You can't get more direct than this in terms of proving that photons exist!
The particular case of the double-slit experiment will be discussed at: single particle double slit experiment.
Production:
Detectors are generally called photomultipliers:
Bibliography:
- iopscience.iop.org/book/978-0-7503-3063-3.pdf Quantum Mechanics in the Single Photon Laboratory by Waseem, Ilahi and Anwar (2020)
Maxwell-Boltzmann statistics, Bose-Einstein statistics and Fermi-Dirac statistics all describe how energy is distributed in different physical systems at a given temperature.
For example, Maxwell-Boltzmann statistics describes how the speeds of particles are distributed in an ideal gas.
The temperature of a gas is only a statistical average of the total energy of the gas. But at a given temperature, not all particles have the exact same speed as the average: some are higher and others lower than the average.
For a large number of particles however, the fraction of particles that will have a given speed at a given temperature is highly deterministic, and it is this that the distributions determine.
One of the main interest of learning those statistics is determining the probability, and therefore average speed, at which some event that requires a minimum energy to happen happens. For example, for a chemical reaction to happen, both input molecules need a certain speed to overcome the potential barrier of the reaction. Therefore, if we know how many particles have energy above some threshold, then we can estimate the speed of the reaction at a given temperature.
The three distributions can be summarized as:
- Maxwell-Boltzmann statistics: statistics without considering quantum statistics. It is therefore only an approximation. The other two statistics are the more precise quantum versions of Maxwell-Boltzmann and tend to it at high temperatures or low concentration. Therefore this one works well at high temperatures or low concentrations.
- Bose-Einstein statistics: quantum version of Maxwell-Boltzmann statistics for bosons
- Fermi-Dirac statistics: quantum version of Maxwell-Boltzmann statistics for fermions. Sample system: electrons in a metal, which creates the free electron model. Compared to Maxwell-Boltzmann statistics, this explained many important experimental observations such as the specific heat capacity of metals. A very cool and concrete example can be seen at youtu.be/5V8VCFkAd0A?t=1187 from Video "Using a Photomultiplier to Detect single photons by Huygens Optics" where spontaneous field electron emission would follow Fermi-Dirac statistics. In this case, the electrons with enough energy are undesired and a source of noise in the experiment.
Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Dirac statistics
. Source. 
A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).
Consider a system with 2 particles and 3 states. Remember that:
- in quantum statistics (Bose-Einstein statistics and Fermi-Dirac statistics), particles are indistinguishable, therefore, we might was well call both of them
A, as opposed toAandBfrom non-quantum statistics - in Bose-Einstein statistics, two particles may occupy the same state. In Fermi-Dirac statistics
Therefore, all the possible way to put those two particles in three states are for:
- Maxwell-Boltzmann distribution: both A and B can go anywhere:
State 1 State 2 State 3 AB AB AB A B B A A B B A A B B A - Bose-Einstein statistics: because A and B are indistinguishable, there is now only 1 possibility for the states where A and B would be in different states.
State 1 State 2 State 3 AA AA AA A A A A A A - Fermi-Dirac statistics: now states with two particles in the same state are not possible anymore:
State 1 State 2 State 3 A A A A A A
GitHub forbade our China Dictatorship auto-reply bot, the reason given is because they forbid comment reply bots in general. Though it was cool to see a junior support staff person giving out what obviously triggered the action:before a more senior one took over.
We've received a large volume of complaints from other users indicating that the comments and issues are unrelated to the projects they were working on.
Ciro was slightly saddened but not totally surprized by the bloodbath against him on the Reddit the threads he created:
- www.reddit.com/r/github/comments/1g7acv6/github_forbade_me_from_running_a_bot_that_would/ deleted by admins becausewhich is stupid, obviously we should be able to discuss GitHub policies in that sub.
We don't work for GitHub and we can't help you with your GitHub support problems. You'll just need to be patient.
- www.reddit.com/r/China/comments/1g7aa6k/american_programming_website_github_forbade_me/: also deleted without reason
So we observe once again the stupidity of deletionism towards anything that is considered controversial. The West is discussion fatigued, and would rather delete discussion than have it.
We also se people against you having freedom to moderate your own repositories as you like it, with bots or otherwise. Giving up freedoms for nothing, because "bot is evil".
I edited the VOD of the talk Aratu Week 2024 Talk by Ciro Santilli: My Best Random Projects about the CIA 2010 covert communication websites a bit and published it at: www.youtube.com/watch?v=QWL7l-5r1a4.
Stochastic Differential Equations course of the University of Oxford Updated 2024-10-28 Created 2024-10-23
Further Functional Analysis course of the University of Oxford Updated 2024-10-28 Created 2024-10-23
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Graph Representation Learning course of the University of Oxford Updated 2024-10-28 Created 2024-10-23
Concurrent Algorithms and Data Structures course of the University of Oxford Updated 2024-10-28 Created 2024-10-23
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