Naked Science Forum

General Science => General Science => Topic started by: neilep on 08/05/2017 12:52:05

Title: Does the end of my ruler travel faster than the speed of light?
Post by: neilep on 08/05/2017 12:52:05
Dearest Academic Tutors Of Puissance Extraordinaire,

As a sheepy I of course luff rulers. Rulers as ewe know were invented in 2012 by Mr C.E,N Timetre  to help him respond when asked how long he would be attending the shenanigans by his good lady wife. Little did he know that his discombobulation as to the nature of her query would result in such a world wide phenomena that now resides within every child's  school bag !

Look here's my zillion mile long ruler

Screen Shot 2017-05-08 at 12.44.06.png (59.34 kB . 448x347 - viewed 4099 times)
Non doctored true bonafide picture of me and my zillion mile long ruler pictured 1-1 scale. It must be true because it says so, so there !!!

If I pivot my end of my ruler to the ground and move it a bit for less than a second , the other end is going to move  a very long way across quicker than the speed of light innit ? How is this possible ?
How can the end end of my zillion mile long ruler move from one location to the other so quickly ?

If you can't imagine my ruler then how about a laser pointer then?

Whajafink ?

If you could answer this problematic query as soon as poss because I need my ruler to measure up my garden for a swimming pool being delivered next Tuesday, and to be honest, holding it up like this is starting to chafe !!

Hugs et les shmishes

Mwah Mwah Mwah !!

sheepyxxxxxxx

As a rule of thumb
I'm not that dumb
But when it comes to speed
It is well agreed
That the use of my rule
Makes a very fast tool

or does it ?

Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: PhysBang on 08/05/2017 13:32:48
First I would suggest that you think about the energy required to move that ruler.

But we can disregard that. You are assuming that the ruler is infinitely rigid. It's not. One of the consequences of Special Relativity is that there is an upper limit to rigidity. Your ruler will bend significantly.
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: neilep on 08/05/2017 13:43:22
First I would suggest that you think about the energy required to move that ruler.

But we can disregard that. You are assuming that the ruler is infinitely rigid. It's not. One of the consequences of Special Relativity is that there is an upper limit to rigidity. Your ruler will bend significantly.

Thank you so much.can we assume it is infinitely rigid ?
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: PhysBang on 08/05/2017 15:47:12
Thank you so much.can we assume it is infinitely rigid ?
If you want to deny Special Relativity.
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: alancalverd on 08/05/2017 23:30:48
Any force you apply to one end of the ruler will cause the other end to move n seconds later where n = r/w, r being the length of the ruler and w the velocity of propagation of transverse waves in the ruler (roughly equal to the speed of sound in an isotropic material).

Now let's idealise the ruler. It is infinitely rigid so w is infinite, and so we don't lose a lot of energy accelerating the bits in between, it consists of a zero-mass rod joining the dot at the far end to the hand at this end. The dot has a tiny but nonzero mass m.

Thanks to Mr Einstein we know that at velocity v, mv = m0/(1-v2/c2)0.5, which has the annoying habit of tending to infinity as v -> c, so no matter how large we make w, you will have to wait for ever and apply an infinite torque before the far dot reaches the speed of light.
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: Kryptid on 09/05/2017 06:00:01
Thank you so much.can we assume it is infinitely rigid ?

In order for that to be the case, a signal moving from one end of the ruler to the other would have to travel infinitely quickly. If the propagation speed is finite, there will be a slight delay (and therefore slight bending) between the time that you start moving the base of the ruler and the time that the far end of the ruler starts moving. The realistic upper limit on signal propagation speed is, of course, the speed of light (which is carried by the electromagnetic fields of the atoms in the ruler).
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: PmbPhy on 10/05/2017 03:46:05
That the use of my rule
Makes a very fast tool

or does it ?
No. Relativity prevents if from happening. As mentioned above all material objects carry compression waves at a finite speed. But let's say that it did travel instantaneously in its rest frame. Using relativity it can be shown that in other frames the other end will move before you pushed it, which violates causality. Therefore the other end cannot move instantaneously.
Title: Re: Does the end of my ruler travel faster than the speed of light ?
Post by: evan_au on 10/05/2017 09:55:35
Quote from: neilep
If you can't imagine my ruler then how about a laser pointer then?
The scenario with the laser pointer is quite different.
- The different photons in the beam are not physically coupled to each other, so the movement of one does not affect the movement of another. There are no limitations due to signals propagating at <= c.
- One photon is emitted in a certain direction, the next photon can be emitted in a very different direction
- It is quite easy to move the laser pointer from one star to another in 1 second, even though the distance between the stars is many light-years.
- So the laser dot panning across the face of the Moon might seem to be travelling faster than c, but the individual photons of which the beam is composed never travel faster than c.