Archive for March, 2015

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Why the Big Bang wasn’t as loud as you think…

Posted in The Universe and Stuff with tags , , , , , on March 31, 2015 by telescoper

So how loud was the Big Bang?

I’ve posted on this before but a comment posted today reminded me that perhaps I should recycle it and update it as it relates to the cosmic microwave background, which is what I work on on the rare occasions on which I get to do anything interesting.

As you probably know the Big Bang theory involves the assumption that the entire Universe – not only the matter and energy but also space-time itself – had its origins in a single event a finite time in the past and it has been expanding ever since. The earliest mathematical models of what we now call the  Big Bang were derived independently by Alexander Friedman and George Lemaître in the 1920s. The term “Big Bang” was later coined by Fred Hoyle as a derogatory description of an idea he couldn’t stomach, but the phrase caught on. Strictly speaking, though, the Big Bang was a misnomer.

Friedman and Lemaître had made mathematical models of universes that obeyed the Cosmological Principle, i.e. in which the matter was distributed in a completely uniform manner throughout space. Sound consists of oscillating fluctuations in the pressure and density of the medium through which it travels. These are longitudinal “acoustic” waves that involve successive compressions and rarefactions of matter, in other words departures from the purely homogeneous state required by the Cosmological Principle. The Friedman-Lemaitre models contained no sound waves so they did not really describe a Big Bang at all, let alone how loud it was.

However, as I have blogged about before, newer versions of the Big Bang theory do contain a mechanism for generating sound waves in the early Universe and, even more importantly, these waves have now been detected and their properties measured.

Planck_CMB

The above image shows the variations in temperature of the cosmic microwave background as charted by the Planck Satellite. The average temperature of the sky is about 2.73 K but there are variations across the sky that have an rms value of about 0.08 milliKelvin. This corresponds to a fractional variation of a few parts in a hundred thousand relative to the mean temperature. It doesn’t sound like much, but this is evidence for the existence of primordial acoustic waves and therefore of a Big Bang with a genuine “Bang” to it.

A full description of what causes these temperature fluctuations would be very complicated but, roughly speaking, the variation in temperature you corresponds directly to variations in density and pressure arising from sound waves.

So how loud was it?

The waves we are dealing with have wavelengths up to about 200,000 light years and the human ear can only actually hear sound waves with wavelengths up to about 17 metres. In any case the Universe was far too hot and dense for there to have been anyone around listening to the cacophony at the time. In some sense, therefore, it wouldn’t have been loud at all because our ears can’t have heard anything.

Setting aside these rather pedantic objections – I’m never one to allow dull realism to get in the way of a good story- we can get a reasonable value for the loudness in terms of the familiar language of decibels. This defines the level of sound (L) logarithmically in terms of the rms pressure level of the sound wave Prms relative to some reference pressure level Pref

L=20 log10[Prms/Pref].

(the 20 appears because of the fact that the energy carried goes as the square of the amplitude of the wave; in terms of energy there would be a factor 10).

There is no absolute scale for loudness because this expression involves the specification of the reference pressure. We have to set this level by analogy with everyday experience. For sound waves in air this is taken to be about 20 microPascals, or about 2×10-10 times the ambient atmospheric air pressure which is about 100,000 Pa.  This reference is chosen because the limit of audibility for most people corresponds to pressure variations of this order and these consequently have L=0 dB. It seems reasonable to set the reference pressure of the early Universe to be about the same fraction of the ambient pressure then, i.e.

Pref~2×10-10 Pamb.

The physics of how primordial variations in pressure translate into observed fluctuations in the CMB temperature is quite complicated, because the primordial universe consists of a plasma rather than air. Moreover, the actual sound of the Big Bang contains a mixture of wavelengths with slightly different amplitudes. In fact here is the spectrum, showing a distinctive signature that looks, at least in this representation, like a fundamental tone and a series of harmonics…

Planck_power_spectrum_orig

 

If you take into account all this structure it all gets a bit messy, but it’s quite easy to get a rough but reasonable estimate by ignoring all these complications. We simply take the rms pressure variation to be the same fraction of ambient pressure as the averaged temperature variation are compared to the average CMB temperature,  i.e.

Prms~ a few ×10-5Pamb.

