10. HISTORICAL
PHYSICS
10.1 The history of mechanics
I. Aristotelian mechanics
Motion is separated into:
Natural motion is
There are four elements:
The rock dropped from rest would fall towards
earth because it seeks its natural place, flames from a fire would similarly
rise up. Objects may be mixtures of the four basic elements and have natural
places somewhere in between. Example: If we drop a red-hot coal (mixture of
earth and fire) into water some of it turns to steam (= mixture of water and
fire) and therefore rises upwards higher than pure water would.
[In
ancient times there were also discussions about a fifth element, a
quintessence, to complete the number of elements to 5 like the then visible
planets and the regular geometrical bodies. This also had something to do with
a pentatonic scale for music and the 'harmony of the spheres']
Outside the mentioned spheres were those of the
celestial bodies (moon, sun, 5 planets, stars) for which exceptionally the natural
motion was circular, except for the stars which were at rest.
Terrestrial and celestial physics
Physics was divided into one set of laws for
terrestrial (sublunar) objects, and one for celestial objects (where as
mentioned the natural place and motion for planets, made of the element earth,
was not the same as for objects made of the same element in the terrestrial
spheres).
Aristotle on mass and gravity
According to Aristotle, there was a stronger
'gravity' (urge to follow the natural motion of earth-element objects towards
their natural place) on heavier objects than on lighter ones. This happens via
interaction with the air or other element around the falling object. If there
was no air around it, every rock would have the same acceleration towards
earth. For this reason (according to Aristotle) vacuum does not exist, the
nature abhors vacuum.
Middle Age developments of Aristotelian
mechanics
One obvious problem with all this is that an
object that has been pushed does not always stop immediately after we stop
pushing (especially on ice) and one thrown upwards will continue up for a while
after leaving the throwing hand. When the pushing force stops, the object
should immediately return from unnatural to natural motion. This was later
explained with a concept called 'impetus', something (invisible) that the pusher
gave to the pushed object and which kept it moving for some time until the
object (for some reason) ran out of 'impetus'.
II. Newtonian ("classical") mechanics
The developed versions of Aristotelian
mechanics were gradually abandoned a few centuries ago.
Galileo (1564-1642) and "the birth of the
scientific method"
Galileo used experiments as a foundation for
theory to a higher degree than Aristotle. On the subject of natural motion for
earth-element objects in the terrestrial sphere he investigated:
From this he made the "idealisation"
that if there was no medium (vacuum) then objects would fall with the same
acceleration, and if there was no friction they would keep sliding. This has
later on been verified by astronauts dropping a feather and a metal object on
the moon.
[But the strength of Galileo's method was that
it allowed him to correctly predict the result without actually travelling to
the moon. In modern astrophysics we can, in a similar way, claim to know
something about distant objects without actually travelling to them and do
experiments on site. In geology and palaeontology we can find out things about
dinosaurs without first building a time machine and travelling to meet them. We
also can meaningfully discuss the environmental impact of various planned
projects and technologies beforehand. The pedagogical idea that we need to find
out everything through immediate experience disregards idealisation as
an essential part of the scientific method. We do therefore not need to let
students see pieces of paper and metal balls fall in a vacuum tube as a part of
Mechanics.]
Galileo also used mathematics to describe
measurements, e.g. that if something is accelerating for twice the time then
the distance covered will be four times greater. Because Galileo did not have
modern stopwatches or data-logging equipment he studied accelerated motion
using balls rolling from rest in an inclined groove (Sw. ränna) rather then
vertically falling objects. This also hade the effect of almost removing
friction as a significant phenomenon, since the force of rolling friction on a
heavy metal ball in a smooth groove is negligible compared to the downslop
component of the force of gravity.
The Galilean scientific method can be summed up
as:
The mechanical investigations of Galileo were
done after his conflict with the Roman Catholic Church (RCC) made it impossible
to continue the cosmological work. These experiments seemed harmless at the
time, but the scientific method in them and the path to Newtonian mechanics
that they opened up would soon cause insurmountable problems for the RCC's
view.
