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 nuclear approach I'm involved in is called a traveling-wave reactor, which uses waste uranium for fuel. There's a lot of things that have to go right for that dream to come true - many decades of building demo plants, proving the economics are right. But if it does, you could have cheaper energy with no CO2 emissions.
Science would not be what it is if there had not been a Galileo, a Newton or a Lavoisier, any more than music would be what it is if Bach, Beethoven and Wagner had never lived. The world as we know it is the product of its geniuses-and there may be evil as well as beneficent genius-and to deny that fact, is to stultify all history, whether it be that of the intellectual or the economic world.
Molecular evidense suggests that our common ancestor with the chimpanzees lived, in Africa, between 5 and 7 million years ago, say half a million generations ago. This is not long by evolutionary standards.
Certainly I see the scientific view of the world as incompatible with religion, but that is not what is interesting about it. It is also incompatible with magic, but that also is not worth stressing. What is interesting about the scientific world view is that it is true, inspiring, remarkable and that it unites a whole lot of phenomena under a single heading.
One can think of any given axiom system as being like a computer with a certain limited amount of memory or processing power. One could switch to a computer with even more storage, but no matter how large an amount of storage space the computer has, there will still exist some tasks that are beyond its ability.
Space, the final frontier. These are the voyages of the starship Enterprise. Its five-year mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.
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