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General Observations Science history Sustainability/environmental

Reflections, deviations…. coffee

The reflections from the surface of a cup of coffee of a building opposite a central London cafe. Towards the edges of the cup, the coffee bends upwards, revealed by the lines bending that would be expected to be straight.

A “flat white” could be ordered from many a coffee shop. A “flat black” may be a physical impossibility. We can realise this by gazing contemplatively, or perhaps even longingly, at a long black while it cools. Notice that the surface of the coffee is ever so slightly curved. Leaving aside the white mists that you may see skipping across the coffee surface, the coffee is flat in the middle of the cup but rises towards the edges. If you have noticed this, it is most probable that you did so because of the different way the light is reflected over the surface of the coffee. It is most obvious if you can arrange the reflections on the cup to reflect something supposedly straight: a window frame or a beam of strip light for example. The reflection is fairly clear and fairly straight until about 5mm from the edge of the cup where suddenly it bends. You can see an example of this in the photograph on the right.

The reason for the curvature is of course surface tension, which is the same effect that makes droplets form into shapes that are close to spheres. First investigated by Agnes Pockels and Lord Rayleigh in the nineteenth century, surface tension is caused by the fact that molecules at the surface of the water (in the coffee) will feel a net attraction to the other molecules within the water. There being no molecules of water above the surface of the cup, the surface molecules are pulled back towards the liquid in the cup. At the sides of the cup something slightly different is happening. There, the molecules in the water will be pulled back towards the liquid but will also experience the uncompensated attraction (or repulsion) from the atoms in the mug material. Exactly analogous to surface tension, but in the solid, the interaction of the surface energy of the mug with the surface tension of the liquid will pull the liquid into different shapes. It is for this reason that highly waterproof surfaces, such as fresh oak leaves, will form spherical drops of water, but wettable surfaces, such as an oak leaf in autumn, will accumulate flatter, less spherical droplets on the surface.

coffee, red wine, wet coffee stain, coffee spill, coffee ring
The interaction between the surface tension of the water and the surface energy of the solid surface it sits on determines the shape of the droplet. These drops of coffee and wine on paper were for an experiment about coffee ring formation. The droplets are: Drops of coffee (left), soapy coffee (middle) and red wine (right)

We see the effects of surface tension too when a bubble, or a small bit of dust, sits on the surface of the coffee. Again, looking at the light reflections, we see how the coffee, or tea, bends near the floating object showing how un-flat the surface really is. Bubbles are usually large enough that we can see them directly. In the photograph on this page for example, you can clearly see the reflections from the surface of the bubble together with the bent reflections of light from the surface of the liquid. However in the case of the dust, sometimes the dust is small enough that the reason that we see it is because of the change of the path of the light reflected from the surface. For a similar reason, the insects that skate the surface of a pond are visible because of the light patterns they make rather than their intrinsic visibility. Each time we are using the deviation of the light from its expected path in order to deduce the presence and shape of an object hidden to our view.

A similar deviation of the expected path of light is seen in the phenomenon of gravitational lensing which has been used to infer the presence of black holes. Such a deviation even provided experimental evidence for Einstein’s (then) recently proposed General Theory of Relativity, just over 100 years ago on May 29, 1919. The idea that light had weight and would be deflected by a gravitational field was not new, indeed, even the Newtonian model of gravity predicted that light would be deflected as it went past a massive object*. The question was how much and, as an important secondary question, how to measure it. As Arthur Eddington later described in his book “Space, Time and Gravitation”*, according to Newton, any object thrown horizontally on the Earth’s surface would fall 16 feet (in his use of units, 4.88 m in SI) in one second. The same was true for light. However with Einstein’s theory, the predicted deflection of light was 32′ (9.75m). The difficulty for the experimentalist is that in the same second, the light would have travelled nearly 300 000 km. Detecting such a small deflection over such a large distance would be difficult, harder than seeing a grain of dust on the coffee surface. Which is where the light deflection comes in. Because if you watch as the light from a distant star travels past a massive and fairly large object, such as the Sun, you should be able to discern the small, but significant deflection. And on May 29th 1919 a total solar eclipse (which thereby blocked the extra and interfering light from the Sun) offered a perfect opportunity for Eddington and an expedition sent by the Royal Society and Royal Astronomical Society (to Brazil and West Africa) to attempt to measure such a deflection.

tea reflections, bubble on tea, surface tension, light bending
The way that light reflects off a surface of a cup of tea in this case, reveals the curvature of the tea surface. In this case the curvature is clearly due to the bubble in the centre. Sometimes you can see distortions on the surface caused by bits of dust which are difficult to see on their own.

