andrew s

You have to go to the AAVSO site the navigate to the database and then the access form. You can put in an RA &Dec plus search radius and download a file. Not tried it myself! Regards Andrew Ps you can down load the whole file.

Hi @vlaiv, you could try the AAVSO Photometric All-Sky Survey . It has BV and sloan data. At a minimum you could test your transform. Regards Andrew

You could try ground to air missiles but they can leave a vapour trail. Other than that as above. Regards Andrew

Hi Stuart, have you checked other people's images to see if it's there? Worth doing and getting a confirmation image if not as you may have discovered something new. Regards Andrew

The whole range of anthropic principles from hard to weak is indeed thought provoking. In the case of Omega I think it would be interesting to no what magnitude range (+ve or-ve) is allowable but I have not researched it. Regards Andrew

Very roughly, The current age of the Universe is about 4 x10^17s and if the current density were about 0.5 then at time t = 10^13 and assuming |Ω(t) – 1|) α t (I.e. a^2*H^2 α t^-1) gives Ω(10^13) ~ 0.5 * 10^13/ 4 *10^17 ~10^-5. The model excludes inflation. If I recall correctly the topology can't change under GR i.e. the k is constant) On the constraints on topology the Plank 2015 results put constraints on the nature of the topology see https://arxiv.org/abs/1502.01593 . There are lots of papers on trying to constrain the topology but they can only provide limits given the size of the observable Universe. In a similar discussion on PhysicsForms "That said, I don't think that it's accurate at all to state that "cosmologist tend to believe that the universe is infinite". A more precise statement would be that cosmologists rarely think about whether the universe is finite or infinite because it's not really something that is answerable. Most cosmologists tend to try to stay within the bounds of answerable questions that have an impact on observations we can potentially make." Reference https://www.physicsforums.com/threads/what-is-the-probability-that-the-universe-is-absolutely-flat.971984/ I was not trying to reopen the the discussion on what the curvature was but rather point out how close to "flat" it must have been in the past (with or without inflation) to be as close as it is to flat today. Regards Andrew

No not imaging flats but the spatial flatness of the Universe. In a thread started by @vlaiv he asked why cosmologists took the Universe to be infinite, with all the problems that poses, rather than finite and closed. While the thread discussed many issues especially about infinity it did not touch on why the Universe being close to spatially flat is surprising. Well why is it surprising? The main reason is the Big Bang Model based on GR normal cosmological assumption (homogeneous and isotropic) and the current LCDM model derived from the latest measurement which put it close to being flat. So what? Well the Friedmann equation (derived from the above) tells us that: |Ω(t) – 1| = |k|/(a^2 H^2) Where Ω(t) is the total mass energy density, a = the scale factor and H is Hubble’s constant. k is a constant that defines of the curvature of spacetime: k = 0 gives a flat Universe, k < 0 Hyperbolic and k > 0 Hyperspherical Now if k = 0 the Ω(t) = 1 a constant i.e. the Universe is and always has been spatially flat. This is just amazing why should it be so? It could be that physics says it has to be like that. No one has shown this to be the case or even got close. It was/is a major problem for the original Big Bang theory. If |k| > 0 then why is it so close to 1 now? The Universe was initially radiation dominated where |(a^2 H^2) α t^1 Then matter dominated where |(a^2 H^2) α t^2/3 So |Ω(t) – 1|) α t or t^2/3 in the past. (It is now thought to be Dark Energy Dominated) Again, so what? Well if it has grown like t or t^2/3 what was it like in the past? At the very worst now 0.5 < Ω < 1.5 so at: decoupling t ~ 10^13 s we need |Ω(t) – 1| <10^-5 and at nucleosynthesis t ~ 1 s we need |Ω(t) – 1| < 10^-18 ! The same issue as before. This was why cosmic inflation was introduced to help solve this problem, as well as the horizon problem, with all the fun issues it brings! Regards Andrew PS Please forgive the indulgence of this post but it helped me get it straight in my mind. All Data and equations from “An Introduction to Modern Cosmology” by Andrew Liddle.

Do you have a reference for your last point as I would like to follow it up. Thanks Andrew PS I found a paper with a simulation that supports your comment. The local cluster remains bound

The Virgo cluster is gravitationally bound. The force of gravity on the scale of the local cluster is 10^7 stronger than the tension caused by the metrical expansion of space. (Sorry I don't have the figure for the virgo cluster.) So this observation is consistent with the expansion theory as @vlaiv explained. Indeed many local galaxies are blue shifted as can be seen in Hubble's original data. Regards Andrew See later post we will not stay bound to the virgo cluster but the local group will remain bound.

