_{Get new ideas }_{and teach your teacher a thing or two}



All of the questions here (except Stumper Zero) are difficult for your teacher to answer, but some are difficult because a teacher has to go against the established norms. The stumpers are labeled as [easy], [intermediate], and [advanced]  but this is your difficulty. You will know the right answers after reading the stumpers but then you will also have fun in case the teacher gives you a wrong answer. Knowing the right answers and the reasons, you don't want to give your teacher an easy way out. 

tunes you to the obvious errors and it is also about you.. [easy] 

One 
is about light's ability or inability to exert pressure on a mirror. Without mass, light's wavelength (color) and energy are the same: what gives? [intermediate] 

Two 
introduces transformations when an electron starts to move [advanced] 

Three 
discusses experiments with light mill (radiometer) that lead to quantum mechanical explanation of gas pressure. Light mill rotates such that the dark sides recede from the light source. But mill's rotation can be reversed in your kitchen without modification  and that's our discovery [easy] 

Four 
is about a mechanism that changes chaos into order [intermediate] 

Five 
blows off general relativity [easy] 

Six 
asks
an easy question about Pi but the teacher is quickly surrounded and surrenders. 

Seven 
asks your teacher to multiply and square the simplest of equations. One time it works, another time it doesn't. This stumper will have him [or her] walking around in a daze, possibly for weeks [easy] 

At Portal (in new window), you will find all of our topics. 

Stumper Zero: 
Can you count beyond five? It is commonly accepted there are five human senses: Hearing, sight, touch, taste, and smell. I'm not sure about you but I can tell temperature, too. I can distinguish between freezing, icy cold, chilled, room temperature, tepid, lukewarm, warm, hot, steaming, and scalding. I can tell temperature through convection (air flow), conduction (direct contact), and radiation (sun's photons). Am I the only one who can tell temperature? The idea here is that you want to be alert. There are, in fact, six human senses. The guy who forgot to put temperature in the science book was sleeping at the switch, but it is every one of us who missed such an obvious thing. Teachers in particular are not very keen when it comes to pursuing the truth, so it just might be up to you. The next sense, of course, is the seventh sense. But that's whole another story  whole another kettle of fish. Sensing of a temperature relates to our body's ability to absorb (quantum mechanically it is the ability to reduce) photons of light inside our skin. The six human senses that we all share equally are: Hearing, sight, touch, taste, smell, and temperature. 

Stumper One: Physics 
Bouncy, bouncy but no pouncy  light is as light as .. Technically, it is called light's inertia. Scientists think that light (photons) can push a mirror when bouncing from it, but that's not the case. After all, if photons of light pounce as they bounce between parallel mirrors, the scientist could build the perpetual work machine, which scientists also claim is impossible. Photons, you realize, do not impart momentum to a mirror at reflection. Your job, then, is to prove scientists wrong and show that light carries no inertia and photons cannot push a mirror.
You may also ask about experiments measuring or confirming laser beam's (light's) pressure on a mirror. There are none because, you guessed it, light does not exert pressure on a mirror. While lightspeed was measured so many times nobody keeps count anymore, there is not a single experiment that would measure light's pressure (momentum) at a mirror surface. If today's laser packs a punch, it certainly could push a mirror. [Yeah,] Photon torpedos are science fiction but you want real answers that might turn out even better than fiction. Keep going on with facts. Light mill's rotation will cease in a vacuum (a fact). That is, the bulb the light mill spins in (using sunlight) is not completely evacuated but if it is, it will not spin. The claim that the light mill reverses rotation in complete vacuum is not a fact but a conjecture. Trying to reverse light mill's rotation in a vacuum is in the same category as trying to measure the pressure a laser imparts to a mirror at a bounce.
At this point you are well on your way if the teacher gets in a bind by stating "facts" without experimental backing — keep in mind equations are worthless without experimental confirmation. If you brush up on the relationship between light's momentum and its energy, you could be squeezing classical daylights out of your teacher. When cornered, the teacher might show his frustration by a public relations battle. Usually, however, the teacher will start talking about his or other scientists' credentials and you will be scoring big should this happen. In summary, classical interpretation of light bouncing off a mirror is in trouble regardless what teacher thinks happens. If light's wavelength does not change then the mirror cannot move. If the wavelength does change then the mirror cannot move by the amount classical equations indicate. Quantum mechanical approach to light finally prevails after, oh, eighty years. If you have a particularly troublesome teacher with lots of classical baggage and if this guy talks mightily about light's pressure on mirror and solar sailing and similar nonsense, you can restate the perpetuum mobile outcome from the classical perspective:
Depending on your attitude, you may add: "Can I quote you as saying that the perpetual motion machine is possible?" Sometimes a teacher will refer you to NASA or another "authority." Do not go for that. You do not have to accept that. You asked your teacher and you want answers from your teacher. Your teacher should lead by being responsible for answers without being told or without referring you to somebody else  unless they admit they know nothing on the subject. If you are researching something on your own and happen to come across an explanation on light's pressure in vacuum, you will notice that 1) There will be no author who actually measured the alleged behavior of light doing the pushing  that is, you are being told nonsense, even lies, by the so called scientists, and 2) there will be no motivation and no hurry to perform the experiment that would use the laser beam to measure the presence or absence of pressure on mirror because scientists cannot handle the nonexistent pressure intellectually. Scientists can heat up some fabric which then rises like a hot air baloon but they will stay away from a mirror because mirrors do not dissipate heat. 

