# A question about distance and time

1. Dec 14, 2008

### BoyangQin

If a star is 14 billion LY away, will its light ever reach earth?
if it does, the light must happened 14 billion YEARs ago, before the big bang(13.7billion years)?

thx :)

2. Dec 15, 2008

### marcus

Boyang, since you want to know how to relate distances and times in cosmology (where distances increase due to expansion) you should practice with the Ned Wright cosmology calculator

http://www.astro.ucla.edu/~wright/CosmoCalc.html

Over at the left you will see "enter values and press a button"

As a beginner, only press the "general" button, and only change the number in the Z BOX.

The number in the z box is the redshift. At first you will see a 3 in the box. That means it is ready to calculate the distance and travel time for a star or galaxy which we observe today and whose light is redshifted by a factor of three.

As a beginner, only pay attention to two of the results on the right side of the screen
1. the light travel time
2. the comoving radial distance---that is the distance the object is today, at this moment, as we are observing the light which it sent out much earlier.

We are usually talking about galaxies, not stars. Because at these distances we can rarely see individual stars. A galaxy, made of some billions of stars, looks like a small fuzzy blob.

In the output on the righthand side, G means billion, Gyr means billion years, Gly means billion light years.

Because these longrange distances are constantly increasing by Hubble law, a flash of light that has traveled for one billion years (1 Gyr) will have reached a point that is much farther than one billion lightyears (1 Gly) from its point of origin.

Light travel time of 1 Gyr does not correspond to 1 Gly of comoving radial distance.

So, for example, try typing 1.45 into the Z box. And press "general" button.
You will see that the travel time is about 9 Gyr
but the distance to the object is 14 Gly---that is the distance today, at this moment, as we are observing the light (which it sent out in our direction some 9 billion years ago.)

=======================

I advise you to try various z numbers and note the travel time and distance, to get practice.

In case you want to know, here is what the redshift z number means: It tells how much the wavelengths in the light have been increased during travel by the general expansion.
If the original wavelength was L, then when the light arrives to us it will be increased by an amount zL

So the light we get in the telescope will have wavelength L + zL

So if the astonomer says the redshift z is 3, he means that the observed wavelength is
L + 3L

That is 4L. That means the all the wavelengths of all the colors of light have been expanded by a factor of 4. They are all four times longer. What was visible color, like red and blue, will now be in the infrared.

3. Dec 15, 2008

### BoyangQin

WOW...like wow...
thx Marcus

but What is the Light Travel year?
if i set z=0,
Light travel year goes to 0
Comoving radial distance goes to 0
does it mean all light rays have been travelling in a 'point' for 13.666Gyr?
&
If i set z=99999999(some silly large number), or even larger, why do the
light travel year stays at 13.666 Gyr and
Comoving radial distance stays at 46.5 Gly?
Aren't they the age and radius of universe?

thx a lot!
thx for the tutorial!

4. Dec 15, 2008

### marcus

You are very welcome! I am glad you have been experimenting with the cosmology calculator at Ned Wright's website.

If you google "ned wright" you will get his website with a tutorial and lots of interesting articles, including some graphics. He is a professor at Univ. California at Los Angeles.

You asked about the light travel time That is not a distance. That is the time it has taken for the light to get here.

From the sun, the light travel time is about 8 minutes. That is on a scale of millions of year approximately zero.

When you specify a very small redshift like z = 0, then you are asking about objects very close to us. Since they are near, the light travel time is approximately zero.

On the scale of the calculator, a travel time of a few minutes, or a few year, or a few hundred year, that is all the same----essentially zero. And the distance is zero also. Because for this calculator the distance scale is in millions and billions of lightyears. Small distances just show as zero.
=======================

If you put in a very large number for z, like z = 5000, then you are going back to the very early universe. Then the light (from something back then) would have been traveling for almost the whole age. It would have been traveling for 13.7 billion years, approximately.

So for z= 5000, say, the light travel time should be about 13.7 billion years.

And this is what you got for an answer, so it was correct.

=========================

I see from your post that you have found out that the radius of the observable universe is 46.5 billion lightyears.
That is approximately correct. Some people say 45, some say 46, or 46.5, maybe even 47. There is some difference of opinion depending on which exact model the person uses. But something around 46.5 is widely accepted.

This radius is the present distance today of the material which in ancient times sent us the oldest light which we are now receiving.
This material must look very different now! We only see it as it was, some 13.6 billion years ago when it was hot and radiated the light which is now coming to us---after a very long journey.

