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andrew s

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Everything posted by andrew s

  1. andrew s
    One can have an interest in astronomy without freezing ones ***s off at night under the firmament. Armchair astronomers are fine by me. Why on earth would one disqualify them from this diverse hobby. I have given up serious observing and now just look up when out at night is this somehow deviant? Don't answer that. 😊 Regards Andrew
  2. andrew s
    For me science is a dance between theory and experiment. No experiment is theory free nor should any scientific theory be freed from experimental verification. At times theory leads and experiments follow other time new observations open up new theoretical advances. Astronomy / cosmology is unusual in that one cannot do controlled experiments but its predictions should be subject to observational confirmation. Regards Andrew
  3. andrew s
    While we don't know how it happened we are 100% sure it did happen. 😊 A single well established example is all you need. Regards Andrew PS why do we always look up for signs of intelligent life?
  4. andrew s
    I had the same issue a while back. It's ice crystals. I fixed it by cooling slowly over 20 mins. Other keep it above 0c. Regards Andrew
  5. andrew s
    Of course if you want the linear magnification work out the size of Jupiter in the image (~pixel size x no pixels across diagonal) and divide by the size of Jupiter! Regards Andrew
  6. andrew s
    It has already happened. Mathematicians were very critical of the idea of the Dirac delta function. It was eventually made "respectable" via the theory of distributions. Regards Andrew
  7. andrew s
    SGL will be offline. Regards Andrew
  8. andrew s
    Good luck with whatever you do next. Regards Andrew
  9. andrew s
    Interesting, given your heritage I would have gone for Maxwell and his equations as your choice. Nurture over Nature? Regards Andrew PS for anyone puzzled by Euler's formula Google Argand diagram and see the light.
  10. andrew s
    I feel there is consistency but as complexity grows our ability to master it seems to rest on being able to "course grain" it, to find a scale that loses the complexity while retaining the key characteristics . For example treating a gas as a whole with PV = RT rather than with the kinetics of the underlying molecules. While we can get away with our point or spherical cow for its bulk motion it does not seem possible to model grass into milk in the same way! In reality we tend to resort to simulation for large complex systems but again the basic units must be simple. Recent advances in AI are making progress but I fear they provide little additional insight. Some things remain too complex to model at a level we can grasp. Whole biological entities being one example. Regards Andrew
  11. andrew s
    I think that's very simple. The ones that allow us to make useful models of some part of the reality we are interested in. You only need to look around you to see the effectiveness of a pragmatic approach. Our technology and engineering, for example, this forum and the nested technologies it relies on. Regards Andrew
  12. andrew s
    It always seems to me that e^ipi= -1 is pure magic. Regards Andrew
  13. andrew s
    Indeed it can, Brownian motion is a classic example, there are many others in classical physics. Also quantum theory is a probabilistic theory and does not (except in special circumstances) predict specific outcomes but only their relative probabilities. Regards Andrew
  14. andrew s
    Mathematical or not a model is satisfactory or not depending on what you want to do with it. The modern way of looking at physical theories is to consider their range of applicability. No model or theory covers all phenomena in all domains. In some areas phyisicts have led mathematician for example the Dirac delta function. Regards Andrew
  15. andrew s
    Evolution has equipped us with a brain that allows us to make sense of our environment. We modelled it and noted its regularities it order to survive and prosper. It seems that as a consequence, this brain, has been able to generate natural languages, the creative arts and the abstract language of mathematics. Not all mathematics (as far as we know) is applicable to modeling the physical world and we have not managed good models of all physical phenomena e.g. turbulence. Even some very old areas, e.g. statistical mechanics, have issues in their foundations. Is it too surprising then that the brain that noted and was shaped by the regularities of its environment, codified a way of capturing them and so much more - mathematics. That we struggle to comprehend the quantum world, so far removed from our experience, other than than through its mathematical formalism is a deep irony though very understandable. Regards Andrew
  16. andrew s
    I was talking about a simple solution to them. The Friedman equations and an equation of state. So you feel integration of t^-x where X =2/3 or 1/2 with respect to t difficult? As I say I think you would find Liddle's book answers your questions in detail. I don't think I can help you further. Regards Andrew
  17. andrew s
    This is not a standard view. Regards Andrew
  18. andrew s
    But the functional form is not wrong. You are missing an equation the relates the scale factor to the material in the Universe and an equation of state for the stress energy. For example taking the Universe as an expanding isotropic gas you get the Friedman equation and the fluid equations which can be solved analytically. For a matter dominated state you get a(t) = (t/t0)^2/3 , and an equation for density. For a radiation dominated state you get a(t) = (t/t0)^1/2 a d a different equation for density. Similarly for the full LCDM model. There are no issues integrating these equations and the standard results apply. I can recommend "An introduction to Modern Cosmology" by Andrew Liddle that covers all this in detail. Regards Andrew
  19. andrew s
    Looking at the last few posts between you and @vlaiv it might be worth noting that in GR spacetime is about geometry and how stress energy shapes it. The standard model has the initial state (or at least as far as we can reliably go back) as hot and dense and it has been evolving from there. Spacetime evolves dynamically as the the stress energy has continued to dilute from it starting point as space metrical expanded with time. The geometry does not stop and start it just is. Regards Andrew
  20. andrew s
    I would put it the gravitationally bound system don't expand as the force is order of magnitude greater that the tension due to metric expansion. Even more so for electromagnetically bound systems. However, metric expansion is still is going locally even if we can't see it. Regards Andrew
  21. andrew s
    Sorry missed that. I think you may have missunderstood the paper. Maybe you could point out which diagrams are incorrect and mathematically why. It's very difficult to get a handle on your concern via "words" when discussing mathematics. The integral is well defined and I belive your concept of " retaining the scale factor from the past" is mistaken or at least I don't know what it means. For a given model, LCDM for example, the scale factor is well defined so the integration has no mysteries. In cosmology concepts such as distance are model dependent, and while I am sure LCDM is not the last word on the topic, there are several other predictions which are observationaly supported such as the time delay in super nove light curves which respect the distance scale it defines. Regards Andrew
  22. andrew s
    Of course they exist and are among us, they are called teenagers. They appeared in the late 50s early 60s coinciding with Sputnik. Before then they were unheard of. We as a species went from child to adult but now this alien infection has modified its behavior much as the jewel wasp turns a cockroach into a zombie. Regards Andrew
  23. andrew s
    You may find this paper worth studying. While it can take some effort to get into the various diagrams I think if will illuminate the issues you are discussing. Regards Andrew
  24. andrew s
    Sadly fraud is not unkown in science especially now the competition for fund makes verifying results unattractive to competing groups. Micro biology has had it's fair share of issues this for example is an interesting read. Regards Andrew
  25. andrew s
    As I mentioned above, the CMB does provide a reference that can be used as an almost "universal " reference for local, on a cosmological scale, motion. At very large distances and due to the dynamics of spacetime comparing relative positions, velocities etc. is very problematic and very model dependent. As a simple example of the effects of spatial curvature. Consider two cars on opposit sides of the equator heading north at a constant speed v. They are initially driving parallel to each other with zero relative velocity. However, by the time they reach the poles the are in for a head on collision at a relative speed of 2v. Physics is fun. Regards Andrew
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