/sci/ - Science & Math

[Anonymous No.4700383]

hi /sci/

why is schroedingers cat both dead and alive?

I never really got it.

[Anonymous No.4700390]

it was a trick. he had two cats

[Anonymous No.4700391]

That's the joke.

[Anonymous No.4700388]

It's not. It's a thought experiment meant to illustrate the retardedness of the copenhagen interpretation of quantum mechanics.

[Anonymous No.4700398]

In another telling of the schroedingers cat joke, he actually names his cat "alive" and then murders it making the statement schroedinger's cat is alive and dead a valid one.

[Anonymous No.4700450]

>>4700388
then come up with a better interpretation

[Anonymous No.4700454]

>>4700450
see >>4700390 pic related

[Richard Feynmann !Hwop/gspA. No.4700479]

his life is on paws

[Anonymous No.4700504]

>>4700383

The detachement of obversation creates the uncertainty of the existance of a particle.

[Anonymous No.4700505]

>>4700388
That it. Also, pic related.

[Anonymous No.4700550]

Schrödinger's cat is an analogy for the collapse of the wave function <span class="math">\Psi (\vec{r},t)[/spoiler].

While the cat is inside the sealed box which contains a killing device he automatically acquires two possible states, being dead and being alive. Upon observation, that is, by opening the box, the cat immediately assumes a state, i.e., he is either dead or alive, or in other words, the device either worked or didn't.

This thought experiment is used to explain the Copenhagen Interpretation of Quantum Mechanics in how "reality" (or the "physical world") is altered upon observation.

[Anonymous No.4700560]

>>4700550
so what if we in modern times conducted that same experiment with a wireless device attached to the cat to record it's heart beating.

Does that count as observing as well?
Doesn't the cat just die at a random time, or makes it out alive.

and does the cat resemble a photon in theory?

[Anonymous No.4700565]

>>4700550
by the way, are you admin?

because you use pictures in your comment
http://boards.4chan.org/jsMath/fonts/cmr10/alpha/120/char09.png

[Anonymous No.4700579]

>>4700390
And you break up the wavefunction into worlds this way and not some other way why?

[Anonymous No.4700604]

For those cats which will be found alive when the box is opened, weak measurement of their liveness will, on average, give the correct value, suggesting the cat was live or dead long before we performed a strong measurement by opening the box.

[Anonymous No.4700677]

One-liner time!

Schrödinger's cat walks into a bar. And doesn't.

[Anonymous No.4700708]

OP Read this.

This is wrong
>>4700388
and this comic is wrong
>>4700505

They state that the copenhagen interpretation is incorrect, and that is not true. In fact the copenhagen interpretation is THE MOST accepted explanation for the wavefunction collapse.


That being said, let me answer your question.
It is true that "the cat is BOTH dead and live" is WRONG.

That is not what the math tells us, if you actually look at what it is saying it is more accurate to state that:
"the cat is NEITHER dead nor alive".

To explain that let me use vectors.
If you have a vector going straight up you could say that it is a "vertical" vector right?
and if you have one going straight to the right then you could say that it is a "horizontal" vector right?
(let's define it that way)

Now, what if I have a vector at 45 degrees to the horizontal.
Is this vector BOTH vertical and horizontal at the same time?
No... That is stupid.. It is NEITHER, but it can still be DESCRIBED by using both right?
You can add vertical and horizontal components to equal the new vector which is neither.. but it can be described with both.
Understand the above point as it is important.


It's essentially the same thing with schrodinger's cat. We describe it's NEW state as a linear combination of "alive" and "dead"
but just like the 45 degree vector it is NOT BOTH, it is something else entirely, but it can simply be DESCRIBED by "alive" and "dead" states.

[Anonymous No.4700733]

>>4700708
That makes so much more sense than everything else I've ever heard.

I hope you're right and not just filling my head full of shit.

[Anonymous No.4700736]

>>4700733
the vector analogy is pretty spot on, it's conceptually not that different from what you do with abstract vectors in a Hilbert space.

[Anonymous No.4700739]

>>4700708
So the cat just IS

[Anonymous No.4700759]

>>4700708
It should be pointed out that for something as large as a cat, getting it into this neither-dead-nor-alive state is practically impossible. If you actually set up the experiment IRL, your best description of its state would be a mixed state represented by a density matrix. It's closer to "either" than to "neither" dead or alive, although "either" isn't quite right either. If dead and alive are vertically and horizontally polarized light, then rather than diagonally polarized light, you have unpolarized light. Of course the reason we have to describe it this way is the limitations of our knowledge, and one may reasonably suspect that the cat really is in some pure state (dead, alive, or neither) before you measure it, but that's just geusswork.

[Anonymous No.4700761]

>>4700733
that is how it works.

In fact I can show you the math, QM with dirac notation really isn't that complicated at all.

The way we would write the state of schrodinger's cat is the following:
<span class="math">|\psi\rangle=A|1\rangle+B|2\rangle[/spoiler]
where |1> and |2> correspond to the states "alive" and "dead".

The above is the "superposition" you always hear about. So the cats state is a superposition of "alive" and "dead" states.

Now... You tell me how to interpret it. but I'd like to point out that again with the 45 degree vector analogy, we would represent that vector as:
<span class="math">\vec{v}=A\hat{i}+B\hat{j}[/spoiler]
looks familiar doesn't it?
So you tell me.. do we say that this vector IS both of the other vectors? Or is it neither, but simply described by them?

