Thoughts on – err… things

Thoughts on – err… things

Do you often get thoughts about random things that flit across your brain and you never get to know the answer to.

For example, why should you never end a sentence with a preposition such as “to”.?

The answer is, ‘you can’. It is one of the many grammar myths that came about when Latin grammar was imported into English. The above sentence could be written as:

Do you often get thoughts about random things that flit across your brain and to which you never get to know the answer? No one really talks like that do they?

Here are few thoughts that I have had recently.

1 – “The wheels on the bus go round and round.” Do they really? 

You walk over to your car, which is waiting for you in the desert of the supermarket car park.  You notice there is a stone jammed in the tread of the front near side tyre. It doesn’t look too big so you decide to drive off without doing anything about it. You get in the car. It is a hot day and the air in the car is cooked and stale so you zip down all the windows. You drive off. There is a ‘tap, tap’ which gradually increases in frequency as you accelerate. You realise it is the noise of the stone in the tyre hitting the road as the wheel rotates.

‘Wait a minute,’ you think. ‘If the wheel is rotating, why hasn’t the stone been scuffed out of the tyre?’

This means that the part of the tyre that holds the stone must be stationary when it is in touch with the ground. But the car is moving forward at 30 mph., how can part of the tyre be stationary? The wheel is part of the car so the centre of it must also be moving forward at the same speed. What about the top of the wheel, the part opposite to the stone? To compensate and to allow the centre of the wheel to be moving at the same speed as the car, it must be moving forward, at twice the speed of the car – 60 mph. This means that the tyre goes from being stationary and in touch with the road surface and then it speeds up until it is moving at twice the speed of the car and then it slows down until it is stopped again as it touches the ground..

So any particular point on the tyre is stopping, speeding up and then slowing down to a stop again on each revolution. It looks though, as if the wheel is smoothly rotating. And the wheel is attached to the car so must be going at the same speed as the car.

How can all these different facts be true at the same time? No wonder tyres are so expensive when they have to do so many different things at the same time.

2 – A fly hitting a fast car head on

A car is driving along the motorway at 60 mph in a straight line. A fly is going in the opposite direction at 5mph. The car hits the fly. The fly is splattered on the windscreen. The car is unaffected by the collision, apart from the splat on the windscreen. Both the car and the splat are now travelling at 60 mph along the motorway in the original direction.

The fly has now reversed direction and is now travelling at the same speed as the car. During that reversal, it must at one stage have stopped. At the moment of impact the car was in contact with the fly which stopped during the process. If the fly stopped and it was in contact with the car, the car must also have stopped.

When you are driving a car do you find that it stops every time you hit a fly? If not, why not?

3 – Ageing whisky

You can go to a whisky distillery in Scotland and arrange buy an oak cask of whisky. ( Quite a lot of money may change hands during this process ).

The distillery will then store this cask of whisky for you until you are ready to drink it. This is often 18 or 21 years later when the child you bought it for comes of age. If this was any other food it would have turned rancid or been otherwise ruined by the passage of time and the attacks of bacteria, fungus and virus. This is why foods have a ’Best Before’ date on them. If that’s the case, how come whisky last so long and improves as it ages – so they say?

It is part of the traditional process that the owner of the whisky returns to sample the quality of the whisky several times over the years. The whisky gradually turns darker and the flavour changes. It is also interesting that, although the barrels do not leak, there is some air borne interchange between the inside and outside of the barrels so the volume of whiskey decreases over the years.  The part that evaporates away is called the angel’s share. Strange, I thought angels didn’t drink, but they obviously do in Scotland.

There is a great deal of mystique about the whole process. My cynical side starts to ask questions at this stage.

The pure distilled whisky tastes of nothing when it is first put into the barrel so the flavour must come from the oak of the barrel. So why not get some cheap alcohol from a chemist, dilue ( using the same magical water from the local burn ) it down to the same percentage as the new whisky and then put it into an oak barrel for several years – I wonder if you could tell the difference?

Finally, if the whisky gets better as it ages because the alcohol stops any spoilage organisms growing, shouldn’t each bottle have a ‘Best After’ date on the label?

4 – Plutonium radioactive decay

First take a lump of plutonium and mould it into a sphere. Don’t make the sphere too big as it will likely go “poof” in your face. This happens when the mass of the sphere reaches 11kg and the diameter is a surprisingly small 10.2 cm in diameter. This is because plutonium has a density of just under 20gm/cm^3.

Now plutonium is one of those strange materials that is radioactive. This means that it will slowly decay to uranium.

This is where things start to get rather strange non intuitive.  You will know, of course that there are about 1.2×10¹⁸ atoms in an average size grain of salt. This is a huge number – 1.2 followed by 18 zeroes. You can now estimate how many grains of salt it would take to make up a sphere the same size as your plutonium sphere, remembering, of course, that plutonium atoms are larger than salt atoms. You can look this up on the periodic table ( BTW. What is it when it isn’t a table ?)

