Why is total mass less than sum of rest masses in bound systems?

[vin300]

I saw today in Ohanian's book:
"It is convenient to separate particle energies into kinetic and rest mass energies:
M=∑m +(∑T/c^2 +U/c^2)
The term in the paranthesis is negative for a bound system,hence the total mass is less than the sum of the particle rest masses"
I thought the rest masses were indeed less.If it is otherwise, there's a problem with the Energy momentum four vector

 

[Dale]

I saw today in Ohanian's book:
"It is convenient to separate particle energies into kinetic and rest mass energies:
M=?m +(?T/c^2 +U/c^2)
The term in the paranthesis is negative for a bound system,hence the total mass is less than the sum of the particle rest masses"

This is correct. The "missing" mass is called the "mass deficit" and that mass/c^2 is called the "binding energy". Note, the mass deficit only appears when the binding energy has been removed from the system, usually either through radiation or through doing work on another system.

I thought the rest masses were indeed less.If it is otherwise, there's a problem with the Energy momentum four vector

The problem goes away if you include the four-momentum of the binding energy which left the system.