# The limit

1. Oct 20, 2013

### alexay95

Wheres the limit between quantum mechanics and classical mechanics.
I mean,when can I expect quantum behavior on a system, is it depends on the system size?Tempature? Something else...and if so what are the numbera for those limits.

As we know in nature everything is continuous, so, the transformation from classical to quantum and reverse must be continuous too, if so what properties this system have right in middle of the change? Its not fully classical nor quantum.what is it then?

2. Oct 20, 2013

### phinds

Really? Do we know that? How about the size of molecules increasing as the number of atoms increases. Is the "size of molecules" a continuous function? How can it be when you have to have a discrete number of atoms?

3. Oct 20, 2013

### alexay95

Im agree.
Of course its not continuous.

To make my question simple.
Consider a ball as the system.
Now I would like to know in which conditions I can relate that ball as a quantum ball.
Its momentum and location in calssical form are continuous function, can get any number, but I wanna know what I need to apply to the ball to consider is characteristics quantized.and how I need to approach to his qualities while he in the middle of the tranformation between classic-quantum system.
Before that, maby there is no "transformation"
But it feel kinda strange that I can shrink the ball nanometer by nanometer and suddenly il see quantum behavior, whats ur opinion?

4. Oct 20, 2013

### craigi

Well there isn't really a limit.

Reagrding size and temperature, the Pauli Exclusion Principle is a very significant effect in neutron stars, for example. They're big and hot.

The concept of dechorence is the closest thing that we have to a boundary between the quantum and classical world.

5. Oct 20, 2013

### phinds

I have read, but do not know for sure that it is correct, that there is NO upper size on object that could experience quantum effects, just that the probability of such events becomes negligible as the size goes up. The example that I remember is that it is theoretically possible that you could disappear and reappear on the other side of a wall. You would just have to wait many orders of magnitude longer than the age of the universe for it to be even remotely likely.

6. Oct 20, 2013

### alexay95

U right.
Thats make sence to me now.
Classical system got small probability to quantum effects and quantum systems got large probability, but they all got probabilty and that's what changes.
Ty

7. Oct 20, 2013

### StevieTNZ

I think that the probability of that occurring exists at the current time.

http://finance.yahoo.com/news/teleport-ourselves-anywhere-world-were-102848994.html

8. Oct 20, 2013

### king vitamin

The classical limit will depend on what system you're looking at. If you're considering a system with a certain characteristic size (like your ball), the classical limit will apply when the DeBroglie wavelength, $\lambda = h/p$, is much smaller than the dimensions of your ball (and every other scale in your problem!). Quantum effects can be important in describing even macroscopic phenomena, such as neutron stars (as pointed out above), because the density in a neutron star is so large, the distance between two neutrons is of the same order as the DeBroglie wavelength.

In general one thinks of the classical limit as taking Planck's constant to zero. This is the problem with taking a classical system and "quantizing" it; going in the reverse order is not well-defined. This is simple to see, for example, if one considers the two quantum mechanical operators $x^2p$ and $xpx$. These are inequivalent in quantum mechanics, but have the same classical limit (since x and p commute when h=0). So we can have two quantum theories with the same classical limit.

9. Oct 20, 2013

### phinds

10. Oct 20, 2013

### StevieTNZ

But still a possibility!

11. Oct 20, 2013

### morrobay

The classical limit where a Bell inequality is valid : 0 ≤ ∅ ≤ pi/4
The question is on the explanation for this pi/4 limit where classical effects change to quantum effects.

12. Oct 20, 2013

### meBigGuy

I'd rather address this problem as : How does the classical emerge from the quantum mechanical?
One way to approach it is decoherence.
http://www.scribd.com/doc/140961861/Decoherence-Essay-ArXiv-Version

This paper is a good one too: