Charm the quantum dog

Alan Dix
School of Computing, Staffordshire University

I married into a family of dog lovers, this cannot help but influence one's intellectual life for better or worse. So naturally when I want to devise a quantum mechanical thought experiment, rather like Schrödinger's Cat, my thoughts turn to a dog. However, my daughters would never forgive me if harm should ever come to this imaginary dog. Hence the challenge to design an experiment whereby the dog is guaranteed to survive unscathed (unlike Schrödinger's Cat who leaves the experiment with only 8.5 lives left). Given a mind contorted by thinking about undo, history and the like, it is not surprising that the experiment is reflexive, an apparatus that not only acts quantum mechanically, but also knows itself to be quantum mechanical.

In fact, the experiment with Charm the quantum dog is only one of a series of experiments probing quantum events, human observers and the observation apparatus itself. The crucial question is whether wave function collapse (and hence the end of time symmetric unitary evolution) is a property of sentient observers or a property of the nature of observational apparatus. Some of these experiments are simply thought experiments, but others move towards scenarios that could be examined empirically or theoretically.

Before looking at these new experiments in detail, we'll recap on Schrödinger's cat and the twin slits experiment.

Outline

Schrödinger's cat: Is it half alive until you watch it?
Twin slits: Photons can only be in one place at a time, but act as if they're everywhere.
A new experiment: A system that knows it is quantum mechanical.
Experiment 2 - how to see half a cat: Can we catch a glimpse of Schrödinger's cat in its superimposed half-dead state?
Experiment 3 - dispensing with the cat: In similar vein if slits are opened randomly, will we detect interference patterns?
More about the twin slit experiment: Detecting particles en-route collapases their wave function.
Experiment 4 - messages through time: if wave function collapse happened only when observations are actually made by humans, then we could send messages back in time
What causes the wave function collapse: we see that the cause of wve function collapse is in the nature of observational apparatus and of memory storage
Challenges: do some experiments in the lab or on paper

Schrödinger's cat

cs so long as it doesn't impinge on real (read big) objects.

Schrödinger's famous mind experiment smashes this sense of security and pulls quantum mechanics fully into the realm of cat-sized things. The experiment is roughly as follows:

Choose your favourite quantum mechanical device with two results. One such device is a light beam split by a half-silvered mirror. Half the light goes through it, half is reflected back. Decrease the intensity of the light until only one photon at a time goes through and then detect which path the first photon takes. A sophisticated version of tossing a coin!
Put the apparatus in a sealed room with a cat.
Arrange the apparatus such that if one path is taken a phial containing cyanide is broken (thus killing the cat). If the alternative path is taken nothing happens.
Wait outside the room for a suitable period and then (cautiously) open the door.

As there is a 50:50 chance for the two paths through the half-silvered mirror there is clearly a 50:50 chance that the cat will be alive. But when did the cat die? The common sense interpretation is that when the photon goes through there is a 50:50 chance of each outcome and at that point the cat either dies or lives. The quantum mechanical view is that the photon exists in its superimposed, neither one way or the other state until it is observed. But, does the cat count as an observer? If so, then the case is similar to the natural, non-quantum mechanical view. The last alternative is that the cat itself exists in some superimposed dead/alive state until the moment the door is opened and the human observation is made; at that point the wave function collapses choosing death or life.

In fact, we can lift the quantum mechanical argument one stage further. Why say that the wave function collapses when the door is opened? Why not consider the experimenter to be in a superimposed half state, 50:50 seeing a dead cat or not? The first time I heard of Schrödinger's cat and similar quantum mechanical paradoxes was as an undergraduate when a physics don gave a lecture on the subject to the Archimedeans, the Cambridge Mathematical Society. When questioned on just this point his reply was that such a view was too holistic. Quite right in a way as it challenges our sense of personal identity, but, however uncomfortable it is, does that mean it is wrong? In fact, this broad view of quantum phenomena is essentially that taken by the many-worlds interpretation, posed first in 1957 and popularised in science fiction as parallel universes. This sees the universe rather like a branching tree with multiple worlds constantly spawning off each other every time a random choice is required, with one universe for each possible choice!

