Split Thread The validity of classical physics (split from: DWFTTW)

[humber]

Nor did I say they did. They simply show that you were - and are - completely wrong in your claims about the flow of rivers, just like everything else.

Gee, I don't know. Rivers have been studied for centuries. Do you think that modern papers may actually be about unusual rivers? Those that exhibit unusual behavior, such as permanent contraflows, eddies? I don't need to wikki, I know the general laws that govern flow. Recently, I read a paper on a metal laminate that distributes its current quite uniformly. Still, for a "normal" wire this is not true. Same for rivers.

That's going to be hard. Know why? Because it's so totally freaking obvious to everyone but an utter fool that no one every bothers to write it down.

It should be so easy, that you would have already done so.
It's going to be hard to find a reference that shows that objects in a river travel at the speed of the water. To avoid the air drag, we can make that at a submerged object.

Why don't you find something which claims they move slower?

Your claim. You made an appeal to my authority by asking if I have paddled a canoe. I say I have. I am no expert, I don't compete, but I that I know enough to deny your claim. The fuel consumption of my motorbike increases as I go faster downwind. Text books tell me that is so. Thermodynamics tells me that is so. Electrical, electromagnetic and acoustical analogues confirm that.

Air exerts drag if you're moving with respect to it. Water exerts drag if you're moving with respect to it. That's why something immersed in water moves at the speed of the water, absent another force. That's why something floating in air moves at the speed of the air, absent another force. It's so completely obvious I can't believe I even need to say it.

Not true even if the object is driven to waterspeed by an external source. It is impossible for an immersed object to reach waterspeed, if driven only by the water. Reference please.
What you are suggesting is that all objects blown by the wind, achieve windspeed. This is odd. The cart will simply do so, then? Why the treadmill to prove the inevitable?
If the air slows a floating object, why? Why do you assume that the drag between the object and the air is greater than the river can overcome?

 

[humber]

I called on my inner hummer to attempt an answer in Humber's (hopefully temporary) absence.



On the other hand I, for one, agree that in your cartoon model, the tube and the wind and the river could all move at precisely the same speed if we assume it was always thus (and also assuming there is no aircraft carrier coming up river at the same time).

Note Clive, it is not me. There is a particularly juvenile mind at work in these parodies. Ignore them.

Note to Huimmer/Humb/Humba/Humby/Humvee/Humster. You will bore yourself, and then stop.

 

[jjcote]

Back to the rubber surface in the foggy dark, if that's acceptable, then is it okay if the fog lifts somewhat and we see that the rubber surface has been laid down on the deck of an aircraft carrier? It's still foggy, so we can't see down to the water or the drydock or whatever, but we still feel the 10 m/s breeze. Is that okay for testing a cart that purportedly goes DDWFTTW, or do you now need to see more of the surroundings?

Haven't we done this? But, OK.

Great. Now, are the following two situations also acceptable for testing?
1) The fog clears some more, we see that the aircraft carrier is not moving through the water, and the wind is blowing across the deck (and across the water, causing ripples/whitecaps)
2) The fog clears some more, we see that the aircraft carrier is actually moving through the water at 10 m/s, and there are no wind effects evident on the glassy-smooth water (no ripples or whitecaps)

 

[sol invictus]

Gee, I don't know. Rivers have been studied for centuries. Do you think that modern papers may actually be about unusual rivers?

Had you read the paper as you said you had, you'd know what they were looking at and why they were studying it. So you lied, again.

There was nothing unusual about it.

Not true even if the object is driven to waterspeed by an external source. It is impossible for an immersed object to reach waterspeed, if driven only by the water. Reference please.

Your claim is the one that goes against the last 400 years of research, not to mention common sense. The burden of proof is on you, and you've failed utterly.

 

[humber]

Humber, if you are serious about trying to resolve the ongoing differences of opinions, then I think there really has to be some "back-to-basics" discussion (from both sides). I say this because it seems pretty clear that often a lot of people don't understand what you are trying to say, and perhaps the opposite is true also. You may already understand everything I'm about to say, but in the interests of trying to establish and confirm some level of common understanding let me now spell out how I see it.

My understanding of a frame of reference is NOT (in the strictest sense) a physical object but rather an imaginary but well defined coordinate system (including a clock). In that "frame" we use those coordinates and that clock to determine position, velocity, and so on. An inertial frame of reference is a frame of reference that isn't accelerating (and that includes not rotating).

