# Play Copenhagen by Michael Frayn

• Gale
In summary, the play Copenhagen discusses the Uncertainty Principle and Complementarity. These principles are used to explain the events that took place between Bohr and Heisenberg in 1941. Additionally, the play uses examples of light and particles to explain how these principles are used.
Gale
play "Copenhagen" by Michael Frayn

Ok, this may seem a bit weird, and maybe it seems inappropriate for the physics forum... but eh, move it somewhere more appropriate if necessary.

Ok, first, this is with regards to the play "Copenhagen" by Michael Frayn. if you've read it or seen it, awesome, if not, i think maybe you might still be able to post something productive for me. Copenhagen is about Neils Bohr and Werner Heisenberg's infamous meeting in Copenhagen, 1941. The interesting thing about the play, (...er in my opinion i guess...) is that Frayn sort of uses physics to explain history sort of, (that might be phrased weird, bare with me.)

So the science used... these are my rough explanations thus far, i don't need super in depth, but i want to have the basic ideas. I read a few books a while ago, so i have a rough understanding of the ideas mostly, and I've looked them up a little to try and gain a more cohernent understanding. But mostly, my memory is very poor indeed, and i keep mixing things up, so eh... here's what i have:

uncertainty: inability to measure with certainty two conjugate variables (ie, position and velocity) simultaneously.
also, this means that our measurements and observations effect the system and therefore we cannot make conclusions about a system that is unobserved. (or we're resticted as for what sorts of conclusions we can make.)

complementarity: we can view er, light, electrons.. everything (?) as a particle or wave, but it/(they) exist as both at the same time.

i haven't done all my research yet, but is shrodingers cat about uncertainty, or complementarity or something else entirely? I just don't remember what I've read so well... hmm... and the dual slit thing... that's complementarity too right? or..? the particle goes through both slits at the same time... that's... complementarity i think, or maybe not...

right well anyways, he uses those two things alot. He talks about how Heisenbergs skiing being up against the uncertainty principle because he skiied so fast, he couldn't know where he was, or if he knew where he was, he wouldn't know how fast he was going. or how when he came to a crevasse, in his mind he swerved both right and left at the same time, like in complementarity.

The skiing examples are most explicit, but he also uses these principles to explain some of the confusion about neils and werner's meeting. that's more in depth, requires much more analysis, and is what my report is mostly on.

anyways. I was hoping to get my definitions better refined. most of what I've read is really lengthy, so i need condensed definetions that will be suitable for my presentation, but also as coherent as possible. Of course, i want to understand the principles best i can as well, so that i can explain if I'm asked questions, but... eh, i think you know what i mean. Also, if you're familiar with the play, or the meeting between bohr and Heisenberg, any general input about that is welcome.

also, there's one thing in the play that seems like Frayn is trying again to use science as a context for what's happening, but I'm not sure what he's doing. There's a scene where neils, werner, and margarethe, (borh's wife,) are looking at each other, and each of them sees the other two, but has difficulty realizing that they too, are in the room... like, because they are both the observer and the subject... i dunno. seems maybe like uncertainty again, and the fact that introducing a means of observation warps their view of themselves or something... i dunno...

Anyways, um, thanks in advance i guess... heh..

~gale~

Hi Gale;
Again, no expertise here, but somebody has to get this started. I'll stick with the cat. The whole premise of the scenerio isn't that we don't know whether or not the cat is alive. It's that the wave functions describing the cat simultaneously exist in all possible states from fully alive to fully dead. Only when some event, such as observation, disturbs the system does one function 'collapse' into reality. A current theory, which I really like just because it weirds people out, is that the unfulfilled functions don't just disappear. They each collapse into a reality of their own and create a new universe parallel to the main one. So somewhere the observer sees a dead cat, and somewhere else the same guy sees a live one. I don't know what level of acceptance this idea has, though.

I'm really looking forward to reading the responses from more knowledgeable folks than myself.

It's somewhat more palatable to remove the hypothesis that a "new universe" is created, and simply say that the superposition extends to you.

The system of you + cat is merely in a superposition of |dead cat + you see dead cat> and |live cat + you see live cat>.

Gale17 said:
uncertainty: inability to measure with certainty two conjugate variables (ie, position and velocity) simultaneously.
also,

Not really. Take the uncertainty relation for momentum p and position x. Now, most people say that you cannot measure both x and p with perfect accuracy at the same time. That is correct but you need to read things right. Suppose (just imagine this) that you measure the momentum of an electron that passes through a detector. You know the position of the detector and therefore you also know the position of the electron. Also, thanks to the measurement you also know the electron's momentum. So you know both x and p at the same time. Now, the clue is that if you were to measure the momentum of that same electron again at the same detector, you will get another p-value. Keep in mind that this not really possible though but it illustrates how you need to look at the HUP. You can simultaneously determine both x and p, only if you measure again you won't get the same values : that is the uncertainty.

