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astro_uk
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Post by astro_uk » Thu Dec 07, 2006 10:45 am

Hi Michael
Here's where I'm having a problem with the expansion issue. Assuming that even subatomic particles have "mass", then the mass and gravitational force of the universe would have swallowed up everything the moment things got started without some undefined force to "push" the whole thing outward. A handwave here is going to look mighty suspicious.
I'm not sure it really matters if we have particles or not, as I understand it GR works on mass/energy so there is still gravity before the "fireball" cools enough for particles to form. I may be wrong on this though.
The solution to this point is actually fairly simple, the Universe at the BB starts expanding with a given expansion velocity, we can't really say why because known physics breaks down close to the start of the expansion. Anyway the Universe starts with some expansion velocity, so it can't simply just collapse, the gravity has to first slow the expansion and then reverse it. How quickly (or if it happens at all) depends on if there is enough mass/energy to overcome the expansion. It doesnt require any constant force, just something to start the expansion off.
You misunderstand. The quantum fluctuations present before inflation are very well understood, we know they exist and we know how they behave. You would agree with this?


Absolutely not. In fact I would say that is a complete statement of faith on your part. It assumes there was an inflation stage in the first place.
What I was asking here was if you accept that we understand QM, that we understand the physics of QM fluctuations, regardless of inflation.


I can see your still having issues with inflation, now it does make sense, but at another level it isnt that important, we could just treat everything before inflation as a black box. We could say right if we have a situation where the universe starts out at a certain size and there are inhomogeneities in the mass distribution. These inhomogenieties have a distribution that appears to follow a Gaussian probability distribution. The Universe is expanding at some rate what do we see? Essentially nothing has changed to the theory except we leave the explanation for what causes the inhomogeneities to the realm of "Here be Dragons".

I find that sort of unsatisfactory so lets have another bash at explaining things better.

Imagine the very early Universe before inflation, all there is a black body radiation of unbelievable temperature, because of QM the entire Universe is not perfectly the same temperature, some parts are slightly hotter or colder, because the Universe is so small at this point these fluctuations actually cover a large fraction of the Universe, the distribution of the temperatures follows some Gaussian distribution.

Now image two possible scenarios:

1) The U continues to expand at a constant rate, as it expands the cools, the gaussian fluctuations have time to cancel out on large scales, though new ones are formed in the microscopic realm. So what you end up with after billions of years is a Universe that is perfectly smooth on large scales, because the gaussian fluctuations are confined to their micorscopic world because they do not last very long. The Universe beacuse it is perfectly smooth has a perfectly smooth mass distribution which makes it impossible for structure to form, at least on a reasonable timescale.

2) The Universe suddenly undergoes a rapid expansion, so fast in fact that the gaussian fluctuations that were microscopic get blown up to macroscopic scales. This extra expansion then cuts out. The temperature of course drops and where it is lower less mass forms, and where it is higher more forms, leading naturally to the Gaussian distributions of structure we see. In this way we link known QMs to large scale structure, without which we would have problems explaining why the Universe isnt perfectly smooth.

The point is that if the expansion is not rapid the fluctuations have time to reorder to remain on the microscopic level, making the Universe appear smooth. This breaks no laws of physics as long as you have some way of producing the inflation period, whether that is believable or not is up to you.

That would be fine actually, but that isn't what Guth suggested when he suggested inflaton fields. Guth suggested that the density of these fields was preserved through several exponential increases in volume. No other scalar or vector field in nature behaves that way, though they do behave the way you just suggested.
My understanding of Guths fields is somewhat analagous to the idea of a cosmological constant. That space itself has some repulsive force, so that the density of the field remains the same, but that the expansion obviously acts exponentially, so once the U has doubled in volume there is 4 times the expansion etc. This only applies to the inflation field though, The matter in the Universe behaves normally.

Inflation is an interesting and elegant solution, its problems really stem from the fact that there are so many competing mathematical descriptions of it that it may prove very difficult to see if any actually fit what we can see in the Universe.

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Post by astro_uk » Fri Dec 08, 2006 10:46 am

The obvious problem here however is that even before the first atom formed, the mass of the universe would have sucked the whole thing back together again.
Not if the expansion was rapid enough, remember the expansion we see now is what is left after gravity has worked to slow it down, in the early stages this would have made a big difference. (Plus possible DE speeding it up again later)

People tend to think of this whole topic in terms of GR, this describes space/time as a a set of 3 possible geometries, which depend on the mass/energy of the Universe. You can have closed (universe recollapses), open (universe expands forever) or flat (universe ceases expansion at infinite size). The solution to the point you are making is also found in the inflationary period, check out the wikipedia article at http://en.wikipedia.org/wiki/Big_Bang look at the section on the flatness problem.

