What exactly are "preferred coordinates"? Or a "preferred coordinate system"?
In which context? It's often said that in relativity there are no "prefered coordinates", which should mean that the physics shouldn't depend on the coordinates. Is that what you mean?
preferred coodinate system
There are physicists who consider that there is an "absolute reference frame" in which the one-way speed of light in empty space is c in any direction, independently of the velocity of the source emitting the light. There is a large literature devoted to the subject. I have not the competence to discuss the problem but the special relativity as presented by Einstein solves all the problems in a way well tested by experiment.
I believe that preferred coordinate systems are those which make the mathematics of a situation easier or make the physics easier to explain. For instance it is probably easier when describing the orbit of the moon around the earth to use polar coordinates with the earth centre as the origin. For other problems, such as linear motion on a geometric plane Cartesian coordinates may be better suited. We are to some degree free to choose what we use. A physicist or mathematician would no doubt correctly qualify such a general statement.
Sometimes the physics will suggest a particular coordinate system. I.e. one in which everything becomes alot more simpler.
For example in big bang cosmology one of the assumptions is that the universe is homogenous and isotropic, The universe though can only be isotropic in one coordinate system so this assumption automatically suggests a preferred coordinate system.
What context did you see this in? As people have said above, sometimes it can just mean a coordinate system that makes the math easier, but at other times physicists say things like "in relativity there are no preferred coordinate systems" meaning that the fundamental laws of physics should follow the same equations in all the inertial coordinate systems of SR, or in all "local" inertial coordinate systems in GR.
Thank you. So if the physics did depend on the coordinates:
One observer would be able to impose his observation on another. (eg. increase in mass with increase in velocity) But, in the case of S.R., Lorentz tranformations (Or even, classically, with Galilean transformations) are a tool used to show what really goes on...that each inertial observer may have a unique set of observations. Do I have a good intuition for this "preferred coordinate" term? I don't have a good enough understanding of G.R. to apply my intuition there yet. I suspect it will have alot to do with 'the principle of equivalence' and 'the principle of general covariance'. If somebody could give a short road map for G.R., I would appreciate it!
Then what happens to relativity theory if the big bang theory admits preferred coordinates?
Perhaps you should make it clear if by preferred coordinates you mean a assumed coordinate system that is a mathematical convenience or if you mean an absolute reference frame such as the Lorentz interpretation that something is only at absolute rest if it is at rest with some form of "aether". In the lorentz interpretation an object lenght contracts or time dilates only if it is moving relative to the aether and in that interpretation the length of an object is not determined by the relative velocities of observers with respect to the object. In the Einstein interpretation there is no absolute reference frame or aether and everything is determined by the relative motion of observers. Interestingly there is no mathematical difference between the two interpretations and there is no experiment (as far as I know) that can distinguish between the two interpretations.
Big bang theory coems from (general) relativity so there's no problem. In nearly any specific situation there's going to be ceratin classes of cooridnates that are preferable to use (dependign on what you want to use them for of course). I suppose the important thing is in general there isn't a ceratin class of coordinate systems that are preferable.
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