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Posts Tagged ‘Physics’

On Saturday 18 June, as some of you may know, Tim Peake returned from his 6-month stint on the International Space Station (ISS). At the end of January, as a bit of fun, in a blog entitled “Is Tim Peake getting younger or older?”  I worked out whether he was getting younger (due to time dilation in special relativity) or older (due to time running faster due to general relativity). The answer was that the special relativity effect of time slowing down for him was greater than the general relativity effect of time speeding up. But, he would need to stay in space for 100 years to age by 1 second less than if he were on Earth! But, now that he is back on Earth time is running at the same rate for him as for the rest of us. 🙂

Peake held a press conference on Tuesday 21 June, and later that day I was on BBC radio making some comments about his time on the ISS. It was only a short 3-minute interview for the evening news programme (you can listen to it here), but one of the things I was asked was whether Tim Peake’s mission to the ISS had inspired young people (school students).

SafariScreenSnapz001

Astronaut Tim Peake returned to Earth from the International Space Station on 18 June 2016 after a six-month period there.

My answer was that yes, it absolutely had. Peake has captured the public imagination with his trip to the ISS, and has inspired a whole new generation to think about space. As the first person from Britain to go into space at the taxpayers’ expense, he may have had instructions to engage with the public in his time spent there. I don’t know. But, what I do know is that he clearly enjoys communicating science and the wonders of space and the oddities of an astronaut’s life to the public, and has done an excellent job of it.

I just about member the last Apollo mission, Apollo 17, which went to the Moon in December 1971. I’m too young to remember the ones before; even though my mother sat me down in front of the TV to see Neil Armstrong take his historic steps in 1969, I sadly don’t remember it. Seeing astronauts going to the Moon was certainly a factor in igniting my own interest in space and astronomy, but since that time there has been very little to inspire later generations. Going up in the Space Shuttle or going to the ISS are not as exciting as going to the Moon; but thankfully Tim Peake has turned what has become a rather routine activity these days into something very exciting for our younger people.

I don’t know how much it cost the DUK taxpayers to put Peake into space, but I can guarantee you that the money will be recouped dozens of times over. There is no surer way to create wealth than through science and technology, and inspiring a whole new generation of school students into taking an interest in physics, mathematics, engineering and science will, hopefully, see more of them pursue such careers in the future. This can only be a boom for our economy.

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I have just spent the last week showing my Physics students the wonderful BBC Horizon interview with Richard Feynman “The Pleasure Of Finding Things Out”. I vividly remember seeing this interview myself when I was 17. I already knew I wanted to go into physics, but this interview confirmed what I already knew, that physics was the subject for me. Thankfully for all, the interview is available in its entirety on YouTube.



When I introduce the video, I also quote what Brian Clegg says about Feynman in his introduction to the chapter on Quantum Electrodynamics in his book Light Years.


Richard Feynman, the magician


Ask a person in the street to name the two greatest physicists of the twentieth century and they will almost inevitably come up with Einstein. The second name, though, might prove harder to pin down.

Ask a physicist to come up with the top two and there will be no hesitation – or at least, if there is any hesitation, it will be over which name to put in first place.

The name that ranks alongside Einstein will be that of Richard Feynman.

The title of my blog comes from the words Hans Bethe (who won the Nobel prize in Physics for his work on nucleosynthesis within stars) said about Feynman. The quote in full is


There are two types of genius. Ordinary geniuses do great things, but they leave you room to believe that you could do the same if only you worked hard enough. Then there are magicians, and you can have no idea how they do it. Feynman was a magician.

Enjoy this wonderful interview with a truly remarkable physicist. And, if you want to read more about the crazy adventures he got up to in his colourful life, then read his autobiography ‘Surely You’re Joking Mr. Feynman


Feynman’s autobiography “Surely You’re Joking Mr. Feynman” is a hilarious read


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In May I was in Edinburgh to compete in the Edinburgh marathon. On the day after the marathon I did a sight-seeing tour of Edinburgh. One of the things I saw was a statue to the Scottish mathematical physicist James Clerk Maxwell. The statue is at the Saint Andrew Square end of George Street, abut 300 metres from the famous Princes Street.

James Clerk Maxwell(1831-1879).



