|
© 1998 Stephen Speicher
INTRODUCTION
Line Number
1.00.01 This is the first of three parts explaining, in non-technical
1.00.02 terms, the brilliant "Theory of Elementary Waves" of Lewis
1.00.03 Little. If you normally shy away from discussions on physics,
1.00.04 please give this a chance - it was especially written for you.
1.00.05 Although I love and revere mathematics, I firmly believe if you
1.00.06 cannot explain a principle of physics in common language and
1.00.07 terms, then you probably do not fully grasp the principle in the
1.00.08 first place. Little's theory is extremely broad-ranging and if I
1.00.09 can successfully communicate the highlights of his achievement I
1.00.10 would consider that to satisfy my goal.
THEORY OF ELEMENTARY WAVES - PART 1
1.01.01 Quantum physics focuses primarily on the atomic and sub-atomic
1.01.02 level, and the evolution of its mechanics spans almost a century.
1.01.03 In 1900 Max Planck developed an empirical formula which described
1.01.04 certain experimental observations about energy. When looking for
1.01.05 a theoretical basis for his formula he advanced the idea that
1.01.06 energy, which at that time was thought to be a continuous flow of
1.01.07 waves, actually consisted of small individual pieces, called
1.01.08 quanta. Several years later Albert Einstein conceived the idea
1.01.09 that light was composed of both waves and particles, and later
1.01.10 the name photon was given to that particle of light. About 1913
1.01.11 Niels Bohr, utilizing the idea of Planck's quanta, created a
1.01.12 model of atomic structure. The next decade saw many physicists
1.01.13 involved in quantum mechanics research, and in 1926 Erwin
1.01.14 Schroedinger formulated what was to become the cornerstone of
1.01.15 this new theory, his quantum wave equation. The decade
1.01.16 following Schroedinger's discovery ushered in the world of
1.01.17 nuclear physics which has continued quantum research through
1.01.18 today.
1.02.01 In the seven decades since the wave equation was created, the
1.02.02 strangeness of this new field of physics has been transformed
1.02.03 into the 'weirdness' of quantum mechanics. The standard theory is
1.02.04 replete with effects without causes and the assertion that matter
1.02.05 exists in an indeterminate state. The 'weird' behavior, according
1.02.06 to the theory's interpreters, is worn as a banner of proof, as if
1.02.07 this difference from known facts of reality should be taken as
1.02.08 evidence to substantiate the theories. In 1996 the physicist
1.02.09 Lewis Little published his paper "The Theory of Elementary
1.02.10 Waves". For the first time since Planck's quanta in 1900, a
1.02.11 rational basis for quantum mechanics has been established. The
1.02.12 purpose of this article is to outline Little's revolutionary
1.02.13 theory, in non-technical terms, and to identify the kinds of
1.02.14 problems that his ideas have resolved. I will present some
1.02.15 highlights of the theory. A full explanation requires a much more
1.02.16 substantial analysis.
1.03.01 The sagacious Caltech physicist, Richard Feynman, was fond of
1.03.02 presenting essentialized models of experiments to his beginning
1.03.03 physics students in order to illustrate basic physics principles.
1.03.04 Feynman believed (rightfully so) that a particular kind of
1.03.05 experiment, one called the double-slit experiment, embodied the
1.03.06 essence of the fundamental issues in quantum mechanics. Following
1.03.07 Feynman, we will look at a few examples of these models, keeping
1.03.08 in mind that, in principle, the actual experiments can and have
1.03.09 been performed. We will then explore some fundamentals of
1.03.10 Little's theory and re-evaluate the experiments in light of what
1.03.11 we have learned.
1.04.01 A particle is usually understood to be an individual coherent
1.04.02 object possessing a specific identity which can be localized in a
1.04.03 given region of space. It is easier to grasp the actions of
1.04.04 quantum particles by first looking at the behavior of a more
1.04.05 familiar particle - a bullet. Figure 1 shows a gun (our 'source')
1.04.06 that shoots a continuous stream of bullets. The source sprays
1.04.07 bullets, in a fan-like manner towards a wall which has two slits
1.04.08 just big enough to allow the bullets to pass through. Some
1.04.09 distance behind the wall is a backdrop which stops the bullets as
1.04.10 well as counts the number of bullets that impinge anywhere along
1.04.11 its surface. Intuitively, if we think of what is the likelihood
1.04.12 of where the bullets going through slit 1 will wind up, we can
1.04.13 see that the maximum number of bullets will be along an angle
1.04.14 from the source directly through slit 1 and, as the bullets
1.04.15 bounce off the edge of the slit, the likelihood of finding
1.04.16 bullets will decrease as we get further in each direction from
1.04.17 the slit. The number of bullets detected having gone through slit
1.04.18 1 is shown as 1's. Similarly the number of bullets going
1.04.19 through slit 2 is shown as 2's. The important point here is that
1.04.20 the total number of bullets counted is just the sum of the
1.04.21 bullets going through slit 1 had we closed off slit two plus the
1.04.22 sum of those going through slit 2 had we closed off slit 1.
Figure 1
| 21111111|
| 211111111|
| 2111111111|
| 21111111111|
| 211111111111|
-slit 1 2221111111111|
22221111111111|
/ - 222222111111111|
/ | 2222222111111111|
/ | 22222222211111111|
source - - - | 222222222211111111| F I G U R E 1
(bullet)\ | 22222222211111111|
\ | 2222222221111111|
\ -slit 2 222222222111111|
22222222221111|
- 2222222222111|
| 222222222221|
| 22222222221|
| 2222222221|
| 222222221|
| 22222221|
WALL BACKDROP
1.05.01 In contrast to particles, mechanical waves are usually understood
1.05.02 to be a disturbance in some continuous medium; the disturbance
1.05.03 propagates through the medium. Water waves and sound waves are
1.05.04 two common examples of this simple wave phenomenon. We can
1.05.05 perform the same double-slit experiment using a wave for a source
1.05.06 instead of the bullets. Figure 2 shows a similar experimental
1.05.07 setup where now the source makes circular water waves. The
1.05.08 backdrop, instead of counting the bullets as before, now has the
1.05.09 ability to measure the intensity of the wave impinging on its
1.05.10 surface. If we cover slit 2 and measure the intensity of the
1.05.11 waves coming through slit 1, and then cover slit 1 and measure
1.05.12 the intensity of the waves coming through slit 2, we get a
1.05.13 distribution that looks very much like the count distribution for
1.05.14 the bullets in Figure 1. However, when we measure the intensity
1.05.15 with both slits open, unlike the case with the bullets, the total
1.05.16 intensity does not equal the sum of the intensities from slit 1
1.05.17 and slit 2 alone. In fact, we get a total intensity which
1.05.18 sometimes is more than and sometimes less than the sum of the
1.05.19 intensities from slits 1 and 2. This difference of wave behavior
1.05.20 as compared to particle behavior is a consequence of the
1.05.21 interaction of the waves coming through each of the slits. This
1.05.22 is actually a very common wave occurrence which you can see if
1.05.23 you watch the waves that result from the passing of two boats.
1.05.24 If the waves meet when both are at their crest the resultant wave
1.05.25 of their combination is larger than the sum of the originals. On
1.05.26 the other hand, if one wave is at its crest and the other at its
1.05.27 trough, the waves cancel each other and you can observe
1.05.28 relatively smooth water. This interaction of two waves is called,
1.05.29 in physics, interference. Constructive interference is the
1.05.30 additive process when the two waves are 'in phase' with each
1.05.31 other; destructive interference is the subtractive process when
1.05.32 the waves are 'out of phase'.
Figure 2
| 211111|
| 2111111|
|) 211111|
| ) 2111|
) | ) 21|
) - slit 1 211|
) ) ) ) 21111|
) ) - ) ) 2211111|
) ) | ) 222111111|
) ) ) | ) 22221111111|
source-)- -)- -)| ) ) 222222111111| F I G U R E 2
(water ) ) ) | )) 22222221111|
wave) ) ) | )) 222222111|
) ) - ) ) 2222211|
) ) ) 22221|
) - ) 221|
) | slit 2 21|
| ) 2221|
| ) 222221|
| 2222221|
| 222221|
WALL BACKDROP
1.06.01 Now that we have seen how classical objects like particle-bullets
1.06.02 and water waves respond to the double-slit experiment, the next
1.06.03 step is to investigate the response of quantum mechanical
1.06.04 particles. All we need do is to use as a source an electron (a
1.06.05 charged particle) or a photon (a quantum of light). When we
1.06.06 perform the double-slit experiment using photon particles, the
1.06.07 result is _not_ like the bullets in Figure 1. In fact, the
1.06.08 interference pattern seen in the wave source of Figure 2 is
1.06.09 observed. The experiment seems to be telling us that the photon
1.06.10 particle acts like a wave. How we don't know, just somehow. This
1.06.11 observation has led quantum mechanic theorists to use the ideas
1.06.12 of particle-wave, or wave-particle. The connotation of this is
1.06.13 that a photon is a particle with wave-like properties, but it is
1.06.14 completely unclear what this means in reality other than pointing
1.06.15 to the results of the experiment. It is possible to detect that
1.06.16 the photons are arriving as discrete packets, so it seems
1.06.17 reasonable to assume a particle goes through either slit 1 or
1.06.18 slit 2. But, if we block off slit 2 we just get the same
1.06.19 distribution for slit 1 as we got for the counting of bullets.