Good, I can get over the obstacle of the hanging post. Thanks for the effort and patience, by the way. Sometimes its easier to make short posts on the spot, but yours demanded more attention.

Yes, I agree. Some may equivocate, but for the purposes of Newtonian objects, that definition is certainly good enough.

In other words, an object that is not subject to a net force is seen to have a constant velocity in an inertial frame of reference. When an inertial frame is used with Newtonian mechanics (which I believe most or all of us agree is essentially all that is required to discuss the cart going downwind to a reasonable degree of accuracy), we are using a single frame of reference at a time and using that for all the measurements of position and time and other derived values such as velocity and acceleration.

Yes!

We can optionally also use other frames of reference but if we do that we can't always directly compare values from one frame to another in any generally sensible way, and we therefore need be careful to specify which frame is being used if there is any chance of confusion. Finally, with Newtonian mechanics as our basis, all clocks are assumed to run at the same rate regardless of the frame of reference being used.

Yes, again. Indeed, taking a new frame is to take another perspective. All links to the other objects, considered or not, remain in place. Force, energy friction, remain the same. There is symmetry between frames. Time is invariant in our case.

So, using this general approach, we choose a suitable (hopefully also convenient) frame of reference, make the appropriate measurements and then use Newton's laws and so on (via mathematical calculations) to predict what will happen in certain circumstances and so on.

Yes, a common practice of convenience. I have said that equivalency is just a reiteration of Newton's laws. Rather, it confirms that Newtons laws do not change with perspective, or from where you take the measurements.

Yes, strictly speaking there are possibly no true inertial frames of reference, but once again we can hopefully agree that things like the curvature of the earths surface, it's rotation and so on, are not likely to be significant issues when it comes to predicting the cart's performance.

Where do we disagree? I have said that, too. The effects are small, or common to all objects under consideration.
To say that the ground is a reference is considered to heresy, but of course equivalency allows that.
It does not mean that is is "absolute" (though that is not so easily dismissed for acceleration), but a datum. If I have a GPS, I can set my home co-ordinates to (0,0), and take relative measurements from there without insisting that my house is the center of the Universe, or that everyone else must do so.

We all understand that in the real world things are often more complicated than in some simplified model that we may choose to use. This, plus other similar factors, all combine to mean that the predicted results from the formulas are almost certainly not an *exact* representation of "reality". But if reasonable assumptions are made to start with, then we expect the discrepancies to be relatively small, and so the predictions to still be "useful".

Yes. These are limits of the model or measurement. The modeler rarely has the freedom to reproduce everything, so simplification removes the superfluous, or leaves an approximation that is deemed to be useful, even if not 100% accurate.

Given all this, we can choose the origin of our frame of reference to be moving at the same speed and in the same direction as the top surface of the treadmill belt.

Yes, but now we are about to disagree.

In that case it is quite easy to verify that we will measure the various speeds and so on as being identical to what we would measure if the cart was in fact rolling along the ground at windspeed (in a "real wind") and the frame of reference used was instead at rest relative to the ground (and was also aligned in the appropriate way). In this way those two frames of reference produce exactly the same measurements and therefore generate the same predictions.

No. The treadmill "works" only for one specific case; windspeed. Even then, it is wrong. It fails quite obviously for all intermediate values.
Treadmill wind, is not like real wind. I have an idea how I can show that.

We can also choose our frame of reference to be at rest relative to the body of the treadmill. Note the treadmill itself is not actually *the* frame of reference.

That is consistent with your views, and mine. I can accept that the treadmill observer is traveling at windspeed. It can be notional or literal. However, the results must be in accordance with my ground side, (or any other) view. That is, I no longer take the windspeed view, but that of someone on the ground. The treadmill is not consistent in this respect.

When someone refers to the treadmill as a frame of reference (or similar) to me that's a kind of shorthand for a notional coordinate system that is at rest when compared to the body of the treadmill and aligned in some sensible and agreed fashion.

I say its a model, but I can accept that interpretation too. It is not actually important to my criticism of the treadmill. I think that it is impossible to create a frame of reference for something that is moving wrt the ground, freeze it at standstill, yet claim it is the same. The dynamic properties of the object are missing, but let's say that is an acceptable simplification.
The real question is whether treadmill wind is like a real wind. No it is not.
It is a conclusion that must be made to support the assumed position that widspeed travel is possible. There is definitely a difference, it is significant, and falsifies the claim.