NASA PhDs are telling you that light will push the white side of the mill's paddle (blade, vane) in a vacuum but it is just wishful thinking. The incoming energy of light has some fixed value and the presence or absence of the passive gas cannot make qualitative difference in the direction of rotation. The army of PhDs become silent if you want to talk to the one who actually did the reversal in a vacuum. The news is that NASA's PhDs think so highly of their equations they have no clue that photons have zero momentum at reflection. (Sometimes I think they are just plain lazy.) The good news is that you can do better. The better news is that you can do even better without the scientists. The best news is that scientists are clueless about the interaction of light and gas, and regardless of whether the global warming is real or not. 
I was once referred by NASA to a 1901 or 1905 experiment done by a Russian  no laser, of course. The author is dead and no one has replicated it, not even the Russians, with or without a laser. There are also references to Gordon F. Hull but his work is also prelaser from around 1948. Before the laser discovery, various contraptions were built with the claim that "something moved" when the light was shined on it. It is most interesting that since the laser appears in the 1960s, nobody wants to do the experiment and maybe talk about the match between the theory and the real pressure measurement, particularly since the laser is hundreds of thousands times more intense than Mr. Hull could muster with his flashlight. The motivation should be there because light's momentum is behind relativity theories that are supposed to be "it" for a hundred years now. Is this about the politics of science or are the scientists really so braindeficient they are afraid to do the experiment because they could not explain the result? Scientists think mostly with their left brain and, in a way, they are brain deficient. The left brain has no answers for scientists in the case of the light putting zero pressure on a mirror and the scientist just does not want to go there. There is this guy Richard Feynman who proposed a lightbouncing mechanism and made a lot of noise about it. His problem is, as it happens so many times with a classical view, that his theory works in one context but doesn't work in another. But of course, Feynman would not say anything about the circumstances where his theory just fizzles out because, well, some people would rather have a small following with a wrong theory than work toward the truth. You do not have to read up on his theory right now but if your teacher brings it up as his/her answer to this stumper then, well, you want to read up on it  along with its weakness  and revisit this stumper with your teacher. 

Stumper Three further down applies the absence of light's pressure to explain the light mill (radiometer) motion. The phenomena of light is not only complex, it is interesting and loaded with promise. There is a section about light that sums up light's articles on this site. For a photon's character and attributes take a look at the definition of a photon. 

Is there, then, a bottom line on light's zero momentum  that is, what does zero inertia mean? Light's momentum is a virtual momentum. Mathematically, we can also call light's momentum the imaginary momentum. Momentum does not just vanish and, even though we cannot measure it, the virtual (or imaginary) momentum is a great way of thinking about transformations. Light's momentum does not just disappear  it steps into the background. There is an analogy in genetics, too. It is the phenotype that is visible while the genotype is also there but does not manifest. Chinese 'above' and 'below' could also be applied here. [The alchemical 'above' and 'below' is about something else.] The idea is that you need to move beyond the strict scientific percept of "if I cannot measure it, it does not exist." To a physicist the virtual variable does not exist. They also miss a lot and are almost always wrong when they generalize. Yet, the virtual aspects are all around us and are useful as well. As you get more comfortable with light, you will be able to appreciate that light has no real mass and light also has no virtual mass. This is because during light's transformation (absorption), light's energy manifests as motion, electrical energy, or pressure but light's mass is not to be found. Light is pure energy that is always the virtual energy. Once light transforms into other forms of real energy via absorption the photon is gone while the real energy remains  for energy is always conserved, be it in the virtual or the real form.


