Mordred

I cant recall which paper it was but all complex shapes have been discounted. If I recall the paper uses the Planck 2012 dataset. The three viable shapes being flat,negative and positive. Any shapes more complex than that were afiak discounted. As far as negative curvature goes only one position on the saddle can maintain a homogeneous and isotropic universe. That being the seat.

Whatever visual aid your developing to help visualize a homogeneous and isotropic expansion. Two key aspects are critical. 1) expansion rate is the same regardless of point of reference 2) the angles do not charge between measurement points

It would certainly give new meaning to "married for life" lol.

Thats why I mentioned the calculator in my signature. Saves time particularly if you correlate redshift to proper distance. Ps it also generates graphs. Unfortunately one of the contributors Marcus passed away

The formulas involved has several steps as Hubbles constant is only constant at all locations at a given time. The lightcone calculator in my signature will greatly simplify the steps for you. The calculator uses proper distance rather than commoving distance. The advanced users section details the formulas the calculator uses and includes the Lineweaver and Davies article to explain those formulas. http://cosmocalc.wikidot.com/advanced-user This page will give your commoving distance formula however again requires several steps https://en.m.wikipedia.org/wiki/Comoving_distance To understand the t_e and t terms in the formula this page will help https://en.m.wikipedia.org/wiki/Hubble%27s_law However this is all covered in the lineweaver and Davies article in better detail

The curvature is the the measure of influence due to mass. It doesn't act upon space itself as that's just a geometric volume. The influence acts upon the standard model particles that reside in space. A common and practical way to express or model this curvature is to assume a field of test particles residing in every point in space. The strength of influence upon those test particles has a curved relation the further you get from a source of mass. Mathematically we express this as a curved geometry change. The density of test particles increases as you approach mass. Each coordinate being represented by a test particle. Now this still works for geodesic relations as the mass density follows the same relation. However this mass density isn't space itself but the standard model particles. A way to learn this is the principle of least action which involves Langrene densities. At no time did GR states that spacetime has substance. That would entail an eather which has been proven wrong. The main tests involve Eather dragging. The above relates to how fields are described. For example a gravitational field is a field like of test particles. https://en.m.wikipedia.org/wiki/Test_particle

Misread the OP

What will change is the wavelength not the speed of light. In the case of a contracting universe you will have cosmological blueshift.

Volume if you remove all standard model particles both real and virtual. You will simply have volume

Time isn't a substance that can be dragged in

The last reply is in reference to the fact comment.

In science there is no real facts. For example related to the topic ... Say one study uses an IQ test to measure two groups. One group does poorly while the other excels... Does this mean one group is worse than the other or does it mean there is a problem in the IQ test itself? I've taken several IQ tests and I know they are not all the same. Some tests actually favor men over women. Just as some tests favor the teachings of one region over. Simply due to the extreme difficulty of coming up with questions that reflect analytical ability as opposed to learned skills. So is it correct to assume that studies that favor one group over another based on an IQ test is a fact? I think not. Take for example pattern recognition and fitting those patterns onto a puzzle. Sounds fair doesn't it? Yet someone who regularly does jigsaw puzzles will be more practiced at these problems.

I haven't looked over the thread in question nor do I desire to do so. However I can testify that a moderators job on a forum is extremely difficult. Particularly in this example. What most people don't see is the complaints on a particular thread. The moderators cannot reveal those complaints nor can they even indicate that there has or has not been complaints. On a world wide forum that involves every ethnic group as its members. I can certainly see numerous problems associated with the thread on question. The nature of the thread itself is incredibly risky and prone to discriminate one group over another. On a forum this should never happen. Particularly one who's intent is to teach science. Is there a safe way to discuss possible disadvantages of one group as opposed to another? Possibly however it sounds as though this thread went from a safe scientific discussion to racial slur and insults which quite rightly entailed being shut down. To safely discuss this particular topic one requires his post to be 100% impartial to any personal feelings. One technique is to discuss the pros and cons in a particular scientific paper. The very minute impartiality is lost then either it is recovered quickly or the thread should be locked.