Descartes or Cartesius (1595-1650)
He developed analytical geometry, the way to
describe geometrical bodies and figures with algebraic equations. This would be
very useful in the development of modern science. In physics he formulated a
law of inertia very similar to Newton's first law - that the 'natural' thing
for an object to do is to remain in uniform motion (although this was not part
of a coherent system like Newton's).
Newton (1643-1727)
Newton's laws are hopefully familiar:
I: An object remains at rest or in uniform
motion if no resultant force acts on it.
II: If there is a resultant force, the
acceleration follows F = ma
III: For every force exerted on another object
there is an equally big reaction force in the opposite direction, acting back
on the first object.
Differences to Aristotelian mechanics:
Newton (in parallel with Leibnitz) also
developed new mathematical tools to describe the effects of his theory on the motion
of planets (calculus: derivatives and integrals).
[Newtonian calculus has by mathematicians been
viewed as not as strictly proven as later developments (19th century) but
physicists have always known that simpled forms of calculus always work as well.
This has recently been more strictly proven (non-standard or Robinsonian
analysis, from the 1960s onwards].
III. Einsteinian mechanics (not required in the IB)
See the Relativity option.
Mechanical determinism
In Newtonian or classical physics, it would in
principle be possible to completely predict the future behaviour of any system
of objects if the initial conditions and the forces between the objects are
known. In "modern" physics this has been shown impossible in two
ways:
10.2 Astronomy
[Describing astronomic observations - from
the Astrophysics topic]
The easiest way to describe where a
star has been observed is to use the azimuth, Az (0 or 360o
for north, 90 for east, 180 for south, 270 for west) and the altitude, Alt
(angle up from the horizon, that is 0o at the horizon and 90o for
zenith = the direction vertically upwards). This system, however, depends on
where on earth the observation was made, and when.
Another system which is independent
of the time and place of observation is the right ascension (RA) and declination
(Dec) system. It is more useful for communicating discoveries with others.
Conversions between the systems are made conveniently with astronomic software,
e.g. the freeware SkyMap demo version (www.skymap.com).]
Stars
As the earth rotates once in ca 24 hours, the
stars seem to rotate in arcs or circles around a celestial pole, in the direction
where an imagined axis from the south to the north pole points. Near this point
is the star Polaris in Ursa Minor. For this reason, the altitude of Polaris is
approximately the same as the latitude of the observation location, and the
star has been used for simple navigation.
[Because of the precession of earth's axis,
Polaris has not always been and will not always be close the the north
celestial pole. The advent of oceanic navigation in the Middle Ages coincided
with the approach of Polaris to the cel. pole. In the ancient world, the
difference between was larger and 'precise' navigation more difficult.
Finding the longitude was a more difficult
problem. It can be done from lunar observations but few sea captains were able
to perform the needed calculations - James Cook being an exception. With the
construction of modern chronometers (Harrison) in the late 1700s, longitude
measurements without prohibitively difficult calculations were made possible]
Sun
The maximum altitude of the sun depends on the
time of year and the location. In the winter, the maximum altitude (at noon) is
lower; near the poles (inside the polar circles at ca 66.5o
latitude) there are times when it never rises or sets. It reaches zenith at
some time during the year in a belt around the equator inside the 23.5o
- latitude lines. These are called tropics (Sw. vändkrets, Fi.
kääntöpiiri) of Cancer (Sw. Kräftan) and Capricorn (Sw. Stenbocken).
Moon
The moon revolves the earth in a lunar month,
ca 29.5 days. It always turns the same side towards the earth (though since the
orbit is not perfectly circular we see a little more than 50 % of its surface).
At full moon the whole surface is illuminated by the sun; the moon is then
further from the sun than earth. At new moon the opposite occurs. Rule of
thumb: When the phase of the moon is changing from new to full - the moon is 'coming'
- the crescent is shaped like a comma sign.
The orbit of the moon is approximately but not
precisely in the same plane as the earth's around the sun. Therefore the
crescent looks more vertical here in Finland than it did on your way home from
the disco at the Mediterranean holiday destination. (NO, this was not because
you were so p-ssed!)
