Quantum Superposition And A Coin

[Agent Smith]

TL;DR Summary

Is a a coin like Schrodinger's cat?

Confetior ... I'm a layman with minimal physics background, but the most happening place in physics, going by media articles, seems to be Einstein's relativity and Max Planck et al's quantum physics.

I did a little reading on Schrodinger's cat and what I could gather is unless an observation is made the cat is both dead and alive. I'm also aware that quantum mechanics is probabilistic and I guess that's one of the ways how a feline can be "both dead and alive".

A coin is the paragon of probability and thought maybe quantum physics could be related somehow to the preliminaries of a game of cricket - the coin toss - that decides who bats first. So I flip a coin and don't observe it. Is the coin now "both dead and alive" i.e. is it both heads and tails until I look? Is there a correspondence between the coin and the cat with respect to the state it's in? Are both states a wave function (I don't know what this actually means, but I reckon it describes the 2 probabilities of the 2 states the cat can be in).

 

[Nugatory]

I did a little reading on Schrodinger's cat and what I could gather is unless an observation is made the cat is both dead and alive. I'm also aware that quantum mechanics is probabilistic and I guess that's one of the ways how a feline can be "both dead and alive".

You have been misled by what you've been reading - that's one of the most common misstatements in popular descriptions of quantum mechanics. Schrodinger invented this cat example to show that something was seriously wrong in the then current (almost a hundred years ago now!) understanding of quantum mechanics: the math said that the cat would somehow be both dead and alive, but of course the cat is one or the other and we just don't know which until we look.

So a tossed coin is analogous to Schrodinger's cat, but not in the sense that you're thinking. The cat is dead or alive but we don't know which until we look, the coin is heads or tails but we don't know which until we look, and neither has much to do with quantum mechanics or wave functions.

Two layman-friendly books that will be much more helpful than whatever you've been reading are:
- "Where does the weirdness go?" by David Lindley, explains how in subsequent decades physicists resolved the problem that Schrodinger had identified. You might also try googling for "quantum decoherence", but be aware that this will take you into some mathematical deep water fairly quickly.
- "Sneaking a look at God's cards" by Giancarlo Ghirardi includes a reasonably accurate presentation of what quantum mechanics really is.

Neither are a substitute for a real textbook, but they're about as good as you can get without several years of non-trivial math: linear algebra, complex analysis, multivariable calculus and differential equations.

 

[PeterDonis]

I did a little reading on Schrodinger's cat

What did you read?

what I could gather is unless an observation is made the cat is both dead and alive.

No, that's not correct. The cat itself has no definite state at all. It is entangled with the radioactive atom whose decay would trigger its death. Only the overall system of atom + cat has a definite state, but that state is an entangled quantum state and has no classical analogue.

Flipping a coin, unlike the Schrodinger's cat scenario, does not involve quantum entanglement and so it is not a good analogy to use.

We have many previous PF threads on Schrodinger's cat which can be found by using the PF search function. Looking at them might help. Also, if you have not read any textbooks on QM, I would strongly recommend taking the time to learn QM from one before even trying to understand the Schrodinger's cat scenario. That scenario is an "advanced" scenario that assumes you already have a good working understanding of QM. Its intended audience was never lay people with no background in QM.

 

[Agent Smith]

So I know a little probability, back from my high school days; basic statistics too.

Does the Schrodinger cat scenario involve superposition? What does that mean probabilistically? Does it mean, for instance, that P(Cat is alive) = 0.5 = P(Cat is dead). Is this probability combination what prompted Schrodinger to say "the cat is both dead and alive"? P(Cat is alive) = 0.5 = P(Cat is dead) is a probability distribution I'm familiar with (Bernoulli distribution, if I recall correctly).

Also, from a logical standpoint, the cat is both dead and alive is a contradiction. If this statement is logically equivalent to the corresponding math (Schrodinger?) equation then, we have a mathematical contradiction, like saying 1 = 0.

Before I forget, gracias for the heads up regarding advanced math. I hope you'll cut me some slack.

