Recent content by robphy

"Proper time" does not exist for the photon. However, there must be a sense of causality, The Emission-event occurs before the Absorption-event. They are distinct-events with a nonzero-displacement-4-vector, even though that displacement vector is lightlike (null, has square-magnitude zero).

I should probably write the relevant formula involving hyperbolic-trigonometry. ##\beta=(v/c)=\tanh\theta ## so, ##\frac{(v_1/c)+(v_2/c)}{1+(v_1/c)(v_2/c)}=\tanh(\theta_1+\theta_2)## and ##\gamma=\frac{1}{\sqrt{1-(v/c)^2}}=\cosh\theta##...

For a ship (with nonzero rest mass), it cannot achieve "the speed of light" physically. Although your Newtonian intuition suggests that you can think in terms of "increments in velocity", special-relativity implies that you should instead think in terms of "increments of rapidity" (which are...

Did you look at the Szekeres "Signal Space" reference? His S relation is reflexive, but not symmetric.

This might be of interest: E. H. Kronheimer & R. Penrose (1967) "On the structure of causal spaces" Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 481 - 501 DOI: https://doi.org/10.1017/S030500410004144X Peter Szekeres (1991) "Signal...

Along these lines (assuming (3+1)-spacetime): "The causal order C determines the conformal structure of space-time, or nine of the ten components of the metric. The measure on spacetime fixes the tenth component." - David Finkelstein - "Space Time Code" (1969), Phys. Rev. 184, 1261...

You might be interested in David Malament’s dissertation: “Does the Causal Structure of Space-Time Determine its Geometry” https://digitalcommons.rockefeller.edu/student_theses_and_dissertations/496/ and "The class of continuous timelike curves determines the topology of spacetime" J. Math...

I think that’s a fair statement.

AA Robb studied the “conical order” in terms of “before” and “after”.

From https://www.nobelprize.org/uploads/2024/02/penrose-lecture.pdf You can read this 1936 Dirac reference here: https://royalsocietypublishing.org/rspa/article/155/886/447/5392/Relativistic-wave-equations

You could try to browse Dirac's collected papers Cambridge U. - https://archivesearch.lib.cam.ac.uk/repositories/9/resources/1531 Florida State U. - https://archives.lib.fsu.edu/repositories/10/resources/1408

This reminds me of a very old post of mine (reconstructed here because the old-style LaTeX on PF appears broken): It might be interesting to see if one could formulate a massless spin-3 analogue of these equations from the appropriate Bianchi identity. If not, what goes wrong? related...

Is this the paper you seek? From the WIkipedia article.... Bel, L. (1958), "Définition d'une densité d'énergie et d'un état de radiation totale généralisée", Comptes rendus hebdomadaires des séances de l'Académie des sciences 246: 3015 It is hyperlinked to...

Here's a 2025 interview with Abhay Ashtekar (Penn State), split into parts. (I was especially interested in his stories with Robert Geroch [his advisor at UT-Austin and UChicago] and Chandrasekhar. I had taken courses with Geroch at UChicago and with Ashtekar at SyracuseU, and both were very...

And so, a model (motivated by physically observed phenomena) and a set of tools to analyze the model lead to testable predictions, which (within its range of application) agrees with many experiments. Many other candidate models (possibly promising when formulated), however, do not agree with...