When the moon blocks the sunlight (partially or
totally) we have a solar eclipse (Sw. solförmörkelse, Fi. auringonpimennys);
when the earth blocks the sunlight on its way to the moon we have a lunar
eclipse.
Planets
Some "stars" appear to be moving
around in a different way from others. In addition to the circular motion
around the celestial pole they move from night to night compared to the
background of ordinary stars. Five such planets are visible to the naked eye
(and this lead ancient philosophers to make deep comparisons to the five
regular geometric objects, the cube, tetraeder, octaeder, dodekaeder,
ikosaeder).
They also appear to make "loops"
(called retrograde motion) against the star background, which needed
some explanation (see below).
10.3. Models of the universe
Mechanics
and astronomy
There are numerous connections between
astronomy (or astrophysics) and other fields of physics. One of the most
important ideas of modern physics is that the same laws of physics are valid both
here on earth and far out in the universe. Based on this idea, we can find the
temperature of a distant star without actually travelling to it by measuring
the wavelength of light it emits and assume that the same relation between this
and the temperature is valid for it as here on earth (e.g. very hot objects
glow red, even hotter ones white). But this idea has not always been used.
The
Aristotelian/Ptolemaic geocentric model
of the universe
This model was suggested by Aristotle (384-322
BC) and Ptolemy (85-165 AD) and was adopted by the medieval Catholic church as
the true model of the universe.
This model of the universe was geocentric
- the earth was in the center (as it according to its adherents should, since
this is where we humans live, and we are the most important part of creation).
Around the earth rotated, in perfect circles (since the heavens had to be
perfect, and the circle was the most perfect geometric curve):
The observed motions of the heavenly bodies was
explained by them moving around the earth. The retrograde motion of the planets
was explained with epicycles, that is i.e. Mars would not only move in a
circular orbit around earth but also at the same time in a smaller circle
around a point on the first and bigger circle.
See
http://www.astro.utoronto.ca/~zhu/ast210/both.html
The
Aristarchian/Copernican (heliocentric)
model of the universe
This model was suggested by Aristarchus of
Samos (310-230 BC) and in modern times Nicolaus Copernicus (1473-1543). It was heliocentric,
that the the center of the universe, if any, is in or very near the sun. In
circular orbits around it followed then the then known five planets with the
moon rotating around the earth. Furthest out, and a lot further from the sun
than any of the above were the stars. The retrograde motion were
explained by the earth and Mars revolving around the sun in different time
periods. Problems with the heliocentric motion.
Arguments for the heliocentric model:
Arguments against the heliocentric model
Brahe - supplier of accurate observational data
Tycho Brahe (1546 - 1601) first became
convinced by the Copernican heliocentric model but since he despite careful
astronomical observations found no parallax instead suggested a modified
version of the geocentric model: with the earth in the center and the moon and
the sun revolving around the earth, but the rest of the planets revolving
around the sun instead of the earth. He made a large number of observations
that were helpful to later scientists, especially his assistant Kepler.
Kepler - from circles to ellipses
Johannes Kepler (1571-1630) continued Brahe's
work and thanks to the amount of good data was able find that a geocentric
model with the planets moving in ellipses rather circles was the best fit to
the available data. Recall Kepler's 3 laws from Mechanics:
I. The planets move in ellipses around the sun,
with the sun in one focal point.
II. A line joining the planet and the sun will
sweep over the same area in the same time (so the planet will move faster near
the sun (perihelium) and slower far from it (apohelium).
III. The ratio between the square of the time
of revolution and the cube of the radius is constant (if the ellipse is
approximated to a circle).
Galileo - found the moons of Jupiter
Galileo Galilei (1564-1642) found mountains on
the moon and four small moons orbiting around the planet Jupiter in ca 1610. He
also found the rings of Saturn and the moon-like phases of Venus. All these
spoke agains the heliocentric model - the Jovian moons orbiting something else
than earth, the moon mountains showing that it was not as a heavenly body
"should" be a perfect sphere, and the Veneric phases which could not
be fit into any geocentric model of the universe.
