Lec 9
Questioning over a large span of time.
“He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever.” Chinese Proverb
“The wise man doesn't give the right answers, he poses the right questions.” Claude Levi-Strauss, French anthropologist (1908-2009).
“What we observe is not nature itself, but nature exposed to our method of questioning.” Werner Heisenberg
“We run this company on questions, not answers.” Eric Schmidt CEO of Google
Links for this lecture:
http://ieeexplore.ieee.org/document/1074413/?reload=true
http://physics.weber.edu/schroeder/software/HarmonicOscillator.html
http://iopscience.iop.org/article/10.1088/0022-3735/14/8/029/meta
http://home.sandiego.edu/~ekim/e171f00/lectures/phasors.pdf
https://www.youtube.com/watch?v=VA9rcaGET2w
https://www.youtube.com/watch?v=lWi_KpBy8kU
https://www.youtube.com/watch?v=sfcMnVpsYlo
Lecture overview for today: We will focus on the cart velocity lab and complete a worksheet on questioning. The topics include asking incongruous questions for a particle in a well and waves. Then we consider a way to measure the velocity of small particles. Answers to this worksheet are discussed after the worksheet is completed.
Lab overview for today: In the lab you will explain the lab you did and start the last of the round robin labs.
Cart velocity extended content: measuring g and the velocity of particulates. Testing models?
Measuring g: look at the abstract. What’s the paper about?
-show paper on measuring g related to the doppler expt. Note how well the title describes the work. Emphasize the working eqn and lack of derivations. Note that there is no reference to this equation. I would reject the paper without a derivation. Is the author trying to impress you by making this working equation look trivial? There are many people like that. Notice the simple statistics used. No chi squared. Note that the signal to noise ratio is proportional to Sqrt[N] where N is the number of photons per second.
http://ieeexplore.ieee.org/document/1074413/?reload=true
Measuring the velocity of particulates:
Note how well the title describes the work. From the abstract determine what the paper is about. It is about testing the model with turbulent air flow. This paper illustrates citing the results from the model rather than deriving them. This corresponds to the Critical Thinking skill “how to tell if a source is reliable.”
-Causal creative question: How could you measure the speed of small particle? A He-Ne beam has 10^14 photons/s so small scattering probability still yields a large number of photons/s. https://www.youtube.com/watch?v=sfcMnVpsYlo
Measure the Doppler shift of the scattered wave. If two He-Ne beams illuminate the particle from different directions then there will be two Doppler shifted waves with different frequencies. These will interfere wit a time dependent fringe pattern. This method of calculation yields the same answer as thinking of the crossed laser beams generating an interference “lines” through which the particle moves. When it moves through a dark fringe no light is scattered but moving through a bright fringe yields scattered light. Use Moire pattern to illustrate interference https://en.wikipedia.org/wiki/Moir%C3%A9_pattern
Paper on Doppler velocimeter. Note the similarity to the Doppler lab expt.
http://iopscience.iop.org/article/10.1088/0022-3735/14/8/029/meta
Critical Thinking skill “how to spot an assumption” is related to assuming turbulence effects the determination of particle speed using this technique.
http://web.mit.edu/fluids-modules/www/exper_techniques/LDA.text.pdf
http://www.dantecdynamics.com/measurement-principles-of-lda
http://users.ece.gatech.edu/~gtz/java/autocorr/index.html
The intensity oscillations tell the time per fringe traversed. The fringe spacing is given by the laser wavelength and angle the beams are crossed. The particle speed is this fringe distance divided by this traversal time.
Critical Thinking skill: how to spot an assumption. To get the particle speed what assumption is made? All the particles travel with the same velocity vector. What if there is turbulence causing particles to move at a different angle thru the interference pattern? Like moving the reflector in the Doppler lab at an angle so it doesn’t move in the direction of the microwave beam? There is extra distance travelled for the time to go thru a fringe.
Then note that in the error discussion no statistics are described. The author is not trying to show that the data support a model but using the data and model to determine how turbulence affects this technique of measuring the particle speed. Note how the parameters of an equation are defined and the eqn not derived but cited. Note how this doesn’t follow the format of a lab report we use. Why?
Answers to worksheet:
1.) Please write one question only in the incongruous category on the quantum particle state shown for the harmonic potential. The “unknown unknowns-the ones we don’t know we don’t know.”
How can the wavefunction oscillate in time while the probability is not time dependent? If the probability is the “square” of the wavefunction then how come there is no oscillation at twice the frequency since sin^(2u) = (1-cos(2u))/2? That is the wavefunction for a standing wave on a string is Sin[kx]Cos[omega t]. Its square should yield an oscillation at twice omega.
