# Inertial reference frame

Are galaxies, quazars inertial reference frame? I think they are at rest or moving at constant velocity relative to the expanding space.

But what is the coordinate system to the scale of the whole universe that can describe these inertial reference frames appropriately? Is the coordinate system expanding together with the whole universe.

But I think that locally, we use a constant (not changing, otherwise the system seems to be a accelerated RF, as universe is expanding at increasing rate) coordinate system which might contradict the changing coordinate system which varies with the whole universe.

For example, if we use the same system to describe galaxies and quazars, they are seemingly "moving" faster than light.

Here's something brief from bcrowell that covers a lot of your question:

There is not just one such frame for the whole cosmos. There is one such frame for every point in the cosmos. Global frames of reference don't exist in GR.

The solar system isn't moving at any large fraction of c relative to the CMB, and there is not a huge amount of gravitational time dilation between the earth's surface and a point that is, say, outside the local group of galaxies.

When measures such as the age of the universe are discussed, we use the cosmic microwave background radiation as our "reference frame"....for convenience and uniformity, not because it's "correct" or "special".....it's expected to be uniform across a rather uniform cosmos.

As for galaxies moving faster than light, it's actually the space between the galaxies over vast insteller distances that is expanding and in aggregate results in distant galaxies moving away as new space is created. Within a given galaxy, gravity holds everything pretty much in place.

Yes, the space itself is expanding, so here I mean isn't the coordinate system changing while the space is changing? If it is not then the quazars are moving faster than light in that coordinate system, then special relativity doesn't hold in all coordinate systems...

Here's an analogy that might help:

As far as we know, the universe is over large scales pretty much homogeneous, that is the same everywhere. So imagine the universe is like the surface of a sphere. The galaxies etc. sit on the sphere and can move around on it. We can measure the position of a galaxy by its latitude and longitude, and this will stay roughly constant over time. Because the universe isn't quite homogeneous, these coordinates will change, and this is what is called the peculiar velocity, which for most things is quite low. But it'll always be less than the speed of light.

However, at the same time, the whole sphere is growing. Even stationary galaxies, fixed at a point on the sphere, are getting pulled further and further apart. The greater the distance between points on the sphere, the greater the speed of this expansion. The rate at which this happens could even be faster than light! Only the speed with which the galaxies move from point to point across the sphere is constrained to be sub light.

The analogy isn't perfect, and shouldn't be pushed too far, but hopefully it makes things clearer here.

Here's an analogy that might help:

As far as we know, the universe is over large scales pretty much homogeneous, that is the same everywhere. So imagine the universe is like the surface of a sphere. The galaxies etc. sit on the sphere and can move around on it. We can measure the position of a galaxy by its latitude and longitude, and this will stay roughly constant over time. Because the universe isn't quite homogeneous, these coordinates will change, and this is what is called the peculiar velocity, which for most things is quite low. But it'll always be less than the speed of light.

However, at the same time, the whole sphere is growing. Even stationary galaxies, fixed at a point on the sphere, are getting pulled further and further apart. The greater the distance between points on the sphere, the greater the speed of this expansion. The rate at which this happens could even be faster than light! Only the speed with which the galaxies move from point to point across the sphere is constrained to be sub light.

The analogy isn't perfect, and shouldn't be pushed too far, but hopefully it makes things clearer here.

Yes, you used an analogy of pumping balloon. So I said they are inertial reference frame when they are not accelerating relative to space itself. But in that reference frame coordinate system must be changing together with space (just like coordinates drawn on the surface of balloon expand with time). However, when we use coordinate system to describe motion we don't use coordinate system that is changing, then won't it be a accelerated RF with respect to space itself?

Yes, you used an analogy of pumping balloon. So I said they are inertial reference frame when they are not accelerating relative to space itself. But in that reference frame coordinate system must be changing together with space (just like coordinates drawn on the surface of balloon expand with time). However, when we use coordinate system to describe motion we don't use coordinate system that is changing, then won't it be a accelerated RF with respect to space itself?

There's a lot of confused terminology here and some concepts that don't really apply in the context so I'm not really sure what you're asking. Have another careful read of Naty1's post.

What do you mean by an 'inertial reference frame'? Indeed, what do you mean by a reference frame? I'd take this to simply mean a choice of coordinates. What does it mean to say that a coordinate system is accelerating? Does it mean that the metric is changing with respect to the time coordinate of the frame? But that's true of any coordinate system in a non-static universe.

Maybe by 'an object in an inertial reference frame' you mean objects that aren't accelerating. But what does acceleration mean? There is a local concept of acceleration, which carries over from special relativity. But an object under the influence only of gravity and no other force is not accelerating by this definition; it is moving in a straight line through spacetime.

