Why do we speak of radial velocities of galaxies, then? Shouldn't we rather speak of speed of space stretching between galaxies and us?

If galaxy 1023 has a radial velocity v = 300 km/s for instance, shouldn't we say "space is stretching at 300 km/s between 1023 and us" instead of saying "1023 has a radial velocity of 300 km/s"?

In that case, is the Hubble Constant the speed of stretching space? Could Dr. Qworm say (he likes so much saying those kind of things!) "On a cosmological scale, the speed of stretching space is comprised between 50 and 100 km/s/Mpc!"?

After the speed of stone and the speed of time, he would have the speed of space - I am sure he would be really happy with that! [img]/phpBB/images/smiles/icon_wink.gif[/img]

Thanks to your help, I'm starting to see where the flaw in Dr. Qworm's reasoning is: I suppose now that the light we receive is not data that is billions of years old. If we were able to see it little time after it was emitted, it would have a very different redshift than it has now, wouldn't it? Thus the light the stars are sending us would indeed be data showing something that happens now. Dr. Qworm (and myself, I must admit) believed redshifts didn't change as light travels through space. Do redshifts change as light travels through space (not counting local gravitational interactions)? If yes, my cluelessness would be gone as far as this subject is concerned.

If somebody could give me an answer for this last set of questions, I'd be very grateful.

Dr. Velikof Vonk, Eminent Quack

Casual shorthand. Most people aren't ready
to really think in terms of General
Relativity, so this is the closest classical
analogue.

Yes, and that's what professional
cosmologists do when they talk to each other.
Recessional velocities are just the blinking
lights on the runway that guide us on a
dark night.

Yes! In fact, if you think about it, you
have just stated the Hubble diagram in words.
The light we see just after emission (from
nearby galaxies) has a very different redshift
from the light we see from a long time ago
(the far distant quasars).

Yes. One phenomenon that I find useful to
imagine the process is what we call the Lyman
Alpha Forest. Lyman Alpha is the name of a
particular transition in the Hydrogen atom.
Light from a far distant quasar might pass
through many clouds of hydrogen between that
distant quasar and the earth. Each time it
passes through a cloud, light at that
transition wavelength gets absorbed.

However, as the light travels between
clouds, it gets stretched as space expands,
so the absorption from the previous cloud is
shifted over a bit when it gets to the next
cloud. By the time it gets to us, we see a
whole forest of absorption lines: the ones
from the clouds closest to the quasar have
been shifted the most, and the lines closest
to the rest frame wavelength of the Lyman
Alpha transition are from the clouds closest
to us.




<center>
<table border=1><tr><td>
<center>


<font size=-1>Here's an example of the Lyman Alpha Forest. Wavelength is along the x-axis, and light intensity is along the y-axis. To the right you can see the (red-shifted) Lyman Alpha emission line, and every downward spike to the left of that is an absorption line from the same atomic transition at a different redshift.
</font>
</center></td></tr></table></center>




Let's say we had 100 people lined up along
100 km of train track, and we all agreed
that as the train passed by, we would shoot
a paint pellet at the train to make a mark
exactly 10 meters back from the front of the
train. But unbeknownst to those 100 people,
the train is stretching as it goes, so that
while each paint pellet hits ten meters back
from the front of the train, the previous
pellet is now 20 meters back from the front
of the train.

I'm not saying the Lyman Alpha forest
disproves the recessional velocity
interpretation. You could always argue
that each of those intervening clouds is
receeding at a different velocity rather
than space stretching (in our train/pellet
analogy, each person agrees to hit 10 meters
behind the previous pellet). I'm just
saying this is the way astronomers think
about it in a GR framework, and I'm using
the Lyman Alpha Forest to illustrate that.

Like I said, all the math to describe the
evolution of the universal expansion is all
done using GR. I'm not surprised Hubble
didn't do it that way, but remember, Hubble's
original graphs isn't even visible on the
scales that the current Hubble Diagrams go
out to. It's way, way, down in the lower
corner. So he wasn't even dealing with
the extremely old stuff. In fact, if you
look at his original diagram (with no error
bars, scandalous! [img]/phpBB/images/smiles/icon_smile.gif[/img]), the slope is not
really significant. A constant recessional
velocity would only fit marginally worse.
Of course, time and much better data have
proven his intuition right, but he only got
the ball rolling -- the field has come a long
way since then.

