# Quantum mechanics simple?

1. Apr 3, 2013

### capcom1983

I only just started my foray into QM and alot I've read about it seems relativly simple to understand. I'm not being egotistical but it seems the answer are to use laymans term common sense. Take shroedingers cat, the cat has only two states alive or dead. It can be both because to say it is one or he other could be wrong and to say is neither is completly worng.

2. Apr 3, 2013

### kith

Quantum mechanics does not defy logic and makes very accurate predictions. Things get only difficult if you try to connect QM with your classical intuition where cats are alive or dead but not both.

3. Apr 3, 2013

### capcom1983

exactly but because you don't know the exact answer even if it is just from lack of evidence. You can't say the cat is alive (even if you are an eternal optimist) because you don't know it for sure. The same applies to saying it's dead. So with evidence saying the cat is in the box in one of two states you can't say either and you can't say none because sayiing none is adding a third state of none. Which makes the cat obsolete and no longer in the box. But the evidence says the cat is in the box so there can't be a third state. So until the box is open allowing for the fact that simply open the box does not change the sate of the cat the only true answer is both.

4. Apr 3, 2013

### bhobba

Yea - its relatively simple to apply provided you are not math challenged - but interpretational issues do exist. Schrodingers Cat isn't really the issue its made out to be for the exact reason you gave - alive and dead cats do not interfere. The issue though is the same with any observation - at some point it makes its appearance in the macro world and since the macro world is a quantum system how it accomplishes this feat is not that simple.

Thanks
Bill

5. Apr 3, 2013

### kith

And already QM is getting difficult. Is there an exact answer or is the cat really both dead and alive? People disagree strongly about this. This leads to different, sometimes very sophisticated interpretations of the mathematical formalism. Also mathematically, it gets more complex if you want to trace where the "evidence" may be stored, i.e. you have to consider the environment of the cat which leads to interesting, QM-specific effects like decoherence.

/edit: Bill is right about the fact that Schrödinger's cat is not as controversial as other (thought) experiments. I recommend the double slit experiment as the gold standard for elementary weirdness in QM.

Last edited: Apr 3, 2013
6. Apr 3, 2013

### DrChinese

I'm sure you also guessed the Heisenberg Uncertainty Principle right away. Did you have a question? Or are you offering to answer some questions?

7. Apr 3, 2013

### capcom1983

Thanks Bill
Can either of you please send me a link to any pdf on the double slit experiment in more detail then i get on google or youtube because I would like to see what would happen if you added a third slit. Maths has never been an issue with me (my teacher wasn't impressed I only got a B because I didnt show working) I really like this forum glad found it.

8. Apr 3, 2013

### Staff: Mentor

Here you go: one, two, three, and five slits!

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html

This is for classical wave optics, but the intensity patterns are the same as the probability-distribution patterns for quantum-mechanical diffraction of electrons etc.

9. Apr 3, 2013

### bhobba

Someone did post a link to a detailed QM analysis of the double slit experiment but I don't know where it is off hand. Maybe someone else can remember where it is.

I think this is it:
http://www.yoavk.net/yoav-homepage/dslit.pdf [Broken]

Thanks
Bill

Last edited by a moderator: May 6, 2017
10. Apr 3, 2013

### kith

/edit: No, you are not. :-) Nice paper, I haven't seen this one yet.

A more elemental introduction is given by Feynman in his lectures and probably in many places all over the internet.

11. Apr 3, 2013

### vanhees71

Well, quantum mechanics is indeed not too difficult, as long as you don't think much about it and just use it to calculate things. This "shutup-and-calculate interpretation" in fact is a good starting point to get used with the formal side.

The real difficulty starts, when you like to get an intuitive picture about nature in terms of quantum theory, and as far as we know, all of nature is described (or at least should be described) by quantum theory.