Calculating the amount of photons in a volume of space is trivial. Science doesn't rely on human senses so terms such as light or dark has very little meaning. The contribution of the number density of photons is easily calculated via the Bose-Einstein distribution formula. Our test equipment can measure all spectrums of electromagnetic radiation which confirms the Bose-Einstein distribution formula. [latex]n_i(\varepsilon_i) = \frac{g_i}{e^{(\varepsilon_i-\mu)/kT}-1}[/latex] Which is roughly [latex]3.71*10^8/m^3[/latex] at universe blackbody temperature of 2.73 K You can check this article to confirm. http://arxiv.org/pdf/astro-ph/0406095v2.pdf "The Cosmic energy inventory"

[latex]\frac {t_1\gamma_1}{(1-\frac {2GM}{ r_1c^2})^{1/2}}=\frac {t_2\gamma_2}{(1-\frac {2GM} { r_2c^2})^{1/2}}=\frac {t_3\gamma_3}{(1-\frac {2GM}{ r_3c^2})^{1/2}}[/latex] Fixed the latex DimaMazin please confirm this is correct to your post. As it looks incorrect

Welcome to SFN. I have heard of the methodology of simulating predators to keep migrating herds bunched together. This practice has excellent results in renewing plant growth due to the manure enrichment. Many farms could reap the beneficts from such a practice as more often than not those lands have a greater ability to support plant life as well as retain more water. It's almost a shame that most farmlands don't rejuvenate their soil in a similar manner. It would in a sense be worth not growing crops for a few years and instead use the cattle etc rejuvenate that piece of land. I recall someone mentioning that one person with a sizable herd, has persuaded several farms to use his livestock to help rejuvinate their lands but never got any details on cost vs gain for the cattle owner or farmer.

Well I'm glad your satisfied with what's hidden in mathematica. Personally if I wanted to fully understand an animation. I'd like to be able to apply it to any programming language. Even basic. ( with the exception of PLC based lanquages I'd hate to try this in ladder logic or booleon lol)

So mathematically model it. Animation isn't math. An animation uses math. If you want to create the animation you need the mathematics.

Think of the blue as tangent to the rotation of green and yellow. Describe the rotation of green and yellow first. You'll need this to describe the tangent plane.

You can't define a tangent plane unless you can describe the object it is tangent to. Step one describe the path of e. Step two describe the tangent plane to path e. Any complex math problem can be broken down into simpler steps. This is what were doing but your trying to reach the end product by ignoring what's prior to derive the end product.

Have you not noticed that value e and value "angle between longitude and tangent plane are not identical? In fact they are opposite when one is zero the other is 90 degrees.

Think of the beige and purple planes as just the original position. Ignore blue. Your simply rotating the The yellow and green plane described by e. As e rotates the blue plane shows the angle between the longitude and the tangent plane. There you can now program this animation.

Ok ignore the blue plane and visualize the rotation without it. Now describe that objects rotation without the blue plane. Then note there is two value mentioned. The value of e and the (degrees between longitude and latitude) as one equals 0 the other equals 90 degrees. So which of the three planes rotating is represented by (degrees between longitude and tangent) as the plane binding point undergoes its rotation.?

Ok ignore the blue plane and visualize the rotation without it. Now describe that objects rotation without the blue plane. Then note there is two value mentioned. The value of e and the (degrees between longitude and latitude) as one equals 0 the other equals 90 degrees. So which of the three planes rotating is represented by (degrees between longitude and tangent) as the plane binding point undergoes its rotation.?

Rough guess I was going to say dihedral angle but that's incorrect. Without knowing the intention of the animation in the first place from Hans directly your guess is as good as mine. The math is reproducable but that doesn't necessarily show the intent. For one thing Hans has several animations. Which he explains yet doesn't include details on this particular one.