Why Doesn't Light Increase in Mass at High Speeds?

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Light, or photons, do not gain mass as they travel at high speeds because they are inherently massless particles, which allows them to always move at the speed of light (c). The concept of mass increasing with speed applies to objects with mass, but photons remain unaffected in this regard. Light is influenced by gravity due to its interaction with spacetime, which causes it to follow curved paths in the presence of mass. This relationship between light and gravity highlights the distinction between mass and energy in the context of relativity. Understanding these principles clarifies why light does not require infinite energy to move.
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I've been reading a lot about quantam physics and whatnot mostly for entertainment, but it suddenly hit me today that I didn't realize something. Why doesn't light get infinitely heavy, and therefore take an infinite amount of energy to move it? I've always accepted both the heavy, energy, and time factors of moving at the speed of light, but why isn't light itself affected by its movement? I must have missed something crucial. What further confused me is that light is affected by gravity, but not by its own speed.

Here's the question (just for a recap)

1. Why doesn't light get infinitely heavy, there fore taking an infinite amount of energy to move it?
 
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Photons are massless? Massless particles, if I am not wrong, only travel at c. We experimentally find them to be as massless as possible. They are affected by gravity because they travel in curved paths which are caused by masses as they bend spacetime.
 
Ohhh! Now I think I get it. :-) Thanks for the answer!
 
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