Although the deflection was significant, working with large telescopes and photographic plates, the magnitude of the deflection of the light that they were looking for was still only 1/1500 of an inch on the photographic plate. Two groups at two different locations took multiple photographs of the eclipsed Sun and the stars around it in order to measure the position of the stars as seen behind the Sun and then compare that to the position of the stars when they had been photographed earlier in the year without the Sun between them and the Earth. Eddington describes the experiment:

“There is a marvellous spectacle above, and, as the photographs afterwards revealed, a wonderful prominence-flame is poised a hundred thousand miles above the surface of the sun. We have no time to snatch a glance at it. We are conscious only of the weird half-light of the landscape and the hush of nature, broken by the calls of the observers, and beat of the metronome ticking out the 302 seconds of totality.”

Finally after developing and comparing the images back in London, the team confirmed a deflection of 1″.98 +/- 0″.12 (Brazil) and 1″.61 +/- 0″.30 (W. Africa) for the stars closest to the Sun (NB. 1″ indicates 1 second of arc). Einstein’s theory had predicted a deflection of 1″.74, Newton’s theory had predicted 0″.87. The results of the light deflection were far more in agreement with Einstein’s new theory of General Relativity than with the classical Newtonian model.

The ‘wobble’ of a few of the stars on the photographic plates had confirmed a prediction of the theory of Relativity. Which could lead to the question: What do you see, or not, as the light dances off of your coffee?

*”Space, Time and Gravitation: an outline of the General Theory of Relativity”, Sir Arthur Eddington, Cambridge University Press, first printed 1920, 1968 edition.

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Uncategorized

Kuro Coffee, Notting Hill Gate

Kuro Coffee London
Outside Kuro Coffee on Hillgate Street.

Just off the busy Notting Hill Gate itself, on a side street, is a small corner cafe called Kuro Coffee. White brick with a couple of benches outside, the cafe is at the corner of Hillgate Street and Uxbridge Street. The area is relatively quiet and sitting on the bench outside while enjoying a coffee is certainly, strangely given the location, fairly peaceful. Kuro Coffee seems to come in two guises. The first, which we tried, was the coffee/cafe guise. This Kuro serves coffee, tea and matcha with a good selection of pastries. The second is the Kuro-late version, which has a license. We’ll have to return to try that another time.

Assuming that you are going for the coffee, you have the usual choice of drink types served either with the regular coffee or a guest single origin. On our visit, the single origin was an El Salvador with an interesting set of tasting notes, so trying the single origin long black became too tempting. It is worth remembering that the entrance to the cafe is up a couple of stairs. While this was no problem on the way in, forgetting the steps on the way out led to a slight coffee loss, though I recovered in time to save both coffee and some dignity. The cafe itself is a small room with the counter on the right as you enter. The large window at the front of the cafe gives the space plenty of light and, if you wanted to stay inside, there is seating upstairs.

Returning to the bench outside with our coffees, we watched as the traffic went past as well as the clients of the nearby dog grooming shop. The buildings around Kuro Coffee certainly give a hint as to the complex history of this area of London, together with a nod towards some of the more colourful buildings that it has become famous for. The Coronet Theatre just opposite the cafe dates from 1898 and is richly decorated in the style of the time. Towards the main road, the buildings take on an appearance far more characteristic of the 1950s-60s when the main road was widened and a lot of the historical area demolished. These block-like buildings contrast with the intricacy of the decoration on the theatre and the individuality of the houses within this part of “Hillgate village”. It has been said that the architecture of an era and location reflects the values of the society that builds it. What does this say as we look around, and which buildings, if any, resonate with us, which do we find beautiful?

Coronet Theatre, Notting Hill
The Coronet Theatre as viewed from the bench outside Kuro Coffee. The statue on the dome of the theatre is a fairly recent replacement of a much earlier statue that had not been there for years.

It is a question with relevance to physics. Many theories in physics are considered to be ‘beautiful’ but what does this mean, particularly when applied to physics? Michael Polanyi captured part of it when he wrote “The affirmation of a great scientific theory is in part an expression of delight. The theory has an inarticulate component acclaiming its beauty…”(1) We may not be able to define beauty, but the delight we feel discovering it as we learn about some parts of physics is something that we can certainly sense.

One of the theories that is considered beautiful in this way is that of relativity, one part of which has become part of our common knowledge, E = mc2. Special relativity holds that the speed of light in a vacuum is the same for all observers. This is remarkable partly because it contrasts so much with our every-day experience. When we think about our every-day, if we were to be travelling on a train and throw a tennis ball forwards, we would see the ball move away from us at, say 15 metres per second. Someone standing on the station platform watching as the train goes by would see the ball move at 15 m/s plus the speed of the train. Perhaps it is more dramatic if we threw the ball backwards, it may appear to the observer on the station platform that the ball was actually stationary as the train moved past the platform. This is not true of light. If I was on a train and could measure the speed of light travelling away from me, I would measure it travelling at 2.998 x 10^8 m/s. Someone on the platform watching light travel away from me would measure it to have exactly the same speed, we call it c.

You may say that trains are (relatively) slow, even the high speed ones, and so maybe this is just within error but it is true irrespective of the speed of the train. The famous example is of Einstein wondering what would happen if he was driving his car and looking in the internal mirror at his reflection. To begin with, everything is fine, he can see his reflection, but as the car’s speed increases to close to the speed of light what would happen then? He would see his own reflection! As if nothing has changed, the speed of light relative to Einstein would be the same, c. Someone watching and seeing that the car was travelling at, say 0.9c would not measure the speed of light in the car to be c + 0.9c = 1.9c. No! They would measure the speed of light within the car to also be, c.

The view to the right of Kuro Coffee. The concrete buildings were built when the road was widened around the position of the old toll gate itself.

The solution to this seeming paradox is how we arrive at the idea that moving clocks go slow and, of course, the famous equation E = mc2, the idea that the energy (E) of an object is equivalent to its resting mass (m) multiplied by the speed of light squared. These ideas have been tested by comparing a stationary and a fast moving atomic clock and, in the case of the energy-mass equivalence in the atomic bomb where a very small amount of mass translates to an enormous about of explosive energy. Another test of the idea is comparing the speed of light on Earth along the direction of the Earth’s rotation around the Sun and perpendicular to it. If light waves did behave like the tennis ball on the train, there should be a difference between the light speed measured in these two directions (which can be done by a technique called interferometry). The result of this experiment, now known as the Michelson-Morley experiment, supported the theory of (special) relativity: light did not behave like a tennis ball in a train(2)!

The beauty comes as we explore the physics, and the maths, that allow these equations and results to emerge. Nonetheless, it is still perplexing and boggling, perhaps even a little bit weird. Beauty can definitely be disconcerting, but it retains an ability to push the intellect into an “expression of delight”. Where else do we experience this “expression of delight”, do we recognise beauty similarly for beautiful physics and beautiful buildings? As we sit on the bench which looks towards the west, we can know that the light reflected back from the buildings is travelling at the same speed whether we look ahead of us or immediately to our right; in opposition to the additional speed of rotation of the earth or neutral to it. The buildings immediately in front of us or to our right however are certainly not of the same level of beauty and aesthetics. What makes it so? Perhaps it would be a good time to go and get yourself a coffee and a space on the bench, and just enjoy the moment as you experience the present, ahead of you and to your right.

