Archive for October, 2013

At number 8 in Rolling Stone Magazine’s 500 greatest albums is “London Calling” by The Clash.

At no. 8 in Rolling Stone Magazine's 500 greatest albums is "London Calling" by The Clash.

At no. 8 in Rolling Stone Magazine’s 500 greatest albums is “London Calling” by The Clash.

This album was released in 1980, and is maybe the high-point of so-called “punk rock” (or “new wave” as it was called in the USA). Of all the albums in the top 10, it is the most recently released, and the only not not released in either the 1970s or 1960s. Interestingly to me, it is placed well above the album which brought punk rock to an unsuspecting World, the Sex Pistols’ “Never Mind the Bollocks, Here’s the Sex Pistols”, which was released in 1977 and is at number 41 in this list of the 500 greatest albums. Here is the link to what Rolling Stone Magazine had to say about the Sex Pistols’ album.

I did not own “London Calling” before seeing this list, although I was a big fan of the biggest hit from this album, the song “London Calling”. But, along with the other album in this top 10 which I did not already own (I will come to that album in a few weeks’ time), I bought “London Calling” about a year ago when I first saw this “500 greatest albums” list. I already had no. 10 “The White Album” and no. 9 “Blonde on Blonde” long before I saw this top 10, so “London Calling” at no. 8 was the first in the list which I did not previously own.

Before buying the album I was not familiar with many of the other songs on the album, but having now listened to it over a dozen times in the last year I can say that there are quite a number of the 19 tracks which I like. To me, it sounds different to all the other albums in this top 10 list, which I guess is testimony to the fresh direction which punk rock brought to what had become a pretty jaded music scene. Until punk rock came along, British and American music was wallowing in “glam rock”, “adult oriented rock”, “progressive rock” (e.g. Emerson, Lake and Palmer) and dreadful (in my opinion) “big hair” middle of the road “rock” bands like REO Speedwagon, Foreigner etc. Music needed a kick up the arse, and punk provided that.

“London Calling” has more energy and more rawness than most of the other albums in this top 10, and certainly does not have the level of studio sophistication which an album like The Beatles’ “Sgt. Pepper” or The Beach Boys’ “Pet Sounds” have. In comparing it to the Sex Pistols’ “Never Mind the Bollocks”, “London Calling” is far more varied musically. Whilst it retains the raw energy of punk, it also shows different musical styles from raw driving rock to ska and reggae and even disco!

Here is the title track of the album, the seminal and apocalyptic “London Calling”. Rock doesn’t get much better than this!

London calling to the faraway towns
Now that war is declared and battle come down
London calling to the underworld
Come out of the cupboard, all you boys and girls
London calling, now don’t look to us
Phony Beatlemania has bitten the dust
London calling, see we ain’t got no swing
Except for the ring of that truncheon thing

The ice age is coming, the sun’s of an end
Meltdown expected, the wheat is growing thin
Engines stop running but I have no fear
Cos London is drownin’ I… live by the river

London calling to the imitation zone
Forget it brother, you can go it alone
London calling to the zombies of death
Quit holding out and draw another breath
London calling and I don’t wanna shout
But while we were talking I saw you runnin’ out
London calling, see we ain’t got no highs
Except for that one with the yellowy eyes

The ice age is coming, the sun’s of an end
Engines stop running, the wheat is growing thin
A nuclear error but I have no fear
Cos London is drowning and I live by the river

The ice age is coming, the sun’s of an end
Engines stop running, the wheat is growing thin
A nuclear error but I have no fear
Cos London is drowning and I live by the river

Now get this
London calling, yes I was there too
An’ you know what they said – well some of it was true!
London calling at the top of the dial
An’ after all this, won’t you give me a smile?
London calling…

I think this album is well worth listening to. But, do you think it deserves to be in the top 10 of the “500 greatest albums” (of all time)? Personally I do, as it is symbolises the revolution punk represented.

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Last Thursday (24th of October 2013) I gave a talk to Swansea Astronomical Society. This is the third year in a row that I have spoken in the autumn to this wonderfully active society on a historical theme. Two years ago I spoke about the early history of Yerkes Observatory (I blogged about that talk here), and last year I spoke about George Ellery Hale (my blog on that talk is here).