There is an infinity of infinities and some have very big ears. Regards Andrew

Oh course @saac you have at this very moment an infinity of masses depending on the velocity of the reference frame you measure it in with relative velocity v where |v| < c 😱 Regards Andrew

I realise that and fully acknowledge it. However, you also apply an argument that in essence says that if you have an infinite state space then repetition is inevitable, there will be boltzmann brains etc. This is a common view and you will find many serious deployments of this argument by many much more capable than I. I however, think it is wrong. I think the way probability is employed in these arguments is in error similar to the error that leads to Olblers' paradox. It is this area I am not motivated to discuss further. Not because I fear being proved wrong but it is just too complex for me to articulate clearly enough. Please forgive my reticence. Regards Andrew

How we perceive the world is indeed very complex and in some cases quite anomalous to the norm as your experience confirms. This is why I teased @saac about what is real. Our perception may all differ to a more or less significant degree and what we naturally take as real might be quite different if evolution had equipped us differently. All the worlds a concept and we are just avatars of a boltzmann brain .🤔 Regards Andrew

And at what time was the worst pong? Regards Andrew

You are right infinity is not a number. You can, however, do mathematical manipulation on it. Not that they are particularly relevant to this discussion. I think as @vlaiv has pointed out you need to be careful what infinity means in this context. We are discussing the LCDM cosmological model in which spacetime is geometry. The geometry of Einstein's Gerneral Relativity. In this context a spatially flat universe has and always has had infinite spatial extent. All this means is that you can continue in any spatial direction without bound. This is a totally respectable geometrical notion. You and others may read more into this beyond the geometrical meaning. For example as@vlaiv does that this leads to multiple repetitions etc. These require logic and physical reasoning beyond LCMD. Perfectly legitimate but I tend to the view that they are often misguided. Regards Andrew

Hi @vlaiv yes I know about analytical continuation etc. As I said a bit of fun ! Hi @saac playing only slightly. I am not trying to say infinity is real in the sense of you or I are but for me it is as real as a googleplex or 0. Although it is not a number! However, I do find it difficult to know if the entities of our physical models are real or not. If you take an electron as an example do they exist in a solid where they have no well defined location or only when free or not at all in the sense a pebble does. I don't know. @vlaiv on renormalistaion that is an interesting quote but I do get tired of physicist saying all problems will dissolve when we "quantise" spacetime and gravity. I have a sneaking feeling we will not find a theory of everything and gravity and QM will remain unreconciled.(No evidence just a hunch. ) Regards Andrew

Ok Jim no problem with that. However, I want you to give me example of what does exist in nature. This is so I can understand how you decide what does and doesn't exist in nature or is real however you prefer to put it. Regards Andrew

Not quite this but fun for a Thursday morning. Consider the sum 1+2 +3 +4 +5... (where ... means keep going for as long as there are new integers to add - forever) If you try this on your calculator you will find it diverges (continues to get bigger) and does not converge to a specific number. (Note the avoidance of the term infinity) All well and good no objections so far I trust! Now Riemann came up with a function now called the Riemann zeta function zeta(s) = 1/1^s + 1/2^s + 1/3^s ... which is defined for all values of s but for s = 1 Now if you put s = -1 you get zeta(-1) = -1/12 (try it here https://keisan.casio.com/exec/system/1180573439 as I doubt it is on you calculator ) All well and dandy. Now put s = -1 into the equation above for zeta(s) and you get zeta(-1) = 1 + 2 + 3 + 4 + 5.... So the same sum both diverges and converges! Does this matter is it just proving the unreality of Mathematics. Well the first divergent sum is just counting (albeit forever). The second crops up in QED and the calculation of the correct strength of the Casimir force. Zee in "Quantum Field Theory in a Nutshell" derives the answer without using the zeta function but there is no reason not to use it any more than not using sin, cos or tan. Happy days. Regards Andrew PS in QED it is often the opposite of @vlaiv request in that you get excellent agreement with the first few term but it diverges when you add significantly more.

I am not sure what this means. What do you feel does exist in nature. Elections, em fields, quantum fields, energy and entropy are all components of our mathematical models of reality. Chairs, tables and pebbles are objects of our naming and of our perceptual model of the world. The integers, reals and irrational are part of our mathematics Which if any of these are part of reality? If not what is? Regards Andrew

By the way I don't know if the Universe is spatially flat or not and is as @vlaiv proposes. All I am trying to do is explain as best I can what the current consensus view is within science community. My understanding is that the best current data indicates that it has a simple topology and is very close to flat. We could as @vlaiv proposes be mistaken and that it is curved and we are making the same mistake as the original flat earth proponents did. However, it is so close to flat that within the currently observable universe we cannot tell the difference so the current working hypothesis is that it is flat. This makes some calculations simpler! Concerns about the I application of if being infinite if true or not are all outside the obsevable universe so it hardly matters if the are real or not -reather a matter of taste.

No it does not. In pop science the Planck length is often seen as a limiting distance but in reality it is just a unit of length like the meter defined in terms of more fundamental constants. The metrical expansion of the universe is of space not a material object and can and does exceed the speed of light. In the flat LCMD model the universe has always been spatially infinite. Metrical expansion is a subtle idea as are ideas about infinity! Regards Andrew

@vlaiv energy is not conserved in General Relativity. Both Einstein and Hilbert recognised this and asked Emmy Noether to look at the problem and this led to her theorem which related conservation laws to symmetries. Conservation of energy is related to time reversal symmetry. This is broken in a curved spacetime. Regards Andrew

Wrong again. The universe is taken to be spatially infinite but has a finite age. This results in a finite observable universe which is expanding and circumvents Olber's Paradox. This is well known. Regards Andrew

I am sorry you are wrong. The space time of QFT is that of special relativity and is continuous. Some results from QFT ( e.g the spectrum of the hydrogen atom) are quantisied but not all (e.g. the position of a free particle). Regards Andrew

Ok one more. If you compare Bose Einstein and Fermi Dirac statistics if e were not exactly e then the +/- 1 would not lead to the divergent behaviour of fermions and bosons but something less dramatically different. The end from me. Regards Andrew Forget the above it's wrong any number to power zero equals one. Opps