Figure 1 – Gravitational lensing as imaged by the Hubble Space Telescope and in the public domain because it was taken by a government agency, NASA. Here a Luminous Red Galaxy is lensing the light from a blue galaxy behind it.

Apologies for disappearing. I have been visiting Bortle 4.7 skies! But I did want to pick up where we left off about reference frames and explore how this connects with Alice and the Rabbit hole.

Remember being on a train and not being able to figure out whether the train or the station is moving. This is the case of trains with constant speed or velocity. That is nothing is accelerating, and such is the realm of what is referred to as special relativity. We, well Einstein actually, recognized, perhaps intuitively, that there is no absolute rest frame which doesn’t move compared to all other possible reference frames. For this to be so, it must be that the laws of physics are the same in all reference frames. One particular law was outstanding, the law for propagating an electromagnetic wave. Fundamental to that law is the fact, verified by the famous Michaelson and Morley Experiment. that the speed of light must be the same in all reference frames. This conclusion leads to some mighty strange or counter-intuitive things;

1. If you measure a distance in one frame, you get a different distance in another – so called Lorentz contraction.
2. If you measure a time interval in one frame, it is different in another – the so called twin paradox.
3. If two events are simultaneous in one frame, they may not be simultaneous in another.

As strange as these may seem they have none-the-less been demonstrated experimentally! As Hamlet famously said, “There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.” These are the ghosts that we must deal with.

Well. I kind of meant to recount not further confound. So just remember that in a world where trains move at different speeds, if you measure the speed of light it will always be the same namely 299,792,458 m/sec if you’re measuring in a vacuum. “I try to be precise, Captain,” said Mr. Spock. Physicists like Vulcans are pesky about being precise.

Moving on! We were told as undergraduates that the situation, where reference frames are accelerating relative to each other, is hard conceptually. Well, really not so! And here is where we return to Alice. Alice falling down the rabbit hole is reminiscent of a overwrought trope in relativity theory, namely of you or often a little Einstein figure inside a rocket ship moving through space, or not, since everything is relative. So here’s Alice in the rocket ready to take off. When she was in Wonderland she had left her kitten Dinah at home but worried whether she was being properly cared for. So this time Dinah is with her in the rocket. Alice perhaps maliciously, but definitely as a true Victorian experimentalist, keeps dropping Dinah upside down pondering the issue of why she always lands on her feet. But that part is a different story. The important point here is that Dinah keeps accelerating towards the floor at 9.8 m/sec squared under gravity. Alice yawns widely, ignoring the fact that it is impolite for Victorian ladies to yawn without covering their mouths. Bored she looks out the window and is surprised to discover that she is no longer on the launch pad but accelerating through space at 9.8 m/sec squared. Well, this certainly puts a different light on it!

This experiment with poor little Dinah, who has now gone off hunting for mice, illustrates an important point. Everything is relative! You nor Alice can distinguish between being at rest on the Earth and subject to a gravitational force with acceleration 9.8 m/sec squared in a rocket moving through space and subject to inertia at 9.8 m/sec squared.

Now here’s the important point or pointer. Alice pulls out of her pocket her handy-dandy, anachronistic, laser pointer and fires it at the opposite wall of the rocket. Since the rocket is accelerating upwards through space at 9.8 m/sec squared the light beam hits the wall along a ballistic path slightly lower than the point on the wall directly across from Alice. Remember that light is moving at a finite speed of 299,792,458 m/sec. No biggie there. But remember that Alice can’t really distinguish between acceleration due to inertia of gravity. All is relative and it becomes a matter of point of view. Soooooo it must be that despite the fact that photons or light particles have no mass that they are bent by gravity. Wow, that is really the fundamental conclusion of general relativity.

This bending of light was triumphantly demonstrated by Arthur Eddington, Frank Watson Dyson, and their collaborators during the total solar eclipse on May 29, 1919. The Sun measurably bent the light path of stars behind it. Indeed, if a star is behind the Sun it can be bent by the Sun’s gravitational force to produce multiple images of the star in front of the sun during an eclipse. Reading about this as an undergraduate I was in awe.

But now we have something more amazing, images from the Hubble Space Telescope and now the Jack Webb Space Telescope. Figure 1 shows one of the best and most impressive of these. Here a Luminous Red Galaxy is lensing the light from a blue galaxy behind it. Here the alignment of the two galaxies is so perfect that a so-called Einstein’s Ring rather than a set of multi image points is produced.

Dinah has now tired of hunting and is curled up on Alice’s lap giving herself a bath and pondering whether an observer outside the rocket would really know if she was alive or dead.