Accelerated Expansion
What does this mean?

T   
he following is an excerpt from an official government "online brochure" about the SNAP satellite (SuperNova Acceleration Probe - a 1.8-meter reflecting telescope fitted with a billion-pixel CCD camera) ... http://snap.lbl.gov/brochure/redshift.html.



REDSHIFT IN AN ACCELERATING UNIVERSE

Light coming from far beyond Earth must cross space that is expanding. The effect is to stretch the light wave as surely as if it had been drawn on the skin of an expanding balloon; as it travels, its color shifts toward the red end of the spectrum.

The redshift of astronomical objects is measured by comparing characteristic spectral lines of elements in them with spectral lines of the same elements measured in the laboratory. The higher the redshift, the more distant the object that emitted the light.

The farthest redshifted galaxies discussed by Edwin Hubble in 1929 were about 6,000,000 light-years away; the light of such "close" galaxies was emitted recently, and the expansion of the universe since then has been relatively small.

Light from the most distant galaxies has traveled billions of years, giving a snapshot of the universe at a fraction of its present age.
If expansion were now slowing under the influence of gravity, as astronomers expected before 1998, supernovae in distant galaxies should appear brighter and closer than their high redshifts might otherwise suggest.

The distant supernovae found so far tell a different story. At high redshifts, the most distant supernovae are dimmer than they would be if the universe were slowing under the influence of gravity; they must be located farther away than would be expected for a given redshift larger-than-expected distances that can only be explained if the expansion rate of the universe is accelerating.

By my reckoning, the above underlined statement is false.
- EBTX 3:33:50 AM 2/21/01



Now just what do we have here?

Our only knowledge of how far away an object is supposed to be comes from extrapolation involving the Hubble Constant (dimensions = kilometers per second per megaparsec). So if we determine that a redshift is "x", we say ... this redshift corresponds to a velocity of "yada" ... now we divide "yada" that by the Hubble Constant and get a distance in megaparsecs.

Now here they say that the distance derived from the above is "x" ... but ... the type 1a supernovae involved are too dim for that distance. Ergo, they are actually farther away than if the universe were decelerating.

Let's say that the currently accepted value of the Hubble Constant is 55 kilometers per second per megaparsec ...

Then it's value in times past must have been one of the following ...

1) Greater than 55
Now, if it were greater than 55 in times long past, then ... the type 1a supernovae would be farther away than extrapolated from an assumed "constant H" because they were always going faster in the past. But this would mean that the expansion is now ... presently ... "decelerating".

2) Less than 55
Now, if H were less than 55 in times past, type 1a supernovae would be closer than extrapolated from an assumed "constant H" because they were always at a slower H in the past. But this would mean that the expansion of the universe is now ... presently ... "accelerating".

3) Always Equal to 55
If H is truly constant all the way out to the Hubble radius ... and ... one assumed that the universe was "decelerating" ... then one would be expecting the #1 option to hold true. That is, one would expect the type 1a supernovae to be farther away, i.e. dimmer than their redshifts would indicate ... not the other way around.

Thus, if the expansion of the universe is decelerating (as expected) the type 1a supernovae should appear to be too far away. And this is what was found to be the case.

4) It varies with epoch haphazzardly
Nothing has been said about this option.



What am I missing? ... Or ... are they missing something?

Any suggestions, corrections or comments are welcome. I'll put your answer

| ------------- here ------------- |

if it seems like a plausible one.






I looked and looked ... 2-26-1

All over the inernet at dozens of sites and found no answer ... even downloaded a 5 meg Perlmutter pdf file (as well as Acrobat 4.0 to read it with - another 5 megs) ... so ... I was forced to do the unthinkable. I had to figure it out for myself. What a drag! ;o)

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Ohhh ... Noooo

Here is is the poop on the "acceleration".

Assume that the Hubble constant is measured at 100 km/sec/mpc ... and ... you've measured the distances to the nearer galaxies by various techniques. Now ... the expansion decelerates over the course of some millions of years.

You measure the Hubble constant again and find it to be about 50 km/sec/mpc. Here again you have an accurate estimate of H using the nearer galaxies. But when you attempt to apply it to the other far galaxies, they appear to be too close since the lower H has not had time to spread through the entire visible universe, i.e. you only have received the "updated" red shifts for the nearer galaxies while the far galaxies' updated redshifts are still "in transit".

You are still receiving the old redshifted light at 100 k/s/mpc which you are now "interpreting" as redshifted in a 50 k/s/mpc universe. But such an interpretation implies a greater distance because a 50 k/s/mpc universe is much larger than a 100 k/s/mpc.

Why is it larger?

