Hypothesis: All space is causally linked.

[tar]

Please help me test my hypothesis against known observations and proven science.

 

My guess is, that at the time the universe became transparent to photons the universe was small enough that a photon emitted at one end, would have been able to reach the other end, even counting for the expansion of space, within 13.7billion years. If this is true, then once two locations in space are thusly causally linked, they will not, indeed cannot, become unlinked, due to the fact that C is the speed limit of the universe, and no location or object can outrun an already arrived photon. Thus as object b receeds from a, a continues to receive b photons at lower and lower frequencies, gamma rays becoming x-rays, x-rays becoming ultraviolet ... visible ... infrared ... microwave ... radio waves of longer and longer wavelengths. When a and b's recession from each other exceeds the speed of light, the flow of photons will not stop. Photons just about to arrive at a from b will still arrive. Only something about the relative age or the apparent age of b will change. Something I have not put my finger on yet.

 

Regards, TAR

[ajb]

Inflation?

[Klaynos]

The speed limit of c is for stuff inside the universe relative to other stuff inside, not the universe itself, it can expand at any speed it likes....

[Martin]

Most of your post sounds pretty reasonable to me, like you have been thinking about this stuff and trying to work out a consistent picture. There seems to be two parts: first, a conjecture you want us to help check. And then also some conclusions that you derive from that, and a bit more discussion.

Please help me test my hypothesis against known observations and proven science.

 

My guess is, that at the time the universe became transparent to photons the universe was small enough that a photon emitted at one end, would have been able to reach the other end, even counting for the expansion of space, within 13.7billion years.

 

This conjecture is something we can check and maybe it can be proven wrong and ruled out. We will see. But then even if the conjecture turns out to be wrong, your following discussion seems completely on track, at least to me. I think you are absolutely right to point out that even if the distance between two objects is increasing faster than c, at present, there will be photons which are already on their way which will continue to arrive! So just having a recession rate bigger than c would certainly not shut off the flow of light. So the discussion makes sense.

 

If this is true, then once two locations in space are thusly causally linked, they will not, indeed cannot, become unlinked, due to the fact that C is the speed limit of the universe, and no location or object can outrun an already arrived photon. Thus as object b receeds from a, a continues to receive b photons at lower and lower frequencies, gamma rays becoming x-rays, x-rays becoming ultraviolet ... visible ... infrared ... microwave ... radio waves of longer and longer wavelengths. When a and b's recession from each other exceeds the speed of light, the flow of photons will not stop. Photons just about to arrive at a from b will still arrive. Only something about the relative age or the apparent age of b will change. Something I have not put my finger on yet.

 

This is OK. So let's get back to the first part where you hypothesize that the whole universe is within our past lightcone, or they also use the technical term "particle horizon". The technical jargon doesnt matter. You say it very clearly. You conjecture that the universe is finite volume, and small enough that any bit of matter could have sent us light that we are receiving or have already received.

 

You know, that is just barely possible! I think that under reasonable assumptions it has been ruled out to something like 95% confidence level. But it is not obviously wrong----I think.

 

I have to go out, so I can't finish this post. But maybe someone else will jump in. Given time, I think I could persuade you that the universe is probably bigger than what we see or could see. There are reasons to think that it is bigger. But I don't believe I could prove it with absolute certainty.

 

The mainstream consensus in cosmology, so far, is that we don't know yet wether or not the universe is finite volume or infinite. And as of January 2009 when a bunch of WMAP data was published (I'll get a link to it later) the best estimate was that if it is finite then with 95% confidence the circumference is at least 600 billion lightyears.

 

And also the best estimate currently is that even allowing for expansion the farthest matter we can see is today only 45 billion lightyears away. (It used to be much closer, when the light started its journey to us, but the distance has expanded to 45.) Now this is not absolutely certain, but it suggests that we are causally connected only out to a current distance of 45 billion lightyears.

But if the universe is finite then the farthest anything is away from us is at least 300 billion, namely half the hypersphere circumference, with 95% confidence. Something like the surface of a balloon, only 3D whereas the surface of a balloon is only 2D----difficult to imagine a finite volume, boundaryless, space but that's the typical model that they use for the finite case.