Regarding "flipping a coin is not a good analogy", firstly, all probability courses begin with computing probabilities for coin tosses and secondly, I recall reading that the universe itself has a wave function and while one may think one is not part of a quantum experiment, one actually is (the lab, you, the instrument, the particles are "entangled"). I hope this isn't quantum woo.

 

[PeterDonis]

Does the Schrodinger cat scenario involve superposition?

It involves entanglement. "Superposition" is not really the right term because it is basis dependent; in other words, it depends on how you choose to describe the state mathematically. "Entanglement" is basis independent; whether or not a state is entangled doesn't depend on how you choose to describe it mathematically.

Again, you really need to spend time learning QM from a textbook. Ordinary language is never a good tool for learning physics, but it's particularly bad for learning QM.

What does that mean probabilistically?

As Schrodinger specified his scenario, the box is opened when just enough time has passed for one half-life of the radioactive atom, which means the probability of the atom having decayed when the box is opened will be 1/2. Since the atom is entangled with the cat, that means the probability of the cat being dead when the box is opened is also 1/2.

However, those probabilities are specific to that particular specification of the scenario. There is no general statement that one can make about probabilities of entangled states that applies to all scenarios. You have to analyze each one individually.

from a logical standpoint

Logic is useless without a set of premises to start from. The set of premises in QM is very different from what you are used to. So unless you've taken the time to learn QM, any logical reasoning you do is going to be useless because you will be using the wrong premises.

the cat is both dead and alive

I have already said that this is not what QM says. So talking about it is irrelevant to this discussion.

gracias for the heads up regarding advanced math

It's not the math that's advanced in Schrodinger's cat. The math is basic linear algebra. What's advanced is the conceptual framework of QM. Schrodinger intended his scenario for people who are already very familiar with that framework and have used it to solve problems.

I recall reading

Where? Please give a reference.

the universe itself has a wave function and while one may think one is not part of a quantum experiment, one actually is (the lab, you, the instrument, the particles are "entangled"). I hope this isn't quantum woo.

It isn't "quantum woo", but trying to make sense of it is not going to work well without the background in QM that I keep advising you to get.

 

[Agent Smith]

It involves entanglement. "Superposition" is not really the right term because it is basis dependent; in other words, it depends on how you choose to describe the state mathematically. "Entanglement" is basis independent; whether or not a state is entangled doesn't depend on how you choose to describe it mathematically.

Again, you really need to spend time learning QM from a textbook. Ordinary language is never a good tool for learning physics, but it's particularly bad for learning QM.


As Schrodinger specified his scenario, the box is opened when just enough time has passed for one half-life of the radioactive atom, which means the probability of the atom having decayed when the box is opened will be 1/2. Since the atom is entangled with the cat, that means the probability of the cat being dead when the box is opened is also 1/2.

However, those probabilities are specific to that particular specification of the scenario. There is no general statement that one can make about probabilities of entangled states that applies to all scenarios. You have to analyze each one individually.


Logic is useless without a set of premises to start from. The set of premises in QM is very different from what you are used to. So unless you've taken the time to learn QM, any logical reasoning you do is going to be useless because you will be using the wrong premises.


I have already said that this is not what QM says. So talking about it is irrelevant to this discussion.


It's not the math that's advanced in Schrodinger's cat. The math is basic linear algebra. What's advanced is the conceptual framework of QM. Schrodinger intended his scenario for people who are already very familiar with that framework and have used it to solve problems.


Where? Please give a reference.


It isn't "quantum woo", but trying to make sense of it is not going to work well without the background in QM that I keep advising you to get.

Richard Feynman, I believe, said that if you understand quantum mechanics, you don't understand quantum mechanics. What conceptual framework are you referring to? It is my understanding that Schrodinger's point is QM is incomprehensible (thus the contradiction in the cat is both dead and alive).

Please note the prefix I chose for this post is B, for basic, which I take to mean beginner-level. I was happily surprised that what is a high-level forum for physics has this feature. Thank you.

 

[Agent Smith]

So P(Cat is dead) = 0.5. That means P(Cat is alive) = 0.5. This is superposition then?

 

[Nugatory]

So P(Cat is dead) = 0.5. That means P(Cat is alive) = 0.5. This is superposition then?

