1/25/00:

1) A number of you still have difficulty with a distinction I emphasised at our first class meeting - the difference between

2) Since lines of force tell you the unique direction that a force would act IF a body were present, they may not cross each other since thatwould mean two different directions at that point. Electrical lines of force go from positive to negative or to infinity - they do NOT go from positive to positive or from nagative to negative. Similarly fro magnetic lines of force. Since gravity is always attractive, gravitational lines of force would go from body to body.

3) "Action-at -a-distance" was too "spooky" for physicists who were trying to get away from angels and Aristotle. They thought of physical forces as pushs or pulls, between bodies touching each other ; they were always looking for a "mechanism" by which one body influenced another. They knew that masses influence (attract) each other (gravity), that charged bodies influence (attract or repell) each other (electrical force), and that magnets influence (attract or repell) each other (magnetism), but what was the "mechanism - angels???? Newton had no answer (he ruled out angels!) so just kept quite - his mathematical inverse-square-law worked, even if he couldn't explain it. The field explanation of Faraday and Maxwell got rid of the spookiness by providing a "connection" between the two interacting bodies; even if you couldn't "see" the field, you could confirm its existence indirectly via the laws of conservation of momentum and conservation of energy. Of course, if you didn't believe in these laws then you didn't "see" the field.

4) A number of you missed some of the similarities and differences between gravitational, electrical, and magnetic phenomena. All of them take place between separated bodies with no obvious physical contact between them. All three effects fall off with the inverse-square of the distance between the bodies. Gravity is only attractive whereas the other two can be either attractive or repulsive. The entities effected by gravity and electrical forces - masses and charge - can appear as isolated bodies whereas magnetic poles always occur in pairs. Electrical and magnetic effects seem to be intertwined, both independent (so far as we now know) from gravitational effects. All three can be "explained" either as "action-at -a-distance" or as field phenomena, with separate gravitational, electic, and magnetic fields, though the latter two are not independent of each other.

5)You all confuse sound waves and electromagnetic wave!

6) It is true that , as the speeding police car gets closer to you, its siren sounds louder (the waves have a bigger

**Comments on IQs for Wednesday, January 26:**

1) (E,p263) In general, the sounds from the two speakers of a stereo
don't have the same wavelength and are not "coherent" = coordinated = definite
relations between their respective crests, etc. So there is no interference
in general. If there were some instants when conditions for interference
existed, and the leads were interchanged, constructive interference would
become destructive and vuce-versa.

(#6, p.263) Generally, time of travel is distance traveled divided
by speed of travel Thus:

(a) Light-3km/300,000 km/s (3km/ 3*10^{5} km/s) = 1*10^{-5}
s = 0.00001 seconds, certainly not very noticeable.

(b) Sound-3km/0.340km/s = 3,000m/340 m/s =8.82 seconds, a very noticeable
time. Thus you see the flash long before you hear it.

(#7, p.263)(a) The fundemental note on a string only has nodes
at the ends of string, 1 meter apart in this case. Since the wavelength
is twice the distance between nodes, the wavelength is 2 meters.
(b) Since the wave velocity is the product of the frequency and the wavelength,
the speed is 440Hz*2m = 880 m/s (since 1 Hz = 1 s^{-1}).

2) If you will look at Fig 7-10, page 89 of the March text, you will
see that the wave length of microwaves is greater than that of infra-red,
the frequency of microwaves less than that of infr-red. Your stove gives
off infra-red radiation, your microwave oven obviously uses microwaves.
The fact that the latter, in some cases, cooks faster than the former has
nothing to do with which frequency is greater but with which frequency
is more in resonance with the molecular vibration frequencies of the food
being cooked.

**Communication with Students**
**4 February, 2000**

A number of you had difficulty with today’s IQ. Here are some
answers:

a)

Jane says Joe is 100miles*cosine(10^{o}) = 98.4miles North,
100miles*sine(10^{o}) = 17.4miles east of her.

Joe says Jane is 100 miles South, 0 miles east of him.

They both agree that they are a distance of 100 miles = Square root
[(98.4)^{2} + (17.4)^{2}] apart.

b) For this problem, gamma = 3.20.

Thus, while Jane thinks it takes 30 minutes for her breakfast, Joe
thinks it takes 30*3.20 = 96.1 minutes.

While Jane thinks it takes 15 minutes to walk back, Joe thinks it takes
15*3.20 = 48 minutes.

While Jane thinks she has walked a distance of 0.5 km, Joe thinks she
has walked 0.5/3.20= 0.16km.

They will agree on “proper times”(rest times) and “proper lengths”
( rest times). For example, J ane thinks she is at rest while eating:
delta x = 0, delta t = 30 minutes = 1800seconds.

For Joe, delta t’ = 96.1 minutes = 5.77*10^{3} seconds and
during this time she has moved (with her space ship) a distance of delta
x’ = 0.95c*96.1 minutes = 1.64*10^{12} meters (distamce = speed
*time) . If you calculate Joe’s space -time interval, you get

(1.64*1012 meters)^{2} - (c*5.77*10^{3} seconds)^{2}
= - 3.0*10^{23} meters squared.

Jane’s space-time interval is just - (c*1800 seconds)^{2} =
- 2.910^{23} which is the same number, given rounding errors.
Thus the two space-time intervals are both the same, time-like, both proper
times.

Try doing the same kind of calculation for her walk - its somewhat
more complicated, but again you get an agreed upon space-time interval,
this time, space-like.

**7 February 2000**

**BRINGING TOGETHER SEEMINGLY OPPOSING CONCEPTS**
**SOMETIMES LEADS TO INTERESTING NEW UNDERSTANDINGS**

**Concept Very different
concept Matchmaker
New Understanding**
**_____________________________________________________________________**

Terrestrial Physics Celestial Physics
Galileo
“New” Physics

Falling Apple Falling Moon Newton Universal Gravitation

Inter-particle forces -Action-at-a-distance Faraday Field lines

Electricity Motion Oersted Magnetism

Electricity Magnetism Maxwell Electromagnetic Fields

Galilean Relativity- Maxwell’s Equations Einstein Special Relativity

Space Time Einstein Space-Time

Lorentz Contraction -Time Dilation
Einstein
Same Phenomenon-

Different Explanations

Mass Energy Einstein Creation of matter and the universe

Cons. of Energy -Cons. of Momentum
Einstein
Cons.of 4-Momentum

Rest mass as invarient

Special Relativity -Gravitation Einstein General Relativity

General Relativity- Hubble Expansion Gamow et al “Big Bang”

Particles Waves Schrodinger,etc Quantum Mechanics

Quantum Mechanics -Special Relativity Dirac, et al Quantum Field Theory

Electromagnetism -Weak Interactions Gell Man et al Electroweak Theory

Strong Interactions -Electroweak Theory Gell Man et al “Standard Theory”

General Relativity-Quantum Mechanics
many
String Theory?