Quantum Superposition

[Luca72]

Can a mathematics/physics major or quantum physics enthusiast help me out here? I'm confused about some of the implications of Schrodingers' Cat and why superposition must exist.

I understand that in the thought experiment the cat has a 50% chance of dying or surviving, so for mathematical purposes, as long as it isn't being observed, it must be considered both a live and dead - in a superposition. So far so good.

The next part is what throws me off. The observer of the experiment opens the box to check on the state of the animal, and in that moment, determines whether it's alive or dead. Quantum physicists describe the observer as causing reality to "collapse into a single position". The cat goes from a state of alive AND dead to alive OR dead.

This is what I don't get - from the cats perspective, it's either alive or dead the whole time. Let's do another thought experiment - say the zombie apocalypse happens while a scientist is trying to carry out the Schrodingers' Cat experiment. The scientist activates the machine, but isn't able to open the box. Well, within that box, the cat, even though it is never "observed", is either alive or dead. Reality doesn't change just because an observer is or isn't present.

Many quantum physicists seem to be in agreement though that superposition is a very real phenomenon, and that's why you, for instance, can't predict where an electron is going to be within it's "cloud". We can predict where it's most likely to be, and what percentage of the time it'll be there, but can never actually determine its position. They say that in quantum physics, probability is not an approximation - it's how the universe actually behaves at a small level. If we had a better understanding of mathematics at the subatomic level though, wouldn't we be able to determine that an electron does have to actually be at ONE position at a given time? What I'm saying is that if an electron is in a position we'll call "A" at a given moment, but has a 20% chance to be at position "B" and an 80% chance to be at position "A", it's still, in reality, at position "A" right? Not at the superposition of A and B?

Any help you can give me is appreciated. I know these things must make sense at some level, and feel like I'm missing some basic point.

 

[FalloutJack]

This also has a philosophical edge, which is MY department.

The thing about physics versus philosophy or perception or even good old common sense is that they clash so extremely because there is so much that is fluid between them.

Science (even physics) suffers from - while being a defined state of being for whatever it is you're examining - having the problem of not knowing everything we have not tested. Everything outside of our experience is indeed guesswork and theory. Some damn GOOD theories, but only that much until proven. The speed of light use to be - without variation - a set amount of kilometers per second until some very clever light beam tests pointed out that their light was arriving back a TINY bit faster than it left. So, light is in constant acceleration. Tbe light-year is no longer an exact distance by a rough estimate pooled by the constant acceleration of light and any significant gravitational effect that can draw it here or there. That is why science is both brilliant and yet...limited.

Where science and proper measurements fail us, we have what we see and sense, as well as what we believe and what we think is right: The perception, the philosophy, and the common sense. All of these are good tools, but far from exact. The mind is not an accurate instrument and only shows us what is there and forces us to try figuring out what that actually was, processing it. It's very complex, but the fact that we DON'T know things off the top of our head is why we have studies and knowledge bases, established rules and rhetorics, a system. Philosophy is like theory and common sense is following instinct. I think sometimes we need more of that, only with the less quibbling and more the introspective capacity to wonder and consider.

ANYWAY, the thing with Schrodinger's Cat. What is the point? It is to demonstrate that we don't know things, and that there are things we can't find out objectively. Not about the cat specifically or a tree falling in the forest. We know perfectly well what that's all about. It's a case of the cat tired of being jammed in these damn boxes and the tree making a very agreeable thump. But...if a powerful star were to go supernova in an area with other black holes just as two galaxies were about to 'collide' with each other (It HAS happened.) and that a grand mayhem of planetary explosions were to happen in such a way that we couldn't even detect it with all our instruments...could you then begin to guess that the 'shrapnel' of such an occurrance - an asteroid - would be catapulted around three black holes past the speed of light and blast through our sun in the time it takes to blink...destabilizing it in a manner that ignites all of its gasses to end our existence?

Never would you have considered that such a Rube Goldberg set of circumstances could ever occur...until now. And that is the point.

