Gravity

[Jaaanosik]

And while this is not necessarily a forum for this sort of discussion, perhaps some CA members will learn some physics.

So referring to my post above, I’d like to clarify a couple of things:

1. Kinetic energy is not invariant under Galilean transformations. That is trivial to see. A body at rest in one inertial frame has zero kinetic energy in that frame. The same body in any other inertial frame (which by defintion is moving at a non-zero velocity v with respect to the first) has velocity v in that frame and non-zero kinetic energy.
2. You can think of the situation of a mass folloing a circular path on the end of a string in two ways:
   a) As a closed kinematic system in which there are no external forces - in order for this to be the case you have to include the finite mass on the other end of the string, and in such an analysis the total kinetic energy of system, while different in different inertial frames, is constant in time in all inertial frames or
   b) As a body constrained to move in a circle by an external force applied by the string. This is the analysis that Jaanosik is attempting. In this case, since there is an external force the work-energy principle applies. Changes in the kinetic energy of the particle equal the work done by the external force. The instantaneous work done is given by the scalar product of the force vector and the velocity vector of the body. But we know that the velocity vector of the body is different in different inertial frames whereas the acceleration and therefore force vector is the same in all inertial frames - we proved that above, So the work done at any instant is different in different inertial frames and so the change in kinetic energy is different in different frames. In the frame at rest with respect to the centre of the circle the acceleration is always normal to the velocity and therefore the dot product is zero - no work is done and so the kinetic energy remains constant. In any other inertial frame the acceleration and velocity vectors are not always normal and so work is done and the kinetic energy of the body changes over time.

I’d say the major error of Jaaanosik is to believe that Galilean invariance demands kinetic energy to be constant in all frames if external forces are being applied. It doesn’t. There are other mistakes too.

Hecd2,
My first name is Jano. What is yours?

Thank you very much for very good responses.
The nature shows us that there is a critical speed and resonance.
The kinetic energy change analysis in the higher frame is in line with that, it predicts it. The moving frame does not have a clue about it.
The only logical conclusion is that the Galilean invariance is wrong in this case.
The relativity falls.

It’s not me, it’s the nature that you are going against,
Jano

 

[inocente]

Anybody serious about studying gravity should read this:
theelectromagneticnatureofthings.com/img/emnature.pdf

The site names the author as Jaroslav Kopernicky.

He’s not a physicist. He says he’s an electrical engineer. His papers on this subject are not peer reviewed. They are on a site grandiosely titled the world science database, which according to Wikipedia is “where authors can post materials not generally accepted and published by scientific journals”. That Wiki article on fringe science says the site belongs to something called the Natural Philosophy Alliance, “founded in 1994 by John E. Chappell Jr., a historian and anti-relativity activist.”

Kopernicky’s gravity-as-EM notion appears to be based on an experiment with two magnets, which is not well documented. He gives an informal demo in this video. The only person to comment told him it’s a well-known effect described by a magnet manufacturer here.

He’s probably a nice guy but this seems to be one of those times when someone stepped outside his field and jumped to kooky conclusions.

Anyway, totally debunked, wrong, wrong and thrice wrong.

 

[hecd2]

hecd2:

I’d say the major error of Jaaanosik is to believe that Galilean invariance demands kinetic energy to be constant in all frames if external forces are being applied.

It doesn’t…Thank you very much for very good responses.

You bolded part of my summary. Did you do so because you believe the bolded part to be true?

Just to be clear, I have shown in my previous post exactly why “Galilean invariance does **not **demand kinetic energy to be constant in all frames if external forces are being applied” (because the work done on the body is **not **invariant under Galilean transformations - and I explained why that is). Your six gnomic statements fail to actually acknowledge any physics.

The nature shows us that there is a critical speed and resonance.

Critical speed and resonance of what? There is nothing in the system under discussion which can resonate. Resonance occurs when a forcing frequency is close or equal to the natural frequency of the system. But the system above (a body revolving at constant angular velocity in a circle on a string) has no natural frequency because it is not an oscillator. For it to be an oscillator it needs a mass (which it has), moving under the influence of a restoring force which is a monotonic function of its displacement (which it doesn’t have). Also, I sense that you claim that the system resonates when observed from one frame but doesn’t resonate when observed from other frames which is a nonsensical claim on the face of it.