Kuro Coffee is at 3 Hillgate Street, W8 7SP

1 Michael Polanyi, “Personal Knowledge, towards a post-critical philosophy”, University of Chicago Press, 1958

2 There is some discussion about whether the Michelson-Morley experiment prompted Einstein to think about his idea of relativity or not. As I am not a historian of science, I won’t get into this as it is incidental to the story. Einstein was certainly aware of the Michelson-Morley experiment and thought it helpful as an experimental support of his theory, the discussion of its importance in the development of the theory can be found in Polanyi cited above.

Categories
Coffee cup science General Home experiments Science history Tea

Reading tea leaves with Einstein and my great-grandmother

tea pot science
It’s not just tea, Einstein is famous for some other physics too

Ask anyone what Albert Einstein is famous for and you’ll probably (hopefully) hear that he came up with the theory of relativity (special and general). Perhaps you may also be told that he came up with a little theory explaining the photoelectric effect for which he won the Nobel prize in 1921. Maybe, if you have read this website before, you will know that he contributed to our understanding of Brownian motion, which is a phenomenon that is frequently found in a coffee cup. But it turns out that Einstein wrote another paper, far more important than any of these others, which was about tea. Or at least, I suspect my great-grandmother would have found it more important than any of these others as it coincided with a special hobby of hers, reading tea leaves.

It seems that my great-grandmother used to enjoy reading tea-leaves. Whether it was something she had learned as a child or merely used as an interesting trick to perform at family functions, stories of her examining the patterns formed by swirling tea leaves in a cup have come down to us in younger generations. Einstein too had noticed the patterns formed by the tea leaves in the cup and had observed a problem. The problem is this: If you drink a cup of (inadequately filtered) loose leaf tea and stir it, the tea leaves collect in a circle in the middle of the base of the cup. At first this may appear counterintuitive. When we stir things, don’t things fly outwards towards the edge of the cup rather than inwards to the centre of the circle? Why is it that the leaves collect in the middle?

Thames, NASA image
How do rivers erode? What causes a river to meander? The meandering Thames, photographed by NASA, Image courtesy NASA/GSFC/MITI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team

For Einstein, this tea leaf problem was connected to another phenomenon, the erosion of rivers. But it turns out that the problem is also linked to issues found in beer brewing and blood tests, and it seems, in how to poach an egg. To see the solution and therefore the connections, we need to think a bit more about how water flows. One of the brilliant lines in Einstein’s paper starts “I begin with a little experiment which anybody can easily repeat.” This experiment is to obtain a flat bottomed cup of tea with some tea leaves at the bottom of it. Now stir the tea and watch how the leaves settle, Einstein continues “the leaves will soon collect in the centre of the bottom of the cup“.

The explanation is connected with the fact that at the walls of the cup, the liquid (tea) is being slowed down by the friction between the walls and the tea. Secondly, as the tea is stirred, the surface of the tea becomes concave with a distinct dip in the centre of the swirling tea. The result of all this is that a secondary rotation is set-up where the tea flows down the sides of the cup, along the bottom and then back up in the centre and once more to the sides (have a look at the diagram, some things are easier with pictures). As they are carried along with the water, the tea leaves move towards the centre of the cup but then, being too heavy to rise again with the tea up to the centre of the cup, they stay on the bottom forming a circular patch of tea leaves.

adaptation from Einsteins paper
The secondary circular flow set up in a tea cup when it is stirred leads to a circular deposition of tea leaves (figure adapted from Einstein’s 1926 paper).

When you think about how water flows as it goes around a bend in a river, you could perhaps imagine a similar secondary flow being set up but this time from the inner edge of the bend to the outer edge and back down (so, like half a tea cup). As the water is going to be moving fastest at the outer edge, just before it plunges down towards the bottom of the river in this secondary cycle, any river erosion is going to be most noticeable on the outer edge of the bend.

It seems the effect is also used in beer brewing in order to introduce a greater concentration of hops into the brew, and to separate different types of blood cell in blood tests. So this just leaves the poached eggs. How do you poach eggs? If you have a proper poacher perhaps you get neat eggs each time but for those of us without them, poached eggs tend to be a messy cooking project. But worry no longer! Just as tea leaves collect in the centre of a tea cup, so will the egg if you ensure that your pan of boiling water is swirling around the central axis before you put your egg in. Cooking helped by physics, perfect.