1.06.20 Likewise for closing off slit 1. Only by keeping both slits open
1.06.21 do we get the interference pattern. Clearly there is some kind of
1.06.22 wave interaction.
1.07.01 If we try to 'peek' and see which slit each particle is going
1.07.02 through (a particle is always detected as going through slit 1 or
1.07.03 slit 2), the results of the experiment are again just like the
1.07.04 counting of bullets. So the theorists conclude that we cannot
1.07.05 definitely say that the particle goes through either slit 1 or
1.07.06 slit 2, since the act of determining that fact changes the
1.07.07 outcome. When speaking about the experiment, the standard theory
1.07.08 treats probability as if it had physical characteristics. There
1.07.09 is a certain probability of the particle going through either
1.07.10 hole, and probability interference (somehow acting like real wave
1.07.11 interference) is what causes the wave-like result. If you can
1.07.12 detect a particular particle, that changes the probability
1.07.13 pattern. So there is a ghost-like quality to the actions of these
1.07.14 particles, where probability replaces a real existent. In fact,
1.07.15 the standard theory is saying that the very act of observing
1.07.16 forces a particular probability and it is then that something
1.07.17 _becomes_ real.
1.08.01 It is this ghost-like quality which leads us to the Schroedinger
1.08.02 wave equation. The solution to the equation is known as the wave
1.08.03 function; it gives the probability of locating a particle at a
1.08.04 particular place and at a particular time. The Schroedinger
1.08.05 equation, then, associates a wave with a particle. A
1.08.06 characteristic of the equation is that if you have separate
1.08.07 solutions, they can be combined together - a process known as
1.08.08 superposition. Think of a particle at the source vanishing and
1.08.09 being replaced by a host of ghost particles that follow different
1.08.10 paths to the backdrop. These ghost-like particles somehow
1.08.11 interfere with each other, which results in the pattern we have
1.08.12 seen for wave-like behavior. These ghosts relate to the wave
1.08.13 function which is a solution to Schroedinger's equation. When we
1.08.14 observe the particle, all of the probability waves disappear
1.08.15 except for the one associated with the real object. This is the
1.08.16 act you may have heard described as the 'collapse of the wave
1.08.17 function'. Nothing is real, until we look at it. This is pure
1.08.18 Kantianism.
1.09.01 Let me try to succinctly sum up what we have learned about the
1.09.02 standard theory. Experiment shows that quantum particles seem to
1.09.03 behave sometimes like particles and sometimes like waves. This
1.09.04 'weirdness' is enshrined in an anti- concept of particle-wave (or
1.09.05 wave-particle) which refers to nothing in reality. Real objects
1.09.06 are replaced by probability functions which somehow govern the
1.09.07 overall wave-like behavior that results in the patterns seen in
1.09.08 experiments. There is absolutely no attempt to establish a causal
1.09.09 basis; in fact this lack is proudly offered as proof of the
1.09.10 theory since 'why should we think quantum reality is anything
1.09.11 like what happens on a larger scale'. In one sense this is true,
1.09.12 in that quantum behavior is uniquely defined, but does that mean
1.09.13 we must abandon all pretense of causality and maintain a
1.09.14 ghost-like existence of matter in some indeterminate state? Yes,
1.09.15 says the standard theory. No, says Lewis Little's Theory of
1.09.16 Elementary Waves.
1.10.01 In one sense the Theory of Elementary Waves (TEW) is very
1.10.02 profound and requires a detailed technical analysis to see how it
1.10.03 operates and how it applies to quantum phenomena. In another
1.10.04 sense, though, it is quite simple, in that it identifies and
1.10.05 integrates some very fundamental parts of reality. As a starting
1.10.06 point to understand his approach, consider some of Little's
1.10.07 thinking regarding the double-slit experiment. Although standard
1.10.08 theory is hesitant to even pronounce judgment as to which slit a
1.10.09 particle goes through, Little realizes that each particle must go
1.10.10 through a single slit and that it must follow a specific
1.10.11 trajectory while doing so. At the outset he rejects the effect
1.10.12 without cause of standard theory. Figure 3 shows the double-slit
1.10.13 setup with a set of supposed trajectories for each particle.
1.10.14 Little now argues that if we moved the target to another
1.10.15 position, B, then as the particles follow the same trajectories
1.10.16 they would intersect the detector at different points than before
1.10.17 and, therefore, would not show the standard pattern. However,
1.10.18 experiment shows that in fact the pattern occurs _wherever_ the
1.10.19 target is placed. This experimental fact cannot be explained by
1.10.20 the standard theory if we are to simultaneously maintain cause
1.10.21 and effect. It can be explained, however, if you consider the
1.10.22 experiment as evidence that there is motion _from_ the target
1.10.23 _to_ the particle source. This is exactly opposite to the way of
1.10.24 thinking in the standard theory.
Figure 3
(B)
| | |
| | x|
| x x| |
| x x | |
| x x | |
slit 1 -x x | |
x x y x | |
x - x y x | |
x | x x y | |
x | x x y | |
source x | x | y| F I G U R E 3
(photon x | x x y | |
particle) x | x x y | |
x - x y x | |
x x y x | |
slit 2 -x x | |
l x x | |
| x x | |
| x x| |
| | x|
| | |
WALL target
1.11.01 What is it, then, that moves from the detector to the source.
1.11.02 Little's theory states that it is the quantum wave that moves in
1.11.03 this reverse direction. But, as we saw before, a wave is thought
1.11.04 of as a disturbance of some medium and the wave propagates
1.11.05 through the medium. What is the medium in this quantum case, and
1.11.06 what is the cause of the disturbance? It is in answer to this
1.11.07 question that Little breaks with tradition and establishes a base
1.11.08 on which to explain the 'weirdness' of quantum mechanics. It is
1.11.09 not a wave in the usual sense at all - it is an elementary wave -
1.11.10 a _fundamental constituent of reality_. In effect, it _is_ the
1.11.11 medium. I cannot stress strongly enough the importance of this
1.11.12 idea. Little's theory identifies the most basic 'stuff' of
1.11.13 existence. This is not just the mathematical representation of a
1.11.14 phenomenon, this is a _real_ wave. The elementary wave cannot be
1.11.15 understood by appealing to anything more basic to explain it -
1.11.16 there is nothing more basic. The elementary waves have a
1.11.17 structure and the effects of the changes in that structure are
1.11.18 all we can know about them. So the ghost-like packets of waves in
1.11.19 the standard theory have been replaced by a real existent, and
1.11.20 the behavior of that wave is contrary to standard interpretation
1.11.21 - the wave moves in reverse, from the target, or more generally
1.11.22 from the detector, towards the source.
1.12.01 In a way, Little's elementary wave is less like a traditional
1.12.02 wave and closer to the idea of the elusive ether, in that it is
1.12.03 like a flow, or a flux of material, while realizing that it makes
1.12.04 no sense to talk about what kind of material it is - it just is.
1.12.05 Twenty-five hundred years ago Parmenides said (and more recently,
1.12.06 as Leonard Peikoff is fond of saying) the universe is a "plenum".
1.12.07 That is, there are no gaps, no voids, no place where there is
1.12.08 nothing. That is what Little's theory has identified, the
1.12.09 elementary waves are what fill the universe - they are
1.12.10 omnipresent. According to Little's theory the waves exist for
1.12.11 every possible quantum state, for every variable parameter that
1.12.12 is possible.
