Why doesn't mass add?

Question

Can someone provide a simple and convincing reason why mass dosen''t always add when two system combine but momentum and energy always does?

Energies and momentum add because of conservation laws but mass is conserved as well isn't it?

Or is it the case that we are dealing with invariant mass hence is special? This sounds a bit mystical.

Answer 1

Momentum is always conserved. Energy is conserved only in very special (non-real-life) situations. Technically, mass is not invariant per the relativistic factor √(1-v²/c²), but this is not noticeable in the vast majority of problems we face.
So, yes the invariant mass is a special case that covers 99.99999% of the time.
Similar to fluidic avatars...........

Answer 2

I'm not really sure what you are asking. If you add 5 kilograms of sand to a bucket containing 5 kilograms already, then you have 10 kilograms total. Obviously mass adds. The Law of Conversation of Matter would prevent any mass from being created or destroyed.

In nuclear reactions, any missing mass has been converted to energy.