The kinetic energy change analysis in the higher frame is in line with that, it predicts it.

Well frames don’t predict things - physicists do. Nothing in the system you have described, when correctly understood (which you plainly fail to do) leads to a prediction of resonance in any inertial frame. In all inertial frames the body is free to rotate at any arbitrary angular velocity. It is not an oscillator.

The only logical conclusion is that the Galilean invariance is wrong in this case.

The only logical conclusion is that you don’t understand the physics.

The relativity falls.

We haven’t discussed anything to do with relativity.

 

[Jaaanosik]

You bolded part of my summary. Did you do so because you believe the bolded part to be true?

Just to be clear, I have shown in my previous post exactly why “Galilean invariance does **not **demand kinetic energy to be constant in all frames if external forces are being applied” (because the work done on the body is **not **invariant under Galilean transformations - and I explained why that is). Your six gnomic statements fail to actually acknowledge any physics.

A work-energy principle consequence is that a kinetic energy change is done by a free force acting on a body. Free means it’s not a constraint force.

Critical speed and resonance of what? There is nothing in the system under discussion which can resonate. Resonance occurs when a forcing frequency is close or equal to the natural frequency of the system. But the system above (a body revolving at constant angular velocity in a circle on a string) has no natural frequency because it is not an oscillator. For it to be an oscillator it needs a mass (which it has), moving under the influence of a restoring force which is a monotonic function of its displacement (which it doesn’t have). Also, I sense that you claim that the system resonates when observed from one frame but doesn’t resonate when observed from other frames which is a nonsensical claim on the face of it.

The system has its natural frequency when v ~ rw(omega).
The system does not resonate when v << rw or v >> r*w; the kinetic energy is almost constant in both reference frames when this is the case.
In the ground frame the ball accelerates from 0 velocity at the bottom of the cycloid to 2v at the top of the cycloid and decelerating back to 0 in the case of the rigid body particle.
There is a[t] on the way up and -a[t] on the way down.
It’s more complicated with the ball on a string.

Well frames don’t predict things - physicists do. Nothing in the system you have described, when correctly understood (which you plainly fail to do) leads to a prediction of resonance in any inertial frame. In all inertial frames the body is free to rotate at any arbitrary angular velocity. It is not an oscillator.
The only logical conclusion is that you don’t understand the physics.
We haven’t discussed anything to do with relativity.

This is relativity.
Right, the kinetic energy change mathematical model used by physicists for the ground predicts the critical speed, the resonance.
No kinetic energy change mathematical model used by physicists in the moving frame fails to predict the critical speed and the resonance.

Now here are two of your quotes:

Remember Galilean invariance - the kinetic energy cannot be constant in time in one inertial frame and not in another.

and

I’d say the major error of Jaaanosik is to believe that Galilean invariance demands kinetic energy to be constant in all frames if external forces are being applied. It doesn’t.

Well, which one is it?

 

[hecd2]

A work-energy principle consequence is that a kinetic energy change is done by a free force acting on a body. Free means it’s not a constraint force.

A constraint force is defined as being one which *constrains *the body to have zero velocity in the direction of the force. For the case of a body revolving on the end of a string, the body has non-zero velocity in the direction of the string (and the force) in inertial frames where the centre of the circle is moving in the plane of the circle. In such frames the string is not applying a constraint force as defined above and therefore it does work and changes the kinetic energy of the body in time. I have explained this already - in the moving inertial frame the force and velocity are not perpendicular, so their scalar product is non-zero and so the force provided by the string does work. Come on, this is elementary classical mechanics - what’s so difficult for you to understand?

The system has its natural frequency when v ~ r*w(omega).

As I have explained and as you have ignored, there is no natural frequency in this system because it is not an oscillator (lacking, as it does, a restoring force that is a monotonic function of displacement).

The system does not resonate when v << rw or v >> rw; the kinetic energy is almost constant in both reference frames when this is the case.

