# Astronomy & Astrophysics

5
How can we analytically calculate the Hurst exponent for a periodic function?

Let's focus on a sin(x) function. I tried using the DMA (changing sums into integrals) and the series width w(l) from Katsev & L'Hereux, Computers & Geosciences 29 (2003) 1085–1089. In the first case I got stuck with some crazy functions, and in the second (expanding logs in time series to first order as l<<T) I got... H= -1/2. I want to precisely understand why H=1 for strict periodicity.

An R/S analysis compares the properties of the time series over many different time scales. The slope of the curve then approximates the Hurst exponent. If you analyze a series with noise and a sine curve you see a discontinuity in the slope at the period of the sine curve (the Suyal et al. 2009 paper has some examples). In the absence of variations at longer timescales, such as trends, there is no information above that period to derive a slope. For the sunspot number we see a discontinuity at 11 years, just as expected, but there are longer-term signals to continue the R/S analysis at longer periods. That gives an estimate of H for the entire time series. A linear trend indeed has H=1 because the variation over a time bin is comparable to or larger than the noise within that time bin.

7
Does anyone know what is the minimum level for detectability of PeV photons by modern telescopes?

One of the important questions concerning this topic is to know sensitivity of instruments - the minimum detectable flux.

Dear Dr Samvel Ter-Antonyan, thank you for the useful references

ZO

19
How can we compute solar position at a given place on a given day and time?
I have GPS obtained UTC time (hours, minutes, seconds), longitude(deg E), latitude (deg N) and date. I have thoroughly search on internet for step-by-step procedure to obtain solar position variables - solar zenith angle, solar azimuth angle, Sun-Earth distance. But every method is different. Some followed geometrical method while most others have some complicated formulae with varying coefficients. I never found a generalized way to obtain solar position variables. Is there any reference which provides step-by-step procedure to obtain them in the most accurate way? Can anyone provide the step-by-step procedure with equations, corresponding explanation for coefficients, accuracy of output and literature references for each equation? Please don't provide me readily available codes / functions or links on internet search.

Dear Lakshmi

you already have many responses, but if you require open source algorithms for sun tracking with matlab simulink or PLC or microprocessors then you can also check Chapter 3 of our free eBook for links to the code:

https://www.researchgate.net/publication/263085113_Solar_Tracking_High_precision_solar_position_algorithms_programs_software_and_source-code_for_computing_the_solar_vector_solar_coordinates__sun_angles_in_Microprocessor_PLC_Arduino_PIC_and_PC-based_sun_tracking_devices_or_dynamic_sun_following_hardware

regards

Gerro

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##### Book: Solar Tracking: High precision solar position algorithms, programs, software and source-code for computing the solar vector, solar coordinates & sun angles in Microprocessor, PLC, Arduino, PIC and PC-based sun tracking devices or dynamic sun following hardware
[Hide abstract]
eBook 08/2014; eBook., ISBN: ISBN: 978-0-620-61576-1
5
What is the use of dark energy in f(r,t) theory?

Can we get any help of dark energy momentum tensor in f(r,t) theory?

Thank  You So much...for the valuable answers!!

12
Is the Sun a pulsar?
Overwhelming experimental evidence from precise measurements shown in three figures indicate:

_ 1. Neutron repulsion is the source of energy in cores of heavy atoms and stars
_ 2. The Sun made our elements, birthed the solar system and sustains our lives
_ 3. Iron-56 is the most abundant and most stable atom in the Earth and the Sun

The Sun's pulsar core was probably first recognized by PAUL KAZUO KURODA while standing in the ruins of Hiroshima in August 1945:

https://dl.dropboxusercontent.com/u/10640850/The_FORCE.pdf

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##### Dataset: Yes, the Sun is a pulsar
[Hide abstract]
ABSTRACT: Thirty-five years ago, Peter Toth asked here, "Is the Sun a pulsar?" [1]. The unequivocal answer from scientific measurements and observations since the time Hiroshima was destroyed on 6 August 1945: "Yes, the Sun is a pulsar." As Kuroda [2] suspected, standing in the ashes of Hiroshima in August 1945, "The sight before my eyes was just like the end of the world, but I also felt that the beginning of the world may have been just like this." – p. 2 The same nuclear force in cores of U atoms that destroyed Hiroshima, is the force in the core of the Sun that made our elements, birthed the Solar System [3], sustained the origin and evolution of life [4], and endowed mankind with intangible qualities -like creativity, faith, hope and love – and the unalienable right [5] to self-governance to live happy, joyous and free. That nuclear force is the fountain of energy from which chains of cause and effect flow out of cores of galaxies and stars, causing the whole universe to expand as compressed neutrons become interstellar hydrogen atoms [6]. Since ejection [3], the edge of the solar system has moved about 18 billion km (18 Gkm) from the Sun [7]. About ten billion, billion (10 19) Earths could now fit inside the gigantic "sphere of influence" of the Sun's pulsar core. The Sun induces abrupt changes in Earth's radiation belt [8] and "has been a driver of these systems more than we had any right to expect," Dr. Daniel Baker just reported at the AGU meeting on 4 December 2012 [8]. Past policies and technologies that ignored the dominant influence of the nearby pulsar face increasing opposition and fear from the public [9,10].
22
Can we use Kepler's third law to calculate orbital period of a star in a galaxy?

Kepler's third law yields correct orbital periods for the planets of the solar system
however, orbital period of the Sun in the Milky Way is computed with the relation    P = 2*pi*r/v.  Analysis given in the article "Supplement to periodic relativity" shows that we can obtain same result by introducing proper time in the form of deviation factor into Kepler's third law. This deviation to flat Minkowski metric satisfies Einstein's field equations and also provides solution to rotation curves of galaxies.

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##### Article: Supplement to periodic relativity
[Hide abstract]
ABSTRACT: Additional explanation relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The diference between the two is due to the curvature term. Lorentz invariant expression for acceleration is derived. Theory of rotation curves of galaxies based on second solution to Einstein's field equation is presented. Unification of periodic relativity and quantum mechanics results in periodic quantum gravity and cosmology theory.

Following article is now published in "Progress in Physics"
Zaveri V.H., Periodic relativity: deflection of light, acceleration, rotation curves. Progress in Physics, 2015, v.11(1), 43-49.

21
Do dark matter and dark energy constitute valid evidence of large spatial dimensions higher than 3?
There are speculations that the gravitational effects of matter in 4 or greater LARGE spatial dimensions might account for the substantial discrepancy that exists between measured gravitational effects on normal baryonic matter and the amount of that matter that exists according to measurements. Could we be measuring the gravitational effects of "normal" matter in higher dimensions? And can large higher dimensions also explain the huge amount of dark energy that seems to be around?

Thomas, thank you for sending the second chapter of your book. The correlations idea adds another angle from which to look at this issue.

99+
Why are mainstream physicists against the super luminal physics?

Why are mainstream physicist generally against theories, which describe faster than speed motion or communication? Is it proven in experimentally that it cannot happen or is it just a bias based on reputation of the existing theories? There are 2 very good papers about faster than light relativity listed at the bottom. Has someone refuted them on specifics?

The papers are:

http://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light .

http://rspa.royalsocietypublishing.org/content/468/2148/4174.abstract

Hello Nainan,

It is clear that you are a materialist and that you think that you know what matter is--the fundamental substance of the material world, and the material world is the only real world for you. You are welcome to your circular opinion, but please do not think that it is logical, or scientific. There is no scientific reason to think that the substance of matter is matter. Substance is that on which matter stands, and that substance does not have to be material-- it may be energy, it may be consciousness, it may be something non-material. Matter is a concept used to help unify our sense impressions, which are surely mental and not material. And concepts are mental also.

with best wishes,

Richard

4
What kind of camera do I need to do transit photometry?

I am working with a small group of students at Hamline University on observing an exoplanet using transit photometry.

Right now, our group is working on buying equipment. The school already has Celestron C-8 telescopes with motorized mounts available for us to use, but we don't have a camera. We need a camera that we can use to take a long-exposure photograph of a single star, and it needs to be able to measure the brightness of the star very accurately.

Our budget is about $1,000, but the cheaper the better. So far, the only camera under$1,000 I have found that might work is the Atik Titan.  One person I asked about this camera said that the anti-blooming technology might cause problems, and that the chip in the Atik Titan is too small.  This person proposed the ST-402ME as a better model, but it costs \$1,500.

