This page on Werner Heisenberg is in three parts (links go to headings lower on page);
1. The Heisenberg Uncertainty Principle
3. A discussion of some important quotes from his book on the Philosophy of Physics
The aim is to show that Heisenberg's conclusions were not correct simply because he (nor any other physicist) realised that Dirac worked out physical reality (mathematically) in 1928 when he factorized Schrodinger's relativistic wave equation for matter into plane wave solutions. We now know that all of modern physics can be deduced from this foundation, where the three dimensional space we all experience exists and has complex (transverse) plane waves flowing through it in all directions. There are four unique phase solutions for these intersecting plane waves where all the complex components cancel and you are left with scalar (longitudinal) spherical standing waves, two pairs with opposite phase that exactly match the properties of the two spin states of the electron and positron (antimatter is just the opposite phase standing wave to matter, thus why they annihilate). You can read more on this on the home page.
Heisenberg's uncertainty principle states that we cannot know both the
position and momentum of a particle. If we know the momentum then we do
not know the position, and visa versa, if we know the position then we do
not know the momentum. This discovery has had profound consequences for
the evolution of physics as it supported the emerging postmodern philosophical
view that all knowledge was uncertain (which is not correct).
Werner Heisenberg discovered his famous Heisenberg Uncertainty Principle in March 1926, working with his matrix mechanics (1925). This was at the same time that Schrodinger independently discovered his wave equations. In May 1926 Schrodinger showed that his wave mechanics was mathematically equivalent to Heisenberg's matrix mechanics. And as history shows, Schrodinger's wave equations proved to be most useful and now dominate the foundations of quantum physics.
The importance of this is that Schrodinger was convinced the waves were real and detested Born's probability wave interpretation which also became universally accepted because it is mathematically true (the problem of physics being dominated by mathematicians who are generally poor philosophers / metaphysicists.)
For the deduction of the uncertainty principle from wave foundations please see the Heisenberg Uncertainty Principle page.
NOTE - I am working on this essay today (12/3/2012) - will be online later!!
If the word "reality" means nothing other than the totality of the connections that pervade and carry our life, then it is probably true that there must exist very different areas or layers of reality.
we simply wish to comprehend the whole world as a single, coherent nexus
of related phenomena.
However, it was in this very question that the scientific exploration of nature during the last decades compelled a change of perception. For us the predictable course of natural phenomena in space and time is no longer the firm skeleton of the world but only one nexus among others that becomes separated from the web of relations that we call the world by the way we examine it, by the questions we pose to nature. This view resulted from the insight into the laws of nature, gained with the advances of natural science, according to which phenomena can no longer be reduced to processes in space and time.
Thus, finally, we must persist until we gain an understanding of reality that comprehends the diverse coherent relationships as part of a single meaningfully ordered world.Of course, it is not only as a result of recent scientific developments that reality came to be described as a web of diverse relations.
However, it was in this very question that the scientific exploration of nature during the last decades compelled a change of perception. For us the predictable course of natural phenomena in space and time is no longer the firm skeleton of the world but only one nexus among others that becomes separated from the web of relations that we call the world by the way we examine it, by the questions we pose to nature. This view resulted from the insight into the laws of nature, gained with the advances of natural science, according to which phenomena can no longer be reduced to processes in space and time.
That imposes anew the task of ordering, understanding and determining the diverse connections or "areas of reality" in their mutual relations. They need to be related anew to the separation of the world into an "objective" and a "subjective" reality. The boundaries of those areas have to be determined and it must be discovered how the one conditions the other. Thus, finally, we must persist until we gain an understanding of reality that comprehends the diverse coherent relationships as part of a single meaningfully ordered world.
Of course, it is not only as a result of recent scientific developments that reality came to be described as a web of diverse relations. On the contrary, what we have here is the renewed consideration of ancient, often explored chains of ideas. The justification to repeat what had been said often before is based only in the fact that the development of natural science in the past decades has thrown a unique new light on this view.