The catholic church forced Galileo to recant
from his views and he later worked with the less controversial mechanics of
falling and rolling balls, which however contributed to the development of
mechanics which was later to be used also in astronomical models.
A problem in the early stages of the
development of the heliocentric model was the question of whether observations
made by a telescope rather than with the naked eye could be trusted in the
absence of a good theory of optics which would show how they could magnify the
image of a planet. Such a teory was developed by Christian Huygens (1629-1695),
see later.
Newton's synthesis of earthbound and heavenly
motion
Newton's (1643-1727) laws of mechanics were the
same for objects on earth and objects in space ("the heavens"). He
showed that if the force of gravity universally follows an inverse-square
law then the planetary orbits must be elliptic and the laws of Kepler correct.
Later developments (not required in the IB)
Edmond Halley (1656-1742) studied observations of
comets and by applying the same theory of elliptical orbits as above in 1705
correctly predicted the appearance of one that bears his name in 1758, after
his death. This further supported belief in Newtonian universal mechanics as
the best explanation for how astronomical objects move.
With new and more powerful telescopes William
Herschel discovered the first planet not known in ancient times, Uranus,
in 1781. A sixth planet further upset the idea of a connection between the five
of them and the five regular geometric bodies. It also more or less followed
Kepler's laws and Newtonian mechanics, but as observations and calculations
grew more and more precise, not well enough. A suggestion that the disturbances
in the orbits of the outer planets were caused by a yet undiscovered one led to
predictions of where it should be observed. The predictions were confirmed and
the planet Neptune discovered in 1846. In a similar way, Pluto
was found in 1930.
The orbit of the planet Mercury also did not
quite follow the standard theory and in the same way as for the outer planets
another one even closer to the sun was predicted and tentatively named Vulcan.
These discrepancies were however explained by Einstein's theory of relativity
as distortions in space-time caused by the strong gravitational field of the
sun.
10.4 The history of thermal physics
The
phlogiston theory of burning
(combustion)
Today the atomic theory is an important part of
the explanations in most areas of physics and chemistry. When something burns -
e.g. C + O2 -> CO2 - (or oxidises like rusting iron)
we explain it as atoms forming chemical bonds with oxygen atoms. The heat that
flows as a result and the increasing temeperatures in the surroundings of a
burning material is explained with kinetic of the atoms or molecules involved.
But the atomic theory became a part of standard modern science in the 1800s, so
before that other explanations were used.
Burning was then (in the 1700s) explained with
the help of phlogiston, an invisible fluid which combustible materials
contained. When something is burning, the phlogiston is released into the air.
This would explain why the ashes left over after wood has been burned weigh
less than the original wood. (We would say that wood contains carbon, and much
of that carbon went up with the smoke as CO2). Materials that could
not burn did not contain phlogiston. The combustion process would eventually
stop either because the burning material ran out of phlogiston or because the
air around it could not absorb any more phlogiston (which is why a candle in a
closed container will go out after a while).
A problem with the phlogiston theory was that
while some materials would decrease in mass when burned, others would increase
in mass (as we would say: because the oxide that is formed is not a gas but a
solid that remains with the burned material, which then increases in mass when
oxygen have been added). Adherent of the phlogiston theory would try to explain
this that phlogiston sometimes had a positive mass and sometimes a negative
mass, but this theory of burning would towards the end of the 1700s lose ground
the the new oxygen theory, where a new invisible fluid, oxygen, would
explain all combustion processes and always have a positive mass.
Further chemical experiments resulted in the
production of pure oxygen gas (O2, but that is was composed of
molecules and atoms was not known then). Something we today know to be the
easily flammable hydrogen gas, H2, was by some consided to possibly
be pure phlogiston, but the oxygen theory gradually won support, partially
because it always had a positive mass (and nobody found any "pure
phlogiston" (H2) with a negative mass, which phlogiston
sometimes should have!); partially beacause oxygen always was involved in
combustion processes, but not necessarily the "phlogiston" (H2).