Although this is philosophically interesting, it doesn't actually make any difference to you as an observer. The interpretation of events is different, but the effects are the same - 50:50 the cat will be DOA. Although, if the many-worlds interpretation is true there will always be some world in which the cat survives!

Twin slits

Before looking at these new experiments in detail, we'll recap on Schrödinger's cat and the twin slits experiment.

A new experiment

We place Charm the dog into a sealed room. A twin slit diffraction device is set-up with a source generating individual photons. Detectors are placed at strategic points behind the screen so that an interference pattern can be detected. A computer monitors the detectors and after a suitable number of photons has been counted (perhaps a million), the computer uses a simple algorithm to decide (i) whether the data represents an interference pattern indicating a quantum mechanical universe, or (ii) whether the pattern is simply twin lines of light as would occur in a non-quantum mechanical universe. If the computer decides the pattern is quantum mechanical it does nothing, but if it detects twin lines of light the computer breaks a phial of cyanide and poor Charm expires.

However, all is well for Charm. Unlike Schrödinger's cat who has only a 50% chance of survival, we can perform the same experiment time and time again and Charm will always survive. the computer is simply a digital means of photographing the emerging diffraction pattern. Just as photographs always reveal a diffraction pattern, so also will the computer. Charm is safe.

We can put Charm's life more at jeopardy and get te computer to examine all the evidence that we can ourselves for a quantum mechanical universe. In particular, we can ensure that the computer releases the cyanide if a single photon gives rise to anything but a single speck on the screen. That is, if the computer sees a single photon arrive at the screen in a smeared out, partial or wave-like fashion it will kill the dog. That is, we can ensure that Charm survives only if the wave function collapses due to the computer's observation. Again, the computer must see the same effects as we would and so Charm survives.

Experiment 2 - how to see half a cat

Let's return to Schrödinger's cat. The crucial issue is the state of the cat in the time between the potential breaking of the phial and the opening of the door to the room. Is the cat either alive or dead with a 50:50 probability, or is the cat in some superimposed quantum state, neither one nor the other until the door is opened? Because the door is closed we cannot tell. In contrast, the twin slits experiment allows us to catch a photon in just such a half-way state. Is it possible to in some way observe an effect whereby the half dead cat in some way interferes with itself?

The answer is yes.

In the box with the cat let's place a twin slits apparatus. However, the apparatus has some additions. Over the slits are shutters that can be opened or closed. In addition, we attach a heart rate monitor to the cat. At some suitable time after the cat has expired the computer measures the heart rate of the cat. If it is zero (dead!) it opens the right slit and closes the left slit, if it is alive it opens the left slit and closes the right slit. We then open a small window into the room which can observe photons hitting the screen exactly half way between the two slits. Because the window is half way between, we cannot tell whether the cat is alive or dead (as observer we are not collapsing the wave function). However, the number of photons hitting that spot will be different if it is simply the result of one slit being open, or of an interference pattern. If the cat is really in a superimposed state, then we would expect to see the intensity due to the interference pattern, but if fully dead or alive the intensity would be that of a single slit.

Imagine we peek into the room and find the cat alive. We then know that the left slit has been open and that we should have seen the intensity corresponding to a single slit. Similarly if we later open the door and find a dead cat, we would expect that the intensity we had earlier observed should be consonant with a single slit. This strongly suggests that we will see the single slit intensity and that, although we may not know which outcome has occurred, wave function collapse has occurred at least to the extent that the possible worlds are not interfering with one another. We'll come back to this issue later, but first let's try and alter the circumstances so that we get back into the realm where we would expect interference to occur. The likelihood of this outcome is also suggested by refinements of the twin slits experiment (discussed below) which monitor photons passing at the slits.

Experiment 3 - dispensing with the cat

There are three factors in experiment 2 which might push it out of the realm of pure quantum mechanical interpretation.

