# Faster than light?

imagine you have this hugely long rod. like a lightyear long. and theres a button on one side of the rod. you, on the other side, push the rod onto the button (as fast/s;pw as you want), conveying a signal to the other side, and basically sending information faster than light. whats wrong with this picture? (i dont know)

also, if that works, than you dont need a physical rod, you can go with something else, electron, particle etc.

anyone know?

## Answers and Replies

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pervect
Staff Emeritus
When you push on a rod, the signal travels through it at a speed FAR slower than light - the speed of sound in the material in the rod.

Another way of saying the same thing - the rod is not perfectly rigid,when you push on one end, the other end does not move right away. You can model the propagation of the displacement of the rod mathematically as a distributed spring-mass system. (The solution to this distributed spring-mass problem is the wave equation, with the characteristic speed of the wave being the speed of sound in the material.

Pengwuino
Gold Member
No you didnt send that information at the speed of light. If you put atomic clocks at both ends and did that experiment, it will actually take an entire lightyear for the push to be noticed at the other end. Each molecule needs ot move say... however many nanometers to hit hte next atom, this is repeated for whatever many molecules there are in that rod. which all add up to be that lightyear noted at the beginning.

At least i think thats how it goes.

@pervect

I think he means the physical displacement of the rod, not sending a sound wave through the rod.

What pervect said is exactly right.

the rod is not perfectly rigid,
wat if the rod was perfectly rigid?

if thats possible... which i am doubting somewhat

Pengwuino
Gold Member
I think even if the atoms were all completely connected to where theres no distance between the atoms, this idea that something can travel faster then the speed of light is still completely wrong. A lightyear long rod is just that, a huge rod, a huge assembly of atoms. Each atom only moves a small distance so although a translation of a information reaching point b from point a at faster then the speed of light does occur, this has no connection to a single atom being able to travel from point a to point b. I mean use common sense on this one.

Integral
Staff Emeritus
Gold Member
Given nonphysical conditions you can only arrive at non physical conclusions. A true geduncken experiment must have a physical basis. This one does not.

When you strike (or attempt to move) a physical object shock waves are created which move at the speed of sound in that material. If you strike it with a force large enough so it is displaced locally with a speed greater then the speed of sound in the material the material will be destroyed (i.e. you will break it).

Pengwuino
Gold Member
So integral, say you have a meter long piece of metal. If its levitating in mid air lol... and you grab the right end and move it to the left 10cm, the left side of the rod will move that 10cm not instantly, but only after a shockwave at v=speed of sound travels that 1 meter to the left side?

jtbell
Mentor
To visualize the situation better, imagine a mile-long length of railroad track instead of your one-meter rod. Remember those stories about cowboys (or was it Indians?) putting their ear down on the rail to listen for an approaching train? Would they have gotten the signal any quicker if someone had grabbed the track a mile away and given it a shove?

So integral, say you have a meter long piece of metal. If its levitating in mid air lol... and you grab the right end and move it to the left 10cm, the left side of the rod will move that 10cm not instantly, but only after a shockwave at v=speed of sound travels that 1 meter to the left side
I think that what Integral meant was that when you push a rod you push only a relativly small group particles (molecules, crystals) which make up the rod. The force acting between the particles that were pushed and their neighbouring particles then "pulls" the neighbouring particles, these particles then "pull" their neighbouring particles, etc.
This mechanism accurs almost instaneously in ordinary life. But for a rod a light-year long it will be far from that.

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pervect
Staff Emeritus
One way to reasonably model the mechanical distributed problem is with the electrical analog.

Let voltages be velocities, and forces be currents.

Then I = c dv/dt is equvalent to F = m dv/dt = ma, so a mass is a capacitor.
Similarly, springs are inductors.

A bunch of masses connected by springs becomes a bunch of grounded capacitors connected by inductors.

This is, of course, the model of a transmission line.

Now, if we apply a constant force to one end of the mechanical system, this is equivalent ot forcing a constant current into one end of a transmission line.

THe boundary conditions at the "free" end are no force, so it's an open circuited transmission line.

We can then sketch out the general behavior of the solution (if we are familiar with how transmission lines act).

