Why is the emitter current of a common emitter slightly greater than the collector current?

I'm trying understand where electricians came to agreement that Ie = Ib + Ic. I know that the base of a NPN transistor is very thin, allowing electrons to flow through to the collector which explains why $I_{c} = \beta I_{b}$. Mathematically, I can also see that when we have $\alpha = \frac{I_{c}}{I_{e}} = \frac{\beta}{1+\beta}$ But I want to understand the actual physics behind this phenomenon, so that I could remember it for my E5 advancement exam.

• $I_e=I_b+I_c$ is a statement of conservation of current. The net current that leaves the transistor must equal the net current that enters it. – garyp Apr 9 '17 at 19:38
• @garyp That seems like an answer, not a comment. – rob Apr 9 '17 at 20:38

$$I_E = I_B+I_C$$