S357 - Space, Time and Cosmology - a student's perspective by Norrette Moore

This third level course makes different demands of the student than other physics courses at this level. Other offerings, such as Quantum Mechanics or Electromagnetism have a high level of mathematical content, and assessment generally involves use of these mathematical skills attained through the course. But with S357, one needs to demonstrate a thorough understanding of, and to draw conclusions from, the physics taught. Usually two essays are required in assessment - and there is an essay component in the exam (not compulsory in 2000).

The course material is divided into four blocks, accompanied by videos, tapes, glossaries and a mathematics guide. The glossaries are more than just a dictionary of terms - they assist the student with concise summaries of concepts, and form a very useful compare and contrast function.

Block 1 is in effect a revision of Newtonian mechanics at the level covered by the foundation course S103 and some of the second level physics course. For those students who have already covered this material - it can be somewhat repetitive and motivation can slip a bit here. Although it's necessary to cover this material - to understand the need for Special Relativity - I would have thought that just a couple of units would have sufficed - there is a lot of other material to cover in the subsequent blocks.

Block 2 opens with a brief introduction to Electromagnetism (again revision if you've already taken the electromagnetism course) and uses Maxwell's equations to question physics knowledge as it stood at that time - either Newton was wrong or something else was needed - Enter Einstein, Special Relativity and the Lorentz transformation equations (very simple - I am relatively hopeless at maths; -) We are introduced here to the Lorentz interval and Spacetime diagrams - which don't appear at this stage of the course to be that relevant.

Block 3 is the first of the heavier loaded blocks - it's difficult to realise that one should start on this earlier than advertised! (OU - a change in the timetable might help here?) Here we study the General Theory of Relativity. It introduces the use of geodesics and metric theory (a substitute for tensor calculus?), to model GR and its effects. If only I knew then what I now know - the language in the unit does not explain clearly that metric theory is just a way of using 'general' equations by substitution of parameters for different scenarios. Instead the material uses what is perfectly correct language for the physics community but which actually confuses the student used to the semantics of other OU physics courses. The block finishes with a unit on Black Holes - brilliant for sceptics like me - makes you want to take up the subject at a higher level - so you can prove it wrong!

Block 4 - AKA the cosmology block. This is popular with the astronomy students. It covers Big Bang theory and the large scale structure of the universe and is so interesting I read it again after the exam. Another good block for the sceptics out there - this student had to really suspend credibility for a while. This is not a criticism - it is the best way to learn - trying to prove the authors wrong!

Overall - A very interesting and attainable course - great to arouse interest in the subjects covered, and makes you want to take cosmology to post graduate level just to satisfy yourself that it really is all true. The main complaint is the uneven work-load, but this could be corrected by timetabling the TMA's differently.

S357 - Space, Time and Cosmology - review update by Brian Steadman

I recently obtained my PhD in general relativity, and Norrrette Moore's review (above) reminded me of some of the snags in understanding the OU course, prompting me to attempt to summarise the contents clearly.

Like Norrette I studied S357, although that was way back in 1982 when it was called S354. I remember enjoying the course, though it was not always easy to see the wood for the trees, and my appetite for general relativity was whetted. Thanks to the OU, last year (2000) I was awarded my PhD - in general relativity. Yes, I know it took a long time! The following is offered as an outline of some important points from S357 which, I hope, may be helpful.

Isaac Newton (17th century) assumed that space and time merely provided the arena for every event in the universe. Space remained equally unstirred by the fall of a leaf or by the collision of galaxies, and space itself had no influence on those events. Time flowed at the same even rate everywhere and for ever, quite unaffected by anything else in the universe. In Newton's theory of gravitation, every object in the universe is subject to a force of attraction towards every other object.

James Clerk Maxwell (19th century) found, theoretically, an absolute value for the speed of light - predicting that everyone, regardless of their own speed, would measure the same value for light from any source, regardless of its speed.

Albert Einstein (20th century) realised that either Newton was wrong about the absolute nature of space and time or Maxwell was wrong about the absolute speed of light. Common sense said that Maxwell was wrong. Einstein postulated that Maxwell was right and went on to publish the theory of special relativity in which space and time are not absolutes and are somehow interdependent, hence the term spacetime. Time and distance measurements of an event may result in different values 'relative' to different observers of the event. However, the theory is valid only for 'special' smoothly moving (i.e. inertial) observers; this also excludes gravity.

Eventually, Einstein incorporated accelerating (i.e. non-inertial) observers into his theory, thereby 'generalising' relativity. In a sense, acceleration mimics gravity and general relativity is also Einstein's theory of gravitation, in which there is no 'force of gravity'. In general relativity, all objects, all matter and energy, affect (curve) spacetime. It is this curvature of spacetime, not a mysterious force, which determines the motion of objects (and light). General relativity is encapsulated in Einstein's field equations.

Black holes and various cosmologies, etc. are found by solving the field equations for different physical situations. A solution gives a metric. the description of space and time. for example, around black holes. The geodesic equations are obtained from the metric. If possible, these are solved analytically, failing that, numerically. In either case we obtain the paths in space-time (i.e. geodesics) of objects and light. But why should we believe Einstein rather than Newton? Because general relativity describes what we observe in nature more accurately than does Newtonian theory.

Dictionaries - by Jim Grozier

Thinking of getting a dictionary of science or physics? To cover the parts the OU cannot reach, or just to help with the Nexus News crossword? Don't know which one to buy? Try this simple, but completely unscientific test - look up Coriolis.

Remember the Coriolis force? Famous as the cause of circular motion in winds rushing towards a region of low pressure, and for the tendency of bathwater to go down the plug-hole in a clockwise or anticlockwise direction depending on which hemisphere you're in; (but don't try to demonstrate this at home - you will need a perfectly symmetrical bath, and you will need to leave the water to settle down for several days to eliminate residual angular momentum which could mask the effect - during which time you will get very dirty and may die of an infection).

It is a consequence of the fact that Newton's laws do not hold in a rotating reference frame, and acts on any object which is moving with respect to such a frame (unless the motion is parallel to the axis of rotation). The Coriolis force on a mass m moving with velocity (vector) v relative to the rotating frame of reference is given by:

F_cor = -2m(w x v)

where (vector) w is the angular velocity of the rotating frame.

But what do the dictionaries say?

The Penguin Dictionary of Physical Geography is fairly close to the mark, quoting the formula 2vwsinj (where j = latitude) but unfortunately describing it as a force! The Chambers Dictionary of Science and Technology correctly labels this expression as the Coriolis acceleration, and even has a diagram - but you'd expect that for £30, wouldn't you? In the Oxford Dictionary of Science and the Oxford Dictionary of Physics, which would normally be regarded as front-runners in this market, the definition is unfortunately full of verbal manure about tangential air velocities and fictitious forces - clearly the author had either never been on a fairground ride, or had had too much to drink the night before, or both. Oxford's Dictionary of Earth Sciences, and even their general Concise English do better than this; and Penguin's Dictionary of Physics is perhaps the most accurate, since, while it steers clear of formulae, it does mention the vector product (which only takes the value vwsinj when v is north/south; for east/west motion, the sinj only appears when you take the horizontal component of the acceleration).

What does all this tell us? Well, not much; the books I have recommended may have their own peculiar deficiencies elsewhere. But you should certainly never regard anything you read as gospel, even if it is in a dictionary; and, as with other texts, read around as much as possible, in order to get a balanced picture. So, buy all of them if you can afford it!