Now, with Schrödinger's cat the quibbles start. If they don't start for you, it's save to say that you haven't yet understood the full implications of quantum theory yet, and in fact a lot of popular-science accounts of quantum mechanics get this and similar topics (like entanglement) simply wrong. Many even make a kind of mystery out of quantum theory, which is contrary to the aims of natural sciences, namely to describe nature by as simple as possible and as general as possible fundamental laws. As Einstein put it, the important thing is to explain things not simpler than possible but only as simple as possible.

Concerning Schrödinger's cat, many popular-science text tell the poor readers, in the famous example by Schrödinger the cat was "dead and alive at the same time". This is plain wrong. It's just one of the common misunderstandings of quantum theory by mixing socalled "common sense" with the correct description according to quantum mechanics.

The well-known setup is the following: A cat is confined in a box, together with some radioactive atom and a device, which destroys a bottle of poison killing the cat as soon as the atom decays. This setup is more complicated than necessary, but Schrödinger has chosen it to demonstrate what he thought to be odd with quantum theory. One has to keep in mind that Schrödinger, although one of the discoverers of quantum mechanics in 1926 (in terms of wave mechanics), he could never accept the probabilitistic interpretation of the quantum mechanical states, i.e., Born's Rule.

Ironically, it's Born's rule, which makes quantum theory consistent, but of course with quite drastic implications, correcting our "common sense", which is built on our everyday experience with macroscopic objects, which behave with high accuracy according to classical physics although in fact they are of course quantum objects as anything, and such common things like the stability of the matter around as cannot be understood with quantum mechanics.

Back to Schrödinger's cat: The point is that according to quantum mechanics, we cannot know with certainty that after a certain time of putting the atom into the box, whether it is decayed or not. We only know the probability that it is decayed. Approximately the probability that it is decayed after a time $t$ is given by
[tex]P(t)=1-\exp(-t/\tau),[/itex]
where $\tau$ is a parameter (the mean life time of the atom) specific for the used radioactive atom.

In turn we don't know, whether the bottle with the poison is broken and finally thus whether the cat still is alive or not. Often it's claimed that the cat is in a pure state of the kine $|\psi \rangle = \sqrt{P(t)} |\text{dead} \rangle + \sqrt{1-P(t)} |\text{alive} \rangle$. This is a vast oversimplification, because it's not even clear, what the pure state for "dead" and "alive" should be, but even if you assume that this very unrealistic assertion is correct, there is no problem with common sense here.

According to Born's rule, before looking into the box and checking whether the cat is dead or alive, you don't know with certainty in which state the poor pet might be. This doesn't mean that it is both dead and alive at the same time neither that it is dead or alive for sure. According to quantum theory the observable "dead or alive" is simply undetermined, and you can give only the probability, whether the cat is dead or alive. It's simply impossible to know about the cat's state from the preparation at the previous time $t=0$ what its state is at the later time $t>0.$ That's all.

Of course, it contradicts our everyday experience about a macroscopic system like a cat, because there you can say with some certainty that the cat is for sure dead or alive, no matter whether I look at it or not. According to quantum theory that's not a priori the case, and that's what's really difficult to understand.

The real question thus is, why our everyday experience with macroscopic systems suggests a classical deterministic behavior! This is answered by decoherence. The problem with macroscopic systems (and even with some not too large objects like a "Bucky Ball molecule" (made up by 60 carbon atoms shaped like a soccer ball)) is that they are very hard to isolate from interactions with the environment. On a microscopic scale a lot of very different states with only tiny differences in energy (compared with the total energy of the macroscopic object) make up the same "macroscopic" state. The reason simply is that we cannot describe even a simple body as a billard ball in all its microscopic details: It's made up of about $10^{24}$ atoms, which themselves are made up finally of quarks, gluons, and electrons. It's impossible to investigate such a number of particles in detail. Fortunately for everyday experimience with billard balls, we don't need such a detailed description! Mostly it's enough to know where the center of mass of the billard ball is located, sometimes you might need it's spin state as a whole too, but that's more or less all you need to know about it. These macroscopic "collective" observables are described averages over all the intrinsic states of the microscopic constituents, and one can show that this average quantities behave classically through the interaction with the environment, which can not easily be avoided.

