Jump to content

Banner.jpg.b83b14cd4142fe10848741bb2a14c66b.jpg

andrew s

Members
 View Profile  See their activity

  • Posts

    4,295

  • Joined

  • Last visited

  • Days Won

    6

 Content Type 

Everything posted by andrew s

  1. andrew s
    As I said above for the calculation of the size of the Universe tr = Now (that's the time we receive the light) and by convention a(Now) = 1 te = 0 ( that is the time of emission of the CMB we observe now) a(0) ~ 0.001 "I remind you, that you need tr=te for a(tr)=a(te) for a=1." This is your error tr can't equal te. The CMB we see now was emitted some 13.6 Gyr ago and we observe it Now. We observe (1+z) = 1101 so using (1+z) = a(tr)/a(te) which for observations Now gives (1+z) = 1/a(te). With a(te) ~ 0.001 I have been consistent on this throughout. Unless you accept your error there is no point continuing this discussion. Regards Andrew
  2. andrew s
    No. I pointed out that te was the time of emission. It is a variable as it depends on what you are observing. For the CMB its zero but for Andromeda it will Now - 2.4 Myrs For GN -z11 it will be 430 Myrs Regards Andrew
  3. andrew s
    Correct. The CMB is the furthest back we can see at a red shift of about 1100 now. So for an observation now we have a(te) ~ 0.001, te = 0 and a(tr) =1, tr =Now Where a(te) is as I calculated before. Regards Andrew PS here is a plot of a(t) based on the Plank18 final mission data from here.
  4. andrew s
    Ok I lied. te is the time light is emitted. We can observer today light from the CMB emitted at te ~ 0 through any value up to now te ~ 13.6 Gyr since the Big Bang. For light we see today te only depends on how faraway it was when emitted. It certainly is not a constant. The end. Regards Andrew PS I lied about not responding again nothing else! PPS "If you don't change the definition of te or tr in a=1, you will never get the equality a(te)=a(tr), but you need it in a=1." No no no. For observations now a(tr) = 1, a(te) depends on when the light was emitted. a(te) = a(tr) if and only if they occur simultaneously.
  5. andrew s
    At te =0 a = 0 Just look at the scale on the right hand scale of the y axis in the Figure 1 that I posted. The CMB we see today has a red shift of about 1100 so (Z+1) = 1101 = a(tr=13.6 Gyr)/a(te) = 1/a(te) a(te) = 1/1101 ~ 0.001 and t ~ 0 I don't think I changed anything tr is always the time received and te the time emitted. This is my last reply. Good evening. Regards Andrew
  6. andrew s
    Absolutely if you emit a light beam now and detect it now + deltat then it will have travelled c×deltat a very short distance in a very short time and to zeroth order a(tr) = a(te) = 1 but to first order a(tr) = a(te) + deltat.da(te)/dt I have done my best to explain this to you. a(tr) = a(te) if and only if te = tr I.e they are at the same time. If the time are different the they are not equal. You seem to be stuck on a basic fact of calculus. I have tried my best. Good luck. I am retiring from the discussion as I don't seem able to help you. Regards Andrew
  7. andrew s
    A final try. I have tried to show normalised values can be greater than one e.g. my age at 25. I think you are hung up on the term normalised. A better term would be scaled. I scaled my age to that at age 12. This led to my scaled age at 0.001 being less than 1 and at age 25 greater than one. That's all ther is to it. Make a cosmic measurement now (say x meters) and its scale factor is defined as 1 i.e. (x/x = 1). If the same measurement had been made in the past the actual measurement in meters would be smaller (say y m) the scale factor would be such that y/x < 1. If made in the future you would get the longer distance (say z m) and the scale factor would be z/x> 1 Say your light ray was emitted at the early time te and received at the later time tr then (1+z) = a(tr)/a(te) = (z/x)/(y/x) = z/y > 1 Regards Andrew
  8. andrew s
    Ok one very last attempt. Note a(tr) and a(te) are the normalised scale factors at the time the light is received and emitted respectively. Looking at my height about age 12 for a small positive absolute increase in time my hight would be 5 + dh ft say and my scaled hight would be 1 + (dh/5) Looking at a change in hight about age 25 for a similar absolute change my hight would change to 6 + dh and my scaled hight would change to 1.2 + (dh/5) I have done my best not sure I can make it any clearer. Regards Andrew
