The electromagnetic spectrumJust how significant was James Clerk Maxwell (1831-1879)? Richard Feynman was in no doubt:
Precursors
Before Maxwell came along, many others had made a contribution, but the field was essentially a hodge-podge of bits and pieces[2].
Maxwell’s contribution was to unite the previously considered separate forces of electricity and magnetism, but he not only united them but incorporated the disparate contributions from a multitude of stakeholders into a comprehensive whole, firstly by utilising mechanical models and then giving them mathematical expression. He also utilised physical analogies to develop a mathematics more suited to electrical science[6] by comparing electricity flowing through space with heat flowing through a fluid, and an electric charge with a pump that forces out a stream of an incompressible fluid like water. He created a model displaying the effects of electromagnetism, with beads as rotating cells acing much like an electric current, replicating the way a changing magnetic field generates an electric current, and an electric current generating an electric field[7]. The Maxwell equations In the end result, Maxwell formulated something in the order of a dozen equations, but ones which were unfortunately devoid of everyday practicality. After his death, these were reformulated by the English self-taught electrical engineer, mathematician and physicist Oliver Heaviside (1850-1925) into four, which still go by the name of Maxwell’s equations:
The equations themselves, with a brief explanation, may be found at https://owlcation.com/stem/Top-Ten-Beautiful-Physics-Equations (equation 4). The sequence has a certain elegance about it. The first equation relates the flow of electric field (E) to the charge density (ρ). The second law states that magnetic fields (B) have no monopoles. Whereas electric fields can have a source of positive or negative charge, such as an electron, magnetic fields always come with a north and south pole and hence there is no net "source". According to the third equation, a changing magnetic field creates an electric field that is also changing, but the fourth says that this last changing electric field now creates a new changing magnetic field[8]. The two interlocked fields thus become one single electromagnetic field that begins to expand in space. Maxwell combined his equations into a single one to show that this electromagnetic field moves through space like a wave at the speed of light, which we now know to be 300,000 kps (186,000 mps)[9] Maxwell’s achievement was to reformulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism and light as different manifestations of the same phenomenon. Enter Hertz Some nine years after Maxwell died, the German physicist, Heinrich Hertz (1857-1894) used Maxwell’s electromagnetic theory of light to generate electromagnetic waves in his lab and measure their speed. Hertz conducted an experiment utilising a pair of one metre copper wires with a 7.5 mm spark gap between them, ending in 30 cm zinc spheres. When an induction coil applied a high voltage between the two sides, sparks across the spark gap created standing waves of radio frequency current in the wires, which radiated what are now called radio waves in the very high frequency range, 50 MHz, roughly the same as that used in modern television transmitters: see diagram below[10]. Hertz was then able to measure the speed of electromagnetic waves generated with this spark setup, and got the same value as the speed of light, mirroring Maxwell. The result was the first radio transmitter and receiver: |
Hertz’s experiment showed that light was an electromagnetic wave. Radio waves[11], light, and other waves that were discovered later are all electromagnetic waves generated in a similar way — by accelerating electric charges. The only difference between them is the waves’ wavelength – how fast they oscillate. Radio waves, like the ones generated by Hertz, have wavelengths that range from about 1 meter to thousands of kilometers. Hertz’s was a short one, about 1 meter in length.
Identifying the electromagnetic spectrum
As Carlos Calle explains[12], visible light has wavelengths larger than x-rays but smaller than those for radio and TV. Because of the small size of the wavelengths, scientists use nanometres to designate their length, a nanometre (nm) being a millionth of a millimetre. Visible light ranges from 400 nm for the colour red to 700 nm for violet. Each wavelength has a different energy; the shorter wavelengths are more energetic. Scientists have invented instruments to detect different ranges, like x-rays, gamma rays, or radio.
The electromagnetic spectrum consists of alternating electric and magnetic fields. A changing electric field induces or creates a changing magnetic field and vice-versa. The wave propagates outwards in all directions. Beginning with those with the lowest energy, longest wavelength, to those with the highest energy/shortest wavelength), we now know that there are many forms of electromagnetic radiation, radiowaves, microwaves, the infrared, visible light, ultraviolet light (harmful rays from the sun), X-rays and gamma rays[13].
Electromagnetic radiation may therefore be described as “a stream of mass-less particles (photons), each traveling in a wave-like pattern at the speed of light”. It can be expressed in terms of energy, wavelength, or frequency. Frequency is measured in cycles per second, or “Hertz”. For example, AM radio station in Sydney broadcast on a frequency of 873 kHz. Wavelength is measured in metres. Energy is measured in terms of electron volts[14].