Answer: The PDF is given by the wavefunction times its complex conjugate and NOT the real part of the wavefunction squared. What does the complex conjugation mean physically? -phasors can only be used to add wavefunctions. Since QM and EM are linear theories this addition works fine. However when you need quantities like power = current x voltage the result is non-linear. You can’t multiply phasors or you will end up with second harmonics.
Show how the wavefunction times its complex conjugate yield a time average using these links.
http://home.sandiego.edu/~ekim/e171f00/lectures/phasors.pdf
https://en.wikipedia.org/wiki/Poynting_vector#Time-averaged_Poynting_vector
Your microwave detector measures a time average over the electric field oscillations at 10^10 Hz. Your eye measures a time average of the electric field oscillations at 10^14 Hz. The radio receiver in your car measures the electric field but an integrator time averages this to audio frequencies. Your scope measures the voltage without time averaging in the LCR circuit decay.
The time average is the result of complex time complex conjugate and taking the real part if this product is complex.
This is why the Harmonic oscillator states oscillate and the PDF does not.
2.) Please write one question only in the incongruous category on the water wave video.
https://www.youtube.com/watch?v=VA9rcaGET2w
https://www.youtube.com/watch?v=lWi_KpBy8kU
Why does the wavegroup start localized and then turn into what looks like a harmonic wave?
Content: EM wavegroup in vacuum does not spread. It does for QM waves, water waves, and sound waves. However, the spread often does not have much effect. For example, when you say hel-lo there are two wavegroups sent out, one for each syllable. One for hel and the other low. If they spread and merged you would not hear two syllables. We would not be able to communicate by sound.
This is because the wavegroup is composed of harmonic waves of different wavelength and frequency via Fourier superposition. Each harmonic wave travels at a different speed. There is one large harmonic component which dominates the others after the wavegroup has spreadout.
Show the picture of water waves in the mountains. Sketch how the boat moved one way and then turned around to go in a slightly different direction so two plane waves of slightly different direction were formed. Note that the wavegroups have turned into almost two harmonic waves. How is it that QM PDF does not have time dependance? This is another incongruous question on the particle in the well.
3.) If you were in a position to set the science curriculum for high schools in some country what would you emphasize?
(a) focus on motivation. What is exciting about science.
(b) some content like Newton’s laws or modeling.
(c) what would I do? Nature is repeatable on some level. Any measurement will not yield the same value when repeated yet we are still able to make sense of the world we live in. Simply repeating the experiment give a distribution but you need to think critically about systematic errors. The world might be like a fantasy movie in which anything can happen. Our world follows rules which are not arbitrary. Yet on some level our world is not predictable! When is it and when is it not?
-You could show at what level nature is repeatable. Somethings are too complicated to set up so they observably repeat. Of course you want to show that it can be modelled and is fun. How can you model if nothing repeats? Would it be fun if you couldn’t figure it out at some level or is fun because it is unexpected and unexplainable (like a magician)? - Critical thinking on repeatability: Assumptions: your science demonstration has to have few dependent variables or I won’t be able to keep most variables constant, resulting in non-repeatable data. It also can have chaotic behavior but the initial conditions need to be carefully repeated. How do you even know if the non-repeatability is due to initial conditions? Logical Fallacy: take a coin and talk about how long it takes to fall a meter and then ask how it would repeat landing on heads? What about all the random stuff that goes on in the world around us? Fundamentally, quantum tells us nature has a random component.
It’s easy to say that nature is repeatable and you will say that’s trivial. But do you really understand that? Here are some examples which, given a situation, demonstrate a deeper understanding:
SAT or ACT scores. On what level do you understand what this means? How repeatable (reliability) are they? Are they valid? How would you test that? What do they really measure (validity)? This (reliability and validity) is the point of the detector characterization lab.
Compare with a voltmeter or the system you are measuring. How repeatable (reliability) are different instruments. Do they really measure voltage (validity) or perhaps due to the 1 Meg internal resistance they affect the measurement.
What examples can you think of where this issue of repeatability is not discussed?
Your grades. Recently CSM instituted plus minus grades. Is the error in grading so small that this finer scale is appropriate? The students voted this in with the stipulation it didn’t apply to them. I made the argument that repeatability is the core issue to be understood. Then we go into the lab and students take data for the time between zero level crossings in the LCR decay lab for one decay. They then don’t understand that the error is obtained by repeating the experiment. The obvious statement that nature is repeatable has not been “internalized.”
Conclusion: Are you questioning what appears to be obviously trivial statements? Are you looking at both positive and negative critical thinking? To do this shows interest in the subject. To not do it can be an indication that the topic is boring. (The critical thinking might involve why doesn’t he teach us some physics? This indicates a motivation associated with training rather than educating. Let's go to such a topic next.)
