Could the linear velocity at an infinite distance exceed the speed of light?

[einstor]

Suppose I have a stick whose length is infinite, then the stick was rotated at one end. Despite playing with a small angular velocity, but should have a linear speed of the other end of the stick (which is at infinite distance) will be very high considering the formula of linear velocity = angular velocity multiplied by the length of the radius. If an infinite radius, it should also be linear velocity at infinite distance is infinite. Could it be the linear velocity at the tip of a rod that is at an infinite distance that would exceed the speed of light? What will happen?
Was broken stick? whether the rod was shortened (the stick towards the player)? Or stick it will not be driven at all?
(Assume this is done immense room is empty so there is no motion that prevents this staff)

There's one more question, I've heard he said during the beginning of the universe formed, there are several dimensions (if not wrong there are 11). However, in its development, only four dimensions namely growing dimensions of length, width, height, and time. While other dimensions continue to shrink. True? Then why are other dimensions to shrink? Is it because we live in four dimensions expanded relatively faster than the other dimension so that the other dimensions seem to shrink?
What is the name of the dimensions of it (besides the four dimensions we live in)?

 

[DaveC426913]

Suppose I have a stick whose length is infinite, then the stick was rotated at one end. Despite playing with a small angular velocity, but should have a linear speed of the other end of the stick (which is at infinite distance) will be very high considering the formula of linear velocity = angular velocity multiplied by the length of the radius. If an infinite radius, it should also be linear velocity at infinite distance is infinite. Could it be the linear velocity at the tip of a rod that is at an infinite distance that would exceed the speed of light? What will happen?

There is no such thing as a perfectly rigid material.

The torsion will propogate down the length of the stick at the speed of sound in whatever substance it is made of. That speed of sound will be much much less than the speed of light.

Diamond, the hardest substance known, has a speed of sound of 12km/s, or 1/25,000^th of c.

There's one more question, I've heard he said during the beginning of the universe formed, there are several dimensions (if not wrong there are 11). However, in its development, only four dimensions namely growing dimensions of length, width, height, and time. While other dimensions continue to shrink. True? Then why are other dimensions to shrink? Is it because we live in four dimensions expanded relatively faster than the other dimension so that the other dimensions seem to shrink?

This is an area of active research. Therre's no real consensus.



What is the name of the dimensions of it (besides the four dimensions we live in)?[/QUOTE]
They have no names. No dimensions have any names except to define their types, of which there are two: spacelike dimensions and timelike dimensions.

 

[russ_watters]

The torsion will propogate down the length of the stick at the speed of sound in whatever substance it is made of. That speed of sound will be much much less than the speed of light.

...but you will be able to accelerate the end of the stick to near the speed of light, at least until it breaks from the tension. But as you do, you'll need more and more torque for less and less acceleration.

 

[Dale]

There is no such thing as a perfectly rigid material.

No such thing as an infinitely long stick either.

 

[DaveC426913]

No such thing as an infinitely long stick either.

Perhaps, it doesn't have to be infinitely long to achieve the desired effect.

 

[Boy@n]

Perhaps better example than the physical stick is a very strong and far reaching laser beam. Imagine having one pointing at the sky and moving it very fast on the ground, how fast would the other end move? What could it be its max speed?

 

[DaveC426913]

Perhaps better example than the physical stick is a very strong and far reaching laser beam. Imagine having one pointing at the sky and moving it very fast on the ground, how fast would the other end move? What could it be its max speed?

Completely different animal.

The spot of laser light has no max speed and can easily achieve superluminal velocities.

However, the catch is this: the 'spot' is not a single 'thing' at all; it is only conceptually a thing in the minds of us humans.

 

[Boy@n]

As per dimensions... what if reality of instant change happening for particles at (great) distance, as it happens with entangled particles, is a proof of more than the well known four dimensions? Seems as if those entangled particles are still staying close in certain (higher?) dimension no matter how far appart we take them in our known dimensions, and thus change happens instantly... Would this mean that known dimensions are 'just' reflection of some higher ones?

 

[Dr Lots-o'watts]

Perhaps better example than the physical stick is a very strong and far reaching laser beam. Imagine having one pointing at the sky and moving it very fast on the ground, how fast would the other end move? What could it be its max speed?

No max speed, it is a series of independent collisions. The vertex of a guillotine can also move at arbitrarily high speed, including infinity (angle zero).

 

[Boy@n]

Completely different animal.

The spot of laser light has no max speed and can easily achieve superluminal velocities.

However, the catch is this: the 'spot' is not a single 'thing' at all; it is only conceptually a thing in the minds of us humans.

Thought so, wanted to extend previous post with saying that I think virtually it would reach speed higher than C, but in reallity that beam would probably not appear whole in one but draw along as it goes...

If this isn't so, then how can we imagine this visually to happen in reallity?

 

[Chronos]

This thread is going nowhere fast. The 'push' thing is irrelevant. The other end of your stick does not 'move' instantaneously,

 

[jtbell]

in reallity that beam would probably not appear whole in one but draw along as it goes...

 

[Boy@n]

Hard to explain what I mean... OK, imagine you move the laser which produces light beam in a big circle in one second, pointed toward the sky, now, the other end creates infinite number of circles at the speed of light as this light beam propagates outwards into space, but at, say, one light-year away from Earth that circle would have enormous radius but the circke itself wouldn't be complited in one second, but many more, right? (Only virtually - in our minds - it is complited in one second, but not for real.)

