The impossibility of knowing the exact state of an entangled particle pair at any given time is a fundamental characteristic of quantum mechanics known as the uncertainty principle. The uncertainty principle states that certain pairs of physical properties, such as position and momentum, cannot both be precisely determined simultaneously with arbitrary accuracy.
In the case of entangled particles, the uncertainty principle applies to their quantum states as well. When two particles are entangled, their states become intertwined in such a way that knowing the exact state of one particle implies uncertainty about the state of the other. This property is known as quantum entanglement.
If we attempt to measure the state of one entangled particle, such as its spin or polarization, the act of measurement collapses the quantum superposition of states into a specific outcome. However, due to entanglement, this collapse affects the other particle as well, instantaneously determining its state in relation to the measured particle.
The outcome of the measurement on the second particle appears random and unpredictable until a measurement is made on it, at which point its state becomes determined as well. This phenomenon is known as quantum non-locality, as the measurement on one particle seems to instantaneously influence the state of the other, regardless of the spatial separation between them.
This behavior is often referred to as "spooky action at a distance" and has been experimentally verified through various tests of Bell's inequalities. The inability to know the exact state of an entangled particle pair in advance is an intrinsic property of quantum mechanics, and attempts to determine both states simultaneously would violate the uncertainty principle.
Therefore, when attempting to measure the state of an entangled particle, we can only obtain probabilistic information about its properties, and the state of its entangled partner will remain uncertain until it is measured.