“Chasing Cars” is a song by Northern Irish-Scottish alternative rock band Snow Patrol. It was released as the second single from their fourth studio album, Eyes Open (2006). It was released on 6 June 2006, in the United States and 24 July 2006, in the United Kingdom.[2] The song gained significant popularity in the US after being featured in the second seasonfinale of the medical drama Grey’s Anatomy, which aired on 15 May 2006.[3]
https://en.wikipedia.org/wiki/Chasing_Cars

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This song makes me imagine being with someone and having no worries about others—just the two of us. Based on research, “Chasing Cars” is only mentioned once, on the bridge, where he proclaims, “Let’s waste time, chasing cars around our heads.” The prepositional phrase that follows that statement clarifies that the titular expression is a mental exercise, not a literal one. Gary learned the metaphor of “chasing cars” from his father. To cut a long story short, it represents a futile pursuit. However, Lightbody does not consider this romance to be an act of vanity. Rather, he appears to be saying that he would rather spend time with his sweetheart doing nothing constructive than doing anything else. https://www.songmeaningsandfacts.com/snow-patrols-chasing-cars-lyrics-meaning/
you can listen at: https://youtu.be/GemKqzILV4w