Not so. As the formula you yourself quoted (in eq 5n) the change in kinetic energy increases as a linear function of v - the higher the velocity of the reference frame with respect to the circle, the higher the amplitude of the kinetic energy cycle (the amplitude equals mvr*omega and so is proportional to v). Do you mean that the ratio between the amplitude of the energy cycle and the mean energy is highest for v=romega? Well, yes, but this isn’t a resonance because the system does not have a natural frequency because it doesn’t have an oscillator. You can drive the system at any arbitrary angular speed and view it from any arbitrary inertial frame - it’s behaviour does not depend in any way on v=romega. There is no physically detectable significance relating to that choice. There is no resonance.

In the ground frame the ball accelerates from 0 velocity at the bottom of the cycloid to 2v at the top of the cycloid and decelerating back to 0 in the case of the rigid body particle.
There is a[t] on the way up and -a[t] on the way down.
It’s more complicated with the ball on a string.

And this is caused, as I have shown you twice now, entirely by the force provided acting purely in the direction of the string (which is the only force in the system causing the only acceleration in the system as observers in all inertial frames will agree). This is really simple stuff - there is no mystery or any failure of basic classical mechanics here.

This is relativity.

When physicists talk about relativity without qualifying the term they mean special or general relativity. If we want to talk about Galilean relativity, then we say “Galilean relativity”. But I suppose you can’t be expected to know that. This discussion is exclusively about a classical and not a relativistic system.

Right, the kinetic energy change mathematical model used by physicists for the ground predicts the critical speed, the resonance.

There is no resonance.

No kinetic energy change mathematical model used by physicists in the moving frame fails to predict the critical speed and the resonance.

There is no critical speed and resonance - and the physics predictes exactly what we observe. There are not two models - there is only one.

Now here are two of your quotes:

Remember Galilean invariance - the kinetic energy cannot be constant in time in one inertial frame and not in another.

and

hecd2:

I’d say the major error of Jaaanosik is to believe that Galilean invariance demands kinetic energy to be constant in all frames if external forces are being applied.

It doesn’t

Well, which one is it?

They are both correct - you have taken the first one, where I was discussing a kinematically complete system without external forces, out of context.

So to be absolutely and pedantically clear: “Galilean invariance does **not **demand kinetic energy to be constant in all frames if *external *forces are being applied” and “Galilean invariance **does **demand kinetic energy to be constant in all frames if the system is kinematically complete and *no *external forces are being applied” Got it now?

 

[Jaaanosik]

A constraint force is defined as being one which *constrains *the body to have zero velocity in the direction of the force. For the case of a body revolving on the end of a string, the body has non-zero velocity in the direction of the string (and the force) in inertial frames where the centre of the circle is moving in the plane of the circle. In such frames the string is not applying a constraint force as defined above and therefore it does work and changes the kinetic energy of the body in time. I have explained this already - in the moving inertial frame the force and velocity are not perpendicular, so their scalar product is non-zero and so the force provided by the string does work. Come on, this is elementary classical mechanics - what’s so difficult for you to understand?
…

???
That’s my first figure.
In the moving frame (train wagon - the observer is inside moving along) the ball on the string is perpendicular to the velocity vector. It’s doing simple circle.
The body has 0 velocity in the direction of the string.
Your bolded quote is wrong.

I can not continue till this is agreed on.

 

[hecd2]

???
That’s my first figure.
In the moving frame (train wagon - the observer is inside moving along) the ball on the string is perpendicular to the velocity vector. It’s doing simple circle.
The body has 0 velocity in the direction of the string.
Your bolded quote is wrong.

I can not continue till this is agreed on.

When I say the moving frame I mean the one that is moving with respect to the centre of the circular motion. In this frame the force and velocity are not perpendicular etc.

 

[Jaaanosik]

When I say the moving frame I mean the one that is moving with respect to the centre of the circular motion. In this frame the force and velocity are not perpendicular etc.

You propose to call ground the moving frame?
I think this would be confusing to readers.
Can we stick to what I proposed in the beginning?

The rotation is observed from the two inertial reference frame systems: ground and a moving train at a constant velocity in a straight line.

 

[hecd2]

Whatever makes it easier for you to understand.

