Anyone here able to explain a formula in Wikipedia about the Tolman Paradox?
https://en.wikipedia.org/wiki/Tachyonic_antitelephone#Two-way_example
The t' definition is a mystery to me. How would we drop in c to get the unit of time? How come a is multiplied with v?
Your driving a car at 100 km/h. Someone passes you doing 10 km/h relative to you.
So they're driving at 110 km/h?
Yes... and no.
Simply adding velocities is a Galilean transformation between your frame of reference and the road's - the relativity of Newtonian mechanics (Newts three laws etc.)
However, turns out to be incorrect... negligibly noticeable here, very noticeable for relative speeds "near" the speed of light.
Just one fascinating consequence of SR.
#Physics #SpecialRelativity I'm about to, yet again, run an online course in Special Relativity (SR) for high school physics teachers. I was going to say "local" but I have two from interstate (WA), and even two from NZ!
I was wondering if there's something *you* don't understand / are confused about, and would like to ask, related to basics of SR (no acceleration / high school level) - "my students" might also want to know!
[Note: answering on social media has limits, but I'll try my best.]
Special Relativity: When you move a clock, it is slower as when it just sits there. When stopped, it runs with the normal speed again. (All relative to the non-moving observer.)
How's that? There are explanations out there, but wrote it down myself to understand it better.
For fun, I added a calculator to see how bad it can get. 4 hours in a plane and your clock lags ~4 nanoseconds (ignoring gravitation).
https://miamao.de/blog/2026-01/22.Moving_Clocks_In_Special_Relativity.html
How does the Twin Paradox work in Special Relativity? There are gazillion more or less correct and useful descriptions out there.
Everyone has their preferred one. Like in University many years ago, I grok things best if I describe them in my own words. So here we go:
https://miamao.de/blog/2026-01/11.Twin_Paradox_Explained_with_the_Light_Clock.html
RE: https://mastodon.murkworks.net/@wrog/115860196660746312
Roger's having another go at explaining special relativity without complex maths. ^_^
#Physics I encountered this misleading throwaway about #SpecialRelativity again the other day:
"We move through spacetime at speed c."
I like that, at the same time, I also discovered someone had written a paper about it, titled:
"Do Objects Move Through Space-Time at the Speed of Light? No."
It'd be an example of "Betteridge's law of headlines" except, perhaps, for the "No" at the end, which I love! 😀 More MSM articles should do that. 1/4
Mass isn't fundamental - it's momentum you can't see in a fifth dimension.
New paper: particles are massless 5D objects. Mass = ℏk_W/c (momentum along W-axis).
Time dilation? Reduced W-oscillation when 3D velocity increases.
Entanglement? Particle-antiparticle pairs are opposite ends of a single 5D spinor.
E² = p²c² + m²c⁴ emerges automatically.
🔗 https://zenodo.org/records/17922219
#physics #QuantumMechanics #SpecialRelativity #TheoreticalPhysics #openscience #preprint
We derive fundamental structures of quantum mechanics and special relativity from 5D geometry. Massive particles are massless 5D objects with momentum in the W-direction, giving m = hbar k_W / c. The 5D null geodesic condition yields E^2 = p^2 c^2 + m^2 c^4 and the Lorentz factor gamma = 1/sqrt(1 - v^2/c^2). Time dilation is reduced W-oscillation when 3D velocity increases. The Schrodinger equation emerges as the non-relativistic limit of the 5D wave equation. Quantum entanglement receives geometric interpretation: particle-antiparticle pairs are opposite ends of a single 5D spinor.
An excellent 1964 pop sci video from the USSR, explaining special relativity in a very accessible way, newly subtitled in English:
https://youtube.com/watch?v=P_1DJhLEHEQ
#PopScience #PopSci #relativity #SpecialRelativity #einstein #AlbertEinstein #USSR
Harald
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Grégoire Locqueville