**2024-04-16**| I didn't believe that light slows down in water (part 1)

Looking Glass Universe
I didn't believe that light slows down in water (part 1)

updated

**2022-11-15**| ...

**2022-11-14**| ...

**2022-11-14**| ...

**2022-11-14**| ...

**2022-11-13**| Here’s the original video:

https://youtu.be/v_uBaBuarEM

**2022-11-11**| ...

**2022-11-11**| Supported by Screen Australia and Youtube through the Skip Ahead initiative.

----------- Safety and where to get the supplies ---------------

I would love for you to try this experiment but please be careful with the lasers. If you're going to buy a green laser then it's crucial that you buy a proper one. Green lasers emit light a lot of invisible IR light and in cheap lasers this often isn't filtered out well. Blue/ violet lasers can also be dangerous for another reason. Our eyes are terrible at seeing these wavelengths, so the laser will look much less strong than it is, which means you might be playing with a dangerously strong laser without knowing it. Red lasers are generally the safer bet. I saw the effect I was looking for even when I used cheap ~1mW red lasers, so it will still work for you!

If you'd like to invest in a nice laser though, this article has some trustworthy green laser brands: https://www.planetguide.net/astronomy-laser-pointer/

Another way to buy lasers that are eyesafe is to get them from school science lab suppliers.

(Note: in some countries it's illegal to sell lasers over 1mW. Please check the laws where you live. In the USA the limit is 5mW)

The smoke machine I got used glycerol. I’m very suspicious of breathing in that smoke though, especially since the room can't be too well ventilated or it won't work. Fine particulate matter is a serious health risk in general so even though glycerol is nontoxic I think it may still be hazardous to inhale. I recommend wearing an airtight n95 mask or similar while doing this experiment.

It found it a bit tricky to source the double slit cheaply in Australia- your best bet might be a science lab supplier. In the USA you can get it on amazon though.

----------- Video credits ---------------

The beautiful animations in this video are made by Kathy Sarpi: https://kathysarpi.com/

Thank you to Screen Australia and Google Australia for funding this project, and to the wonderful people at Screen Australia who helped me throughout the process.

Thanks also to all my beta testers (aka friends)!!

**2022-08-15**| I gave a talk at my high school today and it got me thinking again about my experience of being labelled "bad at mathematics" and eventually doing my PhD at the University of Cambridge.

Btw, just because I think people will be confused, my field (quantum computing) is cross disciplinary, but at Cambridge it was in the maths department. I never know whether to call myself a physicist or a mathematician.

**2022-08-11**| If you'd like to try Brilliant: brilliant.org/LookingGlassUniverse

Here are a few papers that prove this result (there are many more though!):

David Deutsch https://arxiv.org/abs/quant-ph/9906015

Sabine Hossenfelder (yes that one) https://arxiv.org/abs/2006.14175

Wojciech Zurek https://arxiv.org/pdf/quant-ph/0101012

Lucien Hardy https://arxiv.org/pdf/quant-ph/0101012

0:00 - 1:38 Intro to the Born Rule

1:38 - 3:14 Equal probability case

3:14- 3:51 Nerd stuff

3:51- 5:00 Finishing the equal probability case

5:00- 6:00 Talking about my former employer

6:00- 10:14 Example with unequal probabilities

10:14- 12:16 A more general example

12:16- 14:04 How do you generalise?

Music:

Spinning Monkeys by Kevin MacLeod https://incompetech.com/music/royalty-free/music.html

**2022-08-04**| Here's the next video https://youtu.be/cKlRnutiv-k

**2022-05-07**| If the world splits every time you do a quantum measurement... how is energy conserved??

**2022-04-30**| Here's my previous video on the many worlds interpretation: https://www.youtube.com/watch?v=xBlpOGdk-0U&t=46s

**2022-04-22**| Follow up videos answering these questions:

Why don't I experience being in two worlds? https://youtu.be/4dCrNMqvYyg

The many worlds interpretation of quantum mechanics is often criticised for being excessive. Isn't it crazy that there are an infinite number of worlds splitting all the time? In this video I give an introduction to what many worlds actually is, and why I think it's actually a simplification of standard quantum mechanics.

Book recommendations:

The best book on MW in general and the one that inspired this video is Emergent Multiverse by Wallace.

Another fantastic book is Decoherence: and the quantum-to-classical transition by Schlosshauer. It isn’t specifically about MW, and is useful to understand decoherence in general.

**2022-03-03**| This video goes into the mathematics behind the "infinite chessboard" fractal that I designed.

**2021-08-21**| If you (or a friend) have endo symptoms:

Here’s my advice as a person who isn’t a doctor or an expert but has had some bad experiences with this condition.

1. It can be difficult to diagnose this condition partly because the symptoms are so different for everyone and partly because it’s hard to know what counts as “severe” pain. I thought the amount of pain I was having was normal for many years. If you have periods that are painful enough to be bothering you then it’s worth talking to a doctor.