Perhaps this development justifies the hope that it must be possible to determine more accurately than before the mutual relations of the diverse areas of reality. It is likely that much of the confusion in the thinking about reality results from the fact that every single thing participates simultaneously in diverse webs of connection, just as every word relates simultaneously to diverse contexts. We need proof that a clear separation is at all possible, given these circumstances. Only an example that can demonstrate with mathematical clarity the mutual relations of two areas of reality will convince the reader that it is possible to order the various layers of reality clearly and to depict their boundaries.
A complete and exact depiction of reality can never be achieved.
Generally speaking, every attempt to speak about reality will have both "static" and "dynamic" features at one and the same time. Clear, purely static thinking is in danger of deteriorating into form without content. Dynamic thinking can become vague and incomprehensible.Here, a sentence can, generally speaking, not be "right" or "wrong". But one may call a sentence "true" when it fruitfully leads to an abundance of other ideas. The opposite of a "right" sentence is a "false" one. But the opposite of a "true" sentence will often be another "true" one. The most famous systematic formulation of this "dynamic" representation of reality is Hegel's dialectics.
A complete and exact depiction of reality can never be achieved.
Every domain of reality can finally be depicted in language. The abyss that separates different domains cannot be bridged by logical reasoning or coherent linear development of language.
The ability of human beings to understand is without limit. About the ultimate things we cannot speak.The Pythagoreans' studies of the rational relations of harmonic vibrations of musical strings, Plato's ideas about symmetrical bodies, testify to the significance assigned to the mathematical form in the understanding of nature. Exact natural science since Newton is based on the silent presupposition that it must always be possible to order the areas of nature accessible to our experience according to strict laws that can be expressed mathematically. Even if one carefully analyzes other representations of reality as well, such as music or the creative arts, which are far removed from the natural sciences, they will reveal internal orders that are very closely related to mathematical laws. Those orders can be as clearly discerned as in a Bach fugue, for example, or in a symmetrical ribbon ornament; they might be noticed initially through a unique balanced quality, through the immediately evident beauty of a melody line such as that of the famous sub-theme in the first movement of Beethoven's D major violin concerto. Closer examination always shows simple mathematical symmetries comparable to those mathematics deals with in group theory. Thus, mathematics is order par excellence, in its purest form, freed from all content.The Pythagoreans' studies of the rational relations of harmonic vibrations of musical strings, Plato's ideas about symmetrical bodies, testify to the significance assigned to the mathematical form in the understanding of nature. Exact natural science since Newton is based on the silent presupposition that it must always be possible to order the areas of nature accessible to our experience according to strict laws that can be expressed mathematically. Even if one carefully analyzes other representations of reality as well, such as music or the creative arts, which are far removed from the natural sciences, they will reveal internal orders that are very closely related to mathematical laws. Those orders can be as clearly discerned as in a Bach fugue, for example, or in a symmetrical ribbon ornament; they might be noticed initially through a unique balanced quality, through the immediately evident beauty of a melody line such as that of the famous sub-theme in the first movement of Beethoven's D major violin concerto. Closer examination always shows simple mathematical symmetries comparable to those mathematics deals with in group theory. Thus, mathematics is order par excellence, in its purest form, freed from all content.The core domain from which we create reality ourselves constitutes for scientific language the infinitely remote singularity that even though it is indeed decisive for order in the finite sphere it can never be reached. Conversely, the language of faith cannot do justice to the domain of reality that is objectifiable and detached from us. For the words of that language have obtained their meaning precisely through their relation to us.
Religion alone can speak of the meaning of life. For "meaning" signifies that it is we who are addressed here, - this is the point to which science cannot advance. That is why in science's language about the meaning of life one can only say with Bohr: "The meaning of life consists in that it is meaningless to assert that life has no meaning". Science offers so little comfort for that reason. But exactly that insight offers enough comfort to the wise person who has come to know that all ideas through which we seek to fathom life's meaning circle back to the point where they started.
