I am glad that we had this exchange of views on the mechanism behind elastic collisions in the Newton's Cradle. It was definitely useful to me, and I hope it was useful to you too as well.

If you don't mind, I would like to engage in a similar exchange on various electromagnetic subjects in the future. However, I do not feel confident enough to engage you in such a discussion at this point - I will have to study your papers first, with the attention they deserve.

Yes, any time you wish to discuss electromagnetism just let me know.

One last thing I ought to say regarding the fine-grained rotational waves that conduct kinetic energy, is that I had already decided that kinetic energy is directly related to the fine-grained angular momentum of the atoms and/or molecules of the object that is moving, and that changes in kinetic energy are caused by a shear interaction between those molecules and the all pervading smaller molecules of the luminiferous medium.

I would like to point out the utter confusion and flip-flopping that is present in your understanding of the elastic collision process that takes place in the Newton's Cradle.

In my view, all that confusion and flip-flopping comes from a wrong understanding of what "elastic deformation" is. "Elastic deformation" is not a static thing, as you might have imagined, "elastic deformation" is a dynamic thing. And I am not talking about the dynamicity of deformation propagation here, which is obvious for the word "propagation" already means dynamic. I am talking about the dynamicity of simple "static" compression of a solid rod, or simple "static" stretch of a string. There is no such thing as "static" in nature. Potential energy - which seems static at one level - is simply kinetic energy at finer level. That's the dynamicity I am talking about. All energy is kinetic energy in the final analysis. There is no such thing as potential energy.

Please reread my 4-point summarization of your views:

(1) There are two separate waves in the Newton's Cradle - deformation wave and kinetic energy wave; (2) Kinetic energy wave propagates very fast but not instantaneously (speed, perhaps, in the order of speed of light) while deformation wave propagates (for real steel balls) at much slower rate (perhaps, a few km/s); (3) The original kinetic energy of the incoming ball splits into the energy of deformation of the ball material, on one hand, and kinetic energy of increased motion (spin and/or orbital) of electrons in the metal, on the other hand; (4) The share of energy that propagates in the "kinetic mode" is significantly higher than that which propagates in the "deformation mode".

All your confusion will be gone as soon as you realize that point (1) is wrong: "deformation wave" and "kinetic energy wave" are two different names for the same thing. Therefore, "deformation wave" and "kinetic energy wave" cannot have different speeds of propagation. Therefore, it does not make sense to speak of splitting the original kinetic energy of the incoming ball into the energy of "deformation wave" and the energy of "kinetic energy wave".

Consider a straight row of weights equally spaced on a frictionless surface, all joined together with springs.

When we push one end, we will trigger off a compression wave which will move through the row. But the far end of the row will already be moving before the compression wave reaches the end of the row. The compression wave does not cause the movement of the contraption as a whole. It merely represents the internal energy which detracts from the large scale kinetic energy.

On your claim that ultimately potential energy is kinetic energy, there may be something in this idea. I have at times thought the same myself. Certainly centrifugal potential energy is the same thing as rotational kinetic energy. That much is manifestly plain.

As regards gravitational potential energy, we might be able to understand it in terms of the escape velocity, which in turn might be the velocity of inflow of the pure aether. In other words, it may be a kind of negative kinetic energy, but not absolutely negative as such, but merely negative relative to what it would be outside the gravitational field.

Quote: "When we push one end, we will trigger off a compression wave which will move through the row. But the far end of the row will already be moving before the compression wave reaches the end of the row. The compression wave does not cause the movement of the contraption as a whole. It merely represents the internal energy which detracts from the large scale kinetic energy."

We have looked into this already: ; an interesting case, but don't let it fool you.

To understand what is going on in this scenario, here is what you need to do. Pass to the limit in two different ways: (1) stretch the string until it becomes a straight rod; (2) increase the density of string curling to the limit, i.e. to the point where the turns in the string start touching each other (now you basically have the same rod but empty on the inside i.e. you get a tube). What is the speed of compression wave in both limiting cases? It is 3-6 km/s, i.e. the speed of compression wave propagation in steel.

In the case of normal string you get to waves of compression: (1) one propagating along the spiral rod, so to speak, and as such its speed is determined by the elasticity of steel, i.e. V=3-6 m/s, and (2) a wave of "spring compression" the speed of which is determined by the string elasticity, the string being considered as an object on its own at a higher macro level; the speed of "string compression wave" will always be lower than the speed of "steel compression wave". That's where the dispersion of the compression wave comes from in .

