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## Antimatter and Dirac’s Equation

Yesterday I introduced Paul Dirac, number 10 in “The Guardian’s” list of the 10 best physicists. I mentioned that his main contributions to physics were (i) predicting antimatter, which he did in 1928, and (ii) producing an equation (now called the Dirac equation) which describes the behaviour of a sub-atomic particle such as an electron travelling at close to the speed of light (a so-called relativistic theory). This equation was also published in 1928.

## The Dirac Equation

In 1928 Dirac wrote a paper in which he published what we now call the Dirac Equation.

This is a relativistic form of Schrödinger’s wave equation for an electron. The wave equation was published by Erwin Schrödinger two years earlier in 1926, and describes how the quantum state of a physical system changes with time.

### The Schrödinger eqation

The various terms in this equation need some explaining. Starting with the terms to the left of the equality, and going from left to right, we have $i$ is the imaginary number, remember $i = \sqrt{-1}$. The next term $\hbar$ is just Planck’s constant divided by two times pi, i.e. $\hbar = h/2\pi$. The next term $\partial/\partial t \text{ } \psi(\vec{r},t)$ is the partial derivative with respect to time of the wave function $\psi(\vec{r},t)$.

Now, moving to the right hand side of the equality, we have
$m$ which is the mass of the particle, $V$ is its potential energy, $\nabla^{2}$ is the Laplacian. The Laplacian, $\nabla^{2} \psi(\vec{r},t)$ is simply the divergence of the gradient of the wave function, $\nabla \cdot \nabla \psi(\vec{r},t)$.

In plain language, what the Schrödinger equation means “total energy equals kinetic energy plus potential energy”, but the terms take unfamiliar forms for reasons explained below.

## The Beatles rooftop concert (January 30th, 1969)

Today (January 30th) marks the 50th anniversary of the last time The Beatles played live together, in the infamous “rooftop” concert in 1969. Although they would go on to make one more studio album, Abbey Road in the summer of 1969; due to contractual and legal wranglings the rooftop concert, which was meant to be the conclusion to the movie they were shooting, would not come out until 1970 in the movie Let it Be.

It is also true to say that some of the songs on Abbey Road were performed “live” in the studio with very little overdubbing (as opposed to separate instrument parts being recorded separately as was done on e.g. Sgt. Pepper). But, the rooftop concert was the last time the greatest band in history were seen playing together, and has gone down in infamy. It has been copied by many, including the Irish band U2 who did a similar thing to record the video for their single “Where the Streets Have no Name” in 1987 in Los Angeles.

The Beatles were trying to think of a way to finish the movie that they had been shooting throughout January of 1969. They had discussed doing a live performance in all kinds of places; including on a boat, in the Roundhouse in London, and even in an amphitheatre in Greece. Finally, a few days before January 30th 1969, the idea of playing on the roof of their central-London offices was discussed. Whilst Paul and Ringo were in favour of this idea, and John was neutral, George was against it.

The decision to go ahead with playing on the roof was not made until the actual day. They took their equipment up onto the roof of their London offices at 3, Saville Row, and just start playing. No announcement was made, only The Beatles and their inner circle knew about the impromptu concert.

The concert consisted of the following songs :

1. “Get Back” (take one)
2. “Get Back” (take two)
3. “Don’t Let Me Down” (take one)
4. “I’ve Got a Feeling” (take one)
5. “One After 909”
6. “Dig a Pony”
7. “I’ve Got a Feeling” (take two)
8. “Don’t Let Me Down” (take two)
9. “Get Back” (take three)

People in the streets below initially had no idea what the music (“noise”) coming from the top of the building was, but of course younger people knew the building was the Beatles’ offices. However, they would not have recognised any of the songs, as these were not to come out for many more months. After the third song “Don’t Let Me Down”, the Police were called and came to shut the concert down. The band managed nine songs (five different songs, with three takes of “Get Back”, two takes of “Don’t Let Me Down”, and two takes of “I’ve Got a Feeling”) before the Police stopped them. Ringo Starr later said that he wanted to be dragged away from his drums by the Police, but no such dramatic ending happened.

At the end of the set John said

I’d like to thank you on behalf of the group and ourselves, and I hope we’ve passed the audition.

Here is a YouTube video of “Get Back” (which may get taken down at any moment)

and here is a video on the Daily Motion website of the whole rooftop concert (again, it may get taken down at any moment).

Enjoy watching the greatest band ever perform live for the very last time!

## Aberfan – Vera Rich (poem)

50 years ago today, on 21 October 1966, a tragedy happened in a small mining village in Wales which horrified the world. At 9:15am, Pantglas school in a place called Aberfan was engulfed by a river of coal debris. 116 children (more than half of the school’s pupils) and 28 adults were killed. Dozens more were rescued from the horror, with people from Aberfan and surrounding villages digging with their hands in a desperate attempt to save some lives.

