TMA01 to Quantum Tunnelling!

I have just completed part 1 of the test paper (TMA 01), for my University maths course MST121, with the Open University.  The paper consisted of approximately 40 available marks, for answering questions based on the main topics of Linear equations, using a Maths algebra package (Mathcad), and some detailed work on linear recurrence systems in geometric, arithmetic and mixed forms.

I have to say, that I find the linear recurrence sequence work to be particularly dull, as I always associate this type of work with biology or geography sciences; picturing someone using this type of maths, sitting in a cold hut, counting populations of beetles or birds!

Certainly not my cup of tea, which probably isn't helped by the fact that I have had my eyes opened, this week, by some of the Quantum mechanics books that I am reading as supplementary material.

As well as my book of the month, mentioned in a previous post; I have also picked up some other books to browse when the mood takes me.

They are:

Why does E=MC^2?  by Brian Cox and Jeff Forshaw

The Strange World of Quantum Mechanics by Daniel Styer


Having read some Stephen Hawking books in the past, such as 'Brief History et al.'; I am familiar with the warping of Space-Time and the weird effects it can bring.  However,  it still doesn't helpto  make it all easier to accept as true!

Such effects as, time moving slower for someone that is travelling faster, relative to another person.  Or the fact that gravity can warp Space-time causing time to stop inside a black hole; or even, that time actually may not have existed before the 'Big Bang'.  All of this tends to cause a certain amount of uneasiness, inside.


Because we experience a day-to-day reality that appears to be governed by classical physics as extolled by Newton, and because most of us will probably never be able to experience near to the speed of light travel, for example.  We can never actually experience these effects, for ourselves.


This lack of 'first-hand' experience, makes all these things remain almost in the realms of science-fiction, for the layperson.


Interestingly, in my book of the month, 'How to Teach your Dog Quantum Mechanics', there is a photograph, of a layer of individual, copper atoms, as imaged by a tunnelling electron microscope.  The microscope uses a phenomenon where there is a probability that a quantum particle, such as an electron, can approach a barrier like a thin sheet of metal; and then simply appear on the other side, without going through the metal atoms, themselves!  It's as if it just appears on the other side, with no loss of energy, no loss of mass and no tiny hole, that it has gone through, to get there.


It's this property of electrons, that has allowed this photo of copper atoms, to be taken.  If you get a chance, do look at the photo, it's amazing (p.163).  If you look at the middle of the image, you will see some wave-like ripples, in the area around the atoms.  These wave-fronts are actually the electrons, as they pass the atoms.  The electrons are thus being seen in their 'wave' form, rather than as individual particles.  Weird!!!