1.13.01 Before we can revisit the double-slit experiment in the light of
1.13.02 elementary waves, we first need to understand what a particle is
1.13.03 in this new theory. In Little's view the elementary waves are
1.13.04 primary in the sense that they carry dynamic quantities such as
1.13.05 mass, momentum, energy, etc. It is the wave that triggers the
1.13.06 emission of the particle at the source; the state of that
1.13.07 particle, the dynamics of its motion, is determined by the
1.13.08 particular wave that stimulates, or induces, the emission. The
1.13.09 particle then follows the path of the wave; thus the wave moves
1.13.10 from the detector to the source and the particle travels from the
1.13.11 source to the detector. We should keep in mind that these are
1.13.12 _elementary_ waves, not waves in some medium. The wave itself is
1.13.13 moving from the detector to the source; no dynamic information
1.13.14 propagates through the wave; the wave carries the information as
1.13.15 it moves. That is why, as mentioned above, the elementary waves
1.13.16 may be best understood as being a flux or a flow. As a general
1.13.17 statement then, a particle will follow the straight line motion
1.13.18 opposite to its elementary wave, and will continue such motion
1.13.19 unless there is some interaction with another particle which can
1.13.20 change its direction. As in the case with Little's elementary
1.13.21 waves, Little's particles are not ghost-like, they are real.
1.13.22 There is no 'collapse of the wave function' which selects from an
1.13.23 array of probability waves a packet of waves which describe a
1.13.24 'real' photon. In the TEW, _all_ of the elementary waves and
1.13.25 _all_ of the particles are real existents.
1.14.01 Now we can look back at the quantum double-slit experiment and
1.14.02 try to make sense of the experiment using TEW as a guide. We
1.14.03 understand that there are elementary waves, which correspond to
1.14.04 all possible quantum states, that exist as real objects filling
1.14.05 the space around us. Further, think of coherence as a certain
1.14.06 likeness of waves which can then combine by one rule, and
1.14.07 incoherence a certain dissimilarity in waves which can then
1.14.08 combine by another rule. When the target, or detector, is placed
1.14.09 in position, the particles of which the detector consists impose
1.14.10 an 'organization' or coherence upon the existing waves. From
1.14.11 every point on the detector flows a complete set of waves that
1.14.12 uniquely reflect the state of the particle which imposed the
1.14.13 organization on the wave and they are all coherent with each
1.14.14 other; but they are incoherent with the waves flowing from other
1.14.15 points. So for any given point on the detector, the reverse
1.14.16 waves travel back towards the wall with the two slits, through
1.14.17 the slits and continue onwards to the particle source. These are
1.14.18 real waves which will interfere with each other; so, in some
1.14.19 cases there will be constructive interference and in others
1.14.20 destructive interference. The resulting intensity of the wave,
1.14.21 after interference, determines, at the particle source, the
1.14.22 likelihood of inducing the emission of a particle. The particle
1.14.23 then follows the path of the wave back to the detector.
1.15.01 Therefore, the pattern we see at the detector _is_ a consequence
1.15.02 of the interference of waves and the transmission of particles;
1.15.03 but, these are real waves and real particles and the pattern
1.15.04 occurs due to real processes. It is the intensity of the
1.15.05 elementary wave as seen at the source that determines the number
1.15.06 of particles that are induced. The pattern at the detector, then,
1.15.07 is due to the particles that follow the path of each wave back
1.15.08 from the source. In addition, all of the usual quantum mechanical
1.15.09 mathematics remains essentially the same - this new theory,
1.15.10 however, explains _why_ the mathematics works.
1.16.01 To see the dramatic contrast between the standard theory and the
1.16.02 TEW, we can summarize as follows: The standard theory creates a
1.16.03 wave-particle (or particle-wave) out of thin air. It is a
1.16.04 nebulous concept without referents in reality. In opposition to
1.16.05 the standard theory, the TEW identifies the existence of
1.16.06 elementary waves, which are real, primary, fundamental
1.16.07 constituents of reality, and it logically asserts, also in
1.16.08 opposition to the standard theory, the existence of real,
1.16.09 fundamental particles. These real, elementary waves are what
1.16.10 interfere with each other, accounting for the observed
1.16.11 interference pattern on the detector. While standard theory is
1.16.12 unable to state that particles go through either one of the
1.16.13 slits, the TEW unequivocally does so state and gives the
1.16.14 mechanism by which it is accomplished - the particle following
1.16.15 the path of the reverse wave. While standard theory has
1.16.16 ghost-like objects that disappear with 'wave collapse' in order
1.16.17 to give birth, so to speak, to a 'real' object, the TEW always
1.16.18 deals with real objects that do not 'disappear' when the
1.16.19 experiment is done. So, unlike the standard theory, the TEW
1.16.20 establishes a causal basis for the actions of real entities,
1.16.21 and completely contravenes the theory of the existence of matter
1.16.22 in some indeterminate state. This is why I stated above: For the
1.16.23 first time, the TEW has established, a rational basis for quantum
1.16.24 mechanics.
1.17.01 In Part 2 we will look at the famous 'uncertainty principle' in
1.17.02 light of what we have learned so far about the TEW, as well as delve
1.17.03 a little deeper into the mechanics of the TEW by discussing
1.17.04 additional experiments.
sjs@compbio.caltech.edu
(© 1998) Stephen Speicher
THEORY OF ELEMENTARY WAVES - PART 2
INTRODUCTION
2.00.01 This is the second part of a three-part article focusing on Lewis
2.00.02 Little's revolutionary Theory of Elementary Waves. It is
2.00.03 prefaced by a short digest, an "Executive Summary" highlighting
2.00.04 key elements of the article, leaving out technical details and
2.00.05 substantive information. It may also be helpful to establish the
2.00.06 overall context before reading the entire article.
"Executive Summary"
2.01.01 Schroedinger's wave equation is the mathematical cornerstone of
2.01.02 quantum mechanics. Heisenberg's uncertainty principle represents
2.01.03 the intellectual underpinnings of the standard theory.
2.02.01 The standard theory: if anything is definite in quantum
2.02.02 mechanics, it is mathematical; if anything is physical, it is
2.02.03 indefinite; there are uncertainties in the nature of matter that
2.02.04 cannot be overcome. The essence of the standard theory: It is the
2.02.05 measurement of particles that create their reality.
2.03.01 Heisenberg's uncertainty principle: there are fundamental limits
2.03.02 to which the accuracy of pairs of quantum variables can be
2.03.03 specified and measured. Examples: the uncertainty relation
2.03.04 between energy and time means that if you were able to localize a
2.03.05 particle at a given instant, it would not have any definite
2.03.06 energy; the more accurately you are able to determine the
2.03.07 location of a particle the less precise you can be about its
2.03.08 momentum.
2.04.01 The TEW identifies that the uncertainty is a consequence of the
2.04.02 anti-concept of wave-particle, along with the mistaken notion of
2.04.03 the forward motion of the wave.
2.05.01 Part 1 explained the TEW which posits the existence of real
2.05.02 fundamental particles and real fundamental elementary waves which
2.05.03 travel in the reverse direction of what has previously been
2.05.04 considered to be the case.
2.06.01 The standard theory interpretation of the Schroedinger wave
2.06.02 equation relies on probabilities which inherently possess
2.06.03 uncertainties which, in logic and according to the TEW, do not
2.06.04 exist for the real particle and the real wave. The uncertainties
2.06.05 are due to a mathematical construct and an illogical physical
2.06.06 interpretation.
2.07.01 In the TEW, the elementary waves exist as real objects. In the
2.07.02 standard theory, a particle exists as ghost-like particles,
2.07.03 giving rise to the alleged uncertainties. In the TEW, the
2.07.04 elementary waves exist as independent objects and there are no
2.07.05 uncertainties for any quantity or quality of real particles and
2.07.06 real waves.
2.08.01 The TEW refutes the Heisenberg uncertainty principle by
2.08.02 essentially exposing its false philosophical base and illogical
2.08.03 acausal premises.
2.09.01 The EPR experiment: Einstein and colleagues use a 'thought
2.09.02 experiment' to question the lack of causality in quantum
2.09.03 mechanics. EPR becomes a 'real' experiment and appears to violate
2.09.04 causality.
2.10.01 The standard theory interpretation of the experiment says that
2.10.02 even if two particles are separated by half the distance of the
2.10.03 entire universe there is a 'connectedness' between them. The
2.10.04 theory requires 'spooky action-at-a-distance' to explain
2.10.05 interactions that occur instaneously regardless of the distance
2.10.06 of separation.
2.11.01 Another theory: 'hidden variables', a kind of reality that lurks
2.11.02 behind quantum reality. To explain the EPR experiments our choice
2.11.03 seems to be between the acausal ghost-like reality of the
2.11.04 standard theory and the causal view of a 'hidden' reality that
2.11.05 cannot be seen.
2.12.01 The TEW says: again the assumed forward direction of the quantum
2.12.02 waves have misled the theorists; with that assumption causality
2.12.03 was doomed. The TEW explains the experiment with reference to
2.12.04 real particles, real waves, and the identification that the waves
2.12.05 move in the opposite direction of what has been supposed. There
2.12.06 is no 'spooky action-at-a-distance' required and strict causality
2.12.07 is restored.
