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.
The time has come when scientific truth must cease to be the property of the few, when it must be woven into the common life of the world.
If we betake ourselves to the statistical method, we do so confessing that we are unable to follow the details of each individual case, and expecting that the effects of widespread causes, though very different in each individual, will produce an average result on the whole nation, from a study of which we may estimate the character and propensities of an imaginary being called the Mean Man.
There are three stages in scientific discovery. First, people deny that it is true, then they deny that it is important; finally they credit the wrong person.
On Friday the 13th, April 2029, an asteroid large enough to fill the Rose Bowl as though it were an egg cup will fly so close to Earth that it will dip below the altitude of our communication satellites. We did not name this asteroid Bambi. Instead, we named it Apophis, after the Egyptian god of darkness and death.
Given the power and influence that science increasingly has in our daily lives, it is important that we as citizens of an open and democratic society learn to separate good science from bunk. This is not just a matter of intellectual curiosity, as it affects where large portions of our tax money go, and in some cases even whether people’s lives are lost as a result of nonsense.
As in biomedical science, pioneering industrial inventions have not been mothered by necessity. Rather, inventions for which there was no commercial use only later became the commercial airplanes, xerography and lasers on which modern society depends.
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