For reasons of full disclosure, I should emphasise that I have only recently found this suggestion for cooking eggs ‘theoretically’ and not yet tested it. So, if you were looking for reasons to drink loose tea, or wanted to poach an egg without a poacher, perhaps you could try Einstein’s little experiment and let me know how you got on, I’d love to hear your tea leaf readings and see your poached egg results.

Categories
Coffee cup science Coffee review Observations Science history Tea

Coffee innovations at MacIntyre, Angel

MacIntyre Coffee AngelOne motivation behind Bean Thinking is to explore those connections that can be found when we stop to really look around us. Whether your interest is in history, philosophy or science, something in a café will prompt a train of reflections that can lead to interesting and surprising thought journeys. This is surely true for anybody in any café, if we just take the time to slow down. But, I admit a prejudice: while I had heard great things about the coffee in MacIntyre, when I had glanced in from the bus window, I saw the scaffolding seating arrangements and wooden surfaces that can be a type of design found in many new cafés. So I worried. Was it going to be hard to ‘see the connections’ in MacIntyre? Would I end up with a great coffee but a challenge to my assumptions about the ubiquity of connectivity?

Fortunately, I needn’t have worried. The two lovely coffees that I have enjoyed at MacIntyre gave me plenty of time to really savour both the coffee and my surroundings and I was wrong in my assumptions from the bus window, connections really are everywhere. The café itself was a delightful find. Watching other customers while drinking my long black, it seemed that everyone was greeted by a cheery “hello”. Many people were clearly regulars, which is perhaps unsurprising for a friendly café with good coffee in a busy area. The scaffolding and wooden seating also works in the space at MacIntyre, giving a strangely relaxing feel to the café. The café itself is rather narrow, with the seating on one side and pastries/ordering queue on the other. Tap water was delivered with the coffee, without my needing to have asked for it.

Plant, light, scaffolding at McIntyre's Angel
Good scaffolding also has good connections.
Plant and light at MacIntyre.

MacIntyre may also be a great spot if you are into people watching. Amidst the general busy-ness, I could eavesdrop on conversations about the latest coffee news and the rise of artificial intelligence (these were two separate conversations!). Perhaps the conversations were particularly noticeable owing to the acoustics of the wooden walls and the narrow, small space of the café. At various points around the café, plants hung from the scaffolding. Some of the plants were spot-lit, which caused me to wonder whether the light that the plants were receiving was optimal for photosynthesis. The menu was projected onto the rear wall of the café, which was also decorated with hexagons, an immediate connection to graphene.

But then, in my coffee cup, the significant crema on the coffee showed evidence of amazing thermal convective motion together with turbulence. The coffee itself was very sweet with nutty overtones but the movements of the crema reminded me of cloud formation in thunderstorms. Although thunderstorms didn’t make it to the thought train of MacIntyre, another form of surface motion suggested a connection to another, unusual, feature of this café. You see, MacIntyre is a cashless business, no cash is accepted even if you’re only buying a long black. Most customers on my visit paid with their contactless cards.

The idea of a cashless society is one that has obvious advantages for both the business and the government/economy (whether it has such obvious advantages for the consumer I will leave as a point to be debated). While some countries are attempting to move to a more cashless economy, for a business to be entirely cashless is somewhat innovative. Even though MacIntyre is not the only café to go cashless (Browns of Brockley is similarly cash free), it has to be one of the first cafés to do so.

Coffee at MacIntyre Angel
Coffee and water on wood at MacIntyre Coffee. Could you increase the returns on your investments by understanding the movements on the surface of a cup of coffee?

What is the connection between this and the surface movement on my coffee? Well, it is not just at MacIntyre that a café has supported an innovation that has (or may) change our economy. Just over three hundred years ago, Jonathan’s Coffee House in Exchange Alley was a place of similar innovation, though there it was a customer rather than the coffee house itself that gave the change.

