1. This Week Today: Wednesday Friday: We finish up with Gravity
Launch into unit on Conservation of Energy
Wednesday
Problem Sets Due
Quiz!
Details at click on syllabus, click on lecture CMG5
Friday:
More on Conservation of Energy
Then enjoy spring break!
1/3/2019
Physics 253

2. The Concept of the Field
Contact forces are quite common and easy to understand…friction, tension, normal..
However forces at a distance such as gravity and electromagnetism are counter-intuitive.
An alternative is to consider a “field” in which a body is immersed and which exerts a force on the body.
This concept was first developed by Michael Faraday to explain electromagnetism
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Physics 253

3. The Gravitational Field
A body with mass sets up a surrounding gravitational field
A second nearby body interacts with the gravitation field and experiences a force.
We’ve gotten away from action at a distance, but now are obligated to describe and define that field.
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Physics 253

4. The Gravitational Field
Define as the gravitation force per unit mass: g=F/m
Measured with a “test mass”, m
Units: N/kg.
If due to a single body of mass M, then
But it is a vector quantity:
Useful concept when we start to discuss work and energy
Test Mass
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Physics 253

5. The electric field that accelerates charged particles.
Some Other Fields
The electric field that accelerates charged particles.
The magnetic field that describes the magnetic lines of force.
The strong field that interacts with the constituents of nuclei.
The Higgs field which gives the fundamental particles mass.
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Physics 253

6. The Most Exotic Field: the Higgs Field
Electroweak unification postulates the existence of the Higgs field.
This field interacts with all other particles to impart mass - think of walking through molasses.
The field is a microscopic property of space-time, at least one real particle will result, as an excitation of the field.
The collider programs at Fermilab, Large Hadron Collider, and the International Linear Collider are dedicated, in part, to the search, discovery, and study of this particle.
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Physics 253

7. The Principle of Equivalence
Newton’s 2nd law defines mass to be the constant of proportionality between force and acceleration: F=ma, call it inertial mass.
But in the context of gravity we understand mass to determine the strength of gravitational force between two objects, call it gravitational mass.
There is no reason to expect them to be the same. Gravity could have been mediated by some other property of the object, like the electrical force by charge.
Experimentally inertial and gravitational mass have been shown to be equal to one part in a trillion!
Einstein named this equality the principle of equivalence. He used this as a foundation for the general theory of relativity. There is no experiment that can distinguish if acceleration arises from gravity if it arises from an accelerating reference frame.
For instance if you notice an apple “falling” in your spacecraft you would be unable to say whether it was due to a nearby gravitational field or if your spacecraft suddenly started accelerating.
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Physics 253

8. A Consequence of the Equivalence Principle: The Deflection of Light by Gravity
The experimental equivalence of the acceleration of gravity and of an inertial frame leads to the prediction that light will bend in a gravitational field.
To see this let’s perform one of Einstein’s famous “thought experiments.” Imagine:
an elevator in deep space free of gravity.
the passage of a beam of light through a window in the elevator
If the elevator is not accelerating the beam strikes the opposite side
If the elevator is accelerating the beam will seem to curve downward.
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Physics 253

9. Proof of the Equivalence Principle
But by equivalence the bending of the light could be due to a downward gravitational field.
Thus Einstein’s theories predicted that light would bend in a gravitational field.
In 1919 this was proven by observing (during an eclipse) the predicted 1.75” of arc deflection of distant starlight by the sun.
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Physics 253

10. The Curvature of Space-Time
Another pillar of Einstein’s theory of relativity was the notion that nothing can travel faster than the speed of light.
This also means that light takes the shortest and most direct route possible between any two points. (If it didn’t, some other object could travel the interval more quickly.)
But the deflection of light actually means that when passing the Sun the most direct route between a star and earth is actually curved!
Thus we can conclude that space itself is curved and that gravitational fields cause the curvation.
A useful visual analogy has space behaving like an elastic sheet with massive objects distorting the sheet.
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Physics 253

11. Black holes are so massive and the distortion of space-time so
complete that not even light
can escape and background
stars appear as smears.
1/3/2019
Physics 253