Does anyone know either of these cameras would be sufficient for our project?  Is it worth the extra money to buy the ST-402? Or do you have any other recommendations?

Many thanks in advance for any help!

+ 2 more attachments

I always used SBIG ST cameras. ST7 and ST8. I'm pretty sure you can find them as used with a good price (ST7 for sure). With these cameras I achieved great precision (better than 0.002) with a C9.25 at f/10. You can see in my blog (http://fsalvaggio.blogspot.com translate it and go in exoplanet category) and in some paper I published.

29
Telescope for amateur astronomy.
I am a researcher at a science education project in Palestine and I coordinate for an informal science program. Many of the students I work with are interested in astronomy and space. I would like to purchase a telescope for amateur astronomy so as to maintain their interest and have astronomy-related activities at our center. I have been researching for the best amateur astronomy telescope and I have asked for advice, but I would like to hear your thoughts as experts in astronomy. One of the telescopes I am currently looking at is Celestron's CGEM - 1100 Computerized Telescope, what are your thoughts on this one? I truly appreciate any feedback / advice you may provide.

I would strongly recommend to make it as it will teach your young students a lot of things and make them share a great adventure. The book from Texereau is perfect for that http://www.willbell.com/tm/tm3.htm

Would you like to have a look at the telescopes I built myself got to:

https://www.researchgate.net/publication/267630731__Jas_de_Tardivy__Observatory_in_Caussols_-_Brief_History_and_Some_Deep-Sky_Images?ev=prf_pub

Best,

Patrice.

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##### Article: « Jas de Tardivy » Observatory in Caussols - Brief History and Some Deep-Sky Images
[Hide abstract]
ABSTRACT: This notice describes the installation of two telescopes at the "Jas de Tardivy" Observatory in Caussols, one designed for the observation of planets and double stars under the Mosser Dome (6° 56' 19" E, 43° 44' 58" N, 1185m) and another for deep sky observing under the Cardoen Dome (6° 56' 16" E, 43° 44' 57" N, 1145m). Then we report in annex many images obtained, including numerous deep-sky images.
12
Which experiment can determine if our universe is hologram or not?

Which experiment can determine if our universe is hologram or not?

Is it confirmed yet or still is it an open question?

Regards,

Bhushan Poojary.

@Indranil Banik

Perhaps you find it amusing: "Entropy of Real Pendulum" http://vixra.org/abs/1311.0045

1
What are the fan and spine reconnections in the 3D magnetic reconnection of the solar corona?

How do the fan and spine reconnections take place?

This terminology refers to magnetic reconnection in the vicinity of a three-dimensional magnetic null point (a point in space at which the magnetic field strength is zero). Electric current sheets can form in various configurations around these points in response to different external forces, leading to different types of reconnection. A summary of the properties of these types of reconnection, as well as references to various articles with further details, can be found in the attached review.

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##### Article: Three-dimensional magnetic reconnection regimes: A review
[Hide abstract]
ABSTRACT: The magnetic field in many astrophysical plasmas -- such as the Solar corona and Earth's magnetosphere -- has been shown to have a highly complex, three-dimensional structure. Recent advances in theory and computational simulations have shown that reconnection in these fields also has a three-dimensional nature, in contrast to the widely used two-dimensional (or 2.5-dimensional) models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new models that illustrate the current state of the art, as well as highlighting the complexity of energy release processes mediated by reconnection in complicated three-dimensional magnetic fields.
Advances in Space Research 01/2011; 47(9-47):1508-1522. DOI:10.1016/j.asr.2010.12.022
3
What is the charge of a black hole?
What the charge of a black hole?
Neutral? I hope not.
Anyone know of any articles in this area?

You may know certain properties of Electric charge. But, what is electric charge? See: http://viXra.org/abs/1409.0062

Except for its excessive matter-content, a black hole is like any other macro body. It has no mysterious properties. See: http://vixra.org/abs/1310.0195

Electric charges are related to electric fields rather than to macro bodies, which produce electric fields.

Nainan

8
How can I calculate the Earth's orbit, or what is the equation that enable us know its velocity vs. position at given time?

.