 

[McMullen]

Science (even physics) suffers from - while being a defined state of being for whatever it is you're examining - having the problem of not knowing everything we have not tested. Everything outside of our experience is indeed guesswork and theory. Some damn GOOD theories, but only that much until proven. The speed of light use to be - without variation - a set amount of kilometers per second until some very clever light beam tests pointed out that their light was arriving back a TINY bit faster than it left. So, light is in constant acceleration. Tbe light-year is no longer an exact distance by a rough estimate pooled by the constant acceleration of light and any significant gravitational effect that can draw it here or there. That is why science is both brilliant and yet...limited.

Where did you hear that? The Gran Sasso anomaly was shown to be an error.

http://www.sciencedaily.com/releases/2012/06/120608152339.htm

Although it still supports your main point fairly well. Still, I think this is part of why it's unfortunate that people take preliminary results of experiments and run with them; it generates an enormous amount of confusion among the public about what the state of the science is.

 

[FalloutJack]

Science (even physics) suffers from - while being a defined state of being for whatever it is you're examining - having the problem of not knowing everything we have not tested. Everything outside of our experience is indeed guesswork and theory. Some damn GOOD theories, but only that much until proven. The speed of light use to be - without variation - a set amount of kilometers per second until some very clever light beam tests pointed out that their light was arriving back a TINY bit faster than it left. So, light is in constant acceleration. Tbe light-year is no longer an exact distance by a rough estimate pooled by the constant acceleration of light and any significant gravitational effect that can draw it here or there. That is why science is both brilliant and yet...limited.

Where did you hear that? The Gran Sasso anomaly was shown to be an error.

http://www.sciencedaily.com/releases/2012/06/120608152339.htm

Although it still supports your main point fairly well.

I'm sorry, but it was a long time ago, so I'm not entirely sure.

 

[Luca72]

snip

Excellent points, you're actually confirming some of my suspicions about the approach to quantum physics. I understand that science is not an absolute - it's based on observation, and the fact that observation comes from a human mind means there's only so much we can understand. Our theories don't describe the universe exactly the way it works, but as an approximation. Even mathematics at their purest are approximations used to describe the universe - if calculus could describe something infinitely small, we wouldn't need quantum physics to explain subatomic particles.

But my question is why quantum physicists make what seems like a huge logical leap - something in a superposition is, according to the math, inhabiting two states at once (or possibly several states in various parallel universes - bwuh?) even though in REALITY it has to be in one certain position. You mentioned the tree falling - it's the same thing. If a tree falls, and no one is around to hear it, it still displaces matter in the air as it falls, it still crushes whatever is under it, it still makes vibrations. Sound waves don't appear in the universe because someone is there to hear them.

So knowing that the mind is not a perfect instrument, why are quantum physicists basically saying that it is the observer that creates the reality we find ourselves in? Doesn't the reality permeate even if unobserved?

 

[Zeriphor]

If we had a better understanding of mathematics at the subatomic level though, wouldn't we be able to determine that an electron does have to actually be at ONE position at a given time? What I'm saying is that if an electron is in a position we'll call "A" at a given moment, but has a 20% chance to be at position "B" and an 80% chance to be at position "A", it's still, in reality, at position "A" right? Not at the superposition of A and B?

As far as I know, there are no deeper mathematics to determine that. The only way to know where the particle is is by collapsing the wave function. Please note that I'm not an expert, just trying to figure this out like you.

Worthwhile reading that I believe is related:
http://en.wikipedia.org/wiki/EPR_paradox
http://en.wikipedia.org/wiki/Bell%27s_theorem

 

[Zeriphor]

You mentioned the tree falling - it's the same thing. If a tree falls, and no one is around to hear it, it still displaces matter in the air as it falls, it still crushes whatever is under it, it still makes vibrations. Sound waves don't appear in the universe because someone is there to hear them.

Except it's not the same thing. You're trying to apply what you've learned about reality to subatomic particles, which use different rules.

