The Paradox Engine

[Tusk]

Please accept my apologies broli, I am not one to engage in brinksmanship or condescension but my attempts to fashion a 'watertight' explanation may camouflage what little of the social graces remain in this battered and rapidly aging skull. I am very happy to be discussing this with someone of an open mind who is able to maintain more than a passing interest. I can't promise lots of smiley faces but let me know if you interpret something as having negative undertones. When I refer to the difficulty experienced by anyone trying to grasp this material do not suppose that I am being 'high handed'; having spent the best part of three years struggling with it myself, I am well aware of how alien it must seem to others who are reading my poor interpretation in their spare time with little or no reason for confidence in the author. Indeed my chief concern is to place the thing in the hands of someone more capable than myself for whatever good may come of it.

So, 

Is your man, astronaut or alien attached to the main wheel/track, as is the case with your real word experiment, or does he have his own independent axis of rotation?

I hadn't intended that example to go beyond service as a brief illumination of the basic frame of reference manipulation. If it was a bucket of water we would both be drenched by this time. I may as well say that no, the man/astronaut is independent of the other elements in the experiment and must rotate himself at some small cost in effort; whereas the drive unit on the PE apparatus is (as you mentioned) mounted on the main rotor arm and therefore rotates with it at even lesser cost. And the primary reaction to any force applied to the disk by the drive unit goes back into the bench, since the line of force runs across the central axis which is bench mounted. There have been suggestions that this arrangement is only theoretical, and in practice is not fully realised; which is true enough, but in principle and within practical reason as much as any other machine is imperfect I think we can allow it.

Perhaps I can assume then (based on your replies) that you are 'up to speed' with both the secondary linear motion and also the general idea of frame of reference advantage - actually I'll call it frame of reference manipulation for now, since you may not allow there exists an advantage - at least insofar as the central position of the drive unit/man/astronaut changes things sufficiently to warrant further investigation.

In which case if I may forge ahead, and no doubt you will be aware of the following but I must state it for reasons of clarity; any body, be it static, in motion at a constant velocity or in motion and accelerating, is subject to an equilibrium of forces. When we read that the same force is applied to (e.g.) a bowling ball and a golf ball, this exposes the limitations of simplification in physics tutorials. The acceleration of the bowling ball will be far less than that of the golf ball, thus while the force might be measured as equal there is a point of force motion to consider, since there must be some finite period of time over which the force is applied. And the point of force motion in regards to the golf ball must accelerate at a greater rate, requiring additional energy. While there are certainly other ways to examine it, this may rightly be considered as a frame of reference issue.

When in the first instance our roundabout begins it's linear acceleration, we begin to have problems of the same ilk. Even if the roundabout were a flat disk and our applied force was constant and continuous due to the vigorous application of some hand held rotary tool, the man would still need to 'keep up' with the advancing cart. And we could rightly expect to take the measure of kinetic energy stored in both the rotation and linear motion of the apparatus at some point, and comparing it with the energy expended both in motivating the rotation and keeping pace with the linear motion against the reaction of that motivation there should be no discrepancy.

If I may swing past that one more time; ignoring the minutia whatever energy is expended keeping pace with the linear motion is manifest in the final kinetic energy of the linear motion of the roundabout/cart. And it is not inconceivable that by design this energy might be equal to the energy expended motivating the rotation.

Which might bring a sigh of relief to anyone rooting for UU (Under Unity), since it looked for a while there that we were getting two for the price of one. In reality we were putting two in and getting two out, the second input being the point of force motion.

But with apologies to the UU guys, our little frame of reference manipulation eliminates the point of force motion. Not the disk surface, which always had it's own advancing point of force motion issue, but the linear motion, now converted to circular with the point of application of force now static over the centre of the system. Yes the disk accelerates even more rapidly than before, so the point of force motion for the applied force on the disk itself is greater, but this comes with an increase in motion therefore no loss occurs.