It was at Jonathan’s in 1698 that John Castaing published a paper twice a week detailing the latest stock prices titled “The course of the exchange and other things”. Recognised now as the origin of the London Stock Exchange, how stocks are priced and how their prices vary with time are subject to intense mathematical modelling. Although now, these models can be extraordinarily complex, the base of many of them share a mathematical model with the movements on the surface of your coffee cup, Brownian Motion.

Jonathan's coffee house plaque
The site of Jonathan’s in Exchange Alley. Seen while on a Coffee House tour last year.

Brownian motion is the phenomenon in which small particles of dust, or coffee grains on the surface of your coffee move in a random way as a result of collisions between the particles and the molecules in the liquid. First described in detail by a botanist, Robert Brown in 1827, the experimental evidence in favour of the molecular-collision explanation of Brownian motion came in 1910 with Jean Perrin’s careful experiments (that have featured in The Daily Grind previously). The maths behind the explanation relies on the idea of the ‘random walk‘ in which each dust particle is ‘kicked’ in a random direction by the molecules in the coffee, the consequent motion being frequently described with reference to a drunkard attempting to get home after leaving the pub. However, as this concept of the ‘random walk’ was being developed for molecules in a liquid, it was simultaneously being developed to model the movements of stock prices by the mathematician Louis Bachelier. Bachelier’s model of stock prices turned out to be the same as the model of Brownian motion, but both developed independently.

As yet, it is unclear (to me at least) whether there is a link between cashless payments and some of the maths in your coffee cup but, MacIntyre would be a great place to contemplate this as you sip your brew. Never succumb to prejudices, on which note please do let me know what you think of cashless payments, a great convenience or an invasion of privacy?

MacIntyre can be found at 428 St John St, EC1V 4NJ.

Categories
General Observations slow Tea

Tea Gazing

Milky Way, stars, astrophotography
The Milky Way as viewed from Nebraska. Image © Howard Edin (http://www.howardedin.com)

A recent opinion piece about last week’s announcement of the detection of gravitational waves at LIGO drew my attention to a quote from Einstein:

The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed.

Einstein was not the only scientist to have expressed such sentiments. Many scientists have considered a sense of wonder to be integral to their practice of science. For many this has involved gazing at the heavens on a clear night and contemplating the vastness, and the beauty, of the universe. Contemplating the twinkling stars suggests the universe outside our Solar System. Watching as the stars twinkle gives us clues as to our own planet’s atmosphere. Of course, it is not just scientists who have expressed such thoughts. Immanuel Kant wrote:

“Two things fill the mind with ever-increasing wonder and awe, the more often and the more intensely the mind of thought is drawn to them: the starry heavens above me and the moral law within me.“*

light patterns on the bottom of a tea cup
Dancing threads of light at the bottom of the tea cup.

The other evening I prepared a lovely, delicate, loose leaf jasmine tea in a teapot. I then, perhaps carelessly, perhaps fortuitously, poured the hot tea into a cold tea cup. Immediately threads of light danced across the bottom of the cup. The kitchen lights above the tea cup were refracted through hot and not-quite-so-hot regions of the tea before being reflected from the bottom of the cup. The refractive index of water changes as a function of the water’s temperature and so the light gets bent by varying amounts depending on the temperature of the tea that it travels through. Effectively the hotter and cooler regions of the tea act as a collection of many different lenses to the light travelling through the tea. These lenses produce the dancing threads of light at the bottom of the cup. The contact between the hot tea and the cold cup amplified the convection currents in the tea cup and so made these threads of light particularly visible, and particularly active, that evening. It is a very similar effect that causes the twinkling of the stars. Rather than hot tea, the light from the distant stars is refracted by the turbulent atmosphere, travelling through moving pockets of relatively warm air and relative cool air. The star light dances just a little, with the turbulence of the atmosphere, this way and that on its way to our eyes.

Marcus Aurelius wrote:

Dwell on the beauty of life. Watch the stars, and see yourself running with them.Ҡ

Marcus Aurelius of course didn’t have tea. Watch the dancing lights in the tea cup and see yourself sitting with it, resting a while and then watching while dwelling on the beauty in your cup.