2. GO TO A DOCTOR WHO SPECIALISES IN ENDO (once you’ve been diagnosed). Please please please don’t just go to a normal gynecologist. I did that and it was a huge mistake that cost thousands of dollars and caused damage that couldn’t even be fixed in my second operation. The surgery for endo is quite complicated and requires dedicated training to master, and yet the majority of doctors offering it haven’t done that training. For more details on how to find someone good I recommend that you:

4. Read some books about endo. In particular, I liked How to Endo by Bridget Hustwaite. It was approachable and full of useful advice. When I first got diagnosed I looked up endo online but that was pretty useless. It was only after reading this book that I got some idea of what was going on. That said, this condition is not well understood yet and everyone has their own methods of treating it that might not work for you, so don’t trust everything you read everywhere.

Here’s the diagnosis app I used (this isn’t an endorsement): https://ada.com/

If you want to learn about causal Bayesian Networks, The Book of Why by Mackenzie and Pearl is excellent.

Timestamps:

00:00 My medical story

02:48 Using Bayes' Rule for diagnosis

06:17 Causal Bayesian networks

12:34 Homework

**2021-05-07**| In this video I describe my PhD research in quantum computing. Is entanglement really crucial to a quantum computer? The standard wisdom says yes but I wasn't so sure.

Here are a few citations:

2:20 I claimed that entanglement has been shown to cause a small (polynomial time) improvement in quantum computing in a particular circumstance. That was shown in an amazing paper that used Bell inequalities to prove you the fact: https://arxiv.org/abs/1704.00690

2:45 On the role of entanglement in the quantum-computational speed up: https://arxiv.org/abs/quant-ph/0201143

Chapter 4 of my PhD covers the entanglement project. This is the most up to date source on it- we haven't uploaded the new version to the arXiv yet: https://www.repository.cam.ac.uk/handle/1810/315974

**2021-03-13**| People usually think math is a dry uncreative subject. It's really not at all though. Doing math research was surprisingly emotional. There's a joy to doing it that's hard to explain.

**2021-01-22**| This advice applies most for people looking to do a PhD in the UK in physics/ mathematics, although some of it is more general. Please watch other people's videos on this topic as well to get a broader perspective!

https://www.youtube.com/playlist?list=PLg-OiIIbfPj3vwCUeRWweRcnZMWJNXb27

0:00 Intro

0:43 Do something else first

3:11 Look for the right things in a supervisor

4:18 Choose a university with a lot happening

7:09 ...maybe don't do a PhD in the US

8:36 Final words of discouragement

**2020-12-24**| This video is just a little fun :) Merry Christmas!

This video used this delightfully funny track: https://freemusicarchive.org/music/Kevin_MacLeod

**2020-03-18**| Here's an informative video on social distancing by a Dr Rohin from MedLifeCrisis: https://youtu.be/ofSLpDQx1bA

I also highly recommend this site for understanding what the data we have: https://ourworldindata.org/coronavirus

And this video from 3Blue1Brown that explains the mathematics of exponential growth:

https://www.youtube.com/watch?v=Kas0tIxDvrg

REFERENCES:

0:58 To find the fatality rates for different age groups, see: https://ourworldindata.org/coronavirus

1:05 ‘You are likely to spread it to 2-3 other people’ claim is based on the paper: https://github.com/cmrivers/ncov/blob/master/COVID-19.pdf

1:40 Death rates for underlying conditions quoted were based on this information: https://ourworldindata.org/coronavirus#deaths-from-covid-19

2:51 ‘Number of official cases in the USA is likely to be a huge underestimate’ because of how few test have been administered. See Chart 8 on this page: https://www.vox.com/future-perfect/2020/3/12/21172040/coronavirus-covid-19-virus-charts

3:12 The statement “without drastic measures, the problem gets 10 times worse in a week” is based on the data in the graph below. The data from this graph comes from WHO’s official count. The slope of the lines in this graph determine how quick the so-called ‘doubling time’ is: the time till the problem is 2 times worse. You can see that initially, before much has been done, this slope is often consistent with a doubling time of less than 2 days, but it goes to between 2 and 3 days once a country is at least doing something, but has not imposed a lockdown on nonessential gatherings and closed schools etc. The USA (before the recommendation that just came out) had a doubling time of around 2 days (although it’s hard to say because of the testing situation mentioned below). That translates to the problem being 10 times worse in just under a week. In other places the doubling time was more like 2.5 days, in which case it’s 10 times worse in 8 days. Public awareness and bans on mass gatherings seem to help to bring the doubling time, usually to around 4 days. But when lockdowns are imposed it seems to get dramatically lower.

https://ourworldindata.org/grapher/covid-confirmed-cases-since-100th-case

4:34 Flatten the curve infographic: https://twitter.com/SiouxsieW/status/1236721200291655680

5:20 ‘350 thousand beds’ claim can be computed from these two sources:

https://data.oecd.org/healtheqt/hospital-beds.htm

https://www.statista.com/statistics/185904/hospital-occupancy-rate-in-the-us-since-2001/

