Lecture 8

“What people think of as the moment of discovery is really the discovery of the question." Jonas Salk (American medical researcher and virologist. He discovered and developed one of the first successful polio vaccines.)

Review planet occulting star: plot charge distribution from the detector with mean Q0 and sigma std dev. Note that an integrator adds this charge to yield a voltage (you need switches to stop adding after a given time and to reset the cap to no charge). Draw the analogy with cars crossing a line in 10 secs vs 1000 secs. The number of cars increases by 100 while the std dev only increases by sqrt[100].

Review of “How to lie with statistics:” Line the questions the authors wants you to ask with the critical thinking skill list given here https://www.oxford-royale.co.uk/articles/critical-thinking-skills-university.html who says so (item 1: reliable source or citations and/or item 3: how to spot bias)? how does he know (item 7: understanding different kinds of evidence)? what's missing (item 4: how to spot an assumption)? did somebody change the subject (item 5: logical fallacy)?

does it make sense (item 4: how to spot an assumption and from defn of critical thinking: interpret whether conclusions are warranted based on given data)?

Review the watermelon video. http://cactus.dixie.edu/smblack/chem1010/lecture_notes/4B_explosions.pdf The model of an explosion requires -fast reaction -products are gases which expand rapidly (therefore form a shock wave creating a boom). -large amount of energy is released.

Electrical energy delivered very quickly into the watermelon. The electrical discharge occurs on a microsecond time scale converting electrical to thermal energy. The heat energy cannot diffuse on this time scale so it goes to vaporizing the water. This is like lightning which generates a high temperature which vaporizes the water into a gas which expands rapidly.

Compare that with a atom bomb where: a Uranium atom can barely stay together because of the Coulomb repulsion. The nuclear force is binding it. The atom is split by a neutron collision, resulting in the release of a large amount of Coulomb potential energy and more neutrons. The reaction is fast since the neutrons essentially travel at the speed of light and the nuclei are close together. Everything is vaporized from the heat generated (gas expands). Why does the water go up and not to the side? https://www.youtube.com/watch?v=_f2f6zb7Fe8 Questions like “what is the value of capacitance” is informational, while what causes the watermelon to explode is incongruous.

In class work.

Determine the force on a electric dipole in the presence of a point charge on the back of the question handout.

Show voltmeter histogram output with room light input. Ask for questions. Think about what the model is before asking questions. The voltmeter measures a voltage in a given interval then displays it as the number of readings vs voltage.

Collect responses then discuss with a focus on critical thinking. Most responses are of system 1 type. That is responses where you give a “knee-jerk” reaction. System 1: Fast, automatic, frequent, emotional, stereotypic, subconscious System 2: Slow, effortful, infrequent, logical, calculating, conscious From wikipedia https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow

Return to voltage questions: System 2 thinking involves asking questions related to the model. What is the model of the voltmeter histogram display? Voltage is measured and that value is placed on the horizontal axis while the number of readings with that voltage value is place on the vertical axis.

Congruous: I understand how this works but why are there more voltage readings at the extremes rather than at the middle like a gaussian? Congruous: Could a square waveform generate such a histogram? Modify: what happens if the output is displayed on a scope? What happens if the PLC is changed. Creative: What would cause such a PDF in quantum mechanics? PDF for quantum harmonic oscillator https://ocw.mit.edu/courses/nuclear-engineering/22-51-quantum-theory-of-radiation-interactions-fall-2012/lecture-notes/MIT22_51F12_Ch9.pdf

Use the waveform generator to deliver a 60 Hz sinusoidal waveform to the voltmeter and display the histogram. Change PLC to 1 and observe how the histogram changes to a Gaussian. Change to a square wave and compare distributions.

How do you determine the probability density function? collect data and plot it on a histogram. For example, this is how QM is verified. The model predictions come from the Schrodinger equation. The number of ways something can happen divided by the total number of ways possible gives the PDF (this is like Newton's second law in mechanics). For example show the plinko applet.

What is the probability of rolling 2 dice and getting a sum of 4? Ask: how you would calculate the answer?