# general speed of light question

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chuck22    156
scientists say that it is impossible for objects to move at or faster than the speed of light. so i've got a quick example. let's say i'm holding a rod that is a few miles long, and i have room to rotate it freely. if i rotate it at a quick speed the very end of the rod will be moving faster than the end of the rod that i am holding. infact, if it was a couple of miles long it would be moving very quickly. now let's say that i have a rod that either was long enough or that i could rotate (swing) fast enough that the end of the rod would be moving faster than the speed of light. theoretically, this is possible to make the end of the rod go infinitely faster given you could keep adding length to it or increasing its rotational speed. since objects reach a limited speed, would that be to say that the relationship between the radius and rotational speed of an object also reaches a limit?

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Zipster    2359
Well given that linear speed and rotational speed are related by the radius of the object, it would make sense that if there's a limit on linear speed, there's also a constraint on radius and rotational speed. However the relationship is v = ωR, so the limit would really be on the product of rotational speed and radius rather than on each variable independently.

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DrakeSlayer    150
I think the limit would be on the rotational speed. For a particle, the closer you are from the speed of light, the stronger is the force you need to apply if you want it to accelerate. It's like if the mass of the particle was increasing, reaching infinity at the speed of light. Since the lenght of the bar is fixed, the limit would be on the rotational speed.

Now, more interesting : instead of a solid rod, what if you used a laser. if you project a laser on the moon, the spot could move faster than the speed of light. But in this case, no physical object break the speed limit. The photons in the laser ray still travel at the speed of light.

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Darkstrike    206
If you prefer to say that the relationship between the radius and rotational speed of an object has a limit instead of saying that no object can rigidly rotate with angular speed ω and the maximal distance from the rotational axis R when ωR is at least c, sure.

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LonelyStar    192
The reason (or one possible intepretation) why nothing can go faster than light is, that the Mass increases with the speed of the object. If one object would reach the speed if light, it would have infinity Mass, therefor a infinity Force would be neccesary (which does not exit).

You get the same problem in the rotation: If the ends get close to the speed of light, there Mass gets bigger and bigger. You would need a bigger and bigger force to rotate the rod, getting the problem with linear movement.

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Eelco    301
ignoring the forces that would make your rigid body not-so-rigid, you could keep applying torque at the centre of rotation, just like you can keep applying force to a particle indefinitely. yet, as its speed comes closer to that of light, its relativistic mass / inertia will approach infinity, and your applied force/torque wont be able to produce an accelaration that pushes it past lightspeed.

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JasonL220    132
The end of the rod could not go faster than the speed of light becuase of relativity. The rod is a series of particles and as each particle travels faster it need more force to be accelerating by the same amount.

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egwenejs    125
Well what's funny about the speed of light is that there is no such thing as speed at that speed. Before you flame me on this,I have a degree in physics and think about this. Scientist have proven that the faster you go the slower time is. So, that when you go the speed of light there is no time. That's right boys and girls at the speed of light there is no time. With no time the term speed doesn't make sense.

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daniel_i_l    295
chuck22: The answer to you question is this:
there's no such thing as a completly rigid body. if you move one end of a rod then the other end will start moving only after the amount of time that it takes sound (the sped of sound is the speed that vibrations are propagated thru the body) to move thru the rod. so when you start spinning one end of the rod the other end will only start spinning in L/Vs time were L is the length and Vs is the speed of sound in the rod. because of this the rod will get all twisted up and no part of it will move faster than light.

egwenejs: when we say that "at the speed of light there's no time" that means that in the [BOLD]lights frame[/BOLD] no time passes. but obviously in [BOLD]our frame[/BOLD] it takes light a finate time to go between two points. so in our frame there is such thing as speed at light speed and theoreticlly speed has meaning even at more than light speed. but in the frame of the body theoreticlly going faster thaan the speed of light time would be going backwards! that's one of the reasons that nothing can go faster than light, because if there were than it would destroy causulty!

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remdul    176
If an object goes faster than the speed of light it goes back in time, right? There is always stuff moving around the object, seen from the object p.o.v. As long stuff is moving relative to another there is no issue. In the end all is relative and there is no 'absolute'. I don't see a limit anywhere.

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arithma    226
We can increase momentum till infinity... So what are you complaining about :P

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Airo    197
This was a question in a science quiz on tv here I believe. If you wave a spot of light, the spot can move faster than the speed of light but the individual photons in the beam cannot go faster than c.

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Talroth    3247
Where in the math does it say something CAN'T travel 'faster than light'?

It is simply the transition between super and sub light speeds that the math breaks down from what I've been told.

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I'm not a physics guy but:

energy = mass.

light is pure energy with no mass. there for it is the fastest thing that can move.

anything with a mass requires energy to move and more energy to accelerate. basically an object can not contain enough mass(energy) to get to the speed of light.