5:32 ‘3-5% death rate in overwhelmed healthcare systems, and potentially much higher’ claim is from source:

https://wwwnc.cdc.gov/eid/article/26/6/20-0233_article

6:00 The Washington Post simulation is available here: https://www.washingtonpost.com/graphics/2020/world/corona-simulator/

As well as Kevin Simler’s playable simulation (highly recommended!): https://meltingasphalt.com/outbreak/

8:09 Virus symptoms infographic: https://ourworldindata.org/coronavirus#

8:24 ‘20%+ of infections from those who have no symptoms is based on this paper: https://cmmid.github.io/topics/covid19/control-measures/pre-symptomatic-transmission.html

ONLINE RESOURCES FOR LEARNING (to keep you occupied):

www.brilliant.org: You can signup without putting in your credit card details to do the daily challenges. You can also try the first chapter of every one of their courses for free this way. At the moment they have a free trial that let’s you do everything on the site, but you will need a credit card for that one. Disclaimer, I’m going to start working for Brilliant soon, but they’ve not asked me to do this or anything- I just really like the site.

3blue1brown has a lot of fantastic videos and I’m sure you’ve seen them, but have you watched his whole linear algebra series? It’s a gem, and useful to know too!: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

Socratica has beautiful in depth videos on all sorts of topics. I’m going to take this chance to follow their python course: https://www.youtube.com/channel/UCW6TXMZ5Pq6yL6_k5NZ2e0Q

Science4All is run by the extremely likable Frenchman Dr. Lê Nguyên Hoang. Why not learn some general relativity? I know you’ve always wanted to:

https://www.youtube.com/watch?v=0SUs_o6EEVs&list=PL8ovs-QtxcNydaiz8LSPpo8G0fatCqdTQ

Leonard Susskind's Theoretical Minimum series: https://www.youtube.com/playlist?list=PL701CD168D02FF56F

ACKNOWLEDGEMENTS: Thank you Le from Science4All for prompting me to make this video by pointing out how urgent this message is, and helping so much with the script. Thank you also to Josh Silverman for his many invaluable comments on the script that made this a much better video. Thank you Dr Rohin from MedLifeCrisis for offering to check the script even though he’s working so hard because of COVID19. And thank you to Dr M.K. for vetting the medical accuracy here. There are no doubt mistakes left, but those are all my own.

**2019-08-08**| This video gives you a some tips for learning quantum mechanics by yourself, for cheap, even if you don't have a lot of math background.

There's a lot more info in the blog post! https://lookingglassuniver.wixsite.com/blog

Reddit: https://old.reddit.com/r/Looking_glass_u/

Scott's book about learning:

https://www.scotthyoung.com/blog/ultralearning/

About me: in case you’re wondering, my name is Mithuna Yoganathan and I’m currently a PhD student studying theoretical physics at the University of Cambridge. If you want to know more about me, I made a video on my path into physics: https://youtu.be/nEhhQtq9gp4

**2019-06-09**| What does "the electron is a wave" actually mean? Be careful not to take the statement too literally.

**2019-03-05**| My path into theoretical physics wasn't a super traditional, since I started off very very bad at math. I hope this video shows you there's no such think as someone who isn't a maths person- since I ended up majoring in pure maths and loving it.

**2018-12-07**| Vote for GiveWell on the Project for Awesome website!: http://www.projectforawesome.com/watch?v=YMxtImOzyGw

And more info about GiveWell, including how they do their assessments, is here: https://www.givewell.org/how-we-work/process

Many people have the view that charity is either ineffective or corrupt. In this video we discuss why it certainly doesn't have to be that way -if we take a more scientific approach to doing good. (Just to be clear though, this isn't meant to disparage other charities and/or Project for Awesome. I personally am a fan of Partners in Health (one of the main P4A charities) as well as many others that GiveWell doesn't currently list as it's top charities.)

(Ad revenue from this video will go to GiveWell, by the way)

Reading recommendation:

If you enjoyed this video and want to know more, I really recommend Doing Good Better, by William Macaskill. I don't fully agree with every aspect of it (in particular, it takes a very utilitarian approach, even though you can take other moral views and come to similar conclusions). But it is a really excellent introduction to this topic, which is called Effective Altruism.

Citations:

My account of Michael Kremer's work comes from Doing Good Better, but the original papers are below. Just to be clear though, this doesn't mean that textbooks, flipcharts and more teachers are never useful. Just that they were not in these specific places and times tested.

General overview: "Randomized Evaluations of Educational Programs in Developing Countries: Some Lessons" www.jstor.org/stable/3132208?

Textbooks: "Many Children Left Behind?

