How do they know the other electron ‘changed’ without measuring it, and disturbing it’s original state ?
If you measure the polarization of randomly selected photons coming out of a laser, you will generally find that unless you have prepared them in some way (by bouncing them off a refractive surface or passing them through a polarizer, for example) that their polarization states are random. One of the ways you know that someone is messing with them downstream of you would be by measuring their polarization, and discovering that they're all right-handed polarized.
OK, now, let's say, just for the sake of simplicity that you prepare two [very] high energy gamma rays by smashing an electron and a positron into each other. To conserve momentum the γ particles will fly off in pairs, in opposite direction and at right angles to the two incident electron-positron pairs. To preserve angular momentum, the two γ rays will have opposite polarization.
Now, when you put a detector on one side of the room, at right angles to the incident electron-positron pairs, you will see that when you measure the polarization of resulting γ rays, they are all over the place, from perfect alignment with your detector, to perfect misalignment and every angle in-between. But immediately AFTER you take your measurement, quantum theory says that the wavefunction of the measured photon "collapses." It is now in a state of polarization in 100% alignment with your detector. And in fact, if you go slightly downstream with a second detector, you will discover ALL of the photons indeed have 100% alignment with the first detector; they are no longer randomly polarized. Your first polarization detector has put them in a stationary-state or eigenstate of polarization, and the second detector [and third, and fourth, and however many you want to add after the first detector] will always see the polarization eigenstate corresponding to the axis of the first detector.
If, instead of putting your detectors on the left side of the room, you put them on the right side of the room, you will observe exactly the same thing. You will see random polarization states of the produced γ rays, until after they've passed through your 1st detector, and whatever the alignment of your detector was, after they've passed through it, they will all be aligned with your detector 100% when their measured at the second detector.
Nothing mind-blowing so far. In fact, if you did not see the same thing on both sides of the room you would certainly suspect a problem with your geometry, the room, or something. Physics cannot depend on which side of the room you place your instruments.
Now, here's the interesting twist. γ particles are coming off in both directions, so you can look at both γ streams. On the left hand side of the room, put a first detector, say 20 feet from the pair-production collision site. Add a second detector at 35 feet. On the right hand side of the room, put a detector at 35 feet, but leave out the first "collapsing" detector. Guess what you see? On the left hand side of the room, 1st detector sees what it saw before. Second detector sees what it saw before. But on the right hand side of the room, the detector sees γ rays which are 100% polarized -- in the direction OPPOSITE of the 1st detector on the left hand side of the room. The 1st detector has thrown the &gamma photons into collapsed wavefunctions with polarization as expected -- and it has also collapsed the wavefunctions of the photons streaming away to the other side of the room, even though those photons have never passed through the first detector.
This has happened because of entanglement. When the wavefunction of the photons heading left are collapsed into an eigenstate, in order to conserve angular momentum, the photons heading right must also collapse into an eigenstate with exactly the opposite polarization, so that their net angular momentum is zero. The two particles are therefore "entangled." They are actually a two-particle system composed of a single wavefunction. If you change the polarization of one photon, you will change necessarily the polarization of the other. And based on the experiments we can do, it appears that this entanglement is not affected by the distance in between the events of measuring them.