The tragedy was due to a tip of coal waste (“slag heap” as they were often called) which had been piled on the side of the mountain against which the village nestles, and was entirely preventable. For months the local council had been warning the National Coal Board (NCB) of the risk, but the NCB had taken no notice.

In a tribunal held after the tragedy, the NCB were found guilty of negligence and of corporate manslaughter. However, they never paid a penny of compensation to the families, nor did they pay to have the numerous slag heaps rendered safe. Local families had to raise the money to do this themselves. After years of campaigning, in 1997 the newly-formed Welsh Assembly government finally repaid the families the money that they had raised. Some 10 years later the Welsh Assembly government paid the families a much larger sum, to correct for the inflation in the intervening 40 years.

I have been to the cemetery and memorial park in Aberfan. It is a beautiful tribute and memory to the tragedy that happened that wet October day in 1966.

Here is a very moving poem simply called Aberfan by Vera Rich, an English-born poet.

I have seen their eyes, the terrible, empty eyes
Of women in a glimmerless dawn, and the hands
Of men who have wrestled through long years with the dark
Underpinning of the mountains, strong hands that fight

In dumb faith that what was once flesh born of their flesh
And is earth of the earth, should rest in the earth of God,
Not that of the devil’s making…

The Tip had crouched like a plague-god, with the town,
A victim in reversion, held beneath
A vast, invisible paw… Not a lion to toss
A proud, volcano-mane of destruction, crouched
Like a rat, it waited…

I have seen their eyes, and the empty hands of men,
And they walk like victims of a second Flood
In a world no longer home, where the void of sky
Between tall mountains looms as a cenotaph
For a generation of laughter…

I have seen them
Walking, near-ghosts, wraiths from a half-formed legend
Of this more-than-Hamelin, where, on an autumn Friday,
Between nine and ten of the clock, death raised his flute
And the children followed…

## Fortunate Son – Creedence Clearwater Revival (song)

Today I thought I would share this great anti-war song – “Fortunate Son” by Creedence Clearwater Revival. It was released in September 1969, and is specifically about the lucky men who were born into families which, somehow, meant that they were not called up for the draft to fight in the Vietnam war.

These were the senators’ sons, the millionaires’ sons, the fortunate sons. Sons like George W. Bush, who miraculously found himself in the National Guard, far away from any danger, rather than in Vietnam fighting. I wonder why? Oh, maybe because his father, George H. Bush, had the political clout and importance to make sure his precious son didn’t go and fight in the jungles of Vietnam, unlike the poor white and black men who were drafted there.

As the draft went on, it became more and more apparent how many fortunate sons were avoiding going to war, thanks to their family’s influence in bending the rules. And how many poor blacks and whites had no choice, they were forced to go and would be jailed should they refuse. The Vietnam war was wrong on so many levels, but the inequity of the draft was certainly one of its wrongs.

“Fortunate Son” was released in September 1969, and talks of the privileged few who, somehow, avoided the Vietnam war draft.

“Fortunate Son” is rated at 99 in Rolling Stone Magazine’s list of the 500 greatest songs of all time. It really is a great song, I am surprised that I haven’t blogged about it before.

Some folks are born, made to wave the flag
Ooo, they’re red, white and blue
And when the band plays “Hail to the Chief”
Ooo, they point the cannon at you, Lord

It ain’t me, it ain’t me, I ain’t no senator’s son, son
It ain’t me, it ain’t me, I ain’t no fortunate one, no

Some folks are born, silver spoon in hand
Lord, don’t they help themselves, y’all
But when the taxman comes to the door
Lord, the house looks like a rummage sale, yeah

It ain’t me, it ain’t me, I ain’t no millionaire’s son, no, no
It ain’t me, it ain’t me, I ain’t no fortunate one, no

Yeah, yeah
Some folks inherit star spangled eyes
Ooh, they send you down to war, Lord
And when you ask ’em, “How much should we give?”
Ooh, they only answer “More! More! More!”, y’all

It ain’t me, it ain’t me, I ain’t no military son, son
It ain’t me, it ain’t me, I ain’t no fortunate one, one
It ain’t me, it ain’t me, I ain’t no fortunate one, one

Here is a video of the song. Enjoy!