Textbooks and Test Scores in Kenya" www.povertyactionlab.org/evaluation/textbooks-and-test-scores-kenya

Flipcharts: "Retrospective vs. prospective analyses of school inputs: the case of flip charts in Kenya" www.poverty-action.org/study/flipcharts-and-school-inputs-kenya

Price of deworming tablets: www.evidenceaction.org/dewormtheworld/

The study I cited with the 108 health interventions:

Jamison, Dean, et al. (eds.). 2006. Disease Control Priorities in Developing Countries (second

edition) Oxford University Press

But the results are discussed in a paper available online (it's a good read!): https://www.cgdev.org/sites/default/files/1427016_file_moral_imperative_cost_effectiveness.pdf

FINALLY, if you've got this far, I think you'll really enjoy this: https://80000hours.org/

**2018-11-11**| This video explains why the dot product is about how much vectors point the same way.

**2018-09-13**| This video is part of a linear algebra series:

Vectors and Bases: https://youtu.be/3ZfrJ0Sk5iY

Matrices and Linear Transforms: https://youtu.be/CBIO4xJ1Cok

Matrix inverses: https://youtu.be/ESKcF8XFzLM

This video is about changing the basis (or coordinate system) of a matrix or a vector. While the change of basis formula is often presented as something to just memorise, we'll see it's actually very very straightforward to understand.

Hints for homework:

1. You can do it! Think about what it does to the basis vectors!

2. Remember, in the original case you first translate the input vector from Bob's basis to Alice's so you can apply M_a, then translate back. A similar idea applies, but you need to translate to something M_a can take as input.

Answers to homework below!!!

Answers

The answer to question one is 2.

The answer to question two is 3.

**2018-08-26**| Check out Brilliant.org: https://brilliant.org/LookingGlassUniverse/ (it's free to sign up- you don't need to enter credit card details)

Link to my linear transformation/ matrix video: https://youtu.be/CBIO4xJ1Cok

Link to my vectors and bases video: https://youtu.be/3ZfrJ0Sk5iY

Link to my (unlisted) original version of this video: https://youtu.be/pLz_ln0ByXo

This video is about matrix inverses, and in particular, I try to give a bit more intuition for them- rather than just giving you the formula for the determinant, Cramner’s rule, the inverse of 2x2 and 3x3 matrices etc. Along the way, we cover some topics that don’t receive enough attention in linear algebra (at least, they didn’t in my math classes), like the left inverse, and why non square matrices don’t have an inverse. Finally, we will learn an intuitive condition for when the inverse exists.

Homework questions

1. What is the inverse of the following matrix:

1 2

2 5

a)

-1 -2

-2 -5

b)

1 1/2

1/2 1/5

c)

1 -2

-2 5

d)

5 -2

-2 1

2. Prove that, for a square matrix, the left inverse = the inverse

3. Prove the above for the following matrix:

1 2

2 5

by first doing these 2 questions

a) Show that M(1, 0) and M(0,1) for a basis. I.e. the old basis gets mapped to a new basis.

b) Show MLv = v for any vector (this is enough to show the M undoes L, and hence show that the left inverse is equal to the inverse).

To do this, first write v as a linear combo of M(1, 0) and M(0,1).

Hints:

3.

a) is a straightforward if you watch my first linear algebra video: https://youtu.be/3ZfrJ0Sk5iY

b) Sub the expression for v into MLv. Then use linearity!

Q2.

a) (Proving that the basis is always mapped to another basis) This is a bit tricky. I've written out the solution but stop reading at the point you think you know what to do and try it.

Assume v1,...,vn are a basis. Apply M to them to get Mv1,..., Mvn.

They're a basis if they're still linearly independent. But if they were, say:

Mv1= a Mv2+... + d Mvn

Apply L to both sides:

LMv1= L(a Mv2+... + d Mvn)

= a LMv2+... + d LMvn

using LM=identity:

v1= a v2+ ...+ d vn.

But this must be false, since v1,..., vn are linearly indep.

To see it done (SPOILER ALERT) 9:20 in https://youtu.be/pLz_ln0ByXo

b) Once you have that, proceed in a very similar way to Q3, part b)

**2018-07-20**| Brilliant.org: https://brilliant.org/LookingGlassUniverse/

Previous video on vectors and bases (watch this first): https://www.youtube.com/playlist?list=PLg-OiIIbfPj3Wldtb0QfV0Yse8tL2nLGm

Next video:

https://youtu.be/ESKcF8XFzLM

Matrices are often presented as a useful bookkeeping/ commutation tools to students- but there’s much more to them. When you understand what a Matrix really is so many parts of Linear Algebra will be completely obvious to you… including the formula for matrix multiplication and the fact that matrices don’t commute. So here's the big secret: A matrix is a linear transformation that eats a vectors and outputs another vector.

Homework questions:

Not all sized matrices can be multiplied together. Think about it in terms of them representing transformations from one space to another, and figure out which size matrices can be multiplied and explain why in the comments.

Consider a transformation that takes a 3d vector, and adds some fixed vector k to it. Say k is the vector 7 3 3. Is this a linear transformation or not? https://brilliant.org/practice/linear-transformations/?p=1

Imagine you have a matrix A that multiplies the first basis vector by 2, and the second basis vector by 6. How do you write A in this basis? https://brilliant.org/practice/linear-transformations/?p=3

Music: Epidemic sound, Summer nights 2

This video is an Introduction to Matrices but could be useful revision for school/university. If you have an exam, good luck!