Current planetary laws were derived from relative positions of sun and few planets. Hence, they can be used to predict their relative positions only. True orbital paths of planets are different from elliptical/circular paths described in text books. Please see: http://vixra.org/abs/1311.0018

Nainan

19
Can anyone help me with a question about neutrinos?

I recently read a paper saying that, apart from those coming from stars, supenovae, cosmic rays and nuclear power plants, the majority of all the neutrinos in our universe were created at the big bang. But, considering that neutrinos are very elusive particles, that they travel almost at the speed of light and in straight lines, I think they all should be now near the boundary of the universe.

How come that we can observe them? Is my reasoning above not right?

Cosmologists keep saying the neutrino background has temperature T=1.9K while actually they want to say that their energy corresponds to kT, with k Boltzmann's constant.  This habit comes from the time neutrinos were commonly assumed to be massless.  In that case, like for photons, energy can be assimilated to a temperature because if they would thermalize with a thermometer a temperature T would be measured.

But since neutrinos are massive, nowadays a substantial part of their energy is in their rest mass c^2.  A thermometer only measures the random kinetic energy part.  The  temperature that would be measured  if a huge thermometer would be brought to thermal equilibrium with the the neutrino background would be rather in the 0.001K range (depending on their still uncertain actual mass).

25
Could some of the fundamental constants be functions of the gravitational potential?

Based on several assumptions to deduce a cosmological model with three fundamental constants including the speed of light in vacuum, the Planck constant, and the gravitational constant, along with the dimensionless electroweak coupling constant turned into functions of the gravitational potential. Initial research of this model has indicated solutions to avoid the singularity in both special relativity and general relativity.

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##### Article: Functions of the Gravitational Potential
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ABSTRACT: Based on several assumptions to deduce a cosmological model with three fundamental constants along with the dimensionless electroweak coupling constant turned into functions of the gravitational potential. Initial research of this model has indicated solutions to avoid the singularity in both special relativity and general relativity.

The varying Gravitational Constant needs the Dark Matter to satisfy the General Relativity, in the manner described in my book:

3
Does inflating a Planck-scale wormhole to macroscopic size add internal space and "transit capacity", or do its internal measurements remain tiny?

What does it actually mean when we talk about “inflating” a wormhole? If we find a Planck-scale natural wormhole, and we cram exotic matter into its two mouths to stretch it up to, say, one metre wide, then the wormhole may nominally now be a metre across … but have we actually added any additional useful space to the throat interior, or have we taken a throat that only has a fixed amount of internal space and "stretched" that fixed space, so that although it's now nominally one metre across, the internal measurement (and the wormhole's “capacity” as measured with internal rulers) might still be Planck-scale?

Would inflation be adding more space and more useful “transit capacity” to the wormhole throat, or would we still have the original Planck-scale throat, inhabiting a distorted and stretched region of space in which everything is rescaled and magnified?

Dear Baird, let solve your question  mathematically. The Ellis Wormhole is

ds^2 = -dt^2 + dr^2/(1-m^2/r^2) + r^2 (d\theta^2+sin^2\theta d\phi^2). (1) The rescaled one (factor is n=const) has interval dS = ds/n, thus the metric

dS^2 = (-dt^2 + dr^2/(1-m^2/r^2) + r^2 (d\theta^2+sin^2\theta d\phi^2))/n^2. (2)

Hereby to preserve the shape of the motion of test particles, one has to write m = M n, because coordinate transformation  R= r/n, T=t/n then produces the original form of the metric dS^2 = -dT^2 + dR^2/(1-M^2/R^2) + R^2 (d\theta^2+sin^2\theta d\phi^2). (3) It is the metric in rescaled coordinates. Has it more matter than the original metric? Not, because the radius of the rescaled "throat" is R = M = m/n. Which is less, then original throat. So the making wormhole smaller means the removing of "exotic matter" (that shows the integral of T^t_t).

Therefore, to inflate the Planck wormhole one requires the "exotic matter". Therefore the inflated and not inflated wormholes are not equivalent.

However, the Schwarzschild Wormhole ds^2 = -dt^2 + dr^2/(1-2m/r) + r^2 (d\theta^2+sin^2\theta d\phi^2) has T^t_t = 0. So indeed, the size of the throat is not directly linked to the amount of exotic matter for such wormhole (4) and your theory may hold. However, I have the book (look my profile), which tells, that hypothetical "exotic matter" is not matter.

