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GTR Continued. Sections 29.3 - 29.4. Reminders. Lab this week LAB B1- WA Wave Addition : due by 4 p.m. Friday CCR Extra Credit due Thursday , May 1 Examination #3 on Thursday: Addresses Chapters 8, 9, 11-13 only 26 multiple-choice questions 2 extra credit questions

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Gtr continued

GTR Continued

Sections 29.3 - 29.4


Reminders
Reminders

  • Lab this week LAB B1-WA Wave Addition: due by 4 p.m. Friday

  • CCR Extra Credit due Thursday, May 1

  • Examination #3 on Thursday:

    • Addresses Chapters 8, 9, 11-13 only

    • 26 multiple-choice questions

    • 2 extra credit questions

    • 30 points possible (120% maximum)

  • Final: Monday, May 5, 7:50- 9:50 A.M.


Einstein gtr and the universe
Einstein, GTR, and the Universe

  • Einstein’s equation of general relativity:

  • The equation required an expanding universe, so Einstein arbitrarily added a “cosmological” constant to avoid this conclusion…

  • Recall that galactic nebulas had yet to be discovered as galaxies, and neither had the expanding universe!


Friedmann s universe 1
Friedmann’s Universe 1

  • Starts with total energy:

  • Makes 3 simplifying assumptions:

    • Universe is essentially empty (on a larger scale)

    • Universe is isotropic (no preferred direction)

    • Universe is homogeneous (no preferred point)

  • and gets:


Friedmann s universe 2
Friedmann’s Universe 2

  • Inserting E=mc2 and taking into account GTR, the prior equation results in:

  • where k is the curvature of the universe:

    • If k < 0, then universe is closed and bounded (positively curved).

    • If k > 0, then the universe is open and unbounded (negatively curved).

    • If k = 0, then the universe is flat.


Friedmann s universe
Friedmann’s Universe

  • Solving this equation, Friedmann predicted that the universe had to be expanding if it were to exist.

  • Einstein added the “cosmological constant” to his own field equations because he could not believe in an expanding universe. Later Einstein remarked, “That was the greatest scientific blunder that I ever made.”


Hubble s relationship 1
Hubble’s Relationship 1

  • Following in the footsteps of others, Hubble determines recessional velocities from Doppler shifts.


Hubble s relationship 2
Hubble’s Relationship 2

  • Hubble determines distances to “nebulas” using a variety of means:

    • Study of variable stars whose periods are related to their intrinsic brightness

    • Angular diameters by type

    • Presence of brightest stars in a galaxy by type

    • Presence of globular star clusters

    • Presence of supernovas by type (I and II)


Hubble s law for galaxies
Hubble’s Law for Galaxies

  • Hubble used Doppler shifts and distances to study galaxies. He found a linear relationship.

v = HR


Abb georges lama tre
Abbé Georges Lamaître

  • Introduces the “Big Bang”

  • Concludes that time since universal expansion began could be found from Hubble parameter.

  • v = HR; now d/v = t;

  • v/R = H and d/v = 1/H

  • The current value of H (21-23km/s/Mly) shows the age of the universe to around 13.8 billion years.



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