This will in fact produce the same values for velocity and so on as a frame of reference that is moving at the same speed as the "real wind" for a case where the cart is rolling over the ground instead of on a treadmill.

Same velocities perhaps, but the work is wrong, at the very least.
Try an object that moves at 10% windspeed, then the same at 20% and so forth. Something odd happens.

In any of these (close enough to "inertial") frames of reference , we can then do the various calculations of velocity and kinetic energy and momentum, etc., etc. and we "know" that the results of that will be correct, at least in the same sense that we believe "Newtonian mechanics" to be correct.

If the model or frame is accurate enough, yes.

Now, my training in physics is not much beyond high school level, so perhaps I've not been 100% clear or accurate in what I've said above, but hopefully I'm at least "close", and I'll invite others to make appropriate corrections if they believe I've made important errors or omissions.

More than enough, Clive.

Questions:
1. What exactly do you see as being wrong or invalid with this approach? Where does the "nonsense" creep in?

I must go right now. I was working on a reply to your previous post yesterday when on the train. (Avoiding looking out of the window, of course)
I still have the same problem. If I work through it, I reach the same conclusion as all of the other similar experiments, just more convoluted. The models that you cite are also not the problem. The "quibbles" are not about details, or permissible but imaginary devices. I appreciate the effort that you expended to make the details clear, but I still see that it is not like the treadmill, or if I take another view, like it, but similarly flawed. If I answer it as I intended, I see that we would indeed be "back to basics".

I have a thought experiment that I hope will convince you. Later today.

2. If your approach is different (and it certainly seems to be) please spell it out as clearly and concisely as you can, treating me as a rank beginner (which is all I really am) so that there is minimal chance of misunderstandings.

No, they are the same. There is nothing complex. They ideas are that every rational scientist or engineer will tell you, and yours seem quite solid to me. That is why there is no academic support for the treadmill.

(Please ignore any other posts from parasitic namesakes)

 

[humb]

The earth's gravity will keep the submerged object from moving at the speed of the water. As long as it is in the earth's gravitational field, it will be pulled not only down, but also back from whatever other direction it would go. The vector tilts in the appropriate direction relative to the True Frame in order to support the truths that humber and I know. If it were moving at "riverspeed", there would be no force to create your purported "KE = O". Your assertions otherwise are unsupported. Show me an academic or paper that refutes us. You cannot.

This is easily demonstrated. I could construct an apparatus from popsicle sticks, chewing gum, and tinfoil that would suffice and settle this once and for all. I will not, however, as there is no need, and I cannot spare any tinfoil. I need it all for my hat.

 

[humber]

Had you read the paper as you said you had, you'd know what they were looking at and why they were studying it. So you lied, again. There was nothing unusual about it.

I already told you I scanned it. Your claim of deception is denied. You are not familiar enough with the topic to extract the paper's purpose. That is your failure.
You also extended your claim to ignore specific effects or did you "forget".
Quote Sol_invictus:-

"But consider a wide river in a smooth, channel, in which case the velocity gradient tends to zero and we can treat the river as if all the water were moving the same speed. Then (neglecting air resistance) the boat will move at exactly the speed of the water unless someone starts to paddle"

Your claim is the one that goes against the last 400 years of research, not to mention common sense. The burden of proof is on you, and you've failed utterly.

Woah, an appeal to common sense! Folk physics again.
If there are 400 years of evidence, you can find it. Otherwise, readers may assume you are ignorant if it. You have a long history of Wikki finger, but now it deserts you. That inconsistency is telling.
You recently posted to tsig with no other purpose than to say that you knew a lot about physics. You are either ignorant, or avoiding the answer. Your choice.

 

[humber]

<snip>

Your language gives you away. You will tire, and need to back to your pram.

 

[John Freestone]

Do items flowing in a river reach riverspeed? Why not? If you have a power boat, don't you need constant force and energy to maintain riverspeed?

If you were ignoring other drag forces like the air, and considering the river as moving at a single velocity, the obvious answer is yes they do reach river speed. An object immersed in a fluid flow will be accelerated if there is a difference between its starting velocity and that of the fluid, and in the direction of the fluid flow. While there is a difference, there will remain a force to accelerate it further, so at steady state (or, given a sufficient length of time to accelerate) it will reach the same velocity.

It is difficult to find papers that tell us this, it's true, but I've only just started googling and have found a few. I agree that it is one of those facts that is so obvious that it isn't often written about. To be fair, though, maybe we should see how many we can find supporing each position.

