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Schrodinger's Cat


               
2012 Jan 5, 5:04am   35,637 views  68 comments

by marcus   follow (7)  

In this famous thought experiment, which could actually be done, someone might say, "well, since by definition, we don't know whether the cat is alive or dead, the statement that the cat is alive is by definition false."

True, it is false in the sense that we can not know that it's alive. Therefore the statement that it's alive is false.

What might be easy to miss though, by someone who is only parroting this argument and using it in a fallacious way, is that the exact same reasoning can be made regarding someone who says the cat is dead.

That statement is also false.

We just don't know.

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1   Vicente   @   2012 Jan 5, 6:45am  

The cat was just a thought experiment to illustrate quantum entanglement.

Too many people try to apply this to our real world and make sense of it when they should not.

That damn cat is dead, I opened the box and force-fed it the cyanide.

2   marcus   @   2012 Jan 5, 6:55am  

IT's useful in this case for spelling out a simple logical fact to some who otherwise for whatever reason might not be able grasp it.

You're thinking of the Heisenberg uncertainty principle and specifically the concept that the observer affects the observed. While it's true in some ways maybe, that is what people are talking about when they say QM inferences about particle physics don't apply at our gross level.

MY example here is just a very simple easy to understand point about logic, and the aliveness of the cat, and was meant to be 100% independent of any connection to particle physics.

3   Vicente   @   2012 Jan 5, 7:01am  

Haha, good luck with that. 99% of humanity is perfectly comfortable with a head full of paradoxes. They don't care to reconcile anything as long as most of it gets them through the day alive.

4   marcus   @   2012 Jan 5, 7:08am  

MAybe I should have stuck to the thread. In another thread Dan said.

Dan8267 says

First, one does not need to prove something that cannot be disproven by definition. Anything that cannot be disproven by definition is false.

Worded awkwardly, but I'm pretty sure he is using some fallacious reasoning that I attempt to dispel above in as simple and clear a way as possible.

Meanwhile, you're right.

5   Dan8267   @   2012 Jan 6, 2:22am  

http://www.HCOE__N6v4o


I don't even own a cat!

Ah, Schrödinger's Cat, the most misinterpreted experiment, thought or otherwise, in the history of the world. This is quite ironic since Erwin Schrödinger made up this experiment to demonstrate how confusing and misleading some fancier interpretations of quantum mechanics are. Schrödinger's concern was that the general public would misinterpret quantum mechanics to be some kind of voodoo magic, and then the general public completely misinterpreted his thought experiment.

All right, I will try to clarify this subject matter. First off, mechanics is the study of basic physical properties like energy, mass, and how bodies behave when subjected to forces. Mechanics includes studying things like tools (levers, pulleys), friction, and acceleration of bodies including orbits. Quantum mechanics studies similar things as they apply to the very small in size and mass, for example, atoms, protons, electrons, etc.

Ok, now imagine that for a course in mechanics you wanted to measure the temperature of a bucket of ice water. Now, of course, we all know that the temperature of a bucket of ice water at atmospheric pressure is, by definition, 0 degrees Celsius. So we expect our thermometer to read zero when we take the temperature.

But let's say the thermometer we use is an industrial strength thermometer designed to measure the temperature of molten iron. We take the thermometer out of a vat of molten iron and stick it into our small bucket of ice water. Immediately, the water begins to steam and the ice melts and evaporates. We're left with a partially melted bucked containing no water or ice by the time the thermometer settles on a temperature. We read the temperature as 200 degrees Celsius and conclude that an ice water mixture has that temperature. Good science, right?

Well, no. You see, we fucked up. We forgot that "for every action, there is an equal and opposite reaction" and what that means. Well, for one thing, it means that any thermometer we use, any at all, will itself have a temperature and some heat. Normally, we can easily discard the effect on temperature that the thermometer will have on what it's measuring the temperature of. We can normally discard this effect because it is utterly insignificant.

However, in our faulty experiment, we took a thermometer whose temperature and heat content were "big" relative to the temperature and heat content of the thing it was measuring. As a result, the temperature had a comically large effect on the object it was trying to measure a property of. Of course, common sense would keep us from doing something so ridiculous in the real world.