First of all, neither of us know for sure that the laws of physics ever broke down, or that the universe was ever a "singularity" in the first place. That is alleged by the theory perhaps, but we can't simply assume any of this.
We know that the laws of physics as we know and apply them broke down. In this case it is GR that is the problem, GR simply doesn't work at high enough energies, because it is not a Quantum theory of gravity, which we know we need but have not been able to come up with yet. When the energies get too high, the forces merge into strange new forces, the electromagnetic first merges with the weak nuclear force, then the strong, and at some point they all merge into one force with gravity. We have theories that explain how the electroweak force behaves and that have been tested in experiment, I think even the combination of electroweak and strong is fairly well understood, but no one has a clue what happens when gravity is included. This whole field and the behaviour of any singularity requires a quantum theory of gravity and to date that is a real problem.

You are ultimately suggesting the expansion of matter, but you have yet to provide a mechanism to explain that expansion of subatomic matter. There are several possible explanations, none of which require inflaton fields.
No I am suggesting an expansion of space, the matter apart from its gravitiational attraction retarding the expansion is essentially irrelevant, it just gets carried along by the expansion of space.

What is that expansion velocity, and what is driving it? How does this force overcome the speed limit of light as it relates to particles with mass?
Nothing is driving an expansion velocity, the Universe is coasting, the idea has a Big bang which starts space expanding with some velocity high enough that all of the mass in the Universe is not enough to recollapse it immediately. This is not that crazy, it implies some equipartition of energy, that the expansion is energetically equal or greater than the gravitational energy. It hints at some connection between gravity and space and particle physics.


Just focus on one main point it is space that is expanding.

As for what started the expansion I personally have absolutely no idea, their are dozens of theories of this like M or brane theory none of which I understand well enough to talk about.

Same problem with inflation, I know what it is meant to do, but the maths of describing how it does that is far beyond my abilities, the human mind is just not designed for working with concepts with 4 dimensional space time and curved space.

Shall I assuming that you're talking about photons here as it relates to the distribution of "heat"? How large is the physical universe at this stage of the process compared to the size of a photon? What wavelengths are we talking about here?
They have energies well above the TeV regime, far beyond anything we will ever be able to probe on Earth.

Are you saying that the photons related to heat are driving the expansion and the heat within the singularity somehow overcomes the forces of gravity?
No, the expansion starts with given velocity in a quick bang and then coasts.


Driven by what exactly? Light? External and internal EM fields? Neutrinos? Gravitons? What is moving exactly, and what is driving the movements of these "particle/fields"?
Beats me, like I said there are dozens of theories to explain this, none of which is probably correct. :)


ome other process must be involved to A) cause the flux in the first place presumably at some small quantum level we can't even study, and then B) turn into a gravity defying "let there be light" phase. Even light would have no hope of escaping such a gravity well according to contemporary singularity theory. What kind of force would defy that much gravity?
Your quite right, inflation must be some sort of physics we have never come across before.

I'm a bit confused by this use of terminology. Could you please define the term "space" as you are using it here and then explain how it might "repulse" some sort of particle in QM or particle physics for me? I don't understand how "empty space" might hope to "repulse" anything. I can see how a "space"" filled with moving waves of energy might "expand", but your use of terms here seems confusing from my perspective.
We are talking about Vacuum energy, the repulsive force of the virtual particles that QM tells us must pop into and out existance so rapidly we cant see them, though we can detect them in some cases, they are also though to be the cause of Hawking radiation should it exist. The basic idea is that these virtual particles provide a "pressure" that causes the expansion to incease. The virtual particles are also formed in equal (ish) numbers per unit volume, so you get a fixed pressure per volume of space leading to an exponential expansion.

Guth was talking about the density of the inflaton field not the density of the material in the Universe. If the inflaton field acts in a fixed proportion to the volume, as in the case above, it is very natural to get an exponential expansion. But the material in the universe decreases in volume, the volume of space increases and the inflaton field has a fixed density, because it is a property space itself.

