Relativistic Mass and high relative Velocity of distant galaxies

[Tanelorn]

I think I may have asked this before, but I don't think I received a reply that made sense, at least to me.

Does the gravitational force between distant galaxies become larger and more significant due to their Relativistic Mass at high relative velocities and especially at luminal and Superluminal velocities near and beyond the edge of our observable universe? Would this strong gravitational pull from beyond our universe not want to cause our observable universe to expand even more?

Is the real reason why relativistic mass is not significant because "the speed of gravity" is the same as the speed of light, and so there are many Billions of years of delay in the gravitational field reaching us? And also perhaps for the same reason that we have Olber's paradox when talking about the absence of star light? Also there is a square law reduction in intensity, so perhaps relativisitic mass of individual stars and galaxies only becomes more noticeable during Galactic mergers?

I just read somewhere that since the 1950s (shows how old I am!) Physicists no longer like the term Relativistic Mass. It is still real though correct?

 

[bcrowell]

General relativity doesn't provide a uniquely defined way of measuring the velocity of objects that are far away from one another. There is no well defined value for the velocity of one galaxy relative to another at cosmological distances. You can say it's some big number, but it's equally valid to say that they're at rest, and the space between them is expanding. Neither verbal description is preferred over the other in GR. Only local velocities are uniquely defined in GR, not global ones.

Since the velocity is not well defined, it clearly doesn't make sense to calculate gammas. There are no Lorentz transformations in GR that can be applied to the universe as a whole.

GR also doesn't describe gravity as a force, so it's not much use to try to calculate gravitational forces.

 

[Tanelorn]

Does this mean that there is no increase in gravitational field strength due to increased relativistic mass of high velocity particles and masses?

 

[bcrowell]

Does this mean that there is no increase in gravitational field strength due to increased relativistic mass of high velocity particles and masses?

The gravitational field is another quantity that is not well defined in general relativity (not in a frame-independent way, and not in all spacetimes). For example, there is no sensible way to define the gravitational field at a given point in a cosmological solution.

GR doesn't describe gravity in terms of gravitational fields or gravitational forces. It describes gravity in terms of spacetime curvature.

 

[marcus]

Tanelorn,
I agree with everything B. Crowell has said here and it is true that in cosmology you have to make a choice of what frame of reference to use and what ideas of time and distance to use (for things beyond the limits of where your chosen flat reference frame applies.)

There's nothing I can think of to add, except to state a personal preference--what choices work for me (and also for a lot of cosmologists--I just watch the field from sidelines so I like to conform my concepts with pros.)

The important reference for me is the ancient light we call the CMB, which seems to be everywhere and coming from everywhere, and to have almost the same temperature and wavelength mix from every direction.

That gives you a chance to choose a definition of what it means to be at rest. I choose to say that an observer (here or at some distant cluster of galaxies) is at rest relative to the ancient light if he doesn't detect any doppler hotspot. If he is moving "east" he will see a hot spot in the CMB sky with slightly shorter wavelengths, in the direction he is heading, and a doppler cold spot (slightly longer wavelengths) behind him to the "west".

That is called a "doppler dipole". We have measured the solarsystem's doppler dipole and we know rather accurately what its speed and direction is relative to ancient light.
We can correct for that in our observations.

We can eliminate from astro data the effect of our motion.

So we can compensate so the data represents what would be seen by a motionless observer.

So then I imagine the universe populated by motionless observers, who, it turns out, could have synchronized their clocks.

Since geometry is dynamic (not static as we experience here on our rigid rockball planet but) really dynamic like GR says, we have no right to expect that distances between these stationary observers won't change over time. And in fact they do change. That is what Hubble Law describes: An overall average percentage rate of increase in distances between stationary observers.

So that set of stationary observers with synchronized clocks defines a kind of universal point of view which tallies with the standard equation-model that cosmologists use to describe the U. The Friedmann equation model. It uses that kind of "universe time" and you can talk about distances between observers at a particular instant of time (as if you could stop the expansion at that very moment and measure by yardsticks).

Otherwise talking about distance involves a bit of a nuisance---they change while you are measuring. So making this CHOICE of a time parameter can be helpful.

In a sense it's optional. You have to make specific choices (in a curved world) to simplify things for yourself.

