According to the principles of quantum mechanics, it is not possible to simultaneously determine the exact location and velocity of a subatomic particle, such as an electron, with arbitrary precision. This is known as the Heisenberg uncertainty principle, which states that there is a fundamental limit to the accuracy with which certain pairs of physical properties, such as position and momentum, can be known.
The uncertainty principle arises from the wave-particle duality of quantum objects. Subatomic particles, like electrons, exhibit both particle-like and wave-like properties. Their behavior is described by wave functions, which give probabilities for the various outcomes of measurements. The more precisely one property, such as position, is measured, the less precisely the conjugate property, such as momentum, can be known.
Therefore, attempting to determine the exact location of an electron at any given moment would inherently introduce uncertainty into its momentum, and vice versa. This limitation is not due to technological constraints but is a fundamental aspect of the nature of quantum mechanics.
Quantum mechanics provides a probabilistic description of the behavior of subatomic particles. Instead of knowing the precise values of properties, such as position and velocity, we can calculate probabilities for different outcomes. The wave function of a particle evolves over time according to the Schrödinger equation, which describes its quantum state. The interpretation of this wave function gives the probability distribution for the particle's properties.
In summary, within the framework of quantum mechanics, it is not possible to simultaneously determine the exact location and velocity of a subatomic particle like an electron without introducing inherent uncertainty in either property. The principles of quantum mechanics suggest that our knowledge is inherently probabilistic rather than deterministic when dealing with such particles.