Stumper Two: Physics 
A smudge of Schrödinger, a wing of de Broglie, an eye of Heisenberg, pudding of JJ, and a grain of von Neumann. And that's before we up the ante with one anti of Dirac. Fold, do not stir .. Another excellent stumper concerns the electron. Electron's wavelength is proportional to its velocity and a number of experiments confirms that. The good part is that the free electron's velocity is not relative to the frame of reference of the observer and thus the electron's wavelength is absolute. For example, the rotation of the apparatus measuring the electron wavelength should classically yield different values depending on the presumed addition or subtraction of the earth's speed  yet the instrument gives the same result regardless. An excellent example of an instrument that uses electrons' wavelength is the electron microscope. Indeed, this microscope functions just fine and regardless how it is rotated with respect to the earth's velocity. You will want to develop a line of questions and if you are good you can get the teacher to reach this counterintuitive conclusion while you are just one step ahead. (If you think there is a tiein between the absolute wavelength of the electron and the absolute velocity of light — you are on the right track.)
Each person mentioned above made a contribution toward the understanding of the electron. JJ is JJ Thomson with a hint from Aristotle's potentia. The difficulty is in tying, or integrating, the individual components together to make sense of the electron becoming the virtual electron and arriving at the electron's systemic behavior. (Systemic behavior is complete and does not have a dead end.) The best place to start is with electrons forming superposition (some say interference) going through a dual slit, as is treated in the July DSSP topic. A more thorough description is in QM primer that deals with electrons and photons. A complete treatment with additional illustrations is in the Quantum Pythagoreans book. 

Stumper Three: Physics 
Gas pressure is not about rogue molecules .. 'Chaotic' and 'random' are other labels you heard to describe the behavior of gas molecules and consequent gas pressure. Even mathematicians the likes of the Bernoulli brothers are brought into the act tossing billiard balls against the wall. Not to worry. Mathematicians know that if people agree on a concept, the equations will follow. So, you know better. You know that light (photons) have no mo (mirror cannot be moved with light) and so the momentum needs to be conserved by the gas molecule. The way it happens is that two atoms comprising the gas molecule are vibrating in place  they bounce outbound when they absorb a photon and they bounce inbound when they release (create) the photon. Volume and/or pressure increases when photons continue to be absorbed within molecules, yet the increase in volume and/or pressure happens in place for each and every molecule. In reverse, photons continue to be radiated when the surrounding temperature decreases and gas volume or pressure decreases. But of course, Brownian motion happens when very light objects such as pollen come into contact with the locally vibrating molecules. [Don't worry about Einstein, he's toast in more ways than one.] So, photons of light do create force and consequently momentum but only at absorption that, in turn, can happen only when momentum is conserved  and for that you need two atoms (two mass objects in general). Now, prove the new model ..
Classical modeling postulates that gas molecules bounce and collide with walls and that is what accounts for gas pressure. Classically, however, no collision is perfect (without loss) and so the gas molecules' bounce should peter out after a while and, consequently, gas pressure should tend to zero as time goes on. Your teacher's answer to this assertion should be interesting because the explanation is based on quantum mechanics and you can challenge other (classical) explanations  in fact, there is no classical explanation. You can always ask, "Why would new photons be required to keep gas at constant pressure?" Get ready to answer lame arguments such as "this is an ideal gas without friction," with, "how could heat be generated when gas is compressed?" You are in good shape because in the new model the gas compression releases photons and that accounts for heat. Particularly troublesome for your teacher is the textbook explanation of gas pressure where "heat from walls transfers to gas molecules which then bounce faster." Since heat photons have no real momentum, gas molecule cannot suddenly speed up because momentum would not be conserved. In other words, one cannot get a single atom moving no matter how much light the atom is subjected to. Quantum mechanically, gas molecules can convert virtual energy of light into real moving energy if atoms are close together or if they are in a form of a multiatom molecule. (All gas atoms form molecules with two atoms  Ampere's discovery.) Atomic separation is related to wavelengths of light that interact with a molecule. In general, atomatom separations in a molecule accounts for heat photon interactions while electroncore interactions account for visible photons. When a photon of light is absorbed between two atoms, atoms bounce apart and this allows the momentum to be conserved. (In general, momentum can be created only if it is conserved.) In reverse, the emission of a photon of light between two atoms is accompanied by atoms bouncing toward each other and this allows momentum to be conserved while pressure decreases. This is also the mechanism that moves the light mill's paddle, for expanding gas pushes the paddle and gas expands only at dark paddle (black) surface. Gas pressure  and gas heat conduction  is quantum mechanical and this hints at difficulties Maxwell had with explaining the light mill's counterclassical counterintuitive counterrotation. Another way of entering quantum mechanical aspects of gas pressure is by asking the question: "What is the mechanism that increases (decreases) gas temperature when gas is compressed (decompressed)?" Classically, it is okay for pressure to increase when volume decreases but the accompanying temperature increase has no classical mechanism when volume decreases. Quantum mechanically, however, bringing atoms closer together releases photons and the ensuing radiation accounts for increased heat. Physical compression literally squeezes photons from covalent electron orbitals  a quantum mechanical effect. A scientist  and this now includes your teacher  cannot explain why temperature decreases when the volume of gas is increased because classically the number of photons in the volume stays the same. Quantum mechanically, however, all individual molecules are absorbing photons from the neighborhood and the temperature decreases. Your best score will be if the teacher promises to come up with new equations. 