PART 2
2.13.01 In the late 1970's, I attended Richard Feynman's graduate seminar
2.13.02 at Caltech which was based on his book "Quantum Mechanics and
2.13.03 Path Integrals". Feynman told me that there were only two ways
2.13.04 to unseat Heisenberg's uncertainty principle: either you defeat
2.13.05 it experimentally or you find some other way to explain the
2.13.06 results of quantum mechanics. Feynman was right - Lewis Little
2.13.07 accomplished it by the latter of the two methods via his Theory
2.13.08 of Elementary Waves (TEW).
2.14.01 Just as Schroedinger's wave equation is the mathematical
2.14.02 cornerstone of quantum mechanics, Heisenberg's uncertainty
2.14.03 principle represents the intellectual underpinnings of the
2.14.04 standard theory. But, while Schroedinger had some interest in
2.14.05 physical reality, Heisenberg was not confined to such
2.14.06 restrictions. Heisenberg once said:
2.14.07 "The very fact that the formalism of quantum mechanics
2.14.08 cannot be interpreted as visual description of a
2.14.09 phenomenon occurring in space and time shows that
2.14.10 quantum mechanics is in no way concerned with the
2.14.11 objective determination of space-time phenomena".
2.15.01 More succinctly, the standard theory says, in effect, that if
2.15.02 anything is definite in quantum mechanics, it is mathematical,
2.15.03 and if anything is physical, it is indefinite. Quantum variables
2.15.04 are measurable things pertaining to the field of quantum
2.15.05 mechanics which can change, such as position, momentum, energy,
2.15.06 and time. Heisenberg's uncertainty principle states that there
2.15.07 are fundamental limits to which the accuracy of pairs of these
2.15.08 quantum variables can be specified and measured. That is the
2.15.09 uncertainty _principle_. There are many particular uncertainty
2.15.10 _relations_. For instance, the uncertainty relation between
2.15.11 energy and time means that if you were able to localize a
2.15.12 particle at a given instant, it literally would not have any
2.15.13 definite energy. There are similar relations between other pairs
2.15.14 of quantum variables. The most well-known uncertainty relation is
2.15.15 between position and momentum, where momentum is usually
2.15.16 understood to be the product of mass times velocity. The more
2.15.17 accurately you are able to determine the location of a particle
2.15.18 the less precise you can be about its momentum. More formally
2.15.19 stated, the uncertainty in location multiplied by the uncertainty
2.15.20 in momentum can never be less than a certain quantity. That
2.15.21 quantity, which is extremely small, is known as Planck's
2.15.22 constant.
2.16.01 As an illustration of how the standard theory views these
2.16.02 uncertainties, consider the single-slit experiment shown in
2.16.03 Figure 4. In this essentialized model our source consists of
2.16.04 electrons; the single slit in the wall has a width which is
2.16.05 denoted by 'Y'. The (by now) familiar interference pattern is
2.16.06 shown as the intensity experienced at the detector. When an
2.16.07 electron goes through the slit we then know its position, at
2.16.08 least to the accuracy determined by the width 'Y'. Since the
2.16.09 electron is considered to also be a wave, when it goes through
2.16.10 the slit, the wave interference results in the pattern seen at
2.16.11 the detector. Due to the probabilistic nature of the solution to
2.16.12 the wave equation we discussed in Part 1, the intensity due to
2.16.13 that particular electron is only known within a given
2.16.14 uncertainty. If we try to make a more precise determination of
2.16.15 the position of the electron by reducing the width of the slit,
2.16.16 the pattern on the detector widens, increasing the uncertainty in
2.16.17 the determination of the intensity due to this particle at this
2.16.18 particular location. The more precisely we are able to measure
2.16.19 the _position_ of the particle, the less precisely we can
2.16.20 determine its intensity. This is a concretization of Heisenberg's
2.16.21 uncertainty principle.
Figure 4
| IIIIII|
| IIIIIII|
| IIIIII|
| IIII|
| II|
| III|
| IIIII|
| slit IIIIIII|
- - IIIIIIIII|
IIIIIIIIIII|
source- - -> Y (width) IIIIIIIIIIII| F I G U R E 4
(electrons) IIIIIIIIIII|
- - IIIIIIIII|
| IIIIIII|
| IIIII|
| III|
| II|
| IIII|
| IIIIII|
| IIIIIII|
| IIIIII|
WALL DETECTOR
2.17.01 These uncertainties are neither a consequence of our inability to
2.17.02 build more precise instruments for measurement nor a limitation
2.17.03 of the resolution of the devices that are used. The basic idea,
2.17.04 according to the standard theory, is that there are uncertainties
2.17.05 in the nature of matter that, _in principle_, cannot be overcome.
2.17.06 That is the intellectual cornerstone of modern quantum mechanics.
2.17.07 Heisenberg's uncertainty principle, with its various uncertainty
2.17.08 relations, embodies the essence of Kantianism: there are barriers
2.17.09 to our knowledge, limitations on what is measurable, and it is
2.17.10 impossible even to speculate on what cannot be measured.
2.18.01 In the TEW, Little identifies the fact that this whole view of
2.18.02 uncertainty is a consequence of, an artifact of, the anti-concept
2.18.03 of wave-particle, along with the mistaken notion of the forward
2.18.04 motion of the wave. When the particle is thought to be the wave
2.18.05 and when the wave is thought to move in a forward direction from
2.18.06 the source to the detector, the interpretation of the wave
2.18.07 function solution to the Schroedinger wave equation becomes a
2.18.08 probabilistic function that _inherently_ possesses uncertainties.
2.18.09 But these uncertainties do not exist for the _real_ particle and
2.18.10 the _real_ wave; the uncertainties are due to the mathematical
2.18.11 construct and physical interpretation underlying the standard
2.18.12 theory.
2.19.01 Recall that in the TEW, the elementary waves exist as real
2.19.02 objects and are available in a complete range of quantum states.
2.19.03 The waves travel from the detector towards the source, through
2.19.04 the slit, interfere and induce the emission of particles at the
2.19.05 source. The particle then follows the path of the waves back to
2.19.06 the detector. The intensity pattern has already been determined
2.19.07 by the dynamics of the waves prior to the particles even reaching
2.19.08 the detector. In the standard theory a particle exists in
2.19.09 multiple states, the ghost-like particles we discussed
2.19.10 previously, and gives rise to the uncertainties inherent in that
2.19.11 theory. In the TEW, it is the elementary waves that exist in
2.19.12 multiple states, but they exist as independent objects and do not
2.19.13 gain their reality by the 'collapse of the wave function'. In the
2.19.14 TEW there are no uncertainties for any quantity or quality
2.19.15 associated with the real particles and the real waves.
2.20.01 Little is careful to distinguish 'unpredictability' from
2.20.02 'uncertainty'. We may not know which particular wave leads to
2.20.03 particle emission at the source and, therefore, we may not know,
2.20.04 in advance, the particle momentum. But this fact is just a
2.20.05 consequence of our ignorance, our lack of knowledge, of not
2.20.06 knowing in advance the particular parameters which determine the
2.20.07 particle and which characterize the source. There is nothing that
2.20.08 is inherently uncertain in this process, nothing which by its
2.20.09 nature is indeterminate. The entire quantum process as described
2.20.10 by the TEW is determined by the nature of the waves and the
2.20.11 particles and by how they interact. There is nothing _in
2.20.12 principle_ that stops us from identifying the nature of the
2.20.13 parameters involved in the exact determination of particle
2.20.14 emission - it is just our current ignorance, not some inherent
2.20.15 uncertainty, of what strictly determines this level of quantum
2.20.16 processes.
2.21.01 Heisenberg published his uncertainty principle in 1927 and, along
2.21.02 with Niels Bohr, he became one of the founders of the standard
2.21.03 theory, which is sometimes referred to as the Copenhagen
2.21.04 interpretation of quantum mechanics. At that time some
2.21.05 theorists, most notably Albert Einstein, expressed concern over
2.21.06 the lack of causality in the theory. This concern of Einstein
2.21.07 engendered a debate with Niels Bohr in 1927 which, amazingly,
2.21.08 lasted until Einstein's death, almost three decades.