The
caloric theory of heat
The caloric was, according this theory
of what heat is, a fluid similar to phlogiston and impossible to detect with
the senses. This "substance" would feel hot and could even destroy
other materials (like acids and alkalines can do!). It was released from
burning materials at the same time as the phlogiston, but it could also be
released by other processes than burning, for example friction (which is why
friction can produce heat). Since heating by friction can be done with
non-combustible materials, caloric would be more common than phlogiston and
contained also in phlogistonless substances.
Rumford's
cannon-boring experiment
Count Rumford, originally named Benjamin
Thompson (1763-1814), noticed that large amounts of heat was released when the
gun-barrels of cannons were drilled into the solid metal pieces that were used
to make the cannons. This heat release made it necessary to keep cooling the
pieces with water. He made a smaller-scale version of this metal-drilling
experiment and noticed that the amount of heat released was unreasonably high
for the caloric theory. He concluded that the mechanical work that went into
the drilling process was all that produced the heat.
Joule's paddle-wheel experiment
James Prescott Joule (1818-1889) later
continued working with the idea of heat being a form of mechanical energy
rather than a substance. He had noticed that the water at the bottom of a
waterfall generally was warmer than at the top and concluded that the released
potential energy had been turned into heat. Several different experiment
intended to show a connection between heat and other forms of energy were done
by him. The most famous was the experiment (ca 1843) where falling weights are
used to set a paddle wheel to rotate in a vessel filled with water, where the
small temperature increase was measured. From this a quantitative
"mechanical equivalent of heat" could be calculated (more precisely
than Rumford had done). Also other experiments showing a connection between
electrical energy and heat were done by Joule.
10.5 The history of waves (not required in the
IB)
Two important themes in the history of the
physics of waves are:
10.6 The history of electricity and magnetism
Early
discoveries of electricity
In ancient times, the Greeks discovered that
phenomena of static or friction electricity could be observed when amber (Sw.
bärnsten, Fi. meripihka), in Greek elektron, was rubbed. For these basic
phenomena, review the Electricity and magnetism beginning sections:
Little of this early understanding of
electricity was achieved before William Gilbert (1544-1603) who also noticed
that the electric force was different from the magnetic force, see below. Otto
von Guericke (1602 - 1686) developed electrification by friction using an
electrostatic generator, a rotating ball of sulphur which was touched by a hand
kept stationary. Francis Hauksbee (1666-1713) developed the electrostatic
generator replacing the sulphur ball with a hollow glass ball, later a glass
tube. Stephen Gray (1670-1736) discovered that "electricity" could be
conducted and transferred to materials that could not themselves by electrified
by friction, if the conducting thread were properly insulated.
Early
discoveries of magnetism
It was long
before Gilbert discovered that some iron oxides can attract metal and adjust themselves
according to the directions north and south. Primitive lodestones, magnetic
stones, were first used, then
articificially magnetised compass needles. These were used for navigation both
on land by the Chinese and at sea, increasingly by European mariners in the
Middle Age.
Du Fay's
two fluid model of electricity
It had been observed that of the materials that
could be electrified by friction (which only insulators could) there appeared
to be two different kinds. Materials with the same "kind" of
electricity would repel each other but attract those with the other
"kind". Today we would call them positively and negatively charged
objects, but Du Fay (1698-1739) used the terms
"Electricity" was viewed as an
invisible "fluid" which could be stored in or move between objects.
Du Fay's model with two types of fluid was succesful in explaining why many
different kinds of materials could be electrified in either of two ways, which
simplified the theory from describing "electricity" as a property of
many different materials.
Franklin's
single fluid model
Benjamin Franklin (1706-1790), also known as a
politician, simplified the model further to one with only one fluid. What Du
Fay had described as two fluids was according to Franklin only the presence of
one fluid or charge (vitreous electricity, symbolised with +) or the
absence or lack of it (resinous electricity, symbolised with a -).
This model was succesful in explaining why when
objects were electrified by friction both kinds of electricity were formed, and
in equal amounts. There was no good reason for this in Du Fay's model but could
easily be explained as the result of one fluid moving from one object to another.
A difficulty in Franklin's model was to explain
why there was a (repulsive) electric force between two negatively charged
objects, if this meant that both lacked the electrif fluid.
