Three Scientific Revolutions: How They Transformed Our Conceptions of Reality (27 page)

Heisenberg published the results in the April 1927 issue of the
Zeitschrift für Physik
. Having received the proofs of the article, Bohr sent a copy to Einstein “adding in an enclosed letter that it ‘represents a most significant . . . exceptionally brilliant . . . contribution to the discussion of the general problems of quantum theory.'”
¹⁰³
What makes it exceptional is not just the calculated mathematical equation, as significant as that is, but that it reversed the age-old assumption that for the mathematics to be correct it must accurately represent the experimental results. Heisenberg affirmed that it is the mathematics that limits or sets the possible experimental outcome! As he states:

Instead of asking: How can one in the known mathematical scheme express a given experimental situation? the other question was put: Is it true, perhaps, that only such experimental situations can arise in nature as can be expressed in the mathematical formalism? The assumption that this was actually true led to limitations in the use of the concepts that had been the basis of classical physics since Newton.
¹⁰⁴

As an indication of the influence Heisenberg's paper had on Bohr, when a famous article by Einstein, Podolsky, and Rosen (known as the EPR article), titled “Can Quantum Mechanical Descriptions of Physical Reality Be Considered Complete?” was published in the
Physical Review
in 1935,
¹⁰⁵
claiming that although Heisenberg's formalism was consistent with all the known quantum data it was “incomplete” because it did not allow precise measurements of the conjugate attributes' position and momentum and energy and time, Bohr had a ready reply.

In the following issue of the
Review
, in an article with exactly the same title, he replied that in quantum mechanics

we are not dealing with an incomplete description characterized by the arbitrary picking out of different elements of physical reality at the cost of sacrificing other elements, but . . . the
impossibility
, in the field of quantum theory, of accurately controlling the reaction of the object on the measuring instruments. . . . Indeed we have . . . not merely to do with an
ignorance
of the value of certain physical quantities, but with the
impossibility
of defining these quantities in an unambiguous way.
¹⁰⁶

In the draft of a paper in July 10, 1927, Bohr had used the term ‘complementarity' for the first time that became a famous designation for the conjugate uncertainty measurements. Then in a collection of articles published later in his life, there is a clear statement of how he believed quantum mechanics has changed our method and understanding of the subatomic quantum domain in contrast to the macroscopic and atomic level of experience, an explanation that had assumed that a precise description and definite explanation of the external world was always possible, even if out of reach at the time:

Within the scope of classical physics, all characteristic properties of a given object can in principle be ascertained by a single experimental arrangement. . . . In quantum physics, however, evidence about atomic objects obtained by different experimental arrangements exhibits a novel kind of complementary relationship. Indeed, it must be recognized that such evidence which appears contradictory when combined into a single picture is attempted, exhausts all conceivable knowledge about the object. Far from restricting our efforts to put questions to nature in the form of experiments, the notion of
complementarity
simply characterizes the answers we can receive by such inquiry, whenever the interaction between the measuring instruments and the objects forms an integral part of the phenomena.
¹⁰⁷

Just as we found that our sensory system modifies what we observe, so we have learned that what unobservable properties the world discloses experimentally at
a certain dimension
also partially reflects the methods and instruments used in investigating it. This realization that all experience and knowledge is due to an inter­action with the world, not just an immediate awareness or disclosure of it as usually appears to be the case, brought about a radical transformation in our conception of reality and how we come to know it—a reversion especially imposed by Heisenberg's discovery of the “uncertainty principle” and Bohr's “Copenhagen interpretation” that has been a crucial feature of the third scientific transformation of our conception of reality.

What is surprising is that Einstein, in his article with Podolsky and Rosen, did not realize that the uncertainties encountered when investigating a deeper domain of particle physics did not permit the same exact measurements as those made on a larger scale was analogous to his special theory of relativity. His theory also claimed that the exact measurements of space, time, and motion made within the lesser velocities of ordinary experience cannot be made when the velocities are so extreme they effect the measuring devices such that the measurements are relative to the velocities of the measurer rather than being absolute as Newton claimed.

For millennia humans believed that the picturesque world as ordinarily experienced was the actual world. Even as late as the nineteenth century Ernst Mach declared that “Atoms cannot be perceived by the senses . . . they are things of thought” implying they did not exist. Yet at the beginning of modern classical science, with the introduction of the telescope and the microscope, scientists began to realize that the existence of the ordinary world, as objective, determinate, and independent as it appears to be, really depends on very complex, unseen underlying conditions. With every discovery of a new dimension of the world the assumption usually has been that this must be the final reality, not just another level of inquiry.

But even if all existence and knowledge is conditional, it is equally erroneous to infer that we do not know anything about the world or that it has any objective properties as concluded in the article by Einstein, Podolsky, and Rosen
if the quantum mechanical worldview were accepted
. But were their view true, how could we account for the corrective and progressive advances in scientific knowledge and its extraordinary technological consequences before and since their time?

Supposing that whatever knowledge of the universe and human existence we acquire depends upon the physical conditions within which they exist, along with the method of investigation used, this does not preclude their being actual within those conditions, otherwise we would have to deny that the ordinary world we live in exists and that the independent subatomic world does not have any of the physical properties it has because their existence is dependent on a more extensive background physical context. Consider water existing as vapor or ice under different conditions.

What we have to realize is that the meaning of ‘existence' has changed with the acquisition of greater knowledge, just as Bohr argued that the meaning of ‘understanding' has changed. Just because particles are so minute that they
prevent the
measuring
of certain conjugate properties does not mean that these properties do not exist in the object conjointly—that the particle does not have a simultaneous position and momentum or energy and time just because the conditions prevent their being measured conjointly. How could it exist without these conjugate properties?

