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Open Society University Network: Local and global issues

I ran across this plan for education that takes on the challenges facing us in 2020. We have had…See More
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We are a worldwide social network of freethinkers, atheists, agnostics and secular humanists.

“The aim of science is not to open the door to infinite wisdom, but to set a limit to infinite error.” -Bertolt Brecht

One of the most questions I get about the Universe — as a cosmologist — isn’t quite about the Big Bang in and of itself.

The expansion of the Universe in reverse; image source unknown.

The Big Bang is a remarkable idea, of course, that says that, based on the observations that the Universe is expanding and cooling today, it was hotter, denser, and physically smaller in the past. This gets particularly exciting when we extrapolate very far back in the history of the Universe.

Image credit: Addison Wesley.

At some point in the past, it was so hot that individual atoms would have been blasted apart by the radiation in the Universe. This means that — as we come forward in time past that point — there was a point when all the nuclei and electrons in the Universe became stable, neutral atoms for the first time.

Image credit: Pearson / Addison Wesley, retrieved from Jill Bechtold.

And before that, it was so hot that individual nuclei would have been blasted apart. But you might think that this means we can go back to arbitrarily high temperatures, densities, and arbitrarily small sizes. You might be tempted to go all the way to a point in time where spacetime collapses into a singularity, and where all the matter and energy in the Universe were present at a single point, of infinite temperature and infinite density.

Image retrieved from University of Arizona. And yes, longtime readers, this is wrong.

Indeed, this is one of the most tempting things to try.

But physically, it’s also wrong. (Lots of good scientists and science institutions goof this, too. See here, for example.) You see, we know that this isn’t what happened in the Universe’s past, because of what we observe when we look — in detail — at a snapshot of the Universe’s early history, from back when those neutral atoms formed for the first time.

Image credit: © 2005 Lawrence Berkeley National Laboratory Physics Division.

What we learn is that there’s an upper limit to how hot the Universe ever was in its early history. And although it may have been very hot — up to energies between 10^16 and 10^17 GeV, or about 10 trillion times hotter than the Large Hadron Collider can create — that’s actually quite small compared to the scale where we’d need to talk about singularities (which is another factor of ~1000 hotter), or where quantum gravity/string theory effects would become important.

We learn this from looking at the magnitude and distribution of the temperature fluctuations in the Universe imprinted in the snapshot alluded to earlier: in the Cosmic Microwave Background.

Image credit: NASA / WMAP science team; in a projection the way you'd see a globe.

(If you prefer a Mercator projection — the way you typically see a map of Earth — click here.)

What these fluctuations tell us is that, at some point in the very early history of the Universe — where we can be accurately described by this hot, dense, radiation-filled, Big Bang-esque model — the Universe was filled with small-magnitude temperature fluctuations (of a few parts in 100,000) on all measurable scales, where each scale is observed to have the same-magnitudepattern of fluctuations.

Image credit: Chiang Lung-Yih, doing a spherical harmonic decomposition of the CMB data.

As the Universe expands and cools, gravity works to pull the matter and energy in on itself, making overdensities bigger and underdensities smaller, while radiation pressure works to wash those fluctuations out. Normal matter (protons, neutrons, and electrons) interacts with photons and itself, creating “bouncy” features in this pattern of fluctuations, while dark matter can feel the radiation pressure and the gravitational tugs, but has no cross-section with either normal matter, photons or itself.

As a result, we learn what the different components of the Universe are.

Image credit: WMAP / NASA; Ned Wright of http://www.astro.ucla.edu/~wright/CMB-DT.html.

Two important observations that come out of this are that, as far as curvature goes, the Universe is spatially flat, rather than curved positively (like a sphere) or negatively (like the seat of a saddle), and that it has the same temperature properties in all directions, even in regions that have never had an opportunity to exchange information (or transmit photons) between one another.

Images credit: horizon problem (top) via astronomynotes.com; flatness problem (bottom) by Ned Wright's cosmology tutorial.

These two things could be remarkable, finely-tuned coincidences (or, you know, just how things happen to be, for no reason), but they could also be indicative of something preceding the Big Bang. In particular, a phase of exponential expansion of the Universe — known as cosmological inflation — would compel these two things to be true. But cosmic inflation also carries a number of predictions with it: that there would be no magnetic monopoles or other leftover relics from grand unified theories, that there would be no topological defects (e.g., cosmic stringsdomain walls) in the large scale structure of the Universe, and that the temperature fluctuations found in the Cosmic Microwave Background would follow a special type of distribution.

Image credit: Takeo Moroi & Tomo Takahashi, from http://arxiv.org/abs/hep-ph/0110096.

Not only do we find strong evidence against leftover relics and topological defects, but we measured this Harrison-Zel’dovich spectrum very accurately back in the 1990s, which was predicted by inflation more than a decade before it was observed! In other words, the spectrum of fluctuations is precisely consistent with what the theory of cosmological inflation predicted!