## Robert Kennedy – the mindless menace of violence (speech)

Just over 7 years ago, in early 2009, I bought a CD of some of Robert Kennedy’s greatest speeches. Whilst his brother John F. Kennedy gave some memorable speeches, for me Bobby Kennedy possibly surpassed JFK with his eloquence. One of his most moving and wonderful speeches has been passing through my mind these last two weeks or so; with the senseless shootings of innocent black people by police in the United States, the killing of the five policemen by an assassin in Houston, the horrific terrorist attack in Nice on Bastille Day which has killed at least 84 people, many of them children, and the failed coup in Turkey with over 100 dead. And, just as I was putting this blog together yesterday, the shooting of 3 more police officers in Baton Rouge.

Robert Kennedy (RFK) served as Attonery General under his brother’s Prisidency, but in 1965 he entered the Senate as one of the senators for New York. On 16 March 1968, RFK announced that he would run for the presidency, and set about touring the USA to garner support for his campaign. On the evening of 4 April, he was due to give a speech in Indianapolis when he learnt en-route of the assassination of Martin Luther King. He broke the news to the gathered crowd, many of whom had not heard the news until Bobby Kennedy told them. He gave a very moving and powerful speech on that evening, and I may blog about that particular speech another time.

But, today I am going to share the speech that he gave the day after MLK’s assassination, on 5 April 1968. The speech is entitled “The mindless menace of violence“, and it was delivered at the Cleveland Club in Ohio.

Kennedy toured the country as part of his campaign to become President of the United States, concentrating to a large part on some of the poorest communities in the country, where he met with dissaffected whites, blacks and latinos who had been left behind by the ‘American Dream’.

“this mindless menace of violence in America which again stains our land and every one of our lives.”

It is quite a long speech, nearly 10 minutes long, but bear with it and I think you will be struck by its eloquence. Bobby Kennedy wrote the speech himself, putting it together in the hours after the horror of MLK’s assassination had sunk into his mind.

The speech opens with these lines….

This is a time of shame and sorrow. It is not a day for politics. I have saved this one opportunity to speak briefly to you about this mindless menace of violence in America which again stains our land and every one of our lives.

It is not the concern of any one race. The victims of the violence are black and white, rich and poor, young and old, famous and unknown. They are, most important of all, human beings whom other human beings loved and needed. No one – no matter where he lives or what he does – can be certain who will suffer from some senseless act of bloodshed. And yet it goes on and on.

Why? What has violence ever accomplished? What has it ever created? No martyr’s cause has ever been stilled by his assassin’s bullet.

No wrongs have ever been righted by riots and civil disorders. A sniper is only a coward, not a hero; and an uncontrolled, uncontrollable mob is only the voice of madness, not the voice of the people……

But, Bobby Kennedy was also deeply concerned with the economic disparities in the United States, and with the sickening racism which had profoundly disturbed him. He later goes on to say…

……

For there is another kind of violence, slower but just as deadly, destructive as the shot or the bomb in the night. This is the violence of institutions; indifference and inaction and slow decay. This is the violence that afflicts the poor, that poisons relations between men because their skin has different colors. This is a slow destruction of a child by hunger, and schools without books and homes without heat in the winter.

This is the breaking of a man’s spirit by denying him the chance to stand as a father and as a man among other men. And this too afflicts us all. I have not come here to propose a set of specific remedies nor is there a single set. For a broad and adequate outline we know what must be done.

Followed immediately by these words…

When you teach a man to hate and fear his brother, when you teach that he is a lesser man because of his color or his beliefs or the policies he pursues, when you teach that those who differ from you threaten your freedom or your job or your family, then you also learn to confront others not as fellow citizens but as enemies – to be met not with cooperation but with conquest, to be subjugated and mastered.

The entire text can be found here at the John F. Kennedy presidential library website.

There are several versions of this mesmerising speech on YouTube, but many seem to have had an annoying soundtrack of some music added. I feel the added music detracts from hearing Bobby Kennedy’s words, which are powerful enough and do not need any music to make them more dramatic. So, the version I have included here is just RFK’s incredible words.

What strikes me most when I hear or read these words of Bobby Kennedy is how little progress we have made. One could argue that we have digressed; there are more mass shootings now in the USA than in the 1960s when these words were spoken. There is more terrorism and conflict than ever. And, in the presumptive Republican Party presidential nominee Donald Trump, we have a man who is the very antithesis of the wonderful ideals for which Bobby Kennedy stood.

I would say “enjoy” this video, but I am not sure that one can enjoy this speech. It is moving, harrowing, thought-provoking, upsetting, but also uplifting. To think that RFK was himself assassinated within a few months of giving this speech, it only adds poignancy to his words and highlights even more the truth and sadness of the mindless menace of violence

## The Bob Dylan “Judas” heckle

Fifty years ago yesterday (17 May 1966), one of the seminal moments in 20th Century popular culture took place in the Manchester Free Trade Hall. Bob Dylan, who had burst onto the folk scene a few years before, was playing to a packed crowd towards the end of his gruelling 1966 World tour. The first half of his set was vintage Dylan, just the man (poet) and his guitar. The crowd were enraptured.