Any concept of velocity or acceleration that tries to relate objects at different spacetime points relies on a special choice of time coordinate. In the cosmological setting, there happens to exist a convenient, natural choice of such a coordinate as described by Naty1, so we can use this choice to talk about things like Hubble's law and the acceleration of the expansion of the universe. But the 'velocities' as defined in this way are not true velocities in that they depend vitally on the coordinate choice. In particular, there is no contradiction if speeds in this sense exceed the speed of light.

One thing that may help you learn to read previous discussions where mentors or advisors write explanations...then keep those that make sense to you....for example: crowell also wrote this previously, I believe, which I saved because I liked it:

"In an FRW cosmological model, there are preferred observers, who are essentially observers who detect no dipole asymmetry in the CMB. Such observers agree with one another on the amount of clock time since the Big Bang, and this is what we mean when we speak of the age of the universe in such a model."

If you don't know what FRW is, or dipole asymmetry or big bang....look it up. It IS a lot of work, especially early on. But once you begin to understand several pieces, others begin to fall into place.

I like to read the brief history, as in Wikipedia..which says this:

"Eventually Einstein acknowledged the correctness of Friedmann's calculations, but failed to appreciate the physical significance of Friedmann's predictions."

[Friedman is the "F" in "FRW"] So Einstein himself did not fully understand the solution to his own equations!!!! I like to keep statements like that in mind when I think "Why can't I understand that???" Nothing is so important as perseverence.

If it is not then the quazars are moving faster than light in that coordinate system, then special relativity doesn't hold in all coordinate systems...

Maybe this will clarify..or lead to further inquiries:

http://en.wikipedia.org/wiki/Frame_of_reference

or

http://en.wikipedia.org/wiki/Inertial_frame_of_reference

LOTS to consider!

Last edited:
Dale
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Are galaxies, quazars inertial reference frame? I think they are at rest or moving at constant velocity relative to the expanding space.

But what is the coordinate system to the scale of the whole universe that can describe these inertial reference frames appropriately? Is the coordinate system expanding together with the whole universe.
There is no inertial coordinate system on the scale of the whole universe. Over that scale curvature is significant. You can only have inertial coordinate systems over sufficiently small regions of spacetime that the curvature can be neglected.

I'm not expert like crowell or Dalespam or the several "docs", but I agree with henry...seems like some terminology is confused...let me try a few simple minded replies:

Yes, the space itself is expanding, so here I mean isn't the coordinate system changing while the space is changing?

not really ....Usually you pick a coordinate system with fixed coordinates...and measure change relative to those fixed "positions".....space, or space and time for example.

If it is not then the quazars are moving faster than light in that coordinate system, then special relativity doesn't hold in all coordinate systems...

Special relativity applies locally.....Special relativity does NOT describe the cosmos....nor does it say anything about expanding space.....general relativity describes the cosmos.

General relativity is still valid because it does not limit the speed with which space is created. Einstein assumed space was NOT expanding...that the universe was STATIC; he was wrong as Hubble proved. (So don't think much of this is easy or intuitive.)

This may draw howls from experts but I believe it is accurate: nobody understands why space is expanding, what the cosmological constant is (which supposedly drives the expansion), nor exactly how these fit into GR. My take is that if we really understood, we'd be able to explain the value of the cosmological constant from first principles.

GR says that within a given fixed space, nothing moves faster than light....more correctly, no information moves faster than light. But some things DO appear to move faster than light....like the tip of a swinging laser beam from earth to the moon. You just can't pass information that way.

dalespam I see you posted while I was writing....

Over that scale curvature is significant.

But we say space is practically flat, right?? So most of the curvature is time???

Dale
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Yes. By "on the scale of the whole universe" I mean several billion ly in space and several billion years in time.

I don't generally like the idea of talking about the curvature or flatness of space (as opposed to spacetime) because it is a coordinate dependent idea. You can always take a flat spacetime and find a coordinate system where space is curved.

I don't generally like the idea of talking about the curvature or flatness of space (as opposed to spacetime) because it is a coordinate dependent idea. You can always take a flat spacetime and find a coordinate system where space is curved.

Great insight.....Never put those thoughts together.....but of course!!

What do you mean by an 'inertial reference frame'? Indeed, what do you mean by a reference frame? I'd take this to simply mean a choice of coordinates. What does it mean to say that a coordinate system is accelerating? Does it mean that the metric is changing with respect to the time coordinate of the frame? But that's true of any coordinate system in a non-static universe.

Sorry, for the ambiguity here. But if you choose, for example, an accelerated reference frame as the time axis in a flat space, you cannot use cartesian coordinates (maybe still some confusion here, I will try my best).

You can always take a flat spacetime and find a coordinate system where space is curved.

Yes, that is called a conformal (angle preserving) transformation, like the one performed on Minkowski spacetime to get the FRW (all FRW metrics are conformally flat) Milne metric that has k=-1.