Have to go. Nice post by the way!

[bascule]

Isn't the answer to the question "what exists outside of the visible universe" unknowable? If something exists outside the visible universe, isn't it impossible for it to be causally linked to us?

[Martin]

Bascule that depends so much on philosophy and language issues. Unstated assumptions people make and what they mean by various words.

 

the current situation in cosmology is that the LCDM model is generally accepted because it it gives a remarkably close fit to the vast body of data that continues to accumulate. and it assumes a certain uniformity.

 

I think you know. Homogeneity and isotropy. The "cosmological principle". It is a basic assumption and it gets challenged from time to time. Most recently David Wiltshire (a new zealander, very good cosmologist) and a handful of others like him.

 

But the assumption that our location is not special and that things are approximately uniform throughout has turned out to be very durable, and people check it as best they can and of course cannot absolutely prove it true. So that assumption is often made without explicit statement.

 

And I think you see immediately that this assumption goes beyond our particle horizon, outside our past lightcone, and is about stuff we really cannot know. It says no dragons. It says things out beyond 45 billion lightyears are more or less just like here. And of course we can't be sure that there are no dragons! Maybe things are quite different out there.

 

Anyway in January 2009 the five-year Wmap data was published, and essentially everything in that report, all the parameters of every version of the model, assume the basic uniformity thing. That is how you model. Our model of the universe is good, and it wouldn't work if there were dragons all over the place just out of sight over the horizon, exerting forces so far not observed in our part of the universe etc etc. You have to keep it simple in order to get anywhere. So they should have stated that and maybe they didn't make it plain enough.

 

And about the size of the universe there are two main versions of the LCDM model----spatial infinite and spatial finite. Which is right depends on measuring the curvature more accurately. Finite is if and only if the curvature is positive, and once you know the curvature you can calculate the circumference.

 

It is pretty straightforward. The key assumption is uniformity and if you don't suppose that, then the size estimates and pretty much everything else go out the window. Because all the inferences based on what we can observe are made using the model. And if you do assume uniformity (and conventional physics of radiation and matter) then everything else falls into place.

 

Personally I'm very comfortable with the uniformity assumption because of my sense that History has born it out. The farther our instruments look the more it continues to look the same.

 

http://en.wikipedia.org/wiki/Eratosthenes

 

Eratosthenes could not see beyond the Mediterranean world he lived in, but he estimated the circumference of the earth by assuming uniformity which he could not prove. So WMAP has given us a lowerbound estimate of the circumference in essentially the same Eratosthenes way, by assuming uniformity and measuring a curvature. And that involves inference beyond the observational horizon just as in the 200 BC Greek's case.

[tar]

Martin,

 

Thanks so much for your reply. This Lepton felt pretty good to read it.

 

I am still perplexed by much of the math required to properly model the universe and figure out how things can and can't fit together. And I am completely lost with the 10 dimensional stuff. Even your mention of a hypersphere sent me scampering to Wikipedia, and left my head spinning with the symbols, transformations, jargon, and references to named equations that I am just not learned enough nor bright enough to fully comprehend, much less delve into, in terms of their subtleties and implications.

 

So I, like most people who are outclassed, figure that all this dark matter, dark energy stuff was just made up to make the equations work. And I think in terms of Euclidean geometry, analogies to common experience and common sense. Not much of a scientist, really, although, when I understand it, I am fully appreciative of the great body of knowledge that a large number of great minds have gleaned from the study of, and the mathematical investigation of, our universe. And I rely on others to answer the questions I have, pertaining to my hypothesis.

 

The first question is, how big was the universe, when it became transparent to photons?

The second question is, how long would it take a photon to traverse that distance, if that distance was increasing at the Hubble constant?

 

Thanks again for entertaining my thoughts.

 

Regards, TAR

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ajb,

 

"Inflation?"