A useful table appears below[15].
Identifying the electromagnetic spectrum
As Carlos Calle explains[12], visible light has wavelengths larger than x-rays but smaller than those for radio and TV. Because of the small size of the wavelengths, scientists use nanometres to designate their length, a nanometre (nm) being a millionth of a millimetre. Visible light ranges from 400 nm for the colour red to 700 nm for violet. Each wavelength has a different energy; the shorter wavelengths are more energetic. Scientists have invented instruments to detect different ranges, like x-rays, gamma rays, or radio.
The electromagnetic spectrum consists of alternating electric and magnetic fields. A changing electric field induces or creates a changing magnetic field and vice-versa. The wave propagates outwards in all directions. Beginning with those with the lowest energy, longest wavelength, to those with the highest energy/shortest wavelength), we now know that there are many forms of electromagnetic radiation, radiowaves, microwaves, the infrared, visible light, ultraviolet light (harmful rays from the sun), X-rays and gamma rays[13].
Electromagnetic radiation may therefore be described as “a stream of mass-less particles (photons), each traveling in a wave-like pattern at the speed of light”. It can be expressed in terms of energy, wavelength, or frequency. Frequency is measured in cycles per second, or “Hertz”. For example, AM radio station in Sydney broadcast on a frequency of 873 kHz. Wavelength is measured in metres. Energy is measured in terms of electron volts[14].
A useful table appears below[15].
A useful video on electromagnetic waves and the electromagnetic spectrum appears at: https://www.khanacademy.org/science/physics/light-waves/introduction-to-light-waves/v/electromagnetic-waves-and-the-electromagnetic-spectrum
The header graphic is from the same source.
[1] “The Feynman lectures on Physics”, cited by Robert P Crease at the outset of Chapter 5 of The Great Equations, Norton, 2010, 133.
[2] This summary from Ibid, Chapter 5.
[3] https://en.wikipedia.org/wiki/Andr%C3%A9-Marie_Amp%C3%A8re
[4] Robert P Crease, The Great Equations, Norton, 2010, 134.
[5] Ibid, 135.
[6] Ibid 137.
[7] More fully explained in Crease, 139.
[8] See generally Carlos I Calle, Einstein For Dummies (Kindle Location 1707 - 1777). Wiley. Kindle Edition.
[9] Actually 299,792.458 kps; 186,282.397 mps.
[10] https://en.wikipedia.org/wiki/Heinrich_Hertz
[11] For a tabulation of the various radio waves (broadcast bands), see https://en.wikipedia.org/wiki/Broadcast_band
[12] Calle, Carlos I.. Einstein For Dummies (Kindle Locations 1884-1889). Wiley. Kindle Edition.
[13] https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html
[14] Ibid.
[15] Source: https://www.tutorvista.com/physics/electromagnetic-spectrum-frequency-range
The header graphic is from the same source.
[1] “The Feynman lectures on Physics”, cited by Robert P Crease at the outset of Chapter 5 of The Great Equations, Norton, 2010, 133.
[2] This summary from Ibid, Chapter 5.
[3] https://en.wikipedia.org/wiki/Andr%C3%A9-Marie_Amp%C3%A8re
[4] Robert P Crease, The Great Equations, Norton, 2010, 134.
[5] Ibid, 135.
[6] Ibid 137.
[7] More fully explained in Crease, 139.
[8] See generally Carlos I Calle, Einstein For Dummies (Kindle Location 1707 - 1777). Wiley. Kindle Edition.
[9] Actually 299,792.458 kps; 186,282.397 mps.
[10] https://en.wikipedia.org/wiki/Heinrich_Hertz
[11] For a tabulation of the various radio waves (broadcast bands), see https://en.wikipedia.org/wiki/Broadcast_band
[12] Calle, Carlos I.. Einstein For Dummies (Kindle Locations 1884-1889). Wiley. Kindle Edition.
[13] https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum1.html
[14] Ibid.
[15] Source: https://www.tutorvista.com/physics/electromagnetic-spectrum-frequency-range
Einstein’s general theory of relativity confirmed
Einstein’s theory of general relativity predicted that the wavelength of electromagnetic radiation would lengthen as it escaped the pull of gravity exerted by a massive celestial body like a black hole - a co-mingling of space and time in other words. Photons expend energy to escape but always travel at the speed of light, meaning that the energy loss occurs through a change of electromagnetic frequency rather than a slowing of velocity. This causes a shift to the red end of the electromagnetic spectrum, a gravitational redshift, outside the visible realm.