[Edited by - Ultimate_Fusion on November 25, 2006 5:32:42 PM]

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CTar    1134
Quote:
 Original post by Ultimate_FusionI'm not a physics guy but:energy = mass.light is pure energy with no mass. there for it is the fastest thing that can move.anything with a mass requires energy to move and move energy to accelerate. basically an object can not contain enough mass(energy) to get to the speed of light.

Masses aren't guaranteed to be real (as in real numbers), see tachyons for an example of hypothetical particles traveling faster than c. Of course acceleration from subluminal speed to superluminal speed is still impossible.

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This thread hurts my eyes. I don't claim to be great with relativity (the SR module I took was a mistake I'm in no hurry to forget), but there's clearly a lot of confusion in this conversation. For some reason, these trendy topics tend to encourage a lot of speculation-passed-off-as-fact. Please don't make any assertions unless you know what you're saying... or at least put a question-mark on the end [rolleyes].

Mass != Energy. Don't confuse conservation of mass-equivalence with such a degenerate identity.

It says in the maths that nothing can travel faster than light in a lot of places. Perhaps most notably, when Lorentz's factor takes the square-root of a negative value, assigning a complex value to a necessarily real observable.

While we can indeed increase momentum arbitrarily, we no longer have the formula p = mv.

If an object 'goes faster than the speed of light', it doesn't really go back in time, it just contradicts a whole bunch of prior assumptions, leading us to retract something. The idea of going back in time is just one of many such get-out clauses. Equivalently, we could claim that its mass wraps around past negative infinity or that it causes spacetime to curve the wrong way.

Anyways, the real problem is that our Newtonian intuition doesn't even nearly apply to the situation, and so the 'contradiction' is merely a manifestation of the inadequacy of our pathetic brains [wink]. There are loads of places we can break the chain, but my favourite is probably the Lorentz contraction:
Even if this rod were infinitely rigid and straight when stationary, the act of spinning it would impose relativistic effects along its length. An observer, stationary relative to the rod, would see a straight rod at all times. An omnipotent observer, stationary relative to the floor, would see not a straight rod, but a crazy hyperbolic-spiral. No matter where you place your viewer, nothing violates our postulates, Newton's laws notwithstanding.

As for the laser example, we lose on a technicality. While it may seem that a dot on the moon is moving faster than light (and it actually is), there is no actual information incident with that dot. It is only the absence of information that's super-photonic, and that's quite legal. We see only light being reflected according to the positions of the moon, and the photons in the beam, which all obey the usual relativistic laws.

Regards

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tthibault    100
Space and time are not absolute quantities, as supported by Einstein's theories of relativity. Subsequently, you could generate an angular velocity great enough that, while at the basepoint (the point that you are rotating around) you may think that you are generating an angular velocity great enough that the end is traveling faster than the speed of light (linear velocity), but, in truth (according to modern scientific theory) all that really has changed is that the endpoint is experiencing time differently than you are.

Nothing can travel faster than the speed of light because as your 'speed' increases, your passage through 'time' decreases, which is why nothing can travel faster than the speed of light (speed = delta_distance / delta_time).

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Xai    1838
chuck22 ... daniel_i_l gave the most direct answer to your question, but I just wanted to add another aspect to it. Daniel explained well the "reality" and "why" of forces propogating through your rod that translate its position (cause motion). Another point of view is simply to realize the equality of the idea of "inertia", "levers" and "force = mass * velocity * velocity" for this situation.

You see, if you could push on the end with infinite force, you are in an absurd situation already in which all bets are off anyway ... but in the real world, where you are applying a finite amount of force on the end of that rod, a very exact amount of acceleration will be applied to the particles of that rod (ignoring loss due to heat / friction) ... exactly enough acceleration will be applied such that the sum of the accelerations of all particles in the rod will add up to match the "F = mv^2" equation.

Think of applying force to the center axis of a space-station to spin it up to speed. If the space station is small, the force needed is small, just like rotating a pencil in your hands, but if the space station has a radius of 0.1km and your axel's radius is 1 meter, then for every kilogram of mass at the outside of the space-station you want to accelerate a certain amount, you must apply 100 times that force to the axel (simple ratio of 1 meter to 100 meters).

The laws of levers, gears, rods, etc are all the same, it is only a propogation of force causing acceleration amoung an arbitrary amount of particles which define a semi-ridgid body (each particle seeks to keep the same arangement in the "group" due to a balance of positive and negative interatomic forces). Note that a "body" is a relative, not an abolute term. Something is a body if it would naturally stay mostly the same if not force deformation from outside forces, but every body has different amounts of force that it can handle before deformation, and most bodies have some relatively small amount of deformation going on due to the constant forces within their system (glass particles flowing due to gravity, etc)

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Xai    1838
Also wanted to mention, the idea Airo suggested, that if you rotate a flashlight the beam's final resting place might move faster than the speed of light ...

it isn't true in any practical / physical / real sense. Only in a logical sense.

A flashlight (light1) is emiting photons that are traveling at an average of the speed of light.

