Stretched space far from our own

[woodysooner]

Ok I'm sorry if this is a stupid question I read so many books about this stuff but not all sinks in I try but ok here's the question in Martin Ree's book, Just six numbers he talks about how when the universe was made it starts off at a certain speed and the further you go out like on the boundary of space and time it is going so fast it stretches space like bends it in essence can anyone explain that and another thing in the book faster then the speed out light by Joao Maguiejo he explains how speed of light was always a constant by in the beginning it was not 3 E to the 8 m/s but much faster can someone explain this and if it is even a leading idea he said it is but all my teachers frown upon it but I am sure most profound ideas even SR or GR by einstein were frowned upon in the beginning.
Sorry but i have one more, ok someone please paint a beautiful picture for me for i am truly lost with this. Ok singularity with ifinite mass density blah blah some reason boom and we're off the universe begins here's the things i cannot understand or maybe just picture ok a star that is on the boundary of the universe 10 or 15 billion light years use to in the beginning be right beside us?? true or not and i think that's true so what made it out there and us not like why was it chosen to get out of the gates first i understand once its off and runnin the farthest things runs the fasted i think but if someone can explain this it will help also let's say:
right when big bang goes off you have a light in your hand and i have a light in my hand. you get off first and i a lil after you now 15 billion years later you are way way out there and i am where we are on earth, can i see your light and can you see my light? like when galaxies are red shifted away from us just because they are moving away that doesn't mean that there light is moving away does it cause it travels constant every which way right??
just if anyone can answer a few of these i would be happy and sorry for my ignorance i try but maybe not hard enough.

 

[woodysooner]

any idea

sorry to bother everyone but anyone have a clue

 

[meteor]

Please, try to use periods and commas in your writings, you remember me a member called chosenone
VSL cosmology is actually out of the mainstream investigation. It is a theory that eliminates inflation, and had in the past problems to create the observed fluctuations in the CMB, but these problems were overcame, and actually the theory can predict these fluctuations

 

[woodysooner]

sorry bout the periods

sorry about the periods and commas I'll watch that. Ok VSL is out and now what is in? by the way what does VSL stand for? Also what was the stretched space stuff?

 

[meteor]

VSL stands for Variable Speed of Ligth. The idea that the velocity of light was faster in the early universe was first formulated by Moffat in 1991, though it was generally ignored by the scientific community. In 1998, Albrecht and the portuguese Magueijo formulated their VSL cosmology, in this paper
http://xxx.lanl.gov/abs/astro-ph/9811018

 

[woodysooner]

?

so now VSL is gone and what is the stance on how the inflation took place how do you explain the horizion problem.

 

[Prometheus]

VSL stands for Variable Speed of Ligth. The idea that the velocity of light was faster in the early universe was first formulated by Moffat in 1991, though it was generally ignored by the scientific community. In 1998, Albrecht and the portuguese Magueijo formulated their VSL cosmology, in this paper
http://xxx.lanl.gov/abs/astro-ph/9811018

The idea that the speed of light was faster in the early universe makes a lot of sense to me. By faster, I mean greater motion through space, not through space-time, because the speed of light is constant in space-time.

Because the speed of light is constant in space-time, as the universe ages, as it passes through greater time, the rate of motion through space correspondingly lessens.

I think that theories about a slowing through space of light over time might have a rough sell now because we can only see light from such a small part of the universe that our context is not large enough to recognize this phenomenon well.

 

[marcus]

so now VSL is gone and what is the stance on how the inflation took place how do you explain the horizion problem.

yes VSL is gone---it was always fringe, not mainstream.
Another thing: the so-called "horizon problem" has been addressed in various ways
(back in the 1980s it was addressed by Inflation Stories) and most recently it has been resolved by replacing the classical bigbang singularity by a changeover from contraction to expansion

the "horizon problem" consisted of people asking why the CMB Microwave Background is very nearly the same temperature or intensity in all directions. How do the Microwaves from over there KNOW to be the same intensity as these other Microwaves coming from the other side?

that has been answered pretty well by now. I would advise you to worry instead about some more basic things first and afterwards ask again about the "horizon problem" (like, why is it called that---in science almost everything is called by an accidentally chosen possibly misleading name so there is a long story of why it is called "horizon" and not something more reasonable like the "microwave uniform temperature problem"---but naming problems is a technical issue)

You already asked a good basic question which would be good to start with.
You asked how it can be that we two start out close together and then after 13.7 billion years (estimated age of U) we are so far apart.

there is no fixed reference point, no "zero on the x-axis", in Nature. So it is not like you stayed put and I am the one who is far away. Only the distance between has meaning. We were close then. Now we are far apart.

that happens even if neither one of us is aware of moving in our local neighborhood of space. We can both think we are standing still in the space around us. But after 13 billion years we find we are far apart! Distances between stationary points increase. AFAIK there is no way to make that easy to grasp.