B. Crowell you are welcome to correct. I will bail so as not to interrupt any further.

 

[Tanelorn]

Ben and Marcus, thankyou very much for your replies, I missed the posts because I was away for a week or so, but I am glad to see them now.

Marcus, I understand and agree with the doppler dipole which gives us our relative motion to the current CMBR light sphere reaching us now.


What I am trying to do is fully rule out any alternatives or contributions to the magnitude of the change in CMBR frequency:

1. Does light undergo any kind of a doppler frequency shift when it is emitted from a body with a very high gravitational field strength? If so would this doppler shift be even higher because of the effects of additional relativisitic mass of the high relative velocity of the emitting body?

2. If the emitting gas of the current CMBR light sphere was already moving away from us at say 0.95c when the light was emitted, would this produce a doppler shift which would account for at least some of the change in CMBR frequency that we currently see, without needing to explain all of it by the continuing expansion of the space in between?

I don't wish to keep pressing these two points I just don't know how to be more clear. My suspicion is my questions do not make sense (or perhaps amount to the same thing), but I don't know why..

 

[bcrowell]

What I am trying to do is fully rule out any alternatives or contributions to the magnitude of the change in CMBR frequency:

1. Does light undergo any kind of a doppler frequency shift when it is emitted from a body with a very high gravitational field strength?

https://www.physicsforums.com/showpost.php?p=3203479&postcount=16

If so would this doppler shift be even higher because of the effects of additional relativisitic mass of the high relative velocity of the emitting body?2. If the emitting gas of the current CMBR light sphere was already moving away from us at say 0.95c when the light was emitted, would this produce a doppler shift which would account for at least some of the change in CMBR frequency that we currently see, without needing to explain all of it by the continuing expansion of the space in between?

FAQ: What does general relativity say about the relative velocities of objects that are far away from one another?

Nothing. General relativity doesn't provide a uniquely defined way of measuring the velocity of objects that are far away from one another. For example, there is no well defined value for the velocity of one galaxy relative to another at cosmological distances. You can say it's some big number, but it's equally valid to say that they're both at rest, and the space between them is expanding. Neither verbal description is preferred over the other in GR. Only local velocities are uniquely defined in GR, not global ones.

Confusion on this point is at the root of many other problems in understanding GR:

Question: How can distant galaxies be moving away from us at more than the speed of light?

Answer: They don't have any well-defined velocity relative to us. The relativistic speed limit of c is a local one, not a global one, precisely because velocity isn't globally well defined.

Question: Does the edge of the observable universe occur at the place where the Hubble velocity relative to us equals c, so that the redshift approaches infinity?

Answer: No, because that velocity isn't uniquely defined. For one fairly popular definition of the velocity (based on distances measured by rulers at rest with respect to the Hubble flow), we can actually observe galaxies that are moving away from us at >c, and that always have been moving away from us at >c.[Davis 2004]

Question: A distant galaxy is moving away from us at 99% of the speed of light. That means it has a huge amount of kinetic energy, which is equivalent to a huge amount of mass. Does that mean that its gravitational attraction to our own galaxy is greatly enhanced?

Answer: No, because we could equally well describe it as being at rest relative to us. In addition, general relativity doesn't describe gravity as a force, it describes it as curvature of spacetime.

Question: How do I apply a Lorentz transformation in general relativity?

Answer: General relativity doesn't have global Lorentz transformations, and one way to see that it can't have them is that such a transformation would involve the relative velocities of distant objects. Such velocities are not uniquely defined.

Question: How much of a cosmological redshift is kinematic, and how much is gravitational?

Answer: The amount of kinematic redshift depends on the distant galaxy's velocity relative to us. That velocity isn't uniquely well defined, so you can say that the redshift is 100% kinematic, 100% gravitational, or anything in between.

Davis and Lineweaver, Publications of the Astronomical Society of Australia, 21 (2004) 97, msowww.anu.edu.au/~charley/papers/DavisLineweaver04.pdf

 

[Tanelorn]

Ben, ok I see it now:

Question: How much of a cosmological redshift is kinematic, and how much is gravitational?

Answer: The amount of kinematic redshift depends on the distant galaxy's velocity relative to us. That velocity isn't uniquely well defined, so you can say that the redshift is 100% kinematic, 100% gravitational, or anything in between.


