Pls Help Understanding Schroedinger's Cat

[Baskak]

Please forgive a layman's question.

 

Recently my son was outdoors (without his cellphone) and the Weather bureau predicted a probability of a strong thunderstorm. A student (happened to be at our home) tried to calm me down by explaining that my son is in a superposition of two states (dry/wet) described by a probability wave function AS IN A FAMOUS SCHROEDINGER'S CAT experiment, and that we must break up this function/superposition by going out and finding my son (which we did and happily found him in a dry state). 

 

I am much fascinated by the Schroedinger's experiment but somehow do not feel comfortable with the student's comparison. Please explain the differences, if any.

 

Many thanks for attention and your time wasted (hopefully) on my (stupid) question.

[Pmb]

The analogy is valid but the paradox was never meant to be taken seriously by Schrodinger.

[QuantumTantrum]

Macroscopic systems do have wave functions, its just that they have wave lengths which are too small to detect on the macroscopic level. Schrodingers cat believe it or not, is easily explained by saying that the cat cannot violate this - the cat really is either dead or alive, but as pmb explains, it was never taken seriously that the cat was both dead or alive, only that the quantum interpretation would invite this idea and thus raise the so-called paradox. 

[QuantumTantrum]

From a chaotic bath of unpredictability, somehow, systems like us emerge, who seem to live deterministically. We see logical things happens all day, seeing a cat obey the wave function in the physical sense, just doesn't happen. One solution is that the particles which make the cat have all collapsed and are quantum entangled in some particular way.

Edited June 1, 2015 by QuantumTantrum

[CraigD]

Hi and welcome to hypography, Baskak! :) Please feel free to start a introductions forum topic to tell us something about yourself.

 

To grok Erwin Schrödinger famous dead/not dead cat thought experiment, I think you have to back up and get a personal understanding the revolutionary, unsettling scientific ideas that inspired it. So here’s mine – not a historic account, but what make it make sense to me.

 

Start with a deeply and undeniably weird thing: the formation of diffraction patterns when the illumination level is so low that on a single photon is in flight most of the time. You can see this using equipment available to most college undergrads and students in better high schools.

 

First, do the experiment with brighter light. Take any light source, put it in an opaque box with a single hole. Shine it though a diffraction grating – you can make one by pouring ink on a glass place and scratching 2 lines thought the dry ink with an ordinary sewing needle – onto a photographic plate. Develop the plate, and you’ll see a neat pattern of alternating light and dark.

 

This doesn’t look weird – you could do something similar using waves in water, recorded in fine sand.

 

Then lower the illumination, by adding translucent filter plates over the light box’s hole until no light makes it through. (The first time anybody did this, Cambridge’s G. I. Taylor ca. 1909, they had to use photographic plates to figure out when the number of plates. When I did it in class in 1980, we had a nifty electronic photomultiplier/detector gadget that allowed us to do it in less than an hour.) Then take away one plate, so the illumination is about as low as possible without being zero. Then repeat the experiment with the diffraction grating, with a faster (more sensitive) plate and a very long exposure (duration).

 

Looking at the developed plate, you see the deeply weird thing: like the first, bright light experiment, the low light experiment shows the same neat pattern of alternating light and dark.

 

To a person reasoning the way physicists did from the late 1600s through the early 1900s, two things look weird here:

• Mildly weird: Adding filter plates didn’t just lower the light intensity, but at a specific number of plates, zeroed it. Nowadays, we understand this is because light consists of discrete quanta, for which we have a very beautiful and well-confirmed theory, quantum electrodynamics. Ca. 1700, Newton would have found it only mildly weird, because one of the theories he and his contemporaries had for light were corpuscular theories, which like QED, described light as consisting of tiny indivisible particles.
• Deeply weird: The light and dark interference pattern formed even when the light intensity was so low that only a single photon is in flight at any time. Because they explain interference as interaction between particles of light, the old corpuscular theories can’t explain this. Quantum mechanics explains it by describing the photon not as a bodies like the large ones we’re familiar with – bullets, baseballs, planets, etc. – but as fields of probability, described by quantum wave functions. The wave function for each individual photon describes it going thought either of the two slits in the grating, so even a single photon can “interfere with itself” as if it were two separate photons. The wave function describes the photon as in a superposition of states, some passing through the left slit, some through the right.

This sets up the next deeply weird thing about quantum mechanics: if we alter the experiment to detect which slit each photon passes through it doesn’t tell us that each photon is in a superposition of states, but that each passes through either the left of the right slit, just as the old corpuscular theories predict. But when we do this (it’s been done, though it’s a more difficult experiment than most undergrads or highschool students can manage), no diffraction pattern forms. Detecting which slit each photon passes through changes its wave function to describe the photon passing only through that slit, so the wave function can no longer explain the photon “interfere with itself.”

 

About 10 years after this quantum mechanical explanation had become the most popular one for these experiments, lots of physicists and philosophers were deeply disturbed by the implications. Quantum mechanics applies not just to photons, but to practically everything, including the huge ensembles of particles that make up a cat. So in 1935, Schrödinger wrote his thought experiment, calling people’s attention to how weird these implications are.