What inflation — our best scientific theory as to what preceded the Big Bang — tells us about “what came before the Big Bang” is, perhaps, very surprising.

Image generated by me, of the scale of the Universe (y-axis) vs. time (arbitrary units).

If the Universe was filled with matter (orange) or radiation (blue), as shown above, there must be a point at which these infinite temperatures and densities are reached, and thus, asingularity. But in the case of inflation (yellow), everything changes. First off, we don’tnecessarily have a singularity, and we definitely don’t have one at what we traditionally think of as “the moment of the Big Bang.” Instead, we have what’s known as a past-timelike-incomplete spacetime.

Image generated by me, of the scale of the Universe (y-axis) vs. time (arbitrary units).

In other words, we not only don’t know whether there was a singularity at some point in the very distant, pre-inflation past, or whether inflation was truly eternal, we don’t even know whether inflation occurred for less than a yoctosecond or more than the present age of the (post-Big Bang) Universe!

Our prospects for finding out, furthermore, are quite dim, as — by its very nature — practically every model of cosmic inflation wipes out any information about the Universe that existed prior to the last billionth-of-a-yoctosecond before inflation ended, and our Universe began.

Image credit: Cosmic Inflation by Don Dixon.

So, before the Universe was hot, dense, expanding, cooling, and filled with matter and antimatter? There was inflation, the phase of exponential expansion that stretched the Universe flat, made it the same average temperature in all directions, wiped out any ultra-massive relic particles and topological defects, created the temperature fluctuations that led to the large-scale structure of today’s Universe, and ended 13.7 billion years ago, setting up the Big Bang that gave rise to the observable Universe we know and love. If inflation lasted any longer than that last billionth-of-a-yoctosecond that affects our observable Universe and the laws of physics we know still hold, then we almost certainly live in a multiverse as well, where our observable Universe is just one Universe out of many.

Image credit: Me, illustrating how an inflating region of spacetime's exponential properties will create new spacetime more quickly than the dynamics that end inflation can create Big Bangs and matter/radiation-filled regions of our Universe!

But what came before that? We only have theoretical possibilities, with likely no data or information from that time contained within our observable Universe to guide us. We’ll keep searching for clues, but for right now, don’t believe the hype (and I’m looking at you, Steinhardt,Turok, and Greene, among others); keep them as possibilities if you fancy them, but that speculation is no replacement for the best that science has to offer right now!

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Replies to This Discussion

interesting

Interesting and so way beyond me.

Ethan writes:

First off, we don’tnecessarily have a singularity, and we definitely don’t have one at what we traditionally think of as “the moment of the Big Bang.” Instead, we have what’s known as a past-timelike-incomplete spacetime.

Curious, I clicked on the link:

Inflationary Spacetimes Are Incomplete in Past Directions
Received 5 October 2001; revised 24 January 2003; published 15 April 2003


Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating—or just expanding sufficiently fast—must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.
© 2003 The American Physical Society

 ...and it didn't do me any good =)

so way beyond me too! i read the whole of it, will come back to look at it sometime again

Is there a requirement for time at all before the BB and in the picoseconds after the event? 

Davy, I think this falls in the group of topics that you bookmark and look at again when you are fresh, with no alcohol in the system.

I know where you're coming from. 

Starts with a Bang is my favorite astronomy/physics blog. Ethan is just great at explaining stuff, even if it's just theoretical possibilities. I'll need to highlight this in my Fix one of these days!

Adriana, you must have a mind that is scientifically oriented. This stuff on what was before the BB would need to be read several times over just to get an inkling of singularity and inflation and so much else.

I know if i live long enough and keep it here, I will ask for a honorary science degree. 

Good Advice for Ethan for Grad Students and Ex Grad Students who still work and live as Grad Students - I won't mention any names!

The Secret to Writing Your Dissertation

“I spent every night until four in the morning on my dissertation, until I came to the point when I could not write another word, not even the next letter. I went to bed. Eight o’clock the next morning I was up writing again.” -Abraham Pais, physicist

You’ve been in graduate school for many years now, and you’ve come a long way. You’ve completed all of your coursework, formed your Ph.D. thesis committee, passed your preliminary/oral/qualifying examinations, and have done an awful lot of research along the way. There’s a glimmer of hope in your heart that maybe — just maybe — this will be your last year in graduate school.

Image credit: East Tennessee State University's Department of Mathematics and Statistics.

You’ve probably even gotten some papers published along the way, with a handful of them (if you’re lucky) with you as the lead author! But there’s one more task you need to perform before you’re ready to defend in front of your committee: you must write that dissertation!

While there are many guides on how to do that, many of them are either jokes…

Image credit: Flickr user chnrdu.

…or people grossly overstating the task in front of you. There are some very important things that go into a dissertation, but there are also some huge misconceptions about what a dissertation is supposed to be. What follows is my advice for anyone who’s reached that stage in their careers, on how to write a dissertation. (At least, as far as theoretical astrophysics goes, although I’m sure this is applicable to many other fields.)