The concepts "objective" and "subjective" designate two poles from which an order of reality can take its beginning. They also describe two sides of reality itself. Still, it would be a crude oversimplification to divide the world into an objective and a subjective reality. This merely black and white representation created much inflexibility in philosophy of the last few centuries. The evaluation of these two sides of reality also differed a great deal at different times. At times, one side would have only been regarded almost as a deceptive appearance. To our age it seems more natural not to raise the issue of evaluation at all here and, instead, to strive for a more refined and clearer classification of reality. Since that classification is to be scientific, it will proceed step by step from the objective to the subjective. The description and delimitation of the individual domains of reality is carried out with the greatest of care, as is appropriate to the natural science as it has developed over many centuries.
"All effects we become aware of through experience, in whatever form they are, are connected in the most coherent fashion; they flow one into the other and undulate from the first to the last like waves. That people separate them from and contrast them with one another and mix them together is unavoidable. But this had to give rise to an endless conflict in science. Rigid, divisive pedantry and blurry mysticism both bring about the same disastrous results. But those activities, from the most basic to the noblest, from that of the brick falling off the roof to the radiant insight of the spirit that dawns on you or that you share with others: they are linked together." (Goethe)
From the point of view of recent natural science, it is not possible in general to dissociate the concept of substance from that of the rules of nature. If one follows the development of the concept of matter in modern physics, matter, just like force, finally appears to be a kind of structure of space. That structure is subject to the laws of nature and, as a result of certain features of "invariance" in those laws, the word "matter" may be used in the description of processes. However, it is not matter but the law that remains constant as phenomena evolve.
Only when this step has been taken and it has been recognized that there is no "substance" that follows specific laws, but only complexes of connections which we can experience and that when we describe them we also occasionally use words like substance or matter - only then we may correctly understand the sentence that the sought-for classification is one that orders reality according to those connections.
By "domain of reality" - if the word domain is used in the special sense of classification - we mean a totality of complexes of configurations governed by laws. On the one hand, such a totality must present a solid unity, otherwise one could not justifiably speak of a "domain". On the other, that totality must be capable of being exactly delimited from totalities so that a classification of reality actually becomes possible. This raises the question how a totality of laws can become complete in itself and exactly delimited from laws of a different kind.
But, in the end, we must always bear in mind that the reality of which we can speak is never reality "per se" but a perceived reality even, in many cases, one we ourselves have shaped. It may be objected that this last statement concedes that there still is, after all, an objective world wholly independent of us and of our thinking, a world that runs or can run without our help, which we really envisage in our research. One must reply to this at first so plausible objection that the phrase "there is" itself already derives from human language, for which reason it cannot properly signify something that would not be related to our ability to comprehend. For us, "there is" simply only the world in which the phrase "there is" has meaning.
2. (Classical) Physics
a) Newton's Mechanics
Mechanics presupposes further that every body (or its individual parts) is assigned a specific position. Space and time are seen as two firm, mutually independent patterns of order into which the world's processes can be arranged. Newtonian theory renounces from the outset the idea, already proposed in the days of Greek philosophy, that space and matter might be connected with each other. For example, in this sense, one might see space as upheld by matter's structure, or hold that matter is to be considered as a structure of space. Newtonian theory was instead content to objectify space and time in the form we know simply because experience teaches us that such an objectification is possible in a wide range of experiences.
b) Electricity and Magnetism
In the theory of electricity, force is objectified and fixed in space and time by the concept of the "force field" in a manner similar to the way matter is objectified and fixed in mechanics. Force appears not only as an effect of one body on another, but is itself a process in space and time that can detach itself completely from all matter.