4 light years away is a space ship (ship1) which you have been broadcasting to for 1 year. Now you rotate your beam of light to emit to another spaceship (ship2) 4 lightyears away, but 30 degrees off axis from the first ship. The situation in 10 minutes time is this. A "beam" of light exists along the line between light1 and ship1, this beam starts 10 light-minutes from light1 is 1 light-year long. A second "beam" of light exists along the line between light2 and ship 2, this beam starts at the location of light1, is currently 10 light-minutes long, and is getting longer at a rate of 1 light-second per second. Also there some fairly unimportant particles of light in the arc between light1-ship1-ship2 that we're emitted during whatever time it took to rotate the flashlight between the 2 desitinations (perhaps 1/2 second).

Logically we can say that the "target" has moved 2 light years (the distance between the ships) in 1/2 second), but that movement is nothing except the changing of an idea, not any physical existance. In fact, that idea may be wrong, because there may in fact be obsticles in between the source and target that prevent the target from every receiving the signal, or the target may not be in the location we think, in which case the "real" change in target is to whatever the first object actually ends up being when the light does hit it ... perhaps just space-dust, perhaps a star 400 million light-years away.

So you see, this is like asking how quickly an idea can change .... such as "how fast can Constantinople become Istanbul?" The answer is a function of the observering /labeling system, not any truth about the city itself.

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Daerax    1207
Images may move "faster" than the speed of light since they are massless entities.

The solution to the paradox centres around realizing that the the notion of a rigid body is incompatible with relativity (special in this specific example). See this faq on the rigid rotating disk in relativity for more.
Dmytry    1151
This thread hurts my eyes... but not as much as world's largest superconducting magnet thread lol.

The energy of moving massive object increases with speed. As speed approaches speed of light, the energy approaches infinity. You probably don't have infinite energy so you won't break speed of light no matter which mechanics you use to get energy from point A to point B.

The "energy" of moving body with 'rest mass' M and speed u is E=M*c^2/sqrt(1-u^2/c^2) where u is speed and c is speed of light. As u approaches c, the square root approaches zero and result of division approaches infinity. (As u gets higher than c, you get square root of negative number, i.e. no real valued solution for energy, and for many other things. You don't "go back in time" or whatever).

The impossibility of rigid body is also an issue, but difficult one to actually derive the conclusion from, because even with impossibility of truly rigid body to dismiss the chuck22's idea in an intellectually honest way you still have to show that there can't be body hard enough to be rigid enough for chuck22's idea to work.
The handwaver w/o actual knowledge on special relativity would of course prefer to handwave 'bout impossibility of rigid body, whereas somebody who actually got a bit of knowledge on special relativity would focus on other more elemetary violations. (in sciences you only actually know topic if you can predict what happens in example situation; erudition about topics doesn't count)

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etothex    728
for example, you have a double sided flashlight that shines in both directions. In the rest frame of the light, the two beams are diverging at 2c, twice the speed of light. Yet nothing is violated because in no reference frame is anything physical moving faster than the speed of light with respect to a "resting" object in that frame.

As for the rotating rod, the idea that the rod can never be rigid enough is sufficient. To repeat, the rod can never be completely rigid because a rigid rod would transmit information instantaneously which is disallowed.

Now consider the reference frame of the end of the rod (note it is not an inertial one). There is no length contraction of the rod (as motion is always perpendicular to the rod), but there is time dilation. Examine the time it takes for information (i.e., additional torque) to be transmitted along the rod - suppose in the best case it happens at the speed of light. Since the rod's length is constant in this reference frame, and the "speed" of the torque is constant, but there is time dilation - and this time dilation increases as the end of the rod moves faster. As the end of the rod approaches the speed of light, the torque takes longer and longer to "appear" at the end of the rod, with the torque approaching zero as the velocity approaches c.

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Dmytry    1151
see, precisely what i mean. There's simply too much handwaving by people who evidently have very little idea of special relativity just have some erudition on topic and simply bullshit through to the answer they happened to know beforehand (impossible to have end of stick move at faster than light).

Thing is, even if truly rigid body was possible somehow (e.g. body with a lot of spaceship engines attached to it firing in pre-timed manner to keep it behaving like rigid), end anyway won't move faster than speed of light for most elementary reasons (see energy-->infinity as speed-->c).

etothex: give that explanation to my ex physics prof and you guaranteed will be asked how to compute speed of ends [as function of time] of maximally rigid stick (with maximal rigidity that doesn't lead to violations of any fundamental laws of physics) of mass 1g and length 2 meters and torque of 1000 newtons*meter applied to middle of stick. Taking into account time dilation. And show how end can't be faster than light. That's just a fair check if you simply BSed the explanation or not. If you can't, you get rightfully graded as "guy did read something somewhere about relativity but really don't know it and can only BS his way through at conversation'".

[Edited by - Dmytry on November 26, 2006 3:10:16 AM]

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Raghar    96
Quote:
 Original post by chuck22scientists say that it is impossible for objects to move at or faster than the speed of light. so i've got a quick example.

If they would say it they are somewhat dishonest. Nothing in current knowledge could disallow it.