"That velocity isn't uniquely well defined" What does this mean? Well anyway it sounds like we can say either space is expanding OR there is high relative velocity. So why then do cosmologists say hand on heart that it is the expansion of space that is causing the red shift of the CMBR? - and also superluminal velocities at the edge of the observable universe?





Question: Does the edge of the observable universe occur at the place where the Hubble velocity relative to us equals c, so that the redshift approaches infinity?

Answer: No, because that velocity isn't uniquely defined. For one fairly popular definition of the velocity (based on distances measured by rulers at rest with respect to the Hubble flow), we can actually observe galaxies that are moving away from us at >c, and that always have been moving away from us at >c.[Davis 2004]


This goes against my understanding as well. I thought you simply cannot observe something receding from us at >= c... My head hurts someone must be updating or revising the Physics I learned 30 years ago.. So how can you observe galaxies moving away from us at >=c? Only by assuming that the space in between is expanding?




I just found this:

In expanding space, however, not only do individual photons get stretched (thereby losing energy) but the entire train of photons also gets stretched. Thus, it takes longer
than two weeks for all the photons to arrive on Earth. Recent observations confirm this effect. A supernova in a galaxy of redshift 0.5 appears to last three weeks; one in a galaxy of redshift 1, four weeks.


Again however these stars could also be moving away from us at high velocity rather than space expanding?

 

[bcrowell]

"That velocity isn't uniquely well defined" What does this mean? Well anyway it sounds like we can say either space is expanding OR there is high relative velocity.

Yes, that's exactly right.

So why then do cosmologists say hand on heart that it is the expansion of space that is causing the red shift of the CMBR? - and also superluminal velocities at the edge of the observable universe?

People will often speak casually without explaining all their assumptions, which they figure are shared by the people they're speaking to. Another good example is interpretations of quantum mechanics. When you work with quantum-mechanical systems (e.g., an atom of a radioactive isotope), it's often convenient to talk about it using the Copenhagen interpretation, because that matches up well with the way we experience it psychologically. But if I do that, it doesn't mean I believe the Copenhagen interpretation and disbelieve the many-worlds interpretation.

This goes against my understanding as well. I thought you simply cannot observe something receding from us at >= c... My head hurts someone must be updating or revising the Physics I learned 30 years ago.. So how can you observe galaxies moving away from us at >=c? Only by assuming that the space in between is expanding?

This may be helpful: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

 

[marcus]

This goes against my understanding as well. I thought you simply cannot observe something receding from us at >= c... My head hurts someone must be updating or revising the Physics I learned 30 years ago.. So how can you observe galaxies moving away from us at >=c? Only by assuming that the space in between is expanding?

This may be helpful: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

Ben has a good suggestion for you. Read the Lineweaver Davis SciAm article. It explains how we can today be observing the light that a galaxy emitted when the distance to it was increasing faster than c, and also today the galaxy's distance can be increasing faster than c. It uses pictures.

This does not depend on any new physics besides what was available well before 1930. It only needs careful thinking and commonsense math plus the fact that the Hubble rate has been decreasing.

You have to get your head around the idea of the Hubble distance, which is the (instantaneous now) distance which is increasing at exactly rate c.

Because v = Hd, you can solve for it by putting c in for v (the increase rate) so you have
c = Hd. Then you solve for d: you get d = c/H.
that is high school algebra, you can work it out with google calculator and find the Hubble distance if you want.

Galaxies at that distance are receding at exactly rate c.

Since H has decreased greatly over the history of expansion, the Hubble distance and increased greatly.

So a galaxy can have been in a region of space receding >c back then when it emitted a photon in our direction.

And the photon tried bravely to get to us but was swept back, because everything around it was receding from us >c.

But the little photon kept on trying to reach us and eventually the Hubble distance extended out to it! Finally it found itself WITHIN the sphere of where distances expand < c. And then it could make progress towards us---and not be swept back.

The whole thing works because the Hubble distance has been expanding rapidly and reaching out to those struggling photons. It expands more rapldly than the expansion of ordinary distances.

(To understand anything connected with Hubble law and Hubble distance you do need the concept of proper or instantaneous distance, which is a definition of distance cosmologists often prefer to use---what you would measure by ordinary means if you could freeze the exansion process at that moment, freezing it gives you time to measure which takes time.)