So you now have your sphere of plutonium sat on your coffee table. The next question is – how long will it take to decay to something else and no plutonium is left? The answer is unknowable or never. It can be estimated of course but it is complicated by the fact that plutonium decays exponentially so there is a very long tail-off and theoretically zero is never reached.

So this is where the expression ‘Half Life’ comes in. This is the calculated time when half of the atoms have decayed. It can be calculated exactly as the decay curve is a mathematically accurate exponential. The half life of plutonium is when only half of it is left – for plutonium 239 this is 24,200 years. Plutonium decays to uranium 235 by emitting alpha particles. There is an ongoing chain of decay until it is finally all decayed to lead. The chain is Plutonium-239 → Uranium-235 → Thorium-231 → Protactinium-231 → Actinium-227 → Thorium-227 → Radium-233 → Radon-219 → Polonium-215 → Lead-211 → Bismuth-211 → Thallium-207 → Lead-207.

We know the rate of decay of plutonium, we know how many atoms (approximately) are in our sphere and all plutonium atoms are, by definition, exactly the same, then we should be able to predict when any particular atom will decay during the thousands of years it is sitting on your coffee table? Wrong! This is where it becomes counter intuitive. Each atom is the same as every other one so how does it ‘know’ when to decay compared to all the others to give that beautiful exponential decay curve. Now is the time to ask a physicist this question. The answer will be something like this: “We can predict when half of the original plutonium has decayed and any other fraction we specify but we cannot predict when each individual atom will decays as that is a probabilistic event.” No, me neither! This decay is controlled by quantum mechanics which is inherently probabilistic.

If you would like to find out more, I wish you luck. I tried and just dug myself deeper in the mire.

5 – Expansion of the universe speeding up

The universe was thought to be expanding In 1927 by the Belgian Catholic priest Georges Lemaître. He observed the red shifts of spiral galaxies and calculated the Hubble law, named after Erwin Hubble. He based his theory on the work of Einstein and De Sitter, and independently derived Friedmann’s equations for an expanding universe.

If the universe is expanding and everything in it is moving away from everything else then it should be possible to ‘wind the clock back’ until the universe becomes a point or singularity. This was done and then the Cosmic background Radiation ( CMB )was discovered in  1964 which confirmed the Big Bang theory.

This was all fine and everyone agreed that this was all sorted out. The universe was expanded and the expansion was slowing down because of the drag of gravity so eventually the expansion would stop and then go into reverse. This would then result in the Big Crunch as all matter returned to a singularity. It would then start the cycle over again, called the Big Rebound and result in a new universe. This was agreed and everyone was happy.

Then it was found in 1998 by Supernova Cosmology Project and the High-Z Supernova Search Team, that the expansion of the universe was speeding up. This meant that the constant that Einstein put in his general relativity equations to make them work, called Lambda, and later removed by him( He called Lambda his greatest mistake ) could now be put to use again to account for the expansion accelerating. Lamda is also called Cold Dark Matter ( CDM )  and this theory is called the Lambda-CDM model.

I think this a classic case of science working well as each scientist builds on the work of those preceding them. What Newton called ‘Standing on the shoulders of giants.’

This dark matter or the associated dark energy has not yet been found. The hunt continues.

6 – How do polaroid sunglasses work and how can they demonstrate quantum mechanics.

This difficult to explain and requires a large number of words so I think the best way of seeing this is to look at a demonstration.

Here is the explanation in words with no math, from Wikipedia.

Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equivalently, a photon can be described as having horizontal or vertical linear polarization, or a superposition of the two.

The description of photon polarization contains many of the physical concepts and much of the mathematical machinery of more involved quantum descriptions, such as the quantum mechanics of an electron in a potential well^{[dubious – discuss]}, and forms a fundamental basis for an understanding of more complicated quantum phenomena. Much of the mathematical machinery of quantum mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell’s equations in the description. The quantum polarization state vector for the photon, for instance, is identical with the Jones vector, usually used to describe the polarization of a classical wave. Unitary operators emerge from the classical requirement of the conservation of energy of a classical wave propagating through lossless media that alter the polarization state of the wave. Hermitian operators then follow for infinitesimal transformations of a classical polarization state.

Many of the implications of the mathematical machinery are easily verified experimentally. In fact, many of the experiments can be performed with two pairs (or one broken pair) of polaroid sunglasses.

The connection with quantum mechanics is made through the identification of a minimum packet size, called a photon, for energy in the electromagnetic field. The identification is based on the theories of Planck and the interpretation of those theories by Einstein. The correspondence principle then allows the identification of momentum and angular momentum (called spin), as well as energy, with the photon.

Well, that was simple enough wasn’t it?  Here is the link to a demonstration on U tube.

https://www.youtube.com/watch?v=zcqZHYo7ONs

Did you manage to follow this all the way through and understand it?

Now you are ready to move on to  Bell’s theorem – good luck!

© Richard Kefford    2017                                                                             Eorðdraca

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