If the two points are fairly far apart already then the distance between them can be increasing faster than c. Got that?
this is just commonplace mainstream cosmology----not "VSL"
it is a consequence of Hubble's law and goes back to the 1930s.

the distances to lots of the galaxies we can see today are at this moment increasing faster than c------this is a consequence of General Relativity (Einsteins 1915 theory) and does not contradict his 1905 Special Relativity.
the speed limit of Special Rel does not apply to widely separated points where there is curvature. (the never told you the speed limit has limited applicability? it was a surprise to me too)

You are asking a good initial question and the answer is already hard to comprehend. distances in nature actually increase, and they even increase faster than the speed of light. things near each other can be wide apart a few billion years later.

IIRC it is estimated that stuff close to us with the expansion began can now be as far away from us as 46 billion light years. that really takes a stretch to understand. how can it have happened that in only 13.7 billion years some stuff could have gotten from being near us to being 46 billion LY away? It happens because for at least part of the time the expansion of the distance between us was faster than c. I doubt that anybody here finds this easy to understand so if you find it hard don't worry.

 

[woodysooner]

wow that was very well put

thanx so much marcus. I didn't know traveling faster than C was possible at any point no matter what the particle was. Can you explain how this is possible, because these galaxies moving away are constituents of matter itself, and if matter travels faster then c i would think all the time backward issues would start popping up, but i am assuming everything is just fine and there is a good explanation, you say it has something to do with curvature of spacetime and GR, kind of like it was traveling close to c already then it hits the curve and boom massive acceleration above c?

Cheers Woody

 

[force5]

Great description Marcus!

Hi Marcus;

On your reference to expansion/contraction, I must have missed that along the way. But, I am very pleased to learn this from someone in the know. It fits my model to a tee. (sorry for reference to theory) Selfadjoint fussed at me about that. Could you please make reference to where I might find more on this subject. Thanks in advanced for any help.

 

[woodysooner]

?

? any idea ?

 

[Prometheus]

If the two points are fairly far apart already then the distance between them can be increasing faster than c. Got that?

No.

this is just commonplace mainstream cosmology----not "VSL"

Perhaps.

It can also be explained by a slowing of the speed of light over time since the Big Bang. You are very quick to dismiss this idea as completely implausible. I think that it deserves more consideration. The idea that you contend, that space can somehow move faster than the speed of light, is hardly more appealing.

 

[Chronos]

No.


Perhaps.

It can also be explained by a slowing of the speed of light over time since the Big Bang. You are very quick to dismiss this idea as completely implausible. I think that it deserves more consideration. The idea that you contend, that space can somehow move faster than the speed of light, is hardly more appealing.

Marcus is quick to dismiss that idea because it has been exhaustively examined and found inconsistent with observation and prediction many times.

 

[woodysooner]

so which one of you is right, not to start anything please but this kind of stuff confuses me, it happens in every thread i post, two super intelligent people argue or something near that i am i like hmmm no clue.

thanx for anyones help

 

[Prometheus]

Marcus is quick to dismiss that idea because it has been exhaustively examined and found inconsistent with observation and prediction many times.

Thanks for claiming to be able to respond for Marcus, but you seem not to have read his post.

What do you mean by eshaustively. You surely cannot mean that there is no possibility of futher examination.

Marcus says that VSL is not mainstream. This is hardly a way to phrase a complete rejection. Are you seriously contending that the concept of space expanding faster than the speed of light is a reasonable one, or that it has been so exhaustively demonstrated that other ideas should no longer be considered?

Furthermore, what is this it that you refer to as having been exhaustively examined? Surely, you cannot be claiming that there is no purpose at all in considering the possibility that the speed of light, although constant in space-time, might not be constant throughout time. How could it? This violates the notion that the speed of light is constant in space-time.

 

[marcus]

two super intelligent people argue or something near that i am i like hmmm no clue...

this had me laughing out loud----I guess there are superintelligent people in the world but at PF we are all pretty much equally like hmmm no clue (at least I may speak for myself in that regard!)

chronos thanks for the moral support.

the simplest is for me to withdraw what offends Prometheus and to assure him that I do not peremptorily dismiss "VSL"
I just want to make very forcefully the point that faster-than-light recession speed has been a standard premise of mainstream cosmology for 70 years. It is not my idea and it is not controversial

(this is what prometheus apparently has not realized yet)

so it is not a novel scenario like "VSL" . it is not to be compared with somebody's new idea----it is just an everyday feature of mainstream cosmology.