This development from mechanics to the theory of electricity met initially with resistance from many natural scientists because the idea of an autonomous force field apparently leads to the dissolution of the primitive concept of substance in Newtonian physics. Thus, there was no lack of experiments to reinstate the original concept of substance by introducing a hypothetical ether which was to be perceived as a carrier of the electromagnetic fields that appeared to be autonomous in space. But a substance that cannot be localized in space, that we can neither feel, weigh nor see, like ether, deserves this name even less than the electromagnetic force field. As a result, researchers had to decide to drop the primitive concept of matter. After all, the language we use to speak about nature is created in the interplay between action and experience and is not dependent on our often historically conditioned desires.
The discovery of matter-waves by de Broglie may serve as an example; they may be understood as objective wave processes in space-time if one ignores the corpuscular nature of matter. If one does not ignore the existence of elemental particles, then the patterns of the laws relevant here cease to be part of the domain of classical physics but belong to what falls under the comprehensive concept of quantum theory. This example demonstrates that it is not things but the complexes of connections that can be ordered according to different domains.
c) The Infinite
Einstein was the first person courageous enough to articulate the dependence
of space and time and he articulated it in mathematical terms. Later experiments
confirmed over and over again the conclusions of this new view of the space-time
structure with greatest precision so that its accuracy can hardly be doubted
any more.
For the experiences of astronomers suggest that the world's space is finite.
This is not meant, of course, to be true in the simple sense of that earlier
view of the world; - we will not arrive eventually at a boundary somewhere
far away from our earth but, as with travels on our globe, as we proceed
in a straight line into ever greater distances, we should eventually return
to our starting point. The road traveled that way is said to be finite and
can provide a basis for determining the size of the universe. From what
we know thus far, one can conclude that it may be a journey of several billion
light years. Other observations in astronomy lead to the conclusion that
the condition of the universe some five billion years ago must have been
very different from now; the world's matter then was apparently compressed
in a much narrower space under extremely high temperatures. Only much later
did stars and stellar constellations come into existence. This perception
has occasionally been expressed as follows: The universe has only existed
for five billion years.
Since this development occurred, the words "matter", "force", "structure of space and time" seem to represent only different sides of the same event.
Behind the world describable in statistical concepts would presumably lie
an objective reality, namely the position and motion of atoms. Mechanical
concepts would, therefore, have pre-eminence over properties since they
were thought to describe the actual events of the real world.
But that supposition has proven to be incorrect in light of what has been discovered over the past decades about the connections between chemical properties and atomic motion. Before addressing those discoveries, we must stress, by the way, how unsatisfying it would be to think that amidst the great wealth of human language the concepts of mechanics alone would be appropriate to describe the "actual" behavior of the world.
b) The Laws of Chemistry
The following quotes from Heisenberg are based upon the particle-wave duality
interpretation of quantum physics - where the waves are treated as 'probability
waves' for finding the 'particle'. While this is mathematically correct,
the reason for it is because matter 'particles' are really wave structures
(spherical standing waves) where the 'particle' is formed at the wave center.
Thus it turns out Einstein was correct, the uncertainty comes from the fact
that matter is a spatially extended structure of space, connected to all
other matter in the universe, and it is this lack of knowledge of a connected
system that causes the uncertainty.
I have added comments to the quotes (below) to explain the errors.
Both matter and radiation possess a remarkable duality of character, as they sometimes exhibit the properties of waves, at other times those of particles. Now it is obvious that a thing cannot be a form of wave motion and composed of particles at the same time - the two concepts are too different. (Werner Heisenberg, on Quantum Theory, 1930)
The
solution of the difficulty is that the two mental pictures which experiment
lead us to form - the one of the particles, the other of the waves - are
both incomplete and have only the validity of analogies which are accurate
only in limiting cases. (Werner Heisenberg, on Quantum
Theory, 1930)
This is not correct, the particle properties of light and matter are perfectly explained with a pure Wave Structure of Matter. The wave center of the spherical standing wave forms the particle, and the discrete (particle) properties of light are due to discrete resonant wave interactions.
Light and matter are both single entities, and the apparent
duality arises in the limitations of our language.
