Schrödinger’s cat walks into a bar. And doesn’t.
There may be more than one way to skin a cat; but why are we skinning cats at all? The case of Schrödinger’s cat has been the source of wonder, intelligent discussion and excellent t-shirts for some time, however there is a slight risk with the popularity the underlying mechanics of the thought is missed. To anyone familiar with the situation, or indeed quantum mechanics, it won’t come as any surprise that there are different interpretations of the paradoxical situation proposed by Schrödinger, many of which are worth understanding before forming a view on the subatomic kingdom. Before we look at how to skin the cat, we first establish why we are being so cruel in the first place.
The ideas of quantum mechanics are disturbing, leading some of the world’s greatest minds to be extremely spooked. The big problem? It’s an abstract theorem constructed in the realm of mathematics, where classical descriptions of the world have to be left aside. All you have ever experienced is a classical description of the world and indeed all humans before you have ever experienced is a classical description, so it shouldn’t be too surprising that this is a little uncomfortable. Yet despite this complexity, humans have managed to harness the power of the quantum realm to the point where it is estimated a third of the US gross national product is the direct result of quantum mechanics (Tegmark & Wheeler).
This post, along with some future posts are intended to serve as a preamble to a rather more developed post; so if you don’t find the subject overly fascinating in its own right (which you should!) I hope the ideas will weave together later into an acceptable marriage.
All this feline chatter
Schrödinger is most famous for his derivation of the second order partial differential equation known as the wave function, denoted Ψ, which rightfully bagged him a Nobel prize in 1933. The wave function is a complex valued probability amplitude; which in essence is a mathematical expression of all the things something may be with probabilities assigned to them. In the quantum realm for example, we may be talking about an electron around a nucleus; the function is computed using all the possible degrees of freedom the electron have (states it can be in). You should never be concerned if you don’t know how to interpret the wave function at first – because nobody, including Schrödinger himself did when they first looked at it. Wave functions can be produced by including all points of position or momentum space (for example), and allow for the inclusion of discrete degrees of freedom (for example spin of +1/2 and -1/2). The wave function is very complex, but to understand Schrödinger’s cat all you need to appreciate is that the wave function is describing all the states a particle may occupy and the probability associated with being in each state; so if you like anything that can happen is included.
Schrödinger’s cat can be considered a paradox; what he is doing is demonstrating the issues that arise when one links the quantum realm and the macroscopic world that we are so familiar with. To set up the experiment imagine you have a sealed box in which you can extract no information (light is unable to penetrate, sound cannot escape). Within the box you have a radioactive substance, which decays randomly (i.e. puny humans have no predictive power) and a Geiger counter which measures radiation. Next to this you have a cat, a vial of poison and a hammer. If the Geiger counter should sound then the hammer goes, the vial breaks and the cat is dead. Intrinsically the fate of the cat is now the result of the quantum mechanical rules which govern the random decay.
Is the cat dead or is the cat alive? The short answer: you have no idea. To assume the cat is dead or alive is to assume you know something about the conditions within the box to make that prediction; by the construction of the experiment you do not. But if you cannot say that the cat is dead or alive what is it? Being dead or alive is surely a binary construct? We must consider the cat in superposition – which in normal terms is a suspended state of being dead or alive. All we know is that there is a probability of the cat being dead, and alive; it is simultaneously “stuck” in these states until we open the box and we determine the cats luck by conventional means. Sound like nonsense? That’s the point – a cat cannot genuinley be both dead and alive… can it?
The construction is designed to illustrate the weird world of quantum mechanics; you know it is often said that quantum mechanics is like playing dice. Well unfortunately the world is so damn strange that even that is an oversimplification; since when one plays dice the dice obey nice normal classical mechanics, we just don’t have the required knowledge to form predictive assumptions. In the world of quantum mechanics the classical world, we think, melts away. So the paradox provides an interesting way of illustrating the situation where we cannot know the state of an object without observing it and the seemingly paradoxical situations that can arise when we tie the information we have learned about the quantum realm to our more familiar macroscopic surroundings. Now you see why we must skin the cat; we need some answers.
The Copenhagen Interpretation
This is the leading interpretation of the thought experiment (and quantum mechanics in general) and is likely to be what you have been taught (potentially even represented as absolute truth) if you have studied the subject or done some reading. The interpretation was developed by some big names; Niels Bohr and Werner Heisenberg, but interestingly they didn’t fully agree on any approach and never actually laid down a formal description of their interpretation. As such the approach has developed over time with the help of many minds and you many not always see identical descriptions when comparing one text to another. The key point is that a physical system has no definite properties before being measured. The rest flows from here.
So the wave function represents a system with everything that can be known before any observation takes place; the set of all possibilities with all probabilities. The system itself may well contain incompatibility – for example the well known uncertainty principle that asserts one may not know about the position and the momentum of an object to within a certain threshold of accuracy. This function exists in this state, quite happily, until terrible humans come along and measure the thing. At the point of measuring the system, what we are actually doing is collapsing the wave function (into an eigenstate) for the observer. That is when we observe the system we collapse all of the possible outcomes and probabilities into one known outcome of which we can interpret as being classical. So we haven’t actually measured in the quantum realm at all, we have collapsed the “normal” behaviour with our observation and made it fit with our window on the universe. Proponents of this theory point to the fact that humans are classical and not quantum beings and we can only observe quantum systems by reducing them to mere classical situations – the inner workings or a quantum mechanical system are not observable to a human and never will be.