Hope that helps.

Don



<font size=-1>[ This Message was edited by: DoctorDon on 2002-10-22 23:46 ]</font>

Isn't it worthwhile to see the speed that far away / old galazies are receding from us as something that is (in theory) related to BOTH their distance AND their age (expressed relative to ourse, so a negative number)?

So, in the Hubble relation the recession speed would be dependend on two parameters, which we can put in a 3-D picture on an x and y azis, and having the recession speed at the z axis.
Of course, since distance and age of observed objects are interrelated, the data are derived from a very thin straight line on the x/y plane, since our measurements started just 80 years ago or so.

That would indicate maybe, we would have to wait another billion year for all these measurements, to give a better understanding of it.

Or is there a way to interpolate the missing data?

It did. Easy-to-understand examples like a train being painted while it moves and stretches help most. [img]/phpBB/images/smiles/icon_wink.gif[/img]

But reality sure turned weird since we believed the earth was flat.

I'm not complaining. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Hey, why don't you invite your friend Dr. Qworm to this site? I'm sure we could have some lively discussions on the speed of time and the speed of rock. [img]/phpBB/images/smiles/icon_smile.gif[/img]



<font size=-1>[ This Message was edited by: Zathras on 2002-10-23 17:39 ]</font>

<font size=-1>[ This Message was edited by: Zathras on 2002-10-23 17:40 ]</font>

I would almost have written the same thing by saying that maybe Hubble should have made his graph 3-D with the third axis being time.

But as I've been explained recently, it seems that the galaxies' age is already indirectly included in the graph, since their speed is calculated with their redshifts, and their redshifts include the information of how long their light needed to reach us (correct me if I'm wrong).

It will definitely be very interesting to see how the redshifts of galaxies will evolve over the years (unfortunately it seems at least millions will be needed to notice any changes).

It would be expected that they move more and more into the red, I guess. If they do, GR would be confirmed yet again. If they don't... I'll ask Dr. Qworm.

In a few million years.

The redshift implies the speed, which is portrayed (in my model) along the z-axis.
The distance is measured by other means on the x-axis
And in one measurement this also implies the (relative) age (distance = relative age * speed of light) on the y-axis.

So, initially, all data would be gathered along a thin line in the x/y axis.

Btw. Has anyone checked if this interpretation conflicts with the usual interpretation, or we merely simply overlooked an important factor, which makes the standard interpretation to last.
Alternatively, what would this new parameter add up to the Standard Cosmological model?

I don't know... Because of his weird ideas, he's hard to talk with. I can always ask him, though.

In the meantime, here's one more of his strange experiments... [img]/phpBB/images/smiles/icon_rolleyes.gif[/img]

---------------------------------------------

Big Bang


"So you really think the Big Bang was an expression of force of will?"

Dr. Qworm the mad scientist was amazed. He had always been taught that the creation of the universe had been the result of a series of physical laws that still ruled the universe today, but that the earliest of them just hadn't been discovered yet.

"The Flight from Omnipotence[1] theory would tend to prove it, in any case," Sarkon the prophet assessed with the most serious look he could muster. "Fact is, some force must have triggered the starting of the universe, since things don't 'just happen' without a cause. Of course, it could be a force that is not detectable any more, but I like to think it is still present in some form, and not only in some Star Wars movies. What's more, the force at the origin of the creation of time and matter must be independent from those, because otherwise it would have needed time and matter to be set into motion in the first place. And the only force we know that might be independent from spacetime[2] is the force of will!"

"Force of will… Force of will…" Dr. Qworm pondered. "But it must have been someone's force of will!" he exclaimed. "A force of will doesn't exist by itself!"

"Force of will – or name it consciousness if you want to – is a necessary element to the universe. If no consciousness was there to witness it, the universe's existence would be so meaningless that it actually would not exist, since it would exist for no one," explained Sarkon. "What I mean is that in the worst of cases, matter consciously evolved into consciousness, which implies that consciousness had to be there all along, from the beginning of the universe to now. Consciousness is a concept that is much too fundamental to the universe to be the result of a random evolution, because without consciousness, there would be nothing."

