# Newton's Third Law equal and opposite forces

## Main Question or Discussion Point

Although the equal and opposite forces stated in Newton's third law are sometimes referred to as an action-reaction pair in reality they do not share a cause and effect relationship. They arise simultaneously, abide together and disappear simultaneously.

Imagine you are spinning a washer attached to the end of a string in a circle. The force the string is applying to the washer is equal and opposite to the force the washer is applying to the string, which are the centripetal and centrifugal forces respectively.

The action-reaction pain as stated in Newton's third law does not share a cause and effect relationship then as soon as the string is cut both forces no longer exist.

According to relativity no signal can travel faster than light. But it the two forces cease to exist simultaneously the information that the string has been cut is instantaneously transmitted to the washer. So this information travels faster than the speed of light

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Tom Mattson
Staff Emeritus
Gold Member
Originally posted by protonman
According to relativity no signal can travel faster than light. But it the two forces cease to exist simultaneously the information that the string has been cut is instantaneously transmitted to the washer. So this information travels faster than the speed of light [/B]
The conclusion in this paragraph is made under the assumption that the tension in the string drops to zero at all points in the string simultaneously.

In other words, the argument boils down to, "The information travels faster than light because the information travels infinitely fast."

Where is the evidence to back that up?

Originally posted by Tom
The conclusion in this paragraph is made under the assumption that the tension in the string drops to zero at all points in the string simultaneously.

In other words, the argument boils down to, "The information travels faster than light because the information travels infinitely fast."

Where is the evidence to back that up?
Because the action-reaction pair stated in Newton's third law does not actually have a cause and effect relationship. They are produced, abide and destroyed simultaneously.

russ_watters
Mentor
Newton's laws are classical and therefore limited by the fact that they don't take into account Relativity. The example you cite also doesn't take into account the speed of sound - not a limitation of Newton's laws, but a flaw in the model.

The limitations of Newton's laws are quite well known to physicists. So what exactly is the problem here?

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Janitor
Your ideal experiment probably assumes a perfectly inelastic string. Real-world strings are elastic, and a short while after the cut has been made, the washer will still be feeling the string tension. It will take a finite time for any given part of the string to relax, and the speed at which the relaxation propagates along the string will be very much less than the speed of light.

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Tom Mattson
Staff Emeritus
Gold Member

Originally posted by protonman
Because the action-reaction pair stated in Newton's third law does not actually have a cause and effect relationship. They are produced, abide and destroyed simultaneously.
And that would be fine if Newton's laws held absolutely in the real universe. But they don't. In the real, physical universe, the information is not propagated along the string instantaneously.

Originally posted by Tom
And that would be fine if Newton's laws held absolutely in the real universe. But they don't. In the real, physical universe, the information is not propagated along the string instantaneously.
But you are using the thing I am questioning as you reason which is wrong. What I am questioning is the very idea that information can not be propagated instantaneously.

Anyway, are you saying that Newton's third law is does not hold absolutely in the real universe?

Ok let me clarify the point. The action-reaction pair stated in Newton's third law is not really an action-reaction pair because there is no cause and effect relationship. Therefore, they arise simultaneously, abide simultaneously and are destroyed simultaneously.

If this is the case then when I am pushing a stone with my finger the force applied by my finger and the equal and opposite force applied by the stone on my finger arise at the same time. How does the stone know that a force is being applied to it and to push back with an equal force? The information that my finger is pushing on the stone must be instantaneous because, and this is the most important point, the two forces do not share a cause and effect relationship.

russ_watters
Mentor

Originally posted by protonman
Anyway, are you saying that Newton's third law is does not hold absolutely in the real universe?
Yes.
If this is the case then when I am pushing a stone with my finger the force applied by my finger and the equal and opposite force applied by the stone on my finger arise at the same time. How does the stone know that a force is being applied to it and to push back with an equal force? The information that my finger is pushing on the stone must be instantaneous because, and this is the most important point, the two forces do not share a cause and effect relationship.
Forces transfer at the speed of sound. When you start pushing on a stone, a pressure wave travels through the stone at the speed of sound (in the stone) to satisfy Newton's 3rd.

Have you heard of the "water hammer" effect? When you close a water valve quickly, the water right next to the valve stops immediatly, but the water further away does not. The water further away slams into the stopped water, stopping itself. Water even further away does the same thing, etc, etc, etc. This sends a shock wave backwards through the pipe away from the valve at the speed of sound, making a banging noise in the pipe.

When you cut a string pulling on something (in your first example), that information travels in a pressure wave through the string at the speed of sound in that string. When the pressure wave gets to the washer, then the washer "knows" the string is broken.

There IS a cause-effect relationship between the forces, but its not instantaneous and its not absolute for Newton's 3rd, at least in the way you are framing it.

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Michael D. Sewell
Good analogy russ. Rapid closure of the valve results in a localized area of high pressure which compresses the water, and stretches the walls of the pipe(Hooke's law), converting the kinetic energy into elastic energy. This propagates a wave of high pressure upstream at the speed of sound. The momentum in the upstream direction causes a localized area of low pressure at the valve, causing the pipe walls to contract, starting the cycle over again(harmonic motion). Below the valve, the inverse condition causes an area of low pressure to develop, creating the same harmonic motion downstream as well. Internal and external non-conservative forces eventually dampen and end the cycle.

oops! mispelt hook. fikst nowe.