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Post by harry » Fri Dec 08, 2006 2:09 pm

Hello All

Astro said
How many lecture courses on the physics of stellar evolution have you attended? How many peer reviewed papers on the formation of galaxies have you read or even better written? Astronomy is not a back of the envelope science, it is not something you can just pick up an become an expert. It takes ten years of hard full time 9-5 work to get to the point where you know enough to be able to do anything new.

How many times have you simulated the formation of a galaxy? With full hydrodynamic gas physics included, starting from pure hydrogen and helium and building up to heavier elements? You do not understand the first issue with dealing such things yet you think you know better than those that have spent decades in serious study. Your behaviour is nothing short of insulting to a large group of very dedicated people.

As we have seen previously your understanding of the scientific method is very limited, you cannot just decide that a galaxy takes 50Gyr to form because you like nice round numbers. People that have looked at this have published thousands of papers and spent millions of hours researching galaxy formation and find that you need much less than 10Gyr to form a galaxy.

We have not one, not even one single object that is older than ~14Gyr, looking at many different objects, with many different techniques using known immutable laws of physics. Yet because you don't like that it must be wrong. The Universe was not made to make you feel comfortable it is the way it is whether you like it or not.
Astro you fail to understand the principles, and make comments in thinking you are to win some form of arguement. Stella evolution, from reading your comments, i think your in the stone ages.

Your ideas of the BB are so off track that only time will resovle your issues.

You write well, but your points go nowhere and prove nothing.

I have given my point of view, but! it looks like if someone does not agree with you, its up in arms.

I could be wrong in my opinion, but! I take that opinion from well to do cosmologists.
Harry : Smile and live another day.

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Post by harry » Sat Dec 09, 2006 12:12 pm

Hello All

Many talk of the expansion of the universe.

But! nobody can show it to me. Observations in space show clustering of stars and galaxies.

as for singularity, I did not think it could happen.
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Post by astro_uk » Sat Dec 09, 2006 4:41 pm

Im afraid too much of what you require is beyond my meagre understanding of particle physics, I cannot explain to you what causes the inflaton field or even the DE because no one knows.

With DE we at least have observational constraints that will allows us in the next few years to tie down exactly which set of models is correct if not exactly what flavour. The choices are either a cosmological constant or quintessence models, both of which predict different behavior for the DE over time. There is no reason why the original inflaton field should be the same effect as the DE, they could be different phenomena, revealing themselves when the Universe is at vastly different energy scales.

Inflation is an open question which will likely require some breakthrough in mathematics to make any traction with, such as a quantum theory of gravity.

A pure vacuum cannot expand. Only particles and waves can expand. Are you trying to describe some specific particle or wave?

By using the term "space", you do not seem to be speaking in tangible terms of particles and waves, so I do not understand what you are claiming is "expanding". Furthermore I have no way to apply QM or GR to anything that isn't defined and "tangible" in some way. Only physical things can "expand". What is the physical particle or field in QM or GR or particle physics that you believe is expanding when you say "space" is expanding?

I think this is the fundamental misunderstanding you have. You seem to picture the big bang as an actual explosion with all the energy and gas expanding into empty space. This is absolutely not the case. "Space" or more correctly space/time is a real entity, in the simplest manifestation it is 3 spatial dimensions and one of time, before the big bang there was nothing, no space, no time. Outside the Universe there is according to the laws of physics as we understand them absolutely nothing, again, no space, no time. GR depends entirely on the existence of space as a 4 dimensional continuum, as a medium (almost) which is capable of interacting with matter through gravity.

If you leave out VPs it is entirely possible to have an expanding space/time (i.e. Universe) which has absolutely zero mass contained within it. You seem to confuse particles and photons with space, they can affect space/time as is seen clearly by gravity which in GR is simply the curvature of space/time caused by mass, but they are not space.

The Universe is simpy the 4 dimensional space/time and everything contained within that volume, though of course this terminology is misleading because it implies there are regions outside of space time, which there are not.

Now I am very poor at explaining such concepts which to be frank the human brain was not designed to deal with, but there are many good general level books describing GR and the BB in terms of the actual behaviour of space/time.

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Post by astro_uk » Sat Dec 09, 2006 4:52 pm

I have 5 minutes to spare so I'll waste it replying to Harrys comments.