Or if you prefer, just tell me what forces apply to an object submerged in a fluid that keeps it moving at below the speed of the fluid. Clearly (he says, optimistically), if there is a speed difference, there will be drag (actually of two types, but they will both act to accelerate the object towards fluid speed), so what force balances this to maintain lower than fluid velocity?

Of course, if you introduce different fluids (like the air), different flows within the river, etc., you can get different object speeds, but that wasn't the original point, IIRC. All this came about from you saying that the skater with a parachute would experience maximum force from the air at top speed, I think. Why can't you ever just say you got something wrong, humber? This paper also confirms that the force of drag will increase with the difference in velocities.
http://hypertextbook.com/physics/matter/drag/

Drag increases with speed (v). I hope that this is self-evident. An object that is stationary with respect to the fluid will certainly not experience any drag force. Start moving and a resistive force will arise. Get moving faster and surely the resistive force will be greater.

Shall we call that one-nil?

 

[Modified]

No. The treadmill "works" only for one specific case; windspeed.

That is incorrect. Physics computations for a vehicle traveling on the treadmill will be equivalent to those for the vehicle traveling on the ground in a constant wind, for any vehicle speed. There is nothing special about a vehicle traveling at wind speed on the belt, except that it will stay on the belt indefinitely.

 

[sol invictus]

Woah, an appeal to common sense! Folk physics again.
If there are 400 years of evidence, you can find it. Otherwise, readers may assume you are ignorant if it. You have a long history of Wikki finger, but now it deserts you. That inconsistency is telling.
You recently posted to tsig with no other purpose than to say that you knew a lot about physics. You are either ignorant, or avoiding the answer. Your choice.

Very well: http://en.wikipedia.org/wiki/Drag_equation

The drag force is proportional to u², where "u is the velocity of the object relative to the fluid" (my bold). Therefore, according to Newton's 2nd law F=ma (heard of it?), any object moving at a non-zero velocity relative to the fluid will experience a drag force that reduces its velocity. The only solution where the velocity is constant (F=0) is u=0 - zero velocity with respect to the fluid.

This is all totally obvious - it requires no training in physics at all to understand.

 

[mender]

Yes, but now we are about to disagree.


No. The treadmill "works" only for one specific case; windspeed. Even then, it is wrong. It fails quite obviously for all intermediate values.
Treadmill wind, is not like real wind. I have an idea how I can show that.

I have a thought experiment that I hope will convince you. Later today.

I for one am looking forward to this explanation or thought experiment. I suspect that it will lapse back into the KE argument. If so, it will once again collapse under its own weighty mass of contradictions.

The treadmill test does only show what is happening when the cart is at windspeed. It shows that the cart will attain windspeed and if the treadmill were any longer, would show that the cart will accelerate above windspeed, which it is clearly trying to do but has to be restrained to keep it on the treadmill.

During one test, the cart is pushed back with a spork to below windspeed (slower than the treadmill surface). The whine of the propeller changes pitch exactly as expected, i.e., the pitch drops as the cart moves slower w.r.t. the treadmill surface, and as the cart accelerates to and briefly above windspeed as witnessed by the groundside observer (who is also at rest w.r.t. to the air in the room, therefore at windspeed), the whine increases in pitch in direct relationship with the speed attained.

But now I'm arguing the physical results, not the ethereal thought experiment. Let's hear your explanation so we can see whether it maintains your position or catapults you into the humberest category.

 

[humber]

Very well: http://en.wikipedia.org/wiki/Drag_equation
The drag force is proportional to u², where "u is the velocity of the object relative to the fluid" (my bold). Therefore, according to Newton's 2nd law F=ma (heard of it?), any object moving at a non-zero velocity relative to the fluid will experience a drag force that reduces its velocity. The only solution where the velocity is constant (F=0) is u=0 - zero velocity with respect to the fluid.

This is all totally obvious - it requires no training in physics at all to understand.

I told you I understood the theory, and that like your Wikki, tells me that your claim is impossible.

I would like to see some empirical evidence that supports your claim. "Commonsense" must mean that it is a common occurrence, no?

You have a spurious result gained by ignoring the impossibility of the intermediate values that must precede it. The object gains energy as some of the water's momentum is transferred to it. In the process of acceleration, that is, closing the velocity gap between the object and the flowing water, the object must in return some of that energy to the water. A balance between these processes results in a terminal velocity of less than the water. It is obvious. If for example, the amount of force driving object is simply linear with velocity, it will loose the battle against the drag, which is related to at least V^2.

