Introduction | Quantum Mechanics | Whitehead and Bell's Inequality | Whitehead and the Copenhagen Interpretation
Conclusion | Footnotes | Bibliography

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | | 11 | 12
13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |

1. "Energy is another example. Most physicists will initially define energy in terms of its relations to other physical concepts, for instance rest mass and the velocity of light (e=mc2), or Planck's constant and frequency (e=h(). Yet even though the existence of energy is accepted, we don't really know what it is. A signal of the problematic nature of the concept of energy is apparent in the fact that the definitions that do exist are usually framed in such a way as to be tautologies cloaked in equivocatory language, essentially reducing to a statement like "energy is the thing we call 'energy'". Back

2. Actually quantum theory is not considered 'complete' in the strong sense of the word even today. Quantum mechanics, as it is presently, makes certain predictions about the results of experiments. To date, there has been no strong evidence disconfirming quantum theory, as experimental results are always in excellent agreement with theory. This does not necessarily mean that quantum theory is complete, and in fact many would argue the reverse. The work in quantum cosmology and quantum gravity are two examples of areas in which physicists feel that quantum theory needs supplementation. Back

3. Explained later in this paper in its modern form as A. Aspect's experiment. Back

4. For example, -1<0<3 is an inequality. Back

5. Others have since proven similar theorems using slightly different assumptions that result in slightly different inequalities. Inequalities of this type are called "Bell inequalities", and the theorems proving them "Bell theorems". Back

6. The classical conception of reality is essentially Newtonian, and besides being itself a 'locally real' theory, it agrees extremely well with common sense experience. It is because of its seemingly intuitively obvious principles that the classical conception of reality has such staying power, even in light of the fact that both relativity theory and quantum theory (each independently formulated and independently confirmed) prove the invalidity of Newtonian mechanics and the world it implies. Back

7. In effect Bohr agrees with this, stating that the two photons of the above example cannot be considered separate entities until after a measurement has been made to separate them. The measurement itself actually causes the separation. Back

8. One particular interpretation of quantum mechanics, often called the ensemble interpretation, assumes that ontology of probabilities present in quantum mechanics is the end of the line, and that almost no other questions remain to be asked about the nature of the universe on this level. Back

9. Of course this is not the bulk of the work done with or in quantum mechanics, which, far from theoretical, is characterized more by examining possible technological applications of quantum mechanics. Back

10. The Newtonian type of view, because it is so compatible with common sense, and because the ideas of quantum mechanics are not terribly accessible to the average populace, still seems to be dominant among non-scientists, although there is a growing set of layman's books that are beginning to change this. Back

11. There are actually more than just these three assumptions that can result in a Bell inequality, but it is generally agreed that parameter independence, outcome independence, and 'reality' are the most likely candidates for rejection. Linda Wessels has done particularly detailed work examining these various assumptions. Back

12. The initial datum for an actual occasion consists of every already satisfied actual occasion. The objective datum for an actual occasion consists of those already satisfied actual occasions that it positively prehends. A prehension can be thought of as a bringing from the past (as defined above) into the present (of the concrescing actual occasion in question) by a process of perception-Whitehead speaks of a prehension as a 'feeling'. The satisfaction of an actual occasion is the culmination of the occasion's multiple prehensions into one unified feeling; the actual occasion becomes part of the initial datum, loses its ability to prehend, and can now itself be prehended. Back

13. The word "tradition" is my own term, not employed by Whitehead. Back

14. Otherwise one is committing a 'fallacy of misplaced abstractness'! Back

15. An interesting quote from a modern textbook on quantum mechanics may give some force to the idea of the universe as inherently interconnecting processes that cannot be completely abstracted from the whole: "As a practical matter, therefore, it's okay to pretend that electrons with nonoverlapping wave functions are indistinguishable. (Indeed, this is the only thing that allows physicists and chemists to proceed at all, for in principle every electron in the universe is linked to every other one via the antisymmetrization of their wave functions, and if this really mattered, you wouldn't be able to talk about any one electron until you were prepared to deal with them all!)" Griffiths:1995 p.184 Back

16. Again this is my terminology, not Whitehead's. Back

17. This can explain why, for example, electrons always occupy very particular 'orbits' when they are part of an atomic system (the 'quantum leap' phenomenon). Back

18. The relationship is expressed as p > h/4, where x is the uncertainty in position, p is the uncertainty in momentum, and h is Planck's constant. It is easy to see that decreasing the uncertainty of position necessarily increases the uncertainty of momentum, and vice versa. Back

19. This strange thesis of the Copenhagen interpretation stems from Bohr's idea that physics tells us not what is, but what we can say about the world. Back

20. Several properties are complementary besides position and momentum: wave-ness and particle-ness are complementary, as are time and energy. Back

21. This could be taken to mean that each actual occasion is philosophical! Back

22. Although not completely so-for example, how is it that an actual occasion can possibly begin? That is to say, what allows the actual occasion to begin its process in the first place? Back

23. The eventual worldwide impact of the settling of Cartesian metaphysics in the Western mind is one example. Back

On to Bibliography.