Today's
model
Both Du Fay's and Franklin's models were
conceived at a time when the modern atomic theory was not a standard scientific
theory - this was mainly the result of work by Dalton and others in the 1800s.
The charged particles such as electrons and protons were discovered even later.
Today's model otherwise includes aspects of both the two-fluid and one-fluid
models:
At the most fundamental level, what we have is
a two-charge model: positive and negative electric charge are equally
fundamental properties of matter. Positive charge is found in e.g. up-quarks
and positrons, negative in down-quarks and electrons. On a more practical
level, most movement of charge is taken care of by the negative electrons,
since they are situated in the outer part of an atom and are most easily
affected. In this way we have a one-charge model for many practical
applications - positive net charge is caused by a lack of electrons, negative
net charge by a surplus of electrons. But all the time there are the positive
charges in the atomic nuclei in the background.
Regrettably, the kind of electricity Franklin
called negative was that of the electron, which means that many electric rules
since are defined starting from positive charges that more seldom are involved
in practical situations.
Inverse square law for electrostatic force: Franklin/Priestley's
indirect method
The attractive or repulsive electric force F
between two charges q1 and q2 at the distance r from is given by Coulomb's law:
F = kq1q2/r2
Very early in the history of electricity had it
been noticed that the electric forces grew weaker with increasing distance and
that they were stronger the more frictional electrification had been done. A
first indication of an inverse square law (that is, that F is proportional to
1/r2) was given by an experiment done by Frankling in 1755 and
repeated by Joseph Priestley in 1766:
A ball of cork hanging in a thread could be
used to indicate the presence of an electric force. But if a hollow vessel was
charged, the hanging cork ball indicated that no electric force was acting on
it inside the vessel - not only in the center of it, but in all points inside
it. In the study of the force of gravity it had earlier been proven
mathematically that this is true if and only if the force follows an inverse
square law. This was an indirect method of showing that such a law
should be true also for the electric force.
Inverse square law for electrostatic force:
Coulomb's direct method
Charles Coulomb (1736-1806) used a more direct
method of investigating the relation between electric force and the
distance between charges used the turning angle that very small forces (or
torques) caused in a thread to measure force. The amount of charge was not
directly measured, but by taking one charged metal object and letting it touch
an uncharged identical one, the charge in both would presumably be half of what
it originally was in one object. Repeating the procedure would then give 1/4,
1/8, ... of the original charge. In this way a quantitative measurement (albeit
with the charge in an arbitrary unit) could be made. The result supported the
inverse square law.
Electricity
and magnetism - two forces or one?
So far electricity and magnetism had been
viewed as two different forces, although some indications of a connection between
them had been noted, e.g. that lightning strikes (an electrical phenomenon)
could distort the magnetic compass needles of a ship. Strong magnets could also
distort the light arc of an electric discharge phenomenon.
There were two problems in finding clearer
connections between electricity and magnetism:
Oersted's experiment 1820: current-carrying
wire and compass needle
Hans Christian Oersted (1777-1851) was
influenced by the philosophy of Kant and thought (for philosophical rather than
scientific reasons) that all physical phenomena (electricity, magnetism, heat,
light, chemical bonding forces, gravity etc) were related to each other.
It had earlier been noted that electric current
could make a wire hot, and even make it glow and emit light. In 1820 Oersted performed
an experiment intended to show that there was a connection between light and
magnetism, by letting a compass be in the vicinity of a glowing
current-carrying wire. It seemed like the wire did have some effect on the
compass needle, but it was very small and not very convincing. The experiment
was then abandoned as a failure for some time.
As we now know, the problem was that to get a
wire to glow it had to be rather thin to make its resistance high, and
therefore the current (which affects the strength of the magnetic field!) was
low. A few months later the experiment was done again, with a thicker wire with
lower resistance, allowing a higher current to pass when connected to a
primitive battery. It is unclear if it was intentional or if the result was
observed by accident.