Furthermore, the cat's state is NOT uncertain contrary to popular belief.. The cat is ALWAYS in a SINGLE DEFINITE state.
The only thing uncertain about it is how it will collapse.
So this just solidifies the fact that it is neither alive nor dead, it is a completely separate state. But just like vectors we can describe different states using a "basis" of states. (x, y, z for example) with schrodinger's cat our basis is (alive, dead).

[Anonymous No.4700776]

>>4700759
Also what he said ^^

It's actually better to just think of this in terms of electron spins or something.
Doing it with a cat is basically impossible because it's so large and what will happen will more than likely be closer to what you would expect from a classical (non quantum-mechanical) mindset.

[Anonymous No.4700786]

The Copenhagen Interpretation is flawed, because the observer and the act of measurement are treated classically. This is surely wrong: physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe, correct?

The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wave function, the Schrödinger equation, to observers and their apparatus. Nobody does this, they just look the other way and whistle as if it's not a problem.

[Anonymous No.4700795]

Uneducated here.

What does it mean when you say that a waveform "collapses?"

[Anonymous No.4700811]

>>4700786
>because the observer and the act of measurement are treated classically.
How so?

We actually don't have any way to treat the observer or act of measurement in QM at all.... So I don't know how you can say that.

All we do in QM is talk about probabilities for AFTER a measurement is made.

OR, if we really do have to deal with a measurement mathematically, we basically just erase the initial state and write down the result. It's really crappy to be honest, we don't have a formal way to show the wavefunction collapsing at all.

[Anonymous No.4700818]

>>4700677
back to le reddit time

[Anonymous No.4700821]

>>4700811
>act of measurement in QM at all

well, we sort of do
we let an operator act on a state
a bit unromantic, but eh

[Anonymous No.4700831]

>>4700761
>Furthermore, the cat's state is NOT uncertain contrary to popular belief.. The cat is ALWAYS in a SINGLE DEFINITE state.
No. Prior to the wave function collapse, the cat is in a superposed state.

[Anonymous No.4700836]

>>4700795
Basically you have a wavefunction denoted <span class="math">|\psi\rangle[/spoiler]

This contains all the information you need about the state of the system.
Now, when you come to make a measurement you apply to this state some observable <span class="math">\hat{O}[/spoiler]
and we act on the state:
<span class="math">\hat{O}|\psi\rangle[/spoiler]

Now, to do this mathematically we have to work in the basis of the observable, so that means we have to expand the wavefunction in terms of possible measured outcomes of the observable.. For example:
<span class="math">|\psi\rangle=A|1\rangle +B|2\rangle + C|3\rangle +.....[/spoiler]

Now when <span class="math">\hat{O}[/spoiler] is applied to any of it's basis vectors (the |1>, |2>, etc..) the result is that same state times the measured outcome.

But in real life when we measure something we only get one value right?
Do basically what happens is that <span class="math">|\psi\rangle[/spoiler] is said to "collapse" into ONLY ONE of the states.
So instead of the expansion we have above, after the measurement it can be:

<span class="math">|\psi\rangle=|1\rangle[/spoiler]
or
<span class="math">|\psi\rangle=|2\rangle[/spoiler]
etc... any of them.
So it collapsed you see?

How do we know which one it collapses to? We don't..
All we can say about it is the probability that it will land on one of them and the probability is given by the absolute square of the coefficient in the original expansion.

So the probability that it collapses to |1> is <span class="math">|A|^{2}[/spoiler]
and the probability that it is |2> is <span class="math">|B|^{2}[/spoiler]

[Anonymous No.4700839]

>>4700811
Observers/measurement devices are treated as if they were classical objects in the standard Copenhagen Interpretation, because otherwise how could they collapse a superposition of states?

Really, there's no need to think that anything collapses at all. We could well be in a gigantic superposition of all possible universes and we wouldn't know.

[Anonymous No.4700841]

>>4700831
but definite
no ifs or buts
Pure state or mixed state - doesn't matter.
The wavefunction it is in completely defines the quantum mechanical state. Unambiguously.

[Anonymous No.4700848]

>>4700836
I almost understood that.

I think I'll leave QM to the bright people.

[Anonymous No.4700850]

>>4700831
The Schrodinger's-cat state is a superposition (linear combination) of the live and dead cat states, but the live and dead cat states are both themselves superpositions of two Schrodinger's-cat states.

It's like saying a diagonal vector is a combination of up and down. While that's true, it's also true that up and down are each combinations of two diagonal vectors.

[Anonymous No.4700868]

>>4700841
A mixed state DOES represent ambiguity. But I suspect there is some terminology confusion here. The Schrodinger's-cat state <span class="math">\frac{1}{\sqrt2} \left(|1\rangle + |2\rangle\right)[/spoiler] is a PURE state. Anything you describe with a state vector or wavefunction is a pure state. For a mixed state, you have to use a density matrix/operator. An example of a mixed state is <span class="math">\frac12 \left(|1\rangle \langle1| + |2\rangle \langle2|\right)[/spoiler] (what you would actually get if you did it with a real-life cat, because cats are huge macroscopic systems we don't understand the details of).

[Anonymous No.4700883]

>>4700841
>>4700850
OK, it's a matter of wording. I considered "single definite state" as one of the two final states, either |dead> or |alive>.

[Anonymous No.4700895]

De Broglie Bohm fag here. The cat is always either dead or alive, and there is no wavefunction collapse.

[Anonymous No.4700915]

>>4700895
>De Broglie Bohm fag here
HAHA, first learn2 lorentz covariance