"Light mill is a toy as long as you don't try to explain how it works." Mike I As we get into the light mill rotation reversal, a bit of a background. The light mill (radiometer) was invented by William Crookes, a scientistpublisher who also had a hand in designing the first CRT tube, aka the TV set and the CRT computer terminal. Recently, CRTs were replaced by new, flat panel technologies, but Crookes invention is still going strong as the Xray tube (Roentgen has a valueadd here) and, of course, the neon lights. The basic difference is that CRTs use internally supplied electrons while the radiometer uses externally supplied photons of light. Radiometer is at times called the solar engine or the photon mill, and its theory of motion has undergone several revisions, including such finds as "edge effect," "photon shoots molecules," and "thermal transpiration" [a blend of perspiration and inspiration perhaps, but incorrect nonetheless.] The reason for so many revisions is because the classical view of light accepts light's (photon) pressure at reflection  all scientists erroneously assume that light is real. While light cannot push the mirror because light has no real momentum, this fact is being ignored as it calls for significant revisions of physics  opportunities notwithstanding. The following explanation of the mill's rotation and its reversal is based on the latest facts that photons of light have no inertia. If you are familiar with the old (NASA) explanations of light mill operation, you will see and understand that it is not possible to use NASAespoused theories in the explanation of the reversal of light mill's motion. 

{Added June, 2005} Reversing light mill's rotation is as easy as ..
As for the actual experiment that would measure the presumed pressure on a mirror (if it were to exist), take a look at theXperiment. 



Stumper Four: Math/Science 
The big one By far the best stumpers deal with issues the classical scientist would rather ignore and he may have no choice but to fight you rather than deal with your questions. Teachers are 99% classical because the issues have been regurgitated and committeeapproved so much the teacher thinks he is as safe as can be. Take a simple approach so that the teacher does not get upset. You start by arriving at the understanding of chaotic behavior with something like: "It is well established that three or more bodies that come close together and interact gravitationally (or magnetically) begin to move chaotically." If the teacher answers yes, you continue: "Since our solar system has more than three bodies, what is the mechanism that arranges and sizes these bodies to have organized and not chaotic movement?" Your victory is recorded if the teacher quits teaching dogma and commences the search of a solution to nonpolynomial problems. More likely the teacher will pretend to "not understand what you mean by chaos." Be patient. Both of you know the teacher is on thin ice. Once you agree on chaotic behavior, your followup question goes right into the heart of the limitation of classical science. If you know how to define chaos, you may ask the teacher to describe chaos and then field the followup question. A chaotic system is intractable  that is, there exists no mathematical relation (equation) that describes the movement of a chaotic body . Our solar system is [got] organized and the flatness (2D), the central large mass (sun) and the planetary separation are all needed with specific parameters (numbers) for bodies to be tractable. There is an article on three body instability on this site but, really, you need to start with ether  regardless of what your teacher is allowed to say about ether. 

Stumper Five: Physics/Science 
General nonsense There are many easy questions on how to stump your teacher regarding general relativity. Even a child can do that. This is not a play on words but, rather, it is the case of the simpleton logic general relativity is built from. You begin by a declaration of the socalled accelerationgravitation equivalence: "The fundamental postulate of general relativity is that acceleration is gravity." Teacher will answer yes. Your followup: "From where I am standing you are not accelerating. Are you, therefore, not subject to gravity?" I would love to see your teacher trying to redefine the word is — it's been tried before.    It may happen that the teacher comes back in a few days and starts talking about accelerating toward the center of the earth because the earth is rotating. He is now hopelessly confused and you, depending on your attitude, may say something similar to: "If the earth did not rotate or if you were at the pole you would not be accelerating in any way but my guess is that you would still be subject to the earth's gravity." or even better one is: "If acceleration is stronger at the equator then you should weigh more at the equator than at the pole." Enjoy. If you are shy about questioning your (credentialladen) teacher in this manner then you want to think about the investment you are putting into yourself. If you are not a good investment then you cannot invest for or with anybody else. Having said that, you do not want to spend too much time refuting nonsense.
There is a thorough and a bit more technical article disputing light's bending due to gravitation from a star.