Of course Einstein could be wrong and the basic Einstein-Friedmann equation of standard cosmology could be wrong and the universe could be in some clever way NOT be expanding in the linear hubble-law way that cosmologists grow up assuming. Maybe it isn't expanding at all!

But if you want to talk with people you have to understand the basic mainstream model. And it is an essential part of that model that you have FTL recession speeds beyond the Hubble distance. The model WILL NOT WORK WITHOUT THIS. And you have to understand that many of the galaxies we observe today were receding from us faster than c at the moment when they emitted the light that is now reaching us.

If you don't understand this, you remain confused about the standard model.
the standard model is the usual point of departure for discussion so its really hard to have a cogent discussion if you ignore it.

 

[jcsd]

Thanks for claiming to be able to respond for Marcus, but you seem not to have read his post.

What do you mean by eshaustively. You surely cannot mean that there is no possibility of futher examination.

Marcus says that VSL is not mainstream. This is hardly a way to phrase a complete rejection. Are you seriously contending that the concept of space expanding faster than the speed of light is a reasonable one, or that it has been so exhaustively demonstrated that other ideas should no longer be considered?

What exactly is the problem with recession velocities greater than c?
Expansion is just a result of general relativity and you get recession velocities greater than c in any universe described by general relativity that is large enough/ has a large enough scale factor. Do you disagree with general relativity?

Furthermore, what is this it that you refer to as having been exhaustively examined? Surely, you cannot be claiming that there is no purpose at all in considering the possibility that the speed of light, although constant in space-time, might not be constant throughout time. How could it? This violates the notion that the speed of light is constant in space-time.

Clearly a non-varying lightspeed as well as fitting in with observation DOES NOT violate anything in relativity as it axiomatic in relativity.

 

[marcus]

there is a good source for mainstream cosmology on the web
which is ned wright site

he teaches cosmology (grad and undergrad courses) at UCLA and is one of the co-leaders of WMAP (satellite microwave observ.----the world's premier source of cosmology data)
he's an easygoing california dude with a beard who happens to be one of the worlds top cosmologists, check out the site
check out the cosmology FAQ
and the tutorial (introductory cosmology)
and check out the calculator

just say Ned Wright to google
and if you can't find any of that stuff, post back to this thread and
I or someone will give links.
--------
the cosmology calculator is an essential part of the package
because it embodies in a concrete form as nothing else on the web does
the nuts and bolts standard cosmology model
with the standard parameters

H is 71
Lambda is 0.73
Omega-sub-matter is 0.27

you take anybody's cosmology calculator and put those parameters in
and you have the universe in your hand.
If you hear that somebody observed a galaxy with redshift z = 6

which means the wavelengths are stretched out by a factor of 7

then you put z = 6 into that calculator and it tells you how far away the thing is. Anyone interested at all in cosmology shd really try this.

It doesn't just tell you how far away the thing is now. It tells you how long ago it emitted the light and how far away it was when it emitted the light.

I've spent a while trying different z, and trying to picture our U with those galaxies and the overall shape of the expansion. the calculator is a good tool. or I find it so anyway.

Siobahn Morgan's site has a better laid-out calculator than Ned Wright's
even tho he is more the prominent cosmologist. they give the same distances and times but hers gives recession speeds too.
------------------
from post 136407 in Astro sticky:

Ned Wright's
http://www.astro.ucla.edu/~wright/CosmoCalc.html

Siobahn Morgan's
http://www.earth.uni.edu/~morgan/ajjar/Cosmology/cosmos.html

homepage for Siobahn in case you want to see who she is
http://www.earth.uni.edu/smm.html
homepage for Ned in case you want to see who he is
http://www.astro.ucla.edu/~wright/intro.html

https://www.physicsforums.com/showthread.php?p=136407#post136407

 

[woodysooner]

equation

And it is an essential part of that model that you have FTL recession speeds beyond the Hubble distance

Marcus, can you show me how this is derived, I'm sure it can be if you say so, i don't know enuff about the subject so maybe there is a GR way to show or proof it at least in the model we are speaking about. My prof in phys said that galaxies never move faster than speed of light and he is a GR man through and through so i thought maybe if i had a equation of GR for this model it mighthelp.

thanx

 

[marcus]

Marcus, can you show me how this is derived, I'm sure it can be if you say so, i don't know enuff about the subject so maybe there is a GR way to show or proof it at least in the model we are speaking about. My prof in phys said that galaxies never move faster than speed of light and he is a GR man through and through so i thought maybe if i had a equation of GR for this model it mighthelp.

thanx

for people like your prof there is an article
called "Expanding Confusion: Common Misconceptions..."
by Tamara Davis and Charles Lineweaver
it is a tutorial on popular confusion about recession speed.
look at it yourself before you give it to him.