This year I continued the Hale theme, speaking about the history of Mount Wilson Observatory, which Hale established in 1904 after resigning as Director of Yerkes Observatory. Mount Wilson Observatory is most famous of course for its 100-inch telescope, the telescope used by Hubble (and Humason) to discover that the Universe is expanding. The Observatory is located just outside Los Angeles, and despite the light pollution of LA, it is still a very active observatory. This is mainly due its exceptionally stable air, giving it image quality better than pretty much any other observatory in the continental USA.

My connection with Mount Wilson Observatory is not as strong as my connection with Yerkes, but I was lucky enough to be awarded a Mount Wilson Fellowship in late 1999 and so went to use the famous 100-inch on four separate observing runs in 1999/2000. I was using an adaptive optics system, the plan was to study in unprecedented detail the structure of the scattering of visible light from dust grains in reflection nebulae. Unfortunately we were not able to use the AO system to do this work, as the central stars illuminating the reflection nebulae were too far from the dust regions we wanted to study for the AO system to work. In addition, our primary target, NGC 7023, is located at too high a declination for the 100-inch with its yolk mount to be able to reach. I thus undertook an alternative observing programme of observing close binary star systems to determine their orbital properties, systems which were too close to be resolved with conventional telescopes not using an AO system.

During all of these four observing runs I do not remember seeing the stars twinkle when it was clear (which it was most nights), which is testimony to the incredible seeing the Observatory enjoys. Even way down towards the horizon, the stars remained rock steady to the naked eye. It is because of this exceptional seeing that Mount Wilson was the testing ground for Adaptive Optics systems, and is now the testing ground for optical interferometry, with projects like the CHARA project run by Georgia State University (see this link for more information).

Here are the slides from my talk. I hope you enjoy them, and of course if you have any questions please feel free to ask in the comments section.

Here is a video of my talk. Apologies for the quality.

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On Sunday (27th of October 2013) I heard the sad news that Lou Reed had died. He was 71, and died of a “liver related ailment” according to a spokesperson. Reed is probably best known for fronting the highly influential “underground” band The Velvet Underground, I blogged about their album “The Velvet Underground” here in my series of Rolling Stone Magazine’s 500 greatest albums.

Personally I prefer Reed’s solo work. One of my favourites from his solo period is “Perfect Day”, but I will blog about that song at a future date. Here I will include the first song of his that I remember hearing as a teenager – “Walk on the Wild Side”.



Which is your favourite Lou Reed song?

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The ultraviolet catastrophe

In this blog I mentioned the Rayleigh-Jeans law for blackbody radiation, which predicted that the energy density (energy per unit volume) of the radiation emitted by a blackbody as a function of frequency varies as the square of the frequency. This was derived by Lord Rayleigh in 1900, and then more rigorously by Rayleigh and Sir James Jeans working together in 1905.

They found that the energy density (energy per unit volume) of the radiation coming from a blackbody varies as the square of the frequency of the radiation. This is the Rayleigh-Jeans law, and mathematically we can write this as

\epsilon(\omega) \propto \omega^{2} \text{ or, using an alternative nomenclature, } u(\nu) \propto \nu^{2}.

The so-called "ultraviolet" catastrophe".

The black curve is the observed variation of energy density as a function of frequency, the purple curve is the prediction of the Rayleigh-Jeans law, leading to the so-called “ultraviolet” catastrophe”.

Lord Rayleigh

Lord Rayleigh

Sir James Jeans

Sir James Jeans

This law led to what became known as the ultraviolet catastrophe, as it predicted that blackbodies would get brighter and brighter at higher frequencies of radiation, and that the total power radiated per unit area of the blackbody would be infinite. It was in trying to resolve this absurdity in 1900 that Max Planck came up with the idea of the quantisation of energy, which was the first step in what would later become quantum mechanics, an entirely new description of the sub-atomic world. But how was the Rayleigh-Jeans law derived? In order to properly understand what Planck did in 1900, we first of all need to properly understand what Rayleigh and Jeans derived using so-called classical physics.

Radiation and gas in a cavity

We are going to consider, in particular, oscillating electrons which produce Electromagnetic (EM) radiation (light) (I will in a future blog go over the classical theory derived by J.J. Thomson which explains why oscillating electrons radiate EM waves).