Image credit: Jorge Cham of PhDcomics.

First off, here is a list of what your Ph.D. dissertation is not:

  1. It is not the definitive work on whatever your primary research topic is.
  2. It is not going to settle long-standing arguments in your field.
  3. It is not the most important piece of research or writing you’ll ever undertake.
  4. And finally, it is very likely not even a document that anyone outside of your committee (with the exception of a few good friends, and possibly your grandmother) will ever read.

Image credit: Peter Lubbers / Rocky Lubbers of http://runlaketahoe.blogspot.com/.

You must accept number 4 before you’re ready to write, otherwise you run the risk of becoming a perfectionist about a document that — seriously — practically no one is going to read!!!

What is a Ph.D. dissertation, then? Quite simply, it’s your way of proving to your committee that you are a competent scientist in your own right, capable of standing on your own two feet as a scientist, researcher, and academic. It is where you demonstrate the following:

  1. That you are capable of making original, valuable contributions in an active field of research.
  2. That you are aware of and informed about the broad landscape of your field, the background and currently competing work being done on your specific sub-field, and that your professional opinions are well-informed and backed up by your knowledge and legitimate reasoning.
  3. That the body of work you submit in your dissertation is comprehensive enough to merit a Ph.D.
  4. And, perhaps most importantly, that you are ready to go off and continue your research (if you so choose) without the guidance of your mentor(s).

The first, second, and fourth of these are things you must convince your committee of during your defense; the third, however, is something that must speak for itself within your written dissertation.

Image credit: Dalhousie University.

And that’s why the most important thing you can do is to just crank it out. What you may not realize is that 75% of your dissertation is already done, you just need to take advantage of it!

What do I mean? I mean don’t reinvent the wheel!

Let me explain.

Image credit: Gnarlycraig from Wikimedia Commons.

You’ve already written/published some papers, and you’re very likely at least part-way through some more projects that may or may not be completed by time you’re ready to graduate. Well, guess what?

That, right there, is most of your dissertation!

Let’s say you’ll have four papers completed by time you graduate, and another two projects that won’t be completed by graduation. Those four papers that will be finished are chapters 2-5 of your dissertation, and those two unfinished projects are Appendix A and Appendix B.

That’s your work that you created, so be proud of it and don’t re-invent it!

Image credit: Plymouth State University.

Get your University’s unique template, learn how to format your work properly within it, and marvel at how close you are! Here’s what you have to actually write, now, in order to graduate:

  1. Your title. This is important, and it needs to tie together all of the (likely) very different papers and topics you wrote on into one unified idea. “Topics in Physics” won’t cut it here, but “Cosmological Perturbations and Their Effects on the Universe: From ...” will do just fine.
  2. Your abstract. This is just two or three sentences introducing your field, followed by one sentence about each of your papers, and concluded with one or two sentences about future work.
  3. Your introductory chapter. This was — for me, at least — the hardest part. You need to put all of your original work in the context of your broad and specific fields of research. This means giving a broad (and well-referenced) overview of your sub-field, how it fits into the broad context of your field and why it’s important, and how your specific research has addressed some of these particular issues. It should be seamless to transition from the end of this chapter into your (only slightly tweaked) “middle chapters” of your dissertation.
  4. Your final chapter. This is a summary of what you’ve accomplished as well as a detailed discussion of what challenges remain in your field, with some detailed plans for future directions that your work is going to take you. This is where you include references to current, active work being done in your particular sub-fields of interest, and where you set up the motivation for your appendices.

The rest — acknowledgments, dedication, references, etc. — take practically no time or effort. But you must remember that the goal of your dissertation is not to change the world; it’s to finish it and to do a good enough job to graduate!

Image credit: NYU's Leonard N. Stern School of Business.

Once your written dissertation has been okayed by your committee, you’ll still have to defend, but unless your advisor is no good, you won’t be allowed to defend unless everyone knows you’re prepared and ready to pass. You’ll make your dissertation revisions, graduate, and it’s up to you whether you want to participate in the graduation ceremony or not; either way you get your diploma in the mail a few months later.

This isn’t the only way to write a dissertation, for what it’s worth. It’s just the smartest way to do it, and so that’s why it’s my advice. (It’s also advice that — for some reason — is rarely given by others.) Now you know the secret to writing a Ph.D. dissertation, so finish that thing up and graduate already!

doone, this reminds me of what we did in architecture school. we would do the most work of the semester in the last 3 weeks of the semester. I think in retrospect, a semester should just have lasted those number of weeks we would still do all the required work.

When i eventually get to a masters or PhD dissertation, i will remember this advise. 

Starts with a Bang has over 73 Blog Posts on the Big Bang, here is a good chance to get a head start on your Thesis on the Big Bang

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