What is (theoretical) evidence that you need to define all of space with propert
ID: 1373424 • Letter: W
Question
What is (theoretical) evidence that you need to define all of space with properties rather than just stating where all particles are? I mean, does every single coordinate x, y, z have a meaning or would it be sufficient to keep track of particle positions and type. In other words, to specify reality, do you need all of
?(x,y,z,a)
where a is another dimension (charge, spin, etc.) or is there any framework where you just specify a countable number or particles with coordinates
and you do not care about coordinates inbetween particles (obviously there would be distant interaction laws).
Can you disprove sufficiency of the second representation?
What is (theoretical) evidence that you need to define all of space with properties rather than just stating where all particles are? I mean, does every single coordinate x, y, z have a meaning or would it be sufficient to keep track of particle positions and type. In other words, to specify reality, do you need all of ?(x,y,z,a) where a is another dimension (charge, spin, etc.) or is there any framework where you just specify a countable number or particles with coordinates (xp,yp,zpi) and you do not care about coordinates in between particles (obviously there would be distant interaction laws). Can you disprove sufficiency of the second representation?Explanation / Answer
Already to state where your particles are you need space.
Even if you describe where your particles are by saying how they relate to other particles (e.g., in terms of a primitive notion of distance), this defines coordinates in a space of distances. The set of realizable distances then forms a 3-dimensional submanifold (accirding to the known laws of physics), and you have back your space. (This is roughly how the GPS works.)
Thus only the ''existence'' status might be questionable. But if one questions the existence of the space found coordinatized in the above (or any other manner) then one has reasons to question the existence of everything else in phyics - for the way other physical concepts are identified is always by some elaborate reasoning that gives the concept precision and physical reliability.
(On second reading, the question seems to say - can one disregard the space between the particles? In classicle mechanics of point particles, one can indeed, on a formal level, as the state of the particle system just consists of a list of particle coordinates and velocity coordinates. But a moving particle would then have to create at each moment the point in space it is moving to, a somewhat weird assumption....)
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