Relativity

ds2 = ( 1 - ) dt2 – (1 + ) dr2 – r2 dθ2 – r2 sin2θ dφ2 “2GM

R

2GM

R

Twinkle, twinkle little star

How I wonder where you are

“1.75 seconds of arc from where I seem to be

For

Source Unknown

Relativity

Frame of Reference - A set of coordinate axes in terms of which position or movement may be specified or with reference to which physical laws may be mathematically stated. Also called reference frame.

Relativity – the study of the laws of physics in reference frames which are moving with respect to one another.

Relativity

Relativity – the study of the laws of physics in reference frames which are moving with respect to one another.

Two cases:

Case 1 (special case): reference frames move at a constant velocity with respect to each other.

Case 2 (general case): reference frames accelerate with respect to each other.

Special Relativity

Introduced in 1905 by A. Einstein

Special Relativity – the study of the laws of physics in the special case of reference frames moving at a constant velocity with respect to each other.

Inertial Reference Frame – a reference frame that moves at a constant velocity.

Special Relativity

The Postulates of Special Relativity

First postulate

Observation of physical phenomena by more than one inertial observer must result in agreement between the observers as to the nature of reality. Or, the nature of the universe must not change for an observer if their inertial state changes.

Every physical theory should look the same mathematically to every inertial observer.

To state that simply, no property of the universe will change if the observer is in motion. The laws of the universe are the same regardless of inertial frame of reference.

Second postulate (invariance of c)

The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, is the same in all directions, and does not depend on the velocity of the object emitting the light. When combined with the First Postulate, this Second Postulate is equivalent to stating that light does not require any medium (such as "aether") in which to propagate.

Special Relativity

The Postulates of Special Relativity

As a result of the second postulate, once the distance to a celestial object is know, one can determine how far in the past the event occurred.

Given the speed of light and the distance to the Large Magellanic Cloud, Supernova 1987a actually occurred 160,000 years before the observation, in about 158,000

BC !!

Special Relativity

The Postulates of Special Relativity

Furthermore, it is understood that no phenomena can travel as a speed greater than 3 x 108 m/sec

Special Relativity

The Postulates of Special Relativity

Furthermore, it is understood that no phenomena can travel as a speed greater than 3 x 108 m/sec

What about Neutrinos (September 2011)?

Special Relativity

The Postulates of Special Relativity

Furthermore, it is understood that no phenomena can travel as a speed greater than 3 x 108 m/sec

What about Neutrinos (September 2011)?

Probably not.

General Relativity

Introduced in 1916 by A. Einstein

General Relativity – the study of the laws of physics in the general case of reference frames accelerating with respect to each other.

Non-Inertial Reference Frame – a reference frame that accelerates.

General Relativity – A Thought Experiment

Scale reads 170 lb

?

General Relativity – A Thought Experiment

g = 9.8 m/sec2

Scale reads 170 lb

Scale reads 170 lb

??

General Relativity – A Thought Experiment

a = 9.8 m/sec2

Scale reads 170 lb

Scale reads 170 lb

? ?

General Relativity – A Thought Experiment

g = 9.8 m/sec2

Scale reads 170 lb

a = 9.8 m/sec2

Scale reads 170 lb

Scale reads 170 lb

?? ?

General Relativity – A Thought Experiment

g = 9.8 m/sec2

Scale reads 170 lb

a = 9.8 m/sec2

Scale reads 170 lb

Scale reads 170 lb

?? ?

The Principle of Equivalency

General Relativity

Principle of Equivalency - Experiments performed in a uniformly accelerating (non-inertial) reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating (inertial) reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a.

General Relativity

Principle of Equivalency

2001 A Space Odyssey

General Relativity

Principle of Equivalency - Experiments performed in a uniformly accelerating (non-inertial) reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating (inertial) reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a.

2001 A Space Odyssey

General RelativityPrinciple of Equivalency

Centripetal Generotor at COSI

General RelativityPrinciple of Equivalency - Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a.

Centripetal Generotor at COSI

When riding the Centripetal Generotor, you spin slowly at first, while increasing velocity. The force eventually pins you to the wall as the floor drops away. At about 3 g’s or 33 rpm's, the centripetal force is strong enough to make the static friction greater than the force of gravity, so when the floor drops away, you stick to the wall. When the rotor’s speed decreases, so does the centripetal force and the static friction, and you slide to the floor.

General Relativity

How is the Generotor G-force calculated?

The force of Gravity (G) on Earth is used as a baseline for measuring these forces of acceleration. The force of gravity when you sit, stand, or lie down is considered 1 G. In normal activity, we rarely experience anything other than 1 G. As you exert more G's on the body, your weight increases correspondingly. Your 10-pound head will weigh 90 pounds when you pull 9 G's!

If you continue to pull high G's, the G force will push the blood in your body towards your feet and resist your heart's attempts to pump it back up to your brain. You will begin to get tunnel vision, then things will lose color and turn white, and finally everything will go black. You've just experienced the onset of Gravity Induced Loss of Consciousness (GLOC). Riding the Generotor will not result in GLOC.

Generotor G-force Calculations

1) The speed of the Generotor: 1 revolution / 1.82 seconds = 33 rpm (rotations per minute)

2) The Generotor's drum radius = 7.5 feet or 2.29 meters.

3) This translates to: speed = 2 x π x 2.29 / 1.82 sec = 7.9 m/s (meters per second)

4) Acceleration = speed x speed / radius = 7.9m/s x 7.9m/s / 2.29m = 27.3 (m/s)s

5) Since 1 G = 9.8 (m/s)s = 27.3(m/s)s / 9.8 (m/s)s = the G force of 2.8G, which is ~ 3G's

Example

See http://www.cosi.org/visitors/exhibits/big-science-park/generotor/

General Relativity

General Relativity

Implication of the Principle of Equivalency – photons should experience a gravitational force just like all other particles.

The deflection is not observed under “normal” (ie, earth) gravitational fields because the photons move to fast.

In order to observe the deflection of a photon, a large gravitational field is required.

Because of the Principle of Equivalency, General Relativity is often referred to as

the study of gravity

Accelerating Systems and Photons

General Relativity

Experimental test

Einstein wrong

Einstein right

True Position

Apparent Position

General Relativity

Experimental test – Einstein proposed that the deflection of light from a star could be measured during a solar eclipse for a star near the edge of the sun during an eclipse.

Einstein wrong

Einstein right

True Position

Apparent Position

General Relativity

It is common wisdom now that the determination of the defelction of light from a star during the solar eclipse in 1919 by Arthur Eddington and his group was the second observational confirmation of General Relativity and the basis of Einstein's huge popularity starting in the 1920s. (The first one had been the explanation of Mercury's perihelion shift.) Recently, the value predicted by Einstein was confirmed to an accuracy better than 0.02% [104].

The position of the star was off by 1.75 seconds of arc

Relativity

ds2 = ( 1 - ) dt2 – (1 + ) dr2 – r2 dθ2 – r2 sin2θ dφ2 “2GM

R

2GM

R

Twinkle, twinkle little star

How I wonder where you are

“1.75 seconds of arc from where I seem to be

For

Source Unknown