It is not surprising that our language should be incapable of describing
the processes occurring within the atoms, for, as has been remarked, it
was invented to describe the experiences of daily life, and these consist
only of processes involving exceedingly large numbers of atoms. Furthermore,
it is very difficult to modify our language so that it will be able to describe
these atomic processes, for words can only describe things of which we can
form mental pictures, and this ability, too, is a result of daily experience.
Fortunately, mathematics is not subject to this limitation, and it has been
possible to invent a mathematical scheme - the quantum theory - which seems
entirely adequate for the treatment of atomic processes; for visualization,
however, we must content ourselves with two incomplete analogies - the wave
picture and the corpuscular picture. (Quantum Theory, Werner Heisenberg,
1930)
We can picture the spherical standing wave structure of matter quite easily in fact. See the wave diagrams page. And because reality is based upon wave motions of space we find wave phenomena all around us, thus explaining why our minds have evolved the ability to understand this.
This
application of the concept of statistical laws was finally formulated in
the second half of the last century as the so-called statistical mechanics.
In this theory, which is based on Newton's mechanics, the consequences that
spring from an incomplete knowledge of a complicated mechanical system are
investigated. Thus in principle it is not a renunciation of determinism.
The incomplete knowledge of a system must be an essential part of every
formulation in quantum theory. Quantum theoretical laws must be of a statistical
kind. .. This state of affairs is best described by saying that all particles
are basically nothing but different stationary states of one and the same
stuff. Thus even the three basic building-stones have become reduced to
a single one. There is only one kind of matter but it can exist in different
discrete stationary conditions. (Atomic Physics and Causal Law, from The
Physicist’s Conception of Nature, Werner Heisenberg, 1958)
Every
word or concept, clear as it may seem to be, has only a limited range of
applicability. (Heisenberg, Physics and Philosophy, 1963)
The problems of language here are really serious. We wish to speak in some way about the structure of the atoms… But we cannot speak about atoms in ordinary language. (Heisenberg, Physics and Philosophy, 1963)
The most difficult problem… concerning the use of the language arises in quantum theory. Here we have at first no simple guide for correlating the mathematical symbols with concepts of ordinary language: and the only thing we know from the start is the fact that our common concepts cannot be applied o the structure of the atoms. (Heisenberg, Physics and Philosophy, 1963)
The violent reaction on the recent development of modern physics can only be understood when one realizes that here the foundations of physics have started moving; and that this motion has caused the feeling that the ground would be cut from science. (Heisenberg, Physics and Philosophy, 1963)
Correct. But they started with a particle conception of matter and then found that both Einstein's relativity and quantum physics contradicted this. The error was to move to a particle / probability wave duality, rather than to a Wave Structure of Matter (WSM) that deduces the particle properties of light and matter (as Schrodinger realised).
Natural science, does not simply describe and explain nature; it is part of the interplay between nature and ourselves. (Heisenberg, Physics and Philosophy, 1963)
What we observe is not nature itself, but nature exposed to our method of questioning. (Heisenberg, Physics and Philosophy, 1963)
I
remember discussions with Bohr which went through many hours till very late
at night an ended almost in despair; and when at the end of the discussion
I went alone for a walk in the neighbouring park I repeated to myself again
and again the question: Can nature possibly be so absurd as it seemed to
us in these atomic experiments? (Heisenberg, Physics and
Philosophy, 1963)
The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole. (Heisenberg, Physics and Philosophy, 1963)
Matter, as a spherical wave structure of space, is interconnected with all other matter in the observable universe. We humans along with all other matter are wave structures of the universe - and it is this spatially extended structure of matter that both enables us to see and interact with the things around us, and gives rise to the statistical aspects of quantum physics due to lack of knowledge of the ensemble. This confirms Einstein's explanation of the statistical foundations of quantum theory, though Einstein made the mistake of working from continuous fields in space-time rather than real waves in space, as continuous fields do not explain discrete quantum phenomena.
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