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Tom Mattson
Staff Emeritus
Gold Member

Originally posted by protonman
But you are using the thing I am questioning as you reason which is wrong. What I am questioning is the very idea that information can not be propagated instantaneously.
The atoms in the string are held together by electromagnetic forces. It is a well known fact that the EM force does not propagate instantaneously.

Anyway, are you saying that Newton's third law is does not hold absolutely in the real universe?
Of course. It is a fact that they don't

LURCH
Your reasoning is valid, it is only the observation you have mistaken. The thing is, this two-part statement:

Originally posted by protonman
Ok let me clarify the point. The action-reaction pair stated in Newton's third law is not really an action-reaction pair because there is no cause and effect relationship. Therefore, they arise simultaneously, abide simultaneously and are destroyed simultaneously.
If the second statement were true, it would provide a fairly good support for the first. However, the sceond statement is not true. So the fact that these interactions are not simultaneous (which is verified by all observations), actually serves as disproof of the premise that they are not cause-and-effect.

Originally posted by Tom
The atoms in the string are held together by electromagnetic forces. It is a well known fact that the EM force does not propagate instantaneously.

Of course. It is a fact that they don't
So then momentum conservation does not hold in all cases.

So when two particles touch the forces do not arise simultaneously at the mutual point of contact?

russ_watters
Mentor
Originally posted by protonman
So when two particles touch the forces do not arise simultaneously at the mutual point of contact?
Yes, they do. Thats a different issue altogether.

It differs from your string-washer thought experiment in that the point of contact is where the string broke, not at the washer and your hand. At the point the string breaks, the loss of force is instantaneous for both pieces of string where they broke. But at the instant the string breaks, the washer and your hand still feel the force as if the string was intact.

Originally posted by russ_watters
Yes, they do. Thats a different issue altogether.

It differs from your string-washer thought experiment in that the point of contact is where the string broke, not at the washer and your hand. At the point the string breaks, the loss of force is instantaneous for both pieces of string where they broke. But at the instant the string breaks, the washer and your hand still feel the force as if the string was intact.
Same idea. The knowledge that the particles have hit is instantaneously transmitted to each of them.

russ_watters
Mentor
Originally posted by protonman
Same idea. The knowledge that the particles have hit is instantaneously transmitted to each of them.
I honestly don't know what you're getting at. Could you elaborate?

Originally posted by russ_watters
I honestly don't know what you're getting at. Could you elaborate?
The two forces rise simultaneously at the point of contact. Since the particles do not share a cause and effect relationship what is the cause of the force on each one?

russ_watters
Mentor
Originally posted by protonman
The two forces rise simultaneously at the point of contact. Since the particles do not share a cause and effect relationship what is the cause of the force on each one?
The particles do share a cause-effect relationship where the forces are concerned and Newton's 3rd applies for two particles in contact with each other.

Originally posted by russ_watters
The particles do share a cause-effect relationship where the forces are concerned and Newton's 3rd applies for two particles in contact with each other.
Which particle produces the force?

Tom Mattson
Staff Emeritus
Gold Member

Originally posted by protonman
So then momentum conservation does not hold in all cases.
Yes, it does. Momentum conservation does not hang on Newton's laws, it follows from the much more general principle of the invariance of a physical system under translations in space.

edit: fixed an error

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by protonman
Same idea. The knowledge that the particles have hit is instantaneously transmitted to each of them.
No, it is not the "same idea".

Instead of dragging this out for pages without getting anywhere, why don't you re-read Russ' lucid post on the water in the pipe, as well as his explanation of the difference between two particles colliding and two objects connected by a string?

When the cord is cut, the information is communicated at that instant to the two segments of the string at the location of the cut. Your contention that that same information is communicated to the washer and to the holder of the string at that same instant is simply wrong.

Zero
I seem to see a problem that is being missed. There is no cause-and-effect between the two ends of the string.

Tom Mattson
Staff Emeritus
Gold Member
Originally posted by Zero
I seem to see a problem that is being missed. There is no cause-and-effect between the two ends of the string.
Why not? If I jerk on one end of the string, and a short time later the washer makes a sudden move inwards, those two events are causally related. Similarly, if the string is cut, and a short time later the tension drops to zero at the end, the later is certainly caused by the former.

Zero
Originally posted by Tom
Why not? If I jerk on one end of the string, and a short time later the washer makes a sudden move inwards, those two events are causally related. Similarly, if the string is cut, and a short time later the tension drops to zero at the end, the later is certainly caused by the former.
LOL, because when you cut the string, the two ends are not acting against each other, each end is acting against the knife or scissors or whatever is cutting the string, right?

Protonman, it seems, doesn't know to factor in all the forces involved, including the forces holding the individual atoms of the string together, or the force of the scissors acting on particles at the ends of teh cut string.