The H=50 is a bigger universe than the H=100 because when you divide 100 into the speed of light to obtain the "size" of the universe (in megaparsecs) , you get a smaller value than with c/50. Elementary division. Larger divisor results in a smaller answer (smaller distance in megaparsecs to the Hubble radius ... the limiting value beyond which nothing can be seen or interacted with).

But the intensity of the light source has not changed ... hence ... it appears to be closer to you by way of your expectation from the new distance calculation.

Conversely, if your initial measurement of H is 50 and subsequent measurement is H=100 ... an accelerating expansion ... you would find the far galaxies to be too far away, i.e. farther than your expectation by way of the newer calculation.






But ... of course ... I'm not finished with this yet.

Whenever you get two conflicting results from seemingly simple reasoning, it is necessary to redo the whole thing over and over till you see which of them is in error. I mean, you must "ramp up" your thinking to meet the contradiction with "authority".

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Ahhh ... Soooo



The Resolution of the Discrepancy ... 3-1-1 to 3-7-1 finish on 3-17-1
My apologies to the reader for "erasing" what was here previously (from 3-1-1) ... I made a mistake (using x instead of 1-x in my own theory) and retracted it as soon as I noticed. I am "embarrassed" :o(
If the expansion of the universe is accelerating, it means that the observable universe will become smaller and smaller with the passage of time ... till at length you wouldn't even be able to see your hand in front of your face since it would be receding from your face at greater than light velocity.

Weird eh?

That's their interpretation of the phenomenon of accelerating expansion. And I agree completely with this analysis (within the confines of the standard model). If this were so and it held up with increasing experimental accuracy ... it would, in fact ... falsify my fundamental principle ... which is that the universe is just the embodiment of an interger count. After all, if the universe is counting, we can't have numbers being subtracted, i.e. protons disappearing from view. This would render the count logically meaningless.

Here's my solution

And I wish I would have seen this before. It would have been an honest prediction ... though it would have made no difference in my lot since I am an amateur and therefore incapable of "proper reasoning" ;o)

In my "Expansion fo the Universe", I give the apparent receding velocity of an object ... based on paralactic displacement (which we couldn't experimentally detect except over vast amounts of time) ... as R / (2R-1) ul/ut

which would be an apparent velocity of "c" at the Hubble radius since this equation approaches 1/2 c asymtotically ... and ... 1/2 c is the limiting apparent velocity of an object receding from the viewer at c (standard model - because of light travel time back to the viewer - then you re- interpet it back to "c"), The velocities of objects at distances less than the Hubble radius would vary linearly with distance, i.e. an object halfway to the H-radius would be reinterpreted as going at 1/2 c and 1/3 H-radius would be 1/3 c ... 3/4 Hr would be 3/4 c, etc.
So, when we view an object we think is at 1/2 the distance to the Hubble radius, we assume that its redshift will obey the Einstein equations for relativistic motion

1 / (1-u2)1/2

As well as the regular Doppler relationship,

(c + u) /c = 1 + u

Where "u" is its interpreted velocity.

In that same section, I give the Compton wavelength of a particle as proportional to

1 / (2 pi R)1/2

Where "R" is the Hubble radius in "unit" lengths.

And ... make the claim (earlier in another section) that the Compton wavelength is directly proportional (in general) to the wavelengths of light given off by an accelerating charge. This must be so because ... what would one use to determine an initial standard of length if not "unit length", i.e. why would the initial wavelengths of radiation hover around, say, 10-18 ul ?? ... it could be anything at all without a "standard".

Therefore, let those wavelengths correspond to the Compton wavelength ... and thus ... to the size of the particle at any given time which is ... in my theory, the afforementioned ... 1 / (2 pi R)1/2 ul ... and ... there is no Doppler or Relativistic ingredient since I am not dealing in relative motion.

These two equations are different

1 + u (Doppler) / (1-u2)1/2 (Relativity) = (Standard Interpretation)
_______________________________________________________
1 / (2 pi R)1/2 (EBTX interpretation)

In this ratio we may substitue the variable "x" for "u" and "1-x" for "2piR" because u is a number between 0 and 1 ... and u (subtracted from 1) is also the variable multiplier for 2piR (necessary to obtain redshift wavelengths for the corresponding distances between us [0] and the H-radius [1] ).

1/3 of the distance to the Hubble radius in the Doppler theory is where my theory gives the radius as 2/3 of its present value, i.e. their "zero" point is right here while mine is at the Hubble radius.
Therefore, we obtain ...

1 + x / (1-x2)1/2 (Standard Model)
_________________________________________
1 / (1-x)1/2 (EBTX)

Which becomes ...