It wouild help you if you learned to use calculators. Like google "cosmos calculator" and put in parameters .27, .73, 71 on the left hand margin and then put in redshift 1.8 and press calculate. It's simple and it gives hands on experience with the standard cosmo model.
It has helped a lot of people understand. If you want to try and want coaching just ask.

 

[marcus]

Tanelorn as long as you try to understand cosmo in a purely verbal way I think you realize you must get it wrong, because it is a math science---concerned with fitting model to data. English words never quite translate it.

So one way to get acquainted with the model is to play with the calculators which embody it. Here's one that embodies the Hubble Law expansion, and to use it you need to input 3 numbers which have been determined by observation---they make the model fit. In each case there is some percentage uncertainty.

(...connected with Hubble law and Hubble distance you do need the concept of proper or instantaneous distance, which is a definition of distance cosmologists often prefer to use---what you would measure by ordinary means if you could freeze the exansion process at that moment, freezing it gives you time to measure which takes time.)

It wouild help you if you learned to use calculators. Like google "cosmos calculator" and put in parameters .27, .73, 71 on the left hand margin and then put in redshift 1.8 and press calculate. It's simple and it gives hands on experience with the standard cosmo model.
It has helped a lot of people understand. If you want to try and want coaching just ask.

You may recognize .27 as the matter fraction (dark + ordinary) and .73 as a common estimate for the dark energy fraction. And you may recognize 71 as a common estimate for H, namely 71 km/s per Megaparsec. You type those in down the left hand margin of the screen in the appropriate boxes.

Then you can put in any redshift (of some galaxy or of the microwave background or of the earliest stars sofar observed) and it will tell you

distance THEN and also the rate that distance was expanding at that time (when the light was omitted)

distance NOW and also the rate that the now distance is growing at this moment (when the light arrives to our telescope or whatever instrument.)

I suggest you try redshift 1.8. Most of the galaxies we can see have redshift greater than 1.8. So most of the galaxies we can see would have distances larger than what you get for that, and also distances growing faster than what you get for 1.8

 

[Tanelorn]

Marcus, perhaps you are right about maths. However, I often find a good chart or set of charts with comments can get across a concept at least as well, if not numerically as precise. More in the morning..

 

[marcus]

Marcus, perhaps you are right about maths. However, I often find a good chart or set of charts with comments can get across a concept at least as well, if not numerically as precise. More in the morning..

Charts are non-verbal. If I understand what you mean by charts. They can illustrate mathematical relations. They give you at the bare minimum something to think with besides English words.
So also does playing around with one of the online redshift calculators. Typically you put in some number for redshift and it tells you things about a galaxy whose light has that much redshift it reaches us.

If you know how to make charts that can show up online, and we could see, then why don't you make a chart that plots recession speed as a function of redshift?
It should make a nice curve. The cosmos calculator would give you some x,y points and you just run a curve through them.

On the x-axis plot redshift .5, 1, 1.5, 2, 2.5, 3
The most distant quasars and galaxies are in the range 7-10
(wavelengths stretched out by a factor on the order of 10, quite a stretch!)
And on the y-axis plot the rate at which the distance to that galaxy is increasing
(I shouldn't call it a speed because that suggests motion, going somewhere, approaching some destination----but there is no place the galaxy is going, it is just the distance increasing.)

So if you like charts, please make a chart, of how distance expansion "speed" grows with redshift. The online calculators will give you the numbers to plot.

I keep the link to "cosmos calculator" in my signature, but google hits it if you just say its name.

 

[Tanelorn]

Thanks Marcus, I now have a beautiful set of curves (I also have a photographic memory which helps!). For interest I also took the redshift to very high numbers where I believe the CBMR is supposed to be. What is the redshift of the CBMR? ~1000?

Now I have to add some comments on the meaning and interpretation that Cosmologists apply to them. The main thing I am trying to establish at this time is the reason(s) for believing that red shift is due to the expansion of space and not at least in part relative speed and hence doppler.

Is the reason for believing in the expansion of space, because no two objects can travel at faster than the speed of light relative to the comoving sphere of CBMR? And that this means that the maximum relative speed cannot exceed twice the speed of light? Perhaps this would suggest a preferred frame of reference? What would the CMBR look like to COBE if it was moving at 0.5c or 0.9c relative to the preferred frame? Presumably a more exagerated dipole?

