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.
Interpretation
Heisenberg explains that our understanding of quantum mechanics is limited and that both particle and wave models are mere approximations.
In this quote, Werner Heisenberg emphasizes the limitations inherent in our scientific models of quantum mechanics. He suggests that the dual representations of quantum entities as either particles or waves are not fully accurate; instead, they serve as useful analogies that break down under certain conditions. This statement reflects the complexity of understanding the fundamental nature of reality and the challenges faced by physicists in grappling with the nuances of quantum theory.
In practice
In a science lecture discussing the intricacies of quantum mechanics.
Although the theory of relativity makes the greatest of demands on the ability for abstract thought, still it fulfills the traditional requirements of science insofar as it permits a division of the world into subject and object (observer and observed) and, hence, a clear formulation of the law of causality.
It was about three o'clock at night when the final result of the calculation [which gave birth to quantum mechanics] lay before me ... At first I was deeply shaken ... I was so excited that I could not think of sleep. So I left the house ... and awaited the sunrise on top of a rock.
It is generally believed that our science is empirical and that we draw our concepts and our mathematical constructs from the empirical data. If this were the whole truth, we should, when entering into a new field, introduce only such quantities as can directly be observed, and formulate natural laws only by means of these quantities.
When I meet God, I am going to ask him two questions: Why relativity ? And why turbulence ? I really believe he will have an answer for the first.
The end of the First World War had thrown Germany's youth into great turmoil. The reins of power had fallen from the hands of a deeply disillusioned older generation, and the younger ones drew together in larger and smaller groups to blaze new paths or, at least, to discover a new star to steer by.
The Same organizing forces that have shaped nature in all her forms are also responsible for the structure of our minds.
Brain studies of mental workouts in which you sustain a single, chosen focus show that the more you detach from what's distracting you and refocus on what you should be paying attention to, the stronger this brain circuitry becomes.
That we can now think of no mechanism for astrology is relevant but unconvincing. No mechanism was known, for example, for continental drift when it was proposed by Wegener. Nevertheless, we see that Wegener was right, and those who objected on the grounds of unavailable mechanism were wrong.
It is now widely realized that nearly all the 'classical' problems of molecular biology have either been solved or will be solved in the next decade. The entry of large numbers of American and other biochemists into the field will ensure that all the chemical details of replication and transcription will be elucidated. Because of this, I have long felt that the future of molecular biology lies in the extension of research to other fields of biology, notably development and the nervous system.
Geometry is the only science that it hath pleased God hitherto to bestow on mankind.
The most important discoveries will provide answers to questions that we do not yet know how to ask and will concern objects we have not yet imagined.
The world today is made, it is powered by science; and for any man to abdicate an interest in science is to walk with open eyes towards slavery.
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