"So you think some superior being created the world, then?" asked Dr. Qworm, somehow disappointed. "I thought we agreed that the universe must explain itself…"

Sarkon threw his arms wide apart in dismay. "Did I say anything about a superior being? I was just speaking about consciousness, and definitely not a superior one. Why should we look somewhere else for something we have right under our noses? Well, behind our noses, in any case… Anyway, if you want to know, if I had to define the force of will that, as I think, created the universe, I would even say it was the force of will of an inferior being –"

"Inferior? Now there's no need to get blasphemous," Dr. Qworm frowned.

"Well, 'inferior' as in 'less evolved', in any case," Sarkon justified himself. "Have you ever heard of evolution going backwards? If the universe was created by a being's force of will, it must have been the 'zero being' – consciousness at the zeroth stadium of evolution, thus necessarily less evolved than we are. But actually I don't think we can speak of a being. I think it was just a force."

"But what happened to this force, then? Why isn't it represented in any mathematical formula?" asked Dr. Qworm.

"Because nobody did it yet? Or because it is independent from time and matter, and thus cannot be included in formulas based on these concepts?" answered Sarkon. "How would I know? I am no scientist, just a prophet! All I know is that this force is still at work: cars and TV and computers have not been created by any physical laws, but by consciousness – by force of will. The mere fact that this force is still the main creative factor in the world today should be enough of a hint for us to wonder if it might not have been so fifteen billion years ago, too!"

"Hmm…" Dr. Qworm stroked his chin. "But if a less evolved being was able to create a whole universe, shouldn't we be able to do so, too?"

Sarkon just shrugged. "In a way, we do so already - every time we give birth…"

"I mean, not a used universe – a new one! Start a Big Bang, you know!" Dr. Qworm was getting enthusiastic.

"Well, if the Big Bang really was a singularity, all the force of will in today's universe had to be concentrated on one point just as space and matter were, so that there was a lot to start it all… Now it is rather scattered, since trillions and trillions of beings share it… But then, maybe it is a force that is not conserved, so maybe there is much more of it now than there was at the beginning. Maybe only a very little force of will was needed to start the universe… Who knows? In any case, you can always try!" Sarkon patted his friend the mad scientist on the back.

"You bet I will!" Dr. Qworm exclaimed. "You bet I will!"

* * *

Back in his laboratory, Dr. Qworm prepared himself for the ultimate experiment – the starting of a Big Bang. All a matter of force of will? He was certain he had more than enough! He turned off all lights, lay down on his psychiatric couch, closed his eyes and concentrated on creating a Big Bang.

Nothing happened.

He tried relaxing. His muscles were tense from the excitement, so it took quite an effort to loosen them all up. But after he'd exhausted himself relaxing, he still didn't have his Big Bang.

So he tried tensing his muscles again. He just wanted wanted wanted wanted wanted his Big Bang so much, there was no way he wasn't going to get it! His face distorted in a twist of want, his fists clenched, his stomach muscles contracted…


*Fart!*


* * *


After Dr. Qworm had wiped his tears away from a full five minutes of continuous laughing, he had to admit that Sarkon the prophet had been right: the Big Bang was a product of force of will. The forms such a Big Bang could take, however, were rather surprising occasionally: sometimes you got a universe, sometimes you got… well… just a bad smell!

---------------------------------------------

[1] See "The Vanishing Point"

[2] See "The Speed of Stone"

An eminent colleague of mine, Dr. Velikof Vonk, informed me of your request for me to give a conference on this site.

I thank you very much for your interest in my person and my ideas, but the problem is that, as you may already know, I have important experiments scheduled, so I'm really busy. Really, really busy. really busy.

Lately, my heavy load of work even forced me to set up a working schedule. Here is what I ended with...

----------------------------------------------------------

A Short Work Schedule


"There are so many things to do!"

For once, Dr. Qworm the Mad Scientist wasn't arguing with Sarkon the Prophet or with General Kwar the Dictator about the importance or foolishness of one of his scientific projects. In fact, his complaint looked clearly like a call for help, something that Sarkon the Prophet was always ready to offer in form of kind advice. "Are you overwhelmed in some way?" he asked Dr. Qworm in a concerned tone.