------------------------
http://arxiv.org./abs/astro-ph/0310808
Davis and Lineweaver
"Expanding Confusion:common misconceptions of cosmological horizons and the superluminal expansion of the Universe"
-------------------------

Lineweaver and Davis are at the University of New South Wales.
Lineweaver was a co-leader of the COBE project (satellite
mapping the cosmic microwave background in the 1990s)

Lineweaver is one of the world's top cosmologists and Davis is his grad student. She just got her PhD and her thesis is on this very same topic
http://arxiv.org/astro-ph/0402278

Tamara Davis thesis (advisor Charles Lineweaver)
"Fundamental Aspects of the Expansion of the Universe and Cosmic Horizons"
----------------------


the main point is there are two kinds of speed-----so different that it is confusing we have the same word in both cases:

ordinary speed and recession speed

recession speed is the rate at which the distance to a far-off galaxy is increasing----it can easily be 600,000 kilometers a second or twice c.

that is not the same as the speed of a bird flying past your house or of a spaceship flying past the earth

-----------------------
a galaxy can easily be receding at 600,000 kilometers a second but this does not mean that it could ever catch up with and pass a photon of light
because the space around the galaxy and everything else that far away from us is receding at 600,000 km/s.
The galaxy thinks it is sitting still (approximately, say with respect to the microwave background) and for all we know it IS sitting still. the curious thing is the distance from us to it is increasing superluminally.
--------------------

the mathematical proof is easy if you know Hubbles Law
which is
v = Hd
(Ned Wright explains this and makes the point emphatically that v is the current speed and d is the current distance. Hubble's Law is NOT about "doppler shifts" or redshifts----it is a linear relation of presentday recessionspeed and presentday distance)

if your prof knows GR then he probably knows the FRW type of metric that cosmologists normally use. this is how the presentday distance is defined. and it has a distinguished time parameter---these are technicalities
(if he doesn't know the Friedmann-Robertson-Walker metric he may not "get" the idea of the instantaneous presentday distance to a galaxy and he may not understand the v = Hd law.)

Anyway if he knows the Hubble law then the derivation you asked for is clear:
H = 71 km/sec per megaparsec
so just divide 300,000 by 71
that gives the distance in megaparsecs

You go that distance out===and the recession speed is c.
You go twice that distance out====and it's 2c
You go three times that distance out====and things receed at 3c.

this magic distance called Hubble distance, gotten by dividing 300,000 by 71, is 4225 Mpc-------4225 megaparsecs.

a parsec is 3.26 lightyears so a megaparsec is 3.26 million LY.
so Hubble distance is 13.8 or about 14 billion LY.

Anything that far from us at this moment is at this moment receeding at c.

there is lots more potential for confusion. Your prof may say something like "but of course we can't see things that are 14 LY away, they are not in our observable universe." Wrong. get to use Ned Wright's calculator, or Siobahn Morgan's. Dont believe that nonsense. We are currently observing galaxies farther away than that. because the expansion of space actually helped (after a photon has covered a certain distance that distance expands) in a certain sense. But that is another discussion.

of course he many never understand and you risk a bad grade in the course.

 

[woodysooner]

You go that distance out===and the recession speed is c.

You go twice that distance out====and it's 2c

So ten times that distance and your at 10c, makes sense cause in Martin Gardner's Einstein simply explained he talked about speed of galaxies receding at 9C or something to that extent.

But this magical distance equaling 14.5 billion light years , are we not 14 billion years old, this universe so how can distances be past this to make 2C, 3C, etc possible.

Anything that far from us at this moment is at this moment receeding at c.

sorry that i am confused, but are you saying distances up to the Hubble distant of 14 billion light years things are receding at C and beyond that what i explained above.

Your prof may say something like "but of course we can't see things that are 14 LY away, they are not in our observable universe." Wrong. get to use Ned Wright's calculator, or Siobahn Morgan's. Dont believe that nonsense. We are currently observing galaxies farther away than that. because the expansion of space actually helped (after a photon has covered a certain distance that distance expands) in a certain sense. But that is another discussion

You say we are currently observing galaxies father away than that. How far, and how is that if we only go back in time 14 billion years.