Your video was of a Newton's Cradle, but I was talking about a situation where all the weights are actually joined together by the springs, and hence can't fly apart.

If you push one end, the far end moves before the compression wave gets there, and the compression wave detracts from the kinetic energy on the large scale.

Let's just consider two weights joined together with one spring. If we push the contraption at one end, the far end and the centre of mass move, while simultaneously the two weights begin to oscillate about the centre of mass, which is now moving.

Hence we have two modes of activity. (1) The motion of the centre of mass giving rise to the macro-kinetic energy, and (2) the oscillation of the two masses about the centre of mass, corresponding to internal energy.

The point is that as (2) tends to zero, as it would do as the spring constant k tends to infinity, then the kinetic energy at (1) increases.

If the kinetic energy is initially transmitted into the system by fine-grained rotational waves that have a finite speed, this will still necessarily mean a contraction of the system in the direction of motion. But it will be a separate issue to that of any linear displacement which propagates up and down through the system and is absorbed as heat.

The latter elastic linear displacement always begins by radiating outwards from the point of contact, but the kinetic energy wave's direction can't be determined unless we know the absolute speeds of everything relative to the luminiferous medium.

Quote: "Your video was of a Newton's Cradle, but I was talking about a situation where all the weights are actually joined together by the springs, and hence can't fly apart.

If you push one end, the far end moves before the compression wave gets there ..."

Very well, let us consider a situation where all the weights are actually joined together by the springs, and hence can't fly apart. Take 10 balls, 1 cm in diameter each, separated and connected by springs 1 meter long each. You assert: If you push one end, the far end moves before the compression wave gets there. Let us assume that the push was such that the ball 1, that we pushed, acquired speed V = 1 m/s. How long will it take before the ball 10 at the other end starts moving as a whole? We have already agreed that it is not an instantaneous event, so let us denote the time it takes by t ( t > 0). Now I am asking you: will t change if we change spring's elasticity modulus k? Yes, or no? If yes, what does the functional relation t(k) look like?

Yes the speed of the wave propagation will depend on the spring's elastic constant k.

Newton derived an equation for the speed of a wave in terms of elastic constant and density. It's v^2 = k/density

But in the example we are talking about, the value of k for the spring is not related to the speed with which the kinetic energy wave flows into the contraption.

I am asking you straight and very pointed questions. But instead of answering my questions just as straight, you answer your own questions.

Quote: "Yes the speed of the wave propagation will depend on the spring's elastic constant k."

I did not ask you whether the speed of the wave propagation will depend on the spring's elastic constant k or not.

Quote: "But in the example we are talking about, the value of k for the spring is not related to the speed with which the kinetic energy wave flows into the contraption."

I am forced here to guess that your answer to the question I actually asked was "no", that is your answer was: t does not depend on k.

Very well. Let us make now each string thinner and thinner, without changing the number of turns (rings) in the spring, and ultimately push the thickness to zero. This way, according to your answer, t will not undergo any change. But string thickness zero means no string at all, and we can calculate t precisely: t = 10 seconds. And that means that the ball 10 at the other end will start moving in 10 seconds after we hit the ball 1, in other words, V = 1 m/s.

Not exactly the high speed that you would expect for your "speed with which the kinetic energy wave flows into the contraption".

Yes, reading the question on your previous mail again, the answer is "No", in that t, being the time of travel, does not depend on the spring constant k.

As regards your answer of 10 seconds, that is only the time taken for the compression wave to reach the far end. But the far end will already be moving before the compression wave reaches there.

the most simple case scenario that is relevant to all of this is the case of two weights joined together with a spring and set into a state of oscillation. That is an absolute physical effect. It is not relative.

But on top of this, the centre of mass can be in a state of translational motion, and that is a completely separate issue. When we first push this contraption, we set it oscillating, but the centre of mass appears to move as well, which means that there has been a transfer of kinetic energy into or out of the contraption, separate from any issues relating to the energy of the oscillation. Galileo would say that the apparent kinetic energy centred on the centre of mass is only a relative effect.

But if motion is only relative, then when a single ball crashes into a row of balls in a Newton's Cradle, what direction does the transfer of kinetic energy move in?

There are definitely two separate modes of activity occurring in a Newton's Cradle. One is absolute. The other appears to be relative, but that is only because classical mechanics ignores the existence of a physical medium relative to which inertial effects are generated.

