# Conservation laws vs Einsteinian space-time

The way I understand conservation laws - which I am asking you to correct - is that if I observe any slice of the universe perpendicular to the time axis and count up all the mass/energy, momentum, charge, etc., I should obtain the same sum as I would had I observed any other slice of the universe perpendicular to the time axis.

Stop me right there if you have to, but here is where I start scratching my head.

The general theory of relativity informs me that I can't observe a slice of the universe perpendicular to the time axis. The slice I observe is skewed based on my velocity. Yet worse, the special theory of relativity informs me that I can't even observe a flat slice of the universe if I'm accelerating. It's curved based on my acceleration and has all sorts of bumps and such around every massive object. Again, please re-inform me if I'm mistaken.

So let's say I make my observation and sum up some conserved quantity over the entire universe. The slice of space-time that I've integrated over is S1, and my total is Q1. I change my direction of motion but not my speed such that the slice of the universe I observe S2 is an affine transformation of S1 that is not equal to S1. I then integrate the same conserved quantity over S2 and call it Q2.

Does Q1 = Q2? If it doesn't, then how can we ever verify that conservation laws describe our universe, and how did we come up with them in the first place?

If Q1 does = Q2, would this not imply that all conserved quantities are distributed perfectly evenly, since I can tilt my observation to exclude any symmetry-ruining lump of conserved quantity from the total? Since that doesn't appear to be the case, who is the stupid: Einstein, the guy that came up the conservation laws, or me?

• The observable quantity is not preserved. Just the quantity itself. Commented Jan 9, 2014 at 18:28
• @MartinDrautzburg How can you tell? Commented Jan 9, 2014 at 18:31