**2018-06-28**| Vectors may seem very difficult when you're first introduced to them, but I hope this video helps you see they're not that scary! This video will be especially useful for vectors in physics. We'll cover vector addition and what vectors are. This is the start of a whole series of linear algebra, and I will cover vectors, adding vectors physics, the scalar product, matrices, eigenvalues/ eigenvectors and Dirac notation.

Next video: https://youtu.be/CBIO4xJ1Cok

Check out Brilliant: https://brilliant.org/LookingGlassUniverse/

DON'T FORGET TO DO YOUR HOMEWORK:

Prove these 2 statements about bases

1. If you have two different bases for the same space, then they must have the same number of basis elements in them. (E.g, there are many different choices of basis for the plane, but no matter what basis you choose, there are only 2 vectors in each basis.)

2. Once you pick a basis (say {v_1, v_2}), there's only one correct way to write another vector as a linear combination of the basis vectors. Eg, say v=a v_1+ b v_2. Then you can't also write v=a' v_1+ b' v_2, where a' and b' are different from a and b.

The multiple choice questions from Brilliant:

Q1. Which of these vectors is redundant (i.e. can be written as a linear combination of the other 2):

i) (1 2 3)

ii) (1 3 5)

iii) (2 5 8)

iv) Each of the above

The full solution is available here: brilliant.org/practice/linear-independence/?p=2

Q2. Consider the following 3 vector spaces:

A= The vector space spanned by {(1 2)}

B= The vector space spanned by {(1 2), (2 3)}

C= The vector space spanned by {(1 2), (2 4), (3 6)}

Question: which of the following is true?

i) A is a subspace of B, which is a subspace of C

ii) C is a subspace of A, which is a subspace of B

iii) B is a subspace of C, which is a subspace of A

iv) A is a subspace of B and C, which are not subspaces of each other

The full solution is here: brilliant.org/practice/subspaces-and-span/?p=6

ANSWERS FOR THE BRILLIANT.ORG QUESTIONS:

*

*

*

*

*

*

*

*

Q1) D

Q2) ii

HINTS FOR PROOF QUESTIONS:

2 is easier, so let's do that first

Hint 2.1 Let's do the case with just 2 basis vectors first. If there are 2 basis vectors v_1 and v_2, the one thing you know about them is that they are not just a multiple of each other (otherwise it wouldn't be a basis). Try and get a contradiction with this fact.

*

*

*

Hint 2.2 Assume v= a v_1+ b v_2 = a' v_1+ b' v_2, but a and a' aren't equal, and b and b' aren't equal.

*

*

*

Hint 2.3 Use the above equation to write a relationship between v_1 and v_2. Oh no, that looks like they are multiples of each other!

*

*

*

Hint 2.4 Now do the case where there are n basis vectors. What you know about them is that you can't write them as linear combinations of the others. Try and get a contradiction with this fact.

*

*

*

Hint 1.1. Imagine you had 3 vectors and they span 2D space. Doesn't that one of them is redundant? The following in this case first:

B1={u_1,u_2}

B2={v_1, v_2,v_3}

Write each u_i in terms of B1.

Remember that there is a redundancy in B2 if you can write c u_1+ d u_2= u_3. So write this, and let's see if we can find a solution for c and d.

Plug in your equations for u_i into c u_1+ d u_2= u_3

You now have a vector on the right hand side in B1 and a vector on the left hand side in B1

Using the result from question 2 (dammit, I really should have swapped the order of these questions), you know that the coefficient in front of v_1 and v_2 must be the same on both sides (since there is only one unique way to write a vector in B1)

So now you have 2 linear equations with 2 unknowns (c and d- everything else is 'known').

Show that they only don't have a solution for c and d if B2 was actually linearly dependent all along. (Yes this will require you to know some linear algebra to do efficiently (although technically possible without)).

*

*

*

When you assume that the two bases can be any size it's most efficient to do this with linear algebra (sorry!!)

*

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The solution: yutsumura.com/if-there-are-more-vectors-than-a-spanning-set-then-vectors-are-linearly-dependent/

Music: Epidemic sound, Summer nights 2

**2018-04-24**| In this video I cover the common misconceptions I saw in my last video- Understanding Quantum Mechanics.

In particular, I talked a lot about the measurement problem in this video.

**2018-03-22**| This video is an simple introduction to quantum mechanics that explains why there is still so much controversy over the meaning of this scientific theory.

Thanks to Vlogbrothers for their sponsorship of this video! I really really appreciate it!

If you'd like to help transcribe this video into another language, that would be amazing: http://www.youtube.com/timedtext_vide...

Homework questions:

1. We talked about doing the double slit experiment with small things like electrons. But is there any reason in theory we can't do it with bigger things? If not, what would you need to do to make it work?

2.We didn't measure where the electron went in the middle of the experiment. But it is possible. If we measured each door to see if the electron went through it, what would we find? And what would happen to the pattern on the back wall?

