"Speed of Light"

[Umbran]

Not sure what you mean here with regards to FTL?

That article has the followign passage:

"For decades, Guth, Linde and other theorists have advanced the view that the universe somehow inflated itself to huge size in as little as an undecillionth of a second (10 to the negative 36th power). If such an expansion were measured as a three-dimensional spatial phenomenon, the velocity would seem to exceed the speed of light. But in this case, the entire cosmos would have expanded into extradimensional space."

There are a couple of issues with that - they say, "the velocity would seem to exceed". Note that velocities are attributed to objects. They didn't say *what* would seem to have a velocity greater than light. "The Expansion" is not an object with a velocity.

Though, come to think of it, "The Expansion" sounds like a Dr. Who antagonist....

Be that as it may, in inflationary scenarios, it isn't that objects move, it is that space gets added, which is not the same thing. No object moves faster than light, but all objects not otherwise bound together wind up with more distance between them. At that age of the universe, mind you, there aren't much of what we'd call "objects" in existence anyway. We are talking about something that happened when the Universe was between 10^-35 to 10^-32 seconds old. At the *end* of inflation, if I have my numbers right, what we now call the "observable universe" was still less than a millimeter across - still so dense that "things" aren't really a going concern.

 

[Morrus]

I thought the idea of ftl was not possible?

http://www.nbcnews.com/science/space/smoking-gun-reveals-how-inflationary-big-bang-happened-n54686

Objects cannot move through space faster than light. The expansion of space isn't motion through space.

 

[tomBitonti]

Objects cannot move through space faster than light. The expansion of space isn't motion through space.

Is there no frame of reference into which to put co-expanding particles? Say, of one or of the other particle?

I'm not saying that it isn't different, but how is that frame different than other frames of reference? Why aren't the relative particle velocities meaningful in that frame?

Note that we don't need inflation to create pseudo-velocities, of the sort caused by inflation, which are greater than the speed of light. The ongoing, much slower, expansion of the universe is doing so for particles at extreme distances. Inflation shrinks the radius at which the speed of light is reached as a pseudo-velocity.

Thx!

TomB

 

[Morrus]

Is there no frame of reference into which to put co-expanding particles? Say, of one or of the other particle?

I'm not saying that it isn't different, but how is that frame different than other frames of reference? Why aren't the relative particle velocities meaningful in that frame?

I'll leave it to the actual physicists to answer that. You just went above my pay grade. Usually that means the answer = equations, which is where I stop following along!

 

[Umbran]

Is there no frame of reference into which to put co-expanding particles? Say, of one or of the other particle?

Well, there's the trick - pick two particles close enough together that there are no other particles in the space, then the relative speeds will be under that of light. Pick two distant particles... then you have a whole lot of other particles int eh field of view, and you can see the issue.

I'm not saying that it isn't different, but how is that frame different than other frames of reference? Why aren't the relative particle velocities meaningful in that frame?

Ah, there's the phrase we can use. The particle velocities aren't meaningful in that frame, because the frame isn't constant! The frame is expanding!

One way to think of it is thus: when we pick a frame of reference, we don't actually pick just a central point. We pick that central point, and some distant points - usually implicitly we pick "relative to the distant stars" which are fixed for most human purposes. The reference points of the frame, Einstein tells us, are arbitrary, so for most cases they don't matter. But we are now talking about a case where it does matter.

When we are talking about cosmological expansion, we are no longer talking about small distances or times. We are talking about distances and times which span... all. There is no larger, fixed outer edge of the frame of reference to which we can refer, and we have to worry about the fact that the frame itself is no longer constant!

There are other ways to explain the difference.. I remember a really cute video I saw recently. Let me see if I can find it again...

 

[tomBitonti]

Well, there's the trick - pick two particles close enough together that there are no other particles in the space, then the relative speeds will be under that of light. Pick two distant particles... then you have a whole lot of other particles int eh field of view, and you can see the issue.

Ah, there's the phrase we can use. The particle velocities aren't meaningful in that frame, because the frame isn't constant! The frame is expanding!

Not sure what other particles do to change the situation, except to make the observations a lot messier. (Some bad astronomy pun deserves to be attached to "messier", but, being humor impaired, I'll leave that to others.)

Is a non-constant frame of reference a problem? There are all sorts of non-constant frames which are used in physics. There are distinctions made between inertial and non-inertial frames of reference (giving rise to pseudo-forces; for example, a frame of reference defined from a point on a spinning disk is non-inertial, and gives rise to centrifugal forces). But, I thought that a frame of reference was just a coordinate system, with more or less utility based on how well the frame exposes particular physical properties of the system which is being studied.

Is the problem perhaps that frames of reference (which is how we are used to thinking) don't work very well when applied to an expanding (or contracting) region of space-time, because of the non-uniform scale factor which results?

Note, I'm really not trying to say that we shouldn't treat recession velocities as special. I'm trying to understand exactly how we know they are special. At least, how do we know without doing a global analysis. For a pair of particles, how is a recession velocity distinguishable from simple motion?

