After doing some research online, I found out that this is challenging because it's an example of "caustics," which is when light is focused on a specific area (as it is by the glass ball here). Because of its random nature, path tracing has a particularly hard time figuring out the source of the light, and as a result, the generated image has a lot of noise. Lecture slide 104 also goes over these issues.
Slide 104 describes the problem of sampling an exact point on a continuous distribution: What is the connection here?
I'm still confused about why these white noise spots are generated? Is it because of the "randomness" of sampling?