No, the uncertainty principle in quantum mechanics does not allow for the demonstration of anything happening faster than the speed of light or instantaneously. The uncertainty principle, formulated by Werner Heisenberg, states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, or energy and time, can be known simultaneously.
The uncertainty principle arises from the wave-particle duality of quantum mechanics. It implies that there are inherent limits to the knowledge we can have about the precise values of certain physical properties of a particle. For example, if we try to measure the position of a particle with high precision, the uncertainty principle tells us that the momentum of that particle becomes highly uncertain.
While the uncertainty principle places limits on our ability to precisely measure certain properties, it does not imply that particles themselves are moving faster than light or that information can be transmitted faster than the speed of light. The speed of light in a vacuum, as described by Einstein's theory of relativity, is an absolute speed limit in the universe. Nothing can travel faster than light or communicate information faster than light speed.
Therefore, the uncertainty principle does not provide a means to demonstrate phenomena occurring faster than light or instantaneously. It is a fundamental principle of quantum mechanics that describes the inherent limitations in our knowledge of certain properties of particles, but it does not violate the principles of special relativity regarding the speed of light.