So, what does this have to do with quantum mechanics? Well, everything in quantum mechanics is small, damn small. In fact, quantum mechanics deals with the very smallest things in the universe. That's kind of the whole point of quantum mechanics. And since we're dealing with the very smallest objects in the universe, any thermometer we use will be "big" relative to the thing it's measuring.

And wait, that's not all. It's not just thermometers that cause a problem. Any device at all which measures any physical property (location, speed, electric potential, mass, anything) will have a significant effect on that object. We can't even measure the kinetic energy of an electron without significantly affecting the electron.

Fortunately, there is a simple equation that describes how much error our attempts to measure something will introduce. It's called the Heisenberg Uncertainty Principle and it calculates a maximum error in the same way that your calculator uses Taylor Series Approximations to calculate sins and cosines and the upper limit on the error of these approximations. Ah, brings me back to high school calculus.

So the practical side is that in quantum mechanics, you can indeed make the same kinds of measurements that you do in macro-mechanics -- you know, high school physics -- except that in quantum mechanics you have to keep track of the upper limit of error (or uncertainty) in all your calculations because this uncertainty is significant since you're dealing with really small things.

Well, that doesn't sound too bad. It's pretty pedestrian. Hardly seems relevant to the discussion of god or anything mythical. It sounds down right mundane. Enter the people with overactive imaginations…

One of the practical consequences of the uncertainty of quantum mechanics is that you don't know when some particular unstable atom is going to fission itself into a more stable configuration by performing radioactive decay. This is why we talk about the half-life of various isotopes of elements. We don't know when each particular atom is going to decay, but we know that statistically and predictably half of the atoms in a sample will decay in time T. So we call that time the half-life.

Now we're getting close to Schrödinger's thought experiment, so bear with me -- or, if you prefer, bare with me, I won't mind.

First, let me clarify that The Theory of Quantum Mechanics is a very successful theory that has with great precision been verified. It is both a theory and a fact just like evolution and gravity. Theory does not mean "guess". Quantum Mechanics has also proven to be extremely useful in practical matters such as computing, encryption, fuel efficiency, etc. It is a well-established theory that has already bore much economic fruit.

That said, we are dealing with the forefront of scientific understanding. And at that forefront is always brain-storming, imagination, and conjectures. There is nothing wrong with that as long as you can distinguish between "what might be allowed by our theory" and "what we know to be true according to the theory". These are two entirely different things. For example, Einstein's Theory of Relativity predicted black holes and we now know these to exist. Relativity also allows, in that it doesn't out-right prevent the existence of, wormholes. Now wormholes might exist, or they might not. Maybe we'll even expand Relativity to the point where we either prove the necessity of wormholes or the impossibility of wormholes, but that hasn't happened yet. Wormholes are just a conjecture, not something we know for sure exists.

Having clarified that, I will let you know what led Schrödinger to come up with his experiment. Yes, it all ties together.

A very bright and successful physicist, Niels Bohr, was dealing with the troubles that uncertainty introduces in physics -- yes, I'm dumbing this down, but I'll link to a more detail discussion. To deal with these problems, Bohr developed the Copenhagen Interpretation of Quantum Mechanics which is a kind of paradigm for dealing with the counter-intuitive world of quantum mechanics -- quantum mechanics is counter-intuitive because our intuition evolved to deal with problems on our scale and not the scale of the very small. The link above goes into more detail, but the important idea to understand for this discussion is that the Copenhagen Interpretation is not the Theory of Quantum Mechanics, but rather a mindset used to deal with quantum mechanics.

Side Note. Copenhagen is not the name of some long dead physicist. Copenhagen is the capital of Denmark and a city in which a lot of physics including the early works on quantum mechanics took place. In fact, the Niels Bohr's Institute for Theoretical Physics is located at the University of Copenhagen.