2.21.09 Unfortunately, very little was ever resolved. In 1935 Einstein,
2.21.10 along with Boris Podolsky and Nathan Rosen, published a paper
2.21.11 attacking the standard theory's view of physical reality. As they
2.21.12 stated in their paper, they concluded that "the description of
2.21.13 reality as given by a wave function is not complete." Although
2.21.14 their paper cannot be considered to be a fundamental or
2.21.15 devastating attack, the 'thought experiment' they offered
2.21.16 underscored a major problem with the standard theory. In honor of
2.21.17 the authors Einstein-Podolsky-Rosen, this experiment was dubbed
2.21.18 EPR and it has persisted these many decades through today.
2.22.01 There are elements in this 'thought experiment' which are
2.22.02 somewhat subtle, but EPR can generally be thought of in the
2.22.03 following way. Assume we have two particles (1 and 2) which have
2.22.04 interacted with each other and are now moving in opposite
2.22.05 directions at the same speed. If you can measure (without
2.22.06 disturbance) the position of particle 1, then you will
2.22.07 automatically know the position of particle 2, since they are
2.22.08 both moving at the same speed. According to EPR, if we can
2.22.09 predict with certainty "the value of a physical quantity, then
2.22.10 there exists an element of physical reality corresponding to this
2.22.11 physical quantity." Therefore, our knowledge of the position of
2.22.12 particle 1 itself establishes the reality of the position of
2.22.13 particle 2 without in any way making a measurement or observation
2.22.14 of particle 2. But this is contrary to the standard theory which
2.22.15 holds that the reality of particle 2 exists only when an act of
2.22.16 measurement or observation of the particle is performed. In
2.22.17 addition, since we already have an accurate measurement of the
2.22.18 position of particle 1 (which also then tells us the position of
2.22.19 particle 2) we could then accurately measure the momentum of
2.22.20 particle 2 directly. These independent measurements can be made
2.22.21 accurate to whatever precision we like. But this would be
2.22.22 contrary to the uncertainty principle which places limits on the
2.22.23 degree of our accuracy in measuring these combined quantities.
2.23.01 Bohr used his response to Einstein to further entrench his
2.23.02 wave-particle view of the quantum world; his idea of
2.23.03 'complementarity', the joining of wave and particle, was a
2.23.04 scientific pluralism applied to matter. Bohr firmly implanted his
2.23.05 view that an act of measurement, an observation, was what made a
2.23.06 particle 'real'. He identified an 'ambiguity' in the EPR idea;
2.23.07 namely that it presumed the ability to measure _without any
2.23.08 disturbance_ to the overall system. He argued that since no
2.23.09 measurement was taken of particle 2 (which act would have
2.23.10 established it's own reality) then the measurement of particle 1
2.23.11 must be responsible for the 'reality' of particle 2. The
2.23.12 presumption, therefore, is that a wave function must exist that
2.23.13 applies to particles 1 and 2, and the 'collapse of the wave
2.23.14 function' upon measuring particle 1 gives 'reality' to particle
2.23.15 2. This principle of Bohr's applies whether the particles are
2.23.16 separated by an inch or by a light-year. This is the source of
2.23.17 the famous 'spooky action-at-a-distance' (Einstein's words) idea
2.23.18 associated with the standard theory of quantum mechanics. It
2.23.19 represents the complete destruction of the idea of local
2.23.20 causality.
2.24.01 While the EPR 'thought experiment' is interesting from a
2.24.02 philosophic point of view, one might ask in what way does this
2.24.03 relate directly to science and to the TEW? The reason we have
2.24.04 spent time outlining the 'thought' experiment is that in the
2.24.05 decades since the original paper on EPR, a whole family of
2.24.06 _actual_ experiments has been devised. As with the double slit
2.24.07 experiments, the EPR experiments highlight the absurdity of the
2.24.08 standard theory and afford the TEW another opportunity to present
2.24.09 a rational explanation for observed events. In order to
2.24.10 understand the basis for these experiments, we must first
2.24.11 introduce and explain what is known as Bell's theorem, or more
2.24.12 precisely, Bell's inequality. (With apologies to the physicist
2.24.13 Heinz Pagels, who has presented a similar treatment, albeit with
2.24.14 a completely different objective in mind.)
2.25.01 Consider the essentialized model shown in Figure 5. Here we have
2.25.02 a source, similar to the ones we have used previously, except
2.25.03 that this particular source (a gun) is unique - it is a 'No. 2
2.25.04 pencil with eraser' gun. When the gun shoots, two pencils are
2.25.05 ejected simultaneously, each going in opposing directions. The
2.25.06 pencils move sideways; that is, rather than the eraser or the
2.25.07 pointed end facing forward, the length of the pencils face
2.25.08 towards the direction they move. The orientation of the pencils,
2.25.09 as they are ejected, is completely random, meaning that the
2.25.10 eraser end can be pointed anywhere within a circular direction in
2.25.11 the plane of its motion. Each successive _pair_ of pencils,
2.25.12 however, will have exactly the same orientation. Each of the
2.25.13 pencils, call them pencil A and pencil B, move in a direction
2.25.14 towards wall A and wall B respectively. Each wall has a wide
2.25.15 cutout in them allowing pencils of a certain orientation to fit
2.25.16 through. We will call these wall-cutout arrangements
2.25.17 'polarizers', since they allow pencils with a certain orientation
2.25.18 to pass through but effectively block out others. The angle of
2.25.19 these 'polarizers' can be changed during the course of our
2.25.20 experiment, but initially both have the same alignment. Behind
2.25.21 each wall are counters which keep records of the pencils that get
2.25.22 through the 'polarizers' and those that do not.
Figure 5
_ _
| | | |
_ | | | | _
| | | | | | | |
| | | | | | | |
| | | | A * B | | | |
| | --- | |---------<----- *** ----->---------| | --- | | F I G U R E 5
| | | | * | | | |
| | | | | | | |
| | | | Source | | | |
|_| | | (pencils) | | |_|
Counter A | | | | Counter B
|_| |_|
Wall A Wall B
2.26.01 With the 'polarizers' aligned in the same direction, we would
2.26.02 expect the counters to record pencil events that looked something
2.26.03 like this.
2.26.04 A 010010010001100000100100000100...
2.26.05 B 010010010001100000100100000100...
2.27.01 The counters record a '1' for each pencil going through the
2.27.02 'polarizer' and a '0' for an event where the pencil did not make
2.27.03 it through. As would be expected, the events recorded for A
2.27.04 precisely match the events recorded for B, since the pair of
2.27.05 pencils are correlated (that is, they both have the same
2.27.06 orientation) and each of the 'polarizers' have the same
2.27.07 alignment.
2.28.01 Now let us change the alignment of the 'polarizers'. We will
2.28.02 rotate 'polarizer' A clockwise through an angle (say 20 degrees)
2.28.03 relative to B. Since each of the 'polarizers' do not have the
2.28.04 same alignment anymore, some of the pairs of pencils will not be
2.28.05 recorded the same for each counter. Some pencils getting through
2.28.06 A will not get through B, and vice versa. The recorded events
2.28.07 might look like this.
2.28.08 A 000010011000001010001010100010...
2.28.09 B 010010010000001010001010000010...
2.29.01 As indicated, the counting record shows there are events that no
2.29.02 longer match up between A and B due to the different alignment of
2.29.03 the 'polarizers'. In fact, the mismatch is 1 in every 10 events,
2.29.04 a 10% mismatch rate. Had we rotated 'polarizer' B
2.29.05 counterclockwise by the same angle, instead of 'polarizer' A
2.29.06 clockwise, we would expect the results to be essentially the
2.29.07 same. By fixing one 'polarizer' and rotating the other we are
2.29.08 creating results where the mismatches between the two act in an
2.29.09 independent manner. This makes sense. Why should the outcome of
2.29.10 the counter at A have any effect on the counter at B? One of the
2.29.11 counters is always used as the standard to judge the mismatches
2.29.12 with the other counter. If we were to double the angle of
2.29.13 'polarizer' A (from 20 degrees to 40 degrees) we would reasonably
2.29.14 expect the mismatch rate to exactly double.