I think there is a simple explanation to this but i am not at it yet.

 

[Prometheus]

I just want to make very forcefully the point that faster-than-light recession speed has been a standard premise of mainstream cosmology for 70 years. It is not my idea and it is not controversial

Faster than light, with all of its nuances that must be considered, is considered to occur in what is known as inflation. Is this your scenario, or are you considering another facet of faster than light motion?

How does your faster than light motion function in concert with the concept in relativity that the speed of light is constant in space-time?

The fact that it is part of mainstream cosmology is hardly relevant here, is it not. Mainstream does not mean unequivocally correct, such that no other concepts should be considered. The theory of relativity was hardly mainstream when it was introduced, now was it?

so it is not a novel scenario like "VSL" . it is not to be compared with somebody's new idea----it is just an everyday feature of mainstream cosmology.

I am not supporting the theory of VSL as elucidated earlier on this forum. I am saying that the concept of an inconstant rate of motion of light through space would support the idea that the speed of light is constant in space-time.

Of course Einstein could be wrong and the basic Einstein-Friedmann equation of standard cosmology could be wrong and the universe could be in some clever way NOT be expanding in the linear hubble-law way that cosmologists grow up assuming. Maybe it isn't expanding at all!

How clever. Do you really think that "mainstream' cosmology will be around in pretty much its present form 100 years from now? How about in 20 years. Of course, Einstein is wrong, in the same way that Newton and Ptolemy were wrong. Their ideas, no matter how useful, will not last forever as the most useful theories around.

Let me ask you a question. The speed of light is constant in space-time. Increases in motion through space are accompanied by decreases in motion through time. As our space-time travels outward from the Big Bang in space, do you think that it is possible to maintain the constantcy of the speed of light in space-time without a change in the rate of motion through time, and the rate of motion through space-time of light?

 

[Prometheus]

What exactly is the problem with recession velocities greater than c?

Nothing. In the same way, what is wrong with the concept of a changing c? If space-time in different parts of space is moving at different rates through time, such that the speed of light is constant is space-time, then it is quite reasonable that recession velocities are greater than c as we recognize it here in this part of the universe.

Expansion is just a result of general relativity and you get recession velocities greater than c in any universe described by general relativity that is large enough/ has a large enough scale factor.

what do you consider is the reasoning behind the requirement of size?

Clearly a non-varying lightspeed as well as fitting in with observation DOES NOT violate anything in relativity as it axiomatic in relativity.

I agree. The speed of light is constant. However, it is constant in space-time. To consider that the speed of light is constant throughout all of space outside of the context of space as space-time, is a major contradiction, in my opinion. Space has no context outside of time, as space-time.

 

[Chronos]

Nothing. In the same way, what is wrong with the concept of a changing c? If space-time in different parts of space is moving at different rates through time, such that the speed of light is constant is space-time, then it is quite reasonable that recession velocities are greater than c as we recognize it here in this part of the universe.

Not reasonable. If c is not invariant in all reference frames, we are in more trouble than can be imagined. Entire regions of the universe would be 'off limits' to travel. Makes it hard to explain how we can observe them.

I agree. The speed of light is constant. However, it is constant in space-time. To consider that the speed of light is constant throughout all of space outside of the context of space as space-time, is a major contradiction, in my opinion. Space has no context outside of time, as space-time.

You need to rephrase that question/objection. The speed of light outside of the context of space-time is meaningless. Marcus gave an outstanding explanation and excellent links to supporting sources. I encourage you to read and consider them. I learn stuff from doing that most every day. Just my opinion. You ask honest questions. I try to give honest answers. After that, I chicken out and refer you to people I think know a heck of a lot more than I do.

 

[Prometheus]

Makes it hard to explain how we can observe them.

That is good, since we cannot observe the entire universe. Or, do you think that we can?

Not reasonable. If c is not invariant in all reference frames, we are in more trouble than can be imagined. Entire regions of the universe would be 'off limits' to travel.

What are you saying? The speed of light is constant in space-time. Isn't that what your are trying to say? However, the speed of light is not constant in space or time, but only in space-time. There have been numerous demonstrations that the rate of motion of light through space is not constant. Neither is the rate of motion of light through time. It is only within the context of space-time that the speed of light is constant.

Do you understand the implications of space-time? Do you think that the rate of motion of light through space is invariant, and that light can never move through space at a rate less than is commonly given for c? Of course you don't. So, what do you mean?

 

[Chronos]

That is good, since we cannot observe the entire universe. Or, do you think that we can?

I vote for cannot.

What are you saying? The speed of light is constant in space-time. Isn't that what your are trying to say?