First there is the presence of the cat. Is it an observer? Is there something special about living organisms? Is it sentient? Does it have a soul? It is often suggested that there is something special about human minds which force the quantum mechanical wave function collapse. The presence of the cat could mean that if cats share this quality then the event is decided when the cat observes the cyanide release.

Secondly there is the large-scale nature of the decision. There are two possibilities with 50:50 probability: either the left slit is open only, or the right slit is open only. Furthermore, we are in a position to later find out which was the case. Penrose has suggested that wave function collapse occurs when the difference between possible worlds exceeds the scale of a graviton. So, perhaps the sheer size of the event can cause wave function collapse.

Finally, the fact that we are going to open the door and observe the cat's health may cause wave function collapse earlier. We will return to this issue in experiment 4.

Of course, the above experiment can be performed with no cat involved. Instead of a phial of cyanide and heart rate monitor, we directly connect the 2 outcome quantum system to the slit controller. If we modify this further to allow lots of tries, we begin to get a system where it seems reasonable to expect interference behaviour.

Take a 2 outcome quantum mechanical system with equally likely outcomes A and B. Use a computer to monitor the outcome and if it is A the computer opens the left slit, but if it is a B then the right slit is opened. Wait until one photon is observed hitting the screen and then repeat the process many times. Photograph the overall result. Is it an interference pattern, or merely the sum of two single slits patterns?

In case we are worried about the potential sentience of computer systems we can hardwire the complete system, possibly with optical components throughout. To make things really interesting lets make our 2 outcome system be based on photons going in different directions. We have two slits with shutters and by each shutter a detector for photons at a particular frequency w₁. We have a dichromatic emitter which emits photons at frequencies w₁ and w₂. The production of both is slow enough to be effectively one at a time, and the emission of w₁ is much slower than that of w₂. The screen the other side of the slits is sensitive to w₂. When one of the detectors registers a photon at w₁ it opens its corresponding slit. When the screen registers a photon at w₂ it closes both slits. The hits to the screen are also recorded as pattern. Effectively each w₁ photon acts as a gatekeeper allowing just one w₂ photon through the same slit. This so nearly like the w₁ photon going through the slit itself, surely there would be an interference pattern?

More about the twin slit experiment

We return now to the classic twin slit experiment. One variant puts a detector by one of the slits. The detector registers whether a photon goes through that slit. If this experiment is constructed then the pattern on the screen becomes just a simple overlaying of the patterns from the two single slits. By measuring which slit the photons go through we are able to collapse the wave function of each photon.

Now this is partly why it was asserted in experiment 2 that the observed behaviour would be as if only one of the slits were open, rather than a superposition. It would be conceivable to imagine being able to record a mixed state before we opened the door and at that point observe the collapsed wave function. However, nature seems to abhor such inconsistent interpretations!

This would also seem to suggest that experiment 3 would yield no interference pattern, in contrast to the argument proposed above. Now perhaps both can be right. So long as the photon detectors don't output their results to the human experimenter perhaps we will see an interference pattern, but perhaps if the system is such that no direct observations can be made of the detectors and shutters other than the pattern on the screen we might see an interference pattern. In the extreme we could get to the situation where if someone looks at the display showing which slot the photons go through then we get single slit patterns, but if the experimenter happens to be looking elsewhere the interference pattern appears! Although sounding absurd, this not unlike EPR type experiments, and certainly no stranger than many other aspects of quantum mechanics.

Experiment 4 - messages through time

Let's investigate the status of the observational apparatus as opposed to the human observer further. Suppose we set up the twin slit experiment with a detector at one slit. We will see no interference pattern. This has been confirmed by experiments. Now modify the apparatus so that instead of showing us the measurement as soon as it goes through the slit, we store the results in a computer memory ... and then wipe the memory without reading the results. If we look at the pattern on the screen before deciding whether to wipe the memory after having seen the screen pattern it could not be an interference pattern. In fact, we could be particularly perverse and display the memory if we see an interference pattern and wipe it if we don't. If it is actual human observation that causes wave function collapse then we could transmit messages into the past or with trans-light speed.

