# A card game for Bell's theorem and its loopholes/Conceptual

## First day: Syllabus and Quizbank

On the first day we will introduce Quizbank and how students will be tasked with contributing new questions and offering better explanation for the answers to questions already on the bank. We begin with a quiz that discusses how to write quizzes in text form using a script that is easily converted into Extension:Quiz

## Statistical inference

Since only statistical data establishes the conundrum of Bell's theorem, we need to study statistical inference: the binomial and normal distributions will be introduced, the latter as a convent way to analyze binomial statistics if a sufficient amount of data is collected.

Motivating question: Suppose you have a business that you hope will capture 1/6 of your customer market. You have a good first year, but in the next year your sales drop by 3%. Is this a problem or statistical fluke?

w:simple:Standard deviation
w:Binomial distribution
We also need a binomial distribution calculator. Three are currently available online
https://homepage.divms.uiowa.edu/~mbognar/applets/bin.html
http://stattrek.com/online-calculator/binomial.aspx
https://www.di-mgt.com.au/binomial-calculator.html

Activities Until we develop collections of "secret" questions for Quizbank that students will not easily find, quiz questions need to be carefully selected and explained.

1. What would ordinary be a "bad" question can be rendered a "good" question if the instructor explains in class that this will be on the test and offer students guidance on how to learn from the question.
2. What would ordinarily be a "good" question can be rendered a "bad" question if the students see the question in advance. This can eventually be alleviated by having an extremely large bank and/or establishing "secret" question banks on servers that only the instructor can access.

Things you need to memorize for the quizzes

• For a normal distribution 68% will fall with in one standard deviation of the mean(≈70% is good enough).
Each tail beyond 2 standard deviations occupies 2.3% of the population (4.6% in both tails).
• If p<<1 then p(1-p)≈ p

Understand and use (but don't memorize) for the quizzes

• The population standard deviation is the square root of the variance, i.e., the variance is σ2 where σ is the population standard deviation. Two estimators of this standard deviation are:
${\displaystyle {\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}\approx {\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N}}}}$
• The Binomial distribution describes the number of outcomes that result from n independent trials where p is the probability for that outcome. The average number of outcomes is np and the variance,σ2=np(1-p).

Classroom activities

1. Do a lab rolling dice where p=1/6.
2. Compare with an Excel simulation (where the students follow instructions and write the code).
3. Compare with an online calculator
4. Introduce the Gaussian approximation (to reinforce the idea of standard deviation and cumulative normal distribution)
5. Write more quiz questions to supplement QB/d Bell.binomial. To date, no question have been written using images from the gallery shown below.

## Photon polarization

Here we will learn about the polarization of light and the concept of the "photon"

I can't find anything yet.

1. w:simple:Photon isn't bad. Perhaps I could supplement it.
2. w:Photon is a typical long-winded Wikipedia article. It probably has everything I need, but it has too much that I don't need.
3. (Wikiversity) Photon is just a long list of equations.
4. Physics Classroom is a viable option:
http://www.physicsclassroom.com/class/waves
http://www.physicsclassroom.com/class/light
http://www.physicsclassroom.com/class/refln
That gets us up to the particle picture. But why can't this be on a WMF wiki?
5. Wikibooks:The wave of a photon is not bad, but to advanced for my needs.
6. Wikibooks:A-level Physics/Electrons, Waves and Photons/Quantum physics is a viable option.

Conclusion. From the above list, I have three options;

Wikipedia:Simple:Photon
Wikibooks:A-level Physics/Electrons, Waves and Photons/Quantum physics
http://www.physicsclassroom.com/class

Keep on looking;

https://www.youtube.com/watch?v=4UNtA8ZaoAc There are lots of Youtube videos, but they need to be avoided if possible.
https://www.ducksters.com/science/physics/photons.php Maybe I should just turn the class loose on this project and ask them to explain it in a report???

Conclusion: I decided the easiest route is to fix the Wikipedia Simple article.

### Quiz is being planned

My plan is to make two quizzes connecting frequency, energy, and wavelength. The one that counts towards the grade will inform students of the equation required. After they master it, I will give them an experimental quiz (for no grade) to see if they absorbed the basic fact that low energy photons are associated with low frequency and long wavelength (and also the quantum limit of the wave theory).

## Bell's inequality (original form)

We shall read up to and including
Skip all sections involving CHSH

### Activity

The following figures have been created, but not yet incorporated into QB/d_Bell.Venn. Nor have any questions been posed that teach Bayes' theorem, which though not required for understanding Bell's theorem, would be an appropriate topic in a conceptual physics course that uses Benn diagrams to explain Bell's theorem. See also Impossible correlations#Bell's inequality: Venn diagram

## Footnotes

### References

1. When teaching a course, all these references should be permalinks

### To do

1. I need a quiz with space-time diagrams for the communications loophole
2. I need a quiz on Boolean algebra
3. I need a quiz on the tube entanglement and quantum mechanics, especially the probabilistic nature of it.
4. Perhaps a quiz on Baye's theorem (not needed here, but something that can be explained with Venn diagrams)
5. Perhaps a quiz that combines the binomial theorem with questins regarding how many times we need to repeat the partners version of the game (sort of a Fermi question)
6. Perhaps a quiz on the Pascal triangle (counting a choose b) Relevance to (a+b)^n AND to Plank's hypothesis via Boltzmann's statistics
7. I should consider making one of these quizzes a numerical one, since that is on my plate for this summers effort on the advanced courses.