Special Theory of Relativity

What are phenomena which general relativity CAN explain but Newton's theory CANNOT?

- bending of light around sun -gravitational lensing -precession of perihelion of Mercury -slowing of clocks in gravitational field -gravitational red-shift -gravity waves

What are the effects of a massive body on the space and time around it?

-Clocks run slower as they get nearer the sun -Meter stricks are stretched as they get nearer the sun

If errors were not taken into account, errors in GPS would be about ___ km per day

10

Global Positioning System consists of how many satellites orbiting at 20,000 km from the ground with orbital periods of about ___ hours?

24, 12

C = speed of light which is how much?

300,000 km/sec = 648 million mi/h

Mercury's orbit precesses by ______ arc sec per century and _____ years to go around

5600, 23,000

What is singularity?

A place of infinite space-time curvature; the center of a black hole

Example of spacetime using ant path?

Ant's path is determined by the shape of the space (i.e. shape of space) and if the sheet or the space is distorted by a weight, the ant will follow distortions of the space.

Why is gravitational radiation difficult to detet?

Because by nature it's much weaker than electromagnetic radiation

Why is the valley clock running slower?

Because it is nearer the center of the Earth, where gravity is stronger. Clocks slower when moving.

In the rest frame of the Earth (in allowing muons to strike the surface)

Because of time dilation, surface clocks see the muon's lifetime to be about 10 Ms, thus allowing many muons to strike the surface

How does spacetime look like?

Flat when far from source of gravity and clocks tick at their normal rate, but closer to source of gravity, the space is curved and clocks slow down.

What did Urbain Le Verrier do?

French mathematician hypothesized another planet, Vulcan, to explain this precession. If we assume there is another planet (Neptune pullin on here) would explain irregulating of Uranus rings

When was General Theory of Relativity complete?

In 1915, Einstein presented four lectures with the final lecture "Field Equations of Gravitation" to Prussian Academy of Sciences

Define Space-time

In relativity, one-dimension of time proves to be so intertwined with three dimensions of space to create a single four-dimensional entity

What makes theory of relativity special?

It is only valid for observers moving with constant relative speeds (no acceleration).

What does the Special theory of Relativity say?

Laws of physics are the same for all observers moving at constant speeds relative to each other. Speed of light is the same for all observers.

Apply general relativity to test bending of light

Light follows geometry of space time (curved path around the sun). Gravity should bend light rays since paths of rays will be curved when light passes near surface of a massive object like the Sun.

How does ant analogy apply to the path of a planet?

Massive body like the Sun distorts the space AND time around it which then dictates the path of the planet

As gravity gets stronger, what happens to the meter sticks and clocks?

Meter sticks stretch and clocks get slower

In the rest frame of the muon (in allowing muons to strike the surface)

Muon still lives for 2 Ms but due to length contraction, distance to the surface is only 2 km, which allow them to strike the surface

Describe muons

Muons decay into other particles in 2 Means (on average). They can move about 0.6 km. Almost none will make it to the surface, 10 km away.

When do we use Newtonian Gravitation? When do we use General Relativity?

Newtonian Gravitation: When gravity is WEAK (near the sun or Earth), it is adequate for most purposes like going to the Moon or Mars General Relativity: When gravity is STRONG, near neutron star or black hole

In the view of General Relativity, is there a force of gravity?

No

Does general relativity replace Newtonian gravity?

No but it is a more accurate description of gravity.

Is the difference in clocks by gravity noticeable on Earth?

No it is small. Valley clock will be slower by about 10 nanoseconds per day

Does general relativity include quantum effects?

No thus it cannot therefore explain what happens at small distances and not at the singularity

What is time dilation?

Objects observed in motion are shorter in their direction of motion and clocks observed in motion tick more slowly.

What are the two types space is divided into?

Outside horizon: it is possible to orbit the black hole just like any star Inside horizon: escape is impossible, even for light. To cross event horizon, must proceed to the singularity

What was first great test of Einstein's new theory of gravity?

Precession of perihelion of Mercury

Cosmic rays are mostly made up of what?

Protons and helium nuclei

What are consequences to generalizing relativity?

Required that massive objects like the Sun or Earth would distort the space-time around it.

Apply general relativity to Gravitational Lensing

Results from bending of light around galaxies. Galaxy blocks the actual position of the quasar. Its light goes off in directions and sometimes will see 2 images depending on angle

If you drop the gray metal sphere onto the center, what happens?

Ripples will move outward on surface of drum-head, eventually causing white ball to move up and down

Both frames of references (Earth and Muon rest frame) yield same or different results?

Same for different reasons

Gravitational waves were detected where and when?

Sept 14, 2015 by both of twin LIGO detectors in Louisiana and Washington

Two kinds of space and time effects?

Special relativity: moving meter sticks and moving clocks are shorter and run slower (respectively) according to observers at rest. This effect is due to the relative motion of the observers General relativity: - Coordinate grids are stretched and clocks run slow near massive body

How does relativity apply to GPS function?

Special relativity: predicts that satellite clocks tick slower by 7 microseconds per day

What makes the theory of relativity strange?

Speed of light is a constant for all observers.

Consequences of theory of special relativity

Time dilation, length contraction, breaking simultaneity

According to observers ship when sending probe to event horizon..

Time on probe clock FREEZES. Probe never appears to cross the event horizon. Light emitted red-shifts as it travels to the ship and light red-shifted to infinite wavelength. This makes probe disappear from sight.

