Questions on Redshift, Distance and Space Expansion

[Mordred]

After reading that paper I'd like you to read the section on proper distance in particular this section.

 

"Comoving and proper distances are not the same concept of distance as the concept of distance in special relativity. "

 

https://en.m.wikipedia.org/wiki/Comoving_distance

 

That quote is under proper distance. This is something you have to be careful of is learning the different classes of observers, time treatments etc.

 

For time proper time, conformal time, coordinate time, commoving time, cosmological time.

 

length coordinate distance, proper distance, commoving conformal etc.

 

velocity can be apparent, peculiar or inertial. (notice this distinction).

 

The Lineweaver Davies and Hoggs papers I previously linked to you goes into these details.

 

SR uses proper observer and coordinate observer. Which is distinct from a commoving or cosmological observer.

 

Brian Powell adds some key details here.

 

http://tangentspace.info/docs/horizon.pdf

Edited November 29, 2016 by Mordred

[AbstractDreamer]

Conceptually I think I'm close. Every time i re-read some articles, more things make sense.

 

I think some theories make huge mathematical jumps, or substitute in other equations from physics. This always stumps me as i have to get distracted to learn something completely different just to keep pace, only to get further distracted by something else that i don't understand.

 

Is this right:

• peculiar velocity is like local velocity, and it is limited to c
• inertial velocity im guessing is based purely on expansion. It is proportion to distance from observer, and can be superluminal.
• recession velocity (im guessing apparent velocity) is the total of peculiar velocity and inertial velocity, and can be superluminal.

• comoving distance stays the same over time for two distant objects by "including and removing" expansion from the calculation, when the two objects have zero peculiar velocity relative to each other.
• proper distance changes over time due to expansion, for two distant objects with zero relative peculiar velocity.

• comoving objects have zero relative peculiar velocity, so that over time, the change in proper distance is purely down to expansion.

Not really sure on conformal, coordinate or cosmological time/observer. I do have some conceptual ideas i just don't know which way round they are called. Need to process more.

Edited December 1, 2016 by AbstractDreamer

[Mordred]

Well you have a few mixed up. Inertial velocity is due to f=ma. Key note definition of inertia. "Inertia is the resistance of any physical object to any change in its state of motion; this includes changes to its speed, direction or state of rest. It is the tendency of objects to keep moving in a straight line at constant velocity"

 

Peculiar velocity has two definitions depending on application. In cosmology however.

 

"In physical cosmology, the term peculiar velocity (or peculiar motion) refers to the components of a receding galaxy's velocity that cannot be explained by Hubble's law."

 

GR treats it under the first definition on this link.

 

https://en.m.wikipedia.org/wiki/Peculiar_velocity

 

Recessive velocity is a consequence of Hubbles law v=HD.

 

Commoving distance and proper distance

 

https://en.m.wikipedia.org/wiki/Comoving_distance.

 

Details on the particle horizon and conformal time here.

 

https://en.m.wikipedia.org/wiki/Particle_horizon

 

Don't worry about getting all these correct right away. They become clearer when you study the equations involved for each. Which takes time. However be aware of them when reading various papers.

 

Many authors assume you already know these terms and don't show the corresponding metrics. Particularly in arxiv articles, so if your not careful not being familiar with these terms can throw you off and mislead you when reading technical papers.

 

Sean Carroll has a nice write up of some of these hazards.

 

http://www.preposterousuniverse.com/blog/2015/10/13/the-universe-never-expands-faster-than-the-speed-of-light/comment-page-2/

Edited December 1, 2016 by Mordred