Within the context of classical mechanics, which believes in Galilean relativity, if we have two weights connected by a spring in a state of oscillation, and if the centre of mass of the contraption is moving, then we have two modes of activity, one of which is absolute, and one of which is relative,

(1) the oscillation of the spring (absolute) (2) Motion of the centre of mass (relative)

Therefore, we cannot conflate these two modes of activity, because one is absolute and the other is relative.

What is activity? Can you imagine an activity without a motion? Can you imagine oscillation - or any type of activity whatsoever - without some kind of motion involved? If you can, then you have a very vivid and rich imagination, which I can never catch up with, and this conversation would naturally come to its natural conclusion.

If you can't, then we shall continue the discussion. So, if you wish to speak of two modes of activity - absolute and relative - then you will have to define for me the notion of absolute velocity (or absolute motion) without employing (directly or indirectly) the notion of relativity.

In other words, take a stand-alone object (assuming that you can imagine such thing as a stand-alone object, to begin with) and define its velocity operationally.

Yes of course, all activity involves motion. What I was saying was that when we have an oscillating spring in a state of net translational motion, we have two modes of activity. The oscillation is absolute. It is independent of any frame of reference.

The translational motion on the other hand is frame dependent. It therefore follows that we are dealing with two distinct modes of activity that reach require a separate analysis.

It's my own opinion that Galilean relativity is deficient by virtue of ignoring a physical background medium which is the cause of inertial phenomena. And this deficiency contributes towards the mystery of the Newton's Cradle.

It's manifestly plain to me that the transfer of kinetic energy between balls in a Newton's Cradle involves a mechanism that is distinct from the deformation wave that would be associated with an oscillating spring, as well illustrated by that video which you sent to me where the balls are padded with springs. By gluing the balls to the springs, it becomes clear that the oscillation is internal and it is not what causes the net translational motion of the whole contraption. Something else is at play too. Another kind of wave through the row of balls, which interacts with the surrounding luminiferous medium.

## Comments

Hi David,

I am glad that we had this exchange of views on the mechanism behind elastic collisions in the Newton's Cradle. It was definitely useful to me, and I hope it was useful to you too as well.

If you don't mind, I would like to engage in a similar exchange on various electromagnetic subjects in the future. However, I do not feel confident enough to engage you in such a discussion at this point - I will have to study your papers first, with the attention they deserve.

My best wishes,

Arthur

Hi Arthur,

Yes, any time you wish to discuss electromagnetism just let me know.

One last thing I ought to say regarding the fine-grained rotational waves that conduct kinetic energy, is that I had already decided that kinetic energy is directly related to the fine-grained angular momentum of the atoms and/or molecules of the object that is moving, and that changes in kinetic energy are caused by a shear interaction between those molecules and the all pervading smaller molecules of the luminiferous medium.

Best Regards

David

Hi David,

I would like to point out the utter confusion and flip-flopping that is present in your understanding of the elastic collision process that takes place in the Newton's Cradle.

In my view, all that confusion and flip-flopping comes from a wrong understanding of what "elastic deformation" is. "Elastic deformation" is not a static thing, as you might have imagined, "elastic deformation" is a dynamic thing. And I am not talking about the dynamicity of deformation propagation here, which is obvious for the word "propagation" already means dynamic. I am talking about the dynamicity of simple "static" compression of a solid rod, or simple "static" stretch of a string. There is no such thing as "static" in nature. Potential energy - which seems static at one level - is simply kinetic energy at finer level. That's the dynamicity I am talking about. All energy is kinetic energy in the final analysis. There is no such thing as potential energy.

Please reread my 4-point summarization of your views:

(1) There are two separate waves in the Newton's Cradle - deformation wave and kinetic energy wave;

(2) Kinetic energy wave propagates very fast but not instantaneously (speed, perhaps, in the order of speed of light) while deformation wave propagates (for real steel balls) at much slower rate (perhaps, a few km/s);

(3) The original kinetic energy of the incoming ball splits into the energy of deformation of the ball material, on one hand, and kinetic energy of increased motion (spin and/or orbital) of electrons in the metal, on the other hand;

(4) The share of energy that propagates in the "kinetic mode" is significantly higher than that which propagates in the "deformation mode".

All your confusion will be gone as soon as you realize that point (1) is wrong: "deformation wave" and "kinetic energy wave" are two different names for the same thing. Therefore, "deformation wave" and "kinetic energy wave" cannot have different speeds of propagation. Therefore, it does not make sense to speak of splitting the original kinetic energy of the incoming ball into the energy of "deformation wave" and the energy of "kinetic energy wave".