From the same Wikki;
"The equation is based on an idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area. No real object exactly corresponds to this behavior."

"Of particular importance is the u2 dependence on velocity, meaning that fluid drag increases with the square of velocity. When velocity is doubled, for example, not only does the fluid strike with twice the velocity, but twice the mass of fluid strikes per second. Therefore the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid friction, which generally has very little velocity dependence."

I don't believe that you think otherwise.

 

[humber]

That is incorrect. Physics computations for a vehicle traveling on the treadmill will be equivalent to those for the vehicle traveling on the ground in a constant wind, for any vehicle speed. There is nothing special about a vehicle traveling at wind speed on the belt, except that it will stay on the belt indefinitely.

That is not correct, Modified. If you start with the cart going back with the belt and accelerate it towards 'windspeed', it actually loses KE in the process. Also, if you take my parachute/skate example and make it less than ideal, let's say it only gets to 25% of real the wind's velocity, the same device on the treadmill will get to windspeed. Almost anything will.

As to where the KE goes, that is explicable. Assuming that the treadmill is a good model, the KE of the cart wrt windspeed is said to be zero. So where is it?
It must be with the moving object, the belt. I can confirm this, because my (equally valid) ground side view, says that the cart also has zero KE wrt the ground. So, there are two frames giving the same result.
The conclusion is that the KE is in the belt, but not the cart, or there is no KE related to 'windspeed' in either case.

 

[jjcote]

In river of uniform flow, given two objects of the same mass immersed in the water, which will have a terminal velocity closer to the velocity of the stream, one that has a very streamlined shape, or one that has a very draggy shape?

 

[Subduction Zone]

That is not correct, Modified. If you start with the cart going back with the belt and accelerate it towards 'windspeed', it actually loses KE in the process. Also, if you take my parachute/skate example and make it less than ideal, let's say it only gets to 25% of real the wind's velocity, the same device on the treadmill will get to windspeed. Almost anything will.

As to where the KE goes, that is explicable. Assuming that the treadmill is a good model, the KE of the cart wrt windspeed is said to be zero. So where is it?
It must be with the moving object, the belt. I can confirm this, because my (equally valid) ground side view, says that the cart also has zero KE wrt the ground. So, there are two frames giving the same result.
The conclusion is that the KE is in the belt, but not the cart, or there is no KE related to 'windspeed' in either case.

Well there's your problem. You still do not understand that KE is relative. If the cart is not moving relative to the moving belt then its KE with respect to the belt is zero, even though its KE with respect to the ground is nonzero. When the cart is going windspeed on the belt its KE with respect to the ground is zero, but definitely nonzero with respect to the belt. KE is always relative, velocities must be measured with respect to something. If you are going to try to insist that the ground is the reference frame that velocities must be measured against because it is much more massive than the treadmill, then I insist that you must measure velocities with respect to the universe as a whole since it outweighs the Earth by a bigger factor than the Earth outweighs the treadmill.

 

[Modified]

That is not correct, Modified. If you start with the cart going back with the belt and accelerate it towards 'windspeed', it actually loses KE in the process.

In relation to the surface, it gains KE, just as for the cart on the ground. In relation to the air, it loses KE, just as on the ground.

Also, if you take my parachute/skate example and make it less than ideal, let's say it only gets to 25% of real the wind's velocity, the same device on the treadmill will get to windspeed. Almost anything will.

If that is true on the ground, then the same thing will happen on the belt.

As to where the KE goes, that is explicable. Assuming that the treadmill is a good model, the KE of the cart wrt windspeed is said to be zero. So where is it? It must be with the moving object, the belt.

You are still not getting that KE is relative. Just replace "KE" with "speed" in any of your examples and see if they make sense. KE is not "with" anything, just as velocity is not "with" anything.

I can confirm this, because my (equally valid) ground side view, says that the cart also has zero KE wrt the ground. So, there are two frames giving the same result.

Those are the same frame. You still don't seem to understand what a frame of reference is. For the treadmill case, the air, room, and ground are all moving at the same speed.

The conclusion is that the KE is in the belt, but not the cart, or there is no KE related to 'windspeed' in either case.

Again, KE is not "in" anything, any more than speed is.

 

[humber]

I for one am looking forward to this explanation or thought experiment. I suspect that it will lapse back into the KE argument. If so, it will once again collapse under its own weighty mass of contradictions.