In 2019, this phenomenon was corroborated by the study of a star called S0-2, 28,000 light years from earth, with a mass roughly 10 times larger than the sun and travelling in an elliptical orbit lasting 16 years around Sagittarius A black hole. Observers were able to observe the behaviour of the star’s light as it escaped the extreme gravitational pull exerted by the black hole and found that it conformed to Einstein’s predictions.
A slight asymmetry or two here and there ….!.
When applied to moving bodies, Maxwell's electrodynamics “led to asymmetries which do not appear to be inherent in the phenomena”. These are the opening words of Einstein’s “On the electrodynamics of moving bodies”, originally published in his annus mirabilis, 1905[1]. Imagine a magnet in motion and a conductor at rest. According to Maxwell’s equations:
Einstein’s theory of general relativity predicted that the wavelength of electromagnetic radiation would lengthen as it escaped the pull of gravity exerted by a massive celestial body like a black hole - a co-mingling of space and time in other words. Photons expend energy to escape but always travel at the speed of light, meaning that the energy loss occurs through a change of electromagnetic frequency rather than a slowing of velocity. This causes a shift to the red end of the electromagnetic spectrum, a gravitational redshift, outside the visible realm.
In 2019, this phenomenon was corroborated by the study of a star called S0-2, 28,000 light years from earth, with a mass roughly 10 times larger than the sun and travelling in an elliptical orbit lasting 16 years around Sagittarius A black hole. Observers were able to observe the behaviour of the star’s light as it escaped the extreme gravitational pull exerted by the black hole and found that it conformed to Einstein’s predictions.
A slight asymmetry or two here and there ….!.
When applied to moving bodies, Maxwell's electrodynamics “led to asymmetries which do not appear to be inherent in the phenomena”. These are the opening words of Einstein’s “On the electrodynamics of moving bodies”, originally published in his annus mirabilis, 1905[1]. Imagine a magnet in motion and a conductor at rest. According to Maxwell’s equations:
there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise … to electric currents of the same path and intensity as those produced by the electric forces in the former case[2].
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More succinctly put, if you move a magnet towards a wire, an electric current is generated, but if you do the opposite - move the wire towards the magnet, which is at rest - there is no electric field[3]. The same phenomenon would seem to have two different descriptions depending on the frame of reference of the observer. This was the thought experiment known as the moving magnet and conductor problem[4], which was ultimately resolved by Einstein by applying his principle of relativity: that the laws of physics remain the same for any non-accelerating frame of reference (called an inertial reference frame), to the laws of electrodynamics and optics[5] not just mechanics[6],[7].
In other words, the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. He reconciled Maxwell’s equations for electricity and magnetism with the laws of mechanics (motion) by introducing major changes to mechanics close to the speed of light:
Attempts prior to Einstein to reconcile the issue of moving bodies and relative motion
Eons before Einstein, Galileo had grappled with his own version of relativity theory to the effect that the laws of nature (sc: mechanics, motion) should be the same for all observers that move with constant speed relative to each other. Einstein extended this to all physics, not just to Newtonian mechanics[9].
During the nineteenth century, it was assumed that light required a medium through which to propagate itself, because all other known waves, such as air and water, required such. This supposed medium was known as the ether. It was perceived that the Earth’s motion in relation to the ether may have something to do with the problem, but in 1881, the Michelson-Morley experiment, was unable to detect any such thing. Einstein had no need for the notion of an ether in formulating his theory, and ever since then we know there isn’t any.
Then, it was proposed by George FitzGerald at Trinity College in Dublin, Ireland in 1889 and by Hendrik Antoon Lorentz of the University of Leyden in the Netherlands in 1892, independently of each other, that the Michelson-Morley result might be accounted for if moving bodies shrink when they move, the shrinking being along the direction of motion. The faster the object moves, the more it shrinks, the shrinking being exactly in the amount needed to keep the speed of light measurements unchanged, and exactly what was needed to make the Michelson-Morley experiment work[10].
This became known as the Lorentz–FitzGerald contraction. Lorentz later reformulated his equations with a new set that added time dilation to the mix. What his new theory said was that if you’re moving relative to the Earth, for example, not only do objects change in length, but your clock ticks at a different rate. Time has a sort of elastic property that stretches and contracts depending on how you move[11]. Prescient insights indeed!
And then in 1904, the French mathematician and theoretical physicist, Henri Poincaré postulated a clear and simple description of the principle of relativity, which included all the laws of physics to the effect that the laws of physical phenomena should be the same whether you are in uniform motion or at rest. In the process he almost pre-empted Einstein, but not quite[12]. Einstein’s insight that light is the cosmic speed limit and a universal constant differentiated the two.
These developments ultimately formed the cornerstones of Einstein's special theory of relativity.
