` The 'P' Hubble formula
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Comparing cosmic distances calculated by the 'P' Hubble distance formula, with standard Hubble distances calculated on the second page

Consider: The 'P' Hubble distance formula and its calculations are based upon a non-mainstream distance formula that does not require a Hubble constant value. Although both this non-mainstream distance formula and the standard-model Hubble distance formulas calculate distances based upon galactic redshift input values, the calculated results for the 'P' Hubble formula is a little greater than the mainstream Hubble distance formula at low redshift values, but results in much greater distances at higher redshift values. The reason is that the this alternative formula is not based upon an expanding universe cosmology. Instead its calculations were derived from an alternative cosmology called the Pan Theory of Cosmolgy (PTC) requiring its own distance and brightness formulas resulting in somewhat different calculated distances and brightnesses than the Hubble distance and standard brightness formulas. The point is that these alternative calculations, if valid, assertedly explain away dark energy as the result of womewhat wrong distance calculations and interpretations based upon a wrong cosmology, the Big Bang.

The mainstream Hubble distance formula (shown on the second page) was assserted to be derived from the theory of Special Relativity. And mainstream luminosity is based upon what is called the brightness "magnitude scale," which is a unique scale derived by astronomers long ago. Both formulas change the calculations of brightness magnitudes at distances according to the inverse square law of light, but the 'P' Hubble brightness formula has an additional brightness factor that increases intrinsic brightnesses with distances. The 'P' Hubble formula is based upon PTC premises, the link you are now in, and was refined and tested against hundreds of type 1a supernova observation data from 2010 to 2013, showing these supernovae to be true standard candles, with no expansion of the universe or excelerated expansion, contrary to the need for dark energy to explain anything. The original study was performed almost two decades after the original studies declaring the existence of dark energy, but also when there was more than 3 times as many type 1a supernovae known and cateloged for our evaluation.

See these studies and links for explanations:

https://pdfs.semanticscholar.org/18af/86eb09dbf86df826906392e2eb4c9f876d8d.pdf

https://www.researchgate.net/publication/370212804_Replacing_the_Lambda_Cold_Dark_Matter_model

According to the PTC (accronym defined above), the cause of the observed cosmic redshifts would instead be the diminution of matter rather than the expansion of space, a very similar perspective but certainly not the same thing in regards to the related equations and calculations. It can be considered a type of scale-changing theory and steady-state cosmology; the universe would not be expanding, instead matter would be very slowly getting smaller, about 1/000th part every 11 million years. This very small change means relatively larger matter, space, atomic particles and quantum energies etc. in the past. All would have the same appearance to us as an expanding universe, when in fact it's not the same thing. At the same time, new matter would be very slowly created from the decrement, maintaining a generally constant comparative relationship of the so-called constants of nature, as well as the constant density of matter and energy in the universe.

The 'P' Hubble distance formula, like the Hubble distance formula, generally proposes that the distance to a given galaxy is proportional to the redshift of its electro-magnetic spectra. The redshift of these spectral lines is commonly expressed in terms of a "z" parameter, called its redshift, which is the measured change in the collective wavelengths of the standard element's emision lines observed at the specified distances.

One should note that the data being calculated is based upon the users data input of the average calculated redshift value. For calculations of the Hubble distance formula, shown on the second page, a Hubble constant value can be input; if not a value of 71 will be used and displayed instead.

Some of the calculations involve comparisons between the Hubble formula calculations (the Hubble Law) and the 'P' Hubble formula based upon the PTC. As you will see, the 'P' Hubble formulas distance and magnitude calculations, will always be slightly greater than the Hubble distance and brightness calculations based upon the PTC assertion that matter was relatively larger in the past -- although in its own timeframe everthing would have looked and measured the same as it does to us now, based upon larger measuring sticks in the past.

The 'P' Hubble distance formula equation is seen below (where Po is a constant = 1,958.3, similar to the Hubble constant in that it is based upon a constant rate that matter is slowly getting smaller. The "z" parameter is the redshift input value.

Click on the redshifted wavelength value that you have input after entering it, to calculate the entire first page.