 

Was this the answer to what I couldn't put my finger on? If so, then I wasn't clear. I was trying to imagine what effects, on the appearance of b, my scenario should have. For instance should it appear younger or lengthened, faded, move in slow motion, or dissolve into radio waves or something. I have not thought it through. Gives me a thought though. I wonder if it would yield anything, to focus on a small patch of microwave "background radiation" and put it through a computer simulation that would "up the frequency" by the right multiple to put it into the visible spectrum, and "see" if it looked like anything?

 

Regards, TAR

[Martin]

...The first question is, how big was the universe, when it became transparent to photons?

The second question is, how long would it take a photon to traverse that distance, if that distance was increasing at the Hubble constant?

...

 

Can't answer your questions in quite the same way you pose them.

Now this is according to the standard model---space became transparent to light at about year 380,000 after start of expansion.

The CMB, the background microwave, comes from that time, and the matter that emitted it was an estimated 41 million lightyears from here (from our matter that became us and the rest of Milkyway galaxy.)

 

That matter is now 45 billion lightyears from here. The distance has expanded by a factor of about 1090, while the light has been traveling to us.

 

And the wavelengths of the light have been enlarged by the same factor of 1090.

 

The Hubble rate of expansion of distance is not constant over time but has varied greatly. It is believed to be constant over space, the same everywhere at any given time, so it is sometimes called Hubble "constant".

But it used to be thousands of times larger than it is now, it is certainly not constant in time.

 

The current Hubble rate is that distances expand by about 1/130 of a percent every million years. So you asked how long would it take light to travel---say---41 million lightyears, allowing for expansion. Well at the present rate of expansion it would take approximately (just slightly over) 41 million years. Because in that time the distance it had to travel would expand only by about 41/130 of a percent, which is hardly anything. Of course at an earlier more rapid rate of expansion it could take considerably longer, and indeed the microwave background light has taken much of the whole 13-some billion years.

 

You ask how "big" the universe was at the time of last scattering (the moment of effective transparency you mentioned). We don't know. It might have been infinite then and likewise be so now. On the other hand it might be finite and only a few times bigger (say ten times bigger) than what we can see. What we can see has a radius now of about 45 billion ly and a radius then of about 41 million ly.

 

I agree that the basic facts of the standard cosmology are hard to comprehend. They do not obey the conventional nonexpansive Euclidean geometry we are used to, the model does not 'live' in that kind of geometry. So we all face the same conceptual hurdles at one time or another in one way or another. We can only do the best we can and be patient and gradually get used to things. A wise person (I forget who) said that one never really understands mathematics, one merely gets used to it.

 

Heh heh, that is a kind of stoical joke. Anyway, have fun and keep asking questions.

[tar]

Martin,

 

Thank you for the information. It throws a couple of wrenches into my model. I had not considered that the Hubble "constant" changes. Raises some questions though about how various figures and measurements were arrived upon and made. For instance, if we don't know what we are looking at, and we make assumptions about it's age and distance and structure, based on previous assumptions (made when we also didn't know what we were looking at,) it seems we could be multiplying our errors and omisssions.

 

Have to go to work.

 

Regards, TAR

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Martin,

 

Thought about your post off and on all day, driving, lunch, breaks and when I got home, after working on the lawn mower, I reread your post about 6 times, reading Wikipedia posts on time horizons and cosmic background radiation, the size of the universe, how many galaxies there are, how old and how far, etc. etc.

 

And suddenly something started making sense. By the measurements you gave me, the current universe (locations a b and c) are 45 billion lys apart. 13-some billon years ago, they were 41 million lys apart. At that time, the cosmic time at all three locations was 330-360 million years ABB (after Big Bang.) Images of the time of last scattering would reach our location (b or the location that would become the Milky Way) coming from a in a little over 41 million years, let's say 45-90 million years. The time at b, when we see the last of the last scattering at a, is now 450 million years ABB. Meanwhile, c (also at 450 ABB) is looking toward b and sees b's first photons at the time of last scattering, emerging from the wall that appears to c to be receding at the speed of light. Little does c know that to b, the entire universe is crystal clear with photons streaming in from all directions. (Can't tell you what c sees when she turns around though, her being at the end of the universe and all.) Fast forward another 60 to 100 million years to 550 ABB and check the situation again. We (b) take a look over at a and see a region of space that looks about 60-100 million years older, development wise, and is a bit more red shifted and a bit farther then the 41 million lys it was last time. Meanwhile (still 550 ABB) at c, she looks at us and we (b) look to her, pretty much like a looks to us. But when she © looks at the region of a, she sees the last of the last scattering disappearing from the universe forever, and emerging from that last wisp of scattering, is region a, crisp and clear, looking a bit more red shifted than b, but not a day older than 330-360 million years and what, about 100 million lys away.

