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.

 

 

 

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