Stumper Six, part one 
Oh, my Pi in your face 

Math 
In your apparently easy question you give the teacher the opportunity to say something about Pi. Because Pi is not as simple as it seems, chances are your teacher will become lost, confused, and possibly angry. You will need to know this topic well if you want to go all the way. You open with: "What is the definition of Pi?" or, "How do you determine Pi?" You wish your teacher to answer, "Pi is the circumference of a circle divided by its diameter." Chances are excellent this will happen because almost all books and Internet answers are just like that. The circumference of a circle divided by its diameter, or C/D, equals Pi. The trap is set. Your follow up: "I understand that Pi is an irrational number. How could Pi be defined (or described) as a ratio? C/D is a ratio, isn't it?" At this point the teacher will realize he or she is dealing with no ordinary question and possibly with no ordinary student. The teacher may say all kinds of things and you should feel free to end this at any time, for you have made your point well. But if the teacher gives you attitude, you are not done yet. If the teacher comes up with an equation such as C=2·Pi·R, you'll have plenty to say: "Pi, moreover, is a transcendental number and transcendental number cannot come from any equation. You just gave me the equation but Pi cannot come from any algebraic equation." Enjoy. Algebra weakness is at work here and you may also want to visit Circle and Pi on this topic. Pi combines incommensurability with two dimensions (circle exists in 2D) and on top of that the circle is curving and closes upon itself. Way too intense for algebra to handle. This path also leads to gravitation but it is a somewhat obscure path. Algebraic equations proving this or that are suspect and for that we have a page on math proofs. 

Stumper Six, part two 
Teacher walks the line 

Math 
In this version of a Pi stumper you will reveal the limitations of what math teachers call the number line. Teachers generally do what is prescribed and, well, somebody thought that the number line is a useful tool. It is not. You start innocently enough by: "Where does Pi fit on the number line?" Before you ask the question you should know that Pi cannot be put on the number line. You will not have a problem understanding why that is so. Pi has an infinite number of (nonrepeating) digits following the decimal point and so you and your teacher and everybody in your class could never agree on where the Pi should go on the line because no matter how many decimal digits you manage to have  there are always more digits. And because there is an infinity of them, you could never agree on where the Pi point is. The idea behind this stumper is that your teacher is in trouble from the get go. You see, the teacher has no guts (really, he or she has no backing from the school committee) to answer: "It cannot be done." So, the teacher has but two options: 1) Teacher is (over)confident and just puts a single dot or a tick mark somewhere between 3 and 4 and closer to 3.
2) Teacher will put a range on the number line and say: "Pi is between these two marks." For example, the teacher will make marks at 3.1 and 3.2
If you really want to drag your teacher through the mud you might add: "Incidentally, some irrational numbers cannot be put on the number line either." The idea here is that the irrational number also has an infinite number of decimal places  that is, infinite subunity, and so it is not possible to agree on the length of an irrational number. If you think of this in some depth you will discover that you can put some irrational points on the number line and get an irrational distance, but not the irrational length. This is the only yet important aspect of "a line"  really a 1D geometric construct  because diagonals of any and all squares can be lined up along a centerline (you will need to think about the Trough in the Great Pyramid and what waves got to do with it). The transcendental number that is Pi cannot be put on the number line even as a point because the distance of Pi cannot be geometrically or arithmetically obtained [directly]. Thinking about irrational numbers and their construction is a gateway to many interesting things. Surprise, numbers are not just for counting. [You may discover that the Bible as well as the Koran deal with numbers as counting numbers, for they associate numbers with particular things. Using numbers for counting is so rudimentary it misses the power of the numbers.] Enjoy your Pi.


Stumper Seven 
i  i  i (iy  iy  iy is what your teacher will say) 

Math 
Every math and science teacher knows that i stands for the square root of minus one. You know that, too, but you have this little equation and you need help from your teacher because you are getting some funny results. This stumper is easy to present and very difficult for the teacher to explain. You want to start with something familiar to get the teacher involved and so you will say: The reciprocal of minus one is minus one  that is, 1=1/1 and I was wondering if the same holds for i. So I set up the equation like this i = 1/i to see if I can prove that. You see, my dear teacher, [it's okay to be patronizing on this stumper] when I square both sides everything is fine  that is, i^{2} = 1^{2}/i^{2 }and that means 1 = 1 and so I thought I proved that .. But when I multiply both sides by i the result is different: i•i = 1•i/i and that means that 1 = 1



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