Grade Distribution, second exam

1. Grade Distribution, second exam

2. Comments on CTEC • Will be done by the web. • The TA’s offical, sections are 6 & 8

3. Time Reversal Invariance • Then when the slightly different amounts of baryon/anti-baryons meet up, we end up with with just a small (about 1 part in 109) of excess of baryons. Just enough to explain the current ratio of photons to baryons. And the process is hot by definition of having so many more photons. =>Annihilation of baryons and anti-baryons (almost completely) leads to a hot Big Bang.

4. Time Reversal Invariance • When X and X’ particles decay the X decays faster to produce MORE baryons when going forward in time than the X’ particles, and vice versa. Therefore, as the Universe expands as time increase (runs forward), we end up with our imbalance.

5. CPT Theory and Observations • The CPT theorem says if I do a calculation of a particle collision probability and I (flip the positive charges to negative and vice versa plus change all the “lefty” particles to “righty” particles and vice versa, and change the sign on the time I use, I will get the same answer. • This means if I observe a reaction in which I change charge and parity (description of left/right handiness)

6. CPT Theory and Observations • And I see a difference. Then assuming CPT holds ( and it better!), then this means sub-atomic particles can sense the arrow of time. • Such a “CP violating” reaction was detected in the laboratory. => • This makes it plausible that a much higher energy CP violating and hence T violating reaction did occur in the early Universe.

7. CPT Theory • In mathematical terms, C x P x T = 1 means CPT is not violated. But if CP is violated this means by convention C x P = -1, but this then means T better = -1 (means T invariance is violated) so as to get C x P x T and keep CPT “true.” • This is why we say CP = - 1 implies T = -1, or we have a reaction that is not invariant under time reversal or in other words can sense the direction of time. This is truly a remarkable concept

8. More on Inflation • Why does inflation make the universe flat? • starts with KE +kc2/R2 = PE for radiation and matter • PLUS a cosmological constant term for inflation that does not depend on R. • KE Lambda term therefore doesn’t change while kc/R2 hence decreases “dramatically” • Therefore the kc2/R2 term becomes negligible = the same a 0 = same as flat!

9. Reviewof inflation’s raison d’etre 1. It can’t be a cosmic coincidence that the value of Omega is relatively close to 1. If Omega starts out 1, it stays one. This is more natural and inflation will produce a flat universe. 2. Inflation says we must explain why objects that apparently never could exchanged information (were never in causal contact) in the age of the Universe had nearly exactly the same temperature at the time of decoupling.

10. Review of inflation’s raison d’etre 3. The initial “perturbation spectrum” needs to be explained and inflation gives a simple one that can evolve to what we see in the CMB. 4. Inflation people say we need to explain why the Big Bang started out so hot and or why there are so many more photons than baryons and why there aren’t any anti-baryons. Inflation provides a mechanism for such process.

11. OK, Now yet another model:http://feynman.princeton.edu/~steinh/ The official title is “The Endless Universe” Replace Inflation with the existence of a mirror universe. This universe can communicate with ours only by gravity. IF there were people there we could communicate with them via gravitational waves.

12. BranePower to the Max • Each Universe is on a “brane.” • The branes keep colliding with each other and starting a new cycle of big bang to big crunch and on to another big bang. • The branes pull in fresh material from an extra dimension • This allows the universe to start “anew” at low entropy

13. Brane power to the max, cont Besides the existence of another universe, BPM has two special features (at least); 1. We won’t find and non-baryonic dark matter because there isn’t any. Rather the gravitational interaction with the other Universe mimics this effect. 2. We won’t find gravitational radiation

14. Now, on to reality: Measurements! “Just the facts ma‘am” • First we’ll do the distance scale • The overall GERNAL concepts of designing and carrying out a measurement. • Before you even start you have to ask: • Why is this interesting? • Is somebody else already doing this? • If so, can I do better? And why do it think I can do better?

15. General Considerations continued • Howlong is it going to take me? • How much is it going to cost? • Are the time and money worth it?

16. Other Considerations • When to hold’em and when to fold’em • What are the cost drivers in my design? • Do I need any instrument development to allow me to achieve my goals? • Do I have all the skills I need? • If not, can I assemble a winning team?

17. Technical Considerations • What limits the accuracy of my measurement? • How will I calibrate my measurements so that somebody else can judge the results. • What assumptions will I have to make from theory or experiment to build my case. • If I’m looking for an effect (such as WIMPs), will my result be interesting even if I don’t find the effect?

