Why Power Cables Affect Sound

I just bought a new CD player and was underwhelmed with it compared to my cheaper, lower quality CD player. That’s when it hit me that my cheaper CD player is using an upgraded power cable. When I put an upgraded power cable on my new CD player, the sound was instantly transformed: the treble was tamed, the music was more dynamic and lifelike, and overall more musical. 

This got me thinking as to how in the world a power cable can affect sound. I want to hear all of your ideas. Here’s one of my ideas:

I have heard from many sources that a good power cable is made of multiple gauge conductors from large gauge to small gauge. The electrons in a power cable are like a train with each electron acting as a train car. When a treble note is played, for example, the small gauge wires can react quickly because that “train” has much less mass than a large gauge conductor. If you only had one large gauge conductor, you would need to accelerate a very large train for a small, quick treble note, and this leads to poor dynamics. A similar analogy might be water in a pipe. A small pipe can react much quicker to higher frequencies than a large pipe due to the decreased mass/momentum of the water in the pipe. 

That’s one of my ideas. Now I want to hear your thoughts and have a general discussion of why power cables matter. 

If you don’t think power cables matter at all, please refrain from derailing the conversation with antagonism. There a time and place for that but not in this thread please. 
Good stuff, atmasphere, thanks for posting. One thing I would like to explore is whether or not the power cable has to be at the amplifier or could it be at the breaker box. I hypothesize that it would have a greater effect at the amp.
Has anyone checked out the many rave reviews for Audioquest Hurricane power cords? Hel-loo! Maybe there’s something to this directionality stuff, highly polished conductor stuff and whatever else Audioquest has learned in the past thirty years. I know what you’re thinking, they’re just saying that because it sounds cool.
Geoff, you’ve mentioned highly polished conductors several times and I don’t know anything about it. Can you explain more, please?
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Perfectly valid question re highly polished conductors. Here’s what Audioquest says, this paragraph refers to their Dragon High Current Power Cord.

HIGH PURITY CONDUCTORS - PERFECT-SURFACE SILVER (PSS)Perfect-Surface Technology applied to extreme-purity silver provides unprecedented clarity and dynamic contrast. Perfect-Surface Silver (PSS) is AudioQuest’s highest-quality metal. Solid conductors prevent strand interaction, a major source of cable distortion. Extremely high-purity Perfect-Surface Silver minimizes distortion caused by the grain boundaries that exist within any metal conductor, nearly eliminating harshness and greatly increasing clarity compared to OFHC, OCC, 8N and other coppers.

Lizzie, you said you thought they were polished in a non oxygen atmosphere. Do you mean like on Pluto?