May 2018 – Spinor Info

Comoving distance

May 292018

There is an excellent diagram accompanying an answer on StackExchange, and I’ve been meaning to copy it here, because I keep losing the address.

The diagram summarizes many measures of cosmic expansion in a nice, compact, but not necessarily easy-to-understand form:

So let me explain how to read this diagram. First of all, time is going from bottom to top. The thick horizontal black line represents the moment of now. Imagine this line moving upwards as time progresses.

The thick vertical black line is here. So the intersection of the two thick black lines in the middle is the here-and-now.

Distances are measured in terms of the comoving distance, which is basically telling you how far a distant object would be now, if you had a long measuring tape to measure its present-day location.

The area shaded red (marked “past light cone”) is all the events that happened in the universe that we could see, up to the moment of now. The boundary of this area is everything in this universe from which light is reaching us right now.

So just for fun, let us pick an object at a comoving distance of 30 gigalightyears (Gly). Look at the dotted vertical line corresponding to 30 Gly, halfway between the 20 and 40 marks (either side, doesn’t matter.) It intersects the boundary of the past light cone when the universe was roughly 700 million years old. Good, there were already young galaxies back then. If we were observing such a galaxy today, we’d be seeing it as it appeared when the universe was 700 million years old. Its light would have spent 13.1 billion years traveling before reaching our instruments.

Again look at the dotted vertical line at 30 Gly and extend it all the way to the “now” line. What does this tell you about this object? You can read the object’s redshift (z) off the diagram: its light is shifted down in frequency by a factor of about 9.

You can also read the object’s recession velocity, which is just a little over two times the vacuum speed of light. Yes… faster than light. This recession velocity is based on the rate of change of the scale factor, essentially the Hubble parameter times the comoving distance. The Doppler velocity that one would deduce from the object’s redshift yields a value less than the vacuum speed of light. (Curved spacetime is tricky; distances and speeds can be defined in various ways.)

Another thing about this diagram is that in addition to the past, it also sketches the future, taking into account the apparent accelerating expansion of the universe. Notice the light red shaded area marked “event horizon”. This area contains everything that we will be able to see at our present location, throughout the entire history of the universe, all the way to the infinite future. Things (events) outside this area will never be seen by us, will never influence us.

Note how the dotted line at 30 Gly intersects this boundary when the universe is about 5 billion years old. Yes, this means that we will only ever see the first less than 5 billion years of existence of a galaxy at a comoving distance of 30 Gly. Over time, light from this galaxy will be redshifted ever more, until it eventually appears to “freeze” and disappears from sight, never appearing to become older than 5 billion years.

Notice also how the dashed curves marking constant values of redshift bend inward, closer and closer to the “here” location as we approach the infinite future. This is a direct result of accelerating expansion: Things nearer and nearer to us will be caught up in the expansion, accelerating away from our location. Eventually this will stop, of course; cosmic acceleration will not rip apart structures that are gravitationally bound. But we will end up living in a true “island universe” in which nothing is seen at all beyond the largest gravitationally bound structure, the local group of galaxies. Fortunately that won’t happen anytime soon; we have many tens of billions of years until then.

Lastly, the particle horizon (blue lines) essentially marks the size of the visible part of the universe at any given time. Notice how the width of the interval marked by the intersection of the now line and the blue lines is identical to the width of the past light cone at the bottom of this diagram. Notice also how the blue lines correspond to infinite redshift.

As I said, this diagram is not an easy read but it is well worth studying.

Rooting for Andrea Horwath

Canada, Politics No Responses »

May 292018

And now I am rooting for Andrea Horwath.

No, I won’t be voting NDP in the upcoming Ontario election. I live in a strongly Liberal riding (it is said that if the Liberals win one seat in this election, it will be this one), and I am actually quite pleased with our MPP, Nathalie Des Rosiers. The NDP in this riding is a distant third in the polls.

But throughout the province, support for the Liberal Party collapsed, and populist Doug Ford, heading the Progressive Conservatives, seems poised to become the province’s next Premier.

The CBC’s Ontario Poll Tracker

Unless Andrea Horwath and the NDP can stop him.

To be sure, I don’t really like the NDP. I like some of their ideas, but on many things, they are too far to the left for me to feel comfortable. I fear that their policies will have a negative impact on the province: higher taxes, a more business hostile climate. I lived in Ontario a generation ago when Bob Rae led the last NDP government, and while it was no disaster, it was not too good either.