To recalculate, push this reset button to prevent possible errors.

21.2946 log10[ 0.5((z+1)0.5-1)+1](z+1)0.5 P0] /(.5z+1)

When a spectral line is normally nm long, is redshifted to nm long,  then z = .

Enter the desired Hubble constant value in the following input box directly below, for the Hubble distance calculations on the second page. If you enter no Hubble constant value in this box then a value of 71 will be used for the Hubble distance calculations. The value 71 was chosen because only this value results in the universe's asserted age of 13.78 billion years which is often stated in Big Bang coamology.   .


The calculated square root of the increased wavelength (z+1) is = . This square root value is often used for many different astronomical calculations.

The meaning of the word "time," and its calculation shown here, relates to the number of "doubling cycles," wording which is unique to the Pan Theory. Each number over one is asserted to ba a multiple of the relative increase in the size of matter, measurement of space, and the relative length of a second looking backward in time, which increases at a rate indicated by this factor. This number is calculated to be =

The Brightness Enhancement factor is calculated by the Pan Theory brightness magnitude scale below which is based upon the diminution of matter going forward in time, resulting to larger matter in the past, producing brighter galaxies than their distances would otherwise indicate based solely upon the inverse square law of light.

Lu = Log2.512(z+1)

The calculation result is  The brightness magnitude is a relative scale based upon the redshifted wavelength input when using the above formula and its premise that matter very slowly gets smaller as time progresses which explains the source of cosmic redshifts according to the PTC, rather than the expansion of space. Brightness magnitudes less than what would be expected are expressed as positive numbers, and brighter magnitudes and shown as negative numberes for brightness greater than expected. Each point greater than the next lower whole number is 2.512 time brighter defined by mainsteam astronomy.
x x x x x x x x x x
The 'P' Hubble distance =  Mpc = Mly

Mpc = megaparsecs
Mly = million light years


Pan Theory
Distance calculations

with a required

Brightness addendum factor



Comparing Hubble calculated distances and brightnesses with Pan Theory calculations of distances and brightnesses:

    To Calculate this page press here   when you have entered data on the first page.

The standard Hubble distance formula, shown below, like the 'P' Hubble distance formula on the previous page, states that the distance to a redshifted cosmic entity is proportional to the measured increase in its redshifted wavelengths as observed from the spectra of its light. The red-shifted increase in wavelengths is given by the "z" factor. Although the principle is the same, calculations are somewhat different. 'z' is the redshift value, 'c' is the speed of light, and 'H 0' is the Hubble constant input value or 71, if no Hubble constant input value is entered.

[((z+1)2-1) / ((z+1)2+1)] c / H0

A spectral line which is normally measured to be nm long is redshifted to nm. The redshift z =   Wavelengths were input on the previous page. The Hubble constant input value entered above = .

The Hubble distance(km/s/Mpc) = Mpc Mly

The ratio of the calculated 'P' Hubble distance to the Hubble calculated distance is always positive since the 'P' Hubble distance is always at least a little bit greater. This ratio is equal to:

Determining the actual diameter of the galaxy being observed and its real relative brightness is based upon the differences in distances and brightnesses between the two formulas. This is simply a function of the inverse square law of light and the observation angle, since its increased size and apparent brightness is based upon the PTC proposed increases size in the past. So the actual diameter and relative brightness of the galaxy being observed is greater by this factor:

 

With redshifts starting at a little greater than one, galaxies will appear to be brighter than the Hubble distance formula would indicate, simply because matter in the past was relatively larger. The most informative aspect of these alternative equations can be seen in the following calculations. Our conclusions were based upon a three year long research study of type 1a supernova observations which resulted in our derivation of these newly derived equations and calculations used here on this website, showing strong evidence for the non-existence of dark energy, since there is no difference between the expected magnitude and the observed magnitude based upon these alternative formulas.