Suppose these oscillating electrons are mixed with a very thin gas. As the electrons radiate away they will lose energy, and so as they come back into equilibrium with the gas molecules they will do so at a lower average energy, and hence a lower temperature. This is why a glowing furnace cools over time, the radiation takes energy away from the gas or solid producing the radiation.

But, if we enclose the radiation in a box with perfectly reflective walls, the radiation has nowhere to go. Hence the radiation and the gas molecules will come into thermal equilibrium with each other. This is what is meant by Blackbody radiaton, it is when the radiation is in thermal equilibrium with the object producing the radiation.

Rayleigh and Jeans used such an idealised cavity to derive their eponymous law. Here we will go through the steps of their derivation, which will lead to the law which was clearly wrong. In a future blog I will explain what modifications Planck made to the steps laid out here to produce the correct blackbody radiation law, and hence avoid the ultraviolet catastrophe.

Writing the Electromagnetic Field in space and time

We need to satisfy the three dimensional wave equation for the Electric field in a cubic cavity, the length of each side being L. The 3-D electric field is a function of space (x,y,z) and of time t, so it can be written as




To make things simpler we will start off by considering a 1-dimensional travelling wave in e.g. the x-direction. For this we can write

\vec{E}(x,t) = E \sin (kx - \omega t)

The \omega in the above equation is a quantity we have come across before in a previous blog, it is the angular frequency in time of the wave, and is related to the time frequency via the equation \omega = 2\pi \nu where \nu is the time frequency measured in Hertz. The k in the above equation is the spacial equivalent of \omega \text{, } k is called the wave number and is defined as the number of wavelengths per unit wavelength. We can write that k = \frac{2 \pi}{\lambda} \text{ where } \lambda \text{ is the wavelength of the wave }.

The magnetic field can similarly be written as \vec{B}(x,t) = B \sin (kx - \omega t), but according to Maxwell’s equations \frac{ E }{ B } = c \text{, the speed of light} and so the magnetic component is much less than the electrical component, and we can ignore it in this derivation.

The 3-dimensional wave equation

You may remember from AS-level physics the relationship between wavelength, frequency and the speed of a wave, which is written at AS-level as f \lambda = v \text{ where } f \text{ is the frequency of the wave, } \lambda is its wavelength and v is the speed of the wave [for some reason that I have never fully understood, university level physics uses \nu \text{ rather than } f to represent the frequency of a wave]. If we are talking about EM waves, as we are here, then the speed of the waves is of course c \text{, the speed of light }.

This equation can be derived from the so-called “wave equation”, which is a second order differential equation relating the spatial variation of the wave to its temporal (time) variation. For the electric field, if we just consider the x-dimension for now, we can write

\frac{ d^{2}E_{x} }{ dx^{2} } = \frac{ 1 }{c^{2} } \frac{ d^{2}E_{x} }{ dt^{2} }

we can show that this comes back to our expression \nu \lambda =v \text{ (or }c \text{ if we are talking about EM waves)}. Writing E_{x} = E \sin(kx - \omega t) we can write for the spatial component

\frac{ dE_{x} }{ dx } = E k \cos(kx - \omega t) \text{ and } \frac{ d^{2}E_{x} }{ dx^{2} } = -E k^{2} \sin(kx - \omega t) = -k^{2}E_{x}.

Now looking at the temporal component, \frac{ dE_{x} }{ dt } = -\omega E \cos(kx - \omega t) \text{ and } \frac{ d^{2} E_{x} }{ dt^{2} } = -\omega^{2} E \sin(kx - \omega t) = -\omega^{2} E_{x}.
So, if \frac{ d^{2}E_{x} }{ dx^{2} } = \frac{ 1 }{c^{2} } \frac{ d^{2}E_{x} }{ dt^{2} } we can write -k^{2}E_{x} = \frac{ 1 }{ c^{2} } (-\omega^{2} E_{x}) \rightarrow k^{2} = \frac{ \omega^{2} }{ c^{2} }. But, k = \frac {2\pi }{ \lambda } \text{ and } \omega = 2 \pi \nu so k^{2} = \frac{ \omega^{2} }{ c^{2} } \text{ can be written as } \frac{ 4\pi^{2} }{ \lambda^{2} } = \frac{ 4\pi^{2} \nu^{2} }{ c^{2} } \rightarrow c^{2} = \nu^{2} \lambda^{2} which gives us \nu \lambda = c, just as we wanted.

