Farewell to Reality (49 page)

10
  The de Broglie relationship is written λ = h/p, where λ is the wavelength, h is Planck's constant and p is the momentum.

11
  Heisenberg established that the uncertainty in position multiplied by the uncertainty in momentum must be greater than, or at least equal to, Planck's constant h.

12
  Albert Einstein, Boris Podolsky, Nathan Rosen,
Physical Review,
47, 1935, pp. 777—80. This paper is reproduced in Wheeler and Zurek, p.141.

13
 
In Stefan Rozenthal (ed.),
Niels Bohr: His Life and Work as Seen by his Friends and Colleagues,
North-Holland, Amsterdam, 1967, pp. 114—36. An extract of this essay is reproduced in Wheeler and Zurek, pp. 137 and 142—3. This quote appears on p.142.

14
  Paul Dirac, interview with Niels Bohr, 17 November 1962, Archive for the History of Quantum Physics. Quoted in Beller, p.145.

15
  A. J. Leggett,
Foundations of Physics,
33 (2003), pp. 1474—5.

16
  John Bell,
Epistemological Letters,
November 1975, pp. 2—6. This paper is reproduced in Bell, pp. 63—6. The quote appears on p.65.

17
  The expression 2.697±0.015 indicates the spread of experimental results around the mean value. The experiments produced results in the range 2.682 to 2.712, representing 68 per cent confidence limits or one standard deviation.

18
  See Xiao-song Ma, et al., arXiv: quant-ph/1205.3909v1, 17 May 2012.

19
  Why do all these experiments never quite achieve the precise quantum theory predictions? Because entangled quantum particles are easily ‘degraded'. Entangled particles which lose their correlation because of stray interactions or instrumental deficiencies will look, to all intents and purposes, as though they are locally real and will not contribute to a violation of the inequality being measured. The wavefunctions of such entangled particles have been prematurely collapsed.

20
  Niels Bohr,
Physical Review,
48 (1935), pp. 696—702. This paper is reproduced in Wheeler and Zurek, pp. 145—51. The quote appears on p.145 (emphasis in the original).

Chapter 3: The Construction of Mass

1
  Albert Einstein,
Autobiographical Notes,
33 (1946).

2
  Remember, the number of different spin orientations is given by twice the spin quantum number plus 1. For s = ½, this gives 2 × ½ + 1, or two spin orientations.

3
  In fact, Einstein's famous equation E = mc
²
is an approximation of a more complex equation E
²
= p
²
c
²
+ m
²
c
⁴
, where p is the momentum and m is the rest mass. In any relativistic treatment, energy must therefore enter as E
²
and there will always be two sets of solutions, one with positive energy and one with ‘negative' energy.

4
  Freeman Dyson,
From Eros to Gaia,
Pantheon, New York, 1992, p.306. Quoted in Farmelo,
The Strangest Man,
p.336.

5
  Feynman, p.188. This quote appears in the caption to Figure 76.

6
  Quoted in Kragh,
Quantum Generations,
p.204.

7
  Willis Lamb,
Nobel Lectures, Physics 1942—1962,
Elsevier, Amsterdam, 1964, p.286.

8
  Quoted by Kragh,
Quantum Generations,
as ‘physics folklore', p.321.

9
  Nambu, p.180.

10
  Steven Weinberg,
Nobel Lectures, Physics 1971—1980,
edited by Stig Lundqvist, World Scientific, Singapore, 1992, p.548.

11
 
Interview with Robert Crease and Charles Mann, 7 May 1985. Quoted in Crease and Mann, p.245.

12
  Our friends at the Particle Data Group list the mass of the W particles as 80.399±0.023 GeV, or 85.713 times the mass of a proton, and the mass of the Z
⁰
as 91.1876±0.0021 GeV, or 97.215 times the mass of a proton.

13
  Rolf Heuer, ‘Latest update in the search for the Higgs boson', CERN Seminar, 4 July 2012.

14
  The particle ‘consistent' with the Higgs boson was found to have a mass around 125—6 GeV.

15
  CERN press release, 4 July 2012.

16
  Interview with Robert Crease and Charles Mann, 3 March 1983. Quoted in Crease and Mann, p.281.

Chapter 4: Beautiful Beyond Comparison

1
  Letter to Heinrich Zangger, 26 November 1915. The colleague in question was German mathematician David Hilbert, who was in pursuit of the general theory of relativity independently of Einstein. See Isaacson.

2
  Isaac Newton,
Mathematical Principles of Natural Philosophy,
first American edition, translated by Andrew Motte, published by Daniel Adee, New York, 1845, p.81.