 

Fast forward to the present. We (b), along with a and c are now 13.7 billion years old. We each are 45 billion lys away from each other. We (b) had watched a and c age along with us. When we were just 41 million years old we first saw them emerge from the cloud, we watched them develop along with us but each million years they were looking a little more red shifted, farther away, and seemed to be aging slower and slower. Then they red shifted into infrared, and we couldn't quite make them out anymore. When we look in their direction now we see they have red shifted into the microwave range.

 

What do you think?

 

Regards, TAR

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Wow, I just reread my post, and it doesn't express the thoughts I was having.

 

I had a lot of insights last night, and formed a model in my head that made a lot of sense to me, answered a lot of questions, opened the door for a lot of predictions, and ruled out some ideas which, to me, no longer fit with reality. For instance, the idea that since the farther away an object is, the older it is, we should be able to, if we can look far enough, see the beginning of the universe. I concluded last night, that this is a false hope. I thought I was proving it, along with a dozen other insights, with my post last night. In rereading my post tonight I see that everything going on in my head was not relayed to the computer screen. And it does not read anything like the "ahah" moments it grew out of.

 

Regards, TAR

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Bascule,

 

 

"Isn't the answer to the question "what exists outside of the visible universe" unknowable? If something exists outside the visible universe, isn't it impossible for it to be causally linked to us?"

 

My hypothesis could be wrong. But if it is correct, which it seems to me to be, so far, then you start with the premise that everything in the universe has to be causally linked, and figure out afterward what the link is, and how each item in the universe should look to us. So for instance, let's say we figure the universe to be 13.7 billion years old, and let's say it could be 600 billion lys wide. At first blush, it would seem that that location of space is locked away from us by time and distance, because if we sent a message to it, the message would take at least 600 billion years to get there, and the reply would take another 600billion years to return, and that is only if the universe would average the same size that it is now for the next trillion years. So it seems unlikey the two point could be causally linked. But that is just the way it seems. The time and distance that is our enemy in considering any two way communication with a distant object are are friends when considering if there ever was one way linkage. For if the universe expanded to 1000 times it size in the last 13.5 bys then it was 1000 times smaller 13.5 billion years ago. A 600million ly wide universe, although still expansive, might have two way communication possibilities. A message could be sent from one end to the other in 600 million years, if the universe would stay the same size. But it didn't. I am not so good with caluclus, so just sticking with ratios and making rough estimates, let's say that from the moment the message was sent,the universe would double in size every 1 billion years. So the message travels for a billion years, and finds itself 1 billion light years away from the sender, in a universe that is 1.2 billion years wide. 200 million ly short of its target. So like any good photon does, it keeps going for another 200 million years, traversing 200 million lys. But in that time, that 200 million ly stretch of space stretched 20 percent so its still conceivable that it is 40 million lys from its target. Its on the downhill stretch now and that 40 million can be covered while the expansion only adds another 5 percent or about 2 million miles which it should be able to cover in 2 and a bit million years. But it made the trip. Took 1.242 billion years. But it made it. From one side of the universe, to the other. Now the return message might or might not make it. My figures are too vague and my figuring to feable but at this point in the excercise, we are in a universe 1.5 billion lys across that will be 3 billion light years across after the return message covers its first billion miles, 6 billion light year across after 2 billion ly of travel, 12 billion across after 3, 24 billion after 4...seems to be fighting a losing battle. So although it appears there was a time, early on in the universe, when one way communication was possible. There also seems to be a time at which a photon leaving one end of the universe would not make it to the other end, ever. (unless the universe at some point in the future, slows its expansion drastically, stops or shrinks.) But we still have the guess that that first, one way message, could have been sent, from one side of the universe to the other. And if this is true, then the entire 13.7 billion year old universe is populated by locations in space that can see every other location in space. Because each location sent out a continuous stream of photons (starting around 13.4 billion years ago) and if the first photon could reach every location in space, some portion of the following ones could do the same. And the visible universe, is the entire universe. Its just a matter of figuring, when we see a location in space, which portion of that 13.4 billion year history of photon emissions we are seeing.