3
Are jets in AGNs or X-ray binaries leptonic e- - e+, or they can they be also baryonic?

In the literature we find that relativistic e- - e+ jets are not possible. For truly relativistic jests, we need to have e- - p pairs.

7
Has the important astronomical event, supernova 1054 in constellation Taurus, played any role in the discovery of pulsars?
I know that the development of radio astronomy was the most crucial step in the discovery, but still I am convinced that the supernova 1054 may have had some inspiring role in the discovery of pulsars.

I have not worked in the field of Radio Astronomy since leaving Caltech in 1967.

My purpose in joining ResearchGate was to feature my recent researches into the Science of 9/11.  A paper presented at the 2014 IEEE International Conference on Ethics in Science, Engineering etc (May 23-26, 2014, Chicago) is awaiting publication in the IEEE proceedings for this conference. The title of the paper is "Ethics and the Official Reports about the Destruction of the World Trade Center Twin Towers (WTC1 and WTC2) on 9/11: A Case Study" by John D. Wyndham, Wayne H. Coste, and Michael R. Smith.

6
Which of the following is better at plotting 3D graphs, Vectors and Contours, for astrophysical systems, Matlab, Surfer, SuperMongo or Gnuplot?

It would be helpful if the explanations are given for 3 categories:

1. Beginners using GUI

2. Wannabes using both GUI and TUI

3. Experts using TUI

If you go the python way then another excellent library for scientific 3D plotting and visualization is Mayavi from Enthought.

http://code.enthought.com/projects/mayavi/

It can be installed as part of Enthought's Canopy IDE, which is free for academic use.

12
How can you get the temperature of a sunspot?

Hello, im working on a research regarding the correlation of the magnetic flux and different sunspot properties. And so far, there is no archive that has the data I need, is there an archive you could recommend that has the temperature for all sunspots which appeared from 2000-2005? or any equation that can give an approximation of a sunspot's temperature?

To me , the interesting thing is the Energy flux in sunspots, and how it radiates, and

the various energy transport mechanisms into and out of, the Sunspot..

I think the sigma T^4 formula is not bad for just trying to get some idea of a rough

temperature.. As Roger says, of course, there are complexitites involving the complex matter of light flowing into the sunspot, and all the "lines" in the atmosphere inside the spot, so , it is a very complex problem... To me, one can get totally overwhelmed by the complexity of nature, so perhaps some simple flat bottom to the sunspot, and a kind of chromospheric atmosphere above it, in a plane parallel approximation would do

well, to make some kind of associattion of temperature and radiated flux, etc...

There are many interesting variations, i think, in sunspots, as to whether they are growing, or shrinking too. as well as the various complexities as to whether one can view them as a bunch of field lines that inhibit the radiation into the spot, and that is why they are cold (Biermann), or that the convective energy transport and the downflows below the spot cool it, by taking neutral hydrogen from the photosphere to cool the energy transport into the spot... The dynamical approach is one that Gene Parker developed, and the equivalent "ion hurricane" approach one that i and my colleague Hans Mayr used in a simple analogy with our terrestrial atmospheric  situation...

Anyway, they give us various questions to ponder that allow distractions from Earth.

99+
Is there a reasonable alternative to the theory of the expanding universe?
We know that our star, the Sun loses about 10^-14 of its mass per year as a result of electromagnetic radiation and particle emission. That reduction in mass should show up as a decreasing gravitational red shift. Same thing should happen to entire galaxies. But isn't it true that the galaxies we observe that are farther from Earth are also the younger we see (because light has taken millions of years more to come to us) and, as a consequence the more massive when we consider entire galaxies? (Because we cannot possibly see them as they are, but as they were millions of years ago.) Shouldn't we expect, correspondingly that the gravitational red shift of an observed galaxy will increase with its distance to Earth?

Red shift may be not Doppler's red shift at all, but absorbtion im matter, as vacuum is relict radiation (some kind of matter)

46
What is currently the most accurate star catalogue to use for astrometric purposes?
There are many star catalogues available, which star catalogue is currently the most accurate (maybe the USNO CCD Astrograph Catalog, UCAC4)?

In Ducourant et al. 2014 we have looked for the consensual proper motion and was just this that allows us to obtain a convergence in our trace back and so the kinematic age.