This is probably not the radius of the whole universe. There is probably much space and matter out beyond the 46.5 billion lightyear horizon, but there has not been time enough for it's light to reach us.

Our matter, in the very early days, was also hot and sent off light. This light will have traveled the same 46.5 billon year distance and it will be coming to those creatures, if they have telescopes and antennas to receive it. So we are on their horizon, just as they are on our horizon.

All matter was the source of the most ancient light. But then the matter cooled and collected into stars and planets and part of it became us.

Last edited: Dec 15, 2008
5. Dec 15, 2008

### BoyangQin

Cool
it's clear to me now how the red shift(z) affects how light travel in space-time(Light Travel Time & Comoving Radial Distance)

but why would the expansion of space affect photons in this way?
i thought light travels in the speed of light,
and Lorentz transformation garuantee that relative speed can't exceed the speed of light
so how can the relative speed between photon and space-time expansion
makes light travel faster?

6. Dec 16, 2008

### marcus

Boyang, you have asked the right question. How can some matter---a galaxy perhaps---send out some light 9 billion years ago and now the light is 14 billion LY away from the source?
It looks like a contradiction. We know that the speed of light is constant---in one year it travels one LY.

So how can it, after 9 billion years, be 14 billion LY from its place of origin, its birthplace?

The answer is because of the expansion of distances. This helps the light. After it has gotten some distance from home by itself, that distance expands.

Distances increase by a certain percentage each year. Now it is very small, only about 1/140 of a percent per million years. But in earlier times it was a somewhat larger percentage.
So the light is like a man who works to earn money and who saves 1000 dollars each year.
After 9 years you think he must have 9000 dollars. But no! He has put the money in the bank each year and it earns a percentage interest. The first 1000 he put in has had 8 years to accumulate interest. Now if you look in his saving account at the bank you see he has not 9000 dollars, he has 14,000.
You can say that he has saved the 9000 by himself, and the rest is natural expansion.

So with the light, by itself it can only go 9 billion LY in the 9 billion years. But natural expansion has helped it, so now it is farther away from home---it is 14 billion LY.

The best thing to do is to watch the balloon animation of this at Ned Wright's website
If you google that, you will find this:
http://www.astro.ucla.edu/~wright/Balloon2.html
Can you receive computer animation on your computer? You will see the white things are galaxies. They stay in the same place on the balloon---the same latitude and longitude.
The colored wiggly things are photons of light. They travel from galaxy to galaxy. As the balloon expands they are stretched out to have longer wavelengths. To remind us of that, Ned Wright has them change color from purple to blue to green to yellow to red.....

At each moment each photon is only traveling at the regular normal speed across the face of the balloon. But because the balloon is expanding the photon actually can get farther than you expect.
I have to go.
Nice question, maybe more tomorrow.

Last edited: Dec 16, 2008
7. Dec 16, 2008

### BoyangQin

lol
i like that analogy
it really make sense now
'distance' itself is stretching, so light can go farther

But.. what really is 'distance'? if it can stretch longer and bigger, is it a substance?
I know ether, as a medium, was rebutted hundreds of years ago.But is the "balloon", on which the worms and S's expand,made of some kind of modern ether?

8. Dec 16, 2008

### BoyangQin

And another question:

the animation shows the balloon is expand OUTwards.
if the light also goes in the OUTward direction, it gets helped by the balloon expansion.
but if the light goes INward, or against the expanding direction, will the light travel a smaller distance?
the bank have a negative interest ?

9. Dec 16, 2008

### marcus

The balloon example is only an analogy and like any analogy it has limitations. One big thing wrong with the balloon example is that, while we are 3D animals living in 3D space, the balloon surface is only a 2D space where only 2D stars (if there could be any) and 2D creatures could exist.

To understand the example, one should imagine that all existence is in that 2D surface. It is the whole universe. There is no surrounding space. There are no other directions that the 2D creature can point his finger, only the directions that lie in the 2D surface. There is no "outward" or "inward". His finger will not point in those directions and he has never heard of them. So to understand properly requires concentration. You must believe that nothing exists except in that 2D surface, because it is the entire universe.

Now this concentration to understand the example is mental work, so it should have a practical purpose. Why should you or I take the trouble to do this imagination exercise?