 

[FalloutJack]

-Schrodinger's Quote Box-

Quantum mechanics is Dear God Complicated, probably why the most famous speaker for it is the man in the wheelchair who has nothing more to do most days than think extremely deeply on things. Still, the thing about any science that gets so high into things that you build theory on theory on theory and have immensely-extravagent rules to work with...you begin to understand that it's crossed the philosophy line. Math does that too sometimes, which is probably why a good number of famous philosophers have it so engrained in their education. Quantum mechanics is the way it is partially because of the uncertainty principle and because we don't know all of the rules. Out there, under the things we CAN see, there are fields of dark energy which...we dunno exactly what it's for. But it's there! We didn't even know for the longest time. The every-possibility thing synching into one phenomenon is just a measure of possibilities slipping down into the definite because it's not JUST the tree hitting the ground. WHAT does it hit? Will it roll after? Will a bird fly out of it at random? The things we do not know in quantum and in flux are not necessarily the things we predict, but in what ELSE is going on around that tree. It...may be trumped up more than necessary at this time, but there it is.

 

[Eclectic Dreck]

Therein lies the problem with the classic cat in a box thought experiment. It was not designed to demonstrate a fundamental truth of the universe but rather an an absurd example of why the theory of quantum superposition was flawed.

That's why the thought experiment tends to lead to the conclusion that the whole thing is a load of crap. The argument is, in essence, you put a cat in a box where you cannot observe it. You then do something to the cat that would certainly kill it (it doesn't matter what mechanism you choose - nerve gas, drowning, freezing, etc) but does not give any outward appearance that the cat is dead. Something terrible enough to ensure with absolute certainty that the entity known as a cat is dead (you could just wait 20 years without feeding it for example). To assert that one cannot be certain the cat is dead is an argument so very shaky that only philosophers would dare try to defend such a case (and indeed it is the philosophers who most commonly seem to cite the thought experiment).

It does work to express the notion of quantum superposition using easily understood terms though, even if it started it's life trying to do exactly the opposite.

 

[Dryk]

As Eclectic Dreck said Schrodinger's purpose behind the thought experiment was to make the whole thing seem silly, and it doesn't hold up. There are a number of observers within the system that ruin it for one including the cat itself and more importantly the detector used to trigger the release of the toxin.

 

[Redingold]

I believe that one of the main ideas used to to explain Schrodinger's cat is called decoherence, where interacting with another particle in any way causes the appearance of the collapse of the waveform and the conformation of reality to a particular probability. In the many-worlds interpretation, the different possibilities do not superpose, but instead take place in parallel universes.

 

[Navvan]

Therein lies the problem with the classic cat in a box thought experiment. It was not designed to demonstrate a fundamental truth of the universe but rather an an absurd example of why the theory of quantum superposition was flawed.

That's why the thought experiment tends to lead to the conclusion that the whole thing is a load of crap. The argument is, in essence, you put a cat in a box where you cannot observe it. You then do something to the cat that would certainly kill it (it doesn't matter what mechanism you choose - nerve gas, drowning, freezing, etc) but does not give any outward appearance that the cat is dead. Something terrible enough to ensure with absolute certainty that the entity known as a cat is dead (you could just wait 20 years without feeding it for example). To assert that one cannot be certain the cat is dead is an argument so very shaky that only philosophers would dare try to defend such a case (and indeed it is the philosophers who most commonly seem to cite the thought experiment).

It does work to express the notion of quantum superposition using easily understood terms though, even if it started it's life trying to do exactly the opposite.

Pretty much this except it does matter how you kill the cat. The method must tie into the superposition of states at an atomic level (Schrodinger used a radioactive isotope that triggered the release of poison if it where to split) or it means nothing in terms of demonstrating the absurdity of a complete superposition of states on a quantum level. The point is that position A on the quantum level means the cat is alive and position B on the quantum level means the cat is dead. Thus if you have a superposition of states A and B on the quantum level then you have a superposition of the cat being alive and dead.

 

[imnot]

My god, I came here excpecting a joyful romp through the land of science, now I just have a migrane.

 

[VoEC]

The problem with the Coppenhagen interpretation you mentioned here (and which is widely accepted) is the idea that the cat can "observe iteself" or that the "environment observes the cat".
I'm no scientist, even though I have quite a bit of experience with Schrödingers thought experiment, but what I think is that Schrödingers idea wasn't correct 100%.
What I think really would happen is that something (the cat, a photon, the geiger counter) would force the box content to collapse in some sort of state far prior to opening the box.
So while the superposition works fine on a quantum level for electrons and whatnot it can't really translate to the human scale.
In short: The geiger counter collapses the superposition while measuring it.

