From Aeon to Zeon to Zeit, simplifying the standard cosmic model

[RyanH42]

I thought we live in 0.5zeit and we want to calculate how much distance traveled light when times come 0.6zeit.The opposite idea...Well I understand that.Today will be 0.6zeit and we are calculating past time.We did the same thing before

 

[marcus]

The other way is impposible to calculate ? We want to calculate the distance traveled by light from the future.I mean we are emitting light right now.So there must be way to calculate it ?

Yes we can calculate that the same way. there are two possible answers. One is the distance the light has traveled as seen from THEIR perspective, when they receive it (that would be called the "proper distance" at that future time. And also we can scale that distance down by the S factor to be the distance NOW to that galaxy we are sending the light to---that will receive our message at some time in the future.

I believe it is good to first calculate what the proper distance to the galaxy will be when they receive the light.
Let's say they are to receive the light at time t=1.8.

OOPS sorry I have to leave. We are out of food and I have to go to the store.

 

[RyanH42]

Ok,I will go to sleep too.Maybe tomoorow

 

[RyanH42]

You don't have to teach me.Really.I think you are suffering to write these things.If you really want to teach me something that's ok.But If you don't want to teach me "really".Then don't do that please.You are writing so much and I am feeling sad about it.Maybe I can learn these things later.Cause I am feeling I am keeping you busy and you cannot do your other jobs.And that's makes me sad of course

I'll be waiting an answer in next 8 hours.
Thanks for everything.
Ryan

 

[marcus]

The other way is impposible to calculate ? We want to calculate the distance traveled by light from the future.I mean we are emitting light right now.So there must be way to calculate it ?

Yes, I think I understand and there IS a way to calculate directly---I think it is the way you were thinking. The idea is to find the distance NOW to the galaxy which will receive our message at a certain time in the future.

Let me use the two times 0.8 (for now) and 1.8 in future. We can replace them with whatever you want later. I think maybe I don't even have to say the integral because you have already discovered what it must be.

 

[marcus]

...Cause I am feeling I am keeping you busy and you cannot do your other jobs.And that's makes me sad of course...

No, on the contrary you are helping me by your interest and by doing the calculations along with me. I think this approach to cosmology---with zeit and lightzeit units---is potentially a good one because it makes the formulas simple and transparent
one can actually calculate things quickly and easily. So I am interested in this approach. I think it is worthwhile that is worth the time spent on it

Also for a high school or college student it is a good way to practice calculus. You get to know the chain rule better, and change of variable, and the hyperbolic functions sinh and cosh.

So it seems to me worthwhile to find a good way to introduce and explain this approach to cosmology. Also it's just nice to have a hands-on contact with the universe and its expansion process and the light that travels between the galaxies. It is a more direct contact than one gets when one depends entirely on a calculator like Lightcone. (But Lightcone is good too, perhaps you should get some experience using it, and having it draw curves.)

I am on pacific daylight time which I think is about 8 hours earlier than UTC. You seem to sleep between 3pm and 11pm pacific time. I will check again around 7h UTC.

 

[RyanH42]

I am here again.Its really good.If you are ready to teach me then I am ready to learn.Whenever you want to start.Cause it seems times is there 10 pm.

 

[RyanH42]

I don't know lightcone.Maybe I can do that

 

[RyanH42]

Yes, I think I understand and there IS a way to calculate directly---I think it is the way you were thinking. The idea is to find the distance NOW to the galaxy which will receive our message at a certain time in the future.

Let me use the two times 0.8 (for now) and 1.8 in future. We can replace them with whatever you want later. I think maybe I don't even have to say the integral because you have already discovered what it must be.

I will use
1///D(t)=∫sinh(1.5*0.8)^(2/3)dt/sinh(1.5*t)^(2/3) by x on the interval from 0.8 to1.8
And
2///D(t)=sinh(1.5*1.8)^(2/3)/sinh(1.5*x)^(2/3) by x on the interval from 0.8 to 1.8
First equation gave me 0.607
Second equation gave me 1.755
unit is lightzeit and time is zeit.
Light cannot travel 1.7lightzeit in 1 zeit so my first equation becames true.(And also my example which I wrote before and later you also claimed that)
So if we take time for now (t=0.8) then the integral will be always

D(t)=∫1.3dt/sinh(1.5*t)^(2/3)by t on the interval from when t>0.8 → 0.8 to t
when t<0.8 →t to 0.8

When time is not now then we need to pick a time to normalize the scale .The only change , there will be no 1.3 so we need to use

D(t)=∫sinh(1.5*T)^(2/3)dt/sinh(1.5*t)^(2/3)
Again T is here the time which we call now.And the t is just normal time
Again
when t>T→ T to t
when t<T→t to T

This is the way I guess.

