The spacetime diagram for that would look like what I’ve shown. First we see the light, then the light reaches Proxima Centauri. Notice I’ve drawn the light rays from the event traveling at 45 degrees to my time axis. After all, it is light, and light travels at 45 degrees on spacetime diagrams.
When it re-emerged from the prism, it refracts once again, returning to its original speed. When you pass this light through a dispersive medium like a prism, all of the different wavelengths respond slightly differently. The more energy you have in your electric and magnetic fields, the greater the effect they experience from passing through a medium. The frequency of all light remains unchanged, but the wavelength of higher-energy light shortens by a greater amount than lower-energy light.
For example, here are some pictures of quasars with redshifts around 5. We can even see light restaurant godbout all the way back to a redshift of 1000 or so. That may sound counter-intuitive, but as long as H0decreases at a slowerrate than that at which the Universe’s expansion velocity is increasing, the overall movement of galaxies away from us still occurs at an accelerated pace. And at this moment in time, cosmologists believe that the Universe’s expansion will outpace the more modest growth of the Hubble volume.
As far as we know, it’s not possible for a person to move at twice the speed of light. In fact, it’s not possible for any object with the kind of mass you or I have to move faster than the speed of light. Special relativity provides an absolute speed limit within the universe, according to Sutter, but Einstein’s 1915 theory regarding general relativity allows different behavior when the physics you’re examining are no longer “local.” Michelson, along with his colleague Edward Morley, worked under the assumption that light moved as a wave, just like sound.
That may sound counterintuitive, but as long as H0decreases at a slower rate than that at which the Universe’s expansion velocity is increasing, the overall movement of galaxies away from us still occurs at an accelerated pace. To understand this, consider that as the Universe gets older, distant light has more time to reach our detectors here on Earth. We can see objects that have accelerated beyond our current Hubble volume because the light we see today was emitted when they were within it. Looking back over billions of years, these scientists are able to trace the evolution of our Universe in astonishing detail. Fractions of a second later, the fledgling Universe expanded exponentially during an incredibly brief period of time called inflation.
That may sound counterintuitive, but as long as H0 decreases at a slower rate than that at which the Universe’s expansion velocity is increasing, the overall movement of galaxies away from us still occurs at an accelerated pace. And at this moment in time, cosmologists believe that the Universe’s expansion will outpace the more modest growth of the Hubble volume. Some say it is due to the idea that expansion of space occurs faster the farther away from us, as seen in the good ‘ol bakin’ raisin dough model that has served us so well.
The Big Bang itself expanded much faster than the speed of light. But this only means that “nothing can go faster than light.” Since nothing is just empty space or vacuum, it can expand faster than light speed since no material object is breaking the light barrier. Therefore, empty space can certainly expand faster than light. A rendering of time dilation Alpha Centauri is technically 4.5 light-years away, but Wolfram Alpha won’t let me do that calculation, so I’ve set the value for 4. Traveling at 99.9c for 4 years means you’d experience a trip of about 2 weeks .
Just because you have signals that go faster than light does not imply you have causality violations. You get causality violations only if you ignore the existence of an arrow of time. The key point is that every space-like interval is backwards in time for some systems of inertial coordinates. So, if we stipulate that we can’t travel or signal backwards in time for any inertial coordinate system (effect can’t precede cause), it follows that superluminal travel and signaling are impossible.