So, once again I need to simply things as much as I can without distorting their meanings. One of the most direct consequences of the Copenhagen Interpretation is the philosophical principle that a property of an object (say velocity) has every possible value until it is observed. This is different from the Uncertainty Principle which only says we cannot measure properties without affecting them and other properties and thus introducing an error or uncertainty.

Some people, including Schrödinger, had objections to this philosophical interpretation of a physical theory. So Schrödinger devised the following thought experiment to demonstrate the "silliness" of the Copenhagen Interpretation. The Schrödinger Cat experiment is actually a standard argument form (I forget the name) in which you get the proposer of an idea to reject a necessary (even if extreme) consequence of the idea and in doing so discredit the idea. As readers know, I do this all the time.

Schrödinger's Cat Thought Experiment (kids, don't try this at home)
1. Get a box, a cat, some poison, a hammer, a radiation detector, some scrap electronics, and one radioactive atom.
2. Put the cat in the box with a vial of poison and the radioactive atom.
3. Set up the sensor to detect the radioactive decay of the atom and to use the hammer to break the vial when the decay happens. The poison will be released and the cat will die.

The whole purpose of this experiment is to reject the Copenhagen Interpretation by showing that its consequences are ridiculous. Unfortunately, the Copenhagen Interpretation deals with quantum mechanics and everything in quantum mechanics is ridiculous -- true, yes, but ridiculous nonetheless. So, Schrödinger had the brilliant idea to transform the quantum uncertainty into macro-uncertainty.

Remember, that the Uncertainty Principle says that we can't know when or even if the particular unstable atom in our box will decay. The Copenhagen Interpretation says that means the atom is both in a decayed and not decayed state (the only two possible states in our case) until it is observed. Well, as long as we keep the box closed, we're not observing anything. But if the atom is both decayed and not, then the sensor has both gone off and not have gone off. So the poison has both been released and has not been released. So the cat is both dead and alive, but not in the good zombie way.

Well, no one is going to accept that the cat is both alive and dead until we open the box and then it spontaneously and randomly assumes one and only one of those two states. So clearly the Copenhagen Interpretation is wrong.

But wait, the advocates of the Copenhagen Interpretation rebut. The interpretation merely says the event must be observed, not necessarily by humans. So, the cat is either dead or alive because the non-sentient sensor observed the event. No problem. You can't trigger the poison to be released without observing the event and that collapses the wave function -- I'm dumbing things down, but that's the basic point they make.

Fair enough, but everything is always being observed if you include every non-sentient particle in the universe. You are constantly reacting with photons, electrons, and atoms. So if our sensor is enough to render the Copenhagen Interpretation impotent, then wouldn't the mere presence of all the stuff in the universe in effect always render the Copenhagen Interpretation mute?

Put simply, the idea that uncertainly means that a property takes on all possible values simultaneously is utterly meaningless if you also add that once that property has any effect on the universe it is no longer "all possible values" but some particular value. What have you really added to the understanding of quantum mechanics? What phenomenon are you explaining? What would be the difference between a universe in which the Copenhagen Interpretation operated and one in which it didn't? The answer: nothing.

I hope this explains the Schrödinger's Cat experiment and why that thought experiment does not mean "a god that is undefinable might exist" or "a statement that is unprovable by design can be true". What the Schrödinger's Cat experiment demonstrates is that just because we don't know what the value of a property is, doesn't mean the property takes on all possible values. And please, don’t misinterpret the experiment as so many do as believing that the cat really is both dead and alive. That is not the right answer.

6   marcus   @   2012 Jan 6, 2:41am  

Dan8267 says

And please, don’t misinterpret the experiment as so many do as believing that the cat really is both dead and alive. That is not the right answer.

Gawlleee Dan, your smart. Nice job trying to obfuscate my point.

I said very explicitly my point had nothing to do with particle physics.

Even here when I make a point about logic that any smart 10 year old can understand, Dan doesn't even try to understand my incredibly simple point. Instead, he launches in to an effort to show us all how smart he is.

Here:

You are right. If we take the fact that we can not know whether there is a God as an axiom,

Then the statement God exists is false.

My point:

The statement God does not exist is equally false.