[(1 + x) (1 + x)]1/2 / [(1-x) (1 + x)]1/2
_________________________________________________________
1 / (1-x)1/2 (EBTX)

And then ...

A)       [(1 + x) / (1-x)]1/2 (Standard Model)
_________________________________________________________
B)      1 / (1-x)1/2     (EBTX)


Here :
A)     is a number >1 by which you multiply a wavelength to obtain the new longer redshifted wavelength ... in the Standard Model.

And ...
B)     is the number in my theory used for the same thing.

Thus, if some wavelength in the hydrogen spectrum has a measured length (here on Earth) of ... "Yada" ... then my theory predicts that its measured wavelength from a distant star will be ...

1/(1-x)1/2 times Yada

when the Standard Model makes its prediction of ...

[(1 + x) / (1-x)]1/2 times Yada

But ...

If you define light velocity as c=1 and measure other velocities as fractions of 1 ... you can forget about the Yada and just use that "x" instead.

Thus ... you have a wavelength which you measure to be redshifted by some coefficient >1 and then ask, "What x value do I need to produce this redshift?" . Whatever "x" turns out to be is the velocity of that star as a fraction of the velocity of light (in the Standard Model).

Now ...

Whatever velocity they (the Standard Modelers) find, it's associated with an expected distance from the Earth calculated from that model. So they are now measuring distances using Type 1A super novae as "standard candles" (they believe them to be reasonably consistent). However, the evidence indicates that the observed stars (and the galaxies they are within) are too distant and thus ... accelerated expansion ... contrary to the Standard Model which predicts that the expansion should be slowing down.

Hmmmmm .... what is wrong here?

Let's make a table for Standard Model vs. EBTX Model, evaluating their respective expressions at the same x values.

"x" Value

1/100
1/10
1/4
1/3
1/2
4/7
3/5
5/8
2/3
3/4

Standard

1.01
1.106
1.291
1.414
1.732
1.915
2
2.082
2.236
2.646

EBTX

1.005
1.054
1.155
1.225
1.414
1.528
1.581
1.633
1.732
2

S.M. - EB

.005
.052
.136
.189
.318
.387
.419
.449
.504
.646

S.M. / EB

1.0049
1.048
1.1177
1.154
1.224
1.2532
1.265
1.2749
1.2909
1.323




Another table

In the EBTX model, distance is proportional to 1-x. Where "x" IS a distance as a fraction of the Hubble radius. It's subtractd form one because I use the other end of the universe as the zero point. So, an object at 1/3 the distance to the Hubble radius is 1-1/3 = 2/3 from the Hubble radius.

And ...

"x" is the apparent velocity of an object receding from the viewer as a fraction of the speed of light.

Actually, the apparent velocity of an object receding from the viewer would be 1/2 c at the Hubble radius (as judged by parallax (if that were possible) ... but ... you would interpret it to be exactly c for other reasons. All other velocities vary linearly with distance so that an object at 1/2 the Hubble radius would be interpreted as having a velocity of 1/2 c and so forth.
Now, if you give both distance and apparent recession velocity as identical linear functions of expansion ... it will not compare properly with distance if you are thinking in terms of Doppler-Relativistic effects on the wavelengths emitted from distant galaxies.

Remember, my equation for apparent redshift is not the same as the Standard Model. So if the Standard Modelers try to slap a redshift on a Type 1A supernova ... it won't come out right. It can't come out right IF my model is correct.


EBTX Model
Standard
Velocity

1/100
1/10
1/4
1/3
1/2
4/7
3/5
5/8
2/3
3/4

Distance

1/100
1/10
1/4
1/3
1/2
4/7
3/5
5/8
2/3
3/4

Redshift EB

1.005
1.054
1.155
1.225
1.414
1.528
1.581
1.633
1.732
2

Redshift SM

1.01
1.106
1.291
1.414
1.732
1.915
2
2.082
2.236
2.646


This is the same data but how does one interpret the data if the Standard Model holds a linear decrement in velocity from the Hubble radius all the way back to us?

The only interpretation I can apply here is that they are looking at a star much closer than I would give its distance to be. They are interpreting from theory that it ought to be closer when in fact it is much further away as it would be in my model.

For instance ...

I give the redshift for a star at 1/100 the distance to the Hubble radius as 1.005 while they give it as 1.01. Obviously, in my model, that star would not occur till a much greater distance is obtained.

So ...

Given the universe as it presently exists, it might appear to be justified to extrapolate universal expansion at an accelerated rate ... if ... you are a Standard Modeler.

Though my theory does not yet render a picture directly corresponding to observation, it is sufficiently encouraging in its present state to give me no cause for worry. So let's not make any ...


Snap Decisions

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