnes. Not bad actually, we could build a ring like this here on Earth.

When this ring is in orbit, the forces acting inside are zero (neglecting third-body influences). It's weightless. If it spins up to twice its orbital speed, it would feel as if the gravity was working upside down - going away from the sun. That's the centrifugal force going on. As it speeds up, this force increases, until the ring comes apart.

The breakage should occur when the tensile force reaches the breaking force, that is when A*L = (m*((n-1)v)^2)/r, where A is the ring cross-section, L is the breaking strength, m is the total ring mass, v is the orbital velocity, n is the multiplier of this velocity (1 = orbital, 2 = twice the orbital, etc.) and r is the orbital radius (60 AU).

Solved for n, the ring would break at a velocity of just 6.68 times orbital speed, or about 26 km/s (unless my math got wrong at some point, which is very much possible... but I think I got the order right, at least).

That's a ring made of the strongest material theoretically known, with a serious weight cheat, and it still doesn't cut it.

 

[MeteorWayne]

Re: Couldn't the inner part of a ring travel faster than light?

In addition to all the above, since the laser light travels at c, even if the ring had no mass, it would never spin faster than c.

 

[captdude]

Re: Couldn't the inner part of a ring travel faster than light?

If we were to remove all forces that prevent the ring from reaching "C" wouldn't the physical structure of the ring be converted from mass to energy?

 

[theridane]

Re: Couldn't the inner part of a ring travel faster than light?

There aren't any forces preventing it from reaching c. It's their absence that does.

 

[captdude]

Re: Couldn't the inner part of a ring travel faster than light?

by theridane » Sun May 09, 2010 12:50 pm

There aren't any forces preventing it from reaching c. It's their absence that does.


Could you please elaborate for me? :?

 

[theridane]

Re: Couldn't the inner part of a ring travel faster than light?

Well not the forces themselves, their effect.

As you're getting closer to c, your relativistic mass approaches infinity (here's why). Since acceleration is defined as force divided by mass (a = F/m), the higher your mass is, the lower an acceleration does the same force provide. In numbers, suppose you have a spaceship that weighs 10000 kg, runs on magic daisies and puppies, and has an engine that puts out 1 MN of thrust.

Launching from somewhere in Earth's orbit this spaceship would accelerate at 1 MN/10000 kg = 100 m/s² or about 10 gees of acceleration. That's pretty darn good.

Now some time later the spaceship is travelling at 0.9 c and the engine's still burning. Its relativistic mass is now 10000/√(1 - 0.9²) ≈ 52631 kg, so it's accelerating at just 19 m/s², not even two gees. Going even further, at 0.99995c the acceleration drops below 1 cm/s² - that's as good as not accelerating at all.

The acceleration drops down asymptotically, approaches zero, which is why in effect any object with nonzero mass can't reach the speed of light.

 

[captdude]

Re: Couldn't the inner part of a ring travel faster than light?

by theridane » Sun May 09, 2010 12:50 pm

There aren't any forces preventing it from reaching c. It's their absence that does.

I understand all that. But I still do not understand your statement. Your example is explained by forces - not their absence.

 

[Floridian]

Re: Couldn't the inner part of a ring travel faster than light?

Nah. If the outside of the ring is spinning at a velocity v, then the inside of it is going to spin at a velocity lower than v.

The thing with accelerating near the speed of light is that the closer you get to it, the larger your relativistic mass is. So if the ring is spinning at an angular velocity so that the outside-most layer of it is going nearly c, then this layer will have its relativistic mass nearing infinity. And since acceleration is equal to force divided by mass, dividing any force by near infinity yields near zero. That's why you're not gonna reach it - close to the speed of light your forces don't do squat.

Oh yeah my bad, I meant to ask, could the outer part of a ring accelerate faster. That is, you accelerate the inner part of the ring on an axel or something and the outer part moves faster using the reverse of your equation.

Close to to the speed of light your forces don't do squat.

What would happen though. Lets hypothetically say the outer part was moving twice as fast as the inner part. What if you accelerated the inner part to .6c. The extreme mass of the outer part would resist the inner part once it got near .99? That makes sense according to Einstein's theories but doesn't really make sense to me. It seems like physically it would just be an object with mass, and you would be accelerating it.

 

[Floridian]

Re: Couldn't the inner part of a ring travel faster than light?

Plus I would imagine that the forces involved, especially as the outer edge gets closer and closer to c that the whole ring would just rip itself apart.