 

[RyanH42]

No, on the contrary you are helping me by your interest and by doing the calculations along with me. I think this approach to cosmology---with zeit and lightzeit units---is potentially a good one because it makes the formulas simple and transparent
one can actually calculate things quickly and easily. So I am interested in this approach. I think it is worthwhile that is worth the time spent on it

Also for a high school or college student it is a good way to practice calculus. You get to know the chain rule better, and change of variable, and the hyperbolic functions sinh and cosh.

So it seems to me worthwhile to find a good way to introduce and explain this approach to cosmology. Also it's just nice to have a hands-on contact with the universe and its expansion process and the light that travels between the galaxies. It is a more direct contact than one gets when one depends entirely on a calculator like Lightcone. (But Lightcone is good too, perhaps you should get some experience using it, and having it draw curves.)

I am on pacific daylight time which I think is about 8 hours earlier than UTC. You seem to sleep between 3pm and 11pm pacific time. I will check again around 7h UTC.

Sorry I sleep 9 hours.I woke up 12 pm pacific time.I don't know sometimes I sleep 7 hours sometimes 8 sometimes 9.Its good to learning cosmology.

 

[marcus]

I am here again.Its really good.If you are ready to teach me then I am ready to learn.Whenever you want to start.Cause it seems times is there 10 pm.

I just missed you. It is like some comedy. I got sleepy and dozed off right around 10 pm last night. I am rather old, and it had been a big day. You are right---the dateline on your post says 10pm (pacific time). So I fell asleep on the couch where I was reading, just as you were sending your message.
I think actually these days I am not much good after 10 pm.

But I am happy with this---I just woke up (around 6am pacific) and got coffee and I am very glad (!) to see your posts. It will give me something interesting to think about

Here is the version of Lightcone that uses zeit and lightzeit
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7z/LightConeZ.html

The most important button, I think, is "open column selection and definition"
there you get a menu with a number of choices, and also you can choose the number of decimal places.
It is very easy to make it draw curves instead of making tables.

 

[marcus]

To return to that example, we say there is a galaxy which, if we send a message today, will get the message at t=1.8
and we ask how far is that galaxy now?
and we also ask how far will it be when they receive the signal?

I integrate sinh(1.5*0.8)^(2/3)sinh(1.5*t)^(-2/3) and I get .60786...
I integrate sinh(1.5*1.8)^(2/3)sinh(1.5*t)^(-2/3) and I get 1.75520 ...

Oh WOW! I just looked back at your post! You got the same results! This is good. I will go get another cup of coffee to celebrate.

And the light can go farther than one lightzeit in the time of one zeit, because it is helped by expansion. So all is well.

 

[marcus]

The 1.755 lightzeit is the true distance between the two galaxies when they get the signal.
I think of it as measured from their perspective---each little step cdt which the light takes has been enlarged by the time the light gets to them, by the factor σ(1.8)/σ(t)

I am getting tired of writing "sinh(15*t)^(2/3)" all the time so I will write σ(t) with a Greek sigma sometimes.

And the 0.607... lightzeit is the correct distance between the two galaxies at the moment we send the signal.
Because each little step cdt which the light WILL take on its journey has to be shrunk down by the factor σ(0.8)/σ(t)
to give its size NOW when we send the signal. All those little steps which it will take, properly made smaller to give their present size, add up to the present distance to the galaxy.

I hope this makes sense to you.

BTW we could make it more precise by using 0.797 instead of 0.8. What is σ(0.8)/σ(1.8)?
We need that number if we want to use Lightcone to check our answers.

 

[marcus]

google says sinh(1.5*0.8)^(2/3)sinh(1.5*1.8)^(-2/3) = 0.34632345739
Just for a little more precision I think I will use t=0.797 : sinh(1.5*0.797)^(2/3)sinh(1.5*1.797)^(-2/3) = 0.3461246417

So now we can go to lightcone and put in S = 0.3461, and see what "distance then" and "distance now" are.
I go to http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7z/LightConeZ.html
I put 0 for the number of steps, because I don't want a table. I want just one row.
and put .3461 in for S_upper
{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline T_{Ho} (Gy) &amp; T_{H\infty} (Gy) &amp; S_{eq} &amp; H_{0} &amp; \Omega_\Lambda &amp; \Omega_m\\ \hline 14.4&amp;17.3&amp;3400&amp;67.9&amp;0.693&amp;0.307\\ \hline \end{array}} {\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&amp;S&amp;T (zeit)&amp;D_{now} (lzeit)&amp;D_{then}(lzeit) \\ \hline 2.889&amp;0.346&amp;1.797051&amp;0.608533&amp;1.758257\\ \hline \end{array}}
The default does not show D_now so to get it to show the now distance I went to "open column selection and definition" menu and selected D_now. I also "de-selected" a couple of things I didn't want

 

[RyanH42]

I am busy right now like yesterday again 1 hour later I will check again

 

[marcus]

It's fine! : ^)

 

[RyanH42]

I used lightcone and it seems complicated cause I don't know some of the terms.