Yes.

However, the speed of light is not constant in space or time, but only in space-time. There have been numerous demonstrations that the rate of motion of light through space is not constant. Neither is the rate of motion of light through time.

A listing would be helpful. I am not aware of any such demonstrations.

It is only within the context of space-time that the speed of light is constant.

Agreed.

Do you understand the implications of space-time?

No, but, I have a lot of company.

Do you think that the rate of motion of light through space is invariant, and that light can never move through space at a rate less than is commonly given for c?

Yes.

Of course you don't. So, what do you mean?

Quite the contrary. I do think the speed of light is invariant... at least in my own way [GR].

 

[jcsd]

Nothing. In the same way, what is wrong with the concept of a changing c? If space-time in different parts of space is moving at different rates through time, such that the speed of light is constant is space-time, then it is quite reasonable that recession velocities are greater than c as we recognize it here in this part of the universe.

I siad recession velocity and no you don't need the speed of light to be greatr than the local value of c for recession velocites to be greater than c. i.e. recession velocties greater than c are NOT the result of VSL cosmology.

what do you consider is the reasoning behind the requirement of size?

General relativity, examine the Friedmann equation.

I agree. The speed of light is constant. However, it is constant in space-time. To consider that the speed of light is constant throughout all of space outside of the context of space as space-time, is a major contradiction, in my opinion. Space has no context outside of time, as space-time.

"The speed of light is constant in spacetime" means nothing, it's a vague statement. You could be talking about the length of the velocity, but it's hard to tell.

The speed of light is very much believed to be constant throguhout spce, infact this assumption is built into relativity, so arguing that 'spacetime' would say that this is not so is self-defeating.

 

[Prometheus]

A listing would be helpful. I am not aware of any such demonstrations.

I went to google.com, and followed the first link:

The speed of light depends on the material that the light moves through - for example: light moves slower in water, glass and through the atmosphere than in a vacuum.

Were you aware of this example that the speed of light is not always exactly c? You asked for an example to support what I said, and here is one. Please do not sluff it off as irrelevant, as this clearly supports my contention, and refutes yours that under no circumstances can light move through space other than at c.

 

[marcus]

So ten times that distance and your at 10c, makes sense cause in Martin Gardner's Einstein simply explained he talked about speed of galaxies receding at 9C or something to that extent.
------
But this magical distance equaling 14.5 billion light years , are we not 14 billion years old, this universe so how can distances be past this to make 2C, 3C, etc possible.
------

sorry that i am confused, but are you saying distances up to the Hubble distant of 14 billion light years things are receding at C and beyond that what i explained above.

--------
You say we are currently observing galaxies father away than that. How far, and how is that if we only go back in time 14 billion years.
--------
I think there is a simple explanation to this but i am not at it yet.

Hello Woody, I was away from this thread and just got back. JCSD has
replied to about everything I think, except this post of yours. I will try to say more clearly what I said before, because i think any trouble you are having is because I didnt say it clearly enough.

fortunately you have read the Martin Gardner book Einstein Simply Explained. I didnt, but you say he has galaxies receding at 9c and so on, so it covers at least the basics. Also the author is IMHO a really clear writer---we should all be so lucid!
--------------
this post will be rather technical so if you are not up for that simply skip it. Reading too technical stuff will just make confusion worse. but if you are up for it it might help. BTW the current estimate for age of universe is 13.7 billion years and the Hubble distance is different, like 13.8 billion LY, or 14 billiion LY. It confuses people that the numbers are so close. they are different things. Trying to explain the tantalizing closeness would be jumping ahead. Here's a repetition of the basic story, in a more technical getup.
-----------------

there are two basic differential equations in cosmology called the Friedmann equations (1st and 2nd) and often people are in a hurry and lump them together as call the two of them "the Friedmann equation".

https://www.physicsforums.com/showthread.php?p=210120#post210120

they are short simple equations but they are differential equations---they involve derivatives, rates of change, and that means Freshman calculus. first year college calculus is foreign to most people. so the Friedmann equations are considered too hard, and are talked around or avoided in general conversation so as not to make people go away.

this means that all our discussion are a bit lame---because we never touch first base. I'll find a link to a PF page on them so you can look if you want.

the Friedman eqs. describe the co-evolution of three things a(t) and rho(t) and p(t)-----the spatial scale factor, the energy density, and the pressure.

the pressure term is often considered neglible or zero and omitted --- it is only in one of the two equations anyway --- so people often forget about it and just think the equations are a dance between a(t) and rho(t).