If we do this, scaling both pressures in logarithm in the equation in proportion to the ambient pressure, the ambient pressure cancels out in the ratio, which turns out to be a few times 10-5. With our definition of the decibel level we find that waves of this amplitude, i.e. corresponding to variations of one part in a hundred thousand of the reference level, give roughly L=100dB while part in ten thousand gives about L=120dB. The sound of the Big Bang therefore peaks at levels just a bit less than 120 dB.

cooler_decibel_chart

As you can see in the Figure above, this is close to the threshold of pain,  but it’s perhaps not as loud as you might have guessed in response to the initial question. Modern popular beat combos often play their dreadful rock music much louder than the Big Bang….

A useful yardstick is the amplitude  at which the fluctuations in pressure are comparable to the mean pressure. This would give a factor of about 1010 in the logarithm and is pretty much the limit that sound waves can propagate without distortion. These would have L≈190 dB. It is estimated that the 1883 Krakatoa eruption produced a sound level of about 180 dB at a range of 100 miles. By comparison the Big Bang was little more than a whimper.

PS. If you would like to read more about the actual sound of the Big Bang, have a look at John Cramer’s webpages. You can also download simulations of the actual sound. If you listen to them you will hear that it’s more of  a “Roar” than a “Bang” because the sound waves don’t actually originate at a single well-defined event but are excited incoherently all over the Universe.

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Found in Translation…

Posted in Biographical, Books, Books, Talks and Reviews with tags on March 30, 2015 by telescoper

A nice surprise was waiting for me when I arrived at work this morning in the form of a parcel from Oxford University Press containing six copies of the new Arabic edition of my book  Cosmology: A Very Short Introduction. I think I’ve put them the right way up. I was a bit confused because they open the opposite way to books in English, as arabic is read from right to left rather than from left to right.

VSI-Arabic

Anyway, although I can’t read Arabic it’s nice to have these to put with the other foreign editions, including these. I still can’t remember whether the first one is Japanese or Korean…

vsi_6

vsi_2

vsi_3

Vsi_5

vsi_4

…still, it’s interesting to see how they’ve chosen different covers for the different translations, and at least I know what my name looks like in Russian Bulgarian!

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Praise, by R.S. Thomas

Posted in Poetry, The Universe and Stuff with tags , , , on March 29, 2015 by telescoper

Today is Palm Sunday, the start of what Christians call “Holy Week”, which culiminates in Easter. It’s also the birthday of the great Welsh poet R.S. Thomas, who was born on this day in 1913. Thomas spent much of his life as an Anglican priest. I’m not a Christian but I am drawn to the religious verse of R.S. Thomas not only for its directness and lack of artifice but also the honesty with which he addresses the problems his faith sets him. There are many atheists who think religion is some kind of soft option for those who can’t cope with life in an unfriendly universe, but reading R.S. Thomas, whose faith was neither cosy nor comfortable, led me to realise that is very far from the case. I recommend him as an antidote to the simple-minded antagonism of people like Richard Dawkins. There are questions that science alone will never answer, so we should respect people who search for a truth we ourselves cannot understand.

And whether or not it is clear to you, no doubt the universe is unfolding as it should. Therefore be at peace with God, whatever you conceive Him to be.

I will be offline for the Easter holiday so I thought I’d post a poem that I find appropriate to the time of year. You can read it as Praise for God, or for Nature, or for both. I don’t think it matters.

I praise you because
you are artist and scientist
in one. When I am somewhat
fearful of your power,
your ability to work miracles
with a set-square, I hear
you murmuring to yourself
in a notation Beethoven
dreamed of but never achieved.
You run off your scales of
rain water and sea water, play
the chords of the morning
and evening light, sculpture
with shadow, join together leaf
by leaf, when spring
comes, the stanzas of
an immense poem. You speak
all languages and none,
answering our most complex
prayers with the simplicity
of a flower, confronting
us, when we would domesticate you
to our uses, with the rioting
viruses under our lens.

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Nature or Degree

Posted in Mental Health with tags , on March 28, 2015 by telescoper

A thoughtful post to follow on from yesterday’s reaction to the GermanWings tragedy…

Mental Health Cop

It was the timing and tone of yesterday’s newspaper headlines that crossed the line for me: not any of discussion about mental health and airline safety. Of course, occupational health and fitness standards for pilots should be rigorous and we heard yesterday about annual testing, psychological testing, etc., etc.. By now, it may be easy to forget that when papers went to press on Thursday night, we still knew comparatively little about the pilot of the doomed flight. We certainly did not know that he appears to have ripped up sick notes that were relevant to the day of the crash or what kind of condition they related to – we still don’t, as the German police have not confirmed it. Whilst we did have suggestion that he had experience of depression and ‘burnout’ – whatever that means – we don’t know the nature or degree of this, do we?

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It’s Time to Change: Don’t Demonize Depression!