So in the case of our dear cat, what actually is happening is before the event the cat is in its state of being dead and alive – with a probability of 50:50 dropping out for each scenario from our wave function. When we actually observe the cat we collapse this situation into one fixed definite situation – we know the cat is dead or alive. Critics of this theory are often say that it isn’t actually an explanation at all – but rather a work around to the problem by simply stating you cannot observe it and if you do everything that existed before collapses. Unfortunately the Copenhagen Interpretation may well be true; so if the cat is dead I am afraid it’s your fault for looking.
The many worlds interpretation
If you are interested in a full post on this, you should check out Mekhi’s excellent post here.
This interpretation is probably one of my favourites; it’s just so fanciful. What it lacks in rigorous detail it certainly makes up for in imagination. The bedrock of this theory is that anything that can happen…. sort of will. In the quantum mechanical situation particles exist under the rules of probability; in the many worlds theorem everything exists. In parallel. It’s quite a mind-bender; the theory has both the mathematical construction of the Schrödinger equation; and a much less well defined correspondence between the quantum realm and our experiences.
To tackle this theory, understand the difference between a world and the Universe. Simply there is one Universe that contains all the worlds. Drilling down a little further, when we define any world, it becomes unique in the past and many in the future. So interestingly, this theory takes the idea that there is one I; I am unique however there are many Joe’s. Excuse me? I am all of the future Joe’s. All of them; and yet I am only one I, the unique defined present version of myself. So what we have is a situation that looks like this:
|ΨUNIVERSE› = ∑αi |ΨWORLD i›
The wave function of the Universe is taken to be the wave functions of all the different worlds; which are not alternatives but rather all actual realities happening until they are defined. I’m sorry, but if you’re not in neurological heaven right now you are on the wrong page.
Aside from the fact that parallel universes are delightful, the Many Worlds Theory has some other big plus points. Firstly – you don’t need to collapse the wave function like you do in the Copenhagen Interpretation. The idea that you have a system that is totally independent from initial conditions and only influenced by probability is uncomfortable since it is so at odds with out experimental evidence (which under the Copenhagen Interpretation is the measurement problem). But secondly, the Many Worlds Theory resolves many (if not all) of the paradoxes of Quantum Mechanics – one of these being Schrödinger’s cat. In fact is was said Schrödinger himself was waring up to this theory.
Under the Many Worlds Theory, Schrödinger’s cat is in two parallel universes where the cat both lives and dies. It is only when the cat is observed that the situation is fixed in the present; with the many worlds of the future living on. Here is a illustration on the scenario.
This theory is gaining traction as a description of the Universe – but it has work to do. It violates some very old laws around nature that we either need to overcome or rewrite before we are converted (see Ockham’s razor if you are interested).
Does reality contain information? Is information reality? I am rolling with the latter; it would appear that truth is nothing more than a set of propositions – information. It is actually quite a fun game to play, to pick anything then break it down into nothing more than a set of axioms. No matter how complex the system is (like for example a human) you can keep breaking it down into simpler and simpler systems until you get to an elementary system. This is just like a binary system; it is or it is not, which can be represented by a 1 or a 0. When we get to this point we have the smallest unit of information possible (sometimes called a quibit in quantum mechanics). The key idea here therefore is that an elementary system is just a bit of information.
But what about randomness? Well it is a little different; all you looking at is objective randomness which is the result of a lack of information. We are closing in on the cat. The elegance in this theory is that it answers the question of why the world is quantised at all. It is disturbing if you really muse on it. Well the answer is simply the quantisation of information; if reality is merely information, with an elementary system being binary then of course on the smallest of scales the quantised picture will arise. Delightful. The theory also goes on to address quantum entanglement, pointing to the fact that the phenomena arises where the elementary bit is information for more than one of the systems. All tangled up.
Now in the case of our dear cat, the issue is such that there is no information for asking if the cat is dead or alive; and therefore we don’t have the answer. When we look at the cat, information is created (in an objectively random way); this new information arises all the time in information theory and is either subsequently destroyed, or in our case stabilised which then becomes a measurement. In essence the problem with viewing the quantum world is that viewing and taking measurements extracts information from the system – and with information being the currency of reality, we leave ourselves with less in the bank.
Did the cat live?
How should I know. Schrödinger’s cat in all three interpretations is tied to an unknown fate until we observe it – but the situation before and after is viewed differently. Do not forget; this is about creating a thought experiment to highlight quantum mechanics. So whilst, for example, the information theory might seem like a pretentious way of saying I don’t have information before I look, (go figure), its beauty and elegance as a description of the universe on the smallest of scales should not be overlooked. I cannot resist the lure of the quantum realm; it quite literally makes up everything, the building blocks of everything and anything. There are many more interpretations you may wish to explore if you are interested; the three I highlight are the most popular.