Well after attending the 2019 UFO Symposium, as described in last week's blog post, I had to look up some more of the details of closed time like curves (CTC) and time travel. Now where better to begin that study than at the Hotel Irvine bar, since that was open at the end of the symposium.
|One convenient place to continue your physics study is the Hotel Irvine bar (Source: Palmia Observatory)|
Do the equations of general relativity really predict the possibility of time travel? Remember that one of the speakers at the Symposium conjectured that UFOs are really time travelers from the future. Well, yes, they sort of do in that solutions to the Einstein equations do allow for that possibility. We know that there is a strong connection between gravity and time and space and that gravity can distort time and space. We recall from Special Relativity how speed can affect time as illustrated by the Twin Paradox. Similarly, general relativity predicts that gravity can distort space and time also.
One of the solutions to the equations allows for worldlines or timelines to close back on themselves so that the future can come back and influence the past, as described in the Wikipedia text below.
|Closed timelike demonstrate time travel in general relativity (Source: Wikipedia, Closed Timelike Curves)|
These CTCs don't seem to come about near compact objects like neutron stars and black holes even though space and time are distorted near those objects. Of course, we can also say that the weak gravity of the Earth also affects space and time and these effects can be measured and agree with calculations in addition to just keeping our feet on the planet. Also the effects of rotating objects as small as the Earth can be measured as illustrated by the frame dragging measurements of the Gravity B satellite studies. But, when the black hole is rotating, then even more extreme additional time distortion effects and CTCs become possible.
As part of my physicist wannabe studies, I have gone over the Schwarzschild metric, which describes the spacetime around non-rotating black holes, stars and even planets. The modification to the Schwarzschild metric to account for rotation is called the Kerr metric and is illustrated as a 4x4 matrix below. Ok, ok, the matrix is maybe a little too much to spring on you without any warning, but it does start to show some of possible effects. Rotation of the black hole is introduced with the variable, a, while the mass is variable, m, and the radius is variable, r.. When a=0, the Kerr metric becomes identical with the Schwarzschild metric. You can see this right away that when a=0, then the off diagonal terms in the matrix goes to zero. For a>0, these off diagonal terms describe the possible CTC effects. As an aside, when I look at the matrix (below), it seems there is a typo in the matrix. The terms in row 2, column 1 and in row 1, column 2, both are missing the rotation parameter, a.
|Kerr metric shows effect of black hole rotation on spacetime (Source: Matt Visser, arXiv:0706.0622v3)|
You can get into all the details with just about any of the general relativity textbooks (Sean Carroll, Bernard Schutz, or Jim Hartle, for instance) if you want. Another introduction to the possibility of CTCs and how their true nature won't be known until a more complete theory of gravity is formed that includes the effects of quantum mechanics. If you want to stretch a bit and see a pretty good introduction to this connection, check out the YouTube video by Seth Lloyd, MIT, who is one of many trying to connect general relativity and quantum mechanics. Also the first 20 minutes of this video goes over some of the time travel stories in literature and some of the paradoxes involved, such as the Grandfather Paradox. It might turn out that when the quantum theory of gravity is more completely developed that some of these paradoxes might just not be possible at all.
He uses an example of CTCs, illustrated by the coffee cup handle in the slide screenshot below. Some region of extreme gravity and rotation causes the timeline, which normally just flows up in physics type diagrams, to become looped around and come back into the past and then return to the future.
|Seth Lloyd, MIT, explains potential connection between closed timelike curves and quantum gravity (Source: https://www.youtube.com/watch?v=yCQ_3qE6SmQ&app=desktop)|
|Gaia provided updated data for Artistic representation of Milky Way with bar (Source: The Cosmic Companion)|
Of course, it is hard to photograph the bar of the Milky Way, but consider this photograph of the spiral galaxy, NGC4394, which clearly shows arms and a central bar.
|Could these bizarre objects be dark stars? (Source: Katherine Freese tweet)|
Now as you know, I have been following Katherine Freese, U. of Michigan, for several years now, especially after first hearing her years ago now when she appeared at the speakers' podium with a feather boa. Hmm, she knew what she was talking about and did a great presentation and looked good too! This photo, apparently taken at the World Science Festival, reminded me of how she first appeared on stage.
|Katherine Freese, U of Michigan, with iconic feather boa (Source: World Science Festival)|
Ok, anyway, the tweet referenced a futurism.com article, which then referenced an Astronomy.com article and we were off on a discussion of how dark stars were likely to be the first stars to form after the big bang and how they could have grown to enormous size and been the seeds for the supermassive black holes that are observed today at the center of most galaxies.