3. There is another way to interpret the double slit experiment, which I think is really cool- it's called Pilot wave theory. I made a video about it. In that theory, the particle does go through just one door, even though our argument said that's not possible. Find the flaw in our argument. Also comment on why particles still act strange in Pilot wave theory.

Music: Thanks Falcxne for allowing me to use this song: https://m.soundcloud.com/falcxne/phas...

**2018-03-22**| A short update video.

THE NEW SERIES HAS STARTED: https://youtu.be/8Dso6Fv1FUw

Here are the links to videos I've now made unlisted (this means that anyone with the link can view them, but they won't turn up in Youtube's search anymore).

The old old (!) videos on Quantum mechanics (from 5+ years ago):

The wave particle duality: https://youtu.be/zDQH5x7svfg

Superposition ft. Schrodinger's Cat: https://youtu.be/zDQH5x7svfg

What is a measurement?: https://youtu.be/KujEMGZGUTI

Quantum Eraser: https://youtu.be/XcZ3jI1Ph7A

Quantum Eraser explained: https://youtu.be/sQfSm6o-KlQ

Delayed Choice Quantum Eraser: https://youtu.be/MW-AemjSVGY

Heisenberg Uncertainty Principle: https://youtu.be/ZpwZgOumTrs

New old series (from 3 years ago):

Introduction to quantum mechanics: https://youtu.be/b_ddt6J1Bio

The Wave Function: https://youtu.be/02eZMf17wFs

(I will unlist some of the others later as I upload more in this new series.)

**2017-08-16**| An explanation and the pros and cons of Pilot Wave Theory aka Bohmian mechanics.

Links to videos referenced:

Veritasium's video: https://youtu.be/WIyTZDHuarQ

My old Bohmian mechanics video: https://youtu.be/rbRVnC92sMs

Contextuality: https://youtu.be/Qz4CHI_W-TA

Entanglement and the EPR paradox: https://youtu.be/Xzmp7byh77E

Also see:

PBS spacetime's excellent video: https://youtu.be/RlXdsyctD50

This amazing video about 'surreal paths' in Bohmian mechanics (this channel is also very worth checking out): https://youtu.be/CCW93koLNYY

**2017-05-07**| The EPR paradox, that we met in a previous video, tells us 2 entangled particles can effect each other no matter now far away they are. But then why can't we use them to send instant messages across the universe? Einstein's relativity tells us it would be a disaster if we could!

Homework:

Prove that faster than light communication doesn't work for the state in the video, when Alice measures up and down-ness, but Bob measures left-rightness.

Look up and then explain the usefulness of a one-time pad. Also explain whether a one time pad coming from a bunch of shared particles is secure if Eve is trying to measure Bob's particle's before he does.

The EPR paradox, that we met in a previous video, tells us 2 entangled particles can effect each other no matter now far away they are. But then why can't we use them to send instant messages across the universe? Einstein's relativity tells us it would be a disaster if we could!

Homework:

Prove that faster than light communication doesn't work for the state in the video, when Alice measures up and down-ness, but Bob measures left-rightness.

Look up and then explain the usefulness of a one-time pad. Also explain whether a one time pad coming from a bunch of shared particles is secure if Eve is trying to measure Bob's particle's before he does.

Solution to homework question 1:

Sorry Youtube doesn't allow certain brackets in the description, so I've put the solution as a comment.

**2017-03-03**| We usually say that infinity isn't real, but here we'll see how crucial it is to have one very big infinity for the real world; there is an infinite number of numbers. But why do we need real numbers at all? Aren't rational numbers enough? And what about hyperreal numbers?

What we'll see in this video is that discovering or defining the real numbers is what allowed calculus to be made rigourous- and without it, we'd need to divide by 0 every time we took a derivative.

This video is about the seeming mathematical paradox that arises to get Archilles from A to B (that isn't Zenos paradox!).

Check out Nick Lucid's video on whether the universe is infinite: https://youtu.be/fApKpDGGDYk

**2017-02-14**| What is entanglement really? And why is it that it's a uniquely quantum phenomena?

Homework:

1 Explain why Alice can never send any messages through this set up.

2 This is one to practice working with wavefunctions of several objects. Prove mathematically that it’s impossible to write our state as two separate states for the electron and positron

3 This one is very relevant to quantum computing. If you have just one electron or positron, you only need 2 numbers to describe its state. Now suppose you have n of them. If they are not entangled, how many numbers to you need to describe the state? What about for a general state that is allowed to be entangled?

Bohmian mechanics stuff:

In Bohmian mechanics, you still have superpositions, they just mean something very different. A Bohmian mech particle only has one position, however, it still has a wavefunction that is a superposition of many possibilities. The difference is that the particle has one position but is influenced by other things in it's wavefunction. A particle like this behaves very differently to a classical particle that only has one position and is not at all influenced by it's other possibilities.

