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The General Theory of Relativity

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The General Theory of Relativity

We now know that the Special Theory of Relativity provided a more accurate view of the world than had Newtonian Mechanics. Newton’s Laws are EXACTLY correct when speeds are zero, and provide very reasonable approximations when speeds are relatively small. But as speeds approach the speed of light, Newton’s ideas prove quite inadequate and The Special Theory of Relativity provides the correct model.

But, was there any area of physics that could NOT be explained by the Special Theory?

YES, Gravitation (and acceleration…The Special Theory was limited to inertial, or unaccelerated, reference frames)

A Video Clip from Nova’s “Einstein Revealed”

The Limitations of the Special Theory of Relativity and new “Gedanken” Experiments from Einstein

Einstein Revealed 6

More "Gedanken" Experiments from Einstein

Can any experiment be performed inside the spaceship to distinguish between the following situations?

Isolated Spaceship in “free space” – zero gravity

Orbiting Spaceship in ____________

free fall

NO

gravity

____! Zero _________ is “equivalent” to the ______________ of free fall.

acceleration

More "Gedanken" Experiments from Einstein

Can any experiment be performed inside the spaceship to distinguish between the following situations?

Spaceship in “free space” accelerating with a = g

Stationary spaceship in gravitational field, g

NO

Accelerating

____! ___________ spaceship is “equivalent” to stationary ship in _____________ field.

gravitational

The results of these thought experiments lead Einstein to his famous “Equivalence Principle”…

If the effects of acceleration and gravitational fields are the same, then they are equivalent. No Experiment can distinguish between them!

So… why does this matter? Where did this lead Einstein? …

A Video Clip from Nova’s “Einstein Revealed”

More Rocket “Gedanken” Experiments from Einstein

Einstein Revealed 7

One more Rocket "Gedanken" Experiment

Imagine throwing a ball in a rocket…

Rocket in “free space” (a=0)

Rocket accelerating at a = g

Now imagine turning on a flashlight instead …

Rocket in “free space” (a=0)

Rocket accelerating at a = g

To a person on the rocket, light appears to ______, an effect due to ______________… and if acceleration can bend light, then by the Equivalence Principle, so can __________!!!!!!

bend

acceleration

gravity

Back to Nova’s “Einstein Revealed”

Einstein continues to formulate his Theory of Gravity – a warping of “Space-Time”

Einstein Revealed 8

Gravity - A Warping of Space-Time

Einstein described a gravitational field as the curvature or “warping” of space-time. (Space and time are “fused together into a single, 4-dimensional picture of the world”.)

Space-Time without matter would be _____, but add a large mass such as a star, and space- time “______”.

Any mass (or light!!) that comes near the “warp” will travel down and around the warp, taking the “straightest path through the curves in space-time”.

flat

warps

A Demonstration that serves as an analogy:

- Pull a sheet taut and level … (representing space-time without matter)
- Place balls of different masses, such as a tennis ball, baseball, heavy iron ball, in middle of sheet.
- Roll a ping pong ball near the “warped” portion of the sheet and observe the path.
- How can this model of gravity explain earth’s orbit around the sun?
- Earth simply follows the __________________ created by the sun!

“space-time warp”

What would happen to earth if the sun magically disappeared?

- We would no longer orbit, but would _________________________________
- But, WHEN would we do that?
- According to Newton, ________________
- According to Einstein’s Theory of General Relativity, ____________________________ _____________________________________

fly out tangentially in a straight line.

instantaneously

in 8.3 minutes, the moment the “ripples” in space-time would reach us!

Elegant Universe – SunDisappearing

Back to Nova’s “Einstein Revealed”

The Complicated Mathematics of the Curvature of Space-Time

AND the first experimental evidence for the theory in 1915!

Einstein Revealed 9

Experimental Evidence for the General Theory of Relativity

- 1915 – Mercury’s orbit shifted slightly each year and no one understood why! Einstein was able to precisely calculate Mercury’s orbit using the mathematics of the General Theory. His calculations matched observation exactly!
- _____ is the official year that Einstein published his General Theory of Relativity, 10 years after the Special Theory.

1915

Back to Nova’s “Einstein Revealed”

More Experimental Evidence for the General Theory of Relativity… Gravity Bends Starlight - 1919!