2.30.01 If, however, we rotate A an angle of 20 degrees clockwise and
2.30.02 then rotate B an angle of 20 degrees counterclockwise, we
2.30.03 introduce a new possibility. By rotating A we lose the standard
2.30.04 for B and by rotating B we lose the standard for A. That means
2.30.05 when we compare the two counts for A and B, we will completely
2.30.06 overlook any double mismatches that may have occurred. That is,
2.30.07 if a particular event would show up as recording a pencil to go
2.30.08 through the 'polarizers' for both A and B when the 'polarizers'
2.30.09 are perfectly aligned, it might be that they both record a
2.30.10 failure to see the pencils at both A and B when the 'polarizers'
2.30.11 are both rotated in opposite directions. Therefore what might
2.30.12 have been a 1 and a 1 at both A and B is now a 0 and a 0; i.e. a
2.30.13 double mismatch has occurred. Therefore, the best case for
2.30.14 mismatches at a double angle would be twice that of the single
2.30.15 angle. The worst case, however, would not include the double
2.30.16 mismatches which would be undetectable. Therefore, stated more
2.30.17 formally, the mismatch for a double angle is always less than or
2.30.18 equal to twice the mismatch for a single angle. Mathematically,
2.30.19 this is:
2.30.20 M(2*angle) <= 2*M(angle)
2.31.01 This is known as Bell's inequality. These are the results we
2.31.02 would expect from a system that was governed by local causality:
2.31.03 that is, influences in the state of a system are a consequence of
2.31.04 a change in the system itself or are due to energy changes
2.31.05 transmitted into the system. In other words, Bell's inequality
2.31.06 should hold without regard to, or consideration of, 'spooky
2.31.07 action-at-a-distance'.
2.32.01 With this as background we can now look at an actual EPR
2.32.02 experiment. We require pairs of photons that are to be
2.32.03 polarized; that is, similar to the orientation of the pencils,
2.32.04 there is a precise direction in space associated with each
2.32.05 photon. Figure 6 shows a typical setup which appears similar to
2.32.06 the essentialized model we used with the pencil gun. The purpose
2.32.07 of our source is to generate photon pairs, moving in opposing
2.32.08 directions, which have their polarizations correlated, i.e.,
2.32.09 photons which have the same orientation in space. The orientation
2.32.10 of each pair of photons is random, but the correlation requires
2.32.11 the particular pair to possess the exact same orientation. In
2.32.12 general, these kinds of EPR experiments use sources such as
2.32.13 calcium or positronium atoms to generate the polarized photon
2.32.14 pairs. Actual polarizers replace our wall-cutout apparatus to
2.32.15 permit passage of photons possessing the correct orientation, and
2.32.16 photomultipliers (the counters) are used to detect and record the
2.32.17 photon events. There are many more details to these types of
2.32.18 experiments, but the above reflects their essence, which is all
2.32.19 we need in order to understand what is going on.
Figure 6
_ _
| | | |
_ | | | | _
| | | | | | | |
| | | | | | | |
| | | | A * B | | | |
| | --- | |---------<----- *** ----->---------| | --- | | F I G U R E 6
| | | | * | | | |
| | | | | | | |
| | | | Source | | | |
|_| | | (photons) | | |_|
Counter A | | | | Counter B
|_| |_|
Polarizer Polarizer
A B
2.33.01 As in our 'pencil gun' experiment, we first keep both polarizers
2.33.02 aligned with each other so that the angle between them is zero.
2.33.03 The source generates pairs of photons which go off in opposing
2.33.04 directions towards each polarizer. Each pair of photons has the
2.33.05 same orientation, but the particular orientation of each pair is
2.33.06 random. If the orientation of the photon aligns to the
2.33.07 orientation of the polarizer, then the photon passes through and
2.33.08 is counted as a '1' event. If the photon does not pass through,
2.33.09 it is a '0' event. The results of such an experiment are shown
2.33.10 below and are very much like the results from the 'pencil gun'.
2.33.11 As we would expect, since each pair of photons has the same
2.33.12 orientation and the A and B polarizers are aligned the same, the
2.33.13 counts for A and B match perfectly.
2.33.14 A 001000110001001100000100001000...
2.33.15 B 001000110001001100000100001000...
2.34.01 When we rotate polarizer A a small angle, say 25 degrees, we find
2.34.02 results that are very similar to the 'pencil' experiment; that
2.34.03 is, we find a small number of mismatches between the A and B
2.34.04 count. The differences between the A and B count occur 1 in 10, a
2.34.05 10% mismatch rate.
2.34.06 A 001100110001001100000100001000...
2.34.07 B 001000110000001100000100001010...
2.35.01 When we double the angle of rotation for polarizer A to 50
2.35.02 degrees, the event counts are as indicated below.
2.35.03 A 101000110001011000010100001010...
2.35.04 B 001010110000001101000101001000...
2.36.01 The mismatches that have been counted are now 3 out of 10, a
2.36.02 mismatch rate of 30%. According to Bell's inequality, the
2.36.03 mismatch rate for twice the angle should be less then or equal to
2.36.04 twice the mismatch rate for the single angle. In other words,
2.36.05 since the single angle had a 10% mismatch rate we would expect
2.36.06 the double angle mismatch rate to be less then or equal to 20%.
2.36.07 The experiment shows, however, that the rate observed is not 20%,
2.36.08 but 30%. Bell's inequality has been violated! Recall that this
2.36.09 means, philosophically, that the idea of local causality has been
2.36.10 violated. This experiment has been performed repeatedly and the
2.36.11 results are essentially the same in all cases. This appears to be
2.36.12 a substantial confirmation of the 'weirdness' of quantum reality.
2.37.01 The standard theory is perfectly poised to explain this strange
2.37.02 phenomenon; it is, after all, just another example of the ideas
2.37.03 developed by Heisenberg and Bohr. We can speak of a
2.37.04 'connectedness' between these pairs of photons that have
2.37.05 interacted, whether their separation be measured in inches or
2.37.06 they are distanced by the size of the entire universe. We can
2.37.07 speak of how changing the alignment of polarizer A influenced the
2.37.08 polarization of the photons counted at B even if the polarizers
2.37.09 were light-years away. We can speak of the 'collapse of the wave
2.37.10 function' and the role it plays in the final result. We can
2.37.11 speak of these, and many other things, but the real essence of
2.37.12 the explanation of the standard theory lies in the _fundamental_
2.37.13 ideas of Bohr and Heisenberg - speculation about the underlying
2.37.14 reality of this experiment is nonsense. It is a fantasy to think
2.37.15 of the photons existing in a definite state. It is the
2.37.16 measurement we make of the particles that create their reality
2.37.17 and such measurements change the conditions of the experiment.
2.37.18 We really do not know that the polarizations of the pairs of
2.37.19 particles were originally correlated and the act of measurement
2.37.20 changes the very conditions upon which Bell's inequality was
2.37.21 derived.
2.38.01 Bell, like the physicist David Bohm, did not subscribe directly
2.38.02 to all these views; he thought that local causality could be
2.38.03 saved by postulating 'hidden variables', a kind of reality that
2.38.04 lurks behind quantum reality. Our choice seems to be between the
2.38.05 acausal ghost-like reality of the standard theory and the causal
2.38.06 view of a 'hidden' reality that cannot be seen. In the six
2.38.07 decades since Einstein and his colleagues published the EPR, it
2.38.08 was not until Lewis Little and the TEW that a rational
2.38.09 explanation could be given to this 'weird' EPR phenomenon.
2.39.01 Recall that in the TEW, elementary waves exist for all quantum
2.39.02 states which include all values of polarization. There are
2.39.03 elementary waves that flow from the 'counter' as well as waves
2.39.04 that flow from the polarizer itself. The polarizer is able to
2.39.05 impose a coherence, a similarity, on some of the 'counter' waves
2.39.06 with the same orientation as the polarizer. An opposite
2.39.07 orientation wave flows directly from the polarizer. These are
2.39.08 real, independent waves which arrive at the photon source and
2.39.09 independently induce emission of a photon. Each individual photon
2.39.10 will follow its reverse wave back to the source of the wave,
2.39.11 either the counter or the polarizer. The same process as
2.39.12 described, of course, occurs from each of the two opposite sides
2.39.13 (A and B) of the experiment.
2.40.01 The question that now arises is: how does the whole process
2.40.02 change when one polarizer is rotated at an angle relative to the
2.40.03 other? Assume a photon is first induced by an elementary wave
2.40.04 flowing from the detector; the photon will follow this reverse
2.40.05 wave back to the detector. But recall that the photon source is
2.40.06 such that it emits particles in pairs with the same orientation.
2.40.07 Since the polarizers are angled apart, there may not be an
2.40.08 elementary wave coming from the opposite direction that has the
2.40.09 proper orientation required for the induced emission. The waves
2.40.10 from the opposite direction may be offset in their polarization
2.40.11 by the angle that the polarizer has been rotated. Recall from our
2.40.12 discussion of the double slit experiment that it was the
2.40.13 intensity of the elementary wave, as seen at the particle source,
2.40.14 which accounted for the probability of stimulated emission of a
2.40.15 particle. That is exactly the case here, where the offset of the
2.40.16 polarizer reduces the probability of the particle emission at
2.40.17 least as far as the required polarized orientation is concerned.