**2017-01-29**| I talk about a very simple solution to the two envelope fallacy.

Watch this video first: https://youtu.be/OqVFKY504X0

**2017-01-23**| A fallacy arising from a surprisingly simple situation. Can you figure out what the problem is with this reasoning?

**2017-01-15**| This is a follow up to a video where I described a betting system that seems to guarantee you win money- I asked you guys how that's possible. In this video I explain the flaws in the system.

Previous video: https://youtu.be/t8L9GCophac

**2017-01-08**| Here's an interesting paradox for you to consider. We've all been told it doesn't pay to chase our losses gambling- but this video seems to prove that actually this will let you consistently win money. This can't be right- and that's the paradox.

Solution announced at this time where you live: https://www.timeanddate.com/worldclock/fixedtime.html?msg=Gambling+Paradox+Answer+Video&iso=20170115T17&p1=136

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Hints:

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Small hint:

If you lost a lot of times in a row, you're going to run out of money at some point right?

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Bigger hint:

Say you have to stop playing if you ever lost x amount. What's your expected winnings?

**2016-11-16**| A really poorly done video about 3 out of 4 of the homework questions... all I can say is I'm sorry.

**2016-11-14**| In this video we see how the Schrodinger equation comes out very simply from the conservation of energy.

This is the second video. Click here for the first: https://youtu.be/ZfKq3g3MHqE

My twitter: twitter.com/Looking_glass_u

First.

Throughout these 2 videos, I kept talking about predicting the future, and that if you know the present state, you can predict the future. Does this mean quantum mechanics is deterministic? If you don’t think so, comment on where the determinism ends and the randomness starts in this theory.

Second.

Show that, for the Schrodinger equation, this is true: That it’s the same thing to go forward in time t1 plus t2 as go forward t1 and then go forward t2. Seems obvious, but explain what philosophical consequences that might have.

Third.

I said that linearity follows from the shrodinger equation. Can you see why? Try and prove it.

Fourth.

This is for the people who’ve done Quantum mechanics before and know that in this theory time evolution is unitary- yet I just went on about linearity so much in the previous video. Show that linearity plus the assumption that time evolution maps valid states to other valid states is equivalent to saying that the evolution is unitary.

**2016-11-14**| We've talked about the quantum state plenty- but what happens to it over time? That's exactly the question the Schrodinger equation solves. This video we talk about 'Linearity'. In the next video we discuss the equation itself and its derivation. Click here fore that: https://youtu.be/DEgWbrMv6-k

**2016-09-09**| Let's talk about one of the most misunderstood but awesome concepts in physics. The Heisenberg uncertainty principle. Or maybe it should be the Heisenberg 'fuzziness' principle instead? Would that confuse less people?

**2016-09-01**| The wave-particle duality seems to used all the time to explain quantum mechanics to the public, but it is one of my pet peeves. It represents an outmoded way of thinking (old quantum theory), which is replaced by our current understanding of the wavefunction (new quantum theory). I explain how to use the wavefunction to explain one of the most important experiments in quantum mechanics: the double slit experiment.

Update on my life: I'm going to start a PhD! Same place as the masters, on quantum computing. Very very excited. But don't worry, I'm determined to make time for this channel throughout my remaining studies. In fact, expect some videos on quantum comp in the not too distant future (well, at least not too distant compared to the time scales I work on. Don't hold your breath or anything. That will end badly).

Understanding Quantum Mechanics series: https://www.youtube.com/playlist?list...

**2015-09-23**| Homework:

-What do you think of this idea? Have you heard of it before?

-Maybe you’ve heard about things like super symmetry in physics- try find out how that’s related.

-If you know some calculus and classical physics, try and find a proof of this theorem.

-Try come up with strange systems with strange symmetries- then see if you can figure out what’s conserved.

The proof and maths of Noether's theorem:

There are two ways to approach Noether's theorem that I know of. The most common is through Lagrangian mechanics- where the proof is surprisingly simple but unfortunately quite opaque (see http://math.ucr.edu/home/baez/noether...) . The other way, and the way I allude to in this video, is using hamiltonian mechanics. I find this way a bit easier to understand and it involves the generators of the transforms more. A great resource for this is the last lecture in this course: http://www.physics.usu.edu/torre/6010...

but it requires multivariable calculus and a little knowledge of Hamiltonian mechanics.

**2015-09-07**| On why I was very wrong. In my previous video, I said that spin isn't very linked to angular momentum at all- but in fact, there's a key property of angular momentum that spin has, suggesting they are linked after all.

Previous video (What is Spin?): https://youtu.be/cd2Ua9dKEl8

Book recommendation: Modern Quantum Mechanics by Sakurai. This is a classic textbook that I hadn’t read until recently, but I’m now such a fan. However, I think that you will benefit most from this book if you already know the basics of QM and what a deeper look. That said, the only prerequisite is linear algebra.

Homework:

I’m interested, did you guys find this video’s argument convincing? Should we call spin intrinsic angular momentum? Is it weird to even try and explain spin with classical ideas and using classical analogies? Is intrinsic angular momentum inherently meaningless phrase anyway? Every time I ask these sorts of questions I get a really diverse set of opinions all well argued so this should be fun.

