4 ms·

Yes, which is why a photon experiences zero proper time.

by bollu 5y ago

RHSman2 5y ago
They should make a movie called ‘Photon’ and track its life. A parody based on science.
raattgift 5y ago
That proper time is zero everywhere along a photon's geodesic does not mean that the photon cannot evolve from point to point along it, and we can show this by taking advantage of total coordinate freedom. We can parametrize (as in make parametric) arbitrary curves through spacetime however we like. Parametric representations of unique curves are generally nonunique. Some of the infinite possible parametrizations of a chosen curve have useful properties, such as uniquely labelling every point on the curve with some monotonically ordering value and keeping the form of some set of equations reasonably simple. For timelike geodesics, particularly in the Minkowski space of Special Relativity, proper time (being a Lorentz scalar) is a good option. However that is not true for all geodesics in Minkowski space (as you note, the proper time is everywhere zero on a null geodesic, and so a bad option), much less all curves through general curved spacetimes. For null geodesics, following the logic of GP's question, we may wish to preserve the tangent vector under parallel transport; this requires the parametrization to be affine. Some gory details at https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics and a brief useful summary at https://www.reddit.com/r/AskPhysics/comments/9aenid/what_actually_are_affine_parameters/e4uwfda&context=3 https://www.reddit.com/r/AskPhysics/comments/9aenid/what_act... As is noted below the comment directly pointed to by the second link, labelling a timelike geodesic with proper time is choosing one specific affine parametrization on that geodesic, and that this choice is driven by convenience. One of the neat outcomes of affine parametrization is that we can take a point on an affinely-parameterized null geodesic and look at the derivative with respect to the affine parameter there, and define a momentum k^{\mu} = \dot X^{\mu}. In a Lorentzian spacetime, with curvature, we can compare the momentum at two different points on the null geodesic, giving us the gravitational redshift between those two points of the photon's wavelength equiv. frequency.

Yes, which is why a photon experiences zero proper time.

by bollu 5y ago

Yes, which is why a photon experiences zero proper time.

RHSman2 5y ago

They should make a movie called ‘Photon’ and track its life. A parody based on science.

raattgift 5y ago

That proper time is zero everywhere along a photon's geodesic does not mean that the photon cannot evolve from point to point along it, and we can show this by taking advantage of total coordinate freedom. We can parametrize (as in make parametric) arbitrary curves through spacetime however we like. Parametric representations of unique curves are generally nonunique. Some of the infinite possible parametrizations of a chosen curve have useful properties, such as uniquely labelling every point on the curve with some monotonically ordering value and keeping the form of some set of equations reasonably simple. For timelike geodesics, particularly in the Minkowski space of Special Relativity, proper time (being a Lorentz scalar) is a good option. However that is not true for all geodesics in Minkowski space (as you note, the proper time is everywhere zero on a null geodesic, and so a bad option), much less all curves through general curved spacetimes. For null geodesics, following the logic of GP's question, we may wish to preserve the tangent vector under parallel transport; this requires the parametrization to be affine. Some gory details at https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics https://en.wikipedia.org/wiki/Geodesic#Affine_geodesics and a brief useful summary at https://www.reddit.com/r/AskPhysics/comments/9aenid/what_actually_are_affine_parameters/e4uwfda&context=3 https://www.reddit.com/r/AskPhysics/comments/9aenid/what_act... As is noted below the comment directly pointed to by the second link, labelling a timelike geodesic with proper time is choosing one specific affine parametrization on that geodesic, and that this choice is driven by convenience. One of the neat outcomes of affine parametrization is that we can take a point on an affinely-parameterized null geodesic and look at the derivative with respect to the affine parameter there, and define a momentum k^{\mu} = \dot X^{\mu}. In a Lorentzian spacetime, with curvature, we can compare the momentum at two different points on the null geodesic, giving us the gravitational redshift between those two points of the photon's wavelength equiv. frequency.