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Why are Newton’s laws less accurate for electrons and objects moving close to the speed of light?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A.
mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

Newton’s laws of motion are foundational to classical mechanics, but they become less accurate when applied to subatomic particles like electrons or objects moving at speeds approaching the speed of light because they do not account for the effects described by special relativity and quantum mechanics.1

As an object’s velocity nears the speed of light, its relativistic mass increases, requiring infinite energy to reach or exceed that speed, which serves as a universal cosmic limit. Newtonian physics fails to capture this dynamic, as it assumes mass remains constant. Furthermore, at the subatomic scale, particles like electrons exhibit wavelike properties and are subject to the uncertainty principle, which precludes the deterministic predictions central to Newtonian physics.23415

In these extreme regimes, relativistic mechanics and quantum theory are required to accurately describe physical reality, as they account for phenomena such as time dilation, length contraction, and the probabilistic nature of subatomic particles.675