Ben seems to be saying that it is not possible to tell whether CMBR redshift is due to the expansion of space or relative speed and hence doppler. Am I interpreting him correctly?

Of course the biggest thing here is that we can actually see things that were traveling faster than the speed of light when the light was first emitted. I thought that bodies that move away from us at super luminal velocities became no longer visible which is why the size of the observable universe is getting smaller. What was the velocity and is the currrent velocity of the comoving sphere of the CMBR?

 

[marcus]

Thanks Marcus, I now have a beautiful set of curves (I also have a photographic memory which helps!). For interest I also took the redshift to very high numbers where I believe the CBMR is supposed to be. What is the redshift of the CBMR? ~1000?

You did it! That is so great, thanks! This gives me something to think with you about. We could get to questions of a concrete sort that are beyond my ken and need help from some of the others.

Yes the redshift of the CMBR is estimated to be around 1100.
It originally was thermal glow ("blackbody radiation) as from an object at 3000 kelvin and now it is thermal glow as from temperature 3000/1100, whatever that is. 2.7 something kelvin.
Distances in the U have expanded by a factor of 1100 since the light got loose, and wavelenghts have expanded by the same.

Let me offer some numbers as a check for yours, to see if we are using the calculator the same way. You may have found other online calculators, they should all give approximately the same answers if you put the same 3 parameters into them (.27, .73, 71).

Always good to check. I'll go get Morgan's "Cosmos Calculator" and be back in a minute.

Distance expansion rates (as multiples of c) as function of redshift (z)

z      1.5     2.0     2.5     3.0     3.5    1100
THEN  0.92    1.17    1.40    1.62    1.83    57
NOW   1.04    1.24    1.40    1.53    1.63    3.3

If anyone is coming in new to the discussion, I'm using Morgan's calculuator:
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

The reason for the crossover is that the percentage distance expand rate is NOW very moderate, so the expand speed only increases gradually with distance and even out at the farthest matter we can see (the source of the ancient CMB light) is only 3.3 times c.
But in the early universe the percent rate of expansion was very much greater!

So with the THEN numbers one is going back in time, when the light was actually emitted (not now when it is being received), and as you go back you get into regimes of more rapid expansion.

So the ancient light was emitted by matter which back THEN was only 41 million LY from us (million not billion! very close!) or I should say from our matter, that eventually became us. And that small distance of 41 million LY was really expanding fast: over 50 times c.

Remember that in all Hubble Law discussion the definition of distance is the "freeze-frame" or "proper" distance that you would measure if you could freeze the expansion process at that moment (to give time to measure), or if you like it is the instantaneous distance. The rate of increase is defined similarly, also instantaneous.Also no calculator is perfect. So the real answer may be somewhere between 50 and 60 when it says 57. I just don't know the accuracy of Morgan's calculator when you push it to really high redshift numbers. Maybe someone else knows.

A more professional-looking calculator with more features and somewhat better accuracy is Ned Wright's "cosmo calculator" (note: cosmo not cosmos) but his does not give expansion rates! He only gives various distances and times. If you compare you will see they give essentially the same distances, just with different numbers of decimal places. I like Morgan's because it's simple.

 

[bcrowell]

Ben seems to be saying that it is not possible to tell whether CMBR redshift is due to the expansion of space or relative speed and hence doppler. Am I interpreting him correctly?

Basically yes, although I would add a quibble. It's not that it's not possible to tell. It's that the question is one that inherently has no well defined meaning.

-Ben

 

[marcus]

...
Now I have to add some comments on the meaning and interpretation that Cosmologists apply to them. The main thing I am trying to establish at this time is the reason(s) for believing that red shift is due to the expansion of space and not at least in part relative speed and hence doppler.
...

At the moment I only have time to address a small part of the questions in your last post.
I wrote a lot just now, but it was all kind of footnotes to your first paragraph! I'll get back to some of the other issues, or someone else will, in a day or so.

Remember that Special Rel is formulated in a rigid non-expanding reference frame. Words like "traveling" and "relative motion" only make sense if you can capture both objects in the same approximately flat non-expanding region and treat them in the same reference frame.

