/sci/ - Science & Math

[Anonymous No.5579959]

/b/ told me to come here.

I don't understand Schrodinger's cat. I know a little bit of cuantum mechanics but I don't get how the cat is dead AND alive at the same time.

Pls someone explain.

[Anonymous No.5579968]

>>5579959
According to the copenhagen interpretation of quantum mechanics, a particle is both decayed and undecayed until it is observed as being one or the other.

The notion of a cat being dead or alive both at the same time is absurd.

Therefore the Copenhagen interpretation is incorrect.

The cat is ONLY a thought experiment meant to disprove a particular model.

[Anonymous No.5579985]

>>5579959

People who don't know history are the ones who get gripes up by this.

It's like zenos paradoxes, the point isint a proof of anything in of itself, its to demonstrate how the existing model is nonsensical.

[Anonymous No.5579995]

>>5579959
Even though I'm not in college yet, I want to undestand it too.

[Anonymous No.5580065]

I'm not a physicist in any kind, but I think the answer is quite simple?

It's all based on decisions or events. In this case, only an event. 50% chance the event results in dead cat or alive cat.

Now, these are two things that can happen. We only see it as one line from A to B; cat goes in, we wait, outcome shows us what happened. But whatever happens, in a dimension above our understandings, this thing gets seen as:

Cat goes in, cat dies, we see dead cat

But, at the same time, in this dimension, this line from A to B can be rewinded and restarted from point A, but where B contains the result of an alive cat. These are all possibilities within this time range.

This time range is one of many billionsmillionstrillionsgazillions timeranges that were ever there, from creation of life until apocalypse.

We can only experience things in the third dimension, point A in time until point B in time. We can't go back. But imagine we could, then we can go back and forth constantly within time. We would master time.

[Anonymous No.5580069]

It doesn't disprove the Copenhagen interpretation at all. The Schrodinger's cat is just a thought experiment to demonstrate the idea of collapse with a macroscopic example. In this case there are only 2 states that the cat can be measured as:
<span class="math">\mid 1 \rangle : alive cat[/spoiler]
<span class="math">\mid 0 \rangle : dead dead[/spoiler]
The poison-hammer-isotope thing acts as an operator, say Ω, which turns the original alive cat state into a superposition of the two possible states. This could look like:
<span class="math">\omega\mid1\rangle=\frac{1}{\sqrt{2}} (\mid0\rangle+\mid1\rangle)[/spoiler]
Now since the cat can only be measured as one of those 2 states in the basis we have chosen (the alive-dead basis), the cat may only be measured to be alive or dead when we open the box, even though earlier the actual state was a superposition of both. This means the state COLLAPSES into one or the other with .5 probability as per the Copenhagen interpretation. This idea seems very bizarre classically, but in quantum mechanics, this is a ubiquitous occurrence that no physicist would really look twice at. A more realistic example would be, say, an electron orbiting a nucleus. There is a probability that it can be measured at each particular energy level, but in the end, the electron can only be measured to have ONE energy associated with it. You would have to say, then, that the electron's wavefunction in the energy basis is some superposition of every energy level the electron may reside in.

[Anonymous No.5580084]

It doesn't disprove the Copenhagen interpretation at all. The Schrodinger's cat is just a thought experiment to demonstrate the idea of collapse with a macroscopic example. In this case there are only 2 states that the cat can be measured as:
<span class="math">\mid 1 \rangle : alive\ cat[/spoiler]
<span class="math">\mid 0 \rangle : dead\ cat[/spoiler]
The poison-hammer-isotope thing acts as an operator, say Ω, which turns the original alive cat state into a superposition of the two possible states. This could look like:
<span class="math">\omega\mid1\rangle=\frac{1}{\sqrt{2}} (\mid0\rangle+\mid1\rangle)[/spoiler]
Now since the cat can only be measured as one of those 2 states in the basis we have chosen (the alive-dead basis), the cat may only be measured to be alive or dead when we open the box, even though earlier the actual state was a superposition of both. This means the state COLLAPSES into one or the other with .5 probability as per the Copenhagen interpretation. This idea seems very bizarre classically, but in quantum mechanics, this is a ubiquitous occurrence that no physicist would really look twice at. A more realistic example would be, say, an electron orbiting a nucleus. There is a probability that it can be measured at each particular energy level, but in the end, the electron can only be measured to have ONE energy associated with it. You would have to say, then, that the electron's wavefunction in the energy basis is some superposition of every energy level the electron may reside in.