Harry what exactly do you expect so see? Do you think that because space is expanding you should be able to look through a telescope and see it happen as you watch? These things are incredibly far apart, you would have to wait 100Myr before you noticed any change in their positions. And you will never see stars moving apart because of the expansion, as i have explained on numerous occasions gravtiationally bound things dont expand, so planets, stars, galaxies and clusters of galaxies will remain the same size, its only the distance between the clusters of galaxies that will increase.

But if you look to higher redshift (i.e earlier in cosmic history) you do see the effect of the expansion, the distribution of galaxies is smoother, because they havent had time to fall into clusters yet, and the clusters themselves are closer together, because the Universe hasnt expanded as much. End, of, story.

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Post by harry » Sun Dec 10, 2006 2:49 am

Hello All

Its not a question of waiting, its an observation of what is out there.
What is out there is completely different to what many want it to be.

Thank you for you 5 minute waste.
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Post by cosmo_uk » Sun Dec 10, 2006 2:37 pm

Re: inflation

a few posts ago michael and astro were discussing inflation. I was at the RAS on friday and heard an excellent talk on testing inflation. By assuming the only variations in the tiny pre inflation universe are purely quantum (very reasonable at these size scales). we would expect the universe then to look like a 3d gaussian random field (again very resonable). As the universe we see today should have the underlying signature of this gaussian random field still embedded in it we apply a topological analysis to see if it is a grf. The initial results when applied to 2df north and south show that there is extremely good agreement between the topology of the pre inflation universe and the local universe. it was very impressive

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Post by harry » Mon Dec 11, 2006 6:27 am

Hello Cosmo

Do not take this the wrong way.
I take everything with a bit of salt.

Expalin to me what you think inflation is.

Local or total.
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Post by cosmo_uk » Mon Dec 11, 2006 10:24 am

Don't worry harry I wasn't expecting you to be converted from the flat earth society.

Of course I and the speaker at the RAS were referring to conventional inflation, ie the whole universe rapidly increases in size in a very small amount of time.

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Post by harry » Tue Dec 12, 2006 9:32 am

Hello Cosmo

Smile,,,,,,thanks

Inflation of the total universe uses too many ad hoc assumptions.

I cannot see it as reality.

But! you never know if you never ever go.

I was hoping by a year or so we may have enough obsevations to put us on the right track.
Harry : Smile and live another day.

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Post by harry » Wed Dec 13, 2006 10:43 am

Hello All

Hello Micheal

Its always a pleasure reading your response.

So how do you go and prove the expansion of the so called universe?.
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Post by astro_uk » Wed Dec 13, 2006 11:29 am

So essentially you personally have "faith" that inflaton fields are somehow related to the quantum field of gravity? Is the only evidence to support this idea based on the acceleration we see in the universe itself? How did you personally rule out more "mundane" explanations like EM fields as the cause of this acceleration?
No you really dont seem to be listening, Inflation is a theory, a theory that explains some observations of the behaviour of the early Universe. I do not know if it the correct description, I don't know what the cause of inflation is if it exists, to be honest I really dont care. It all happens in a realm beyond anything that really affects the BBT, as long as you have the initial gaussian fluctuations in the matter distribution at the time of recombination it doesnt matter to the theory what caused them. We still have an expanding Universe that cools as it goes, whether the initial distribution is due to inflation or some wierd physics that only manifests itself at energy scales we cant probe is a matter for the particle theorists.

I can rule out more mundane explanations in two words Lab experiments. We know how EM works, we know how it works in the most precise detail and it cannot act in the way required, or so the particle theorists tell me.



Unless there is some *thing* to work with, you're going to have a hard time explaining what is "expanding" exactly. This explanation of "space" sounds more metaphysical than something we can apply "physics" to. What are we using as a reference point to measure expansion of "space" as you define it?
You seem to have read a great deal about QM but essentially nothing about GR or the big bang, ill try to give a brief summary but it really would be better if you read something more specific.

You want me to define space/time. Well its pretty simple space/time is the Universe. The Universe by definition is everything there is, in physics and GR in particular the Universe is defined as the region contained in the space/time. You seem to be fixated on the idea of the Universe expanding into "empty space" let me reiterate, there is no empty space outside the Universe, the Universe is all there is, there is absolutely nothing outside, not even space or time. You cannot find an edge to the Universe because of the curved 4 dimensional geometry in a closed universe you simply continue till you arrive back where you started but from the other direction. As I have stated in GR and hence the real world, space/time is a real entity, imagine a grid of lines in three dimensions, just ignoring the time dimension for now, and expanding Universe simply has the distance between the lines increasing. Space/time can expand or contract as is seen by the effect of mass on it which warps space time to form curved paths which we interpret as gravity.

