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According to the second law of Newton f=ma only objects with mass can experience a force. But light can be bent by gravity and is not supposed to have a mass. How come?

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This is because gravity doesn't exert a "force" on objects, gravity works by bending spacetime. Light doesn't tend to accelerate so it will take a geodesic path through spacetime; this means that it takes a "straight" path through curved space, which is what gravity is. The reason we experience gravity is because when not accelerated we will take a geodesic path, when at rest we move through time at the speed of light but when spacetime is bent our motion through time will begin to move us through space as well, which is what causes gravity. When we talk about "gravitational force" we are referring to the force it takes to counter gravity, if we want to keep something from falling we must accelerate it to counter it's gravitational acceleration and to do that we must apply the force mg.