*Immanuel Kant, Critique of Practical Reason

†Marcus Aurelius, Meditations

Categories
Coffee review Coffee Roasters Observations Science history slow

Waiting for a green light at Alchemy, St Pauls

8 Ludgate Broadway, St Pauls
Alchemy Coffee

Alchemy, “a seemingly magical process of transformation, creation or combination”, is certainly a cafe that lives up to the dictionary definition of its name. The branch, on Ludgate Broadway near St Pauls, is the outlet that ‘showcases’ the coffee of Alchemy Roasters. On walking into this cafe, I was presented with a menu of two types of beans for espresso based drinks or two different beans for filter/aeropress. Both sets of coffees came with tasting notes. After a brief chat with the friendly barista I went for the San Sebastian with aeropress. Notes about the origins of the coffee are dotted around this superbly sited cafe (its location is ideal for people watching). The coffee is directly traded (where possible) and, if lattes or cappuccinos are your thing, there are also details about the farm that produces the milk.

Although there were cakes on the counter, I had just had lunch and so had to pass on what looked to be a good selection of edibles. The coffee though was certainly very good and definitely an experience to be savoured. As, perhaps I should have expected, when the coffee arrived it came in a beaker reminiscent of chemistry laboratories. From my chair in the corner, I could watch the preparation of the coffee behind the counter, the people coming into the shop to order their coffee and the crowds passing by outside.

E=mc2 Einstein relativity in a cafe
Scales at Alchemy. Weights on one side, chocolate on the other, it can only mean one thing: energy-mass equivalence

Close to where I was sitting was an old style set of measuring scales. This see-saw balance had weights on one side and chocolate on the other. Perhaps this connection seems tenuous, but for me weights on one side of the scales and an energy bar (chocolate) on the other side could only mean one thing:

E=mc²

The equation relating energy and mass for a particle at rest derived, and made famous by Einstein. The equation comes from Einstein’s theory of special relativity which states that nothing can be accelerated to faster than the speed of light (in a vacuum). First set down in 1905, the theory has some very odd predictions, among which the best known is probably the twin paradox (details here). The idea is that a moving clock will be observed to run slowly by a stationary observer, a prediction that has been confirmed several times by experiments using atomic clocks (here).

San Sebastian via Aeropress
Coffee is served at Alchemy

Moreover, the equation states that mass and energy are equivalent and that a small amount of mass can produce an awful lot of energy, (details here). A detail which will bring this story of a cafe-physics review nicely back to the Alchemy cafe, to London and to the importance of slowing down. The connection is through a set of traffic lights in Bloomsbury. Back in 1933, Leo Szilard was waiting to cross the road at the traffic lights at the intersection of Russell Square with Southampton Row. Szilard had recently escaped from Nazi Germany and was spending his time as a refugee in London pondering different aspects of physics†. That September day, Szilard was thinking about a newspaper article featuring Ernest Rutherford that he had read earlier. In 1901  Ernest Rutherford, together with Frederick Soddy, had discovered that radioactive thorium decayed into radium. The changing of one element into another could be considered a type of modern day alchemy. However Rutherford did not believe that there could ever be a way of harnessing this nuclear energy. In the article read by Szilard in The Times, Rutherford had dismissed any such ideas as “moonshine”. Szilard was forced to pause his walk as he waited for the traffic lights to change. Those few moments of pause must have helped clear Szilard’s mind because as the light went green and Szilard was able to cross the road, a thought hit him: If every neutron hitting an element released two neutrons (as one element was transmuted into another), a chain reaction could be started. As part of the mass of the decaying atom was released as energy, it would mean that, feasibly, we could harness vast amounts of energy; E=mc².

This idea, a consequence of spending five minutes waiting for a traffic light rather than checking Twitter (not yet invented in 1933), proved to underpin both the nuclear fission which we use in electricity generation and the nuclear fission that we’ve used to develop weaponry. It makes me wonder what alchemy we could conjure in our minds if we stopped to enjoy the transformations of the coffee beans at Alchemy.