No. Superposition is a quantum phenomenon with no classical analog and which can only be described using mathematics, which is why I recommend the Ghirardi book.

 

[PeterDonis]

Richard Feynman, I believe, said that if you understand quantum mechanics, you don't understand quantum mechanics.

What he meant was that nobody has an intuitively satisfying explanation for why QM works the way it does. But Nature doesn't care about our intuitions. The fact that QM works is indisputable. And the reason we know it works is that there are plenty of people who do understand how to use it to make accurate predictions.

What conceptual framework are you referring to?

The conceptual framework you will have after you have learned QM from a textbook and learned how to make correct predictions using it.

It is my understanding that Schrodinger's point is QM is incomprehensible (thus the contradiction in the cat is both dead and alive).

Your understanding is wrong. Which is not surprising since you apparently have not learned QM from a textbook, nor have you apparently read Schrodinger's actual paper or any of the actual peer-reviewed literature that discusses it. If everything you think you know is from random pop science sources on the Internet, you should assume that everything you think you know is wrong.

Please note the prefix I chose for this post is B, for basic, which I take to mean beginner-level.

Yes, I see that. That's why I took the trouble to point out to you that the topic you have chosen is an advanced topic. Any discussion of it at the "B" level is going to be very limited.

 

[PeroK]

So P(Cat is dead) = 0.5. That means P(Cat is alive) = 0.5. This is superposition then?

QM doesn't work on classical probability. It works on complex probability amplitudes (as in complex numbers).

 

[pines-demon]

TL;DR Summary: Is a a coin like Schrodinger's cat?

Confetior ... I'm a layman with minimal physics background, but the most happening place in physics, going by media articles, seems to be Einstein's relativity and Max Planck et al's quantum physics.

I did a little reading on Schrodinger's cat and what I could gather is unless an observation is made the cat is both dead and alive. I'm also aware that quantum mechanics is probabilistic and I guess that's one of the ways how a feline can be "both dead and alive".

A coin is the paragon of probability and thought maybe quantum physics could be related somehow to the preliminaries of a game of cricket - the coin toss - that decides who bats first. So I flip a coin and don't observe it. Is the coin now "both dead and alive" i.e. is it both heads and tails until I look? Is there a correspondence between the coin and the cat with respect to the state it's in? Are both states a wave function (I don't know what this actually means, but I reckon it describes the 2 probabilities of the 2 states the cat can be in).

I think that your confusion is legitimate. Indeed if we consider just the results, the Schrödinger's cat scenario and the coin scenario behave the same. That's why colleagues here tell you that it is not a good way to understand quantum mechanics, the Schrödinger cat is more about microscopic-to-macroscopic issues (decoherence and so, that appear in more advanced topics).

The issue with Schrödinger's cat is that there are no (obvious) alternative basis to observe, you can only check if it is alive and dead but you cannot (easily) check if it is dead+alive. The Schrödinger's cat problem does not have any interference effect that make the wavy effects evident, and finally it does not have a (easily) discernable sub-system to consider entanglement effects. So in principle you cannot distinguish it from a coin flip. To better understand where the real differences in probability expectations are between classical and quantum, it is preferable to check the double slit experiment or Bell tests about entanglement.

 

[Agent Smith]

No. Superposition is a quantum phenomenon with no classical analog and which can only be described using mathematics, which is why I recommend the Ghirardi book.

I forgot to thank you for the book recommendation. Gracias.

 

[Agent Smith]

What he meant was that nobody has an intuitively satisfying explanation for why QM works the way it does. But Nature doesn't care about our intuitions. The fact that QM works is indisputable. And the reason we know it works is that there are plenty of people who do understand how to use it to make accurate predictions.

That's an insightful comment as far as I'm concerned. Arigato gozaimus.

The conceptual framework you will have after you have learned QM from a textbook and learned how to make correct predictions using it.

Cogito I understand that I either didn't understand or I misunderstood. QM was never meant for lay folks; it needs a good grasp of mathematical objects used therein.