2.40.18 The wave that corresponds to the opposite orientation associated
2.40.19 with the polarizer will induce emission of a photon, but the
2.40.20 photon will traverse its reverse wave back to the polarizer and
2.40.21 is never seen by the 'counter'. The dependence of the mismatches
2.40.22 on the angular rotation of the polarizer is therefore explained
2.40.23 without reliance on 'spooky action-at-a-distance' or otherwise
2.40.24 acausal behavior; the elementary waves _at the particle source_
2.40.25 determine the entire dynamic outcome of the experiment. The
2.40.26 dependence on the degree of angular rotation of the polarizer
2.40.27 turns out to be a consequence of the intensity of the elementary
2.40.28 waves experienced there, whose characteristics have already been
2.40.29 determined due to the reverse direction of the wave.
2.41.01 Of necessity, there were a number of simplifications that were
2.41.02 made in describing the above process. One area in particular, in
2.41.03 which the TEW clarifies a particle physics process, is in the
2.41.04 emission of the two correlated photons. The TEW represents the
2.41.05 cascade, the rapid succession of particles, to be all of a single
2.41.06 quantum process. This is important because it underscores that it
2.41.07 is the elementary wave interactions which determine all of the
2.41.08 dynamics prior to the emission of a single particle. This is lost
2.41.09 in the standard theory because of the anti-concept of
2.41.10 wave-particle, where the real elements of particle and wave
2.41.11 physics are disembodied.
2.42.01 It should be mentioned that there is a whole class of EPR
2.42.02 experiments which change the structure of the experiment while
2.42.03 the photons are in flight. For instance, the rotated polarizer
2.42.04 may be brought back into alignment after the photon particles
2.42.05 have been emitted. There is, in fact, one experiment, referred to
2.42.06 as a double delayed choice (both polarizers independently rotated
2.42.07 after particle emission), where the results, under certain
2.42.08 circumstances, are predicted by Little to validate the TEW while
2.42.09 contradicting the expectations of the current theory. It is
2.42.10 beyond the scope of this article to detail the process involved.
2.42.11 Suffice it to say that there is nothing fundamentally different
2.42.12 required for the TEW to make sense of such experiments. I just
2.42.13 want to note here that the TEW does not require a particle to
2.42.14 always follow a single reverse wave back to its source in all
2.42.15 instances. Such a rigid requirement could not and would not
2.42.16 account for any dynamic system changes that might occur, which is
2.42.17 the case for most conditions outside of the laboratory
2.42.18 environment. The TEW details the physics of the 'jump'
2.42.19 conditions which permit a particle to follow more than just one
2.42.20 wave. This 'jump' also helps explain the scattering of particles
2.42.21 where their direction changes at a point of interaction. The
2.42.22 actual 'jump' of a photon requires the annihilation of the
2.42.23 original along with the creation of a new particle, which in turn
2.42.24 is dependent on the organization of the wave which produced the
2.42.25 scattering in the first place.
2.43.01 In summary, we have seen in Part 2 how the TEW refutes the
2.43.02 Heisenberg uncertainty principle by essentially exposing the
2.43.03 false intellectual base upon which it rests. Bell's inequality
2.43.04 and a whole class of EPR experiments were explained without
2.43.05 consideration of the philosophically illogical acausal premises.
2.43.06 As in Part 1 with the explanation of the double slit experiment,
2.43.07 a rational analysis is made possible primarily by positing the
2.43.08 existence of real fundamental particles and real fundamental
2.43.09 elementary waves which travel in the reverse direction of what
2.43.10 has previously been considered to be the case.
2.44.01 In Part 3 of this article we will focus on relativity and how it
2.44.02 relates to the TEW. We will also briefly mention some of the
2.44.03 philosophic and scientific concerns about the TEW theory.
sjs@compbio.caltech.edu
(© 1998) Stephen Speicher
THE THEORY OF ELEMENTARY WAVES - PART 3
INTRODUCTION
3.00.01 This is the third part of a three-part article focusing on Lewis
3.00.02 Little's revolutionary THEORY OF ELEMENTARY WAVES. It is prefaced
3.00.03 by a short digest, an "Executive Summary", highlighting key
3.00.04 elements of the article in order to establish a preliminary
3.00.05 context, but omitting technical details and substantive
3.00.06 information.
"Executive Summary" - Part 3
3.01.01 Recall from our previous discussions that in the TEW space is
3.01.02 filled with elementary waves, the fundamental constituents of
3.01.03 reality. When a detector is placed in position, it imposes an
3.01.04 'organization' or coherence upon the elementary waves flowing in
3.01.05 its vicinity. The organization of the waves uniquely reflects the
3.01.06 state of the particle from the detector which imposed the
3.01.07 organization; the state of this particle includes the reference
3.01.08 frame of the detector.
3.02.01 Where, then, is the divergence between the standard theory and
3.02.02 the TEW and what are the consequences of it?
3.03.01 Two areas of quantum mechanics that have been popularized are
3.03.02 quantum computing and quantum teleportation.
3.04.01 In quantum computing, a quantum bit (qubit) replaces the familiar
3.04.02 binary bits of computers. A qubit represents a quantum state
3.04.03 (i.e., either on or off), but it is thought of in the standard
3.04.04 theory as existing in _both_ states simultaneously, a condition
3.04.05 which supposedly permits parallel operation of both states at the
3.04.06 same time.
3.05.01 In quantum teleportation, transmission and reconstruction of
3.05.02 quantum states occur over arbitrary distances. Recent experiments
3.05.03 claim to have achieved this.
3.06.01 The standard theory holds that many possible states exist at the
3.06.02 same time (superposition) in a single particle as well as in a
3.06.03 pair of particles, until 'collapse' makes them real. The standard
3.06.04 theory holds that two particles can become "entangled" so that
3.06.05 when collapse occurs for one particle it simultaneously occurs
3.06.06 for the other particle, with no concern for the distance
3.06.07 separating them, distance being irrelevant to this occurrence.
3.07.01 In the standard theory, quantum computing "entanglements" and
3.07.02 quantum teleportation "entanglements" both rely on standard
3.07.03 theory concepts in the same manner as does the Schroedinger cat
3.07.04 paradox which asserts that an animal can be both alive and dead
3.07.05 at the same time.
3.08.01 The TEW rejects the postulate of 'entanglement' holding (a) this
3.08.02 erroneous view is a consequence of the notion of a _forward_
3.08.03 moving wave and (b) the idea of entanglement arises in the
3.08.04 standard theory because it misidentifies the fundamental nature
3.08.05 of quantum reality.
3.09.01 Einstein's Special Theory of Relativity (STR) postulates that the
3.09.02 speed of light in a particular medium is constant - that the
3.09.03 speed is the same in any observer's frame of reference,
3.09.04 regardless of the observer's own speed. The objective nature of
3.09.05 reality has no absolute meaning in the STR. In the STR, the
3.09.06 contraction of objects and the retardation of time occur as
3.09.07 objects approach the speed of light. Mathematical laws remain
3.09.08 objective in the STR, but reality becomes relative to the
3.09.09 observations made of it and the objective nature of the objects
3.09.10 changes.
3.10.01 In contrast, the TEW establishes a _physical_ basis for the
3.10.02 constancy of the speed of light and, as a consequence, the
3.10.03 objective nature of objects does not change. The elementary wave
3.10.04 from the observer (the detector) determines all the dynamics of
3.10.05 the photons from the object, the source. It is only the _means
3.10.06 of observation_ that changes among reference frames, not the
3.10.07 objective nature of the objects themselves. The key element is:
3.10.08 it is not the same light that is being seen by different
3.10.09 observers!
3.11.01 Regarding Einstein's General Theory of Relativity (GTR),
3.11.02 fundamentally it is a geometric theory of gravitation. According
3.11.03 to Einstein, gravitation is a consequence of the curvature of
3.11.04 space-time -- "space-time" being thought of as an entity.
3.12.01 The TEW rescues the GTR, holding (a) that space is not distorted;
3.12.02 (b) that it is the elementary waves which become curved due to
3.12.03 wave interactions; and (c) that the photons from the light source
3.12.04 follow the curved path of the reverse waves. What is real stays
3.12.05 real in the TEW and, at the same time, the Theory of Elementary
3.12.06 Waves is consistent with the mathematics of the GTR and the
3.12.07 curvature of light which the GTR predicted.
PART 3
3.13.01 Two areas of quantum mechanics have received a lot of attention
3.13.02 in the past several years, both in scientific journals and in the
3.13.03 popular press - quantum computing and quantum teleportation. The
3.13.04 miniaturization of electronic components continues at an
3.13.05 astonishing rate and it will eventually collide with a physical
3.13.06 limit as reductions in size approach the atomic scale. Intending
3.13.07 to avoid this limitation, quantum computing proposes replacing
3.13.08 the familiar binary bits of computers (where each bit represents
3.13.09 an on-off condition, a 0 or 1) with a quantum bit, a qubit.