Diffraction through an opening (like the Young experiment) really is a manifestation of the uncertainty principle in 'classical physics' : the smaller the opening, the more the wave will spread out. Just think of pushing on a water-tube when you are gardening : that's the real HUP for ya.

this means that our measurements and observations effect the system and therefore we cannot make conclusions about a system that is unobserved. (or we're resticted as for what sorts of conclusions we can make.)

No, these are the non-commuting observables of QM. When performing measurements to determine the (eigen)values of such operators, the actual measurement will influence the system that you are measuring. So the measurement of operator A has an influence on the measurement of operator B and the other way around.

complementarity: we can view er, light, electrons.. everything (?) as a particle or wave, but it/(they) exist as both at the same time.

That's a classic. I refer to my journal : the 'five socalled easy pieces entry'
Complementarity, according to mr Bohr means that some experiments are best described using the wave-like notion (like the Young experiment) and others are best treated with a particle like notion (like the photo-electric effect). We need both visions in order to acquire a complete description of mother nature.

No, keep in mind that this duality does NOT mean that there are TWO different ways in QM to look at light (for example) : either a wave or a bunch of particles. That is just how we (humans) look at this with our "classical" eyes. Besides when we talk about particles, don't think of classical particles (ie entities with finite spatial boundaries) but think of entities with finite amounts of energies (this is the actual energy quantization). So what we call space in our classical minds, now really is "energy-space" you see? In energy-coordinates, these particles would look like point particles, where every point denotes a certain energy value.

Read Joachain and Bransden 'intro to QM' for this...they do a great job at explaining this.

i haven't done all my research yet, but is shrodingers cat about uncertainty, or complementarity or something else entirely? I just don't remember what I've read so well... hmm... and the dual slit thing... that's complementarity too right? or..? the particle goes through both slits at the same time... that's... complementarity i think, or maybe not...

The double slit thing and the cat thing really are a manifestation of another basic ingredient of QM : superposition. A QM state really is a summation of all possible states. You can be either alive or dead so prior to any measurement, you state is a summation of dead and alive. A qubit is a summation of 0 and 1. and so on...When you measure, the wavefunction collapses, meaning that the superposition is broken and only one of the states remain.

Beware of the double slit thing though. The actual interference happens between the two possible states of an electron : pass through opening 1 or pass through opening 2. These things are expressed by the wavefunction which is not the same as the actual electron. The wavefunction gives you a probability to find the electron in a certain finite spatial area. The interference, thus happens between the actual paths that an electron can follow.

regards
marlon

there are other ways of interpreting the QM-measurements like Multi Universa, decoherence,...but they all suck, trust me
[/QUOTE]

Gale17 said:
There's a scene where neils, werner, and margarethe, (borh's wife,) are looking at each other, and each of them sees the other two, but has difficulty realizing that they too, are in the room... like, because they are both the observer and the subject... i dunno. seems maybe like uncertainty again, and the fact that introducing a means of observation warps their view of themselves or something... i dunno...
Sounds like the claim that the observer is inseparable from the observed. It is impossible to oberve a phenomenon without affecting the outcome. (A metaphor: a scientist tries to fish a coin out of his living room couch. Every time he pulls the cushion back to reach in, the coin slips further down.) More practically, you cannot know where a photon is (i.e. you cannot observe it) without altering its trajectory, velocity or position.

Many attempted refutations of Heisenberg's Uncertainty Principle rely on determining a particle's position with arbitrary accuracy and then determining its position with some arbitrary level of accuracy. Heisenberg points out that the first contaminates the second, destroying the information gained.

Good play BTW, I enjoyed it.

## What is "Play Copenhagen" by Michael Frayn?

"Play Copenhagen" is a theatrical production written by Michael Frayn. It is a two-act play that explores the events of a real-life meeting between physicists Niels Bohr and Werner Heisenberg in 1941 during World War II.

## What is the significance of the title "Copenhagen"?

The title refers to the city where the meeting between Bohr and Heisenberg took place. Copenhagen is also known as the birthplace of quantum mechanics, which is a major theme in the play.

## Is "Play Copenhagen" historically accurate?

While the play is based on a real event, Frayn has taken creative liberties in his portrayal of the meeting between Bohr and Heisenberg. Some aspects of the play may not be entirely historically accurate.

## What themes are explored in "Play Copenhagen"?

The play explores themes of science, friendship, morality, and the consequences of one's actions. It also delves into the uncertainty and ethical dilemmas surrounding the development and use of nuclear weapons during World War II.

## Is "Play Copenhagen" suitable for all audiences?

The play contains mature themes and may not be suitable for all audiences. Viewer discretion is advised.

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