The famous equation for mass energy equivalence: $E=mc^2$
It cannot conserve energy or momentum without some loss in one way or another. To elaborate further if I take $1kg$ of mass and I also take electromagnetic radiation with same energy as the $1kg$ mass and ensuring its accuracy using the above equation. Then use this radiation and I use it to smash it into a "crash" mat I would get this:
$$E=mc^2$$ $$E=1.c^2$$ $$E=89,401,000,000,000,000$$ Approx.
That being the energy we then use this to calculate the momentum of the electromagnetic radiation transferred onto the "crash" mat which would be:
$$p=mv$$ $$p=mc$$ $$p=e/c^2 . c $$ $$p=e/c$$ $$p=89,401,000,000,000,000/c$$ $$p=299,000,000$$ Approx.
where as if I now take $1kg$ of matter and accelerate it to high velocity (say, 10,000 kilometers per hour ) to measure its momentum we get roughly $10,000 kg.m/sec$
That being said, momentum cannot be conserved, why is that? Next, Energy cannot be conserved.
For example if I used the same $1kg$ and I shoot it into space at a $x$ velocity and after say 1000 years I recieve it and measure mass of the object it would weigh exactly the same as 1000 years before therefore I can conclude it has same energy in its mass however if I use the mass-equivalent of electromagnetic radiation and do the same but my conclusion would be vastly different as first due to travelling in long fabric of space it would get slightly or even highly redshifted due to doppler effect. That being said the observer would get different energy reading to that of 1000 years ago. That in mind where did that energy go?