general speed of light question
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.
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.
It is simply the transition between super and sub light speeds that the math breaks down from what I've been told.
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]
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]
Quote:Original post by Ultimate_Fusion
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 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.
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
Admiral
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
Admiral
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).
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).
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)
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)
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.
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.
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.
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.
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