In 3-dimensions the 1-dimensional wave equation becomes

\frac{ \partial^{2} E }{ \partial x^2 } + \frac{ \partial^{2} E }{ \partial y^{2} } + \frac{ \partial^{2} E }{ \partial z^{2} } = \frac{1}{c^2} \frac{ \partial^{2} E }{ \partial t^2}

where we need to use the partial derivatives as we need to differentiate the x-component, the y-component, the z-component and the time-component of \vec{E}(x,y,z,t).

In part 2 of this blog I will show what form the 3-D equation of a travelling wave has, and what conditions the 3-D Wave Equation needs to satisfy because it is enclosed in our previously-mentioned cubical cavity (with each side of length L), and how this determines the number of modes the Electric Field can have.

Part 2 of this blog is here.

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Today I thought I would post this lovely song, “The Sun Ain’t Gonna Shine Anymore” by The Walker Brothers. It was released in 1966 and reached number 1 in The Disunited Kingdom and number 13 in the United States. The song was originally recorded one year earlier by Frankie Valli, but had no chart success and sunk without a trace, to be resurrected by The Walker Brothers the following year.


Loneliness is the coat you wear
A deep shade of blue is always there
The sun ain’t gonna shine anymore
The moon ain’t gonna rise in the sky
Tears are always clouding your eyes
When you’re without love

Emptiness is the place you’re in
Nothing to lose, but no more to win
The sun ain’t gonna shine anymore
The moon ain’t gonna rise in the sky
Tears are always clouding your eyes
When you’re without love

Without you
Oh, I need you
I can’t go on

The sun ain’t gonna shine anymore
The moon ain’t gonna rise in the sky
Tears are always clouding your eyes
The sun ain’t gonna shine anymore
When you’re without love

The sun ain’t gonna shine anymore
The sun ain’t gonna shine anymore
Not anymore
The sun ain’t gonna shine anymore
Bring it back, baby
The sun ain’t gonna shine anymore
Oh, baby


Which is your favourite Walker Bother’s song?

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The redshift men

And Hale created Yerkes Observatory in the 1890s, with the then World’s largest telescope, the 40-inch refractor.


The redshift men

The Mount Wilson Observatory in California had been built around a telescope with a 60-inch reflecting mirror, which came into operation in 1908. Just ten years later, this was joined on the mountain by the 100-inch Hooker Telescope (named after the benefactor who paid for it), which was to be the most powerful astronomical telescope on Earth for nearly 30 years, until the completion of the famous 200-inch Hale Telescope (named after George Ellery Hale, the astronomer who created both the Mount Wilson and the Mount Palomar observatories), at Mount Palomar, near Los Angeles (not far from Pasadena), in 1947. There were two people who would push the 100-inch to its limits in the 1920s.
The first of those pioneers, Milton Humason, was born in Dodge Center, Minnesota, on 19 August 1891; but his parents moved the family to the West Coast when he was a child…

View original post 5,136 more words

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Legend has it that it was Galileo who first noticed that the period of a pendulum’s swing does not depend on how large the swing is, but only on the length of the pendulum. The swinging back and forth of a pendulum is an example of a very important type of motion which crops up in many places in Nature, so called Simple Harmonic Motion (SHM). In this blog I will derive the basic equations of SHM, and then go on and talk about the deep connection between SHM and circular motion.

A swinging pendulum

If we start off by looking at a simple pendulum which has been displaced so that the bob is to the right of the vertical position, the angle the line of the pendulum makes with the vertical is given by \theta, and for this derivation to work \theta needs to be small.

A simple pendulum will swing back and forth, exhibiting Simple Harmonic Motion.

A simple pendulum will swing back and forth, exhibiting Simple Harmonic Motion.

The force restoring the pendulum bob back to the middle, which I have called F in the diagram above, is given by F = -T\sin(\theta) (the minus sign comes about because the the force is back towards the centre, even though the angle \theta increases as we move the bob to the right).

The restoring force, F, can be written using Newton’s 2nd law as F=ma=-T\sin(\theta). The angle \theta is measured in radians (see my blog here for a tutorial on radians). When \theta is small, \sin(\theta) \approx \theta and so we can write that

\sin(\theta) \approx \theta = \frac{x}{l}

where l is the length of the pendulum and x is the horizontal displacement of the pendulum bob.