You are partially right, but you think KE is unimportant? That is not the my entire argument though.

The treadmill test does only show what is happening when the cart is at windspeed. It shows that the cart will attain windspeed and if the treadmill were any longer, would show that the cart will accelerate above windspeed, which it is clearly trying to do but has to be restrained to keep it on the treadmill.
During one test, the cart is pushed back with a spork to below windspeed (slower than the treadmill surface). The whine of the propeller changes pitch exactly as expected, i.e., the pitch drops as the cart moves slower w.r.t. the treadmill surface, and as the cart accelerates to and briefly above windspeed as witnessed by the groundside observer (who is also at rest w.r.t. to the air in the room, therefore at windspeed), the whine increases in pitch in direct relationship with the speed attained.

But now I'm arguing the physical results, not the ethereal thought experiment. Let's hear your explanation so we can see whether it maintains your position or catapults you into the humberest category.

Good, that breaks the chain. The result is real, so my ground view is also valid ( it always was).
You must agree that going back with the belt is equivalent to a standstill in real wind. A small battery-powered car on the belt, it would first need to achieve beltspeed to get to zero wrt the ground, and then again, to get to windspeed wrt the ground. This is because the belt is an image.

Even if I allow 'treadmill windspeed' to be the same as the real thing, the videos show that it is going to take a very long time to get there, should it start from back with the belt.
Also, it would seem that even a small obstacle would stall it. The motion is not appropriately dynamic, but slew limited.
The "whine" is hardly evidence. Yes, it slows, it would do that if it works as I say. My balance model predicts that.

I have independent supporting evidence that the cart is where it is because of low friction to the belt. I will include that.

 

[spacediver]

No, Spacediver. This is NOT the point. I have repeatedly said that. KE = O is a mathematical possibility, but has no meaning. You do the calculations. How can you actually DO ANYTHING, without moving one object out of its frame?
To maintain zero KE, the objects can never change, collide, accelerate or change direction. Were are your KE's for all the other infinite number of directions that the objects could move?
Your calculations work only for objects that are in exactly the same "frame", and only those you see. If there is another object, but 100km away from the above two, are they in the same "frame" and also have zero KE? If that object is stopped, do the others know about it? Any influence at all?
Your zero KE objects, have to have the same speed, same direction, for all time. Cartoon world.
If you still disagree, then please tell me how that relates to the treadmill, other than to tell me again that the cart has zero KE. How does that influence the cart and treadmill?

I asked you to forget about treadmills. Did you not read my post carefully? I just want you to examine the scenario i provided and answer the questions.

Pretend it's a high school physics exam and you have to answer those three questions.

Forget about the rest of the thread for now. I never said any of the objects had zero KE, I only provided their mass and velocities. I asked YOU to provide me with the kinetic energy value.

If you do not do this, then I'll have confirmed my suspicion that you are not able or willing to read and think carefully.

 

[humber]

In relation to the surface, it gains KE, just as for the cart on the ground. In relation to the air, it loses KE, just as on the ground.

The road is the ground if the treadmill observer is said to be at windspeed. The cart has zero KE from the view of the cart and winspeed observer.

An ground observer, viewing the cart 'as is' also finds zero KE. If the treadmill cart is said to be a cart at windspeed, it must have KE from some frame. So which frame remains? Only the belt.

However, three observers already say zero KE, so to reconcile all views, the KE must be in the belt, but not the cart.
For example, the only conclusion acceptable to the ground observer is that all of the KE must be in the belt. One other possibility remains. There is no KE relative to the belt, either. This is indeed the case, and I can show that.

If that is true on the ground, then the same thing will happen on the belt.
You are still not getting that KE is relative. Just replace "KE" with "speed" in any of your examples and see if they make sense. KE is not "with" anything, just as velocity is not "with" anything.

No, I get it, but KE is real in some frame for any object in motion, or it is not moving at all.
KE is energy, it cannot be destroyed. KE is not speed. Speed is the result of the object gaining KE as it is accelerated. Acceleration is absolute for our purposes.

Those are the same frame. You still don't seem to understand what a frame of reference is. For the treadmill case, the air, room, and ground are all moving at the same speed. Again, KE is not "in" anything, any more than speed is.

Yes, that is correct. I can be on the belt, on the ground, in the cart, or a windspeed observer. All views must produce the same result. That is a fact.

The cart is balancing. I cannot convince you of that, but I do have a supporting example I found a few days ago. I will scan that and post it.