D(t)=∫cdt/a(t) we used this formula to find "How much light traveled" not "How far the galaxy away"You saud me like that I guess.

 

[marcus]

((s/1.315)^3+1)^(-1/2) integrated between .3463 and 1
gives .607813...

I used lightcone and it seems complicated cause I don't know some of the terms.

D(t)=∫cdt/a(t) we used this formula to find "How much light traveled" not "How far the galaxy away"You saud me like that I guess.

I should speak more carefully. I sometimes say things like "how far the light has traveled with the help of expansion"
and "how far the light is from home"
I always mean to include the effect of expansion.

Sometimes I have forgotten to make that obvious. But in Nature space is always expanding so the the distance always includes the effect of expansion---this is why we have redshift or wavestretch. It is only with shorter distances and times that we can neglect the effect.
If the light is only traveling a few million years the expansion is negligible and we can neglect it. We can pretend that space is not expanding and as an approximation take the speed to be c.

 

[RyanH42]

How far is that now ? We don't have enough information isn't it ?.Why we call it 0.608 ? The distance of galaxy will be a(1.8)/a(0.8)*R when t=1.8
The distance which light traveled is integral 1.3dt/sinh(1.5t)^(2/3) t from 0.8 to 1.8

 

[RyanH42]

I understand ok

 

[RyanH42]

There must be a galaxy which he will receive a signal 1.8zeit when we send the signal in t=0.8

 

[marcus]

...D(t)=∫cdt/a(t) ...

That formula explicitly includes the effect of expansion. By itself, in a non-expanding space, the light would go a little step cdt
but that step is magnified by expansion, and we show that by the 1/a(t) factor

 

[RyanH42]

I got it now.Light travels just a little distance cdt but as you said universe expands ,thats the important thing so we can use that formula.

 

[marcus]

There must be a galaxy which he will receive a signal 1.8zeit when we send the signal in t=0.8

Well I was imagining something there, to make a definite place in space. It is some place for the signal to go. I hope this is OK. It does not have to be a galaxy but there should be some material destination (I think). Otherwise I am not sure how we can define the distance to it now and the distance to it then.

I'm glad to know that you visited the Lightcone calculator. It has a lot of things we have not discussed so must be confusing. But later...

 

[RyanH42]

Yeah,Is it finished ? Is This the all thing ?

 

[RyanH42]

I will check again ehat we did in a couple minutes and If I come up a question I wil ask you

 

[RyanH42]

I understand the idea thank you there's no question to ask

 

[marcus]

Yeah,Is it finished ? Is This the all thing ?

I think that has to depend on you. I enjoy this kind of discussion and I could probably think of more cosmology topics to talk about if you wanted to continue. But I also understand that you must have many different areas of interest and other people you want to ask questions of. And sometimes one just needs to rest. So we should not feel compulsive, there is nothing we have to do. nothing that we *must* do.

 

[marcus]

I understand the idea thank you there's no question to ask

Good. So now I will probably continue posting in this thread, because I like the model with zeits and lightzeits---but this will not be necessarily addressed to you. I will just be talking to nobody in particular, or to myself. It helps me organize my thoughts to post about this.
I am always here if you have questions.

 

[RyanH42]

Actually my only interest is Cosmology.I like GR,and Quantum mechanics but I am a high school student(I will pass university in two months and I will read physics engineering)

I think I need to do examples before I contiue.I have an idea.You can make me a quiz ,10 questions.If I fail let's stop here and I look again what I learn.If I pass the I can start to learn new things

 

[marcus]

WOW! you are really serious, Ryan! I will make a little quiz (but I am not so experienced as a teacher, it may be kind of a dumb quiz---I will do my best to make it interesting)
I think I cannot make 10 questions all at once. Maybe I can propose questions only one or two or three at a time---and so gradually build up to 10.