[1] https://en.wikipedia.org/wiki/Annus_Mirabilis_papers#Special_relativity
[2] Cited in https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
[3] Carlos I. Calle, Einstein For Dummies (Kindle Locations 2081-2083). Wiley. Kindle Edition
[4] Unless otherwise indicated, what follows is an edited summary of the Wikipedia piece. https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity
[5] The branch of physics which involves the behaviour and properties of light: see https://en.wikipedia.org/wiki/Optics
[6] The branch of physics that has to do with motions and the forces involved.
[7] Well prior to Einstein, Galileo had grappled with his own version of relativity theory to the effect that the laws of nature (sc: mechanics, motion) should be the same for all observers that move with constant speed relative to each other. Einstein extended this to all physics, not just to Newtonian mechanics: Carlos I. Calle, Einstein For Dummies (Kindle Location 2359). Wiley, Kindle Edition
[8] Ibid, Locs 2307-2312.
[9] Ibid, Loc 2359.
[10] Ibid, Locs 2133-2136.
[11] Ibid, Loc 2326.
[12] Ibid, Locs 2140-2143.
In other words, the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. He reconciled Maxwell’s equations for electricity and magnetism with the laws of mechanics (motion) by introducing major changes to mechanics close to the speed of light:
- light is a universal constant.
- all observers in uniform (non-accelerated motion) measure the same value c for the speed of light: the speed of light has the same value in all frames of reference, independent of the state of motion of the emitting body[8].
Attempts prior to Einstein to reconcile the issue of moving bodies and relative motion
Eons before Einstein, Galileo had grappled with his own version of relativity theory to the effect that the laws of nature (sc: mechanics, motion) should be the same for all observers that move with constant speed relative to each other. Einstein extended this to all physics, not just to Newtonian mechanics[9].
During the nineteenth century, it was assumed that light required a medium through which to propagate itself, because all other known waves, such as air and water, required such. This supposed medium was known as the ether. It was perceived that the Earth’s motion in relation to the ether may have something to do with the problem, but in 1881, the Michelson-Morley experiment, was unable to detect any such thing. Einstein had no need for the notion of an ether in formulating his theory, and ever since then we know there isn’t any.
Then, it was proposed by George FitzGerald at Trinity College in Dublin, Ireland in 1889 and by Hendrik Antoon Lorentz of the University of Leyden in the Netherlands in 1892, independently of each other, that the Michelson-Morley result might be accounted for if moving bodies shrink when they move, the shrinking being along the direction of motion. The faster the object moves, the more it shrinks, the shrinking being exactly in the amount needed to keep the speed of light measurements unchanged, and exactly what was needed to make the Michelson-Morley experiment work[10].
This became known as the Lorentz–FitzGerald contraction. Lorentz later reformulated his equations with a new set that added time dilation to the mix. What his new theory said was that if you’re moving relative to the Earth, for example, not only do objects change in length, but your clock ticks at a different rate. Time has a sort of elastic property that stretches and contracts depending on how you move[11]. Prescient insights indeed!
And then in 1904, the French mathematician and theoretical physicist, Henri Poincaré postulated a clear and simple description of the principle of relativity, which included all the laws of physics to the effect that the laws of physical phenomena should be the same whether you are in uniform motion or at rest. In the process he almost pre-empted Einstein, but not quite[12]. Einstein’s insight that light is the cosmic speed limit and a universal constant differentiated the two.
These developments ultimately formed the cornerstones of Einstein's special theory of relativity.
[1] https://en.wikipedia.org/wiki/Annus_Mirabilis_papers#Special_relativity
[2] Cited in https://en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem
[3] Carlos I. Calle, Einstein For Dummies (Kindle Locations 2081-2083). Wiley. Kindle Edition
[4] Unless otherwise indicated, what follows is an edited summary of the Wikipedia piece. https://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity
[5] The branch of physics which involves the behaviour and properties of light: see https://en.wikipedia.org/wiki/Optics
[6] The branch of physics that has to do with motions and the forces involved.
[7] Well prior to Einstein, Galileo had grappled with his own version of relativity theory to the effect that the laws of nature (sc: mechanics, motion) should be the same for all observers that move with constant speed relative to each other. Einstein extended this to all physics, not just to Newtonian mechanics: Carlos I. Calle, Einstein For Dummies (Kindle Location 2359). Wiley, Kindle Edition
[8] Ibid, Locs 2307-2312.
[9] Ibid, Loc 2359.
[10] Ibid, Locs 2133-2136.
[11] Ibid, Loc 2326.
[12] Ibid, Locs 2140-2143.