# Forces and Speed

Just speed as a magnitude; forces don't have speed correct?

I was trying to explain something to a friend, and it was very hard for me to express or explain in English.

He had to drop Physics after classical mechanics. So it's very difficult arguing with him.

We got on the subject of gravity and the idea of, "speed of gravity." Is it instant or does it travel at the speed of light. According to something done in 2003, Einstein was correct that gravity correct on that there is a speed of gravity and it's the speed of light. However, I've read other things done where it refuted that their experiment wasn't valid? We have not taken upper-level Physics yet.

I referred back to Einstein and Newton. He believed in what Newton believed and I believed in what Einstein believed. He believed gravity was instant and I believe it was at the speed of light.

Forces don't have speed, but their affects may affect speed? Force of gravity is instant, but the affect of gravity travels at the speed of light? If that is true, then how does gravity have a speed and is not instant? It has to either travel as a wave or a particle or as something "physical?"

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## Answers and Replies

No one has measured the speed of gravitational waves. That is what you call "the speed of gravitation forces". In fact there are and had been a lot of experiences to try to detect them. And they are very hard to detect. If you are not able to detect them (nowadays) it is impossible to measure their speed.
Anyway, if gravitational waves do exist, it is assumed that their speed is that of light.

Forces do not have speed. But the forces that a body or a charge exerts on another do not appear instantaneously. Electric and magnetic fields (and "its forces") propagate at the speed of light.

Okay, so forces don't have speed but a force acting on a body have speed? Still kind of confused.

Basically, does the force of gravity have speed or does gravity have speed?

Let's write it otherwise. Imagine that the Sun (all the mass of the Sun) disappears at 10h00. It is assumed that, in the Earth, the attraction of Sun will persist for about 500 seconds. That is the time that the light takes to make the distance Sun-Earth. The attraction of the sun will cease at 10h08.33, in fact, at the same time as the light of the Sun.
But I repeat, this is just an assumption. Nobody has ever measured the speed of gravity waves.

I think this is a rather common confusion, so let me try to explain. Let's start by thinking about light. We know that light is related to electric and magnetic fields; but, to understand what we mean by the propagation of light, we need to take a moment to understand what these fields are.

A field is a quantity that takes on a value at every point in space and time. So, fields are defined everywhere at every time. In the case of electric or magnetic fields, the value at each point in space and time is a vector. So, we can think of these fields as a collections of vectors. It may be that at some places, they are null vectors, while in others they are quite large.

Now, the force acting on an object at some time is related to the values of the fields at the point where the object is sitting at that time. So, in that sense, there is nothing associating a velocity with the force - it's just a particular function of the value of the field, combined with certain properties of the object (like its electrical charge).

Now, the value of a field at any given point can change over time. And, the field equations for E&M guarantee that a change in the field values at one point will cause changes in their value at nearby points. But, these changes will take finite time to propagate from one place to another. The speed with which they propagate will, in fact, be the speed of light. Light itself is essentially a self-propagating "ripple" in the field values.

So, to recap, forces are related to the field values at a particular place at a particular time, while the speed of light is really the speed at which changes in the fields propagate.

Now, in General Relativity, gravity is the effect of a different sort of field, called a metric, which specifies the geometry of spacetime at every point in spacetime. The motion of an object through a point in spacetime is determined by the metric at that point. However, changes in the metric field will, again, propagate at the speed of light.

russ_watters
Mentor
The speed is a speed of propagation. Contact forces have a speed of propagation too. If you have a long metal rod and you push on one end, the force is transmitted through the rod at the speed of sound in the rod. Something on the other end won't feel the force until the pressure wave propagates to the other end of the rod.

The speed is a speed of propagation. Contact forces have a speed of propagation too. If you have a long metal rod and you push on one end, the force is transmitted through the rod at the speed of sound in the rod. Something on the other end won't feel the force until the pressure wave propagates to the other end of the rod.

Could you explain it a bit elaborately??

russ_watters
Mentor
I'm not sure how to make it any more basic. What part don't you understand?

The speed of sound in steel is about 4500 m/s. That means if you have a rod that is 4500 m long and you push on one end, the other end won't start to move for one second.

Does it imply that a long rod become shorter (may be, the effect is too little to observe ) when you push it along it's length?
What happens when a force of quite large magnitue is applied?

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russ_watters
Mentor
Does it imply that a long rod become shorter (may be, the effect is too little to observe ) when you push it along it's length?
Yes. When you pluck a guitar string and it oscillates, it becomes longer, right? Same idea.
What happens when a force of quite large magnitue is applied?
You destroy the rod. Above a certain force, the elasticity of the rod can't keep up and you start deforming the rod. Additional, faster moving shock waves are possible in this scenario.

We were talking about, let's say we were to do things in incredible slow motion.

We had two magnets doing something (attracting/repelling), the magnetic force is there. We were to destroy a magnetic instantaneously. Does that force act instantaneously or does it take time?

I haven't gone through this section in Physics yet, but, Photons are the carriers of the force correct? So the force is not a particle or is it? If it is, then it travels at the speed of light?

We were talking about if you took the other magnet away, the photons or whatever left from the other magnet will just act as if it were part of the other magnets own photons or something and would not feel anything. That the force once cut off, the affects will be cut off and its own momentum would move it.

russ_watters
Mentor
We had two magnets doing something (attracting/repelling), the magnetic force is there. We were to destroy a magnetic instantaneously. Does that force act instantaneously or does it take time?
It takes time to propagate.