  9. andrew s
    Sorry that totally wrong. Let's take a simple example my hight. When born I was about 1.7 ft tall at 12yrs I was 5 ft and at 25yrs 6 ft. Now I decide to scale myself about age 12 so the scale the a0(12) = 5/5 = 1. At birth my scaled hight was a(0.001) = 7/5 = 0.34 and at 25 yrs a(25) = 6/5 = 1.2. Yes a0 is fixed but "a" varies continuously about a0 = 1 As I age I will srunk but the Universe is not expected to. Regards Andrew
  10. andrew s
    It is always normalised about 1. In the region about now. It is continuous on 0 to infinity. To make matters concrete let's fix now to epoch 2000 and assume t = 13.6 Gyr then. Then a0 = a(13.6Gyr) =1. Now consider light from andromeda arriving in the year 2000 tr = 13.6 Gyr a(tr) = 1 It was emitted ~2.5 Myr prior to 2000 so te = 13.6 Gyr - 2.5 Myr when a(tr) = 1 - every small amount say 0.999999 (made up number) So (1+ z) = 1/0.999999 ~ 1 i.e we would not detect any red shift due to expansion but only peculiar velocity in fact it's blue shifted as its moving towards us. So to answer your question yes these points have physical meaning but the effect are very small until you get to large distances. Indeed Hubble' 1929 data showed significant scatter due to the relatively close proximity of the galaxies he measured and their peculiar motion. Regards Andrew
  11. andrew s
    No. a(te) is the scale factor for when the light was emitted I.e. in our past. a(tr) is the scale factor at the time it is received. Consider a light ray emitted when t ~ 1Gly I.e. te = 1 Gly (about 40 Glyrs away) a(te) ~ 0.01. It is received today tr ~ 13.6 Gly so a(tr) = 1 so (1+z) = 1/0.01 = 100 Now consider a light ray emitted today te = 13.6 Gyr about 10 Glys away it will reach us at tr ~ 25 Gyr and a(tr) ~ 2 so (1+z) = 2/1 = 2 I have taken the numbers very approximately from the diagram. Regards Andrew
  12. andrew s
    a0 = 1 always that is the scale is fixed so that the scale factor is normalised to one now. At future epochs a will be greater than 1 as the universe expands and was less than 1 in the past but a0 I.e. a at t = 13.6Gyr will remain 1. That's why you need the full equation for (1+z) = a(tr)/a(te) when doing sums about redshifts seen in the past or future not the one only valid for now. The key is that "a" is a normalised scale. Cosmologists chose to normalise it to 1 at the current time to make their sum with data colleted now simpler. Regards Andrew
  13. andrew s
    Ok. In the past t ~ 0 Gyr a ~ 0 (see attached image from the paper). By about 1 Gyr a~ 0.2. At 13.6 Gyr (now) a = 1 in the future at about 25 Gly a = 2 . It will not get to 1100 until 60 or more Gyr. So you have it in reverse so its the other way round. Regards Andrew PS It's confusing the a is sometimes labelled a0 for now. In all the above t=0 is at the start of the current expansion/ big bang and a0 refers to t ~ 13.6 Gyr
  14. andrew s
    Your equation (z+1) = 1/a only holds for the current now. In general the equation is (z+1) = a(tr)/a(te) where a(tr) is the scale factor at the the time the light is observed and a(te) the scale factor at the time of emission. In an expanding Universe a(tr) > a(te) and so no problems arise. Figure 1 of the Expanding Confusions paper show a plot with a -> infinity. Its equation 23 is the one I quote but with R in place of a. Hope this helps. Regards Andrew
  15. andrew s
