Tag Archives: Einstein

What a waste

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20120609_wom915Einstein’s famous equation, E=mc², does not influence everyday interactions of energy, E and mass, m.  The speed of light, c is 299 792 458 m/s which is very big number and implies a huge amount of energy is required to create a small amount of mass.  This means that energy and mass are independently conserved.  For energy, this is the first law of thermodynamics while the law of conservation of mass is usually attributed to Antoine Lavoisier.  On a planetary scale, the conservation of mass implies that we can assume that the quantity of matter is constant.  Can we apply the second law of thermodynamics to matter as well as energy?  One interpretaton of the second law is that Gibbs energy, or the energy available to do useful work, must decrease in all real processes.   This also applies when matter moves through our economic system.  For instance, we must do work to convert mineral ores into useful products which gradually degrade through use and natural processes, such as corrosion, until they become scrap and we must expend more resources to recycle them and make them useful again.  The sun provides us with a steady supply of useful energy, so that in energy terms planet Earth can be considered an open system with energy flows in and out.  Conversely in mass terms, planet Earth is effectively a closed system with negligible mass flow in or out, so that we do not have a steady supply of new matter from which to manufacture goods.  However, most of us behave with open-world mindset and throw away matter (goods) that are no longer useful to us when we should be repairing and recycling [see my post entitled ‘Old is beautiful‘ on May 1st 2013].  Maybe we can’t reach the zero-waste status aimed at by people like Bea Johnson, but most of us could do better than the 2.2 kg of solid waste produced each day by each of us in OECD countries. That’s 2.1 tonnes per year for an average OECD household (2.63 people)!

Sources:

The New Sustainable Frontier – principles of sustainable development, GSA Office of Governmentwide Policy, September 2009.

Daniel Hoornweq & Perinaz Bhada-Tata, What a Waste: A Global Review of Solid Waste Management, World Bank No.15, 2012.

http://www.economist.com/blogs/graphicdetail/2012/06/daily-chart-3

Undermining axioms at the speed of light

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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/

Impact vs. breakthrough

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Last week I was at a meeting to recommend the award of research grants to scientists and engineers at universities.  Weighing the relative merits of research proposals from physical scientists and from engineers is a little like trying to compare chalk and cheese.  The scientists at such meetings tend to argue that none of the engineering research proposals will lead to scientific breakthroughs, which is one criterion for the awarding of grants; while engineers might suggest that the societal impact of scientific research proposals are intangible and remote.  There is an element of truth in both perspectives since broadly speaking engineering is about the application of science for the benefit of society.  Scientists need to make breakthroughs so that there are new ideas for engineers to apply; however often it is not clear how to apply the breakthrough beneficially, reliably, safely and cheaply, thus engineers also to perform research to establish the best route to the application of existing breakthroughs.

Or to quote Einstein: ‘scientists investigate that which already is; engineers create that which has never been’.