Month: February 2016

No beginning or end

milkywayNASAIn the quantum theory of gravity, time becomes the fourth dimension to add to the three dimensions of space (x, y, z or length, width and height), and Stephen Hawking has suggested that we consider it analogous to a sphere. Developing this analogy, we imagine time to be like a flea running around on the surface of a ping-pong ball. A continuous journey, without a beginning or an end. The ‘big bang’, frequently discussed as the beginning of everything, and the ‘big crunch’, proposed by physicists as how things will end, would be the north and south poles of the sphere. The Universe would simply exist. The radius of circles of constant distance from the poles (what we might call lines of latitude) would represent the size of the Universe. Quantum theory also requires the existence of many possible time histories of which we inhabit one. Different lines of longitude can represent these histories.

If you are not already lost (the analogy does not include a useful compass) then physicists would give you a final spin by dropping in the concept of imaginary time! Maybe it is time for the flea to jump off the ping-pong ball, but before it does, we can appreciate that it might move in one direction and then retrace its steps (or its hops if you wish to be pedantic). The flea can travel backwards because in this concept of the Universe, time has the same properties as the other dimensions of length, height and width and so it has backwards as well as forwards directions.”

This is an extract from a book called ‘The Entropy Vector: Connecting Science and Business‘ that I wrote sometime ago with Bob Handscombe.  I have reproduced it here in response to questions from a number of learners in my current MOOC.  The questions were initially about whether the first law of thermodynamics has implications for the universe as a closed system (i.e. one that can exchange energy but not matter with its surroundings) or as an isolated system (i.e. one that can exchange neither energy not matter with its surroundings).  These questions revolve around our understanding of the universe, which I have taken to be everything in the time and space domain, and the first law implies that the energy content of the universe is constant.  The expansion of the universe implies that the average energy density of the universe is getting lower, though it is not uniformly otherwise we would have reached the ‘cosmic heat death’ that I have discussed before.  However, this discussion in the MOOC led to questions about what happened to the first law of thermodynamics prior to the Big Bang, which I deflected as being beyond the scope of a MOOC on Energy! Thermodynamics in Everyday Life.  However, I think it deserves an answer, which is why reproduced the extract above.

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Undermining axioms at the speed of light

International Prototype of the Kilogram (IPK)

International Prototype of the Kilogram (IPK)

An axiom is a statement so evident or well-established that it is accepted without controversy or question.  However, in his review of Sokal’s Hoax, Steven Weinberg has suggested that ‘none of the laws of physics known today (with the possible exception of the general principles of quantum mechanics) are exactly and universally valid’.  This propels physics to the same status as biology (see my post entitled ‘Laws of biology?‘ on January 13th 2016) – in lack exactly and universally valid laws and it suggests that there are no scientific axioms. 

‘Things that are equal to the same things are equal to each other’ is Euclid’s first axiom and in thermodynamics leads to the Zeroth Law: ‘Two things each in thermal equilibrium with a third are also in thermal equilibrium with each other’ (see my posts entitled ‘All things being equal‘ on December 3rd, 2014 on ‘Lincoln on equality‘ on February 6th, 2013).   Thermal equilibrium means that there is no transfer of thermal energy or heat between the two things, this leads to the concept of temperature because when two things are in thermal equilibrium we say that they are at the same temperature.   Last week I explained these ideas in both my first year undergraduate class on thermodynamics and my on-going MOOC.  This week, I have challenged MOOC participants to try to identify other measurement systems, besides temperature, that are based on Euclid’s first axiom.

For instance, its application to mechanical equilibrium leads to Newton’s laws and from there to mass as a measure of a body’s inertia.  We use Euclid’s axiom to evaluate the mass of things through a chain of comparisons that leads ultimately to the international kilogram at the Bureau International des Poids et Mesures in France.  Similarly, we measure time by comparing our time-pieces to an international standard for a second, which is the duration of  9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. 

However, given Weinberg’s statement perhaps I can give you a harder challenge than MOOC participants: can you identify exceptions to Euclid’s first axiom?

I think I can identify one: if you calibrated two very accurate timepieces against a cesium 133 clock and then took one on a journey through space travelling at the speed of light while the other remained on Earth, when you brought the two together again on Earth they would not agree, based on Einstein’s theory of relativity, or what he called relativity of simultaneity.  Now see what you can come up with!