3
  Of course, this doesn't mean that the flashlight is really ‘stationary'. The flashlight is spinning along with the earth's rotation on its axis and moving around the sun at about 19 miles per second. The solar system is moving towards the constellation Hercules at about 12 miles per second and drifting upwards, above the plane of the Milky Way, at about 4 miles per second. The solar system is also rotating around the centre of the galaxy at about 124 miles per second. Add this together, and we get a speed of about 159 miles per second. This is the speed with which the earth is moving within our galaxy. Now if we consider the speed with which the galaxy moves through the universe …

4
  Albert Einstein,
Annalen der Physik,
17 (1905), pp. 891—921. An English translation of this paper is reproduced in Stachel, pp. 123—60. This quote appears on p.124.

5
  The relationship can be worked out with the aid of a little high-school geometry. The time interval on the moving train is equal to the time interval on the stationary train divided by the factor
, where v is the speed of the train and c is the speed of light. If v = 100,000 miles per second and c = 186,282 miles per second, then this factor has the value 0.844. This means that the time on the moving train is dilated by about 19 per cent. So, 24.1 billionths of a second becomes 28.6 of a second.

6
  Actually, this experiment is complicated by the fact that, when transported at an average 10 kilometres above sea level, an atomic clock actually
runs faster
because gravity is weaker at this height above the ground. In the experiment described here, this effect was expected to cause the travelling clock to gain 53 billionths of a second, offset by 16 billionths of a second due to time
dilation. The net gain was predicted to be about 40 billionths of a second. The measured gain was found to be 39±2 billionths of a second.

7
  Again, the GPS system requires two kinds of corrections — the speed of the satellites causes a time dilation of seven thousandths of a second and the effects of weaker gravity at the orbiting distance of 20, 000 kilometres from the ground causes the atomic clocks to run faster by about 45 thousandths of a second. The net correction is therefore 38 thousandths of a second.

8
  The length of the train contracts by a factor
where, once again, v is the speed of the train and c is the speed of light. If the train is moving at 100,000 miles per second and the speed of light is taken to be 186, 282 miles per second, then this factor is 0.844.

9
  Albert Einstein,
Annalen der Physik,
18 (1905), pp. 639—41. An English translation of this paper is reproduced in Stachel, pp. 161—4. This quote appears on p.164.

10
  Poincaré's paper is cited by Lev Okun,
Physics Today,
June 1989, p.13.

11
  See note 3 in Chapter 3, above. The full equation is E
²
= p
²
c
²
+ m
²
c
⁴
, where p is the momentum of the object, m is its ‘rest mass' and c is the speed of light. For massless photons with m = 0, the equation reduces to E
²
= p
²
c
²
, or E = | p | c, where | p | represents the modulus (absolute value) of the momentum. Photons have no mass but they do carry momentum. You might be tempted to apply the classical non-relativistic expression for momentum — mass times velocity — and so conclude that for photons | p | = mc, so E = mc
²
after all. But this is going around in circles. For photons m = 0, so we would be forced to conclude that photons have no momentum. What this means is that the non-relativistic expression for momentum does not apply to photons.

12
  The equation is M = m/
, where M represents the ‘relativistic mass', m the ‘rest mass', v is the speed of the object and c is the speed of light. This seems to suggest that a passenger with a rest mass of 60 kg travelling at 100, 000 miles per second would acquire a relativistic mass of about 71 kg. However, there are caveats — see text.

13
  Letter to Lincoln Barnett, 19 June 1948. A facsimile of part of this letter is reproduced, together with an English translation, in Lev Okun,
Physics Today,
June 1989, p.12.

14
  Hermann Minkowski, ‘Space and Time', in Hendrik A. Lorentz, Albert Einstein, Hermann Minkowski and Hermann Weyl,
The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity,
Dover, New York, 1952, p.75.

15
  Greene,
The Fabric of the Cosmos,
p.51.

16
  Newton,
Mathematical Principles,
op cit., p.506.

17
  Albert Einstein, ‘How I Created the Theory of Relativity', lecture delivered at Kyoto University, 14 December 1922, translated by Yoshimasa A. Ono,
Physics Today,
August 1982, p.47.

18
  Wheeler, with Ford, p.235.

19
  In A. J. Knox, Martin J. Klein and Robert Schulmann (editors),
The Collected Papers of Albert Einstein, Volume 6, The Berlin Years: Writings 1914—1917,
Princeton University Press, 1996, p.153.

Chapter 5: The (Mostly) Missing Universe

1
  Albert Einstein,
Proceedings of the Prussian Academy of Sciences,
142 (1917). Quoted in Isaacson, p.255.

2
  This is commonly known as Olbers' paradox, named for nineteenth-century German amateur astronomer Heinrich Wilhelm Olbers. If the universe were really static, eternal, homogeneous and infinite, then it is relatively straightforward to show that although distant stars are dimmer, the fact that there are many more of them should mean that their total brightness does not diminish with distance. Consequently, the night sky would be expected to be ablaze with starlight. Recent investigations suggest that history has been rather kind to Olbers, and that others, such as sixteenth-century English astronomer Thomas Digges, deserve rather more credit for articulating this paradox. See Edward Harrison,
Darkness at Night: A Riddle of the Universe,
Harvard University Press, 1987.