a(t), the spatial scale factor in the metric or "distance measure", is an index of the size of the U. If it gets bigger that means distances are increasing. rho(t) is the average energy density thoughout space. So the equations describe a kind of mutual influence these two quantities have on each other. If you assume they start off some way then the equations let you map their progress.(so as not to sound technical popularizers call a(t) the "size of the universe" or "average distance between galaxies" but the U could be infinite and not have a radius so a(t) is not the radius.)

rho(t) is the energy density

I think you'll find it intuitively right that these two things "scale factor" and "density" should be related. Expansion must thin the density out. On the other hand, a high concentration of mass-energy should slow down expansion. The equations, as I say, are simple----its just that they involve a derivative a'(t) which makes them technical for most people. a'(t) is the rate of change of the "size", it is da/dt if you use that calculus way of writing. to get "accelerating expansion" into the picture we also can have a''(t) the second derivative or the change in the change in the scale factor. Naturally the density (and pressure if it is not negligible) is going to effect THAT. it is going to speedup or slowdown the expansion. so at some point if one is going to do cosmology at all one bites the bullet and considers some simple rather intuitive relations among
a(t) and a'(t) and a''(t) and rho(t) and (in case it isn't neglible) p(t).

That would be all right, but the first thing the crafty cosmologists do is define something (scientists are always doing this to us). They define
H(t) = a'(t)/a(t)

this is the famous Hubble parameter which at the present moment is
71 km/sec per Mpc.

why, if they already have a(t) the scale factor and its derivatives do they need to define this extra bit of notation? Various reasons. For one it is something that you can measure. Also the distance scale has an arbitrary quality and if you divide the rate of increase by the scale factor it gets rid of some arbitrariness----you have, like, a "percentage growth" indicator.
It is kind of subtle but H = a'/a is actually more useful-----by what fraction of itself does a typical distance grow each year----than either a' or a, sometimes. I am going to start leaving off the (t) and writing H instead of H(t).


from the Friedmann eqs. one can derive a nice formula called Hubble Law

v = H d

v(t) is current recession speed of some object and d(t) is the object's current distance from us
(defining v and d requires the cosmologists' usual metric, the distance measure called FRW metric)

So you can see the proportionality of recession speed to distance! It is right here in the Hubble law v = H d
there is nothing to it. double the distance and you double the recession speed! There has to be some distance at which things are receding at c, obviously (we will calculate that, it is called the Hubble distance). And if you go out 3 times that distance you find things receding at 3c.
the expansion has to be proportional---it is the only way it could be if it is going to look the same from different points of view.

in the next post I will calculate the Hubble distance, by setting v = c
and solving the Hubble law equation for distance d, in that case:
c = H d
You may already have done that or can go ahead and do that on your own.

 

[jcsd]

I went to google.com, and followed the first link:

The speed of light depends on the material that the light moves through - for example: light moves slower in water, glass and through the atmosphere than in a vacuum.

Were you aware of this example that the speed of light is not always exactly c? You asked for an example to support what I said, and here is one. Please do not sluff it off as irrelevant, as this clearly supports my contention, and refutes yours that under no circumstances can light move through space other than at c.

That's irrelevant, we're talking about the speed of light in a vacuum. VSL proposes that the speed of liught in a vacuum c is variable.

The fact that the speed f light varies in different mediums is due to the fcat that it inetracts with the material and these interactions change the amount of time it takes to travel through the material. This 'slowing' of light could not be a signifacnt factor when observing l;ight from stars and distant galaxies.

 

[marcus]

here is a link to Friedmann equations post at PF
https://www.physicsforums.com/showthread.php?p=210120#post210120
this link should be better---dont happen to have a better at the moment tho.
I actually am not sure I understand some of your questions about the
Hubble law proportionality.
Earlier I may have spoken too quickly or sloppily and given the impression that it is not a simple proportionality.
It is really really straightforward

Lets say we solve c = H d for a distance d at which things are receding at speed of light. and say it comes out d = 14 billion LY

then at 7 billion, things are receding at 1/2 c
and at 14 billion, at c
and at 21 billion, receding at 3/2 c
and at 28 billion, receding at 2 c
and so on

this is at this moment.

the presentday Hubble parameter does not tell about the past.

to find out about the past you have to solve the Friedmann equations going back into past----this is what Ned Wright and Siobahn cosmology calculators do for you and why it is important to play with the calculators a bit---there are also animations on the web that track a(t) graphically with various assumptions about how it starts off---but I like the calculators.

the thing is, in the past a(t) was different and a'(t) was different, and
H(t) was different! So how can you expect me to talk about past just using the information that right at this moment the expansion parameter H
is 71 km/sec per Mpc? Cant do it.

Yes one can do approximations, because H(t) changes only very slowly. So if you only go back 10 million or 100 million years it might look roughly the same.
But if you want to go back 10 billion years then H(t) will be very different.
However the Ned and Siobahn calculators will tell you what it is!
Like, I often see figures like H = 200 back early because expansion was faster then. then it slowed down, now it is very gradually speeding up.
this is what differential equations do. they generate beautiful curves.
but the curves have to be calculated! so you need a calculator to track the past history of a(t)-----the past history of the expansion of the U.

maybe I can find a graphic plot of the a(t) curve and give you a link.

anyway, at anyone instant of time there is a Hubble parameter H(t) and the recession speeds are proportional to distance by this straightforward
linear proportion v = Hd.

solving for the Hubble distance is easy, put c = 3E5 kilometers/sec
and put c = H D and solve for D
so 3E5 km/s = (71 km/s per Mpc) D

So you divide 300,000 by 71 and find that D has to be like 4225 Mpc :zzz:
or 4.2 Gpc and since a Gigaparsec is 3.26 billion LY you multiply by
3.26 and get that D is around 14 billion LY.

The problem here is that
specialists habitually use awkward units and for historical reasons astronomers got the nasty habit of saying parsec----a somewhat off-putting synonym for 3.26 light years.

 

[woodysooner]

thanx a lot that was very vey helpful but just one thing i asked that i wondered about. Is not the universe 15 billion years how do we see past that if it is nothing. I know it has to do with recesion speeds so can we not say how far it is to the end?? if so what is it, i though hawking mentioned it in his book like 45 billions yr but not sure.

 

[Nereid]

What are you saying? The speed of light is constant in space-time. Isn't that what your are trying to say? However, the speed of light is not constant in space or time, but only in space-time. There have been numerous demonstrations that the rate of motion of light through space is not constant. Neither is the rate of motion of light through time. It is only within the context of space-time that the speed of light is constant.

I too would also like to ask you Prometheus to please clarify this.

The only thing I can think of - re 'numerous demonstrations that the rate of motion of light through space is not constant' - is some difficult observations which seemed to show that alpha (the fine structure constant) is not constant, over cosmological time (a.k.a. billions of years). There have indeed been a number of projects to determine whether alpha does vary, and some teams have reported a positive result. However, later more detailed/more accurate work hasn't confirmed these results. So, the best observations we've got to date show alpha to be constant, to a few parts per million (IIRC), over the last 10 billions years (and ppb over the past ~2 billions years).

Of course, it's not possible (today) to determine whether alpha was constant or not over the first ~300,000 years since the BB.

 

[Prometheus]

That's irrelevant, we're talking about the speed of light in a vacuum.

I disagree. The statement that people seem to be making here is that the speed of light is constant, period, with no conditions. I claim that this is not true, that there must be a condition, and that the condition should be, in my opinion, that the speed of light is constant in space-time. Chronos maintained that no condition is needed, that the speed of light is invairant in space. I provided a simple demonstration that this is not true. You now cry foul, and tell me that we have an assumed condition, a vacuum. I disagree. How can you claim what "we" have an "assumed" condition as your justification for refuting my claim that we need to state our condition because we cannot have no condition?

VSL proposes that the speed of liught in a vacuum c is variable.

I am not attempting to support the theory known as VSL, because I do not know all of its tenets. However, I do consider that it is quite probable that the speed of light, even in a vacuum, is not constant in its rate of motion through space. Is it not well understood that as the rate of motion through space increases, the rate of motion through time decreases (recall the twin paradox). As the universe expands outward through space, why would this motion through space not have an impact on motion through time? If so, then the speed of light, although constant in space-time, would not be constant in space.

 

[Prometheus]

I too would also like to ask you Prometheus to please clarify this.

The only thing I can think of - re 'numerous demonstrations that the rate of motion of light through space is not constant' - is some difficult observations

Space and time are bound up as space-time. Examples such as the twin paradox show that as the rate of motion through space increases, the rate of motion through time decreaes. Motion through space time is constant, howver.

Rather than show a complex, controversial example that the rate of motion through space of light is not constant, I used a simple example of light through a medium such as water. This demonstrates that the rate of motion is not constant through space. Even a simple example such as this invalidates the gross generalization that the speed of light is constant in space.

What is the point of such a contension anyway? Space and time are bound up as space-time. To separate these into space and time is to introduce error. To integrate them into space-time forces us to consider, I believe, that as the universe continues in motion through space, there is an impact on motion through time.