Thx!

TomB

 

[Umbran]

Not sure what other particles do to change the situation, except to make the observations a lot messier. (Some bad astronomy pun deserves to be attached to "messier", but, being humor impaired, I'll leave that to others.)

They make the situation obvious. Like Edwin Hubble noted, *everything* is moving away from us? Really? *Everything*? How does that make sense?

Is a non-constant frame of reference a problem?

It isn't a problem, insofar as we can work with it, once we identify it. It is a problem if we assume that the thing is constant, and interpret our observations as if it were constant, but it isn't!

There are distinctions made between inertial and non-inertial frames of reference (giving rise to pseudo-forces; for example, a frame of reference defined from a point on a spinning disk is non-inertial, and gives rise to centrifugal forces).

Okay, so if you understand that - special relativity, in which the whole "limit to the speed of light" is initially given to us, is about inertial frames of reference. Choosing the rest frame of one of the two particles is an attempt to choose an inertial frame of reference. And, locally, that works. But, on the cosmological scale, that rest frame is not actually an inertial frame, and special relativity does not hold.

Note, I'm really not trying to say that we shouldn't treat recession velocities as special. I'm trying to understand exactly how we know they are special. At least, how do we know without doing a global analysis. For a pair of particles, how is a recession velocity distinguishable from simple motion?

Here's how:

Take the expanding universe. The apparent speed of an object is related to the object's distance away from you. This is Hubble's Law: v=H*D, where v is the apparent velocity, and D is the distance. The farther a thing is away from you, the faster it is moving away from you.

So, at a given time, an object is some distance away, and moving at some speed away. At a later time, it will then be farther away, and thus moving *faster*. The object is accelerating!

But now, we can go back to Newton. Objects at rest stay at rest, unless a force acts upon them. That thing is accelerating, but there's no force acting on it!

Moreover, we note that while it is moving quickly relative to us, we can also note that it is *not* moving quickly relative to it's neighbors or its own local space.

Voila! We know something is hinkey!

 

[tomBitonti]

Right right. But, what we think of as forces is a little trickier than that: Note that the force of gravity can be viewed as a fictitious force. From:

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

Definition and basic properties

General relativity is a metric theory of gravitation. At its core are Einstein's equations, which describe the relation between the geometry of a four-dimensional, pseudo-Riemannian manifold representing spacetime, and the energy–momentum contained in that spacetime.[33] Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow.[34] The curvature is, in turn, caused by the energy–momentum of matter. Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve.[35]

Bold added by me.

Here's how:

Take the expanding universe. The apparent speed of an object is related to the object's distance away from you. This is Hubble's Law: v=H*D, where v is the apparent velocity, and D is the distance. The farther a thing is away from you, the faster it is moving away from you.

So, at a given time, an object is some distance away, and moving at some speed away. At a later time, it will then be farther away, and thus moving *faster*. The object is accelerating!

But now, we can go back to Newton. Objects at rest stay at rest, unless a force acts upon them. That thing is accelerating, but there's no force acting on it!

Moreover, we note that while it is moving quickly relative to us, we can also note that it is *not* moving quickly relative to it's neighbors or its own local space.

Voila! We know something is hinkey!

I'm thinking we need to be a big more careful to define what we mean by velocity to understand recessional velocity.

Velocities already don't add in a simple linear fashion -- v_ab + v_bc != v_ac (v_xy == velocity of y measured by x) -- because of special relativity. That there are other non-linear phenomena should not be too much of a surprise.

Thx!

TomB

 

[tomBitonti]

Ok, to get more funky:

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

See the section "Uses of the proper distance":

Uses of the proper distance

If one divides a change in proper distance by the interval of cosmological time where the change was measured (or takes the derivative of proper distance with respect to cosmological time) and calls this a "velocity", then the resulting "velocities" of galaxies or quasars can be above the speed of light, c. This apparent superluminal expansion is not in conflict with special or general relativity, and is a consequence of the particular definitions used in cosmology. Even light itself does not have a "velocity" of c in this sense; the total velocity of any object can be expressed as ...

The tail has this statement, which links to:

http://arxiv.org/abs/astro-ph/0310808

The issue of how best to describe and popularize the apparent superluminal expansion of the universe has caused a minor amount of controversy. One viewpoint is presented in (Davis and Lineweaver, 2003).

Thx!

TomB

 

[tomBitonti]

Ok, got some time to scan over that last referenced paper.

In the ΛCDM concordance model all objects with redshift greater than z ∼ 1.46
are receding faster than the speed of light. This does not contradict SR because the
motion is not in any observer’s inertial frame. No observer ever overtakes a light beam
and all observers measure light locally to be travelling at c. Hubble’s law is derived
directly from the Robertson-Walker metric (Eq. 15), and is valid for all distances in
any homogeneous, expanding universe.

pp 3-4

Thx!

TomB