Ampere: quantifying the phenomenon
André Marie Ampère (1775-1836) was first
involved in mathematics and later in chemistry and physics. He defined voltage
and current quantitatively as we do today and also found proofs that the
magnetic force between two parallel current-carrying wires was proportional to
the product of the currents and inversely proportional to the distance between
them:
F µ I1I2/r
These proofs involved both experimental and
mathematical parts: Ampere had discovered that current-carrying coils and
solenoids act like permanent magnets; by letting them turn on an axis and
varying the distances involved it was possible to show that the magnetic force
caused by a small (in principle infinitesimal) "current element"
followed an inverse-square law (µ1/r2); by integration the
force on a whole wire or loop would then follow an inverse law (µ1/r).
The phenomenon of currents in a solenoid
causing magnetic fields in and around them made it possible to construct sensitive
instruments like the galvanometer (a magnet attached to a needle inside
solenoid) to detect and measure electric currents.
Faraday
and the electromagnetic induction
When the magnetic effects of currents were
discovered in 1820, the search for the inverse phenomenon - magnets causing
electric currents - started. The difficulty was that the researchers did not
realise that it was changing magnetic fields that could induce a
current.
Typical experiments involved inserting a
permanent bar magnet into a solenoid connected to a galvanometer or creating a
magnetic field with one current-carrying solenoid near another solenoid where
the presence of any current would be measured (similar to a primitive
transformer). But if the magnet was at rest or the current in the
"primary" of the "transformer" was DC, then no current
would be induced except at the moment of inserting the magnet or closing the
"primary" circuit. These phenomena were first dismissed as
disturbances and only the negative result, the absence of an induced current
when the experiment was running, noted. Since the galvanometer would be very
sensitive to magnetic fields it was sometimes placed in a different room, and
connected to the test solenoid with long wires. By the time the experimenter
had inserted the magnet or closed the "primary" circuit and moved to
the galvanometer room, the initial indication on the galvanometer needle had
often died out!
Eventually Michael Faraday (1791-1867) in 1831
used so strong a battery (Volta pile) and an iron core in the
"transformer" that the galvanometer needle reacted in a way to
violent to ignore. Also the corresponding effect of moving a bar magnet in a
solenoid was observed by Faraday shortly thereafter. Faraday constructed a type
of generator.
Based on these effects, simple versions of what
we would call generators and motors were built, and all this lead to
electricity becoming gradually cheaper and more important during the second
half of the 1800s.
Modern
physics: relativity unifies electricity and magnetism (not required in the IB)
Today we can describe magnetism as a
relativistic distortion of electric phenomena. In the simplest case, we have
two parallel current-carrying wires, A and B. In these we have the easily moved
negative (N) outer-shell electrons, call them AN and BN and the stationary
remaining positive (P) ions AP and BP. Between the wires there will be four
electric forces
1. AP-BP (repulsive) 2. AP-BN (attractive) 3.
AN-BP (attr.) 4. AN-BN
(rep.)
The magnitude of each force depends, among
other things, on the linear charge density = the number of charges per length
of wire, for some arbitrary chosen length that we study.
Case I: No current in either wire: the
repulsive and attractive forces balance out.
Case II: A current flows in one wire, say wire
A, but not in wire B. Then AN are moving but BP are at rest (or vice versa,
depending on which is chosen as the rest frame) so relativistic length
contraction decreases the chosen length of wire, which increases the linear
charge density and the attractive force AN-BP. However, the repulsive
AN-BN-force is also increased for the same reason, so the resultant force is
still zero.
Case III: Currents (assume for simplicity
equally strong) flow in both A and B, in the same direction. Now the attractive
forces AN-BP and AP-BN are increased but the repulsive AP-BP and AN-BN
are unaffected since these are between charges at rest relative to each other.
Therefore there will be a resultant attractive force between the wires.
Case III: Currents flow in both A and B, in
opposite directions. Now the attractive AN-BP and and AP-BN are increased as
before, and the repulsive AP-BP unaffected as always. Counterintuitively, the
repulsive AN-BN is increased so much (the relative velocities of the electrons
moving in opposite directions is higher than that between moving electrons and
stationary positive ions) that there is a resultant repulsive force between the
wires.