 

Alchemy (cafe) is at 8 Ludgate Broadway, EC4V 6DU

† A book that some may find entertaining is:

“Hitler’s Scientists”, John Cornwell, Penguin Group publishers, 2003. The book contains this anecdote about Szilard: As Szilard was of Hungarian-Jewish descent, he fled Germany to Britain via Austria on a train a few days after the Reichstag fire of 1933. On the day he left, the train was empty. One day later, the same train was overcrowded and the people leaving Germany were stopped at the border and interrogated.  An event that prompted him, a few years later, to reflect “This just goes to show that if you want to succeed in this world you don’t have to be much cleverer than other people, you just have to be one day earlier than most people.” Something to reflect on in today’s refugee crisis perhaps.

Categories
Coffee cup science Observations Science history

Perpetual motion in a coffee cup

V60 from Leyas
Could your coffee be used to power a perpetual motion machine?

There can be no such thing as a perpetual motion machine right? Yet less than two hundred years ago it seemed possible that there could be. Not just that, the source of this perpetual motion machine was in your coffee cup. How would you explain Brownian motion?

Brownian motion is the random movement of small bits of dust or coffee/tea particles on the surface of your brew. To see it, you may have to use a microscope though you should take care not to confuse Brownian motion with motion caused by convection currents. There will be Brownian movement even a long time after the coffee has got cold. What causes this continuous movement? When he observed it for the first time in 1827, Robert Brown (1773-1858) had thought it was to do with a ‘life force’. He had been observing pollen suspended in water and noticed that the pollen kept moving under his microscope lens. In 1827, this was a very reasonable explanation, after all, weren’t several people looking for a motion, a force, that gave life?

Sphinx, Brownian motion
Brown used some dust from the Sphinx (shown here with the Great Pyramid) to show that ‘Brownian’ motion could occur in inorganic materials. Postcard image © Trustees of the British Museum

So, he checked if he saw the effect in pollen that was one hundred years old (he did) and then in truly inorganic matter, he looked at the dust from a fragment of the Sphinx. Again he saw the dust fragment move in the water. He had therefore shown that it was not associated with a life force but was something that happened for every small particle suspended in a liquid. What was driving it?

Without knowing what caused it, some people in the nineteenth century had already suggested a device to exploit it, using tiny levers to carry the energy from this continuous motion into devices. Others insisted on finding out what was causing the motion but it was here that the physics of the day hit a philosophical problem. It was proposed that molecules in the water could be hitting the dust on the surface and moving the dust in seemingly random directions. And yet there is a problem with this explanation. At that time there was no way of seeing or measuring molecules. How could physics postulate a theory – or suggest a reality – that could not be tested?

Nasa, Norway, coastline, fratal
How long is a section of coastline? Coastlines can be described as fractal like. Mathematics that grew out of studying random walks and Brownian motion. Image credit NASA Visible Earth/Jeff Schmaltz

An answer came one hundred years ago in a paper published by Albert Einstein (1879-1955) in 1905. In it he made some mathematical predictions that, for the first time, allowed the theory (that it was molecules causing Brownian motion) to be tested by experiment. Jean Perrin (1870-1942) of the Sorbonne, Paris, was the experimentalist who, by careful observation of droplets of water containing a pigment used by water colour artists, provided evidence for Einstein’s theory of Brownian motion. The experiment was so important that Perrin later wrote “.. the molecular kinetic theory of Brownian movement has been verified to such a point in all its consequences that, whatever prepossession may exist against Atomism, it becomes difficult to reject the theory.”

The consequences for our world have been profound. The mathematics that describes Brownian motion is that which we use as the basis to predict the movements of the stock exchange. Extensions of the mathematics have been used to develop new areas of mathematics such as fractals. Even art has grasped the theory of Brownian motion, the Anthony Gormley sculpture “Quantum Cloud” is based on mathematics describing Brownian motion. Everywhere you look there are phenomena described by the movements in your coffee cup. What we have yet to do is find that perpetual motion machine.