
Originally Posted by
sigurdV
Does that mean that the amount of energy is dependent on the observer?
Yes, energy is a frame-dependent quantity, however, invariant mass is not. Perhaps it is better seen if we bring our relation into a slightly different form :
As relative speed changes, energy changes, but so does momentum. The invariant mass m however remains the same for all observers, which is why it is called "invariant".
Does it mean that there is no determinable value on the amount of energy our universe contains?
No, that's not what it means. The situation here is rather complicated, because "the universe" is not an inertial reference frame, so the above relation does not hold. Also, when talking about the universe as a whole one needs to consider quantum effects, like vacuum energy.
Isnt this a paradox? Will it mean that it also has no determinable size? And how about the age of the universe?
See above.
I am not sure what this has to do with size or age.
IS ENERGY A FRAME DEPENDENT QUALITY?
Yes.
Running faster produces more energy in our universe!
No it doesn't, because in order to run faster you have to first expand energy in order to accelerate yourself. In other words, you have to add energy to the system - it does't just magically appear from nowhere.
Tell me that the amount of energy or the size and age of our universe is not an effect of observation?
There is no connection here to size or age.