What happens when gravity waves (distortions of space-time) hit LIGO?

Two arms of LIGO expand and shrink

What did Einstein envision gravity as being caused by? How did he describe it?

curvature of space. He described it entirely in geometry of both space AND TIME (spacetime)

When one identical clock is taken to the top of a mountain, the other identical clock will differ or not differ? Will the valley clock run slower or faster than the mountain clock?

differ, slower

What are quasars?

extremely bright objects (contains black holes)

Precession of Mercury's orbit has a ____ orbit. But if put 6-7 planets that pull/tug on mercury, it begins to ____

fixed, move

In curved space and time, the ______ the mass of the body, the ________ the distortion of space-time

greater, greater

Wavelength _______ as measured against the local coordinate grid, thus the energy_______

increases, decreases

As Mercury approaches the Sun, it is pulled ______ than Newtonian gravity predicts, putting it in a new slightly rotated ___________orbit

little more strongly, elliptical

How does general relativity apply to GPS?

predicts that satellite clocks tick faster than clocks on the ground by 45 microseconds/day

The coordinate grid spacings are ___ more and more near the sun

stretched

According to general relativity: as meter sticks get nearer the sun, what happens?

they are stretched

According to general relativity: as clocks get nearer the sun, what happens?

they run slower

According to general relativity, as gravity gets stronger, what happens to the meter sticks and clocks?

they stretch and clocks get slow

Are both kinds of space and time effects contained within general theory?

yes

After publication of special relativity, what happened?

Einstein began to generalize it to include accelerated reference frames. This would prove to be profoundly difficult and revolutionize thinking about space, time and gravity.

What does each satellite of the GPS carry?

atomic clock with accuracy of 1 billionth of a sec

Laster Interferometric Gravity Wave Observatory (LIGO)

Designed to detect gravity waves and can detect changes in length of 1/1000 of an atomic nucleus Split laserbeam into 2 difference pieces: one laserbeam comes back earlier because it gets shorter

What are the light beams used to monitor?

Distance between mirrors precisely positioned at ends of arms.

Scwarzschild Radius?

Distance from the center of a non-rotating black hole to its event horizon

According to Einstein's theory, distance between the mirrors will?

Change by an infinitesimal amount when a gravitational wave passes by the detector. Change in lengths of arms smaller than 10^-19 meter the diameter of a proton can be detected.

How are muons formed?

Collision of cosmic rays with upper atmospheric nuclei that produce other particles, particularly muons. This can only be explained by special relativity.

What provides an example of length contraction and time dilation?

Cosmic rays which originate outside of Earth's atmosphere.

Apply general relativity and special relativity to GPS

General relativity predicts satellite clocks tick FASTER than clocks on ground by 45 microseconds per day Special relativity: preducts that moving statellite clocks tick more SLOWLY by 7 microseconds per day Satellite clocks tick 38 microsec per day FASTER than clocks on the ground.

In 1918 when Einstein finished theory of general relativity, what did he state?

General relativity states Newtonian gravity is not quite correct. It predicts that from far from the Sun, gravity is essentially Newtonian but near the Sun, it is slightly stronger

What does Equivalence principle show us?

General relativity will somehow be connected to gravity. It predicts new non-Newtonian phenomena such as bending of light near a massive body. It allowed Einstein to focus entirely on motion when discussing gravity.

_______dictates the _________

Geometry, orbit

What does the theory of relativity describe? Why is it "special?" Why is "relativity" used?

How motion affects our measurements of distance and time. Someone moving in a different way would measure different lengths for objects and different duration of events. It is special because it does not include the effects of gravity. Relativity is used because one of the key ideas of the theory is that all measurements are made relative to an observer.

Apply general relativity to Precession of Mercury's orbit

If there is one planet that orbits the Sun...Newtonian gravity demands that its orbit is a closed never changing ellipse. But each planet's orbit is distrubed by gravity of all the other planets, so each planets orbit "rotates" over time

What do we notice when we send a probe to the event horizon?

If we observe pulsed light signals coming from the probe as it approaches event horizon, we notice: 1) slowing of time 2) gravitational red-shift

What does equivalence principle say?

That in small volume of space, the downward pull of gravity can be accurately and completely duplicated by an upward acceleration of the observer.

What does general relativity tell us about a body like Earth?

That massive body distorts space AND time around it so these distortions then dictate the orbit of the Moon.

What is length contraction?

The length of an object depends on how that object is moving. The faster it moves, shorter its length along along its direction of motion. The observed decrease in length of an object which is moving at high speeds. An observer at rest measures the length of moving objects to be shorter. Effect is noticeable only at very high speeds, near the speed of light.

Slowing of clocks by gravity

When gravity slows down, clock speed increases

What is gravitational red-shift

When light moves away from a massive object like a white dwarf or neutron star, it loses energy Coordinate grids are stretched more and more near the sun. The wavelength increases, thus energy decreases Probe falls, light reaching you from the probe is shifted to longer and longer wavelengths.

What happens if Astronaut falls along event horizon with probe?

Wouldnt notice anything unusaul about her clock. She sees herself cross the horizon without noticing gravity. Molecules proceed to the singularity.

Can stars be observed orbiting a massive but unseen objective at the galactic center?

Yes. It is thought that every galaxy has a super black hole at its center.