 

[Jaaanosik]

…
Not so. As the formula you yourself quoted (in eq 5n) the change in kinetic energy increases as a linear function of v - the higher the velocity of the reference frame with respect to the circle, the higher the amplitude of the kinetic energy cycle (the amplitude equals mvr*omega and so is proportional to v). Do you mean that the ratio between the amplitude of the energy cycle and the mean energy is highest for v=romega? Well, yes, but this isn’t a resonance because the system does not have a natural frequency because it doesn’t have an oscillator. You can drive the system at any arbitrary angular speed and view it from any arbitrary inertial frame - it’s behaviour does not depend in any way on v=romega. There is no physically detectable significance relating to that choice. There is no resonance.

When v<<rw then eq 5n is left with 1/2mr^2w^2
When v>>rw then eq 5n is left with 1/2m*v^2

That’s why I said the kinetic energy is almost constant in the ground frame as well.

 

[Jaaanosik]

Let us assume m=1, v=1, r=1, w=1, all equal 1
When v ~ rw (actually v=rw in this case) then eq 5n gives us:
at 0 the kinetic energy is 1/2(1 + 1 - 2) = 0
at pi the kinetic energy is 1/2(1 + 1 + 2) = 2

… and back to 0 at 2pi and back to 2 at 3pi, …

How does it happen? Do you still think there is no oscillation?

 

[Jaaanosik]

…“Galilean invariance does **not **demand kinetic energy to be constant in all frames if *external *forces are being applied” and “Galilean invariance **does **demand kinetic energy to be constant in all frames if the system is kinematically complete and *no *external forces are being applied” Got it now?

So when the train moves at a constant velocity what external forces are being applied?
There are no external force acting on the ground reference frame and there are no external forces acting on the train because it has a constant velocity.
From the beginning I specified two inertial reference frame systems so it’s clear the scenario is in line with the fact that the Galilean invariance does demand the kinetic energy to be constant.

 

[hecd2]

When v<<rw then eq 5n is left with 1/2mr^2w^2
When v>>rw then eq 5n is left with 1/2m*v^2

That’s why I said the kinetic energy is almost constant in the ground frame as well.

As I said before, I’m not sure this is the right forum for this discussion. As far as I can tell, no-one is reading this other than you and me, which, in effect, means that I’m giving you a personal physics tutorial. I’ll answer these most recent questions of yours, but I can’t continue to teach you physics via this forum.

As I said, as v increases so does the amplitude of the kinetic energy cycle The amplitude of the cycle for a given romega increases as a linear function of v. The bigger v, the bigger the amplitude of the kinetic energy cycle. However if you consider the amplitude of the kinetic energy cycle as a fraction of the mean kinetic energy it looks like this for romega=1:

rolling | Alec Mac&roo | Flickrfarm9.staticflickr.com/8601/16048514099_f3450f706a_n.jpg

where the x-axis is v and the y-axis is (amplitude of kinetic energy cycle)/(mean kinetic energy). As you can see this ratio is maximum for v=r*omega but this is **not **a resonance because this system does not have a harmonic oscillator.

Let us assume m=1, v=1, r=1, w=1, all equal 1
When v ~ rw (actually v=rw in this case) then eq 5n gives us:
at 0 the kinetic energy is 1/2(1 + 1 - 2) = 0
at pi the kinetic energy is 1/2(1 + 1 + 2) = 2

… and back to 0 at 2pi and back to 2 at 3pi, …

How does it happen? Do you still think there is no oscillation?

How many times do I have to repeat the same thing? The kinetic energy cycles because work is being done on the body in what you call the ground frame by the force of the string which is an external force. This force, acting in the direction of the string is not always perpendicular to the velocity of the body in this frame and so work is done which is the source of the varying energy. There are no other forces or accelerations other than in the direction of the string. (In the frame moving with the centre of revolution, the acceleration and velocity are always perpendicular, no work is done and so the kinetic energy remains constant).

Again, how many times do I have to repeat this - there is no natural frequency because there is no oscillator. An oscillator requires a restoring force which is a monotonic function of diplacement (like the force of gravity on a pendulum, or the tension in a spring). Another way of looking at it is that an oscillator requires energy to be exchanged between two forms of energy - in a mechanical oscillator between kinetic and potential energy for example which is also not occurring here.

So when the train moves at a constant velocity what external forces are being applied?