    I always enjoyed practical science. Pops, bangs, unintended explosions and the odd rogue projectile enlivened the day. As did a near blind chemistry teacher spending some time trying to put a rubber bung into the wrong end of a test tube. He also created a flame thrower to melt a students bag. Having struck a match to light a Bunsen burner he could not get the rubber tube on the gas tap. As the flame reached his fingers he turned on the gas and lit it with the obvious result. He was a brilliant chemist who help develop the first epoxy resins. He could also be easily distracted into his favourite topic fireworks and suitable demonstrations followed. He did nearly axasphyxate us demonstrating oxygen would burn in ammonia gas as well as vice versa. (Health and Safety had yet to ..) The one area I did find a tad tedious was organic chemistry. Boiling up various clear liquids to produce another one with not quite melting or boiling point was somewhat dull. One trick was to get in with the stores personnel where a request for a sample of the target chemical could pull said melting or boiling point into the correct range. 😊 Regards Andrew PS recalling my days at Cambridge College of Arts and Technology reminded me of the wonder of nature. The class was a mix of 11 plus failures (including me) doing A levels and foreign students. One day the teacher had obviously lost the students attention. It had stated to snow and half the class had never seen it before. To his credit we stopped and went outside. Brilliant.
  16. andrew s
    Me too earth, fire, air and water. 😊 Regards Andrew
  17. andrew s
    This paper has a good discussion on the difficulties in doing the theoretical calculations. This diagram from the link shows the difference from two approaches Time and more experiments and theoretical number crunching will tell. Regards Andrew
  18. andrew s
    I did an experimental PhD it involved woodwork, metalwork, plumbing, electronics (lots of soldering), stick and ball models (plasticine, tooth picks and group theory), bent paper clips and window cleaning (laser mirrors). All good life skills. However, the group theory and Raman scattering of laser light by crystals of moly slip (more generally transition metal dicalcogenieds ) proved a good in to astronomical spectroscopy but little else. Memories what memories. Regards Andrew
  19. andrew s
    Yes, I read that some years ago. It just goes to show how enigmatic photons are, the most difficult of quantum "particles ". However, if you read any criticism of what is art you would find just as much variation and confusion. I recall an issue of what a Farm is in US law. The conclusion was that anything important enough was in effect too difficult to pin down. As with all models defining terms for "useful " components or elements depends on perspective and is in some sense a matter of choice. What one understand by terms like electron or table are dependant on ones formal education, culture and motivation. Bring it back to @Macavity point what a scientists can gain from it, likes, notoriety or income. Photonics expects seem to get by ok. Regards Andrew
  20. andrew s
    Absolutely Regards Andrew
  21. andrew s
    In that sense we don't know what anything actually is. What's a table or chair? What's water or air? All we have are mental or mathematical models Regards Andrew
  22. andrew s
    We have had QFT since the late 1950s that give a very clear picture. As it's a field theory waves won out with "particles" with mass only being localised in some special circumstances. Massless "particles" e.g. photon, can't be localised at all. In its QED form it has been experimentally verified to 1 in 10^-8 for its perdition of the fine structure constant. For QCD we have the standard model which has yet to be overthrown dispite the effort of many and millions of Euro. Unfortunately, it serves the pop science market to keep it mysterious with talk of waves-particles and spooky action at a distance. I am not sure why educators still stick to the historical approach (via wave particle duality) maybe @saac can shine some light on that. Regards Andrew
  23. andrew s
    Yes falling off a building never hurt anyone. It's the stopping at the bottom that does the damage. To miss quote Simon and Garfunkel. "I'd rather be a feather than a ball" Regards Andrew
  24. andrew s
    What you need to remember @Macavity is that You Tube is just one more source of income along with grant's, TV etc. I think it's more about money than politics as such. Regards Andrew PS and as @saac just posted below power and influence I.e. politics with a small p.
  25. 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
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue. By using this site, you agree to our Terms of Use.