Spacetime just when you thought it was it

Spacetime: just when you thought it was it throws you a

Newton’s Law of gravity depends on an “instantaneous” distance r That is not consistent with relativity! Minimal ways to fix it led Einstein to a deeper problem At the same time Einstein was intrigued by an apparent coincidence the equivalence of gravitational and inertial mass….

PRINCIPLE OF EQUIVALENCE (Einstein’s happiest thought) No experiment in an isolated space can distinguish between a gravitational field an equivalent uniform acceleration. So all Einstein had to do was understand acceleration!

No experiment would help you distinguish between being weightless far out in space and being in free-fall in a gravitational field.

An accelerating frame is defined by a frame of clocks under uniform “proper” acceleration (i. e. in clock frame) Simultaneity is relative between Bs frame at t=0 and t=4 Equivalence principle implies same is true in a gravity field http: //www. pitt. edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/

Simultaneity planes are parallel and of same length but have varying time intervals Distance between parallel lines decreases on a curved surface

Two people are walking in parallel lines at the equator. They continue along lines of constant longitude, until, much to their surprise, they meet. • They conclude they must have been attracted by a force. • You see that they were actually walking on a curved surface.

GR POSTULATES • PRINCIPLE OF EQUIVALENCE: IN THE VICINITY OF ANY POINT, A GRAVITATIONAL FIELD IS EQUIVALENT TO AN ACCELERATED FRAME OF REFERENCE IN THE ABSENCE OF GRAVITTATIONAL EFFECTS • THE LAWS OF NATURE HAVE THE SAME FORM IN ANY FRAME OF REFERENCE, WHETHER ACCELERATED OR NOT (clearly light doesn’t have constant velocity - geodesics)

A new way to look at why the Earth rotates around the Sun. Einstein’s guess + curved space time simultaneously resolves why mass cancels in acceleration and the action-at a distance problem – Gravity just curves the space-time around it and particles Follow curved geodesics

Lensing

Gravitational Lensing

Gravitational Lensing

Clusters produce distinctive tangential patterns

Distortions of our view of the sky

Gravitational Lensing

Measuring the energy in the Universe • We can measure the mass of clusters of galaxies with gravitational lensing • These measurements give Wmass ~0. 3 • Cosmological constant gives Wenergy ~0. 65 Gravitational lensing

What do we learn about the universe? • Isn’t obvious that most of the matter in the Universe is in Stars? Spiral Galaxy

Another Consequence: GRAVITATIONAL WAVES • Particular kind of phenomena (e. g. orbiting stars) produce ripples in the space-time curvature… • Ripples travel at speed of light through space • These are called gravitational waves.

Early instrumentation to detect gravity waves, , “Weber bars”, were pioneered by UMD professor, Joseph Weber! Go Terps!

LIGO - Laser Interferometer Gravitational Wave Observatory Like Michelson Morley, but each arm is kilometers long!

Black-hole accretion (simulated image)

Black Holes vs. Solar System VY Canis Majoris Quasar M 87 OJ 287 100 Solar Mass 18 Billion. Solar. Mass. BH BH 3 Billion 4900 ly Away 3. 5 55 Billion Million ly ly Away 8. 3 lmi n 4. 4 ly

M 87 • 1/4 size of Milky Way Galaxy • 10 X More Massive 25, 000 ly

Inside M 87 25, 000 ly • Nearly every galaxy has BH • BH surrounded by disk • Some BHs make jets

Tune in next time when we talk about…. …the quantum theory of light.