Applied to what? We don’t have a real train here - we just have something to visualise an inertial frame of reference. Unless you want to include an actual train in the kinematic system to which the other end of the string is attached. We can do that analysis if you want but it’s not the analysis represented by your maths. In that case you have to include the train in the energy calculations and you’ll have a kinematically complete system in which the kinetic energy is constant in all inertial frames (whatever energy is gained or lost by the revolving body is lost or gained by the train so that the total energy of the system remains constant - in all inertial frames.)

But at the moment the problem is set up so we are considering a massless infinitely stiff string being the means for revolving the body. You haven’t specified what is on the other end of the string (but you specify that it moves in an inertial frame). So the force provided by the string is an external force to the system under consideration and therefore the energy of the body as an isolated kinematically incomplete system can be constant in some inertial frames and vary in others.

There are no external force acting on the ground reference frame and there are no external forces acting on the train because it has a constant velocity.

If you are attaching the revolving mass to an actual train with a finite mass (as actual trains possess) then the train cannot be at rest in an inertial frame because the reactive force of the body revolving will cause the train’s velocity to vary in an inertial frame (in such a way that the total energy of the entire system - revolving body plus train - is constant in all inertial systems. So to summarise - if you include the train as a kinematic element of a complete system, there are no external forces and the energy of the complete system is constant in all inertial frames. If you consider the body only (as you have been doing in the maths etc) then this is not a kinematically complete system and the string is applying an external force to the system of the body. In this case, as we have seen, the kinetic energy of the revolving body on its own is constant in some inertial frames and not in others.

From the beginning I specified two inertial reference frame systems so it’s clear the scenario is in line with the fact that the Galilean invariance does demand the kinetic energy to be constant.

It doesn’t if there is an external force applied as in the scenario as described.

I recommend that you read my reply very carefully and think very hard about it. Try to forget you preconceptions (they are wrong) and don’t focus on arguments to prove me wong (I’m correct - I do this stuff as a profession). If you can think about this very carefully, accepting that you don’t understand the physics (you don’t, you really don’t), then it’s possible that you’ll learn some physics. Otherwise you are doomed to keep repeating the same elementary mistakes.

 

[Tomdstone]

As far as I can tell, no-one is reading this other than you and me,…

No. I have been following along.

 

[hecd2]

No. I have been following along.

Great. So we can continue our menage a trois for the moment.

So, feeling guilty about pursuing this topic in a philosophy forum, I wanted to make a couple of comments about the process we’ve been following (rather than focusing on the actual physics content of the discussion), which, hopefully, will be a little closer to the spirit of the forum.

So, what do we have here as a process? Jano began this particular meander of this thread by announcing that there is a simple way to explain flat rotation galactic curves (while disproving special and general relativity), without dark matter or any of this scalar-vector-tensor field malarkey; that there is an understanding of classical mechanics which solves the problem and which has been hiding here in plain sight if only physicists and astronomers were clever enough to see it. He is convinced from the outset that he is right (regardless of the fact that he clearly has no training in physics). He has not been striving to understand the standard physics, but to prove it wrong.

Basically his claim is that Newtonian mechanics is internally inconsistent, a quite remarkable claim given that it has been considered in excruciating detail by minds far better than any in this thread, not for years or decades but since the 1650s, and has been used to build the modern world and put probes on comets. So there is a stark contrast in humility between someone like Jano and a serious physics student. If the latter cannot reconcile some aspect of the physics, her first thought isn’t that the physics is inconsistent but that her understanding is flawed, and she works until she finds out where that flaw in her understanding is. This is a common, almost daily occurence for someone learning physics at the undergraduate or graduate level where the concepts and the mathematics are almost infinitely more difficult than the kindergarden stuff we’ve been dealing with in this thread.

And the relevance to philosophy? Well, we are all “folk philosophers” like we are all “folk physicists”. In the same way that some can confuse intuitive but fallacious understanding of physics for physics itself, we can also confuse intuitive and muddled thinking for philosophy itself. We think we have easily disproven some major philosophical argument, say Aquinas’s Five Ways, while having no proper understanding of the subtleties of the arguments and the meanings of the terms. I say this, because I’ve done it myself. We do have to rely to some extent on others in fields outside our own expertise, (or do the work to become expert ourselves).