 

To me, the main point of Schrödinger’s cat is not some sort of attack on quantum mechanics, but that physicists and philosophers were and continue to be sloppy with defining the meaning of an observation, that thing that causes wave functions describing superpositions like single photons going through both slits in the grating, an atom of a radioactive element that has decayed or not decayed, a cat that’s both dead and alive, or a son being both wet and dry.

 

Obviously a physicist collecting data from reliable detection equipment, or the person in thought experiment opening the box and looking at the cat, constitutes an observation. Why, though, doesn’t the cat, which has some sort of mental awareness of being alive rather than dead, qualify?

 

This question was obvious to Schrödinger’s and his contemporaries. In 1961, physicist Eugene Wigner ran with it, proposing the “Wigner’s friend” thought experiment, in which he notes that if the system of atom + decay detector + poison release mechanism + cat in-a-box can be in a superposition of states, so can the system of all of this + the person checking the box in the room containing the box. To collapse this ensemble of wave fuctions, a second person needs to visit and be told if the cat is dead or alive. But this 1 cat + 2 people system can itself be in superposition, so a third person is needed, and so on.

 

Wigner was trying to promote the idea that something mysterious – “consciousness” - is needed to collapse a wave function, by assuming the Schrödinger’s cat scenario is true, but the Wigner’s friend one isn’t, because humans have consciousness but cats don’t. These days I think people are skeptical of making speciesist distinctions like this, but the scenarios can be tweaked to have a simple mechanical cat in place of a flesh one, satisfying people’s intuition about what is and isn’t conscious.

 

A few people – highbrow science fiction writer Steven Baxter, in his 1992 novel Timelike Infinity, among them – ran a different direction with Wigner’s friend, taking seriously its need for an endless succession of observers to imply that reality only works if it has a God-like “supreme observer”, perhaps at the “omega point” end of time.

 

Others have suggested that ascribing some special quantum mechanical meaning to consciousness and observation is a kind of mysticism that should be avoided. Objective collapse theories, in which wave functions change in a mathematically consistent way when the number and kind of particles in a system becomes sufficiently large, are an example of this approach.

 

This is what I believe. Unfortunately, nobody has yet worked out the mathematics of such a theory in details. Whether an objective collapse theory is correct or not has a greater impact that determining definitively whether Schrödinger’s cat is true or not, because it could define how large a quantum computer could be – that is, the maximum number of quantum bits one could have. If this number is very low, quantum computers won’t be able to do the things people hope they will someday be able to, such as factor large numbers much more quickly than ordinary computers.

[Pmb]

I thought I'd again mention the fact that Schrodinger didn't mean for his experiment to be taken seriously. I can't quote anything since I can't paste so I suggest you look this up in Wikipedia under Schrodinger's cat. Search for the term "serious".

[CraigD]

I thought I'd again mention the fact that Schrodinger didn't mean for his experiment to be taken seriously.

I disagree slightly.

 

Quoting the Wikipedia article Schrodinger’s cat:

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics.

According to this view, Schrodinger did want his though experiment to be taken seriously, in order to provoke his 1935 contemporaries to consider the conflict between the Copenhagen interpretation of quantum mechanics and the their intuitive, common sense.

 

I think that in the last half of the 20th century, on-track quantum physicists and science-focused philosophers have reject the Copenhagen interpretation in favor expanding quantum mechanics to provide an theoretical explanation of decoherence (wavefunction collapse) rather than relying on an interpretation of the theory to explain it. Wikipedia categorizes such theories as quantum decoherence theories.

 

To me, the approach of creating interpretation of QM seems weaker than that of extending the theory itself, because it introduces informal, intuitive, even mystical ideas centered around concepts such as “observation” and “consciousness”.

 

I’m hopeful that the field of quantum computing will produce techniques and devices capable of experimentally confirming or refuting decoherence theories.

[Pmb]

I apologize. That's not what I meant by it not being taken seriously. What I meant was that the idea of a cat being in a superposition of two states, one where he's alive and the other where he's dead, was to Schrodinger "patent nonsense." I read this in Griffiths text and am assuming his knowledge of historical facts like this are better than mine. My comment about it not being meant to be taken seriously was from something Griffiths himself told me in an e-mail on the subject. I forgot exactly what I said so I sent him another e-mail.

[CraigD]

I apologize. That's not what I meant by it not being taken seriously. What I meant was that the idea of a cat being in a superposition of two states, one where he's alive and the other where he's dead, was to Schrodinger "patent nonsense."

I believe you’re right about Schrodinger opinions and motivation for his cat thought experiment.

 

However, I don’t think Schrodinger and like-minded 1930s physicists’ opinions were based on more than intuition. It would take a generation – about 30 years - before physicists began to build theory to replace these intuition, and by no means is there a consensus that these intuitions were correct.

 

As I said in my last post, I hope the near future will bring experiments that allow us ot settle a correct theory of quantum decoherence.