The statue of James Clerk Maxwell, which is at the Saint Andrew Square end of George Street.



James Clerk Maxwell was an important physicist and mathematician. His most prominent achievement was to formulate the equations of classical electromagnetic theory. These four equations are known as Maxwell’s equations. They are shown on a small plaque at the rear of the statue’s plinth.


The rear of the statue’s plinth. The larger plaque is illustrated in the bottom photograph. Below this is a small plaque with Maxwell’s four famous equations of electromagnetism.


Maxwell’s four equations, which I have written out below.



\boxed{   \begin{array}{lcll}  \nabla \cdot \vec{D} & = & \rho  & (1) \\   & & & \\  \nabla \cdot \vec{B} & = & 0 & (2) \\   & & & \\  \nabla \times \vec{E} & = & - \frac{\partial \vec{B}}{\partial t}  & (3) \\   & & & \\  \nabla \times \vec{H} & = & - \frac{\partial \vec{D}}{\partial t} + \vec{J} & (4)  \end{array}   }


These equations are written in differential form, where the symbol \nabla is known as the vector differential operator. I will explain the mathematics of vector differential operator, and the meaning of each equation, in a series of future blogs.

The four equations can also be written in integral form, which many people find easier to understand. In integral form, the equations become


\boxed{  \begin{array}{lcll}  \iint_{\partial \Omega} \vec{D} \cdot d\vec{S}&  = & Q_{f}(V) & (5) \\   & & & \\  \iint_{\partial \Omega} \vec{B} \cdot d\vec{S} & = & 0 & (6) \\   & & & \\  \oint_{\partial \Sigma} \vec{E} \cdot d\vec{\l} & = - & \iint_{\Sigma} \frac{\partial \vec{B} }{\partial t} \cdot d\vec{S} & (7) \\   & & & \\  \oint_{\partial \Sigma} \vec{H} \cdot d\vec{l} & = & I_{f} + \iint_{\Sigma} \frac{\partial \vec{D} }{\partial t} \cdot d\vec{S} & (8)   \end{array} }



The inscription on the front of the statue’s plinth. It reads “James Clerk Maxwell 1831-1879”.



The larger plaque on the back of the plinth.

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Relativity has been in the news quite a bit recently with the detection of neutrinos apparently travelling faster than the speed of light. Although most people don’t know the details of Einstein’s theory of Relativity, many are aware of the “cosmic speed limit” predicted in it, and also the most famous equation in physics which came from his theory – E=mc^{2}.

Many people, however, are unaware that the idea of relativity had been around long before Einstein. In fact, we can trace the idea of relativity back to Galileo. Galileo was one of the first scientists to do experiments on the motions of bodies (what we would now call mechanics), and was also one of the first scientists to use “thought experiments” to make scientific arguments.

Galileo

Galileo started thinking about whether mechanical experiments would behave differently if one were in motion or at rest. For example, if a ship is anchored in the port and one were to drop a stone from the top of the mast, we all know that it would strike the deck at the bottom of the mast, i.e. vertically below the place from where it was dropped (as long as we were careful not to give it any sideways motion). This is, of course, a pretty obvious statement.

But, what would happen if the ship were in motion? Let us suppose the ship is sailing at 5 metres per second (5m/s) in some direction on a perfectly smooth lake. If someone were now to drop a stone from the mast, surely it would fall behind the mast because the ship has moved forwards whilst the stone was dropping. If the stone were to take 1 second to drop to the deck, surely the stone would land 5 metres behind the bottom of the mast, rather than at the bottom, because the ship has moved 5 metres forwards in that 1 second.

NO, Galileo argued, this would not be the case. He argued that it would hit the deck at the bottom of the mast, just as in the case when the ship is not moving. If you think about it carefully you can see why.

When the person drops the stone from the mast, they are moving forwards with the ship. So the stone is actually given a forwards motion as it is dropped, and it is this forwards motion which leads it to land at the bottom of the mast, not behind it. As the ship moves forwards at 5 m/s, so does the stone. By performing this simple mechanical experiment one would not be able to tell whether the ship were anchored in the port, or moving on a smooth lake.