[Anonymous No.5580098]

It doesn't disprove the Copenhagen interpretation at all. The Schrodinger's cat is just a thought experiment to demonstrate the idea of collapse with a macroscopic example. In this case there are only 2 states that the cat can be measured as:
<span class="math">\mid 1 \rangle : alive\ cat[/spoiler]
<span class="math">\mid 0 \rangle : dead\ cat[/spoiler]
The poison-hammer-isotope thing acts as an operator, say Ω, which turns the original alive cat state into a superposition of the two possible states. This could look like:
<span class="math">\OMEGA\mid1\rangle=\frac{1}{\sqrt{2}} (\mid0\rangle+\mid1\rangle)[/spoiler]
Now since the cat can only be measured as one of those 2 states in the basis we have chosen (the alive-dead basis), the cat may only be measured to be alive or dead when we open the box, even though earlier the actual state was a superposition of both. This means the state COLLAPSES into one or the other with .5 probability as per the Copenhagen interpretation. This idea seems very bizarre classically, but in quantum mechanics, this is a ubiquitous occurrence that no physicist would really look twice at. A more realistic example would be, say, an electron orbiting a nucleus. There is a probability that it can be measured at each particular energy level, but in the end, the electron can only be measured to have ONE energy associated with it. You would have to say, then, that the electron's wavefunction in the energy basis is some superposition of every energy level the electron may reside in.

[Anonymous No.5580099]

>>5580065
See

>>5579968
and
>>5579985

[Anonymous No.5580100]

>>5579968
we can see an electron at certain points, but not its trajectory, right?

idk if Im still on topic
but we can only see where it is, not wether it moves or not.

[Anonymous No.5580104]

It doesn't disprove the Copenhagen interpretation at all. The Schrodinger's cat is just a thought experiment to demonstrate the idea of collapse with a macroscopic example. In this case there are only 2 states that the cat can be measured as:
<span class="math">\mid 1 \rangle : alive\ cat[/spoiler]
<span class="math">\mid 0 \rangle : dead\ cat[/spoiler]
The poison-hammer-isotope thing acts as an operator, say Ω, which turns the original alive cat state into a superposition of the two possible states. This could look like:
<span class="math">\Omega\mid1\rangle=\frac{1}{\sqrt{2}} (\mid0\rangle+\mid1\rangle)[/spoiler]
Now since the cat can only be measured as one of those 2 states in the basis we have chosen (the alive-dead basis), the cat may only be measured to be alive or dead when we open the box, even though earlier the actual state was a superposition of both. This means the state COLLAPSES into one or the other with .5 probability as per the Copenhagen interpretation. This idea seems very bizarre classically, but in quantum mechanics, this is a ubiquitous occurrence that no physicist would really look twice at. A more realistic example would be, say, an electron orbiting a nucleus. There is a probability that it can be measured at each particular energy level, but in the end, the electron can only be measured to have ONE energy associated with it. You would have to say, then, that the electron's wavefunction in the energy basis is some superposition of every energy level the electron may reside in.

[Anonymous No.5580121]

Erwin Schrödinger: The present situation in quantum mechanics, 1935

...

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

[Anonymous No.5580137]

>>5580104
How does that work with the operators? I thought the eigenvalues are the things we can measure. But then dead and alive are not states but eigenvalues.

[Anonymous No.5580152]

>>5579959
>I don't get how the cat is dead AND alive at the same time.

Very simple:
the statement applies to the consideration of the state of the cat MATHEMATICALLY -- not in reality.
It is said that (mathematically) the cat must be considered as having both states, because it is truly uncertain, and one or the other must certainly be true.

