Author Topic: Alice's MSc Astrophysics reports  (Read 37404 times)

zookeeperKevin

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Re: Alice's MSc Astrophysics reports
« Reply #30 on: October 05, 2011, 07:06:08 pm »
Quote
Citations are when another author writes a paper and references your paper. The first Galaxy Zoo paper has over 100 citations!  Of course, getting 100 citations might mean it's a fabulous paper that others are building their work on - or it might be that 100 people have pointed out why your paper is wrong. I wonder how many citations that faster-than-light-neutrino paper has?

Yep. Citations are really a measure of "interest" not "correctness". Lots of "wrong" and controversial papers are highly cited because they created a discussion in the community.

Like Galaxy Zoo threads ;D ;D ;D

That's actually a very good analogy!

klmasters

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Re: Alice's MSc Astrophysics reports
« Reply #31 on: October 05, 2011, 07:45:20 pm »
Yes very good analogy! And a reminder that scientists are people too!

I'll try to follow a bit, but I'll have a hard time keeping up at the moment. No excuses other than the usual! ;)

 Karen.

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #32 on: October 06, 2011, 11:06:37 am »
Well I just handed in my first homework 15 minutes before the deadline :D

My flicking through BBC science articles led me to this paper, about molecular oxygen in space - which is really interesting. But the very best thing is that through this paper I discovered the SPLATALOGUE. I laughed so much I had to just stop working and go to bed. (I think cracking up laughing that much was a sign I needed to go to sleep??)

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #33 on: October 06, 2011, 10:28:12 pm »
Whew. Those lectures last well into the evening. And then getting home takes quite a while, and I'm always absolutely starving and need to eat, so it's really very late by the time I get onto the computer on a Tuesday or Thursday night :D

That assignment I was in a flap about in the last post? Turned out I'd done masses more work than most people had. And what was especially entertaining was that the lecturer had deliberately kept the assignment quite vague, so we'd all interpreted it fairly differently. Some people thought they had to write a science report based on a media article plus its paper. Some thought they had to describe how they went about finding the science paper. I thought we were supposed to summarise both the media report and the background material and write a critique of the media report. Anyway, it was a lot of fun, and it was worth every second of it to find out that there really is such a thing as a splatalogue. :D

paulrogers

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Re: Alice's MSc Astrophysics reports
« Reply #34 on: October 07, 2011, 06:00:06 pm »
By the way, Paul has asked me to keep my separate lecture topics in separate threads. Personally I wouldn't have chosen to do this as the lectures are only twice a week, there won't always be that much to comment on and it will look really big-headed taking up that much of the library. However, a majority of you may agree with Paul. (I'm flattered that anyone would read my notes at all.) So please let me know your preference - I can always change things later by merging or splitting a topic.

I expect by far the greater part of what you will post, and the comments, will be the actual texts.  Whether those are in one thread or several, the total content will be roughly the same, won't it?

Hey, why wouldn't we follow your notes?  It's like "auditing" the class and having someone else doing all the legwork for us!  ;D ;D ;D ;D ;D

paulrogers

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Re: Alice's MSc Astrophysics reports
« Reply #35 on: October 07, 2011, 06:23:19 pm »
Research, Jim (the professor) said, is furthering the understanding of some field - it usually builds on what has gone before. We need to know the background, or we'll make all the mistakes people before us have made. Literature is usually vast, so we need to get good at selection before reading it. For example, research projects usually start with this following, say, a calculation that hasn't been tried yet. In literature review we need to be a bit critical of others' work by checking it occasionally, even if it's just checking their maths. That's the way mistakes are found.

Allow me to suggest that scientific "mistakes" is a much broader issue, more causes and many examples where the label "mistake" was a mistake.  As just one example, look at Wegener's work on matching not only the coastlines of South America and Africa, but including matching up mountain ranges and rock types.  It was widely and generally decried as a "mistake" because "no known force or geologic process can move the continents".

Science relies on the concept of falsifiability.  One Australian black swan destroys centuries of evidence that all swans are white.  That means everything "Science knows" is provisional.  I'm often pointing out that "truth" and "facts" are less frequently observed in Science than in faith.  "Mistakes" aren't always.  It's a good thing if we can sometimes tear the edifice Science has constructed all down, and reconstruct it all given all the new information, to see if we get the same structure.  But alas, that's hardly ever done. :'(

[Edit: spelling corrections.  My mistake correction was a mistake. ;) ]
« Last Edit: October 07, 2011, 06:30:39 pm by paulrogers »

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #36 on: October 11, 2011, 01:20:59 am »
Cosmology lecture 2: the Cosmological Equations

Sorry for leaving last week's lecture notes until this week :D

Well we started off by getting a 60 page handout which is not available online - here is just some of it!