69
Why are there no stable states with more than three or less than two quarks?

It is known that hadrons can be divided in baryons (fermions of three quarks) and mesons (bosons of two quarks). The sum of their electric charge is always an integer number, e.g. the proton is one and the neutron is zero. What is the reason that we have not found one particle with, say, five or seven quarks?

Matts,

Thank you very much for your answer and sorry for my delay in responding. The application to cosmology is not obvious at all, but it seems that in the first moments previous to the hadron formation, around 10^(-35) seconds, i.e. in the inflationary age, it seems that the implications of having so massive particles could change the application of theorems as the of Borde-Vilenkin-Guth for singularities. I know that this far of my original question but it could help to understand a little better hypothesis as the dark matter, what do you think about?

3
How are the space and time related to biocentrism?
Robert Lanza’s Biocentrism Theory

Space is as per Descartes/Newton; with time is a bit more complicated- but, believe, not in Your case.

3
How is the tagging of photons from astronomical sources, done?

How are the photons from different astronomical sources, which lie in the same solid angle from an observer, emitting in the same energy (i.e frequency or wavelength) region, tagged as coming from different sources? Does the Doppler shift play a vital role here? Or other techniques come in handy?

If you just have fluxes through bandpass filters, the separation is difficult and model dependent as discussed.  If you can do integrated spectroscopy (often difficult) over the solid angle in question, you an do much better at resolving the individual components of the emission.

4
What is the limiting magnitude for detecting a galaxy in the SDSS image?

See above

It's complicated by the fact that SDSS uses "luptitudes", instead of standard Pogson magnitudes. SDSS Luptitudes are designed to asymptote to fixed magnitude values. This avoids the weird magnitudes that you would otherwise get when you integrate noise.

2
Looking for an advise on nebulae (molecular clouds, globules, protoplanetary disks)?

Our group of geochemists, geologists and chemists is looking for a astrophysicists or astronomer who will be interested to participate in our research. We discovered the correlation between ionization potential of elements and their abundance in planets and other bodies. This correlation could be explained by a simple termochemical equation. Predictions by this equation correlate impressively well with observed chemical composition of surface of planets. We propose a theoretical process which could explain observed facts. Details of our work are described in this document http://arxiv.org/abs/1208.2909
We are looking for a person who could help us (in collaboration way) to improve and connect our theoretical model with observations of nebulae.

It is correct. In our work we tested it on new data from space probes then interpreted the observed correlation as a Boltzmann distribution depending on the distance from the Sun. We tested our model on factual data for Moon, Mars, Venus and Meteorites. We find that predictions force of the model is excellent. Then, we made surface-to-volume analysis for elements. We find periodical trends, related with affinity of elements to hydrogen and with their mass. This suggests that radial differentiation of elements inside the planet was chemically- and gravity-driven. We have far more interesting results, which are out of scope of this paper.

32
Radiation can lose energy by collisions with other particles. Does all radiation tend to end up being infrared radiation?
The loss of energy results in an increase in wavelength for radiation. If the time this progress takes is infinitely long, could all radiation (gamma, x, UV, etc.) finish with a larger wavelength.

Your question depends upon infinitely long. How and when we introduce infinity changes the results of a calculation. The result is a paradox if infinity is not properly introduced. A popular concept of entropy is that the entropy of a system increases. A closed, insulated system has constant entropy. When is it proper to introduce infinity in a closed system? Is the universe a closed system?

Suppose we begin with the most intense gamma ray burst attainable. The gamma rays will lose energy with each interaction with matter or other photons (except for some exceptions noted in other answers). Nevertheless, if this gamma ray burst occurred at the beginning of the universe, at the current age of the universe, we still have a probability that some of the initial gammas have not interacted. Is this a case of improper use of infinity, even if the probability is ridiculously small?

All the photons from the initial burst will have lost energy until some final gasp when that energy is absorbed in some process. We can say that the energy of the photons goes asymptotically to zero. So the answer to your question is that the photons degrade until they quietly absorb. That is the effect of carrying the equations to infinity.

If the universe is a closed system and the entropy does not increase, do we require continuous bursts of intense gamma rays? Will the universe finally degrade to the average with a small distribution in energy? I do not believe there is an equation that will answer these questions, but there is an equation that says a burst of gamma rays will asymptotically degrade to zero.