My apologies if I didn't make that clear enough. Also my apologies for thinking that this simple and elegant thought experiment might be used to illustrate a logical point outside of the quantum mechanics context it's known for. I'm such a fool sometimes.

7   marcus   @   2012 Jan 6, 2:48am  

I will admit his response was predictable, but not what I was hoping for. Next prediction: My New "Enlightened Atheist" Thread which is meant to be appreciated in it's entirety will be broken apart in a statement by statement, phrase by phrase, Shrek like manner, probably before he even reads the whole thing.

8   Dan8267   @   2012 Jan 6, 5:25am  

marcus says

Nice job trying to obfuscate my point.

To even suggest that I attempted to obfuscate your point or anyone else's is clearly disingenuous. Frankly, I would have thought by now, Marcus, that you would have at least understood the basic philosophy of men like me. We believe that no lies or trickery are necessary to defend the truth and nothing false is worth defending. It therefore goes against our core beings to obfuscate any opposing idea, make any straw man arguments, or use any deception of any kind to make a point (unless, of course, we then reveal the deception to demonstrate a greater truth).

You just don't get it, Marcus. For me, it's not about being right. It's about what is right.

If an opponent were to show me that I was wrong about an idea, I would then immediately correct my worldview to correct the mistake. By my standard, I win any debate which ends with me saying, "You're right. I was wrong.". After all, I come out of such a debate more knowledgeable than I went in. You really don't understand that, do you?

marcus says

I said very explicitly my point had nothing to do with particle physics.

And that has nothing to do with my reply.

marcus says

Even here when I make a point about logic that any smart 10 year old can understand, Dan doesn't even try to understand my incredibly simple point.

I'd like to put that hypothesis to the test, but I get to design the experiment.

marcus says

Instead, he launches in to an effort to show us all how smart he is.

I don't consider myself smart. I consider other people dumb. In my head, you all should know the stuff I discuss simply on the basis of graduating from high school.

Nevertheless, your misinterpretation of my posting says far more about you and your insecurities than it does about me. I merely explained as clearly, concisely, and completely as I could what Schrödinger's thought experiment means and the background on why it was created. You were supposed to come out of this experience with a better understanding of what quantum mechanics is, what the Uncertainty Principle says, how the Copenhagen Interpretation differs from the Uncertainty Principle, and what Schrödinger was trying to convey. I have no idea why you would interpret that as intellectual bragging, especially when none of these things have anything to do with me personally. If I pointed out that someone's proof that the square root of two is rational is incorrect and provided the correct proof that it was irrational, would you call that bragging, too?

marcus says

If we take the fact that we can not know whether there is a God as an axiom,

Then the statement God exists is false.

My point:

The statement God does not exist is equally false.

My apologies if I didn't make that clear enough.

I hate to break this to you, but you're still not being clear. The statement "We cannot know whether or not X exists." cannot be an axiom regardless of what you substitute for X. Perhaps it could be a conclusion, but as a premise it makes no sense. The best you could do is make it an assumption, but assumptions can be incorrect. Allow me to demonstrate.

We cannot know whether or not lunar water exists.

Wait, we could crash a spacecraft and see if we detect any water vapor. And, in fact, that's what NASA did. And even if it were not technologically possible, the assumption itself would have either been correct or incorrect. So, your conclusion is still wrong.

Perhaps the whole English language thing is tripping you up. I suggest using the language of mathematics to demonstrate your point. Math was made to precisely to discuss such issues. Might I suggest Finite Model Theory and First-Order Predicate Logic? The precise nature of that language leaves no room for bullshit or inconclusiveness about the correctness of a logical argument.