But, it all turned sour in the second half, when Dylan was joined by his band, The Hawks, and proceeded to do an ‘electric’ set. The crowd became restless. Many left; others booed, stamped their feet or started chanting. When he came back on to do his encore, things came to a head.

“Judas!” a man shouted.

“I don’t believe you.” Dylan replied. Then he started getting ready for the encore song. A few seconds later Dylan added

“You’re a liar!”

Then, he turned to his band and said “Play it fucking loud”,  and they ripped into an angry version of Like a Rolling Stone. This is the moment as captured on film, it forms the closing scene of Martin Scorsese’s fascinating documentary No Direction Home.

There is also a very interesting in-depth audio documentary about this whole seminal incident, Ghosts of Electricity, made by Andy Kershaw for BBC Radio 1 and broadcast in 1999. It is available here on Andy Kershaw’s website.

Andy Kershaw’s fascinating documentary about the Bob Dylan “Judas” incident, which was originally broadcast in 1999 on BBC Radio 1.

The whole concert was recorded and circulated as a bootleg for many years. For some reason, it became known as the Royal Albert Hall Concert, even though it had happened at the Manchester Free Trade Hall; possibly because the 1966 World tour ended at the Royal Albert Hall on the 26 and 27 May. Dylan sanctioned an official release of the concert in 1998.

The cover for Bob Dylan’s “Royal Albert Hall Concert” CD, which includes the “Judas” heckle. In fact, the concert was recorded at the Manchester Free Trade Hall on 17 May 1966.

## Who invented calculus?

One of the physicists in our book Ten Physicists Who Transformed Our Understanding of Reality (follow this link for more information on the book) is, not surprisingly, Isaac Newton. In fact, he is number 1 in the list. One could argue that he practically invented the subject of physics. We decided to call him the ‘father of physics’, with Galileo (whose life preceded Newton’s) being given the title of ‘grandfather’.

Newton was, clearly, a man of genius. But he was also a nasty, vindictive bastard (not to mince my words!). He didn’t really have any close friends in his life; there were plenty of people who admired him and respected him, and of course he had colleagues. But, apart from a niece whom he seemed to dote on in later life, and two men with whom he probably had love affairs, he was not a man who sought company. He was probably autistic, but lived at a time before such conditions were diagnosed or talked about.

Isaac Newton (1643-1727), the ‘father of physics’. He relished in feuding with other scientists

One sort of interaction that he did seem to enjoy with other people though was feuds. In fact, he seemed to thrive on feuding with other scientists. He loved to argue with others, which is not uncommon amongst academics. He had strong opinions which he liked to defend; this is normal. But, Newton took these disputes to an extreme; if he fell out with someone he would do everything he could to destroy that person.

Although I am sure that he had many ‘minor’ arguments, he had three main feuds with fellow scientists. These three men were

• Robert Hooke – curator of experiments at the Royal Society
• Gottfried (von) Leibniz – the German mathematician
• John Flamsteed – the first Astronomer Royal

In each case, he did his level best to destroy the other man. Each of these feuds is discussed in more detail in our book, but in this blogpost I will give a brief summary of his feud with Leibniz.

The feud came about because Newton refused to believe that Leibniz had independently come up with the mathematical idea of calculus. It was a recurring theme throughout Newton’s life that he sincerely believed that he was special. He had deep religious views (some would say extreme religious views). As part of these views, he believed that he had been specially chosen by God to understand things that others would never be able to understand.

Thus, when he heard that Leibniz had developed a mathematics similar to his own ‘theory of fluxions’ (as Newton called it), he naturally assumed that the German had stolen it from him. There then ensued a 30-year dispute between the two men, with Newton very much the aggressor.

Gottfried (von) Leibniz (1646-1716), German mathematician and co-inventor of calculus

It escalated from a dispute to a feud, and culminated in the Royal Society commissioning an ‘official investigation’ to establish propriety for the invention of calculus. When the report came out in 1713 it came out in Newton’s favour. But, by this time Newton was not only President of the Royal Society, but he had secretly authored the entire report. It was anything but impartial. Leibniz died the following year, a broken man from Newton’s relentless attacks.

One should, of course, be able to to admire a person for their work but not admire them in the least for the person that they were. Newton, in my mind, falls very firmly into this category. His contribution to physics is unparalleled, but I don’t think he was the kind of person one would want to know or even come across if one could help it!

Ten Physicists Who Transformed Our Understanding of Reality is available now. Follow this link to order