There is not much I can really say about the cosmological equations at this stage. Mathematics not being my strong point, I am not going to try to explain the equations because I am not ready. Clearly they're going to need a lot of work. I will just reproduce the interesting snippets from my notebook. (In fact, if my maths was stronger, I would have applied to do this course long ago. I reasoned myself into applying by telling myself again and again that public speaking used to be one of the things I'm worst at, and now it's one of the things I'm best at, so hopefully I can do the same for maths with enough work . . .)

None of the cosmological equations are simple to solve at local levels. But at the level of the Cosmological Principle - at a scale of 100 Mpc - the Universe is homogenous, so we can neglect density gradients and indeed all gradients. At that point, things become much simpler.

In the past, we had the perfect cosmological principle. That added a fourth dimension to the homogeneity of the Universe: time. In other words, the Universe would be the same no matter where we looked and when we look (past, present, future). Now we know the Universe is expanding, we have had to jettison this one.

100 Mpc is a huge area. But it is still only a tiny, tiny fraction of the observable Universe, whose radius is roughly 6 gigaparsecs! So we can still do good statistics with the Universe using a "cell" of 100 Mpc.

We started by looking at equations involving spheres and potential energy - taking into account radius, mass, etc. A sphere acts on such and such a mass with gravitational energy. This is very "primitive" - we get very different results by including all the spheres whose gravity is felt, etc.

A thought experiment: Imagine the Universe is infinite. Start integrating gravitational points across the whole thing. For example, right and left. If you add up everything in every direction, ultimately we get the same force acting on us from all directions, so we get stretched equally everywhere. :D To do any simple calculations about a body on a sphere we need to assume there are no net forces from outside.

Someone once asked Einstein how he understood an infinite Universe. Was it a sphere with a centre? The centre is everywhere and nowhere.

Incidentally, at this point, we were told, there was no one more skeptical of Newtonian theories (I take it this meant Newtonian gravity) than Newton himself. (This is not the first time I have heard that a scientist didn't believe his own answer.) He found a Newtonian universe unsatisfactory. One of his laws states that force changes with distance, which made him unhappy, but he knew of nothing better.

Einstein's universe changed this a lot, as I expect most of you know. Newton assumed absolutes of space and time. He separated them. Einstein realised you couldn't do that: if you separate space from time, you get different speeds of light. For example, half of Earth's year would see light coming from such and such a direction as a different speed from the other half of the year. This effect was looked for and never found. We can now measure the speed of light to a 10-12 accuracy.

We heard a lot about conservation of energy (kinetic and potential) - I think this had to do with the Friedmann equations - but let's put it this way, things were going too fast for me to write anything comprehensible here. :-[ But anyway, even while a sphere (eg the Universe) expands, the law of conservation of energy applies.

The internal energy of an object is its pressure (the opposite of pressure is tension). Thermodynamics comes into this. If the Universe has the same temperature all over (to a 100 Mpc scale), there should be no heat transfer. Heat transfer occurs when there is a gradient. The energy inside a volume is, you guessed it, E=mc2 - can't get away from relativity! We were told to imagine the second law of thermodynamics as a consequence of relativity.

By this time the lecturer must have noticed we were sitting there looking a bit stunned (I certainly was). He asked us if we knew how Einstein had arrived at E=mc2. Well, he said, he had a look at the blackboard and he wrote E =ma2. That didn't look right. So he tried E=mb2 . . .

Then it got serious again and we were informed that the scale factor describes the Universe as a whole, so we need . . . . another equation! (We were going through the equations but as I have said I am not writing any of them out, because I can't yet explain them. But it's the conservation equation - 2.16 on the handout if you want to look.)

When starting from the first law of thermodynamics, we get the conservation equation. Scale factor, pressure, and density are all relevant. If we can't solve one equation from two variables, can we solve two equations from three variables? Not just like that (apparently) - but we know what to do now: we need an equation of state, which relates pressure and temperature.

Now we can start looking at what's in the Universe: what are their pressure, temperature, density etc? Cosmic streams, black holes, dust, dark matter, plasmas . . . all these things have different properties.

Dust is very simple: the pressure is 0. If we have a Universe filled with dust, the pressure is negligible. Structure and stability can form in dust. (We get equation 2.19 for that. I am also wondering what this was about only 10 equations :P)

In dark energy, we were looking at a constant called gamma which won't as far as I know paste here and which is not quite the same as pressure . . . but anyway, dark energy seems to have negative pressure. Anything that makes a certain part of an equation - pressure and gamma - end up negative will be dark energy, and that's what makes whatever it is unique.