Posted in Mental Health with tags , , , , , on March 27, 2015 by telescoper

Like everyone else I was shocked and saddened on Tuesday to hear of the crash of an Airbus 320 (GermanWings Flight 4U 9525 from Barcelona to Dusseldorf)  in the French Alps.  That initial reaction turned to consternation and confusion when it appeared that flying conditions were good and no “Mayday” signal was sent for the eight minutes it steadily lost altitude until it hit the mountains., and then to complete incomprehension yesterday as evidence emerged that the crash, which resulted in the deaths of 150 people, appeared to have been the result of deliberate action by the co-pilot, Andreas Lubitz.  It seems that the co-pilot waited for the pilot to leave the cockpit to use the lavatory, then locked the door and proceeded to put the plane on a descending trajectory designed to take his own life along with everyone else on board. The horror of these events is beyond imagining. It’s also beyond imagining what could have possessed Andreas Lubitz to do such a terrible thing, for this was an act of mass murder.

Although it seems a paltry gesture, I’d like to take the opportunity to express by deepest condolences to the families, friends and loved ones of everyone who lost their life on that day, including Andreas Lubitz whose family must be experiencing pain on a scale the rest of us are completely unable to contemplate.

I’m not going to speculate at all about what drove this man to behave the way he did. I’m not qualified to comment and it would obviously not be helpful to anyone for me to do so.

That has not stopped the gutter press, however, who have seized upon the fact that Andreas Lubitz had a history of depressive illness to sell copies of their rags by labelling him “a madman” and splashing lurid details about his private life. A Daily Mail article (to which I refuse to link) clearly implies that anyone who has ever suffered from depression is potentially a psychopathic killer. Not for the first time, I am ashamed that people exist with so sensitivity that they could think this sort of journalism could ever be justified.

What this tragedy says to me is that only a better understanding of mental illness will help prevent similar things happening in future and that will not happen if the media continue to demonize those who suffer from depression and/or other mental health problems because the stigma that causes makes it so difficult to seek treatment. I know this for a fact. It is difficult enough to ask for help, even without  headlines screaming in your face from the front page of the Daily Fail or the Sun or even the Daily Telegraph.

I agree completely with Professor Sir Simon Wessely, President of the Royal College of Psychiatrists who is quoted in today’s Guardian as

The loss of the GermanWings Airbus is a ghastly horror. Until the facts are established, we should be careful not to rush judgements. Should it be the case that one pilot had a history of depression, we must bear in mind that so do several million people in this country.

It is also true that depression is usually treatable. The biggest barrier to people getting help is stigma and fear of disclosure. In this country we have seen a recent fall in stigma, an increase in willingness to be open about depression and most important of all, to seek help.

We do not yet know what might be the lessons of the loss of the Airbus, but we caution against hasty decisions that might make it more, not less, difficult for people with depression to receive appropriate treatment. This will not help sufferers, families or the public.

A conservative estimate is that about one in every four people in the UK suffers from depression at one time or another, many of whom struggle with mental illness without either asking for or receiving medical help. Help is there, but we need to much more to encourage people to use it.

Here’s another quote from Time to Change, for whose organization in Wales I wrote the piece linked above,

The terrible loss of life in the Germanwings plane crash is tragic, and we send our deepest sympathies to the families. Whilst the full facts are still emerging, there has been widespread media reporting speculating about the link with the pilot’s history of depression, which has been overly simplistic.

Clearly assessment of all pilots’ physical and mental health is entirely appropriate – but assumptions about risk shouldn’t be made across the board for people with depression, or any other illness. There will be pilots with experience of depression who have flown safely for decades and assessments should be made on a case by case basis.

Today’s headlines risk adding to the stigma surrounding mental health problems, which millions of people experience each year, and we would encourage the media to report this issue responsibly.

It is Time to Change attitudes to mental health, and a good place to start is to realise that it’s Time to Change how the media approach the subject. If you would like to complain about inappropriate reporting of mental health issues in the media then please follow the link here.

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How Arts Students Subsidise Science

Posted in Education, Finance with tags , , , , on March 26, 2015 by telescoper

Some time ago I wrote a blog post about the madness of the current fee regime in UK higher education. Here is a quote from that piece:

To give an example, I was talking recently to a student from a Humanities department at a leading University (not my employer). Each week she gets 3 lectures and one two-hour seminar, the latter  usually run by a research student. That’s it for her contact with the department. That meagre level of contact is by no means unusual, and some universities offer even less tuition than that. A recent report states that the real cost of teaching for Law and Sociology is less than £6000 per student, consistent with the level of funding under the “old” fee regime; teaching in STEM disciplines on the other hand actually costs over £11k. What this means, in effect, is that Arts and Humanities students are cross-subsidising STEM students. That’s neither fair nor transparent.

