Stop codon Updated 2025-07-16
Twin paradox Updated 2025-07-16
The key question is: why is this not symmetrical?
One answer is: because one of the twin accelerates, and therefore changes inertial frames.
But the better answer is: understand what happens when the stationary twin sends light signals at constant time intervals to each other. When does the travelling twin receives them?
By doing that, we see that "all the extra aging happens immediately when the twin turns around":
  • on the out trip, both twins receive signals at constant intervals
  • when the moving twin turns around and starts to accelerate through different inertial frames, shit happens:
    • the moving twin suddenly notices that the rate of signals from the stationary twin increased. They are getting older faster than us!
    • the stationary twin suddenly notices that the rate of signals from the moving twin decreased. They are getting older slower than us!
  • then when the moving twin reaches the return velocity, both see constant signal rates once again
Figure 1.
Twin paradox illustration with twins sending light signals at regular intervals
. Source.
Another way of understanding it is: you have to make all calculations on a single inertial frame for the entire trip.
Supposing the sibling quickly accelerates out (or magically starts moving at constant speed), travels at constant speed, and quickly accelerates back, and travels at constant speed setup, there are three frames that seem reasonable:
  • the frame of the non-accelerating sibling
  • the outgoing trip of the accelerating sibling
  • the return trip of the accelerating sibling
If you do that, all three calculations give the exact same result, which is reassuring.
Another way to understand it is to do explicit integrations of the acceleration: physics.stackexchange.com/questions/242043/what-is-the-proper-way-to-explain-the-twin-paradox/242044#242044 This is the least insightful however :-)
Bibliography:
Twin prime conjecture Updated 2025-07-16
Let's show them how it's done with primes + awk. Edit. They have a -d option which also shows gaps!!! Too strong:
sudo apt install bsdgames
primes -d 1 100 | awk '/\(2\)/{print $1 - 2, $1 }'
gives us the list of all twin primes up to 100:
0 2
3 5
5 7
11 13
17 19
29 31
41 43
59 61
71 73
Tested on Ubuntu 22.10.
TwinsUK Updated 2025-07-16
Two.js Updated 2025-07-16
Examples at: two-js/.
JavaScript library, works both on browser and headless with Node.js to SVG.
Feels good. Maybe not ultra featured, and could have more simple examples in docs, but still good.
One of the main features of Two.js appears to be the fact that it can natively render to either SVG and canvas, rather than creating SVG through DOM hacks as done by other projects.
CC BY-NC-ND Updated 2025-07-16
CC BY-SA 4.0 Updated 2025-07-16
Nature (journal) Updated 2025-07-16
Ended up under Springer in 2015 after a massive merger.
Two photon interference experiment Updated 2025-07-16
Can be achieved in two ways it seems:
Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.
Video 1.
Quantum Computing with Light by Quantum Light University of Sheffield (2015)
Source. Animation of in-silicon single photon device with brief description of emitting and receiving elements. Mentions:
Video 2. Source. More theoretical approach.
Video 3.
Building a Quantum Computer Out of Light by whentheappledrops (2014)
Source. Yada yada yada, then at youtu.be/ofg335d3BJ8?t=341 shows optical table and it starts being worth it. Jacques Carolan from the University of Bristol goes through their setup which injects 5 photons into a 21-way experiment.
Typeface Updated 2025-07-16

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