If the person at the port were able to see the motion of the stone against some sort of background, he would see the stone move in a parabola, which is exactly the motion a falling object which is also given some sideways velocity has. But, at every point of its travel down towards the deck, it will be next to the mast, as this is moving forwards as the stone falls.

Galileo then went on to generalise this specific thought experiment to say that there was no mechanical experiment that one could perform which would be able to tell the difference between being at rest or moving with a constant velocity (that is, with no acceleration). This principle is know as Galilean relativity, and we define a set of equations known as the Galilean transforms which allow us to switch between what we would see in two frames of reference, for example what someone standing on the shore would measure and what someone on a moving ship would measure.

If the ship is moving with a constant velocity v then in time t it will move a distance v t (distance = velocity x time). To make it easier for ourselves we will set up the x,y,z axes so that the ship is moving only along our x-axis. If we refer to the position and time of any event in the person on the shore’s frame of reference as (x,y,z,t) and those in the frame of reference of someone on the ship as (x^{\prime},y^{\prime},z^{\prime},t^{\prime}) then the equations which relate the two (known as the Galilean transforms) are:

\begin{array}{lcl} x^{\prime} & = & x + vt \\  y^{\prime} & = & y \\  z^{\prime} & = & z \\  t^{\prime} & = & t \end{array}

What these equations mean is that the only variable which is different in the two frames of reference is the x-displacement. The y and z-displacements are unaltered (as the ship is only moving in the x-direction), and time is the same for the two frames of reference. Let us look at how the x-displacement is transformed in going from one frame of reference to the other.

Suppose the ship is moving in the positive x-direction at 5 m/s. We want to measure the position of an object which is on the deck of the ship, let’s say the mast, as time goes by. For the person on the ship, it’s position is say, 15m in front of the stern of the ship. This is clearly not going to change with time, the mast does not move relative to the ship! So, we shall call this x.

For the person on the shore, the position of the mast is going to change as the ship sails away from him. So if the ship is sailing away at 5 m/s and the mast is initially 15m away from the person on the shore, then after 1 second it will be 15+(5 \times 1)=15+5=20m away. This is the x-position x^{\prime}, the x-position for the person in the other frame of reference, as given by the Galilean transformation equations above.

You can get this straight from using the equation x^{\prime} = x + v t = 15 + (5)(1) = 20m

The Galilean transforms are mathematically very simple, and conceptually simple too. As I will discuss in a future blog, the idea of performing experiments to determine between a state of rest or uniform motion, which Galileo argued could not be done, haunted scientists for centuries. In the 19th Century, with the development of electrodynamics (the study of the electricity and magnetism of moving bodies), physicists thought they could devise experiments to distinguish one’s state of uniform motion. They were wrong in thinking this, and it led to Einstein overthrowing the whole ideas of absolute time and absolute space in his Special Theory of Relativity.

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Last night the BBC showed a programme on the faster than light neutrino experiment which has made the physics world go into overdrive in the past few weeks. If you haven’t see the programme, it is available on iPlayer here. I don’t see any bits of it on YouTube yet, but keep a look out for it as, I realise, only people within the Disunited Kingdom can watch programmes via the iPlayer.

The programme was presented by the mathematician Marcus du Sautoy, whom I have seen present some excellent programmes on mathematics in the past. As a physicist/astrophysicst, I appreciate the fact that du Sautoy said right up front that he was not a physicist. I am curious why the BBC chose du Sautoy instead of e.g. the darling of the media at the moment Brian Cox, but then again maybe the BBC feel BC is suffering from over exposure.

I put a post on FaceBook alerting people to the programme going out at 9pm last night, and a colleague of mine commented “Gosh. So they can make science tv progs quick when they need to!” (I’ll excuse her poor grammar, this time 🙂 ). Indeed, it is amazing how quickly the BBC have put the programme together. And, considering how quickly it has been put together, I thought it was excellent. Maybe du Sautoy and the film crew were able to send their finished product from 2 years in the future back in time by using faster than light neutrinos to bring the video to October 2011!

I wanted to go into a lot more details about this programme, but I don’t have time today. I will be returning to the topic of relativity in the near future – I am in the process of writing some lectures on the whole historical development of relativity, from Galileo through to Einstein, so will post bits of that story on this blog over the next few weeks.

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