Initlally, there will be some voltage wave, of magnetiude v = z*i, propagating to the right, with Z being the impedance of the transmission line.

The mechanical analog is that there will be some initally velocity v which will propagate to the right at the speed of sound in the material. This velocity will be given by the force times the "impedance" of the bar, which will depend on the material it's made out of (it's bulk modulus and its density).

When the velocity wave reaches the right side of the transmission line, it reflects. Because the line is open circuted, the refleciton coefficient is unity.

This means that the velocity then doubles, and a new velocity wave heads back towards the left side, moving at the speed of sound in the material.

The result is a sort of "staircase" motion, where the velocity of individual points on the rod changes in discreete steps, rather than a smooth linear curve, a "staircase" approximation to v=a*t.

This analysis has ignored any damping effects, which would be modelled electrically by resistors. If you look at the length of the rod, you'd see it changing (oscillating) slightly with the above solution. The simple trnasmission line solution gives oscillations that never die out - a more realisitc solution would include some damping (due to unmodelled frictional forces and losses), so that eventually the oscillations in the length of the rod decay.

Integral
Staff Emeritus
Gold Member
Pengwuino said:
So integral, say you have a meter long piece of metal. If its levitating in mid air lol... and you grab the right end and move it to the left 10cm, the left side of the rod will move that 10cm not instantly, but only after a shockwave at v=speed of sound travels that 1 meter to the left side?
That is exactly what I meant. If you attempt to move the rod at a velocity which is close to the speed of sound in the material it will bend, if you attempt to move it faster then the the speed of sound in the material it will break.

Notice that I repeat the phrase "in the material" The speed of sound in solids is much higher then the speed of sound in a gas.

Pengwuino
Gold Member
Yah thats what i was originally thinking for hte original question in mind. Wouldnt each particle have to move in orrder for the whole rod to move and adding up all the particle movements would ahve equalled probably that light year. Can atoms be arranged so they are 'hooked up' where you can make like a chain of 10 atoms? And if you pushed from the left side of the chain, would the rightmost atom be displaced literally instantaneously?

pervect
Staff Emeritus
As I said in my last long post, if you push on one end of a long rod, the other end will not move instantaneously. Using an idealized distributed spring mass model with no friction, damping, or dissipation, one gets the following results:

If the following is a long rod, and you push on the left end at x=0
(x=0)|||||||||||||||||||||||||(x=d)

The right end of the rod at x=d will first move at a time t = d/cs, where cs is the speed of sound in the rod.

The velocity of any point on the rod will be a function of the position on the rod, and the time, i.e.

velocity = v(t,x)

For 0<t<T, with T = d/c, (the length of the rod over the speed of sound in the rod)

v(x,t) will be given by

0 if t < x/c
v if t >= x/c

v is a constant depending on the exact characteristics of the rod and the applied force - it will be proportional to the applied force.

The plot of the above function would require three dimensions, x,t, and the dependent variable v(x,t). It represents, however, a "velocity wave" propagating to the right along the rod at the speed of sound.

For T < t < 2*T, v(x,t) will be

1*v if (t-T) < (d-x)/c
2*v if (t-T) >= (d-x)/c

This represents a wave moving to the left at the speed of sound. Like the previous wave, this wave is a plot of velocity vs time.

Note that the rod will compress during the time interval 0<t<T, and the rod will expand during the interval T<t<2T. The total change in the length of the rod will be

delta-L = v*d/c, where 'v' is the constant velocity previously mentioned, d is the length of the rod, and c is the speed of sound in the rod.

If delta-L/d is too large a quantity, the material will break, but usally delta-L will be very small.

Pengwuino
Gold Member
But what if the atoms were like, strung together. Can atoms be so close together that they move in litteral unison?

russ_watters
Mentor
Pengwuino said:
But what if the atoms were like, strung together. Can atoms be so close together that they move in litteral unison?
No. Atoms themselves are not rigid objects.

Pengwuino
Gold Member
Ok gotcha.

is there anything that is packed in amazingly tight? i mean if you go to something the siaze of a quark (or something) and string a bunch together in a rope and pull on it...?

i get the feeling you just cant do it...