We have mentioned this idea of dark stars before, which is what very likely occurred during the early universe, when dark matter and ordinary matter starts to collapse due to gravity. But, the difference with a dark star is that the collapse does not reach the point of high temperature and pressure sufficient to cause nuclear fusion, but instead the annihilation of dark matter particles provide the pressure to sort of counter balance the force of gravity. See the screenshot below.
|Dark stars generate energy by dark matter annihilation, not fusion (Roen Kelly, Astronomy.com)|
The difference in terms of stellar evolution is now such that the dark star can continue to grown in size and mass and does not experience the same limitations of size that occurs with stars with fusion which push much of the collapsing gas away from the proto star. So, the dark stars could grow to enormous size. The diagram taken from the Monthly Notice of the Royal Astronomer Society shows the conjectured development of dark stars around redshift of z=10 or so. This article by Cosmin Ilie and others including Katherine Freese.
|Dark Star formation rate as determined by redshift, z (Source: Ilie et al, MNRAS, 422, 2164-2186 2012))|
These stars would have been some of the very first stars to form in the universe after the big bang. In case you are wondering what time in the history of the universe a redshift of about z=10 was, the following chart helps to the calculation. We see that redshift of about 10 corresponds to a lookback time of about 13 billion years. So the stars formed less than a billion years after the big bang.
|Converting redshift, z, to look back time (Source: Rob Jeffries, astronomy.stackexchange.com)|
So how bright were these first dark stars and what was their spectrum of emission. Depending on the mass of the dark matter particle, and of course assuming that the dark matter particles were their own antiparticle, then the wavelengths of emitted radiation are shown below. Note the peak wavelength is sort of in the blue optical range.
|Calculated detection limit with JWST for light from Dark Stars (Source: Ilie et al, MNRAS, 422, 2164-2186 2012))|
Ok, so we can see that astronomers and theorists are planning ahead for the launch of JWST and how it hopefully can and will answer many of these questions about our cosmos, we can do our own little investigation. You will be happy to know that this Resident Astronomer went outside, in the hot sun, and verified that the sun was still there and very quiet and had no sunspots. Ok, that was expected, but let's see what we can find in the night sky. Jupiter is up and very bright. What can we see about Jupiter's moons? The prediction, as shown in this Sky Safari Pro screenshot, is the current location of the moons as observed from Earth. Notice how the moon, Ganymede, is passing in front of Jupiter at the time noted. An hour earlier and the moon would have been just at the left hand side of Jupiter, Hmm, I wanted to try to photograph the position of Ganymede just before it crossed Jupiter but the skies were really just not quite dark enough at that time.
|Sky Safari Pro screenshot shows position of Jupiter's moons (Source: Palmia Observatory)|
The image below, is taken with 300mm DSLR and 1/15 second exposure, which results in greatly overexposed Jupiter, but this helps make the three major moons of Jupiter visible. This photo was taken with a Canon T6 DSLR on a very flimsy lightweight tripod. It was in fact the same tripod that was used for our eclipse shots and Milky Way shots in Chile. But here, with the 300mm lens and tiny, tiny Jupiter, it was hard to focus the camera without wobbling the tripod all over the place. So,
Lesson Learned: Don't just grab the lightweight tripod available, but pick the right tripod for the photography session at hand!
Anyway, it seemed to turn out ok. The moons seemed to be where they were predicted to be! Even a student physicist wannabe can do some predictions and observations of the real world!
|Moons of Jupiter, 300mm DSLR, 1/15 second (Source: Palmia Observatory)|