 

Regards, TAR

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P.S. Bearing in mind that by "visable" I mean a photon strikes us. It does not have to be in the visible spectrum. It could be stretched out to infrared, microwave, or radio waves.

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correction: I used 330-360 million years after big bang as the time of recombination, or last scattering, and Martin, you gave me a time of 380,000 years for that era. Off by a factor of 1000. Pretty bad. But its even a better number for my argument. Light could make a 41-82(plus expansion) million light year trek well before the universe's 550 million year birthday. Probably closer to it's 200 million year birthday.

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Early on in the universe, right after the last scattering, each location in space saw the wall of fog, of the last scattering receed from their location at the speed of light, until each location could see the entire universe edge to edge. The clumps of matter at the farthest edge (to each observing location) were the last to emerge from the fog and looked to be 380,000 year old clumps, while each observing location was 200 million years old and probably a massive population III star in some stage of its development. As the universe aged, this type of effect continued to exist. Each location would see its stage of development spread out to the edge of the universe at the speed of light, and at all times, could see to the very edge of the universe.

 

But the edge of the universe kept getting farther away and locations at the edge though still developing were appearing to develop at a slower and slower rate, and they were red shifting more and more. All the billions and billions of stars that Olber was looking for ARE lighting up the night sky, lighting it up in the microwave frequency. And they are probably the population III stars we've been looking for, to boot.

 

Regards, TAR

Edited August 1, 2009 by tar
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[tar]

What is the conventional meaning of "causally linked"?

If an object in space is "visible" to our equipment, then photons from that object are striking our eqiupment. Is this sufficient proof that that object is causally linked to our equipment?

Would it be correct to assume that an observer located on that object, in the current, mind's eye, 13.73 billion year old universe, would "see" the Milky Way as a "younger" object, the same age, redshift and distance away, as the observer on the Milky Way sees the object?

Is the fact that that object sees us (at some age,) and we see it (at the same age that it sees us,) proof that our location in space is "causally linked" to that location in space?

What is the conventional meaning of "distance" to that object? Distant object then, to the Milky way then? Distant object then, to the Milky Way now? Or current object to current Milky Way?

 

Regards, TAR

[tar]

Martin,

 

Do we have estimates of the size of the universe at each of the billion year marks since the Big Bang started?

 

Regards, TAR

[tar]

Martin,

 

Do we have estimates of the size of the Earth's location's observable universe at each of the billion year marks since the Big Bang started?

 

Regards, TAR

[tar]

I am perplexed.

 

If we figure the age of the universe, based upon the relationship of the observed bits of matter and energy in it, are we not accounting for all the energy and matter that there is? Does this not imply finiteness? That is, that there is a certain finite amount of space, expanding in a certain finite manner, carrying a certain finite amount of matter and energy with it?

 

And if the whole universe was at one point very early in its history, causally linked, followed by a small period of drastic expansion, which inflated the whole universe so fast and much that regions were now no longer causally linked, followed by a period were gravity had regained its footing, followed by the last scattering after which photons were free to travel at light speed, we have postulated a very early causually unlinked universe (330,000 to 380,000 years old) which is huge, but only a percent of a percent as huge as it is now, with two very fast vehicles of causal connectivity, gravity and light, present, to begin reconnecting regions causually.

 

Although now, light and gravity crawl along at the rate of around the order of .01 universe diameters per billion years, then they sped along at first, at a rate more on the order of 10 universe diameters per billion years. Seems to me that light and gravity would have been able to relink the entire universe casually before the continuing expansion could dwarf their rate.

 

But I am perplexed. There is talk of an infinite universe, there is talk of the universe never being able to be causually linked. I don't get it. What am I missing?

 

Regards, TAR