A laser beam will continue to travel indefinitely into space after being turned off, unless it encounters an object or is absorbed by dust. However, the light will gradually dim due to the thin gas in space and the natural spreading of the laser beam. Additionally, the photons will experience redshift as the universe expands, further diminishing their brightness over time. The discussion also touches on the relationship between the speed of light and the expansion of the universe, noting that while galaxies are moving apart, this expansion does not significantly affect light as a force. Overall, the conversation explores the persistence of light in the cosmos and its interaction with the universe's expansion.