But, further science revealed that for the subatomic particles that are the real center of the discussion (not large things like cats), the actual reality is that the particle has NEITHER state, until it is forced to exist from something outside (a necessity of physics).

[Anonymous No.5580165]

>>5580152
Can you write down the math? How does the hermitian operator of opening the box look like?

[Anonymous No.5580170]

>>5580165
>Can you write down the math? How does the hermitian operator of opening the box look like?

Don't be a smartass.
We're trying to help someone who DOES NOT understand the concept to understand it.
That calls for a summary description, not details of the tiniest nature that YOU are familiar with.

[Anonymous No.5580169]

>>5580137
You're both right and wrong. You can only measure the eigenvalues, but in the operator's eigenbasis, that eigenvalue must be associated with some eigenstate. In this case, the two eigenstates are |0> and |1>, so if we measure in the alive-dead basis, we will measure one of two eigenvalues, each of which is associated with one of those 2 eigenstates (alive or dead).

[Anonymous No.5580172]

>>5580169
What if an eigenvalue has eigenspace of dimension >1. How can we infer the state from the measurement then?

[Anonymous No.5580200]

>>5579959
Think about this. Flip a coin into the air. Now it's spinning and you don't know if it will fall with heads up or tails up. Until the coin completely falls you don't know which of them it will be.

The fact schrodinger didn't use the previous example to explain quantum shit is because he wanted an excuse to kill cats.

[Anonymous No.5580209]

>>5580170
Just because OP may be looking for a more simplified explanation, doesn't mean that he should be denied a more technical one.

>>5580165
To answer your question, the Hadamard transform is probably the simplest example. If the input in 2 dimensions is a |0> or |1> it outputs orthogonal superpositions of the 2 states that have equal probability of being mesured as either.
http://en.wikipedia.org/wiki/Hadamard_transform

>>5580172
I'm not quite sure what you're asking. An eigenvalue is defined to be a scalar, so it always has a dimension of 1. If you're talking about the operator, I have defined it to have a dimensionality of 2. If you're asking about degeneracy, where you may have the same eigenvalue repeated, then there are multiple eigenstates associated with the same eigenvalue. You won't really get to have a nice "Oh cool we found the state of the particle" but the eigenvalue is usually sufficient, and you just work with the fact that the state is now an eigenvector associated with it, which is generally sufficient.

[Anonymous No.5580225]

>>5580209
>You won't really get to have a nice "Oh cool we found the state of the particle" but the eigenvalue is usually sufficient

Can you give an example?

[Anonymous No.5580301]

>>5580225
Absolutely, if we go back to our electron in an atom example, multiple electrons may exist in a shell. Each shell is associated with a particular energy. So lets say we are in the second shell. We have only one energy, so H will be degenerate, and we only get one eigenvalue. As long as we stay in the energy basis, it doesn't matter WHICH eigenstate we're in, since the energy basis doesn't care (will make a bit more sense in a second). Of course, if you took chem, you'll know that there are subshells (s and p in this case) that define the angular momentum. So if you measure in THAT basis, you will still have degeneracy, but instead you get 2 eigenvalues associated with s and p subshells. If you measure in the spin basis, you get degeneracy with another 2 eigenvalues associated with spin up or down. Degeneracy just means there is additional information that is impertinent in the basis you're working in. In our example, if you're looking at energy, S and L^2 dont matter, but if you're looking at the angular momentum, E matters (some shells don't have p, d or f) but S doesn't. If you want a more textbook example rather than the explanation of the intuition behind it, I can break out my copy of R. Shankar but I think it's downstairs.

[Anonymous No.5580312]

>>5580301
Makes sense. Thanks.

[Anonymous No.5580341]

FUCK ALL OF YOU PLEBIAN SHEEP.

Schrodinger's cat was a thought experiment proving how absurd the idea is having something in 2 states at once. The point is, without total information we cannot know the state with 100% proability. It's as simple as that.

But you get all these sheep-/sci/entists and in other communities as well who try to impress others with there shit-tier knowledge by adding overly complex equations.

Most if not all theoretical physics is wrong. Did you know that?

It makes sense, because all it is is an extrapolation of statistical evidence lacking unknown variables.

