Understanding Phase Space
Space Time within Relative Locality
The Math
Applications of Relative Locality
100
In basic terms, the phase space
What is a multidimensional space in which all possible phases in a given space are represented?
100
The problem with using space time as a basis for relative locality
What is that space time is subjective?
100
In order to determine the curvature of space within the phase space we must...
What is determining the sign of the parameter K?
100
If the energy and momentum of all particles was the same, what would the phase space be?
What is space time?
200
Any degree of freedom within phase space
What is another axis on the multidimensional phase space?
200
The opposite of a space time -- the basis for a phase space
What is a momentum space?
200
What common variables do we hold constant to be able to deal in what other variables in the phase space?
What is we hold constant gravity and quantum effects because they maintain a constant ratio, so that we can deal in momentum and energy?
200
Returning to the lightning striking the train while we stand on separate platforms, would you and I see the the lightning strike at the same time? Would you and I even necessarily be looking at the same train?
What is no, we would see it strike at different times, and no, we may be looking at a different train?
300
The key factor of phase space that allows for its use in relative locality
What is it is invariable and its coordinates are not local
300
Subjective space times are dependent on...(i.e. what makes them subjective?)
What is that different observers see different space times dependent on energy and momentum and thereby changing from space to space?
300
Distance is a function of...
What is momentum?
300
Traveling back to our block universe vantage point, seeing everything, how would an individual space time appear to exist in relation to the phase space?
What is the space time would be a small slice of the over all phase space that would make up the universe?
400
How does phase space allow for relative simultaneity?
What is by deforming relative linear velocities?
400
Can events happen simultaneously within the phase space?
What is yes? Coincidences of events are still objective but may not appear to be for distant observers.
400
What properties can you not assume will hold in the algebra given in the article?
What is the commutative, associative, and linear properties?
400
Given that many particles have different energies and momentums, and that all phases exist simultaneously and many regular laws of physics and mathematics do not necessarily hold, is energy still conserved?
What is yes? Energy is definitely conserved, and its conservation is a defining part of the mathematics given to justify the phase space!
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