"There are so many things I need to do, and it doesn't seem like I have enough time to do them all," lamented the Mad Scientist. "There's just too much!"

Sarkon looked around. The Welgon Age was such a small world that it was hard to conceive there could be too much of anything to do; usually, they spent most of their time thinking or arguing precisely because their world just wasn't large enough to do much else.

Apparently, the Mad Scientist was being very much himself once again. "Tell me what's bothering you," Sarkon proposed in the most soothing tone he could muster.

"To start with, we've a really huge pile of laundry. I'll need hours – probably even days – to get it all clean!" complained Dr. Qworm. "I mean, I have a pile of socks that gets almost up to my ceiling!"

"Socks?" wondered Sarkon.

"cookie's socks, mostly," specified Dr. Qworm.

Sarkon realized that he couldn't remember the laundry getting done even once since he dwelled in the Welgon Age, so he guessed it had to have accumulated somehow, indeed. And cookie was always running around with nice, clean socks. But where did he get them? Did he have a mom somewhere, after all?

"And the laundry is only the smallest of my tasks: scores of unexplained natural phenomena are waiting to be rationalized by theories, theories are waiting to be confirmed by experimentation, experimentations are waiting to be done! I have so many scheduled that I don't even know where to start! On top of that I have to clean up my lab, sort out my genes -"

"Your genes? Why do you want to sort out your genes?" asked Sarkon.

"Know thyself, isn't that the kind of advice you usually give, Prophet?" snarled Dr. Qworm.

"Sure," admitted Sarkon, "but I didn't mean –"

"Whatever you meant, a thorough personal genetic analysis is how it is done best," affirmed the Mad Scientist. "Such a screening allows us not only to identify any dysfunctions our body has to live with or any diseases we might be most exposed to, or to know how old we might become, but also to know if we will tend to be violent or meek, thrifty or generous, egoistic or self-sacrificing, furious or sad, and, in case of need, compensate any of these tendencies imposed on us by our material constitution with the one force that we master, the force of will!"

"That's… actually impressive," admitted Sarkon. He hadn't known science was already that far ahead.

"The problem is that such a thorough personal analysis would take a few decades," sighed Dr. Qworm. "Do you see my problem now? I just don't seem to have enough time!"

Sarkon the Prophet stroke his beard. "Maybe we should draft a working schedule for you, so that you can plan the things you want to get done. This way you'd also know how much time you have available for each thing you want to do," he proposed.

"So now I have even one more thing to do," grumbled Dr. Qworm. "Draft a working schedule."

"Excuse me - I'm only trying to help!" Sarkon was getting a little angry at Dr. Qworm's attitude.

"…And I think you should do a personal genetic analysis, too," added Dr. Qworm. "Some of your behavior definitely needs conscious compensation!"

Sarkon sighed. Dr. Qworm was right: angriness seldom lead to anything positive. "Let's just try, ok?" he proposed.

"Well then," it was Dr. Qworm's turn to sigh. "Let's start." He got a notebook out of his pocket and began writing.


0. Draft a working schedule.


"At least that's something that I'll get done soon enough," said Dr. Qworm.

"See?" said Sarkon. "You just started and you can already see the end of it. The start is the biggest hurdle to overcome! Now we also need to estimate the time that each task will take."

"You don't think we'll need more than ten minutes for this, do you?" asked Dr. Qworm.

"Ten minutes could be enough… If you only want to listen the important things," guessed Sarkon.

"Ten minutes, then," agreed Dr. Qworm, and wrote it down.


0. Draft a working schedule: 10 minutes.


"Now the laundry," reminded Sarkon, and Dr. Qworm wrote that down too.


1. Do the laundry: 2 hours.


"Doing the laundry will help us solve a mystery, too," remarked Dr. Qworm.

"What mystery?" asked Sarkon.

"Well, we will then know from where cookie gets his clean socks," explained Dr. Qworm.

"How on the Welgon Age will our doing the laundry give us this knowledge?!" asked a baffled Sarkon.

