Relativity – Bean Thinking

Outside Treelogy on Eastbourne Terrace, Paddington. The topiary could suggest a series of strontium atoms lining up on top of each other.

Good coffee near a mainline train station? It’s often difficult to find a good spot to take time to enjoy a coffee if you only have about 30 minutes (or less) before your train. Fortunately for coffee lovers in London, both Kings Cross (/St Pancras) and Paddington have several very good speciality coffee places nearby. There’s the cafe in the Pilgrm hotel just across the road from Paddington on London St, but Treelogy is perhaps even closer, directly opposite the buildings that house the new Elizabeth Line on Eastbourne Terrace.

Treelogy appears to have opened in April 2023. There does not seem to be much information online about it apart from Trip Advisor reviews so, having approximately 50 minutes before we needed to catch a train, we decided to stop at this new cafe. The interior is very modern and open. The counter is in front of you on the left as you enter with plenty of seats in the window and along the wall, as befits a cafe that is also close to a station. The style of some of the seats in the cafe and the fact that it is going to attract people who are about to embark on journeys (or have just come off a journey) means that there are elements here that could remind you of the scene in Edward Hopper’s Nighthawks. The coffee appears to be roasted by Treelogy themselves. There was a wide selection of pastries and breakfast bagels arranged on the counter and so we ordered two coffees to stay, and a bagel for the train.

The “Real Time” clock by Maarten Baas in Paddington. How much do they pay that man to be there all day?

We intended to sit on the bench just outside the cafe with our coffees but nonetheless we were offered our coffee in ceramic cups which was a nice touch. Inside, there was plenty to notice: circular lights on the wall leading to the back of the cafe which resembled ship lighting. A coffee dictionary book (and a book by Martin Wolf) that could offer a good read or a thought train on the physics of finance and the (Brownian-motion) links to coffee. The travellers with their roller bags going in and out of the cafe, who are they and where are they going? Yet, moving outside and settling down, the oat milk flat white and long black were both a very enjoyable way to spend time with a coffee.

As we were ‘spending the time’ with the coffees, the hands of the “REAL TIME, Paddington” Maarten Baas clock were being re-drawn every minute. Installed back in 2021, this clock appears as if the time is being painted onto the clock face by a man who seems trapped inside the clock. Each minute he erases the minute hand before redrawing it into its new correct position. Literally marking the minutes before our train is due.

For a physicist waiting for a train, an immediate thought may occur: what does ‘Real time’ mean? Admittedly, this question fades into the background again as the man wanders around, points at something on the clock, adjusts his position and then gets ready to move the clock hand again. The art is distracting from the question. But the question keeps surfacing: what is a minute, what is a second, is time absolute? There is perhaps a diversion that could be made here to a more philosophical question about the nature of time and our perception of it but we only had one long black and one flat white, the physics may take longer than that anyway!

A closer view of the man in the clock as he is erasing the minute hand of the clock. The colour bands on the clock face are not really there but are the result of the projected video onto the clock face and the way that the camera images that.

The physics bit remains because you may remember hearing about Einstein’s twin paradox, a thought experiment arising out of an aspect of his theory of Special Relativity. Relativity in general in physics refers to moving ‘frames of reference’, a classic case is that of a person on a train relative to a person on a station platform. For the person on the train, they are stationary, with respect to the train carriage. If they bounce a ball on the floor of a carriage, the ball bounces straight back up at them. They do not experience themselves moving (apart from when the train is accelerating or braking) and instead to them it appears that the person standing on the station platform is moving, backwards at the speed of the train.

Ordinarily our brains will process this and recognise that it is we who are on the train that are moving and we identify the ‘rest frame’ (the frame that is not moving) with the station platform. However we may all have experienced the sensation when on a train in a station next to another train. As the guard whistle blows the train moves but we cannot immediately tell whether it is our train that moves or the train next to us. This is the essence of relativity: all reference frames move relative to each other. The frame that is genuinely at rest is the one we define so (even the station platform is moving relative to the Sun, we just don’t notice this movement of the Earth at all).

Einstein’s theory of special relativity arises out of the special case when one of the moving frames is travelling at close to the speed of light, c. As the speed of light in a vacuum is constant, what would happen if someone travelling in a car at a speed just less than c looked at themselves in the rear view mirror? Einstein’s answer was that they would see themselves as anyone would because, relative to the reference frame of the car, the speed of light is still constant, it is still c. However an observer outside the car looking at the car and the person looking at themselves in the mirror also measures the speed of light as c, not nearly 2c (the speed of light plus the speed of the car). The speed of light in a vacuum is constant!

The explanation for this apparent problem is that our perception of time (and of distance) is not the same at different speeds. A person moving at a fast speed (relative to a person defined at rest) would have a wrist watch that was slow, relative to the person at rest – moving clocks go slow. This is the origin of the twin paradox which is that if one of a pair of twins travels away from Earth at close to the speed of light and returns, they will return younger than their twin who remained ‘at rest’ on Earth (but not relative to the twin who travelled who considered themselves at rest too so their earth bound twin should, to them, be younger).

Topiary at the entrance to Treelogy. The atomic clocks used in the study described in the text used super cold strontium ions positioned just above each other.

The solution of the twin paradox comes with Einstein’s second theory of relativity: General relativity. Special relativity only concerns the case when different frames of reference move at constant relative velocity to each other. General relativity extends the case to accelerating frames and gravity. In order to meet again, the twin in the space ship had to turn around (decelerate and accelerate again). This changes the situation from the case expected purely from special relativity. There is a lot of experimental evidence for both special and general relativity, but recently one test of general relativity tested the idea on a very small scale.

The theory of general relativity postulates that it is not just moving clocks that go slower. Clocks in strong gravitational fields will also run more slowly. The extreme example of this would be the event horizon of a black hole, but even on Earth, a clock closer to the centre of the Earth will tick more slowly than one that is further away. Remarkably this prediction has recently been verified using extremely accurate clocks by measuring time using atoms spaced just 1 mm apart. The ‘clocks’ of the atoms 1 mm lower moved slower than the clocks of the atoms 1 mm above. Absolutely astonishing! And yet absolutely expected because one remarkable and weird feature about physics is that it seems to be universally applicable: what happens at the event horizon of a black hole shares the same physics as what happens in conditions far less extreme, conditions found in a coffee cup.

The Real Time clock is 7.8m above the pavement where I was enjoying my coffee. These experiments mean that I can be confident that the clock is going very slightly faster than the time I experience sitting on the bench. However, I shouldn’t use this thought to justify enjoying my coffee much longer and thereby miss the train! It seems that our trains aren’t quite so precise as the deviations implied by the theory of General Relativity. It is still necessary to get through the barriers with several minutes to spare. Treelogy, and the clock man, will have to wait for a return visit.

Treelogy is at 48 Eastbourne Terrace, W2 6LG

More about Einstein’s theories of relativity can be found here or in a good book in a library.

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.