Stretching the Uncertainty Principle in Frayn’s Copenhagen

How far is one allowed to stretch principles of science by relating them to what is more familiar to the general population? Are similarities drawn between concepts in quantum mechanics and the world the average human understands, as seen in popular culture correct? Is it right on Michael Frayn’s part to have implied a parallel between the Uncertainty Principle and the uncertainty in his play Copenhagen¹? Although similarities can be drawn between Copenhagen and the Uncertainty Principle, the comparison is not justifiable by Physics.

The origins and meaning of ‘uncertainty’ in the Uncertainty Principle must be clearly established. When explaining the Uncertainty Principle in his initial paper, Heisenberg uses the German word Ungenauigkeit meaning² inexactness, inaccuracy or vagueness. Later on, he refers to it as Unbestimmtheit roughly translating to indeterminacy. The Principle itself does not talk in terms of us being uncertain about the quantities or about how precisely anything can be known, rather it says that some pairs of properties are linked in such a manner that they cannot both be precisely measured at the same time. For example, the more precisely we know the position of a particle, the less precisely we know its momentum and vice versa. The Principle talks about an ‘indeterminability’ rather than an ‘uncertainty’. Unfortunately, for Science, a distorted notion of uncertainty is extrapolated from the Uncertainty Principle in popular culture.

The problem with this is that more often than not, the Principle is subject to misuse. Jim Holt in his article Uncertainty about the Uncertainty Principle: Can’t anybody get Heisenberg’s idea right? says, “No scientific idea from the last century is more fetishized, abused, and misunderstood—by the vulgar and the learned alike—than Heisenberg’s uncertainty principle.” The idea that a quantum system will collapse to one of its Eigen values by the act of observation is corrupted in popular culture. In the television series Numb3rs³, the protagonist Charlie Eppes claims that since they have observed the robbers and the robbers know that they have been observed, the robbers will change their actions. The film What the Bleep do we know?!⁴ takes it a step further. Using the fact that observing water molecules can change their molecular structure, its claims that since humans are made up of ninety percent water, according to Physics we can fundamentally change our nature through mental energy. Heisenberg must be rolling in his grave! Misinterpretations of such principles of Science lead to a false understanding.

The Uncertainty Principle is a very attractive concept in popular culture. In his New York Time’s article Nothing to see here: Demoting the Uncertainty Principle⁵, Craig Callender suggests changing the name of the Uncertainty Principle to a more accurate but less provocative ‘Quantum Standard Deviation Constraints’. He claims that with a name like this, not a lot of people other than Physicists will invoke the Principle and convolute its idea with misinterpretations. Heisenberg’s Uncertainty Principle is nestled in quantum mechanics. The subject is popular because it ‘sounds cool’. It has some very non-intuitive principles than continue to surprise us. The symbols used are overwhelming and the mathematics is unfathomable to the untrained eye. Attempting to explain quantum mechanics in simple English does not do justice to the subject, it takes away a wealth of knowledge form it. Furthermore, drawing parallels between concepts of quantum mechanics to the world that the average human knows, without understanding the Physics is a disaster!

Moving on to literature pertaining to Heisenberg and his Principle, David Cassidy in Uncertainty: The Life and Science of Werner Heisenberg⁶ says, “It is as if, for some, the intense emotions unleashed by the unspeakable horrors of that war and regime have combined with the ambiguities, dualities and compromises of Heisenberg’s life and actions to make Heisenberg himself subject to a type of uncertainty principle.” Cassidy stops here and does not explore the parallel any further. In Heisenberg’s War⁷, Thomas Powers says that Heisenberg’s hesitation on his role in the failure of the German bomb programme ‘introduces an element of irreducible uncertainty’. Powers asks for forgiveness in the ‘mistake’ of drawing a parallel between the Uncertainty Principle and uncertainty in Heisenberg’s life by adding a footnote to the above comment saying “Forgive me”. These works seem to have been an inspiration to some ideas in Copenhagen.

We must question the validity of Frayn applying Heisenberg’s Uncertainty Principle to the intrinsic uncertainty of his play. The story depicts the characters being uncertain about what transpired at their meeting in Copenhagen. Bohr and Heisenberg themselves are uncertain about the intentions of the meeting, what they discussed, its outcome and repercussions. On reflecting upon it after they have died, they try to reconstruct what happened, but end by coming up with different versions of the story. They are uncertain. Can this uncertainty about what happened in that eventful meeting be justly related to Heisenberg’s very own Uncertainty Principle?

Frayn implies a comparison between the uncertainty in his play and the Uncertainty principle. In the postscript to Copenhagen¹, he draws a clear parallel which is made evident when he writes, “There is not one single thought or intention of any sort that can be precisely established… And since, as the Copenhagen Interpretation establishes, the whole possibility of saying or thinking anything about the world…depends upon human observation, and is subject to the limitations which the human mind imposes, this uncertainty in our thinking is also fundamental to the nature of the world.”The problem lies with how the Uncertainty Principle is interpreted. To understand the Principle, it is important to understand how one can arrive at it. To understand where it can be applied, one must understand exactly which variables satisfy it. To prevent its misuse, one must understand the Physics of it. For readers familiar with the basics of this Physics, the derivation⁸ of the Uncertainty Principle has been provided in Appendix A.)