Your understanding is wrong. Which is not surprising since you apparently have not learned QM from a textbook, nor have you apparently read Schrodinger's actual paper or any of the actual peer-reviewed literature that discusses it. If everything you think you know is from random pop science sources on the Internet, you should assume that everything you think you know is wrong.

Apologies for not having done my homework.

Yes, I see that. That's why I took the trouble to point out to you that the topic you have chosen is an advanced topic. Any discussion of it at the "B" level is going to be very limited.

I see. Bit off more than I can chew I suppose

Gracias. Do you have a book recommendation, one within 200 pages? Perhaps a website/articles?

 

[Agent Smith]

I think that your confusion is legitimate. Indeed if we consider just the results, the Schrödinger's cat scenario and the coin scenario behave the same. That's why colleagues here tell you that it is not a good way to understand quantum mechanics, the Schrödinger cat is more about microscopic-to-macroscopic issues (decoherence and so, that appear in more advanced topics).

The issue with Schrödinger's cat is that there are no (obvious) alternative basis to observe, you can only check if it is alive and dead but you cannot (easily) check if it is dead+alive. The Schrödinger's cat problem does not have any interference effect that make the wavy effects evident, and finally it does not have a (easily) discernable sub-system to consider entanglement effects. So in principle you cannot distinguish it from a coin flip. To better understand where the real differences in probability expectations are between classical and quantum, it is preferable to check the double slit experiment or Bell tests about entanglement.

So my confusion is natural, it's a feature of QM. With the coin, I "know" that after I flip it (I don't look at the result) it's either heads/tails, but "definitely" not both heads and tails. For Schrodinger's cat, there's a difference in that the cat is both dead and alive when we don't make the observation. Also @PeterDonis and @Nugatory have made it clear that there can't be classical analogs to quantum phenomena and therein lies the rub I suppose.

 

[PeterDonis]

Do you have a book recommendation, one within 200 pages?

No textbook on QM that I'm aware of is that short. For a textbook, I would recommend Ballentine, but it's more than three times that length.

For non-textbooks, @Nugatory's book recommendations are good ones.

 

[PeroK]

Gracias. Do you have a book recommendation, one within 200 pages? Perhaps a website/articles?

This is perhaps the most accessible serious treatment of QM.

http://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

 

[martinbn]

That's an insightful comment as far as I'm concerned. Arigato gozaimus.


Cogito I understand that I either didn't understand or I misunderstood. QM was never meant for lay folks; it needs a good grasp of mathematical objects used therein.

Apologies for not having done my homework.


I see. Bit off more than I can chew I suppose

Gracias. Do you have a book recommendation, one within 200 pages? Perhaps a website/articles?

You can read the first 200 pages of a textbook. That will cover a lot of quantum mechanics, about 200 pages worth.

 

[weirdoguy]

I would recommend Ballentine

Hm, I would say it's not a first read, rather second one. But brilliant one, if someone gets to that level.

How about Feynmans lectures? Third volume. I haven't seen any opinions on this particular one, only about Feynmans lectures as a whole. Which by the way are recommended for polish physics olimpiad, for high school students Interesting choice

 

[martinbn]

What about Mackey's book? It is less than 150 pages.

 

[pines-demon]

So my confusion is natural, it's a feature of QM. With the coin, I "know" that after I flip it (I don't look at the result) it's either heads/tails, but "definitely" not both heads and tails. For Schrodinger's cat, there's a difference in that the cat is both dead and alive when we don't make the observation. Also @PeterDonis and @Nugatory have made it clear that there can't be classical analogs to quantum phenomena and therein lies the rub I suppose.

"Is both dead and alive until we make the observation" is an interpretation, a way to talk about it. However the interpretation of quantum mechanics is an open problem. A way to say it without issues is "the cat is in a superposition of dead plus alive", but for that to have any meaning you need to check other examples of quantum mechanical systems.

The measurement probabilities of the standard Schrödinger's cat (no caveats of different basis measurements) are identical to the coin flip. So in principle, the experiment can be simulated/explained with a classical mechanism. However the thought experiment is not about that, but about the realization of the whole experiment.

To understand what a superposition and entanglement are, and to convince yourself that no classical analog can simulate those effects, you need to take a read at other quantum experiments.