Einstein Revealed 10

More Experimental Evidence for the General Theory of Relativity

2. 1919 – For the first time, measurements are taken that proves that a Gravitational Field bends light!

- The angle between 2 stars had been carefully measured in the night sky.
- Months later, when the stars are in the daylight sky, the angle was measured again during an eclipse. The angle was __________!

Exaggerated diagram!

larger

bent

Light from Star 1 was ______ as it passed near the _______________________ of the sun.

Gravitational Field

The Space-Time warp of the sun is ultimately responsible for this phenomena…

Exaggerated diagram!

More Recent Experimental Evidence for the General Theory of Relativity

3. Signals sent from the Viking lander on Mars have been observed by NASA to be delayed by about 100ms when Mars happens to be on the far side of the sun compared to Earth. This time is consistent with the time predicted by the General Theory as the light takes the warp in space-time.

Back to Nova’s “Einstein Revealed” for the last time!

Einstein tackles “The Unified Theory” and opposes the Atomic Bomb

Einstein Revealed 11 and 12

- The craziest application of gravity bending light is the Black Hole!
- Recall that the escape speed for any object from the surface of a body of mass, M, is given by:
- In 1783, the Reverend John Mitchell, an amateur astronomer, first hinted at the idea of a Black Hole. He noted that it would be possible for the escape speed to be _______ than the speed of light. He said, then:

greater

“All Light emitted from such a body would be made to return toward it.”

We can estimate the size of a star that will form a black hole by setting Vesc = ___. (Actually, this will give us the correct result, but the actual derivation is more complicated!)

Solving for R…

c

Rs is called the Schwarzschild Radius, after the German astronomer who developed the concept in 1916.

- Any event occurring inside this Schwarzschild radius is ________ to outside observers, since light (or anything else) cannot escape!
- The surface of the sphere with radius, Rs, is called the ______________ of the Black Hole.

invisible

Event Horizon

What Determines whether a Star will become a Black Hole?

mass

- It depends on the ______ of the star. Current Theory suggests that a “burned-out” (not enough hydrogen left for _______ to occur) star will collapse under its own gravity to form a Black Hole if its mass is greater than ________ the mass of our sun.
- If the mass of the star is less than that amount, the star will collapse to a final radius that is __________ than the Schwarzschild Radius, and will, then, NOT form a Black Hole.

fusion

twice

larger

An Example: Calculate Rs for a star that has a mass twice that of our sun. (Msun=1.99x1030 kg)

Less than 4 miles!!

Calculate the resulting average density of the star at this point.

Comparable to the densities of atomic nuclei!!

Once a star collapses to a radius of Rs, calculations show that __________ can prevent it from collapsing further!!!

- All the mass is “crushed” down to a single point of _____ size called a _____________. This point would have ______ volume, and thus ___________ density.

NOTHING

singularity

zero

zero

infinite

- The curvature of space-time becomes ________ at this point (like a bottomless pit!)

vertical

If our sun had enough mass to become a Black Hole, what would happen to the earth?

___________! Far from the Black Hole, gravitational effects are the same as before the star became a Black Hole. The earth would continue in its orbit!

NOTHING

If all light/information from within the Event Horizon cannot escape, how can we “know” whether Black Holes actually exist?

- You might say that the evidence is “circumstantial”, but it is fairly overwhelming!
- Observations of ______ Star Systems (two stars orbiting their mutual ______ ________)....

Binary

center

of mass

We have observed a star whose spectrum shows periodic Doppler _____ shifts and _____ shifts, indicating ________ motion. BUT, no companion star is visible! Perhaps the companion star is a Black Hole!

- This alone, is NOT enough evidence, for maybe the companion star is just too faint to be observed with our telescopes…

Blue

Red

orbital

Scientific models of Black Holes predict that high frequency radiation (X-rays) should be emitted from the area outside of the Event Horizon of a Black Hole. This radiation is a product of gas/dust from the visible star being accelerated towards the Black Hole, heating up to temperatures greater than 106 Kelvin!

- These X-rays have been observed coming from the area of the “Companion Star”!

If Time… 28 minute video on Black Holes…

BlackHolesCondensed

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