# Newton's Third Law, Speed of Light, and Relativity question

#### FattyRNL

Highschool physics student here with a thought experiment I would like some input on.

While learning about Newton's Third Law (are reactions are immediate and there is no delay) I had a thought about the speed of light and relativity. Imagine You have a stick with a length of one light-year. Person A and Person B are on either side of said stick, like so:

A ----------------- B

Let's say Person A moves the stick an inch or so to poke Person B. By Newton's third law, the entire stick moves instantaneously, meaning Person B feels the stick poke him instantaneously (ignoring the time it takes the end of the stick to travel an inch or two to get to him). Because the entire stick moves at once, he would see his end of the stick poke him at the same moment he was getting poked. However, if he looked down the stick at Person A (because he has eagle eyes), he would not see the stick near Person A move for another year. Would, given Person B's frame of reference, it appear the stick has stretched out to him, and that over the course of the next year the stick would look like it got smaller?

If this is so, is it safe to assume the opposite would occur to Person A? Would the stick contract into itself and get larger over the next year?

And if this is all stupid, I apologize. One quarter of honors physics and a couple of pop-sci books doesn't quite qualify me for good questions or explanations.

#### nicksauce

Homework Helper
Let's say Person A moves the stick an inch or so to poke Person B. By Newton's third law, the entire stick moves instantaneously, meaning Person B feels the stick poke him instantaneously (ignoring the time it takes the end of the stick to travel an inch or two to get to him).
This is false. The "poke" travels through the stick at the speed of sound - the pressure wave has to travel through the stick.

See: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#4

#### FattyRNL

Code:
This is false. The "poke" travels through the stick at the speed of sound - the pressure wave has to travel through the stick.
QUOTE]

I may be wrong (please correct me if I am) but your link applies to hitting an object, and the waves that pass through it as a result. Imagine the end of the stick nearest Person A as DeltaXA. By Newton's third law, if DeltaXA were to move 2 inches, shouldn't DeltaXB amove two inches immediately?

If you are right, however, would that imply that Person B would see Person move the stick before the stick poked him? It would take a year for that light to get to him, and would take [However long it would take a sound wave to travel one light-year] to actually poke him?

#### Dale

Mentor
nicksauce is correct.

Note, this is not anything to do with relativity, even in classical Newtonian mechanics the poke travels at the speed of sound in the rod. The only difference between Newtonian mechanics and SR in this case is that in SR the speed of sound must be less than the speed of light.

#### Doc Al

Mentor
While learning about Newton's Third Law (are reactions are immediate and there is no delay)
By Newton's third law, the entire stick moves instantaneously,
By Newton's third law, if DeltaXA were to move 2 inches, shouldn't DeltaXB amove two inches immediately?
I think you have a misunderstanding of Newton's Third Law. If you push the stick, the stick pushes back on you. Those pushes are the 'action/reaction' pair that occur together. But the effect of your push on one part of the stick doesn't immediately affect the next part of the stick; As has been mentioned, the push travels along the stick at the speed of sound.

#### FattyRNL

Ah, thanks for the explanation on that.

However, would that then imply that Person B would see the stick being moved by Person A before he felt it?

#### grav-universe

Ah, thanks for the explanation on that.

However, would that then imply that Person B would see the stick being moved by Person A before he felt it?
Yes. Both A and B would see person A pushing the stick, then watch the pressure wave move down the stick to poke B.

#### mappy

Re: Newton's Third Law and the stick

hello i am new to this site, this long rod problem has been with me for a long time,
how dose newtons 2nd law hold up. if a and b know the mass of the rod and, have more than enough power to move it. can they double their expected rate of acceleration if singled by c at the middle of the rod and prearrange to move it one way? ie when A push and B pulls?

#### John232

I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound. It would mean that if you spun any length of rod that was made of the most rigid material known to man would go completely flimsy if spun at the speed of sound.

A rod a foot long spun at the speed of sound would turn to jelly, lol, I have seen small rigid objects respond instantly to an end being moved, I don't see why they have to be a light year long.

Say a jet goes mach one, the back of the jet being pushed by the engines can only make the front of the ship be pushed forward to respond to the back as fast as it is moveing, the length contraction of going mach one would smash the jet and the sound barrier would never be able to be broken...

#### Fredrik

Staff Emeritus
Gold Member
I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound.
It's the other way round. The speed of sound in the material is determined by how rigid it is. The most rigid an object could be (in principle, and according to SR) is determined by the speed of light. Of course, actual matter is composed of atoms, and the interactions between them ensure that the speed of sound is many orders of magnitude slower than the speed of light.

Say a jet goes mach one, the back of the jet being pushed by the engines can only make the front of the ship be pushed forward to respond to the back as fast as it is moveing, the length contraction of going mach one would smash the jet and the sound barrier would never be able to be broken...
The push from the engine propagates through the plane at the speed of sound in the material it's made of, which is a several times faster than the speed of sound in air. If you could make a plane out of a material in which the speed of sound is slower than the speed of sound in air, and you tried to accelerate it to a speed faster than the speed of sound in air, I think it would just be torn apart by all the vibrations.

#### DaleSwanson

I find it hard to beleive that the most rigid an object could be would be determined by the speed of sound.
Here, the "speed of sound" means the speed of sound in whatever material is being discussed. The speed of sound is much faster in a rigid material than it is in air. The term speed of sound, could probably be better described as the speed which particles in a material move. When you push a rod that movement begins moving down the rod in a wave at a certain speed which depends on how rigid the material is.

The speed of sound (or of particle movement in general) in steel is about 5000 m/s or 11,000 mph. That is why you will never see this wave of movement traveling through a rod. The time the wave would cover and distance you could reasonably see at once would be a tiny fraction of a second.

#### Dale

Mentor
Re: Newton's Third Law and the stick

hello i am new to this site, this long rod problem has been with me for a long time,
how dose newtons 2nd law hold up. if a and b know the mass of the rod and, have more than enough power to move it. can they double their expected rate of acceleration if singled by c at the middle of the rod and prearrange to move it one way? ie when A push and B pulls?
Hi mappy, welcome to PF!

Double the force will produce double the change in momentum, that is Newton's 2nd law.

#### John232

Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?

A rod a kilometer long would end up flopping the speed of sound less than the other end even if it was made of diamond?

The elasticity of an object would break down when ends of it had relative speeds close to the speed of sound. I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.

#### DaleSwanson

Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?

A rod a kilometer long would end up flopping the speed of sound less than the other end even if it was made of diamond?

The elasticity of an object would break down when ends of it had relative speeds close to the speed of sound. I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.
It would be deformed for however long it took for the motion to travel through the object. The speed of sound in diamond is 12 km per second. If you had a 1 km long diamond rod, and pushed one end towards the other end, the rod would contract in length while that movement traveled through it as a slight bulge. During that time (1/12 of a second) the far end of the rod would be motionless. Once the motion reached the far end the length would move however far the rod was pushed and the length would return to the original length.

Note all this is only limiting how fast movement can move through a solid object. Certainly an object as a whole can travel much faster than the speed of sound through it.

#### Dale

Mentor
Then wouldn't that mean that any object that had one end move relative to another by a force would then always end up slightly bent because of its relative motion?
Yes.

I don't think any object rotating at the speed of sound at the equater would have to be turned to jelly.
What do you mean here?

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