Now here’s a nice graphic from the Times Higher that demonstrates the extent to which Science students are getting a much better deal than those in the Arts and Humanities.

Subsidy

The problem with charging fees relating to the real cost of studying the subject concerned is that it will deter students from doing STEM disciplines and cause even greater numbers to flock into cheaper subjects (which where much of the growth in the HE sector over the last decade has actually taken place in any case). However, the diagram shows how absurd the current system (of equal fee regardless of subject really is), and it’s actually quite amazing that more Arts students haven’t twigged what is going on. The point is that they are (unwittingly) subsidising their colleagues in STEM subjects. I think it would be much fairer if that subsidy were provided directly from the taxpayer via HEFCE otherwise there’s a clear incentive for universities to rake in cash from students on courses that are cheap to teach, rather than to provide a proper range of courses across the entire curriculum. Where’s the incentive to bother teaching, e.g., Physics at all in the current system?

I re-iterate my argument from a few weeks ago that the Labour Party’s pledge to reduce fees to £6K across all disciplines would result in a much fairer and justifiable system, as long as there was a direct subsidy from the government to make good the shortfall (of around £6K per annum per student in Physics, for example).

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Quantum Technology and the Frontier of Computing

Posted in The Universe and Stuff with tags , , , on March 26, 2015 by telescoper

Here’s a short video I just found featuring our own Winfried Hensinger, Professor of Quantum Technologies at the University of Sussex.

It’s part of a pilot documentary that explores the connection between science fiction and science reality. Here is the official blurb:

“The science fiction genre has a history of playing with our imagination; inventing “impossible” technologies and concepts such as time travel and teleportation. The “spooky” discoveries that quantum physicists have recently made are challenging the very “impossibility” of sci-fi. This documentary will explore the ways in which sci-fi has catalysed the imagination of scientists who are pioneering these discoveries.

The theme will explore the causal link between science and science fiction, using the inner workings of the quantum computer that Dr Winfried Hensinger is currently developing as a case study. Dr Hensinger, the head of the Sussex Ion Quantum Technology research group, was inspired early on by the well known 60s science fiction television show Star Trek. Having led multiple breakthroughs in the field of Quantum Computing research, he speaks to the importance of not losing our imagination, citing his childhood desire to be the science officer on Star Trek’s Enterprise as the prime motivator of going into the scientific field. Exploring the relationship between the human beings developing this technology and the non-human genre of science fiction, we will demonstrate that the boundaries between imagination and reality are blurrier than conventionally thought.”

I’ll take the opportunity presented by this video to remind you that the University of Sussex is the only university in the UK to offer an MSc course in Quantum Technologies, and this year there are special bursaries that make this an extremely attractive  option for students seeking to extend their studies into this burgeoning new area. We’ve already seen a big surge in applications for this course this course so if you’re thinking of applying don’t wait too long or it might fill up!

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One Fine Conformal Transformation

Posted in Brighton, Cute Problems with tags , , , , , on March 25, 2015 by telescoper

It’s been a while since I posted a cute physics problem, so try this one for size. It is taken from a book of examples I was given in 1984 to illustrate a course on Physical Applications of Complex Variables I took during the a 4-week course I took in Long Vacation immediately prior to my third year as an undergraduate at Cambridge.  Students intending to specialise in Theoretical Physics in Part II of the Natural Sciences Tripos (as I was) had to do this course, which lasted about 10 days and was followed by a pretty tough test. Those who failed the test had to switch to Experimental Physics, and spend the rest of the summer programme doing laboratory work, while those who passed it carried on with further theoretical courses for the rest of the Long Vacation programme. I managed to get through, to find that what followed wasn’t anywhere near as tough as the first bit. I inferred that Physical Applications of Complex Variables was primarily there in order to separate the wheat from the chaff. It’s always been an issue with Theoretical Physics courses that they attract two sorts of student: one that likes mathematical work and really wants to do theory, and another that hates experimental physics slightly more than he/she hates everything else. This course, and especially the test after it, was intended to minimize the number of the second type getting into Part II Theoretical Physics.

Another piece of information that readers might find interesting is that the lecturer for Physical Applications of Complex Variables was a young Mark Birkinshaw, now William P. Coldrick Professor of Cosmology and Astrophysics at the University of Bristol.

As it happens, this term I have been teaching a module on Theoretical Physics to second-year undergraduates at the University of Sussex. This covers many of the topics I studied at Cambridge in the second year, including the calculus of variations, relativistic electrodynamics, Green’s functions and, of course, complex functions. In fact I’ve used some of the notes I took as an undergraduate, and have kept all these years, to prepare material for my own lectures. I am pretty adamant therefore that the academic level at which we’re teaching this material now is no lower than it was thirty years ago.

Anyway, here’s a typically eccentric problem from the workbook, from a set of problems chosen to illustrate applications of conformal transformations (which I’ve just finished teaching this term). See how you get on with it. The first correct answer submitted through the comments box gets a round of applaud.

conformal transformation

 

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Operation Varsity

Posted in History with tags , , , , on March 24, 2015 by telescoper

Today provides me with an occasion for a short post in a very irregular series marking the momentous events that unfolded seventy years ago.

At 1000 hours on 24th March 1945, nine battalions of the 6th British Airborne Division together with six from 17th US Airborne Division began landing on the German (east) side of the River Rhine, near Wesel. This was the last mass parachute and glider assault of the Second World War, and was designed to pierce the final great physical barrier to a ground advance into Nazi Germany. It was codenamed Operation Varsity.

airborne-rhine

The airborne troops were given the task of seizing and holding high ground overlooking a stretch of the Rhine which was to be crossed by elements of the British 21st Army Group, which included the British Second Army. The airborneassault involved 540 aircraft towing 1300 gliders into heavy anti-aircraft fire, so casualties during the first phase of the operation were heavy. However, within six hours of the commencement of the operation, all objectives were taken and the airborne troops subsequently linked up with ground forces who had crossed the river in assault boats in what was known as Operation Plunder.

This was all a part of a coordinated series of airborne and amphibious attacks by British, Canadian and American forces that began overnight on 23rd March 1945 and went on during the morning of 24th March 1945. The Applied troops, crossing the River Rhine in large numbers and beginning a rapid advance into Germany. By 27 March, they had established a bridgehead 35 miles (56 km) wide and 20 miles (32 km) deep.

Following the link-up with the ground troops, the 6th Airborne led  a 300 mile advance through Germany, marching approximately 11 miles per day until they managed to capture enough enemy transport. Second Army reached the Weser on 4 April, the Elbe on 19 April, the shore of the Baltic Sea at Lübeck on 2 May. On 3 May, Hamburg capitulated. By 7 May the Soviet Army had met up with the British forces at the Baltic port of Wismar.

I mention this because one of the troops that crossed the Rhine the British Second Army that day was a new recruit, a young man by the name of Richard Shaw, my mother’s brother. He took part in the subsequent advance through Germany and spent most of the year after the end of the Second World War stationed in Hamburg. He died just a few years ago, after a fall in his home, at the age of 85.

Lest we forget.

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NAM 2015: Abstract Submission Reminder!

Posted in The Universe and Stuff with tags , on March 24, 2015 by telescoper

Time for another quick plug of this year’s  Royal Astronomical Society National Astronomy Meeting, which will be taking place at the splendid Venue Cymru conference centre, Llandudno, North Wales, from Sunday 5th July to Thursday 9th July 2015. I’ve posted about  this before, but I thought I’d post it again because there is just a week left to submit an abstract for a contributed talk or poster; the deadline for doing that is April 1st. I’m actually on the Scientific Organizing Committee for NAM 2015 and as such I’ll be organizing part of this meeting, namely a couple of sessions on Cosmology under the title Cosmology Beyond the Standard Model, with the following description.

Recent observations, particularly those from the Planck satellite, have provided strong empirical foundations for a standard cosmological model that is based on Einstein’s general theory of relativity and which describes a universe which is homogeneous and isotropic on large scales and which is dominated by dark energy and matter components. This session will explore theoretical and observational challenges to this standard picture, including modified gravity theories, models with large-scale inhomogeneity and/or anisotropy, and alternative forms of matter-energy. The aim will be to both take stock of the evidence for, and stimulate further investigation of, physics beyond the standard model.

It’s obviously quite a broad remit so I hope that there will be plenty of contributed talks and posters. NAM is a particularly good opportunity for younger researchers – PhD students and postdocs – to present their work to a big audience so I particularly encourage such persons to submit abstracts. Would more senior readers please pass this message on to anyone they think might want to give a talk?   To further whet your appetite, here are some pictures of lovely Llandudno  I took at the last National Astronomy Meeting there, back in 2011.     If you have any questions please feel free to use the comments box (or contact me privately).

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