Do be aware, though, that I do this shit for a living. Why just today I wrote a recursive stored procedure in TSQL, Microsoft's implementation of the Structured Query Language, and SQL is just sugar-coated first order predicate logic. The sproc does content composition through macro expansion allowing you to plug in different content independent of its structure. Here's a taste of what real, hard-core logic looks like. So if you can't handle the stuff below, don't be surprise that you can't beat me at logic.

marcus says

I will admit his response was predictable

Of course, you clearly wrote this thread in response to another one in which we were discussing metaphysics. I would be disappointed in you if you didn't only anticipate my replying to the thread, but in fact were counting on it.

marcus says

but not what I was hoping for. Next prediction

Sorry to disappoint, but I really don't know what you were hoping for. I'd likely be willing to oblige though as long as doing so doesn't involve deception.

marcus says

Next prediction: My New "Enlightened Atheist" Thread which is meant to be appreciated in it's entirety will be broken apart in a statement by statement, phrase by phrase,

Of course, I always do you the favor of being systematic and precise in addressing each statement in your logical sequence no matter how misguided that sequence is. The corrections I give to you are always specific, just like what your math teachers used to do.

marcus says

Shrek like manner

Nothing I do is Shrek-like in manner, a point even Shrek himself would agree with. Just take a look at some of the Shrek/Dan arguments. I've trounced him far worse than you. I do not discriminate based on political views. Bad logic is bad logic regardless of its conclusion.

marcus says

probably before he even reads the whole thing.

Actually, I do tend to read all your entire posting before tearing it apart. However, for clarity I follow the argument line by line rather than jumping around randomly. Also, it is not necessary to read an entire mathematical proof before pointing out where it is wrong. A proof is a very sequential thing by nature. As soon as you come across the first incorrect statement, you can discard the proof in its entirety. A single mistake kills a proof. If you don't believe me, ask one of your old math teachers.

Marcus, don't take it personally. I'm not picking on you. I hate for any bad idea to spread and do my part to snuff them out no matter where they come from. If you look at the totality of my postings, you'll see that I tear down bad arguments from both the left and the right. I even tear down arguments in favor of my own conclusions if those arguments are flawed. Reaching the right answer for the wrong reason is also bad.

9   uomo_senza_nome   @   2012 Jan 6, 6:30am  

marcus says

If we take the fact that we can not know whether there is a God as an axiom

If I may help you marcus -- the starting point on any of these discussions has to be 'let us define God'.

For most people (as the Genius George Carlin rightly observed), God means 'Old man in the sky'. This definition is obviously false and delusional. Dangerous too, as we fight wars based on delusions.

Dan's point is: Take all the definitions of God ever existed (as stated by humans over the course of human history). They should be subject to scientific scrutiny as much as anything else. This scrutiny is the best method we've had so far to eliminate BS and get to the truth.

marcus says

Then the statement God exists is false.

My point:

The statement God does not exist is equally false.

You haven't even defined what God is. Is God Schrodinger's cat? Is it something else?

I think atheism by definition has the ability to doubt and be skeptical about anything.

Could there be a definition of God that we're not aware of that may come up in the future? Sure, but that definition is subject to the same scrutiny as everything else.

http://www.YltEym9H0x4

"I find it much more interesting not knowing" - Feynman

Being comfortable with the unknown is a foundational aspect of science. Because as Feynman says, we're trying to find out.

10   Truthplease   @   2012 Jan 6, 9:22am  

Dan, if you just sat down and wrote that out yourself, then you must be a very good teacher or professor. I understood the information completely.

11   Dan8267   @   2012 Jan 6, 9:43am  

Truthplease says

Dan, if you just sat down and wrote that out yourself, then you must be a very good teacher or professor. I understood the information completely.

I'm not a teacher, but I have been accused of thinking like a mathematician.

I did just sit down and cranked out the explanation of Schrödinger's Cat, but I could do that because I have read a lot about physics. And I've read a lot about physics because I find it very interesting. It's amazing how much curiosity can motivate a person to learn about a subject, but you have to be curious.

The more you're curious, the more you learn, the more you understand, and the better you can explain a subject matter. In this respect, curiosity is more important than intelligence.

Still, it's great to hear that my explanation was indeed clear. I was afraid that I was omitting too many details about a rather complex and deep subject matter.