Sources:

Steven Weinberg, ‘Sokal’s Hoax’, NY review of Books, 43(13):11-15, August 1996.

Oliver Byrne, First Six Books of the Elements of Euclid, London: William Pickering, 1847

Joseph Schwartz & Michael McGuinness, Einstein for Beginners, London: Writers and Readeres Publishing Cooperative, 1979 & Penguin Random House, 2013.

Albert Einstein, Relativity: The Special and the General Theory, (translated by Robert W. Lawson), London: Methuen & Co Ltd., 1979 & on-line at www.bartleby.com/173/

Writing backwards

honey&mumfordschematicMy regular readers will know that I am a fan of the 5E instructional method and in particular combining it with Everyday Engineering Examples when teaching introductory engineering courses to undergraduate students. Elsewhere in this blog, there is a catalogue of lesson plans and examples originally published in a series of booklets produced during a couple of projects funded by the US National Science Foundation. Now, I have gone a step further and embedded this pedagogy in a Massive Open Online Course (MOOC) on Energy! Thermodynamics in Everyday Life. If you follow the MOOC, you’ll find some new worked examples that I explain while writing ‘backwards’ on a glass board. My film unit are very proud of the ‘backwards’ writing in these examples, which they tell me is an innovation in education filming-making. Our other major innovation is laboratory exercises that MOOC participants can perform in their kitchens. Two of these are based on everyday experiences for most participants: boiling water and waiting for a hot drink to cool down; the third is less everyday because it involves a plumber’s manometer. In each case, I am attempting to move people around Honey and Mumford’s learning cycle, which is illustrated schematically in the figure, i.e. having an experience, reviewing the experience, concluding from the experience and the planning the next steps. The intention is that students progress around the cycle in the taught component, then again in the experiments.

If you want to have a go at the one of experiments, then the instructions for the first one are available here. Alternatively you could sign up for the MOOC – its not too late!  But if you don’t want to follow the course then you can stil watch some excerpts on the University of Liverpool’s Stream website, including the backwards written examples.

Sources:

Atkin, J.M. and Karplus, R., 1962. Discovery of invention? Science Instructor, 29 (5), 45–47.

Honey P, Mumford A. The Manual of Learning Styles 3rd Ed. Peter Honey Publications Limited, Maidenhead, 1992.

And then we discovered thermodynamics

sunEnergy, matter, space and time came into existence in the Big Bang 13.5 billion years ago. 10 billion years later biological organisms started to appear. 70,000 years ago one of those organisms, man started to organise in structures, called cultures and history began. For most of history if you wanted something moved then you had to do it yourself or persuade someone else to do it. The agricultural revolution began 12,000 years ago and shortly afterwards we realised that if you fed fuel to an animal then it would ‘burn’ it and do work for you. And that’s how it remained for thousands of years – we didn’t know how to convert heat into work or work into heat. The average energy consumption per capita was about 20GJ per year. Then, 200 years ago we discovered how to imitate nature by burning fuel and producing power in the steam engine. We had discovered thermodynamics and our average energy consumption started rising towards 80GJ per year today.

As a consequence, ‘we have now all but destroyed this once salubrious planet as a life-support system in fewer than two hundred years, mainly by making thermodynamic whoopee with fossil fuels’ as Kurt Vonnegut wrote. And that’s because nature starts from solar energy and recycles everything and we haven’t learnt how to do either very effectively. But energy or power engineering has been around for less than a blink of eye relatively speaking and we are just learning how to perform a trick nature has been using for billions of years: convert solar radiation into other energy forms. The sun delivers about 340 Watts per square metre to the Earth so we have plenty energy available.

If you would like to know more about energy engineering or thermodynamics and its potential then join the 5000 people who have signed up for the MOOC that I am teaching for five weeks from next Monday.  Listen to me interview Ken Durose, Director of the Stephenson Institute for Renewable Energy on the prospects for renewable energy.

Sources:

http://ourfiniteworld.com/2012/03/12/world-energy-consumption-since-1820-in-charts/

Yuval Noah Harari, Sapiens: A brief history of mankind. London: Vintage (Penguin, Random House), 2014.

Kurt Vonnegut, A Man without a Country, New York: Seven Stories Press, 2005.