Even though they say information is conserved, can information be biased at the first place?
Example:
Example 1:
Observer A and B saw a 10 *10 matrix. However, due to technique reason(for example, A was very short and B was tall enough) A could only say the last role, yet B was able to see all 10 rolls. Thus even the matrix was the same, A and B had different answers due to observation limits.
Example 2:
Observer A and B saw a 10 character string 0101010101. However, A use the binary system reading and got 341, B use decimal reading thus got 101010101. Thus even the character string was the same, A and B got different answers due to interpretation.
Example 3:
Observer A and B was in a massive gravitational field near a black hole, yet non of them was aware of the situation. B was close to an object and observed it as a cube, A was far away from the field and the object and observed it as an "oval". Thus even the object was the same, A and B got different answers.
e.t.c.
That was, even though the observer agreed on the result/measurement, or agreed on the observation of the outcomes; can the information they preserved being biased towards each other?
Bias can occur anywhere. In relativity the only unbiased observation is in the frame of the action. Example energy is not conserved in 4D relativistic transformation because a sequence of events is not the same for all observers.
The statements aren't sharp enough for any conclusions to be drawn. The only quantities that are relevant in any observation, are those that are invariant under the transformations of interest-other quantities carry, by themselves, no information at all, in that sense.
The examples aren't meaningful, since changing a mathematical representation, e.g. a base of counting, doesn't change the information content.
The three examples lead to confusion, because they get known physics and mathematics wrong.
Thank you! But is it possible that: for different observable, the uncertainty and number of a group of particle $A$ being measured, being different. Not only photon but also classical particles?
These statements don't mean anything, unfortunately, so it's impossible to answer.
I agree that these statements don't mean anything. E.g. what on earth do you mean that you "saw" a 10x10 matrix. In special relativity, you can have length contraction and time dilation but different observers looking at the same events have to agree on the events themselves.
Quote:"Accelerating charges radiates....observable see different ground states." There had transformation and invariance about energy-time and motion.(In GR and SR) However, the observations also changed. Since not all the operator was linear, Is it possible for them to disagree with some results? i.e. Suppose a particle had uncertainty with value $\alpha (x,t)$, for different observer $A$ and $B$, we integrate $\alpha$ in an invariant space-time. Could the result be different? Further, does this apply to any other quantities? Such as the "order" (I used the word order because I'm still trying to figure what I'm thinking yet.) of particles?
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