18. Why Distance • Why bother with the distance scale? • Because nearly every thing we derive in astronomy depends on knowing the distance. • For cosmology, we want to know: • The expansion rate (Hubble constant) which requires distance versus velocity measurements. • We want to measure the mass density of the universe, we need to know the mass within a given volume, which means a knowledge of the distance.

19. Why Distance • For cosmology, we want to know: • The distance along with a measure of the redshift so we can test different geometries of the Universe • The distance to objects can tell us how these objects form and evolve. • The spatial distribution objects is another test of cosmology.

20. Back to distance • Overall design calls for a “bootstrap” approach. We start with small distances we can effectively measure with a ruler. Now, our next step in the design is to figure out that the “parallax” can tell us distances. • Parallax is the effect of noting you can discern the distance to an object if you can measure how much it appears to move around as you do.

21. Overall design calls for a “bootstrap” approach. • We start with small distances we can effectively measure with a ruler. • Next step in the design is to figure out that the “parallax” can tell us distances. • Parallax is the effect of noting you can discern the distance to an object if you can measure how much it appears to move around as you do.

22. Parallax Demo • Take a piece of paper and draw a stripe on it. Hold the paper at arm’s length with your nose pointed at the stripe. Then hold 1 finger (your choice; I used my index one) about half way. Then close your left eye. Then open it and close your right eye. Notice how much your finger appears to move RELATIVE to the stripe. Now move this same finger to arm’s until it is almost touching the stripe and try again. Now there won’t be much apparent motion of your finger relative to the stripe.

23. OK now what? • The effect is caused by moving your vision relative to your finger and you have accomplished the “motion” by using different eyes. The effect is the same as using one eye and moving it the distance between you two eyes perpendicular to the line-of-sight. • Now how far can we determine distances that way? We need to answer two questions first: (1) How far apart are our eyes, and (2) how small a change in apparent motion can we measure.

24. OK now what, cont. • My eyes are separated by about 7 cm, and I know also I can see an angular separation of about 1 arc minute. So the diagram I draw is like this: So using trigonometry, d*sin(0.5arc min) = 3.5 cm or d = 240 meters tops, q = 0.5 arc min. l about = d, s = 3.5 cm Apparent motion Each right triangle has a base of 3.5 cm and the apex angle of 0.5 arc minutes q d l s eyes

25. Parallax cont. • => If we know s and q we can calculate d (and or l). This give us the distance. A person’s distance or depth perception via binocular vision” is about 15 times worse than what I’ve calculated. The true number is about 50-60 feet. (cf., http://online.sfsu.edu/~psych200/unit6/66.htm) • Where did I go wrong? (a) Our eye needs a reference frame and the reference frame should be distant enough not to show parallax; (b) the eye doesn’t have the luxury of being able to accumulate data for hours and to look at objects with extremely well defined centers.

26. Parallax and astronomy • We want the equivalent of s to be as large as possible and accurately measured. => Here to Chicago won’t “do it.” One side of earth to the other can allow us a low tech way of measuring the distance to the Moon. Fine, but the closest star besides the sun is four million times further away. We need a larger “s.” This is

27. Parallax and astronomy • The Earth’s orbit around the sun! • Our most accurate measure now is by? Radar! And 1 arc second for q in our diagram with the earth’s motion around the sun to define s, we find that 1 arc second gives a distance called a Parsec (for parallax and arc second!)

28. The parsec Taking s = 1.50 x 1013 cm and q = 1 arc second and sin(1 arc second) = 4.85 x 10-6. Or, d = (1.50 x1013)/(4.85 x 10-6) = 3.09 x 1018 cm! Or in round numbers, 3 x 1018 cm = 1 par sec. A year = p x 107 sec of time=> p x 107 sec x 3 x 1010 cm/sec = 1018 cm, or 1 par sec = about 3 light years, where speed of light = c= 3 x 1010 cm/sec 1 parsec (pc) = 3 x 1018 cm 3 light years = 1 parsec

29. But will parallax work beyond the stars in our galaxy? • NO! => We need to determine parallax to a standard candle, if we can get it. • What do we need? Precise, small images, the better to find the centers of, and a well defined non-moving background for reference. • Stars are good for making small images, and distant stars or small galaxies are good for reference.

30. Limitations to parallax method • Swing around sun: Going to Pluto would get us a much larger swing, but the period is over 200 years! • Image quality; Rule of thumb is we can measure a center to about 1/10 of an object’s width. The best we could do on the ground a few years ago was 0.5 arc second images => about 20 pc distance. If can go into space can get a factor of 100 improvement without the blurring effects of the Earth’s atmosphere.