So now we really are getting two for the price of one (ignoring the minutia, most of which can be mitigated in the engineering and design). And looking next to the PE apparatus, if we recover the energy stored in the motion of the rotor arm first so that it comes to a stop, when we then recover the energy stored in the rotation of the disk (from regenerative braking at the drive unit) our quirky little secondary linear motion reappears and the main rotor arm regains it's original motion - in the opposite direction - as the disk is brought to a stop. You can see this bonus feature in action on the PE device video hereunder (although I have no brake on the main rotor arm and must employ the phenomenon to halt the initial rotation; but it manifests well toward the end of the run):

http://www.youtube.com/watch?v=dG8YOp_njFs&feature=youtu.be

Three for the price of one 

[broli]

I agree that the accelerating part and regenerative breaking part of the EM drive should expend/give theoretically the same amount of energy, and if you then end up with any additional rotation you could start to consider it "free". However in both your experiments the inner wheel did have an initial rotational velocity. How can we rule out that this initial kinetic energy is not equal to the final one? Your inner wheel and rotating arm setup is not that complex to calculate its moment of inertia from there you can easily derive the kinetic energy based on final angular velocity. Imo this step is key if you want to do any meaningful energy comparisons.

[Tusk]

in both your experiments the inner wheel did have an initial rotational velocity. How can we rule out that this initial kinetic energy is not equal to the final one?

I assume here that you are referring to the two videos of the PE apparatus, due to a stalling effect at low rpm the disk must be hand started. It's not clear to me what point of logic you are employing in this instance; if I had corrected the stalling problem and started from a motionless state using the EM drive unit there could be no such question yet the apparatus would behave as before, unless you are suggesting that by hand starting the device I can somehow induce the reverse rotation at the end of the test? In which case may I suggest that you perform a simple build yourself, I found that a small disk mounted on an arm which in turn is mounted on a handle (both free to rotate) and counterbalanced, allows a 'hands on' experience which demonstrates readily the motions involved both in acceleration and deceleration of the disk.     

if you then end up with any additional rotation you could start to consider it "free"

Working backwards then I expect that the complimentary reverse rotational motion of the main rotor arm under drive unit braking of the disk might seem quite paradoxical. Just viewing the process at the fundamental level it soon becomes obvious that :

1. the total potential energy (or kinetic energy) of the apparatus (disk rotation + main rotor arm rotation) = the total input energy (less inefficiencies).

2. once the energy is recovered from these motions there should be no remaining energy; all motion should cease, not reverse.   

3. since the main rotor arm motion does indeed reverse in full measure (in comparison to the original motion) there can be only one conclusion.

Perhaps I should have made this point sooner, instead of attempting to hold back the tide of disbelief regarding both the secondary linear motion and the frame of reference advantage.

Your inner wheel and rotating arm setup is not that complex to calculate its moment of inertia from there you can easily derive the kinetic energy based on final angular velocity. Imo this step is key if you want to do any meaningful energy comparisons.

It would be significantly easier to run the numbers on a hypothetical apparatus, that way the design can incorporate features (i.e. mass distribution etc) more convenient for the purpose. The input force can be specified arbitrarily, with the secondary reactive force equal to it; the mass of the various elements is again arbitrary, although some value which might reasonably produce realistic values for the various motions might be in order. I think the disk should have a mass bias around the outer edge for best results, ideally all the mass around a single circumference of known radius would make things easier, and actually I would go for two identical disks and a weightless main rotor arm.

While this would represent an idealised apparatus, it would be a good starting point since any result in terms of output close to 100% would suggest no advantage. But if the equations allow a reversal of motion in the main rotor arm in full measure of the original motion then you will have some indication that the numbers are adding up correctly (since this is suggested by observation).

But I'll leave that for someone else. Previous experience presenting mathematical proofs indicates the need to employ another approach; nothing chokes off a thread like a page of equations. If this were a physics forum, maybe; although the typical physicist would likely lose interest at first sight of the abstract, which would appear foolish at best against the background of conventional wisdom, especially considering the simplicity of the concept.

[broli]

if I had corrected the stalling problem and started from a motionless state using the EM drive unit there could be no such question yet the apparatus would behave as before, unless you are suggesting that by hand starting the device I can somehow induce the reverse rotation at the end of the test?