12   marcus   @   2012 Jan 6, 5:00pm  

Dan8267 says

I hate to break this to you, but you're still not being clear. The statement "We cannot know whether or not X exists." cannot be an axiom regardless of what you substitute for X. Perhaps it could be a conclusion, but as a premise it makes no sense. The best you could do is make it an assumption, but assumptions can be incorrect. Allow me to demonstrate.

Of course we can make that an axiom, if we agree to, and if you knew what an axiom is. Note my use of the word "if"(in "If we take the fact that we can not know whether there is a God as an axiom"). You can of course say that you reject that as an axiom, that is that for the purposes of our discussion you will not accept it as an axiom.

But yes, of course it could be used as a starting point (if we agree (again that's why I said "if"))from which a logical argument can be built. Yes, it is basically an assumption. This is what an axiom is - something you assume to be true (something that can not be proven true, but which seems to obviously be true) to be used as a starting point, for building other provable truths which use the axioms as their basis.

Okay. I have given up before, and I will again. Should have stuck with my instincts. The funny thing, and what makes me not want to even participate in this forum anymore, is that I doubt there is anyone reading this that even comprehends how full of it (and yourself) you are. Well, God only knows they must see the latter.

I've rarely in my life (an I'm an old man compared to you) witnessed such trollish and adolescent like arrogance. I said before that I thought you are a teenager or perhaps in college. I really hope, for your sake, that you are.

13   Dan8267   @   2012 Jan 7, 5:14am  

marcus says

I've rarely in my life (an I'm an old man compared to you) witnessed such trollish and adolescent like arrogance.

You haven't been around the block if I'm the worst thing you've ever encountered. Marcus, just admit that you suck at reasoning and try to find something else that you might be good at, like being a grumpy old man.

I've actually tried to enlighten you by showing you precisely where your logic fails and how to correct it. A mature adult would have welcome that help. Instead you throw these little tantrums and get all emotional like a 6-year-old.

Luckily, any objective person reading the various threads on patrick.net will clearly see that your illogical rambles are well refuted by the more rational of us. So, although I have failed to bring you up to the level of adult conversation, I believe my responses may have saved countless others from taking the descent into your lavatory of misreasoning and blatant falsehoods. And I count that as a victory.

marcus says

I said before that I thought you are a teenager or perhaps in college.

No, but I do date college-age women.

14   TPB   @   2012 Jan 7, 5:52am  

Quantum Mechanics are not real, it only acts to serve as an abstract thought compiler. With out Quantum Mechanics, thought processes that would otherwise be gobbledygook can be placed in context parsed and compiled. You get micro processors the size of a flake of dandruff, but no where in Quantum Mechanics is there a blueprint for such technology. It only served as an abstract modeler.

Much like religion has kept mankind from flogging its self into oblivion, with a fetid bacterial tainted morning star. It creates a moral boundary, a frame work that says such atrocities are wrong. Unless of course you are doing it in the name of God.

15   marcus   @   2012 Jan 10, 9:23am  

Obviously it was a mistake for me to use Schrodengers Cat for my simple point. And I think that I already apologized for using it totally out of any particle physics context.

It is true that there are different types of logic. But if we say that a statement has to be either true or false, and if we assume that we can not know with certainty whether God exists , then if someone says "God exists" that is indeed a false statement. Likewise if someone says "God does not exist," that is a false statement.

Some would limit their definition of God so as to say that it is such an outlandish possibility, that they can deny it out of hand, and that this is logical. Just as it would be logical to deny that there are tiny living unicorns in the clouds (without proving it).

But this denies that that there are many definitions of God, some which are relatively sophisticated and subtle and or vague, or even intentionally somewhat undefined. I think it can reasonably be argued that since a majority of humans believe in God in some way, including millions of humans that are more intelligent than any atheist reading this, it is therefore questionable to equate belief in God as being as out there as belief in unicorns in the clouds or leprechauns.

If you still don't get the context of my point or what I was responding to, at this point I'll let it go. Basically I was arguing with someone who had no intention of understanding my point of view and truly responding to it, which interestingly, for some people is a good substitute for an argument. I'll admit, as a trolling tactic it is very effective (see Shrek).

I'm not going to do this anymore:

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