Inertial frame of reference:
An inertial frame of reference is a state of motion in which an object experiences no net force when not acted upon by an external force. Imagine you're floating freely in space without any engines or propulsion. You'd be in an inertial frame! Everything in that frame is considered "at rest" even if they're moving relative to something else.
Constant speed of light (c):
One of the pillars of special relativity, proposed by Albert Einstein in 1905, is that the speed of light in a vacuum is the same (approximately 299,792,458 meters per second) for all observers, regardless of their own motion. This seems counterintuitive at first, but numerous experiments, including the Michelson-Morley experiment, have confirmed this surprising fact.
The connection:
The connection between these two concepts lies in the foundation of special relativity. Einstein observed that the laws of physics should be the same in all inertial frames. If the speed of light were not constant, these laws wouldn't be consistent across different frames. Imagine two observers, one stationary and one moving fast, trying to measure the speed of light. According to the classical idea, their measurements would differ. However, the constant speed of light ensures that everyone, regardless of their motion, observes the same value for c, upholding the universality of physical laws.
This constant speed of light has profound implications, leading to phenomena like time dilation and length contraction. It's crucial for understanding our universe at high speeds and has had significant applications in technology, like GPS and particle accelerators.