Physics and Mathematics
What are the concepts in Physics and Mathematics that students find difficult? In this blog I will post tutorial sheets that I hope will stimulate thinking and so broaden the knowledge and understanding of students allowing them to write thorough examination responses. Tutorial sheets, structured to assist student learning, will be posted on IB SL and HL Physics syllabus topics as well as the general HSC topics of relativity, electromagnetism, mechanics, thermodynamics, quantum physics and calculus. The overall purpose of these pages is to encourage and promote learning in Physics and Mathematics and so open new horizons in learning.
Permission is granted to use the material on this blog provided that recognition is given to its source,
the Sydney Physics and Mathematics Tutor
the Sydney Physics and Mathematics Tutor
It's About Time*
/Continuing with the study of relativity the next concept we come to is that of time. Einstein stated that time intervals were not the same in all reference frames but depended on the relative speed of the reference frames. Einstein called this effect time dilation (sometimes the term time dilatation is used). Students find time dilation a difficult concept for at least two reasons:
- Time is an abstract concept in itself. What is time? What does time dilation mean?
- Many time dilation questions in textbooks are poorly worded and this causes confusion.
What is time?
When a ball rolls along a track in the science laboratory its distance from the starting point changes as its travel time increases. To generalise this we can say that time is a number that increases as events happen in a reference frame. Time can be thought of as nature’s arrow. As time increases events happen in their natural order.
Read MoreDoes Length Contraction Actually Happen?
/Students are taught that one of the consequences of Einstein’s special theory of relativity is that moving objects contract in length in the direction parallel to their velocity vector. But does this contraction actually happen or is it some sort of illusion? The answer is yes, length contraction actually happens and no, it is not an illusion.
Einstein in 1904 stated (as quoted in the book One, Two, Three … Infinity by George Gamow, 1961 page 97) “we deal here with the contraction of space itself, and all material bodies moving with the same speed contract in the same way simply because they are imbedded in the same contracted space”.
A common misconception is that the high speed of the object causes its length to contract as if caused by some process in the object. Length contraction occurs due to the high relative speed of the reference frames in which the observation is made.
Read MoreEinstein, Michelson and Morley.
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As this is the first Sydney Physics and Mathematics Tutor Blog I will outline its rationale. The purpose of the SPMT Blog is to raise awareness of concepts in Physics and Mathematics that are often mistaken or overlooked. 2015 marks the anniversary of two great breakthroughs in Physics. These are Albert Einstein’s use of his general theory of relativity in 1915 and James Clerk Maxwell’s publication of his theory of the electromagnetic field in 1865. Both of these areas, relativity and electromagnetism, are difficult for students to grasp so the emphasis of the blogs this year will be on relativity and electromagnetism. We will start with relativity. Permission is granted to use the material on this blog provided that recognition is given to its source, the Sydney Physics and Mathematics Tutor.
Physics students are taught about the experiment with light rays moving on perpendicular paths carried out by Michelson and Morley in 1887. They rotated their apparatus through various angles and later Morley and Miller performed the experiment at different times of the year but the same near null result in the shift in their interference pattern was obtained. The null result implied that there was no detectable movement of the Earth relative to the ether and so removed the notion of the ether as an absolute reference frame.
As this experiment was performed before Albert Einstein proposed his special theory of relativity in 1905 a common misconception is that Einstein referred to the Michelson-Morley experiment when he published his special theory of relativity in 1905. Einstein may have been aware of the experiment and its results may have confirmed his own beliefs, but there is no direct mention of the Michelson-Morley experiment in his great paper on relativity entitled "On the Electrodynamics of Moving Bodies" (Annalen der Physik, 17, 1905, 891-921).
Einstein stated in the introduction of his paper that "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body". Einstein further stated that "the introduction of a luminiferous ether will prove to be superfluous inasmuch as the view here to be developed will not require an absolutely stationary space provided with special properties". It was due to the genius of Einstein that he was able to put these ideas together to form a theory that changed our understanding of space and time.
What then is the long term role of the Michelson-Morley experiment in science? This experiment started a series of new ideas to explain its null result. These included FitzGerald’s hypothesis that the dimensions of the interferometer were contracted in the direction that the Earth was moving and Lorentz’s formulation of equations, now known as the Lorentz transformation, which allowed Maxwell’s equations of electromagnetism to have the same form in moving reference frames. These developments were brought together in Albert Einstein’s special theory of relativity in 1905 in which our understanding of space and time was radically changed.
Further information on Einstein and the Michelson-Morley experiment can be found here and here.
In summary, Einstein’s two postulates on which his special theory of relativity is based are (Einstein 1905 The Standard of Greatness by John S Rigden, Harvard University Press, 2005, p87):
The Principle of Relativity: The laws of physics are the same in all inertial reference systems or, by means of physical experiments, one inertial coordinate system cannot be distinguished from another inertial coordinate system.
The Principle of the Constancy of the Speed of Light: The speed of light is the same in all inertial reference systems, independent of the speeds of either the source of the light or the detector of the light.