These assumptions will make an armchair physicist have a field day.

I watched your video over and over, and yes from an empirical point of view, the nudge you gave it to start the acceleration due to the EM drive SEEMS negligible but details like that matter. At 0:29 particularly when the main wheel comes to rest in order to start spinning the other way is also significant, I can't tell how fast the inner wheel is spinning but it sure looks much faster than the starting condition which would already be a violation of conservation of angular momentum right there, and every other moment when the main wheel reverses, it just LOOKS like the inner wheel has way too much angular momentum than it started with.


So, and I believe I got it wrong again, to conclude everything what you are saying is you ended up with more angular momentum than you started with in a closed system?  The reason why I think I got it wrong is because you previously mentioned that CoM was not broken. So if angular momentum is conserved where does the final rotational energy come from?

And I'm actually quite eager to see how the math corroborates your result too. Integrals don't scare me, second order differential equations might do the trick though.

[Tusk]

Fair enough broli, I'll backtrack a little since I failed to emphasise an important point. From memory I mentioned the additional energy in the disk (I always refer to the two main components as the disk and the rotor arm btw) which manifests due to the inertia of the disk and (I suppose we could say) basic geometry:

I can't tell how fast the inner wheel is spinning but it sure looks much faster than the starting condition which would already be a violation of conservation of angular momentum right there, and every other moment when the main wheel reverses, it just LOOKS like the inner wheel has way too much angular momentum than it started with.


So, and I believe I got it wrong again, to conclude everything what you are saying is you ended up with more angular momentum than you started with in a closed system?

I can't recommend strongly enough that you construct a simple freewheeling apparatus; it really does assist in understanding the dynamics. I'll proceed as if you had one to hand, if not then perhaps you can imagine it, else sketch out a quick diagram.

Let's allow that from motionless, the rotor arm begins to accelerate by whatever means (we'll work in a clockwise direction for the rotor arm). Since the disk has inertia it will maintain it's orientation (notwithstanding friction, air resistance etc) so that one turn around on the rotor arm causes one rotation of the disk in an anticlockwise direction according to the frame of reference of the rotor arm (included in this frame of reference is the axis of the arm thus also the drive unit when dealing with the PE apparatus).

Back with the freewheeling model, in the observer's frame of reference the disk manifests no rotation. (notwithstanding friction, air resistance etc). But in the frame of reference of the rotor arm (thus the drive unit on the PE) the disk manifests rotational motion.

Note that this anticlockwise rotation serves to advance our efforts to rotate the disk (with the EM drive unit on the PE) since if the rotor arm is compelled to rotate clockwise (by the secondary linear force at the axis of the disk) then we must be driving the disk anticlockwise.

So here again an advantage; if you check the data from a typical experiment you will observe that the 'main rotor free' test uses significantly less power and achieves significantly higher RPM in an equal period.

http://img201.imageshack.us/img201/5488/paratach2.jpg

As we motivate the disk, the secondary motion of the rotor arm serves to advance the disk rotation in our favour, in the frame of reference of the drive unit.

I imagine if that were the sole advantage of the device it would be enough to attract investors. There are at least two strikes against this however; first and foremost I am not motivated by profit, and running a close second the concept goes so far beyond this simple phenomenon in advantage as to beggar belief.

There is no violation of CoM. This entire concept has it's roots in the manipulation of frames of reference. As such, kinetic energy (which is 'not invariant') seemingly 'pops out of nowhere', in truth I suspect with no actual violation of CoE (apparent but not actual). The frame of reference issue is known, but nobody has taken advantage of it before. So that when energy unexpectedly manifests, is it a violation of CoE if it does so due to a frame of reference manipulation?

Whatever the consensus, energy is gushing out of this device from the several holes it makes in convention. The decision you must make broli, is whether or not you are communicating with a person of sufficient intelligence and integrity to be trusted, since the concept itself seems initially quite incredible and even alien. You may very well be the first to actually grasp it (after my own faltering efforts).