My best.

Hi Arthur,

Consider a straight row of weights equally spaced on a frictionless surface, all joined together with springs.

When we push one end, we will trigger off a compression wave which will move through the row. But the far end of the row will already be moving before the compression wave reaches the end of the row. The compression wave does not cause the movement of the contraption as a whole. It merely represents the internal energy which detracts from the large scale kinetic energy.

On your claim that ultimately potential energy is kinetic energy, there may be something in this idea. I have at times thought the same myself. Certainly centrifugal potential energy is the same thing as rotational kinetic energy. That much is manifestly plain.

As regards gravitational potential energy, we might be able to understand it in terms of the escape velocity, which in turn might be the velocity of inflow of the pure aether. In other words, it may be a kind of negative kinetic energy, but not absolutely negative as such, but merely negative relative to what it would be outside the gravitational field.

Best Regards

David

Hi David,

Quote: "

When we push one end, we will trigger off a compression wave which will move through the row. But the far end of the row will already be moving before the compression wave reaches the end of the row. The compression wave does not cause the movement of the contraption as a whole. It merely represents the internal energy which detracts from the large scale kinetic energy."We have looked into this already: ; an interesting case, but don't let it fool you.

To understand what is going on in this scenario, here is what you need to do. Pass to the limit in two different ways: (1) stretch the string until it becomes a straight rod; (2) increase the density of string curling to the limit, i.e. to the point where the turns in the string start touching each other (now you basically have the same rod but empty on the inside i.e. you get a tube). What is the speed of compression wave in both limiting cases? It is 3-6 km/s, i.e. the speed of compression wave propagation in steel.

In the case of normal string you get to waves of compression: (1) one propagating along the spiral rod, so to speak, and as such its speed is determined by the elasticity of steel, i.e. V=3-6 m/s, and (2) a wave of "spring compression" the speed of which is determined by the string elasticity, the string being considered as an object on its own at a higher macro level; the speed of "string compression wave" will always be lower than the speed of "steel compression wave". That's where the dispersion of the compression wave comes from in .

My best.

Hi Arthur,

Your video was of a Newton's Cradle, but I was talking about a situation where all the weights are actually joined together by the springs, and hence can't fly apart.

If you push one end, the far end moves before the compression wave gets there, and the compression wave detracts from the kinetic energy on the large scale.

Let's just consider two weights joined together with one spring. If we push the contraption at one end, the far end and the centre of mass move, while simultaneously the two weights begin to oscillate about the centre of mass, which is now moving.

Hence we have two modes of activity. (1) The motion of the centre of mass giving rise to the macro-kinetic energy, and (2) the oscillation of the two masses about the centre of mass, corresponding to internal energy.

The point is that as (2) tends to zero, as it would do as the spring constant k tends to infinity, then the kinetic energy at (1) increases.

If the kinetic energy is initially transmitted into the system by fine-grained rotational waves that have a finite speed, this will still necessarily mean a contraction of the system in the direction of motion. But it will be a separate issue to that of any linear displacement which propagates up and down through the system and is absorbed as heat.

The latter elastic linear displacement always begins by radiating outwards from the point of contact, but the kinetic energy wave's direction can't be determined unless we know the absolute speeds of everything relative to the luminiferous medium.

Best Regards

David

Hi David,

Quote: "

Your video was of a Newton's Cradle, but I was talking about a situation where all the weights are actually joined together by the springs, and hence can't fly apart.

..."If you push one end, the far end moves before the compression wave gets there

Very well, let us consider a situation where all the weights are actually joined together by the springs, and hence can't fly apart. Take 10 balls, 1 cm in diameter each, separated and connected by springs 1 meter long each. You assert: If you push one end, the far end moves before the compression wave gets there. Let us assume that the push was such that the ball 1, that we pushed, acquired speed V = 1 m/s. How long will it take before the ball 10 at the other end starts moving as a whole? We have already agreed that it is not an instantaneous event, so let us denote the time it takes by t ( t > 0). Now I am asking you: will t change if we change spring's elasticity modulus k? Yes, or no? If yes, what does the functional relation t(k) look like?

My best.

Hi Arthur,

Yes the speed of the wave propagation will depend on the spring's elastic constant k.

Newton derived an equation for the speed of a wave in terms of elastic constant and density. It's

v^2 = k/density

But in the example we are talking about, the value of k for the spring is not related to the speed with which the kinetic energy wave flows into the contraption.