 

[georgir]

Boyan, you need to work on your English a bit ;)

Yes, this circle will be completed in one second, even at a lightyear away, according to a stationary observer (stationary relative to us here, for those nitpicky enough)

For observers that are moving, the order in which points on that circle get lit up will be completely different though. They might very well see some segment of it get completed in reverse, while the rest of it get completed in the same direction but faster, etc...

Any two events on this circle are spacelike separated, i.e. it is impossible to have a reference frame in which they happen at the same place, and it is impossible to agree universally for all reference frames in what order they happen - there always are some frames in which they are simultaneous, some where one is before the other and some vice-versa.

 

[DaveC426913]

Hard to explain what I mean... OK, imagine you move the laser which produces light beam in a big circle in one second, pointed toward the sky, now, the other end creates infinite number of circles at the speed of light as this light beam propagates outwards into space, but at, say, one light-year away from Earth that circle would have enormous radius but the circke itself wouldn't be complited in one second, but many more, right? (Only virtually - in our minds - it is complited in one second, but not for real.)

No, the spot of laser light really can move from one point to another faster than the speed of light.

You could shine a spot of laser light on the west limb of the Moon, then flick it to the right limb so fast that the spot of light moves from west limb to east limb faster than c.

 

[einstor]

from most post that I read above, so is the law of relativity does not work on irrelevant systems?

 

[Mentz114]

No, the spot of laser light really can move from one point to another faster than the speed of light.

You could shine a spot of laser light on the west limb of the Moon, then flick it to the right limb so fast that the spot of light moves from west limb to east limb faster than c.

As you said above, the spot of light is not a single thing so this isn't strictly true. If we take the distance between the extremes of the where the beam lands and divide by the elapsed time, the result may be > c, but it is not the velocity of anything.

 

[DaveC426913]

from most post that I read above, so is the law of relativity does not work on irrelevant systems?

Relativity states that nothing with mass can move at or faster than the speed of light (locally), nor can information be transmitted faster than c.

The spot of laser light is not a thing with mass, and can not be used to transmit information.

It is not a "thing" at all.


The best comparison is the venerable machine gun analogy.

I point my machine gun due north at a hilltop one kilometer away and I fire off a steady stream of rounds. The bullets have a muzzle velocity of 750m/s.

I now whip the machine gun around in less than a second to a hill top due south.

The impact point of bullets has traveled 2300+ metres in less than a second. That is more than 3 times the maximum possible velocity of the bullets! Yet no bullet has exceeded 750m/s.

As you said above, the spot of light is not a single thing so this isn't strictly true. If we take the distance between the extremes of the where the beam lands and divide by the elapsed time, the result may be > c, but it is not the velocity of anything.

Well it's semantics. The spot is single thing, it's just not a physically manifest thing; it's a conceptual thing.

 

[Dr Lots-o'watts]

Well it's semantics. The spot is single thing, it's just not a physically manifest thing; it's a conceptual thing.

The spot can be seen as the vertex of the angle formed by the reflecting surface and the extended wavefront of the beam.

 

[DaveC426913]

Diamond, the hardest substance known, has a speed of sound of 12km/s, or 1/25,000^th of c.

In reading Wiki about the Pauli Exclusion Principle, I came across this:

Neutrons are the most "rigid" objects known; their Young modulus (or more accurately, bulk modulus) is 20 orders of magnitude larger than that of diamond.

I wonder what the speed of sound through neutronium is...

 

[Dr Lots-o'watts]

I wonder what the speed of sound through neutronium is...

Both density and modulus seem to be defined for neutronium, so it seems to be quite straightforward to calculate a speed of sound. But whether classical sound theory applies to degenerate matter etc. I have strong doubts. Perhaps it can (has been?) measured in condensed helium-4? which is perhaps the closest thing in a lab. Or maybe a sound wave would heat the BCE to much and kill the state... (particles would have to jump up a level wouldn't they?)

 

[Anamitra]

For the far end of the stick to be aware of rotation having started at the origin some signal has to travel from the center of rotation to the far end of the stick and this signal should not travel faster than light no matter what the mechanism is.
In time 2 seconds the signal can travel up to a maximum of 2c metres . If the stick is 5c metres long the the last 3c metres should not be aware of the ongoing rotation in the rest of the stick at time t=2s
But the sad thing is that we are measuring time from an inertial frame[the Earth in this case,I hope] but the stick is a non-inertial frame. If the acceleration could be replaced by some equivalent gravitational field metric the problem becomes a general relativity problem.For the stick to understand what is happening we should consider a series of clocks placed on the stick then we should consider the metric.Perhaps this could help.

[For an observer on Earth the light ray has to go on rotating with the stick if it is used as a signal and this should not happen in a "natural way" in flat space-time]

 

[Drakkith]

I don't think you could accelerate the end of this stick to faster than light speeds. The ends of the stick would break off before you could get to the speed of light, and the faster you rotated this stick the further down the ends would continue to break. Either that, or you would be almost unable to rotate the stick because of the energy required to move it anywhere near the speed of light.

 

[DaveC426913]

I don't think you could accelerate the end of this stick to faster than light speeds. The ends of the stick would break off before you could get to the speed of light, and the faster you rotated this stick the further down the ends would continue to break. Either that, or you would be almost unable to rotate the stick because of the energy required to move it anywhere near the speed of light.

Correct on all counts.

 

[Anamitra]

A large angular speed is not required for our job:

$${v}{=}{\omega}{r}$$

If r is sufficiently large v automatically becomes large at a distance.For r=3c metres, v=3c m/s for $${\omega}{=}{1}$$ radian/sec!For information to travel to that distance it will take 3 seconds,at least.