The purpose of it is to learn to imagine how the distances between all the galaxies are increasing while each galaxy stays at the same place---the same latitude and longitude on the spherical balloon.

The wiggling photons of light do not stay at the same place, they constantly move at a fixed speed like one millimeter per second. No matter how big the balloon gets they are always traveling over the surface at one millimeter per second. And they get farther away from one galaxy and closer to another galaxy. So they are really moving.

But the galaxies, if you think in terms of longitude and latitude as one does on the globe map of the earth, are always at rest, each in its place, even though the distances between them are increasing.

This surprising thing is approximately realistic! Galaxies are in fact nearly at rest, as far as we can tell.

What are they at rest with respect to? I agree with you that there is no "rubber". That is a fault of the example of the balloon. It would be better if there were no rubber material (which makes one think of the discredited ether.)

So the dots are not at rest relative to some material rubber. The galaxies are (approximately) at rest relative to the Cosmic Microwave Background.
It is very easy to measure one's speed and direction relative to the Background. If you are moving you will see a Doppler hot spot ahead of you. And a Doppler cold spot behind you.
This has been done for the solar system and we know that our speed relative to universe as a whole is 380 km/second in a direction corresponding to the location of the constellation Leo.

By cosmological standards 380 km/s is not so big. The rates that distances increase, on large scale, are usually much larger. So the solar system's motion relative to Background can be considered negligible. For some purposes one compensates for it in the data but it is not a big deal. Other objects, as far as we can tell, also have small individual motion relative to Background.

We can understand motion relative to the Background as motion relative to the collective matter of the early universe. Because at a time like 380,000 years after start of expansion the matter was a hot gas at 3000 kelvin, similar to the glowing surface gas of a star. Partly ionized which makes gas not transparent. At that time the gas cooled just enough to become transparent, so the light escaped and was able to travel freely from that time onwards. So it has come to our time still nearly undisturbed. It has only been redshifted (as wavelengths are) by the same factor that distances have been expanded since that time. A factor of about 1090. Wavelengths and distances are expanded by the same factor, in any given interval of time.

So the Background light is no longer hot glowing red and orange, like a 3000 kelvin star. It is 1090 times longer wavelength, microwave, around 2 millimeter. All the matter in the universe collectively produced that light, at a time when it was a big hot cloud. Our matter produced Background light that other creatures can see if there are any other creatures at the correct distance. And their matter produced light which we can see. It is all one.
And this is why we know that if we are moving relative to the Cosmic Microwave Background we are moving, in a sense, relative to the ancient matter. If we are at rest relative to background, we are at rest relative to the collective hot gas of ancient matter.

The Doppler hotspot/coldspot was located precisely and the temperature difference was measured by the satellite COBE (cosmic background explorer) in the 1990s. I can get the URL for their publication if you want to read it. It will say exactly how many microKelvin hotter the Background is in the direction of constellation Leo. This slight increase of temperature translates into a speed like 370-380 km/s.
This was called measuring the CMB dipole. Wikipedia might have something about it.

So, in brief terms, there is no ether and in the balloon picture there should be no rubber! And yet the universe has a measure of being at rest, one can be at rest with respect to the collective expansion process, or equivalently the ancient matter, or equivalently the CMB.
And General Relativity allows for the distances between stationary objects to increase. Indeed this is just what the Hubble law is about. It is about the rate of increase of distances between widely separated stationary objects.

Last edited: Dec 16, 2008
10. Dec 16, 2008

### Chronos

Expansion of space stretches the wavelength of light traversing it. The energy of a photon is a fixed quantity. No energy is lost due to expansion because of time dilation - photons received are redshifted, but, you receive them over a longer period of time. It all balances out.

11. Dec 16, 2008

### BoyangQin

what do you mean by receive them over a longer period?
the total number of photon changed?

12. Dec 17, 2008

### marcus

I also would echo the same question. I don't understand the thinking behind post #10.

BYQ, I've been enjoying your questions and hope you will have more. If there is any question where I've overlooked something and haven't answered sufficiently, please repeat the question. Also if you are puzzled any of my responses, please ask further and I will back up and take another shot at answering.

===============
BTW here is curious fact, not directly connected to our discussion. It is counter-intuitive---goes against the way we usualy think and can be puzzling:

http://arxiv.org/abs/0808.1552
Note on the thermal history of decoupled massive particles
Hongbao Zhang
(Submitted on 11 Aug 2008)

"This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in [Weinberg's new Cosmology text], the strategies employed here are simpler, and the results obtained here are more general."