This is not a metaphysical point, this is a fundamental property of nature, you will continue to have problems grasping BBT if you do not understand what the Universe actually is. The problem is that our brains simply cant picture these things we have to rely on the maths to guide us.

Space itself is a real entity, otherwise gravity would not exist, it is perfectly acceptable in GR to have expanding space/time. All of the waves and particles that make up the things we see in the Universe are essentially carried along in this expansion, forever trapped within the 4 dimensions of the Universe.

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Post by harry » Fri Dec 15, 2006 10:23 am

Hello Michael

In your above post, are you saying that the universe is expanding?
No, not really. Space/time involves mass. Mass cannot move faster than light according to Einstein, though "space/time" could theoretically "spread out" as the mass of the universe physically spreads out. You however described the expansion of "space". I'm curious what you're suggesting is expanding here, since you are not describing a particle of mass and space/time can only expand and apply to something with mass in GR.
I'm not uncomfortable with the notion that space/time "expands" as the mass of the universe expands. In fact I'm quite comfortable with the idea. This idea however requires the presence of mass, and the expansion of particles of mass. Furthermore, all particles of mass, especially the big particles of mass, have an upper speed limit according to Einstein.
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Post by astro_uk » Sat Dec 16, 2006 4:21 pm

Hi Michael

I want to focus on one point from your previous post if I may because its a very important point.
No, not really. Space/time involves mass. Mass cannot move faster than light according to Einstein, though "space/time" could theoretically "spread out" as the mass of the universe physically spreads out. You however described the expansion of "space". I'm curious what you're suggesting is expanding here, since you are not describing a particle of mass and space/time can only expand and apply to something with mass in GR.
I'm not uncomfortable with the notion that space/time "expands" as the mass of the universe expands. In fact I'm quite comfortable with the idea. This idea however requires the presence of mass, and the expansion of particles of mass. Furthermore, all particles of mass, especially the big particles of mass, have an upper speed limit according to Einstein.

From my persepective however, you are not talking about an expansion of particles of mass with a speed limit of light speed. You somehow seem to be describing the expansion of "space" without "matter" in some way that allows for particles of mass to have traveled faster than C. That's not how it works in GR. GR requires mass, and all particles of mass have a maximum speed limit of C.
There are several points here but the most important is that nothing is observed to travel faster than the speed of light. Even distant galaxies with a redshift of 1 or above are not travelling above c.

Now why is this the case?

Because you have been treating redshift as a Doppler phenomenon and using the simple Doppler equation z = v/c. But redshift is not a doppler phenomena it is due to to the expansion of space which is a GR phenomenon.

When GR is used to derive the redhshift equation you get z = (1+v/c)*Gamma - 1

Where Gamma is the Lorentz factor and is equal to c / SQRT(c^2 - v^2)

When this is taken into account you can see that it is possible to get huge redshifts but still to be travelling less than c. Its also possible to get redshifts introduced by transverse motions, those not along the line of sight, something that is flatly impossible in a Doppler interpretation, something that had never really occured to me before.

Of course this is not the full story. I came across an interesting link at http://www.astronomycafe.net/cosm/expan.html its from sky and telescope and does a good job of explaining why we have real troubles when we try to understand GR and its implications.

Check out the link and hopefully it will answer some of your other points.

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Post by BMAONE23 » Sat Dec 16, 2006 4:55 pm

Wouldn't it be probable to get a red shift factor indicating a speed of >c if two objects were traveling at .51c in opposite directions? Their total combined speed of separation should be 1.02c away from a relative centralized point.

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Post by Nereid » Sat Dec 16, 2006 5:03 pm

BMAONE23 wrote:Wouldn't it be probable to get a red shift factor indicating a speed of >c if two objects were traveling at .51c in opposite directions? Their total combined speed of separation should be 1.02c away from a relative centralized point.
In a word, no.

Why? Gamma ... your post assumes that the rule for calculating speeds (in this case and others) is the same as that which you use in your everyday life: speed between A and C = speed between A and B + speed between B and C.

In SR (special relativity), speeds don't add like that, there is a formula involving square roots (it works for everyday speeds too, but the difference between the above and the SR formula is unmeasurable).