From these "standard-candle" calculations we are now able to do the same calculations for galaxies as we did concerning type 1a supernovae. In astronomy one solar mass represents the mass of the sun; this enables the judgment concerning the mass of other stars in comparison to our sun. So we have done the same thing for the Milky Way galaxy, for it to represent one galactic mass concerning galaxies as a standard. We will call this kind of galaxy the "MW standard" galaxy. It can also be used as a standard for a galactic sizes and brightness. For spiral galaxies, to be able to judge the angular size (diameter) and luminosity for a galaxy exactly the same as the Milky Way, would also be a good standard size calculation feature.

For instance, for a galaxy just like the Milky Way in every way at the so-called edge of the observable universe (once they are able to come to the conclusion that there are many of them), at a redshift of z = 16, its calculated distance based upon the 'P' Hubble formula would be about twice the distance calculated by the Hubble formula. This would make its apparent galactic size about 1/4th the diameter of what would be expected for the Milky Way at that redshift, because of greter distances in the past. Although of their smaller appearance, these most distant galaxies will appear to be denser and brighter than they should for a standard galaxy of today. The problem is simply that the correct distance and brightness equations are not being used by mainstream astronomers. Mainstream Hubble distance equations is likely the only redshift-distance equations they know of.

On the graph that follows, you will see what to expect from a "Milky-Way-standard-galaxy" concerning its brightness magnitude vs. its distance. These are comparitive brightness calsulations based upon the differnces between the two distance formulas. The blue line on the graph below, the curved line, represents what you will observe using the Hubble distance formula and brightnesses, and the red line shows the zero comparitive brightnesses one sees when using the 'P' Hubble distance formula and brightness. What you will see with the 'P' Hubble formula, is that distances are directly proportional to their redshifts, no matter how close or distant.

For example, on the first page put in the redshift you are interested in concerning observations, and you will realize what to expect of the most distant observable galaxies, concerning their "unexpected" over-brightnesses and generally smaller sizes (angular diameters) based upon calculations of the Hubble distance formula.


Luminosity Comparison, graph seen below:                 
                              

When using the Hubble distance formula, a galaxy brighter than the Milky Way would be more negative than the luminosity value indicated, and a galaxy less luminous would be more positive than the value indicated.

The 'P' Hubble formulas are based upon matter in the past having been relatively larger. From our perspective, larger cosmic entities in the past would appear brighter which can be seen by the Brightness Enhancement factor calculated on the first page.

A decreased brightness factor, as a result of increased Pan Theory distances, results in a dimmer luminosity, a plus factor, and a brighter magnitude, a negative factor. lumens.

The standard formula for this calculation is based upon the inverse square law of light. The combined total of the two factors, the first is of increased brightnesses due to larger atoms in the past, and the second factor decreases brightnesses due to increased distances. The overall decrease in brightness at a redshift of about z = .5 was the basis for the dark energy proposal concerning type 1a supernova. At distances above z = 1, brightness magnitudes are always negative because the larger size of matter outscales greater distances according to the 'P' Hubble formula and brightness formulas.

The inverse of this factor is often used by astronomers to represent angular size of matter (its diameter). If distances in reality are greater than what you calculate, then the angular size will always be smaller than it would have been, therefore less than 1. Based upon the input variables the angular size is:

Calculations in the box below are a more-certain evidence concerning the validity of the 'P' Hubble distance formula and the PTC. The equation is based upon just one changing size factor, a positive factor looking backwards in time. It is a negative factor going forward in time because accordingly matter would be very slowly getting smaller, an alternative to space expanding. From a strictly relative perspective this could be considered the same as space expanding. But instead accordingly, matter actually is getting smaller -- about 1,000th part every 11 million years. As one inputs the redshift values, they should be able to see how close the calculated results are to the red and blue lines on the graph shown below. Only the blue line is calculated since it is based upon the Hubble distance and mainsteam brightness formula. The red line, according to the PTC, should only be a relatively straight line of brightnesses based upon type 1a supernovae being standard candles. The graph shown below was drawn about 10 years ago concerning our study of type 1a supernovae, and is still valid in terms of many times more type 1a supernovae now available for evaluation.