In this phase transition, substances are interacting. We can neglect this to give each substance its own equation of state.

We can differentiate the Friedmann equation with respect to time.

Acceleration of the Universe is proportional to the scale factor.

Starting from Newtonian law, we have now taken conservation of energy into account, and also found Newtonian law neglects pressure. Integration still obtains the Friedmann equations, and makes pressure appear to disappear. For the record, I have not the faintest idea as yet what this means. "It is cheating," we were told, "but very clever cheating, because it obtains something very useful."

If the pressure is negative but the density is positive (and of course we cannot have negative density . . . I wonder what the density of a black hole is?), this is called tension. It is a commonplace thing, for example surface tension on water which allows insects to skip around on a pond. Pressure is proportional to kinetic energy, including heat, a collision, etc. (Van der Waals forces are important here.)

On the border between energy and dark energy are Cosmic Strings. These cause zero acceleration of the expansion of the Universe.



All in all, I am exceedingly confused, and think I will have to work through those equations quite a few times - which will be hard as I don't even have any values to put into them. Oh well. Fortunately I am not the only one who is confused, even the maths graduates looked how I felt . . . and besides, why go on a course where you already understand everything?

zookeeperChris

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Re: Alice's MSc Astrophysics reports
« Reply #37 on: October 11, 2011, 09:22:06 am »
Hiya

They're really dropping you in the deep end, aren't they? There's a really very nice description of much of the territory that you're covering in Longair's 'Galaxy Formation' book which you might see if the library has. I seem to remember that saving my life a few times...

Chris

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #38 on: October 11, 2011, 01:02:11 pm »
Well do you know I just ordered my own copy of his "History of Cosmology" that you once recommended to me, Chris, and which I was sad to give back to the local library - I will go and sniff out that book, since I was going to check out the library anyway. There's a Costa Coffee in it and all :D

Paul, I love your reminder about the black swans (I once spent a summer teaching in Dawlish, one of the places where black swans live!). The lecturer was talking about mistakes that are made repeatedly by person after person, because these people are ill-prepared - those are best avoided. But the "mistake" you describe - as in a piece of knowledge honestly brought about that is later demolished and then rebuilt - that I would not call a mistake, but someone doing their best ;D

stellar190

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Re: Alice's MSc Astrophysics reports
« Reply #39 on: October 11, 2011, 01:55:25 pm »
I love these reports! ;D ;D ;D Some of it is relevent to my course too 8) Though obviously my course is *much* less advanced :D
« Last Edit: October 11, 2011, 01:58:42 pm by stellar190 »

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #40 on: October 11, 2011, 02:18:37 pm »
A friend on the course (who I am really hoping is going to come to the forum ;D) tells me the maths is only around A level standard. So I hope it doesn't go up to postgraduate level too soon! :o Actually, the equations themselves are pretty straightforward, it's just working out what means what in them and what on earth to actually do with them (not to mention why they are what they are) that is tricky :D

Glad you love the reports! I am sure I have made errors here and there, and I know I have written things that make no sense at all :D So I hope nobody is looking at these notes for Ultimate Scientific Truth or anything ;D

waveney

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Re: Alice's MSc Astrophysics reports
« Reply #41 on: October 11, 2011, 02:36:22 pm »
I have found in mine none of the maths was much beyond what I did for A level (I did double maths and Physics), just that it was a very LOOONNNNNGGGGGG time ago and much has escaped.

Calculus - only at what I did at A level (if that) but the hardest bit to get back into my brain and I have done a little since University.

Matracies - I didn't do these at A level, but nothing more than first term at University level.

Vectors - Less demanding than what I did at A level (Largely forgotten too)
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stellar190

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Re: Alice's MSc Astrophysics reports
« Reply #42 on: October 11, 2011, 02:39:13 pm »
There's hope for me then :D :D :D

Alice

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Re: Alice's MSc Astrophysics reports
« Reply #43 on: October 11, 2011, 02:40:14 pm »
And me :D

One of the people at the AAS conference, when urging me to do a PhD, said: "Maths? Oh come on, I don't use any maths in my work." ;D

(Although I am sure most astronomy contains some . . .)

JohnF

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Re: Alice's MSc Astrophysics reports
« Reply #44 on: October 11, 2011, 03:08:10 pm »
Probably need to know how to derive an equation to a graph, that was 'O' Level standard.

Equation of a circle, or a parbola.

Matrix arithmetic that was fun, though in derviving the Queen's move on a chessboard for a computer class project, I used an equation, should have used a matrix.

Vectors - forces on an object, might need to know.

Used to enjoy in using Pythagoras Theorem, to dervive other equations in 'O' level.
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