Velocity of particle waves in an object?

[David Burke]

I require help with understanding the velocity of colliding particles along the length of an object under acceleration from a vector force...

Problem: If a rod were constructed with a length of 1 light year and sufficient force were applied at one end to move the rod, it is assumed a pulse of colliding particles would move along the rod causing the rods position to change over time. However, I am unsure of the mechanics of how this occurs. I know that the wave of colliding particles is restricted to a maximum velocity of c; otherwise the rod would be breaking the laws of relativity.

Question: So how fast would this wave travel along the length of the rod and what does this process mean if we consider small objects like a pencil being pushed slowly across a desk? Is the pencil continuously contracting and expanding at the speed of light as a wave of colliding particles moves along its length?

 

[PAllen]

I require help with understanding the velocity of colliding particles along the length of an object under acceleration from a vector force...

Problem: If a rod were constructed with a length of 1 light year and sufficient force were applied at one end to move the rod, it is assumed a pulse of colliding particles would move along the rod causing the rods position to change over time. However, I am unsure of the mechanics of how this occurs. I know that the wave of colliding particles is restricted to a maximum velocity of c; otherwise the rod would be breaking the laws of relativity.

Question: So how fast would this wave travel along the length of the rod and what does this process mean if we consider small objects like a pencil being pushed slowly across a desk? Is the pencil continuously contracting and expanding at the speed of light as a wave of colliding particles moves along its length?

The rate it would move is called the speed of sound in the material. Yes, every time you push an object, you are actually propagating displacement waves through it; they are just too fast to see under ordinary circumstances.

With modern equipment, it is possible observe the delay between one end moving and the other end moving as a hammer taps one end of rigid 1 meter ceramic rod.

 

[ghwellsjr]

The problem with a question like this is that we have to suspend some aspect of reality to pretend like we are answering the question.

Just to start with, there can never be a rod of that length simply because the gravitational attraction of one end of the rod to the other end would collapse it into a sphere, just like every other huge body in the universe. There's probably enough mass there to create a black hole and it would probably suck in all the mass in a huge area around it to make an even bigger black hole.

Actually that would never happen because the rod itself would break up into many segments, each of which would form a separate body, maybe even a bunch of black holes.

The next problem is that you could never accelerate one end of a rod at any where near the speed of light so that you would have to apply relativity to explain what was happening because long before that speed was achieved, you would have already reached the speed of sound for whatever material the rod was made out of and that speed is several orders of magnitude slower than the speed of light.

For realistic rods, like a pencil, you just don't have to concern yourself with relativity or the speed of light to understand or explain what is happening when one end is accelerated.

I would suggest that you consider a different problem: what happens to the electrons in a long piece of wire (several miles long) when you apply a voltage from a charged object to one end of the wire? Now you actually do have a wave consisting of displaced electrons traveling down the wire at relativistic speed.

 

[PAllen]

The problem with a question like this is that we have to suspend some aspect of reality to pretend like we are answering the question.

Just to start with, there can never be a rod of that length simply because the gravitational attraction of one end of the rod to the other end would collapse it into a sphere, just like every other huge body in the universe. There's probably enough mass there to create a black hole and it would probably suck in all the mass in a huge area around it to make an even bigger black hole.

This is not strictly true. I just calculated that a filament of lithium a few atoms across and one light year long would weigh a few kilograms. Plausible no. Trivially rejected by elementary laws - also no.

Actually that would never happen because the rod itself would break up into many segments, each of which would form a separate body, maybe even a bunch of black holes.

The next problem is that you could never accelerate one end of a rod at any where near the speed of light so that you would have to apply relativity to explain what was happening because long before that speed was achieved, you would have already reached the speed of sound for whatever material the rod was made out of and that speed is several orders of magnitude slower than the speed of light.

As I read the OP, he simply noted that the pulse couldn't be as fast as c, not that it would be anywhere close. He was asking what the speed would be.

 

[David Burke]

I just looked up the speed of sound in a material and now understand the compression/decompression of an object under force. Thank you very much as I have been puzzling over this for a long time. However, it has led me to another problem...

I'm confident this question is stupid but I’m going to ask anyway because I’m not smart enough to know for sure...

Question: Is it correct to think of solid matter as an illusion and therefore the universe is formed from the fundamental forces in a constant state of flux? E.g. Different interactions of the EM, Gravity, Strong nuclear etc. without any physical substance at the origin of the forces such as point particle matter?

Note: I understand that this is a very poorly worded and open ended theoretical question but I am not in possession of the cognitive skills to do better at this time :)

 

[PAllen]

I just looked up the speed of sound in a material and now understand the compression/decompression of an object under force. Thank you very much as I have been puzzling over this for a long time. However, it has led me to another problem...

I'm confident this question is stupid but I’m going to ask anyway because I’m not smart enough to know for sure...

Question: Is it correct to think of solid matter as an illusion and therefore the universe is formed from the fundamental forces in a constant state of flux? E.g. Different interactions of the EM, Gravity, Strong nuclear etc. without any physical substance at the origin of the forces such as point particle matter?

Note: I understand that this is a very poorly worded and open ended theoretical question but I am not in possession of the cognitive skills to do better at this time :)

Yes, mostly. Apparent solidity is mostly a consequence coulomb repulsion between electron fields of two objects. In QM, 'particles' are not simply localized particles, in classical sense, so the 'nothing at the origin' part of your picture also has some validity. However, nominally, the fundamental particles of the standard model are dimensionless point particles.

 

[DaveC426913]

For the record, diamond, being the hardest substance we know, has a speed of sound of just 12km/s - a mere 1/15,000th the speed of light.

Just to start with, there can never be a rod of that length simply because the gravitational attraction of one end of the rod to the other end would collapse it into a sphere, just like every other huge body in the universe. There's probably enough mass there to create a black hole and it would probably suck in all the mass in a huge area around it to make an even bigger black hole.

None of this is true.

 

[ZealScience]

Not quite well understood, are you talking about longitudinal waves for the compression and rarefaction. But I think it depends on the young's modulus. Because youngs modulus shows the property of the particles that form the material. If the young's modulus is higher intermolecularforce is stronger which means particles interact more vigorously, thus transmitting faster.