If by "isotropic observer" you mean "an observer that sees the spacetime as isotropic", then yes, this is true. At least, it's true of the standard example of a homogeneous and isotropic spacetime, FRW spacetime.It is said that in the case of a homogeneous and isotropic spacetime, the surfaces of homogeneity must be orthogonal to the tangents to the world lines of the isotropic observer.
Yes. This is a bit of a strange way of stating it, though; the more standard way of stating it requires you to first set up the standard FRW coordinate chart, and then observe that what you are calling isotropic observers (the more usual term is "comoving" observers) remain at the same spatial coordinates in this chart for all time, hence are "at rest" in this chart.Does this mean that the isotropic observers are always at rest in a surface of homogeneity?
From this it seems "isotropic " observer means measuring isotropic CMBR readings , is this right?If by "isotropic observer" you mean "an observer that sees the spacetime as isotropic", then yes, this is true. At least, it's true of the standard example of a homogeneous and isotropic spacetime, FRW spacetime.
Yes. This is a bit of a strange way of stating it, though; the more standard way of stating it requires you to first set up the standard FRW coordinate chart, and then observe that what you are calling isotropic observers (the more usual term is "comoving" observers) remain at the same spatial coordinates in this chart for all time, hence are "at rest" in this chart.
It's also good to bear in mind that these comoving observers, although they are "at rest" in the standard coordinate chart, are *not* "at rest" relative to each other in other senses in an FRW spacetime. For example, if two comoving observers exchange light signals, they will see the round-trip travel times of the light signals continually increase or decrease (depending on whether they are in an expanding FRW spacetime or a contracting one).
In a universe with a CMBR, such as ours, yes. More generally, whatever matter/energy/radiation is present will appear isotropic to an "isotropic observer". (Obviously this only holds approximately in our actual universe.)From this it seems "isotropic " observer means measuring isotropic CMBR readings , is this right?
I've read it in "Wald - General Relativity". It means an observer who sees the universe as isotropic.oh yea isotropic is pretty commonly understood, especially in a physics forum. "Isotropic observer", given the definitions of "observer" & isotropic from a physics perspective, left me unsure if something besides plain ol' "observer" was implied.
I tried adding the definitions together...and it didn't add up.
The problem is that the worldline is always orthogonal, so the observer will always be at rest relative to the surface of homogeneityalialice said:At a given instant of course an observer is "at rest", but then it can move along its worldline!
Uhm.. if I take a picture of the universe at a frozen time t, then that is a surface of hoogeneity, is it right?PeterDonis said:Yes. This is a bit of a strange way of stating it, though; the more standard way of stating it requires you to first set up the standard FRW coordinate chart, and then observe that what you are calling isotropic observers (the more usual term is "comoving" observers) remain at the same spatial coordinates in this chart for all time, hence are "at rest" in this chart.
I find the question as worded in the OP kind of awkward.I've read it in "Wald - General Relativity". It means an observer who sees the universe as isotropic.
The problem is that the worldline is always orthogonal, so the observer will always be at rest relative to the surface of homogeneity
Uhm.. if I take a picture of the universe at a frozen time t, then that is a surface of hoogeneity, is it right?
If the time "t" is the time in the standard FRW chart (which is the same as proper time for "comoving" observers), then yes.Uhm.. if I take a picture of the universe at a frozen time t, then that is a surface of hoogeneity, is it right?
The reference to Wald makes it clear that the OP is talking about FRW spacetimes and their properties. I don't think the OP meant to raise any issues about measurements, the invariance of c, etc. (though he can of course correct me if I'm wrong).Personally I see it as asking about measurements, and the "consequence/effect" the invariance of c has on those measurements.
I did say that, but now I need to clarify that it's not *just* coordinates.Like Peter said this is "coordinates".
http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metricI don't even know what FRW is.
So if I am an isotropic observer (then "t" is the time in the standard FRW) I must be at rest in a given surface of homogeneity, can't I move?If the time "t" is the time in the standard FRW chart (which is the same as proper time for "comoving" observers), then yes.
Of course you "can" move (meaning you can have a worldline that does not stay at the same spatial coordinates for all time in the standard FRW chart). But if you move, you won't be an isotropic observer any more--you won't see the universe as being the same in all directions.So if I am an isotropic observer (then "t" is the time in the standard FRW) I must be at rest in a given surface of homogeneity, can't I move?
On re-reading this, I realized I should comment on the phrase "take a picture". I was interpreting that to mean "take a particular spacelike slice of constant FRW coordinate time t out of the entire spacetime". Any such spacelike slice is a surface of homogeneity.Uhm.. if I take a picture of the universe at a frozen time t, then that is a surface of hoogeneity, is it right?