3.14.01 A qubit would be represented by a quantum state which, according
3.14.02 to the standard theory, can exist not just as a 0 or 1, but
3.14.03 simultaneously as a superposition of both states. Unlike a
3.14.04 classic computer where increasing the quantity of bits results in
3.14.05 a simple increase in storage ability, a quantum computer, it is
3.14.06 claimed, would increase its capacity exponentially as the number
3.14.07 of qubits increase. Not only that, but since the various states
3.14.08 allegedly exist simultaneously, quantum computations can be
3.14.09 performed in parallel with all of the superpositioned states,
3.14.10 rather than the single individual operations required for classic
3.14.11 computers.
3.15.01 Closely allied to quantum computing is the idea of quantum
3.15.02 teleportation - the transmission and reconstruction of quantum
3.15.03 states over arbitrary distances. Quantum teleportation evokes
3.15.04 thoughts of science fiction travel (like Star Trek), yet several
3.15.05 recent experiments claim to have achieved the transfer of the
3.15.06 polarization property between photons by this means. What
3.15.07 connects quantum computing and quantum teleportation in the
3.15.08 standard theory interpretations (and what makes them of interest
3.15.09 in regard to the TEW) are some principles which we have already
3.15.10 discussed in parts 1 and 2 of this article, but which we can now
3.15.11 integrate under the broadly ascribed name - entanglements.
3.16.01 Entanglement is often invoked as a mechanism uniting the quantum
3.16.02 states of two or more particles (its usage also applies to the
3.16.03 superposition of the states of a single particle). Via a
3.16.04 mathematical analysis, Schroedinger noted that part of a quantum
3.16.05 formula (known as a state vector) could not be separated into its
3.16.06 constituent parts without invoking some sort of indeterministic
3.16.07 collapse - it was 'entangled' with its constituent parts.
3.17.01 In 1935, the same year as the publication of the Einstein EPR
3.17.02 paper (which we discussed in Part 2), Schroedinger made public
3.17.03 his now famous cat paradox. In essence, Schroedinger thought of a
3.17.04 steel chamber that contained a cat, a radioactive source, a
3.17.05 particle detector, and a poison gas bottle. The radioactive decay
3.17.06 of the substance obeys the same probabilistic laws of quantum
3.17.07 mechanics such that, given its known half-life, there is a
3.17.08 fifty-fifty chance of decay in a specified time. If the detector
3.17.09 senses a particle from the decay process, it breaks the poison
3.17.10 gas bottle and the cat dies. If no particle is detected, the cat
3.17.11 survives. According to the standard theory, the cat, just as in
3.17.12 the state vector of the mathematical formula, is neither dead nor
3.17.13 alive; instead, it exists in some superposition of both states -
3.17.14 an entangled state.
3.18.01 Previously, we briefly alluded to this indeterminate state of
3.18.02 existence when we discussed the double slit and the EPR
3.18.03 experiments. In the double slit experiment, in one instance,
3.18.04 according to the standard theory, the particle did not go through
3.18.05 either slit 1 or slit 2. Instead, the particle existed as a
3.18.06 superposition of both choices simultaneously until the 'collapse
3.18.07 of the wave function' gave actual reality to the particle.
3.18.08 Likewise, the entangled state of the cat, both alive and dead, is
3.18.09 said to exist until the 'collapse' of the entanglement is caused
3.18.10 by looking into the box to observe the outcome, which does not
3.18.11 occur until the instant of observation.
3.19.01 Similarly, quantum teleportation relies upon a relationship
3.19.02 between two particles (their postulated 'entangled' state) where
3.19.03 the alleged collapse of the superposition of quantum states of
3.19.04 one particle results in a similar (and simultaneous) collapse
3.19.05 in the other particle, independent of the distance between them.
3.20.01 The TEW rejects the postulate of 'entanglement' holding (a) this
3.20.02 erroneous view is a consequence of the notion of a _forward_
3.20.03 moving wave and (b) the idea of entanglement arises in the
3.20.04 standard theory because it misidentifies the fundamental nature
3.20.05 of quantum reality. The mathematics in the standard theory are
3.20.06 consistent with the combination of entangled waves and collapse
3.20.07 of the wave function, but the consequences are the bizarre and
3.20.08 false notions of the indeterminate state of matter and 'spooky
3.20.09 action-at-a-distance', as Einstein aptly put it.
3.21.01 In the TEW, it is the _reverse_ motion of the wave, from the
3.21.02 detector to the source, that accounts for a deterministic view of
3.21.03 quantum mechanics. It is embedded entanglement which is at the
3.21.04 root of the issues of quantum computing and quantum teleportation
3.21.05 and which accounts for their mystical experimental
3.21.06 interpretations and fallacious conclusions. Without detailing an
3.21.07 analysis of the experiments themselves, suffice it to say that
3.21.08 the claims of teleportation are a consequence of the erroneous
3.21.09 notion of entanglement, an ineffectual attempt by the standard
3.21.10 theory to explain observed phenomena.
3.22.01 Quantum computing, on the other hand, does offer a valid
3.22.02 potential, not as a consequence of entangled states, but as a
3.22.03 sub-miniaturization of computing functions. However, the notion
3.22.04 of the qubits existing as a superposition of both states (0 and
3.22.05 1) and the parallel operation of such states, comprise a fantasy
3.22.06 that has no more reality than the alive-dead state of
3.22.07 Schroedinger's cat.
3.23.01 Perhaps one of the most remarkable effects of the TEW is, as Dr.
3.23.02 Little says, that it is "automatically relativistic", meaning
3.23.03 that other physical theories must modify their basic assumptions,
3.23.04 their basic formulations, in order to account for situations
3.23.05 dealing with speeds that approach the speed of light.
3.24.01 Consider the following: The speed of light, referred to as "c",
3.24.02 is its velocity in 'empty space' (when light travels through a
3.24.03 material medium, such as water or glass, its speed is less than
3.24.04 c). When we think about motion, we observe how velocities obey a
3.24.05 simple additive law. That is, if we are traveling on a train
3.24.06 heading east at 60 mph, and if we walk on the train in the
3.24.07 direction of travel at 2 mph, our speed (relative to the fixed
3.24.08 ground) would be 60 + 2 for a total of 62 mph. If, on the other
3.24.09 hand, we walk on the train in a direction opposite to its motion
3.24.10 (west) our speed would be 60 - 2 for a net of 58 mph. Similarly,
3.24.11 if the motion we consider is the rotation of the Earth, the
3.24.12 surface of which is moving east at some rate, say x mph, we
3.24.13 would expect a light coming from the east to reach us more
3.24.14 quickly than if it were coming from the west, because the motion
3.24.15 of the surface of the Earth toward the east decreases the
3.24.16 distance the light travels coming from the east and increases the
3.24.17 distance it travels when it is coming from the west. The light
3.24.18 from the east would be expected to arrive at a speed of c+x mph
3.24.19 and the light from the west at a speed of c-x mph. But, did
3.24.20 experiment verify this?
3.25.01 The famous Michelson-Morley experiment was designed to measure
3.25.02 these differences in speed as the Earth traveled through the
3.25.03 'ether wind', the posited medium of 'empty space' through which
3.25.04 light propagated. Rather than relying on difficult-to-do
3.25.05 measurements of distances and times, Michelson invented the
3.25.06 interferometer, a device which relied on interference patterns
3.25.07 similar to those we have seen in the double slit experiments. The
3.25.08 device split a beam of light in two with one beam traveling back
3.25.09 and forth along the line of the Earth's motion and the other beam
3.25.10 perpendicular to the first. The two beams combined to produce
3.25.11 interference patterns. When the entire experimental apparatus was
3.25.12 rotated, it was expected to produce different interference
3.25.13 patterns, representing the difference in speeds of the light beam
3.25.14 which traveled back and forth, and thereby demonstrate the
3.25.15 movement of the Earth through the ether. Upon executing the
3.25.16 experiment, no difference in light speeds was found.
3.26.01 It was this null result of the Michelson-Morley experiment which
3.26.02 Einstein credited, in a speech given in 1922, as "the first path
3.26.03 which led me to the special theory of relativity". Einstein was
3.26.04 aware that H. A. Lorentz had developed his contraction formula
3.26.05 which specified a supposed amount of contraction which a moving
3.26.06 object undergoes in the direction of its motion. This contraction
3.26.07 was believed at the time to be a consequence of changes in the
3.26.08 electric forces affecting the size, t |