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Post by harry » Sat Dec 16, 2006 11:49 pm

Hello All

Thanks Micheal,,,,,,,,,,

If I was to consider expansion it would only be parts of the universe and not the total universe.

We know that matter clusters and collects in MECO,,,,,,,,,,ultra dense plasma matter,,,,,,,,,,,,blackholes. We also know that these objects expell huge amounts of matter as part of a recycling process.

The size of the UDPM can be from a neutron star to a so called black hole billions and billions the size of our star.

This is the type of contraction and expansion I can understand.

As for the BB well, I cannot accept the idea with ad hoc add ons.

When people talk about the expanding universe. It does not add up.

Infinity cannot expand within itself.

The parts within can do what ever they want, expand contract, transform and so on. These are the areas that need to be looked at.
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How far we travel in a lifetime, yet at a snails pace.

Post by kovil » Sun Dec 17, 2006 5:20 am

BMA123,

Even at .91% of light speed < and > at .91% of light speed
the recessional velocity between the two objects, as seen from either one,
will be the speed of light. Thus Spaketh Einstein.

This of course makes no sense in light of our genetic programing which makes us think Newtonian. (seeing that much Truth is not necessary for survival ! , at least on that level, as we are planet-side dwellers not intra-galactic dwellers, nor inter-galactic dwellers.)

To jump the programing; think of it this way, and see if it helps.

The 'speed of light' is not a speed at all,
it is the 'Ratio of Space to Time'.

Space and Time can not diverge from each other faster than the "speed of light" or 300,000 km /sec, thusly nothing ""appears"" to go faster than that.
It is built into the system.
Light is not something moving by a force of some kind,
through the space-time continuum.

It is the inherent design of the space-time continuum itself.
The speed of light is it's Ratio of Construction.

This is a radical way to look at it, and I was only able to hold the concept for a few seconds, before slipping back into my previous viewpoint.
Repeated grasps, and it held for longer and longer viewing times.
Now I can see it this way extendedly.

So when one spaceship is looking at the other spaceship receding at a Newtonian speed of 1.81 X speed of light; all they can receive in information coming from the other ship, is at light speed, and it is greatly redshifted; but because the Ratio of Space to Time cannot be exceeded, information conveyed by light arrives at light speed to either party, regardless of the Newtonian recessional velocity, (or converging velocity in the opposite case). (this may have something to do with how the time dilation effects of Special Relativity are calculated, I'm not sure, I'm much less versed in that.)

Is this any help?

If an object is moving away from us faster than light speed, we would get no information back from it to us, in any form of light or EM spectrum that travels at light speed. The information contained in the light would not reach us. It would cease to exist to us, for all intents and purposes.

Anything beyond that recessional velocity limit of distance is beyond our 'observable universe'. Would not exist to us as we would have zero information about it. We are living in a hole in a swiss cheese. That bubble is our 'awareable universe'. The swiss cheese is the 'real universe' , but we can only be aware of our hole in it, all else is beyond our 'physical awareness'.

Now when religion gets into the scuffle, faith and consciousness come into play and claim to have awareness beyond our physical awareness, but that's an entire 'nother song, as Rambling Jack Elliot would say !


Harry; Here's a wrinkle for you to look at !

As the quality of Inertia/Momentum is how Time shows up in this Universe,
and the Ratio of Space to Time is what determines the 'Speed of Light',
that is why objects get more massive the faster they go, and excessively so at 99.9% of light speed and faster. This is the mechanism of enforcing that the Ratio of Space to Time cannot be exceeded. And it is thusly because Time is contained within Inertia/Momentum.
Time cannot move faster thru Space, than the Ratio allows. Momentum/Inertia is what enforces the Ratio.
As physical matter has momentum/inertia, it is carrying Time as it moves.
And that is why the Ratio of Space to Time is 'invoked'.

If it was Inertialess/Momentumless it would not have to obey the Ratio of Space to Time.
There is some debate about if Gravitons are in this class of event.
Time will tell. (teehee)

I'll be thinking of you at the summer cricket matches having afternoon tea and contemplating the Universe and Ratios. Taa, Kovil

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Post by BMAONE23 » Sun Dec 17, 2006 6:54 am

nereid and kovil,
thanks for the food for thought. I'm gonna go take some asprin now and have a lie down. I'm probably bound for some interesting dreams tonight as most new ideas/concepts tend to bring about for me. I'll need to crunch the information for a little while.

Thanks Again

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