From the derivation, it can be seen that it is essential that the two quantities position and momentum do not Commute to satisfy the Uncertainty Principle(§).(Position and momentum do not Commute) They are Canonically conjugate variables. Examples of other pairs along with position and momentum are energy and time, potential and current, etc.
If they were to Commute, there would be no uncertainty in the problem, which is not the case. For two measurable to obey the Uncertainty Principle, they must not Commute and they must be Canonically conjugate variables. (Canonically conjugate variables, Measurables and Commutation are specific mathematic properties which we shall not get into for the benefit of readers unacquainted with such Mathematics.) Clearly only very specific quantities satisfy the Uncertainty Principle and the uncertainty in the story is not one of them.

Thinking of the uncertainty principle in terms of merely the word ‘uncertainty’ is like looking at the tip of an iceberg. There is much more to the Uncertainty Principle than what can be seen at face-value, rather name value. The principle carries a lot more information than the fact that we do not and cannot have complete information. The principle can only be applied on Measurables that do not Commute. Frayn very conveniently disregards this when trying to compare his story to the uncertainty principle. As a student of Physics, I believe that the comparison is a bit of far-fetched. The concrete comparison between the uncertainty principle and the intrinsic uncertainty in the story cannot be justified. Richard Feynman, in his autobiography What do you care what other people think?⁹ says , “I learned very early the difference between knowing the name of something and knowing something.” The fact that they both have the word ‘uncertainty’ in them is not enough to relate the two to such a great extent.

A popular joke among physicists is that Heisenberg was once over-speeding. The police-man stops him and asks him, “Do you know how fast you were going?” Heisenberg replies, “ No, but I know where I am!” This joke is not far-fetched because it discusses the fact that uncertainty in position and momentum (hence speed) are inversely related, which is depicted in the uncertainty principle. When you do not know how fast you are going, the uncertainty in momentum is high hence the uncertainty in position is low, so you know where you are. At the macroscopic scale that we observe and live in, the uncertainty is of little consequence because plank’s constant ( h = 6.626 x 10-34 J.s) is very small while the scale at which we are looking at things is large. Although the joke is not absolutely correct, it is not too far-fetched as it still deals with quantities that obey the uncertainty principle. This joke is an example where stretching the uncertainty principle is justifiable to some extent whereas Copenhagen is an example where stretching the principle is not justifiable when viewed through the lens of Physics.

Merely knowing the name of something such as the Uncertainty Principle in Copenhagen does not count as truly knowing it. Furthermore, one must not trick ones-self into believing that one understands it. According to Feynman, “The first principle is that you must not fool yourself and you are the easiest person to fool…I think it’s much more interesting to live not knowing than to have answers that might be wrong.” For an audience that is ignorant about these matters pertaining to quantum mechanics, Frayn’s comparison to the uncertainty principle seems very clever. It makes the audience think the comparison is justified and gives them a false impression of now understanding the uncertainty principle. Are such vague analogies justified? Which references are permissible and which are not? What are the consequences of deriving wrong implications from popular culture references to Science. These are questions a writer must keep in mind while implying such references or drawing such comparisons.

In conclusion, comparing the Uncertainty Principe to the uncertainty in Copenhagen is not justifiable because of the very nature of the Measurables involved. Frayn has stretched the principle on the basis of the name ‘uncertainty’. The use of the Uncertainty Principle in popular culture has resulted in a convoluted idea of the concept. The elasticity of Science may not be enough to withstand such stress, especially when an unacquainted audience is made to believe that that such comparisons are apt and leaves thinking that they understand the uncertainty principle.

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Appendix

A. Derivation of the Uncertainty Principle

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Sources

¹Frayn,Michael. Copenhagen. Anchor(2000)
² Collins German Dictionary.Collins
³ Numb3s, Season-1: Episode-4, CBS Television Studios ( USA, 2005)
⁴ What the Bleep do we know?!, Samuel Goldwyn Films (USA, 2004)
⁵ Callender, Craig. Nothing to see here: Demoting the Uncertainty Principle. The New York Times (2013)
⁶ Cassidy, David. Uncertainty: The Life and Science of Werner Heisenberg. Henry Holt and Company (1993)
⁷ Powers, Thomas. Heisenberg’s War. Da Capo Press Inc (2000)
⁸ Jain, M.C. Quantum Mechanics: A Textbook for Undergraduates. PHI Learning Private Limited (2011) : 109-110
⁹ Feynman, Richard. What Do You Care What Other People Think? Further Adventures of a Curious Character. Penguin (2007)

 

Note: This was submitted as part of my assignment for the writing course at YIF