This is even true for pretty small objects like the Bucky Ball molecules. However, physicists nowadays can prepare those molecules very carefully and are able to demonstrate that these objects behave quantum mechanically. For that purpose the group around the Austrian physicist Zeilinger cooled down Bucky Ball molecules very close to 0K temperature. Then they could perform a double-slit experiment, demonstrating quantum-mechanical behavior by leading to wave-like interference patterns of Bucky Balls on a screen.

Now, it is very easy to excite such a large molecule. But Zeilinger's group could also heat the Bucky Balls up by a tiny amount of heat energy. This makes the Bucky Ball irradiate thermal photons ("Planck radiation"). This tiny rate of thermal-photon emission was shown to be sufficient to blur the interference pattern. At quite small temperatures due to this photon emission it is completely gone, and the Bucky Balls show a pattern after the double slit as expected for classical point-like particles.

It's of course the more difficult to perform such experiments with really large objects although even this has been made possible recently (even at room temperature):

http://physicsworld.com/cws/article/news/2011/dec/02/diamonds-entangled-at-room-temperature

12. Apr 3, 2013

### DrChinese

Hey, there used to be a double slit simulation that showed the effect of placing polarizers in front of the slits. You could then vary the relative angle setting and see the results. Does anyone have a link to something like that?

Thx,

-DrC

13. Apr 3, 2013

### Maui

Your common sense is somewhat weird if it allows cats to be both alive and dead. Maybe i am too old-fashioned to grasp this but it seems a number of psychiatrists would frown at the idea.

14. Apr 3, 2013

### capcom1983

Maybe but as long as no one tells them they'll won't put me away again.
My point was about making assumptions about results until everything is known.
Plus thanks for links my laptop busted this morning talk about the unforseen so I'll check the pdf's once I saved them on my phone.

15. Apr 3, 2013

### capcom1983

I'm here to learn and expand my horizons and be corrected (probably alot).

16. Apr 3, 2013

### DrChinese

Moi aussi!

17. Apr 3, 2013

### dlgoff

18. Apr 3, 2013

### Staff: Mentor

Sure, so long as the initial conditions for the particle source correspond to the light source setup assumed to generate your plot.

You're making me "flash back" to trying to explain the Cornu Spiral to my students, when I used to cover it in our optics course, years ago. :uhh:

19. Apr 3, 2013

### bhobba

Exactly - and why I admire the guy. Before getting involved in this interpretational stuff understand QM at the level of shut up and calculate.

Once comfortable with that the best book I have found for interpretaional stuff is not an actual book on it, but rather Decoherence: and the Quantum-To-Classical Transition by Maximilian Schlosshauer:
https://www.amazon.com/Decoherence-...F8&qid=1365035650&sr=8-1&keywords=decoherence

In explaining decoherence he explains the interpretational issues pretty well and exactly what decoherence does and does not do. Of course decoherence is contained in any interpretation because its part of the formalism - but, aside from it being very interesting in its own right - which it is, it sheds a lot of light on interpretational stuff. And once you understand it you realise, this time at a much deeper level, a lot of the prattle written about foundational issues, stuff like Schrogengers Cat - is just that - prattle. Don't take my word for it though - study it for yourself.

BTW that doesn't mean issues do not remain - they do - but you will be able to understand what they are rather than the half baked misconceptions of the popular press. The one that really gets up my goat is the consciousness causes collapse carry on. I know guys who must be respected like Von Neumann and Wigner held to it but in Wigners case when he learned about some early work by Zurek on decoherence he abandoned it realizing it was no longer required - which it isn't.

Thanks
Bill

Last edited by a moderator: May 6, 2017
20. Apr 4, 2013

### vanhees71

There is this very fascinating "quantum-eraser experiment":
http://arxiv.org/abs/quant-ph/0106078