Special Rel is not about CURVED spacetime. It is the 1905 flat little brother to the grownup 1915 General Rel. Same way with its famous "speed limit". Objects in curved spacetime (and expansion is a type of curvature) do not obey the SR rules. To apply SR you need objects that are close enough together so you can consider the geometry surrounding them to be approximately, for all practical purposes, flat rigid and foursquare.

So when you go largescale you have to chuck out a certain portion of your preconceptions.

Things really aren't "traveling" unless there is somewhere they are going to, some destination. If the distance between them is merely increasing that doesn't necessarily constitute travel.

I have to go but will check in later. Did you get the same numbers as I did in the previous post?

 

[Tanelorn]

"Consider the following proposal for defeating relativity's prohibition on velocities greater than c. Suppose we make a chain billions of light-years long and attach one end of the chain to a particular galaxy. At its other end, the chain is free, and it sweeps past the local galaxies at a very high speed. This speed is proportional to the length of the chain, so by making the chain long enough, we can make the speed exceed c."

Ben, I am still enjoying this too much to figure it out, but what is the answer?



I am also stuck on how expanding space would increase the wavelength of a photon, if it is considered to be simply a very tiny particle. I recall reading that the expansion of space only affects things over enormous distances, but at any instant the photon is only occupying a very tiny distance.

 

[Tanelorn]

Hi Marcus, in response to your table of values in post 15, I am getting a discrepancy:

eg. For redshift 3, I get speed now 0.99c, and speed then 1.99c.

I tried various other values of Omega, Lambda and Hubble constant but I was still only able to match one of your numbers, not both at same time.


Marcus, by the way, thanks very much for the responses, that was quite a few lines you wrote there, thanks!
Perhaps the problem is I didnt cover GR at all, just SR, I was studying Physics and Electronics.



Post edit:

Re: values of Omega, Lambda and Hubble constant

I just saw your values 0.27, 0.73, 71 and now confirm your numbers!


I especially liked redshift 1100, speed away from us now 3.3c, speed away from us then 57c! that is cool. This is not inflation correct? This is dark energy expansion of space?

 

[Tanelorn]

Marcus, I am now reading your post 10, which explains how CMBR can still just reach us despite moving at 57c then and 3.3c now. I wil probably have to spend more time on it.

I assume this also applies to galaxies moving at superluminous velocities? Their light can still reach us because it always travels at the speed of light towards us? - And provided that the expansion of space between us is not also increasing at the speed of light, making that part of the universe unobservable.

Marcus, do you have a chart showing how the radius of the observable universe has changed over time, this would be very interesting to see. Also how it is expected to change in the very distant future.

 

[marcus]

...
Marcus, do you have a chart showing how the radius of the observable universe has changed over time, this would be very interesting to see. Also how it is expected to change in the very distant future.

There are good charts in a 2003 paper by Charley Lineweaver called "Inflation and the Cosmic Microwave Background"
http://arxiv.org/abs/astro-ph/0305179
What you are asking about (radius of observable) is called the "particle horizon" and he plots that as a function of time. In his plot time axis is vertical going upwards from time zero, and proper distance is horizontal.

You should also get familiar with another handle on expansion which is the scale factor a(t).

He plots that too. It is sometimes called "average distance between galaxies" and is abbreviated a(t) and normalized so that a(time=0) = 0 and a(present) = 1.
It is a handle on the overall size of the universe, not just the radius of the observable.
It shows how any given distance has increased over time.

See how you like the charts in that 2003 paper. I think Charley is world class. Australian guy.

 

[bcrowell]

I am also stuck on how expanding space would increase the wavelength of a photon, if it is considered to be simply a very tiny particle. I recall reading that the expansion of space only affects things over enormous distances, but at any instant the photon is only occupying a very tiny distance.

It's not size that matters, it's binding.

 

[Tanelorn]

I don't suppose that there is any chance that the dark energy expansion of space, which appears to only act between objects separated by very large distances, could be explained by gravitational fields turning negative in a similar way in which the strong force changes its sign at atomic scales?


[PLAIN]http://www.fpsasm.co.uk/sitePictures/electrostatics/snf_graph.jpg


Chalnoth, thanks for the papers with charts showing the change in the size of the universe over time. They were very detailed, I may need some guidance on how to read the information they contain. Although I am not still not sure how anyone can estimate the size of the rest of the universe to anything under about 30 orders of magnitude!