I think most of us understand that expansion drains energy and momentum from photons. It may be surprising to note that it also drains energy and momentum from particles with mass. Steven Weinberg has a proof of this in his new Cosmology textbook, apparently (I don't have the book.) Hongbao Zhang has offered what he says is a simpler proof.

Both processes appear to violate conservation laws, but those laws have limited applicability where geometry is changing so perhaps that part is not so surprising.

Last edited: Dec 17, 2008
13. Dec 17, 2008

### BoyangQin

Marcus, thanks so much for the answer and discussion.
i am new to PF and never expected someone would answer my questions with such details and patience

But starting from today, until to about after christmas, i'll be engaged in some college application.

Perhaps catch up more inquiry about CoMoS then..

14. Dec 17, 2008

### marcus

Good luck with the applications. Don't forget to apply to U. Waterloo
I'd rather be a neighbor of Perimeter than a neighbor of the IAS at Princeton, right now.
If you can stand the winters, several Canadian places are looking really good from my point of view.

15. Dec 17, 2008

### Chrisc

Hi Marcus, that was a very impressive explanation and a pleasure to read.
I didn't want to interrupt your discussion but as BoyangQin is done for now, I have a question
The expansion in front of the light will put the light travel time at a distance greater than the
distance at time of emission.
So if I use your example and type 1.45 in the Z box I get a travel time of 9Gyr and a present
distance of 14Gly.
Does this mean the calculation for the expansion in front of the light is already done?
So I should find a shift of 1.45 would be from a galaxy that was less than 9Gly distance
from Earth 9Gry ago?

16. Dec 17, 2008

### marcus

I don't fully understand what you would like explained but have a strong hunch that you would like to know the distance then, when the light was emitted. And I can help you get that.

The reason I think you would like to know that---how far the object was from us when it emitted the light we are right now receiving----is that you already have two big parts of the picture. You know the distance now, and you know the travel time. To complete the picture, it's natural to also want to know what the distance was back then.

Part of the read-out of the Ned Wright calculator is what he calls the angular size distance. Just to keep the same example, how about you go back to the calculator and put in z=1.45 again, and see what the angular size distance is. This is the same as the distance it was then. Just another name for it. (I think it's 5.7 billion LY, do you agree?).

Notice that the true expansion ratio is always z+1. that is the factor by which wavelengths are expanded and also the factor by which the universe distances expanded during the time that the light was traveling. Just an accidental convention that they always deduct 1. So in your example the number you really want to have handy is not 1.45 but 2.45.

Now let's compare the distance now, 14, with the distance then, which was 5.7. Heh heh. What is the relationship between those numbers.

Crisc you might also enjoy Morgan's cosmos calculator. the link is in my sig. The only thing is you have to put in 3 parameters by hand that Ned Wright puts in for you.
Morgan makes you type in 0.27 for the matter fraction, and 0.73 for the Lambda or dark energy fraction, and 71 for the Hubble ratio. You can see these are the numbers that Ned Wright puts in the boxes for you, in his calculator.
I hope you check Morgan's calculator out, and get it to work so it gives the same distance now, and distance then, numbers as Wright's, to a reasonable approximation.

Last edited: Dec 17, 2008
17. Dec 17, 2008

### Chronos

With redshift you also get time dilation. Objects at great distances appear to age more slowly than local objects [e.g., light curves of SN1-a are 'stretched' out consistent with their redshifts]. The result is lower energy photons [than emitted] appear to be received, but, over longer periods of time [by local clocks]. The number of photons is not affected. Their total energy is merely smeared out over a longer time interval, not 'lost'. A citation may be in order:

http://arxiv.org/abs/physics/0407077

Last edited: Dec 17, 2008
18. Dec 18, 2008

### Chrisc

Thanks Marcus
I see what I missed in the CosmoCalc. I didn't know what the angular size distance was. (distance then)
After typing in the values you suggested for matter fraction, Lambda and Hubble, I do get close approximations
to CosmoCalc . Morgans seems to allow for inflation as it returns an age "then" which is less than the distance "then"
in light years. Whereas CosmoCalc goes to zero.

I've played with the variables in Morgans version and noticed the present speed (as a measure of velocity and expansion) can exceed the speed of light.
This is very interesting, especially when one considers the observable effects of an inverse expansion.

19. Dec 19, 2008

Marcus