 

[RyanH42]

Ok.Yeah I am serious.Its good for me I want to learn something

 

[RyanH42]

I will going to go eat something.So don't hurry.You have least 30 min

 

[marcus]

CMB stands for cosmic microwave background. It is very old light which used to be visible and near-visible infrared from temperature around 3000 kelvin, but is now stretched out to temperature 2.725 kelvin---or something like that.

It cools in proportion to expansion. When distances are twice what they are now, the CMB temperature will be half what it is now.

I like this question---you are transported somewhere and some time in the past. Your only way to tell the time is from the temperature of the CMB. (there is no one with a calendar and no big clock there to tell you)

You discover the CMB temperature is TWICE what it is today. What time is it. (I mean in zeits, the expansion age of universe).

 

[marcus]

Remember that H(S) = ((S/1.3)^3 + 1)^(1/2)

and remember that t = ln((H+1)/(H-1))/3
=======================
Or if we are using the reciprocal R = 1/H then recall that R(S) = ((S/1.3)^3 + 1)^(-1/2)

and that t = ln((1+R)/(1-R))/3
==========
Maybe this is a bad question. Could be too hard. Or we didn't go over H and R enough.

 

[marcus]

I am not confident of my ability to make up quiz questions that are the right level. Can you suggest a possible question that you would like to see on a quiz? I can use it as a model.

 

[marcus]

(just ignore the first question if it is bad, too hard, too ridiculous or anything)

Second question: Some light comes in and you measure and discover it is stretched by a factor of 2. Its wavelengths are TWICE what they were when it left its source galaxy. How far is the light from its source?

 

[RyanH42]

I am not confident of my ability to make up quiz questions that are the right level. Can you suggest a possible question that you would like to see on a quiz? I can use it as a model.

The question types which we did previous chapters or post.

I have just finished my lunch.I am looking the question right now

 

[RyanH42]

S=2 then we can calculate S=1.3/a(t) a(t)=sinh(1.5t)^(2/3)=0.65
We need to find t here.Take the 3/2 power both sides
sinh(1.5t)=0.524
Then I will try to give numbers which fits the given answer.
t=0.338 ??

 

[RyanH42]

You are asking the distance oppss

 

[RyanH42]

Wait I will going to fimd it myself then I will take an integral so D(t)=1.3∫dt/sinh(1.5t)^(2/3) and 0.338 to 0.8

 

[marcus]

I have an errand, I will be back in an hour or slightly more. Have to run.

 

[RyanH42]

Integral answer is 0.6389

 

[RyanH42]

Ok,No problem

I find the solution in 20min that's bad.But I wasnt sure enough that I am doing right or wrong.My mistake

 

[RyanH42]

I am trying to find more easy way
D(t)=-∫dS/H the integral between S=1(Now) and S=2 H will be as you said H=[(S/1.3)^3+1]^(1/2)

I made and I found 0.6347

It took time to realize the question and prepare an answer.

Did I pass ?

And also I checked my answer to use lightcone(Which I learned I guess) and it seems my answer is true.

 

[marcus]

Hi, I just got back. The errand was more work than I thought.
Before I forget it, I will say a problem that came to mind while I was out. I am still learning how to think up cosmology quiz questions.

In ancient times there was a race of giant stars called "PopIII" stars. The name is an historical accident and meaningless. They lived when distances were about a TENTH the present size. These stars are very interesting because they formed before there were heavier elements---they were made of H and He (with traces of Li) and their light had the wavelengths of hot H and He but not other gases.

It is very hard to find the small protogalaxies or regions with these PopIII stars. They were 100 to 1000 more massive than Sun and so burned very hot and had short lives. Sometimes astronomers have detected these ancient stars. How far away is the matter which once formed them?
Of course they are no longer. The actual stars exploded in SNe long ago, but the matter is still there, that made the light.

Suppose you are an astronomer who is just now getting some S=10 light from a region with these giant stars. How far away is that?

 

[marcus]

...

And also I checked my answer to use lightcone(Which I learned I guess) and it seems my answer is true.

: ^) Yes it seems it is.

 

[RyanH42]

D(t)=-∫dS/H integral between 1 and 10
H=[(S/1.3)^3+1]^(1/2) so the answer is 1.7564

 

[RyanH42]

Great story

 

[marcus]

I just had lunch. It is getting near 3pm pacific when you end the day, I think. There may be no more time. until tomorrow.
Here is a quick variation on an earlier problem.

You are transported to some unknown place and time in the future. You measure and find that the CMB is HALF the temperature it is today.
What time is it?

By an amazing coincidence, while you are listening to the radio you receive a message that was sent by us at PF today. What distance are you from Earth?