Second, I mentioned that you can only get an electron back to its original state by rotating it twice. Last time, some people commented that this isn’t so weird- some classical things do this. What do you think of this? Do you know an example?

Finally for the classical mechanics fans, I explained why a rotating thing in a stern-gerlach machine doesn’t just flip and point up. But now explain why the force that it experiences is proportional to how much it was pointing up to start.

**2015-07-31**| Follow up video: https://youtu.be/z_6B2M12H9w

Research assignment: Teach me about spin.

Below there are suggested questions, recommended sources and my social media accounts:

QUESTIONS:

Questions that require less research:

1. This is our first real example of quantization, the phenomena that gives quantum mechanics it’s name. Here’s what it means. In the classical case of magnets going through a Stern Gerlach machine, the magnets can end up any where in the range. But in quantum mechanics, its can only be exactly up or down, these discrete values rather than a continuous range in between. This sort of quantization really bothered physicists. Can you understand why? And is there any classical physics phenomenon that also has sort of quantization?

2. Do you think that eventually all quantities in physics can be explained in terms of deeper physics? Are there any examples of quantities that later on did get explained through a more encompassing theory?

3. How can you use the Stern-Gerlach machine to measure spin in the ‘forward-backward’ direction?

4. Why do half the particles go left, half right at 4:24?

Questions that (probably) require research:

5. What are bosons and fermions? What’s spin got to do with it? If you really want to get into it, read ch 4, volume 3 of The Feynman Lectures: http://www.feynmanlectures.caltech.ed...

6. Electrons are so-called spin 1/2 particles. Are there any other spin types? What determines what spin a particle will have?

7. How does spin relate to the Pauli exclusion principle?

8. Explain how the Stern-Gerlach machine works

9. Is light polarization a type of spin? What are arguments for and against this? What spin does a photon have (spin 1/2, spin 1 etc)?

10. Why is it that charged particles moving causes magnetic fields- according to Einstein? (Look up relativity and electromagnetism)

11. What’s wrong with saying the electron is infinitely small? What experiments measure the electrons size? Are protons also infinitely small?

12. Find other reasons we don’t believe electrons are actually spinning. (An interesting one is about rotating a spin particle 360 degrees, and not getting back the exact same wavefunction.)

13. a) What is the Bloch Sphere, and why can we use it to represent spin? How do you visualise the spin left state on it? how about spin forward? (http://comp.uark.edu/~jgeabana/blocha... , note that a 2-level system is any particle that only has two options when measured (eg only up or down). |0) and |1) are the generic labels we’ll put on these options)

b) Also, How do you write spin forward in terms of up and down (i.e. |forward)=a|up)+b|down))? You will probably need to look this up, so it’s useful to know the spin “up/down”ness is usually called spin in the z direction, spin “left/right”ness is spin in the x direction, and spin “forward/backward” is spin in the y direction. You can figure this out by looking at the Bloch sphere.

14. Magnetic Resonance Imaginging (MRI) is an important clinical technic that completely relies on manipulating spin. Explain it! http://www.scholarpedia.org/article/M...

15. What happens to the electrons if you put them into the Stern-Gerlach machine and then slowly rotated from up and down to side and side, do some of the electrons switch places? (Thank you Majoofi)

16. Why aren't there magnetic monopoles? (Thanks Culwin)

17. What is isospin? Why is it that, even though it hasn't got the units of angular momentum, it still 'formally acts like spin?' according to Wiki? (Thanks Hythloday71)

RECOMMENDED SOURCES ON SPIN

The Feynman lectures, Volume 3: http://www.feynmanlectures.caltech.ed...

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particle Physics- Eisberg and Resnick, the chapters of angular momentum and spin. This is a good one if you already know basic classical electromagnetism. Don't buy it, just visit your local university library and just read it there.

Sneaking a Look at God's Cards - Ghirardi. This is one of my favourite quantum books. It talks about the Stern-Gerlach experiment.

Wikipedia or Scholarpedia. These are always a good place to start- though sometimes they can throw you into the maths. Don't panic if you don't get all of it. Just try to glean the main idea, and that's more than enough to report here. Hopefully then others can help with any details that were confusing.

The Story of Spin. Thank you Michael Sommers for the recommendation. I haven't read it, but it seems good! Hard to find though.

https://www.goodreads.com/book/show/1...

A Veritasium and Minute Physics video about electromagnetism! Thanks EnellGmz for reminding me about it. https://youtu.be/1TKSfAkWWN0

SOCIAL MEDIA:

Twitter:

@Looking_glass_u

www.facebook.com/LookingGlassUniverse

Tumblr

http://looking-glass-universe.tumblr....

**2015-07-11**| A follow up for the previous video: https://youtu.be/tt8gVXDsh7Q

**2015-06-21**| We finally learn the rule of quantum mechanics responsible for a lot of the strangeness of the theory.

Solution: https://youtu.be/EiQlbNAF5cU