## Math vs Physics

• Imagine you are sipping tea or coffee while discussing various issues with a broad and diverse network of students, colleagues, and friends brought together by the common bond of physics, graduate school, and the physics GRE.

htam9876
Posts: 20
Joined: Mon Mar 04, 2019 8:16 pm

### Math vs Physics

E = mc² is Dynamic mass – energy relationship in nature. (“Dynamic” means the particle is moving and hints it has momentum);
Next square both sides: E² = m²c ^4, namely: m²c² = E² / c², then, add a negative mark on both side: – m²c² = – E² / c²;
Add two Redundant items m²v² on both sides: m²v² – m²c² = m²v² – E² / c²;
Because m²v² = p², then, m²v² – m²c² = p² – E² / c²;
Because m = γm0, (pay attention here, it just means that you can consider the magnitude of the moving mass m is γm0, but not means the particle be rest). Square both sides: m² = m0² / (1 – v² / c²);
Then, m0²v² / (1 – v² / c²) – m0²c² / (1 – v² / c²) = p² – E² / c²;
A mathematical calculation: m0²v² / (1 – v² / c²) – m0²c² / (1 – v² / c²) = - m0²c²;
Then, - m0²c² = p² – E² / c²;
Transform it in math, then, E² = p²c² + (m0c²)².
It’s the so called energy – momentum equation.
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If it’s the stationary situation, v = 0, so, no math game can be played. Then, it’s just a stationary mass – energy equation: E0 = m0c².

Liqiang Chen
aug 20, 2020