Theoretical physics is useful because it has the capacity to give a general indication where experimentalists should look for further evidence. Once that evidence is found, adjustments are made to existing theories and models to account for the new discoveries.

It works just like numerical pharmacology. In theory you can have a viagra that makes your dick 20 times larger, but in practice the drug actually gives you stroke and kills you, and as a dead person you lose your capacity to grow the dick. All because you extrapolated and forgot about that one variable that was not apparent in the previous application but has become a serious factor now.

String theory is so far out there that it has no credibility anymore. It's more of a sport, or a religion. The church of super sudoku solvers, but they did a very smart thing; they covered all their bases with variables: "oh, you have discovered that this particle doesn't behave like anticipated? Well, that doesn't matter, we'll just plug it in here." To make use of string theory, you need to know everything there is to know about the universe. But at that point, you no longer need string theory, and until then, it is also useless.

Well, about as useful as the bible just being updated from old to newer testaments, from a scientific standpoint at least.

[Anonymous No.5580359]

Schroedinger's cat was originally designed to point out the absurdity of the Copenhagen interpretation. Yet, it failed in that task because the Copenhagen interpretation is still one of the most popular interpretations of QM.

The real answer is we don't actually know what's going on here. Someone needs to come up with an experiment to resolve the question of how to interpret quantum mechanics.

It doesn't make you smart to have an opinion on this. You are permitted to speculate and form conjecture though. Just don't pass it off as understanding or a physicist will call you on it.

[Anonymous No.5580393]

>>5580341
>Most if not all theoretical physics is wrong
>viagra that makes your dick 20 times larger
>String theory is so far out there that it has no credibility anymore

[Anonymous No.5580463]

>>5580359
That's not really true. Quantum mechanics is VERY well supported and we're probably more certain in its correctness than anything else in scientific history. It doesn't make sense with classical intuition at all, but what physicists have learned to accept is that the universe is NOT deterministic, and that we simply have to live by the rules of probability. Also, the copenhagen interpretation isn't just popular, it's correct. So is the many-worlds interpretation. The trick is to remember that neither exactly disproves the other. Sometimes you simply use the one that makes your current work more convenient at the time. Perhaps for modeling some atom trap experiment, using the copenhagen interpretation as an intuitive reference makes designing a good model easier, but for implementing Shor's algorithm on your new quantum computer from best buy you may want to think about the problem in terms of the multiple worlds interpretation.

[Anonymous No.5580489]

>>5580463
I didn't say anything about the correctness of QM. Nothing so far has challenged it's correctness. The issue is the interpretation. There are a number of interpretations of what quantum mechanics means. None of the interpretations admit testable predictions for the moment so there is no way to tell which interpretation is correct. So it is not possible to answer the question of what is real when it is not being observed.

[Anonymous No.5580653]

It's not "a cat" that's dead and alive at the same time.

It's a superposition of states (/worlds (/blobs of amplitude)), one of which describes a live cat and one of which describes a dead cat.

(There was just one amplitude blob, describing a live cat, until the cat-blob became entangled with the superposition of blobs describing a "state with a decayed particle" and a "state with a not-decayed particle")

[Anonymous No.5581092]

>>5580341
>Most if not all theoretical physics is wrong. Did you know that?

Everyone does.
Same issue as saying
'did you know half the working lawyers graduated in the BOTTOM HALF of their class?'

Theoretical physics is, by it's name, the UNVERIFIED stuff.
If it is verified, it simply isn't part of theoretical physics any more.

Therefore, whether 30%, 70% or 100% -- theoretical physics is about concepts, not validation.

[Anonymous No.5581097]

>>5580653
>(There was just one amplitude blob, describing a live cat, until the cat-blob became entangled with the superposition of blobs describing a "state with a decayed particle" and a "state with a not-decayed particle")

That was beautiful, in a really nasty-stupid kind of way.
Only the math nitwits are doing better at making this less clear.

[Anonymous No.5581161]

I layman's terms, because we cannot see the cat, we don't know if it has died or not. This means that until we open the box and look at the cat, both possibilities are equally likely.