As added evidence of this conception of “contextual realism” that I referred to in a previous book bearing that title and again in this book, I'll continue the review of additional scientific discoveries showing the
limits
, not necessarily the negation, of Newton's corpuscular-mechanistic view of reality at a deeper level of inquiry, along with illustrating that additional physical or quantitative properties of subatomic particles have been discovered despite their existence being dependent upon the type of measurement used to identify them.

The first is the property of spin. It is common knowledge that microscopic particles are not defined by sensory qualities, but by their primary properties of mass, charge, energy, and momentum. At about the time the previously described quantum mechanical discoveries were being made, two physics students in their mid-twenties from the University of Leyden in Holland, Samuel S. Goudsmit and George E. Uhlenbeck, suggested that on Bohr's model, electrons like planets, in addition to having an orbital motion around the nucleus, also revolve on their axes with an invariant angular momentum called “spin,” whose value is ½
h/2
π. This value remains constant “even when the electron is outside the atom, and is totally independent of the linear speed or environment of the electron,”
¹⁰⁸
indicative of its inherent though conditional nature. Furthermore, because the electron is electrically charged and follows the laws of quantum mechanics, it has two additional properties.

First, having an electrical charge it acts as a tiny magnet whose movement creates a magnetic moment that creates an electromagnetic field. Second, in quantum mechanics an entity with the properties of angular momentum has just two possible spin orientations: “If we perform any measurement whatsoever to determine the angle between the direction of the electron spin and any given direction in space, we find that the angle is
always
either 0
⁰
or 180
⁰
—in other words, the spin is either parallel or antiparallel to the chosen direction” (pp. 53, 55). Moreover, the spin of certain pairs of subatomic particles are such that measuring the spin of one particle will instantly cause its twin particle to begin spinning in the opposite direction at the same rate, however great the distance between them, a discovery made by John Stewart Bell and published in the
Review of Modern Physics
in 1966
.
Given these perplexing features of quantum mechanics, it has been claimed that the concept of spin as an
actual
rotary motion of the electron should not be taken literally: “it is more accurate to say that the electron has an intrinsic angular momentum of ½
h/2/π,
called spin,
as if
it were rotating about its axis” (p. 57). But how is it possible to use “as if states” in scientific theorizing?

For example, the concept of spin is considered an additional important property of electrons and other particles, having explanatory as well empirical consequences that
have been experimentally confirmed
. The electric charge along with its spin gives the electron its magnetic moment that helps explain the emission and reabsorption of photons. In addition, the two possible spin orientations imply two energy states that help explain “the peculiar pattern of close lines or doublets in the Balmer series of the hydrogen spectrum.” Called quantum electrodynamics or QED for short, the theory measured the magnetic moment of the electron “in a unit called the Bohr magneton, denoted
µ
_e
” that has “a very great accuracy . . . found to be 1.001 159 652
µ
_e
” (p. 58).

As another example of the remarkable influence Bohr's Institute had on the development of quantum mechanics, during the time that Schrödinger and Heisenberg were at the Institute, Paul Dirac also was present doing postdoctoral work from September 1926 to February 1927. Like Schrödinger, he hoped to reconcile quantum mechanics and relativity theory by incorporating Einstein's concept of the field and reformulating Heisenberg's quantum mechanics, along with incorporating the Hamiltonian, the operator corresponding to the total energy of a system. As described by Crease and Mann:

Using Heisenberg's quantum mechanics, Dirac was able to come up with the Hamiltonian for the atom from quantum mechanics. Dirac was thus able to say that the Hamiltonian for the entire process could be found by adding up the separate Hamiltonians for the atom, the field, and the interaction. . . . The result was the first quantum field theory. Because it linked quantum theory with the dynamics of electromagnetic fields, Dirac called it
quantum electrodynamics
.
¹⁰⁹

He submitted his results in an article to the
Proceedings of the
Royal Society
toward the end of January 1927, just three weeks before Heisenberg conveyed his uncertainty principle to him. In succeeding papers he published his well-known relativistic wave equation, which has come to be known as the “Dirac equation” that Pais says “ranks among the highest achievements of twentieth-century science.”
¹¹⁰
In 1928 he devised “a relativistically invariant equation for an electron” whose mathematics “introduced a new internal degree of freedom of the particle. This degree of freedom turns out to have all the properties of the electron spin, starting from its value
h/
4π. It also has a magnetic moment of value
eh/
4π
mc
.”
¹¹¹

As proof of its validity, these properties of spin and magnetic moment were not introduced ad hoc but as properties predicted by the equations. Along with sharing the Nobel Prize with Schrödinger in 1933, in the previous year, as an acknowledgment of his outstanding achievements, Dirac was appointed to Newton's chair of Lucasian Professor of Mathematics at Cambridge University that was occupied by the famous cosmologist Stephen Hawking until his recent retirement.

Yet like medicines that have wonderful curative powers but also unexpected side effects, Dirac's equation produced very puzzling outcomes. For instance, his equation predicted that when the electromagnetic field was quantized and included Heisenberg's uncertainty principle space was no longer empty, but filled with bizarre entities and occurrences, as described by Crease and Mann:

The spaces around and within atoms, previously thought to be empty, were now supposed to be filled with a boiling soup of ghostly particles. From the perspective of the quantum field theory, the vacuum contains random eddies in space-time: tidal whirlpools that occasionally hurl up bits of matter, only to suck them down again. Like the strange virtual images produced by lenses, these particles are present, but out of sight; they have been named
virtual particles
. Far from being an anomaly, virtual particles are a central feature of quantum field theory, as Dirac himself was soon to demonstrate.
¹¹²