That makes sense

 

[Floridian]

Thanks for the replies, looks like tensile strength is the barrier to this happening.

In regards to the light speed barrier, lets theoretically say,

You are using a matter laser or photon beam, whatever it is, to propel a spacecraft. If you were using an extremely focused series of photon beams, say you accelerated the craft to .9c, ignoring how long this would take.

Once at that speed, if the craft had an antimatter engine or something futuristic it could turn on, could it a accelerate pass light speed?

The obvious problem with be that, it would require infinite energy as the mass increases infinitely, that doesn't seem like it would be true to me though.

 

[Mee_n_Mac]

Once at that speed, if the craft had an antimatter engine or something futuristic it could turn on, could it a accelerate pass light speed?

Nope. And you already know why.

The obvious problem with be that, it would require infinite energy as the mass increases infinitely...

 

[theridane]

Re: Couldn't the inner part of a ring travel faster than light?

Lets hypothetically say the outer part was moving twice as fast as the inner part. What if you accelerated the inner part to .6c. The extreme mass of the outer part would resist the inner part once it got near .99? That makes sense according to Einstein's theories but doesn't really make sense to me. It seems like physically it would just be an object with mass, and you would be accelerating it.

Oh now I get it. Yeah, that would work in a newtonian universe, but not here. Because it doesn't matter what kind of an intricate mechanism you use to deliver the force, ultimately it boils down to something acting directly on the outer part. If your ring looked something like the Ø sign, the outer ring's resistance to motion (its relativistic inertia) would generate a force on the crossbar acting against your input force. And since you're closer to the axis of the rotation you're actually pushing against a force on a lever, multiplying its resistive effects. Like trying to move a door panel by pushing an inch from its hinge. I hope this makes some sense )

The resistive force generated by the increasing inertia is similar in its progression as a force pushing on a piston in an air-filled closed cylinder. Initially there's almost no resistance, because the air is at one atmosphere. As you push on it, the air compresses more and more and the force acting against you increases, until you're unable to push it any further.

 

[MeteorWayne]

Thanks for the replies, looks like tensile strength is the barrier to this happening.

In regards to the light speed barrier, lets theoretically say,

You are using a matter laser or photon beam, whatever it is, to propel a spacecraft. If you were using an extremely focused series of photon beams, say you accelerated the craft to .9c, ignoring how long this would take.

Once at that speed, if the craft had an antimatter engine or something futuristic it could turn on, could it a accelerate pass light speed?

The obvious problem with be that, it would require infinite energy as the mass increases infinitely, that doesn't seem like it would be true to me though.

No, what part of NOTHING CAN EXCEED THE SPEED OF LIGHT do you not understand ?

What it "seems like to you" seems to have little to do with real physics....

 

[csmyth3025]

No, what part of NOTHING CAN EXCEED THE SPEED OF LIGHT do you not understand ?

What it "seems like to you" seems to have little to do with real physics....

I do have a question about your reply. It's a bit off-point from the original post but I hope some clarification of the statement that "...Nothing can exceed the speed of light.." can help me with the following:

I understand the rationale that no two massive objects in "local" space can be observed to exceed the speed of light (towards or away from each other) due to the widely accepted and experimentally verified effects of Special Relativity and Einstein's 1905 paper entitled "Does the inertia of a body depend upon its energy-content?" (essentially, E=mc^2).

That said, there is seemingly ample observational evidence that distant galaxies and quasars are moving away from our little corner of the universe at superluminal velocities. I understand that this "faster than light" recessional velocity is attributed to the expansion of the intervening space between us and the distant object.

Regardless of the mechanism by which these distant objects have attained their motion away from us, aren't they nonetheless "exceeding the speed of light" away from us?

Chris

 

[yevaud]

No, because the limiting factor of C refers to objects within our spacetime, not spacetime itself.

 

[ramparts]

Exactly - spacetime can expand however it wants because you can't use the expansion of spacetime to send a signal, and it's sending information faster than the speed of light that's really the problem. When you send information, it goes through spacetime, rather than just sitting in one spot and "going with the flow," as galaxies do (ignoring their local motions).