The trans-light speed communicator would work thus. We perform many twin splits experiments photographing the screen for each and also storing the photons detected going through one of the slits. The photographs are either examined then or sent to a far distant destination. We turn the photographs into binary digits thus: each interference pattern counts as a zero, each overlaid single-slits pattern counts as a one. The memory chips with the detector output are sent to a different location which at any point in the future can send a message to the viewer of the photographs by either wiping a measurement without reading it to code a zero or examining it to record a one.

To be perverse yet again, we could remove the human from this loop. We build a machine which stores the results of the detector and examines the pattern on the screen. If it decides the screen represents a diffraction pattern then it prints the pattern and the slit measurements out. If it decides it is not a diffraction pattern, it deletes the readings and prints nothing out. Clearly any output would portray an inconsistent set of quantum events hence the machine could never produce any output. That is the very existence of the measuring device connected to the computer is enough to cause wave function collapse at the slits.

What causes the wave function collapse

We have seen several thought experiments now each of which demonstrate ways in which wave function collapse can be produced by automatic and sometimes quite simple apparatus. This is important as wave function collapse is part of the arrow of time which distinguishes past from future and also critical in relating observer and observed system.

Two popular approaches to wave function collapse are the hypothesis that in some way the human mind causes collapse and Penrose's suggestion that any system experiences collapse when the possible worlds diverge by more than a graviton. Given the states of our brains are quite complex they will exceed the graviton limit so the latter implies the former.

In fact, when asserting Charm's safety I was perhaps a little over-confident. How can I be sure that a computer examining the screen will not see a twin spots pattern? Of course, if it keeps a photograph I know what will happen, but isn't it possible that indeed I could open the door to find a residual smell of almonds, a dead dog and a computer asserting (albeit wrongly) that it doesn't live in a quantum universe. So long as it is possible for me to observe, after the event, the computer's inputs I can be sure what will happen. Without this I am confident that Charm will survive, but not absolutely certain. However, if the computer records its observations on a floppy disk I can be absolutely sure that Charm will survive.

It seems that the key element is not the computational aspect. Experiment 4 demonstrates that even the potential to observe something must cause wave function to collapse, hence all that is required is a measuring device and storage medium. This is a pity. Being a computer scientist, it would have been nice to find that it is , for example, the information lossy operations such as AND that cause collapse, but alas, although this may still be true, it is not necessary from the evidence.

So we get to the position that any equipment that can detect photons pass and record them will cause wave function collapse - even if it is never actually observed by a human.

We are therefore left with two components. Each of which we could imagine being constructed using nano-technology and thus falling well below the 1 graviton size. Penrose calculates this at the order of 100th of the Planck mass (m_p = 10^-5 grams). That is, equipment below the scale of 50 microns does not pass the Penrose threshold. This is the size of fine spray mist and large enough by microchip standards. Even allowing another order of magnitude in case graviton effects influence smaller scales, we still have plenty of room to design small detection and recording devices, perhaps even based on recent molecular engineering.

If the presence of such a device gives rise to wave function collapse, this could either be due to the effects of the measurement device, or the memory. Both are constructed out of particles, atoms and molecules obeying quantum mechanical laws. Memory perhaps has some of the most interesting behaviour at this level. Memory devices typically rely on some form of meta-stable system. Is it the non-linear response (and often feedback loops) of these which cause the wave function collapse?

Although it sounds as if we have shown the necessity of non-unitary behaviour at below the graviton level some further properties of the data we need to store may conspire to make this impossible. In fact, we need to store quite a bit of data in order to mimic any of the experiments described above. If we measure only a few photons, we would not get enough marks on the screen to be sure statistically that it was an interference pattern. Also each bit remembered will require energy to keep it fresh or else it will decay. It is possible that these two factors together may push the size of a definitive wave function collapsing system to the graviton level.

Challenges

Although we started with mind experiments we have moved towards more practical experiments. Perhaps some have already been carried out, if so please let me know. Also it seems possible that one could construct simplified quantum mechanical models of some of these systems which could be solved numerically.