Best Regards

David

Hi David,

I am asking you straight and very pointed questions. But instead of answering my questions just as straight, you answer your own questions.

Quote: "

Yes the speed of the wave propagation will depend on the spring's elastic constant k."I did not ask you whether the speed of the wave propagation will depend on the spring's elastic constant k or not.

Quote: "

But in the example we are talking about, the value of k for the spring is not related to the speed with which the kinetic energy wave flows into the contraption."I am forced here to guess that your answer to the question I actually asked was "no", that is your answer was: t does not depend on k.

Very well. Let us make now each string thinner and thinner, without changing the number of turns (rings) in the spring, and ultimately push the thickness to zero. This way, according to your answer, t will not undergo any change. But string thickness zero means no string at all, and we can calculate t precisely: t = 10 seconds. And that means that the ball 10 at the other end will start moving in 10 seconds after we hit the ball 1, in other words, V = 1 m/s.

Not exactly the high speed that you would expect for your "speed with which the kinetic energy wave flows into the contraption".

My best.

Hi Arthur,

Yes, reading the question on your previous mail again, the answer is "No", in that t, being the time of travel, does not depend on the spring constant k.

As regards your answer of 10 seconds, that is only the time taken for the compression wave to reach the far end. But the far end will already be moving before the compression wave reaches there.

Best Regards

David

Thanks again, David, for this most interesting discussion.

My best,

Arthur

Hi Arthur,

the most simple case scenario that is relevant to all of this is the case of two weights joined together with a spring and set into a state of oscillation. That is an absolute physical effect. It is not relative.

But on top of this, the centre of mass can be in a state of translational motion, and that is a completely separate issue. When we first push this contraption, we set it oscillating, but the centre of mass appears to move as well, which means that there has been a transfer of kinetic energy into or out of the contraption, separate from any issues relating to the energy of the oscillation. Galileo would say that the apparent kinetic energy centred on the centre of mass is only a relative effect.

But if motion is only relative, then when a single ball crashes into a row of balls in a Newton's Cradle, what direction does the transfer of kinetic energy move in?

There are definitely two separate modes of activity occurring in a Newton's Cradle. One is absolute. The other appears to be relative, but that is only because classical mechanics ignores the existence of a physical medium relative to which inertial effects are generated.

Best Regards

David

Hi Arthur,

I'll try to state my last mail more simply.

Within the context of classical mechanics, which believes in Galilean relativity, if we have two weights connected by a spring in a state of oscillation, and if the centre of mass of the contraption is moving, then we have two modes of activity, one of which is absolute, and one of which is relative,

(1) the oscillation of the spring (absolute)

(2) Motion of the centre of mass (relative)

Therefore, we cannot conflate these two modes of activity, because one is absolute and the other is relative.

Best Regards

David

Hi David,

What is activity? Can you imagine an activity without a motion? Can you imagine oscillation - or any type of activity whatsoever - without some kind of motion involved? If you can, then you have a very vivid and rich imagination, which I can never catch up with, and this conversation would naturally come to its natural conclusion.

If you can't, then we shall continue the discussion. So, if you wish to speak of two modes of activity - absolute and relative - then you will have to define for me the notion of absolute velocity (or absolute motion) without employing (directly or indirectly) the notion of relativity.

In other words, take a stand-alone object (assuming that you can imagine such thing as a stand-alone object, to begin with) and define its velocity

operationally.My best.

Hi Arthur,

Yes of course, all activity involves motion. What I was saying was that when we have an oscillating spring in a state of net translational motion, we have two modes of activity. The oscillation is absolute. It is independent of any frame of reference.

The translational motion on the other hand is frame dependent. It therefore follows that we are dealing with two distinct modes of activity that reach require a separate analysis.

It's my own opinion that Galilean relativity is deficient by virtue of ignoring a physical background medium which is the cause of inertial phenomena. And this deficiency contributes towards the mystery of the Newton's Cradle.

It's manifestly plain to me that the transfer of kinetic energy between balls in a Newton's Cradle involves a mechanism that is distinct from the deformation wave that would be associated with an oscillating spring, as well illustrated by that video which you sent to me where the balls are padded with springs. By gluing the balls to the springs, it becomes clear that the oscillation is internal and it is not what causes the net translational motion of the whole contraption. Something else is at play too. Another kind of wave through the row of balls, which interacts with the surrounding luminiferous medium.

Best Regards

David