But we survived. And policy mistakes are one thing… ignorant alpha-male populism is in another league altogether.

So do I look at Horwath as the lesser of two evils? Not really. I don’t consider Horwath evil. At worst, the NDP are misguided. But they seem like reasonable folks, willing to listen to the facts. Which means that, more than likely, once they are in power, they will actually disappoint some of their most ardent followers as they moderate their views and adjust to the realities of everyday governing.

Ford, on the other hand, is likely to do far more damage. Reckless tax cuts combined with a march toward balanced budgets will lead to catastrophic cuts in public services, with damage likely lasting generations. OHIP, public transport, potholes, the energy infrastructure… all of that and much more are on the line. Then there are those campaign promises (such as new hospital beds) that have not been budgeted for, and in my opinion, will never be, as these are empty promises with no real intent to follow through, once elected.

In short, in Horwath I see a responsible leader committed to some leftist ideas that I am not unduly fond of. In Ford, I see a naked hunger for power, reckless populism, ignorance, irresponsibility.

So for the first time in my life, I am actually rooting for the NDP.

Thank you, Trupanion

Cats, Personal No Responses »

May 242018

For years now, we’ve been insuring our cats with Trupanion. We picked this insurer because they offered something we actually wanted: insurance for catastrophic expenses. (We don’t need an insurer to cover routine exams and vaccinations.)

We expected professional and courteous service from Trupanion, and that’s what we always received. Even when specific claims were denied, the explanation was always clear, unambiguous, and consistent with their written policies. We never had any complaints.

What we did not expect was this level of personalized care: this postcard.

The back side, not reproduced here, contains several hand-written offers of condolences from Trupanion employees on account of us losing our kitty Pipacs.

If their intent was to generate goodwill towards the company and view them as something more than just a faceless corporation, but rather, as a group of caring people, they certainly succeeded. Thank you. I have a feeling that we are going to remain your loyal customers for years to come.

Two-cat household

Cats, Personal No Responses »

May 112018

This was our not quite 12-year old kitten, Pipacs, just over an hour ago, less than fifteen minutes before he was euthanized.

It appears that we picked the right time as it was the end of the line for him anyway. His bladder was now blocked by the bone tumor that he has been battling with so bravely for the past three years, beating all odds (and using up all nine of his lives) in the past three months in particular. So quite likely, he would have died a much more painful death soon, perhaps within the next 24 hours.

We are now a two-cat household. Good-bye, Pipacska. It was a privilege to have you for the past ten and a half years.

Rise of the strongmen

Politics No Responses »

May 052018

In the late 1960s, early 1970s, Hollywood responded to social upheavals and perceived lawlessness by creating a series of renegade, vigilante cops, played by the likes of Charles Bronson or Clint Eastwood.

Today, perceived changes, threats to “us”, fear from “them”, seem to be bringing about another result: the rise of political strongmen around the world. This is the topic of a new article in TIME, also featured on the cover of their upcoming issue.

Pictured are Putin, Duterte of the Philippines, Orban of Hungary and Erdogan of Turkey. Not shown but extensively covered in the article are Xi Jinping, Egypt’s al-Sisi, and, of course, Donald Trump. Other strongmen are also mentioned.

What is this world coming to? Why are people who benefited the most from liberal democracy so keen to reject its values?

And in particular, why do we let the free Internet, one of the greatest inventions of liberal democracy, become a tool of state propaganda, a conduit for fake news? Why do we let the powers-that-be censor it or, worse yet, use it as a tool of oppression, as a means to build a totalitarian surveillance state?

Nor do I believe that Canada is immune. We are about to elect our very own strongman here in the province of Ontario. Doug Ford, brother to the scandal-plagued former mayor of Toronto, the late Rob Ford, is destined to become the next premier of this province. And who knows what will happen next… I am sure Doug Ford’s ambitions do not end with Queen’s Park.

In the end, it becomes a test of the strength of democratic institutions. In the US, Trump cannot ignore the courts, and may soon face a hostile legislature. In Canada, the Prime Minister may control Parliament, but the court system is strong and the press, too, remains independent. Even so, I’d rather not stress-test our democracy.