The predictions of these calculations at high redshifts should be observable by the James Webb, or course interpretations will likely be wrong if interpretations are based upon mainstream cosmology, which we believe nearly all will be.

if valid the big question becomes: what is more likely, that the Hubble distance formula is off by about 10% at a redshift of about z=.5, or that the entire universe is accelerating in its expansion and that 2/3rds of the universe is made up of a type of unknown energy called dark energy? We believe the later answer is far more probable. If the Hubble formula is off by at least 10% at a redshift of z=.5, then the whole dark energy proposal would be wrong and the wrong alternative was chosen. These calculations, like the Luminosity comparison calculations above, are directly in accord with the Pan Theory of Cosmology, while being totally contrary to mainstream cosmology.

It should be noted that the original comparisons concerning the granting of the Nobel Prize for the discovery of Dark Energy related to type 1a supernovae calculated distances based upon the Hubble distance formula, compared to the inverse square law of light. In these calculations we can now compare the Hubble distance formula with the 'P' Hubble distance formula. In both cases the Hubble distance formula is off by a factor of at least 10% compared to the alternative 'P' Hubble calculation. Mainstream theorists proclaimed the existence of dark energy because they had no other alternative to consider. For us this difference simply requires a "slightly different" distance formula, The 'P' Hubble distance formula, and the universe does not have to change at all, asserting no dark energy (also no dark matter, expanding universe, or Inflation) is needed. And calculaions at great distances closely match James Webb observations, where the mainstream Hubble formula calculates distances as half of what they are concerning the 'P' Hubble formula at a redshift of 16, wrongly implying that galaxies then were much smaller, denser and brighter, none of which are true based upon the PTC. Accordingly then, everything was the same as we can observe it in our present galactic neighborhood.

Observed brightnesses and angular sizes of galaxies and other cosmic entities are also calculated and predicted by the PTC, with different results, which are believed to be evidence for the conclusions of our extensive study of type 1a supernova, link below.

http://www.ccsenet.org/journal/index.php/apr/article/view/32603/19463

Explaining well-known theoretical and observational problems with the Big Bang model, while for the same reasons and observations support the PTC, is explained in another published research paper, link below.

http://www.aijcrnet.com/journals/Vol_4_No_9_September_2014/2.pdf


This graph is based upon the Luminosity Comparison calculation shown above. Its basis came from our supernovae study completed in 2013. Type 1a supernovae are standard candles, link shown below. The chart above also applies to galaxies where the Milky-Way-galaxy brightnesses ("MW standard") can be considered a standard concerning galactic brightnesses for now. Later on studies my suggest using another galaxy as a standard for brightnesses at a distance

https://pdfs.semanticscholar.org/18af/86eb09dbf86df826906392e2eb4c9f876d8d.pdf

The horizontal scale on the bottom represents "redshifts" "z" which equal the proportional wavelength increase of these "MW standard" galaxies, and the entire observed wavelength is equal to (z + 1). The vertical scale on the left-hand side represents ΔDM, the change in luminosity of the standard galaxies you are observing based upon changes in their redshift input values.

The blue line is what you should expect to see concerning "MW standard-galaxy-brightnesses" (MW), when using the Hubble distance formula, and the red line is what you should expect to see of brightness of a MW standard-galaxy when using the 'P" Hubble formula, neutral relative brightnesses neither positive nor negative. We have no calculation for this since when using the 'P' Hubble equation to calculate distances, any non-nuetral luminosity would mean a galaxy that is either more, or less luminous than the Milky Way. This would only be interesting for astronomers who are looking at such entities. And if so they should contact us at the email listed below and we would expect that ASAP we could include such a calculation based upon their need. Also, all those who have comments about this site or calculations should also please contact us about typos, context, questions, etc. at the email address below. We will apprediate every comment, some of which might help us provide a better understanding of the information that we are trying to convey.

Again, I think we should illiterate that if one is instead using the 'P' Hubble formulas to calculate cosmic distances and brightnesses, then the brightness line should be almost completely straight when viewing MW-like galaxies, like the red line and dots in the diagram above.

pantheory.org@gmail.com
Comparison of Pan Theory calcualtions

to Hubble Distance and Brightness calculations

 
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