(I note however that while there is no professional controversy regarding the internal consistency of Newtonian mechanics and its accuracy as a model of reality within certain well-defined limits, the professionals do disagree about the validity of the scholastic proofs for God).

 

[Jaaanosik]

Well, let us think about an experiment:
(Please Note: This uploaded content is no longer available.)

Steel balls B1 and B2 on steel rods aligned in a straight line that are attached to the axle via ‘frictionless’ bearings.
The well balance green disk with place holders is firmly attached to the axle. It rotates with it at constant angular velocity (uniform circular motion).
Balls, rods, disk, … everything well balanced; one rigid body system on a train that moves at a constant velocity.

We drop the place holders so each rod with its steel ball is free:
(Please Note: This uploaded content is no longer available.)

at this position:
(Please Note: This uploaded content is no longer available.)

The question - are the steel balls going to stay in a straight line - 180 degrees between the rods?

 

[hecd2]

Well, let us think about an experiment:http://theelectromagneticnatureofthings.com/img/i2/trinity03.png

The question - are the steel balls going to stay in a straight line - 180 degrees between the rods?

Well, first of all, I don’t see why you are introducing another scenario when you don’t understand the one we have already discussed. However, I’ll humour you for now.

The answer is easy - of course the balls will remain at 180 degrees as they are both rotating at the same angular speed.

By the way, you show an acceleration a[ct] in your diagram above which doesn’t exist. The only accelerations are in the direction of the lines joining B1 and B2 to A, which you have labelled a[cp]. As accelerations and forces are invariant under Galilean transformations all inertial observers will agree that this is so.

 

[Jaaanosik]

Well, first of all, I don’t see why you are introducing another scenario when you don’t understand the one we have already discussed. However, I’ll humour you for now.

The answer is easy - of course the balls will remain at 180 degrees as they are both rotating at the same angular speed.

By the way, you show an acceleration a[ct] in your diagram above which doesn’t exist. The only accelerations are the lines joining B1 and B2 to A, which you have labelled a[cp]. As accelerations and forces are invariant under Galilean transformations all inertial observers will agree that this is so.

So what you are saying is that there is no centrifugal force caused by inertia of the steel balls. Correct?
Wow. Good you are not my teacher.

 

[hecd2]

So what you are saying is that there is no centrifugal force caused by inertia of the steel balls. Correct?
Wow. Good you are not my teacher.

The centrifugal force is a fictitious force experienced only in the rotating frame so obviously irrelevant to the inertial frames. In these we observe the centripetal force which is a real force which causes the acceleration of the balls. I don’t know why you want to talk about the centrifugal force when we are supposed to be discussing Galilean relativity which is valid only in inertial frames. But anyway if we observe the balls from the rotating frame you will experience the centrifugal force which will be opposite to the real centripetal force and in line with B1/B2 to A. I repeat that a[ct] as you have drawn it doesn’t exist either in an inertial frame or indeed in the rotating frame. The only force observed in inertial frames is a[cp] which causes the actual acceleration observed from all inertial frames. But I proved this mathematically many posts ago. This is what I mean about the arrogance of crackpots.

 

[Jaaanosik]

The centrifugal force is a fictitious force experienced only in the rotating frame so obviously irrelevant to the inertial frames. In these we observe the centripetal force which is a real force which causes the acceleration of the balls. I don’t know why you want to talk about the centrifugal force when we are supposed to be discussing Galilean relativity which is valid only in inertial frames. But anyway if we observe the balls from the rotating frame you will experience the centrifugal force which will be opposite to the real centripetal force and in line with B1/B2 to A. I repeat that a[ct] as you have drawn it doesn’t exist either in an inertial frame or indeed in the rotating frame. The only force observed in inertial frames is a[cp] which causes the actual acceleration observed from all inertial frames. But I proved this mathematically many posts ago. This is what I mean about the arrogance of crackpots.

The reactive centrifugal force is opposite to the centripetal force causing curved path. It’s always 90 degrees to the velocity vector.
The centrifugal force can not be ignored when acceleration analysis is done in any inertial reference frame.