"Because if we do the laundry, cookie'll get his clean socks from us, silly!" exclaimed Dr. Qworm, amazed at how he had to explain even the simplest of things to Sarkon. But then of course Sarkon was a prophet, so that he couldn't master logic like a scientist does.

Sarkon opened his mouth, but just couldn't think of anything to say.

"Then I want to clean up my laboratory," resumed Dr. Qworm. "That's going to take even longer!"


2. Clean up the lab: 4 hours.


"What is next on your list?" asked Sarkon, and Dr. Qworm answered by writing it down.


3. Finish my report on afterlife: 5 weeks (I hope).


"Afterlife? What happens during afterlife?" asked Sarkon.

"You end up in a very small cloud-like place and have to put up with… Never mind," Dr. Qworm dismissed Sarkon's question with a wave of the hand. "What did I want to do next already? Ah yes," he wrote it down again.


4. Do a personal genetic analysis (and figure out why things went wrong): 10 years.


"This is getting long-term," commented Sarkon.

"Not yet," answered Dr. Qworm.


5. Do something for the advancement of humanity: 30 years.


"That's great, Dreitos," encouraged Sarkon. "A very motivating task, indeed! I guess your list is done now!"

Dr. Qworm raised his eyes from the list up to Sarkon. "I said there were a lot of things to do; I didn't say I had to do them all personally!" he explained, and went on writing.


6. Regenerate the ozone layer, solve any population problems that might arise, implement alternative energy sources, save the whales (and other friends), eradicate the most dangerous diseases, allow all children to learn and to discover knowledge by themselves, reduce poverty, understand each other: 100-1000 years.


"These are things that must get done, indeed," agreed Sarkon.

"We need to work on our survival, and we don't want our living standards to degrade too much," explained Dr. Qworm.


7. Work out the right theories explaining all natural phenomena and confirm them all by observation or experimentation (or the other way round): 100'000 (crossed out) 1'000'000 (crossed out) a lot of years.


"I don't really know how long it will take," Dr. Qworm admitted after having changed his mind twice for the duration of that task, "but I can tell you that now we're getting long-term," he smiled.


8. Work out interstellar travel (or another way to get somewhere else) so that we don't get burned by the sun: a billion years.


9. Work out intergalactic travel so that we don't end in our galaxy's central black hole: 10 billion years.


"Always the survival problems," commented Dr. Qworm. "And finally…"


10. Engineer a Big Bang in case it doesn't get done by some other force so that we can start over again instead of fading into nil: 20 billion years.


"Well – that's it!" marveled Dr. Qworm. "Thank you for the advice, Sarkon! It already looks much easier this way!"

"It… still seems a lot of work to me," admitted a staggered Sarkon. "A lot. I guess…" he took a deep breath and went on, "…We better start with the laundry soon!"

"We better start with the laundry now," the Mad Scientist agreed. "cookie needs new socks, remember?"

------------------------------------------------------------

Look at all these things that are yet to be done! Do you understand now how incredibly busy I am?

And, by the way, aren't you? What have you done for humanity today? Why are you even reading this? Hurry off to work, and don't bother me no more!

_________________
"Existence is an exploration from which no one comes back alive."

- Dr. Qworm

(At least not with memories.)

<font size=-1>[ This Message was edited by: Dreitos Qworm on 2002-10-28 20:06 ]</font>

<font size=-1>[ This Message was edited by: Dreitos Qworm on 2002-10-28 20:09 ]</font>

Dr. Don can't be right. If that were so, then longer wavelengths wouldn't stretch more than shorter. They'd all stretch the same amount from a single distant source. They don't. The change in wavelength is proportional to the original wavelength.

No, John, Don has it right. You just aren't used to thinking about relational forces. The point of the matter is that whenever we deal with comparing scales (trying to see if certain local phenomena stretch as the global phenomena) we are overwhelmed by the stronger local phenomena which mask the overall change. So, in effect, we have standard measuring sticks on our local scales since we live in a locally inhomogeneous universe.

First I would like to thank everyone (especially Don) who answered my questions.

Then I have another headscratcher: since it is gravity that bends spacetime (as with black holes), is it the lack of gravity that stretches it? What I mean is, is it the dwindling gravitational influence between galaxies that stretches space between them at the speed of the Hubble constant?

Or what else would stretch space this way?