But that is the fundamental problem with the cat and the box. It was not conceived to somehow proove quantum theories. It's more like a philosophical idea to show how this is all very strange and stupid. Schrödinger himself said in the end that he regretted ever having anything to do with it.

 

[dvd_72]

While the shrodingers cat thought experiment was designed to show how absurd the idea of superposition is, from what we know that is actually how it works but only on the quantum level. The cat, and in fact any macro-physical system (made that term up) cannot maintain any meaningful superposition. The system will collapse into one of it's possible states.

In quantum mechanics we have an equation called the shrodinger equation. This equation strangely holds all the information of a particle in a quantum state and we only need to apply mathematical tools known as operators to extract this information. One of these operators is to square the psi value to gain the probability distribution. This, as the name would indicate, describes the probability for the particle at any point in space. This is how the maths as we have it works. Unless something changes in our knowledge of maths, or new knowledge comes forward this is how the world works at that level.

It is this probability distribution that allows for quantum tunneling to take place. The probability distribution is able to exist beyond a potential barrier and allows things like alpha radiation and the tunneling electron microscope to work. This is all strong evidence in favor of superposition. If the particle existed in exclusively in one place then phenomena like this likely couldn't happen.

Keep in mind though that the beauty of science is that with new evidence our understanding will change to adjust. I hope this helped clear up a little of your confusion. I'm always happy to exercise the knowledge I've gained in my physics course at uni.

 

[Luca72]

So it seems like superposition doesn't work at the macro scale (by macro I'm going to assume anything bigger than an atom), but Schrodingers' Cat is meant to illustrate how superposition works at the subatomic scale. My main point of contention was that at the macro scale it doesn't seem like there's an "event", like the presence of an observer, that causes the wave function to collapse - in the alive or dead sense of this example, the cat is either alive or dead, it's never "potentially both".

But when it comes to an electron, I instinctively want to believe the same rules of matter apply, but apparently they don't. Superposition is what allows for things like quantum tunnelling and entanglement right? Those are obviously things that wouldn't work under a Newtonian model, but have been observed at the subatomic level.

 

[Dami0]

My opinion on this;

The error you make when trying to comprehend quantum physics [for clarity I'll also refer to it as quantum "reality"] is you apply some definite sense of the right reality [a set of rules that stem from your beliefs] when comprehending the ramifications of a quantised world. For you life as we see is it whereas for me life is just a limiting case of a reality that cannot be defined unless two or more events are linked and a baseline is created to "ground" things in their state, eg. Money, [on it's own totally useless, but linked with gold which is in turn linked to...] is legal tender used as a standard in trade to assign value to things. To further expand on this metaphor, if you cannot assign monetary value to something [for argument's sake] it can hold any value possible.

My understanding of superposition is that it's kind of viewed from the other end up. If you were to start with a hypothetical case of an isolated particle from everything ever, it can be anywhere it wants because technically it's the only reference of position. Then you add another particle and suddenly a force is able to act on the other particle and vice versa [e.g. gravity, technically reaches out over infinite distance given infinite time]. This now creates a reference for both particles and they now have to be localised as opposed to permitted to be anywhere due to lack of constraints [think rowdy teenagers].

Does this even sort of make sense?

 

[Kordie]

Watch this, it should either help clear things up or make you more confused. Either way it's educational.
http://www.youtube.com/watch?v=DfPeprQ7oGc
Granted, it's not actually about schroedinger's cat but the double slit experiment that gave rise to the observation.

 

[IndomitableSam]

I'm just happy I followed to conversation and understood it. Until I got bored and stopped reading.

... Anyone want to discuss the benefits of Dewey versus Library of Congress? ... Anyone? No?

Yay science.

 

[Use_Imagination_here]

Schrodingers cat was an argument AGAINST quantum physics, not for it. Read the bloody wikipedia article.