B Four Velocity Sign of Time: \dot t>0?

Onyx
Messages
141
Reaction score
4
TL;DR Summary
Is it generally the case even with light like paths that ##\dot t>0##?
Is it generally the case even with light like paths that ##\dot t>0##?
 
Physics news on Phys.org
A four velocity is not defined for a light like path.
 
Up to you, really. It is true that all future-pointing vectors will have the same sign in their time component, assuming your time coordinate is reasonably named and the spacetime has a global distinction between past and future. But there's nothing to stop you having your time coordinate increase towards the past, in which case all future-pointing four vectors would have negative time components.

As @Sagittarius A-Star points out, four velocity is not defined for null paths. However, you can define other four vectors tangent to null curves, such as the four momentum.
 
Last edited:
  • Like
Likes topsquark and PeterDonis
It's convenient to have the world-line parameter defined such that ##\dot{t}>0##. For massive particles you have time-like worldlines, and you can choose the proper time, ##\tau## as a natural world-line parameter. Then the four-velocity is "normalized": ##u_{\mu} u^{\mu}=c^2##.

For massless particles ("naive photons") of course you cannot choose proper time, because it's not defined but you can choose any affine parameter you like. Then you have ##\dot{x}^{\mu} \dot{x}_{\mu}=0##, i.e., light-like worldlines.

In both cases it is natural to choose ##\dot{t}>0##, where ##t## is the time-like coordinate since then with increasing world-line parameter you describe a motion into the future.
 
Thread 'Can this experiment break Lorentz symmetry?'
1. The Big Idea: According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box. 2. How It Works: The Two-Stage Process Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
Does the speed of light change in a gravitational field depending on whether the direction of travel is parallel to the field, or perpendicular to the field? And is it the same in both directions at each orientation? This question could be answered experimentally to some degree of accuracy. Experiment design: Place two identical clocks A and B on the circumference of a wheel at opposite ends of the diameter of length L. The wheel is positioned upright, i.e., perpendicular to the ground...
According to the General Theory of Relativity, time does not pass on a black hole, which means that processes they don't work either. As the object becomes heavier, the speed of matter falling on it for an observer on Earth will first increase, and then slow down, due to the effect of time dilation. And then it will stop altogether. As a result, we will not get a black hole, since the critical mass will not be reached. Although the object will continue to attract matter, it will not be a...
Back
Top