Qfyilyi

Really I know entanglement exists, but what I have never found is experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed.
e.g. using the spin up spin down example we know that one of the particles will be spin up and the other spin down, so when we measure one and find it is spin up we know the other is spin down.
Is there any situation after creation that the particle with spin up will change to spin down.

The assumption that a measurable property exists whether or not we measure it is inconsistent with the experimental facts.

Here's a relatively simple example. Suppose we have four observables, $A,B,C,D$, each of which has two possible outcomes. (For example, these could be single-photon polarization observables.) For mathematical convenience, label the two possible outcomes $+1$ and $-1$, for each of the four observables. Suppose for a moment that the act of measurement
merely reveals properties that would exist
anyway even if they were not measured.
If this were true, then any given state
of the system would have definite values
$a,b,c,d$ of the observables $A,B,C,D$.
Each of the four values $a,b,c,d$
could be either $+1$ or $-1$,
so there would be $2^4=16$ different possible
combinations of these values.
Any given state would have one of these 16 possible combinations.

Now consider the two quantities $a+c$ and $c-a$.
The fact that $a$ and $c$ both have magnitude $1$
implies that one of these two quantities must be zero,
and then the other one must be either $+2$ or $-2$.
This, in turn, implies that the quantity
$$
(a+c)b+(c-a)d
$$
is either $+2$ or $-2$.
This is true
for every one of the 16 possible combinations
of values for $a,b,c,d$,
so if we prepare many states,
then the average value of this quantity must be somewhere
between $+2$ and $-2$.
In particular, the average cannot
be any larger than $+2$.
This gives the CHSH inequality
$$
langle{AB}rangle
+langle{CB}rangle
+langle{CD}rangle
-langle{AD}rangleleq 2,
$$
where $langle{AB}rangle$ denotes the average of the
product of the values of $a$ and $b$
over all of the prepared states.

In the real world, the CHSH inequality can be violated, and quantum theory correctly predicts the observed violations. The quantity $langle{AB}rangle
+langle{CB}rangle
+langle{CD}rangle
-langle{AD}rangle$ can be as large as $2sqrt{2}$. Here are a few papers describing experiments that verify this:

• Kwiat et al, 1995. “New high-intensity source of polarization-entangled photon pairs,” http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.75.4337




• Kwiat et al, 1998. “Ultra-bright source of polarization-entangled photons,” http://arxiv.org/abs/quant-ph/9810003




• Weihs et al, 1998. “Violation of Bell’s inequality under strict Einstein locality conditions,” http://arxiv.org/abs/quant-ph/9810080

The fact that the CHSH inequality is violated in the real world implies that the premise from which it was derived cannot be correct. The CHSH inequality was derived above by assuming that the act of measurement merely reveals properties that would exist anyway even if they were not measured. The inequality is violated in the real world, so this assumption must be wrong in the real world. Measurement plays a more active role.

Just for a moment, if one (you) imagine that the entangled particles are determinated in their states from the beginning of their entanglement, would it change something in the outcome of the experiment? In the pair production of two photons from nonlinear optical crystals the result of the experiments shows a statistical dependency; the orientation of the electric field components of the photons is orthogonal to each over.

Producing such a pair of photons we are not able to control the direction of the polarisation, we only able to design the process so that the polarisations of two particles are orthogonal on each over, the orientation by itself is randomly distributed around 360°. The uncertainty is in the phenomenon, that using a polariser to find the orientation of the particles, we do not get a result in 50% of our measurements (with the best designed polarizer and for the right wavelength).

Let the polarizer be orientated to the vertical (0°). Getting a result, we will know that the photon has had an orientation from -45° to 45° and from 135° to 225°. Not getting a result, we are allowed to say, that the photon has an orientation in the opposite to the above mentioned angles. To count for the statistics these not measured photons we are able only after getting the information from the second measurement device, that a photon in their setup was measured. In reality simply the number of measured incidents is compared.

What is the proof of entanglement

Firstly a lot of experiments for a given process, in this case for photons from nonlinear optical crystals in a well definded setup. And later the knowledge, that in this process are produced entangled particles.

Is there any situation after creation that the particle with spin up will change to spin down.

This happens all the time due to “impurities” in the experimental setup. The produced particles colliding with other particles and are under the influence of external fields. The longer the distance and the time between production and measurement, the weaker the measurable coincidence. But the swap of a spin by itself is impossible.