Finally, the tension T in the pendulum chord can be written as T \approx mg where m is the mass of the bob and g is the acceleration due to gravity (9.8 m/s/s for the Earth).

Putting all of this together, we can write that the restoring force F can be written as

F = - mg\theta = -mg\frac{x}{l}

This means that the acceleration a can be written as

\vec{a} = -\frac{g}{l} \vec{x}

It is more common to write this as

\boxed{ \vec{a} = -\omega^{2} \vec{x} }

where \omega^{2} = \frac{g}{l} for the pendulum. \omega is called the angular frequency and it is related to how long the pendulum takes to complete one full swing, the period, by the equation T = \frac{2\pi}{\omega}. The frequency is just the reciprocal of the period, so we can write \nu = \frac{\omega}{2\pi} and so the angular frequency is related to the time frequency as \omega = 2\pi \nu.

Whenever the acceleration can be written as being proportional to the displacement, and in the opposite direction to the displacement, we have Simple Harmonic Motion. Other examples of SHM are an object bouncing vertically on a spring, or moving horizontally back and forth due to a spring attached at one end, even the vibrations of atoms in molecules.

Solutions to the SHM equation

What are the solutions to the second order differential equation \frac{d^{2}\vec{x}}{dt^{2}} = \vec{a} = - \omega^{2} \vec{x}? We have a displacement, \vec{x}, and it is proportional to the acceleration \vec{a}, but the acceleration acts in the opposite direction to the displacement.

We differentiate the displacement twice with respect to time to produce the acceleration (remember \vec{a} = \frac{d^2}{dx^2} \vec{x}), and for SHM, when we do this, the acceleration is proportional to the displacement and in the opposite direction.

Let us suppose we try the displacement

x = A \sin(\omega t) \text{ (remember that } \theta = \omega t)

If we differentiate this once with respect to time we get the velocity

v = \frac{dx}{dt} = \frac{d}{dt} A \sin(\omega t) = A\omega \cos(\omega t)

To get the acceleration we need to differentiate the velocity with respect to time so

a = \frac{dv}{dt} = \frac{d}{dt} A\omega \cos(\omega t) = - A \omega^{2} \sin(\omega t) = -\omega^{2}x

Loh and behold, we now have that a \propto - x, so we have shown that, if x = A \sin(\omega t) that an object which has this displacement as a function of time will display SHM.

As the acceleration is proportional to the displacement, it will be at its maximum when the displacement is maximum, so for a pendulum when the bob is at its extreme positions. The acceleration at the centre is zero, as the displacement at the centre is zero.

Conversely the velocity behaves in the opposite sense. Remember, as \vec{v} = \frac{d}{dt}\vec{x} = A\omega\cos(\omega t) it means that the velocity and displacement are 90^{\circ} out of phase with each other, when the displacement is a maximum the velocity is zero, and when the displacement is zero the velocity is a maximum. So, the bob will be travelling at its quickest when it passes through the centre, and at its extremes the velocity is (temporarily) zero.

SHM and circular motion

If an object is moving at a constant speed in a circle in the x-y plane we can write that it’s position at any time is given by

x = A \cos(\theta) \text{ and } y = A \sin(\theta)

For an object moving with a constant speed in a circle, its x-position and y-position can be written in terms of the radius A and the angular velocity.

For an object moving with a constant speed in a circle, its x-position and y-position can be written in terms of the radius A and the angular velocity \omega.

But notice that the expression for x is exactly the same as the expression which we had above, so an object moving in a circle performs SHM. But how? Surely, if it is moving with a constant speed (and hence constant angular velocity \omega), how is it also displaying SHM?

The SHM comes in when we look at the object’s x or y-position as a function of time. So, for example, if we look at the circle from below, as if we were looking along the plane of the screen from below, we would only see the x-displacement of the object, as the y-displacement would be invisible to us. The x-displacement is given by x=A \cos(\theta) = A \cos(\omega t), so the x-position will move back and forth about the central point, displaying SHM. This regular “wobble” is one of the things we look for in trying to find exoplanets – planets around other stars. If we see a regular, rhythmic wobble in the position of the parent star, it’s a pretty good bet that it has a planet going around it with the force of gravity between the host star and its planet producing the apparent SHM.

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