 

[MeteorWayne]

In addition, we can't see galaxies that are receding from us faster than the speed of light, since the light from them would never get here

 

[csmyth3025]

In addition, we can't see galaxies that are receding from us faster than the speed of light, since the light from them would never get here

I came across this paper (via a link in the Wikipedia article on the expansion of the universe):

http://arxiv.org/PS_cache/astro-ph/pdf/ ... 0808v2.pdf

It's entitled:
"Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe"

Authors: Tamara M. Davis, Charles H. Lineweaver
(Submitted on 28 Oct 2003 (v1), last revised 13 Nov 2003 (this version, v2))

The relevant portion of this article is section 3.3:

"3.3 Misconception #3: Galaxies with recession velocities exceeding the speed of light exist but we cannot see them"

At the top of page 9 the following is stated:

"...Our teardrop shaped past light cone in the top panel of Fig. 1 shows that any
photons we now observe that were emitted in the first ∼ five billion years were emitted
in regions that were receding superluminally, vrec > c. Thus their total velocity was
away from us. Only when the Hubble sphere expands past these photons do they move
into the region of subluminal recession and approach us. The most distant objects
that we can see now were outside the Hubble sphere when their comoving coordinates
intersected our past light cone. Thus, they were receding superluminally when they
emitted the photons we see now. Since their worldlines have always been beyond the
Hubble sphere these objects were, are, and always have been, receding from us faster
than the speed of light...."

I don't want to sound argumentative, but the authors of this paper seem to be saying that your statement is one of the common misconceptions about the expansion of the universe.

As a layman I can't say whether or not these authors are authoritative. Their paper seems well thought out and well explained (at least to the extent of their narrative that I'm able to follow).

Does this paper accurately present the current thinking on misconceptions about the expansion of the universe? If so, it would be well worth devoting my time to study since it seems to offer a wealth of explanatory information on the subject of the expansion itself.

Chris

 

[SpeedFreek]

Yes Chris, that paper does accurately present the current thinking on misconceptions about the expansion of the universe!


I think the point MeteorWayne was probably making was that if it were possible for a galaxy to actually recede through space faster than light, we would not be able to see it.

Even though the expansion of the universe increases distances across the universe such that, if you were to achieve that distance through your own peculiar motion relative to the universe around you, you would have had to exceed the speed of light to have done so, (sharp intake of breath due to incredibly long run-on sentence!) nothing ever overtakes a photon in its own local frame of reference. Everything is dragged along by the expansion of the universe, including the photons!

Have a good read of that paper, it is the one on which the "simplified" version in my signature was based (they are by the same authors). It explains the basis of the current model in cosmology, the Lambda-CDM concordance model.

Then, just to perhaps confuse things a little, there is another paper I would recommend for you:
http://arxiv.org/abs/0707.0380

Expanding Space: the Root of all Evil?
Authors: Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis
(Submitted on 3 Jul 2007)

Abstract: While it remains the staple of virtually all cosmological teaching, the concept of expanding space in explaining the increasing separation of galaxies has recently come under fire as a dangerous idea whose application leads to the development of confusion and the establishment of misconceptions. In this paper, we develop a notion of expanding space that is completely valid as a framework for the description of the evolution of the universe and whose application allows an intuitive understanding of the influence of universal expansion. We also demonstrate how arguments against the concept in general have failed thus far, as they imbue expanding space with physical properties not consistent with the expectations of general relativity.

Slices of spacetime "expand" as described by the Davis/Lineweaver paper, but we have to be careful not to imbue space itself with properties of expansion where they may not be scientifically justified!

There, as clear as mud!

 

[csmyth3025]

Thanks SpeedFreek. I actually read the Scientific American article your signature line links to. That was some time ago and I didn't recognize the similarity between the article and the paper (not to mention the authors!).

As I understand the situation, astronomers by the late 80's had narrowed down the Hubble Constant to ~70 km/sec per Mpc. As they were able to look farther into space using more refined "standard candles" to estimate absolute distances, they expected to find that this velocity/distance relationship would do - what?
Get smaller due to the gravitational drag of the rest of the matter in the universe on these distant objects?
Or, rather, get larger due to the fact that they were looking back farther in time when the universe was younger and gravitational "drag" had not yet slowed down these objects as much as closer ones that they were seeing in the more recent past?
I've often wondered which of these effects would predominate.

The third possibility, that the velocity/distance relationship would remain the same as far as they looked would imply, I think, that gravity has no effect at all on the rate of expansion and that distant objects were just "coasting along" with their own little piece of local space in a purely inertial fashion.

The fourth (unexpected) possibility was that the rate of expansion would be accelerating. How did they determine that as it relates to my two questions above?

Chris