Short circuit

 We set up a circuit with two bulbs in it. The ammeter reading was 1.00A. Note that I'm holding a spare unconnected lead.

Then the lead was connected to the other side of the bulb. That bulb went out straight away and the current went up to 1.39A. The spare wire is called a SHORT CIRCUIT. The increased current can be dangerous because current is what heats in a circuit. The extra heat can sometimes set fire to the insulation and cause house fires.

Interesting design of car park light at Dobies

This design of light is at Dobies at Dalston. It seems to be designed to reduce light pollution. All of the light should be directed downwards. The silvered surfaces are also dimpled. I assume this is the ensure diffuse reflection so that an image is not focused anywhere below.

Thermistor experiment

Today we put a thermistor into hot water with a thermometer and watched the resistance as the water cooled down. The resistance went up. I now understand the band theory idea better after learning some solid state quantum mechanics. Single atoms have clearly defined electron energy levels but as you bring atoms closer together to bond them, the electron energy levels cannot merge. Instead, for neighbouring atoms, one has its level nudge slightly up and the other has it nudge slightly down. On a grand scale, this results in a lot of almost but not quite identical electron energy levels. They form bands because they are grouped around the same energy. In semi-conductors, there is a clear gap between the valence band for bonding and the conduction band. Thermal energy is enough to move some electrons up from the valence band to the conduction band. More conduction electrons means higher current so we conclude that the resistance has fallen. The converse is true for cooling.

Shadows in the sky

 In the picture above, there is a thin dark band stretching down and right from the edge of the cloud. It is a shadow of the cloud as the Sun was away over to the left at the correct angle. Consider the photograph below. The shadow appears on the solid surface. There is no evident shadow visible in the air between us and the concrete. I have seen higher clouds project shadows onto lower levels so it suggests that tenuous water vapour in the air above the Solway might be substantive enough to scatter light from the Sun back to us, making it obvious where there is no light getting through to be scattered. It's like seeing a shadow projected onto smoke.

Considering eigenvalues and eigenvectors

I'm reading this wonderful book again. I have been stuck for a long time trying to get an understanding of what a state actually means in Quantum Mechanics. I started with eigenvalues and eigenvectors for spin. If the spin operator acts on |u> then it remains unchanged. So |u> is an eigenvector. The eigenvalue is the multiplier - in this case it is +1. Notice that applied to |d> you get the same vector |d> but multiplied by -1. So |d> is an eigenvector with eigenvalue -1. The significance of the eigenvalues is that whatever state the system is in, you only ever measure it out as +1 or -1. So I picked another state vector and multiplied it out. I showed that it could be written in terms of the eigenvectors |u> and |d>. However if the system is in this mixed up state and you measure, you still get either +1 or -1. These are the eigenvalues. I have been wondering what the significance of the eigenvectors are.

 Susskind says that this component state vector tells us the probability of measuring +1 or -1. I experimented myself with the maths, so what is below might be wrong but I think that the expectation value is the inner product squared. I get a probability of 1/2 which is what I expected. I think I have uncovered the significance of the orthogonal basis. The zero result for removes it from the equation. Orthogonal products give either 1 or 0. 

I have struggled with degenerate states. Different eigenvectors but with the same eigenvalue. So only one value is measured. The eigenvectors are not orthogonal but you can construct an orthogonal basis by putting together linear combinations of them. I am trying to get this in writing whilst I am thinking about it and may have to publish corrections later.

Maths on In Our Time

Melvyn Bragg is Lord Bragg of Wigton and through his Radio 4 programme In Our Time has been a great friend of Physics. Recently I have been enjoying back issues on Maths. Try these: https://www.bbc.co.uk/programmes/b09gbnfj and https://www.bbc.co.uk/programmes/b00dshx3 I have been trying to learn about Hilbert Spaces to understand Quantum Mechanics and the second programme gave me an insight into Hilbert's character.

Learning about Hemititian Hamiltonians

Today I have learned that a Hermitian matrix like a Hamiltonian is real on its diagonal but has complex conjugates the other way. Leonard Susskind says that any operator L can be made up up components of the spin operators and the identity. a, b, c and d are real.

 Dagger means the complex conjugate of the transpose. I then did an example with numbers.