10.7 Electrons, protons and neutrons
Atoms
As seen earlier, the model of materia as
consisting of small particles, atoms, plays an important role in many areas of
physics. The development of the atomic theory itself during the 1800s is not
required here, but an interesting theme for investigations involving the
history of both physics and chemistry. Here we will focus on the developments
leading to the discovery of smaller parts of the atom - electrons, protons and
neutrons - and the inner structure of the atom. Many of these issues have
earlier been presented in the Atomic, Nuclear and Quantum physics topic.
Cathode
rays (= electrons)
Around the mid-1800s good vacuum pumps had been
developed which made it possible to study the behaviour of electricity in
(almost) vacuum. In an evacuated glass tube, two electrodes were inserted
through air-tight seals; as one would do in chemistry with electrodes dipped
into a beaker the one connected to the positive pole of a voltage source was
called anode and the one to the negative pole cathode. Geissler, Pluecker,
Hittorf were among the involved persons.
It was discovered that some "rays"
were emitted from the cathode and that they could produce a visible reaction
when hitting a screen, especially one made of fluorescent materials. (The
cathode ray tube or CRT was an early version of what is today used in TV sets
and oscilloscopes).
Crookes
William Crookes showed in 1879 that the cathode
rays traveled in straight lines by putting a Maltese cross-shaped metal piece
in their way and noticing that a pattern of the same shape appeared at the end
of the tube. Crookes believed the cathode rays to be particles.
Hertz
and Lenard
Heinrich
Hertz and his student Philip Lenard did experiments which they thought
indicated that the cathode rays must be waves rather than particles:
This was
done in ca 1890.
Thomson's
experiment - charge to mass ratio
Others - based on experiments where the cathode
rays could be deflected by magnets - believed that they were particles,
possibly ions of some kind. J.J. Thomson presented in 1897 an experiment which
gave a value for the charge to mass ratio q/m (or e/m) for these
particles.
He used a CRT where the "rays" would
first travel from the cathode to the anode (over which a voltage was
connected). But the anode had a hole in it, and some particles would pass
through the hole and continue in a narrow ray instead of being sucked into the
anode.
In the following part of the apparatus (still
air-tight and evacuated) there would the crossed electric and magnetic fields
arranged so that the electric and magnetic forces balance out:
Fe = Fm => qE = qvB =>
v = E/B
This allowed their velocity to be measured
(essentially this is the same setup as in the speed filter of a mass
spectrometer, see the At,Nuc&Quant.-topic). By then shutting off the magnetic
field, and letting only the electric force act on the particle (assuming here
that the effect of the force of gravity during its high-speed travel through
the equipment was negligible) it was possible to find q/m for example by
considering its deflection from the straight path to be circular motion and the
centripetal force supplied by the electrical force caused by an electric field
E':
qE' = mv2/r =>qE' = mE2/B2r
=> q/m = E2/E'B2r (if E' = E then we have E/B2r)
The radius of the circle (or part of it) that
the particle traveled in was found experimentally by studying how far the
"rays" hitting a fluorescent screen were deflected from the case when
the electric and magnetic forces were in balance. (This can also be studied as
a form of projectile motion with the electric force instead of the the force of
gravity).
The resulting q/m value was surprisingly high,
indicating that the charge of the particles were high or the mass very low.
Earlier electrochemical experiments and in the early 1900s Millikan's oil-drop
experiment suggested a smallest value for the chargen involved in any reactions
which together with the value for q/m given by Thomson's experiment would
reveal the mass m of these particles - if they were the same. Thomson showed
that the same q/m-value was the same regardless of which materials were used in
the electrodes, indicating that the particles were not ions but a fundamental
part of any atom.
The combined q and q/m-values gave a mass value
smaller than that of the lighest known atom, hydrogen. This indicated that
atoms were not the smallest possible particle but consisted of some even
smaller particles.
Thomson's plum-pudding model and Rutherfords
nuclear model of the atom
Thomson believed the negative parts of the
electron to be embedded in a positive material like raisins in a cake.
Rutherfords experiment 1911 where charged He-ions (alpha particles) were shot
at a thin gold foil and sometimes passed through unaffected but sometimes were
reflected back in almost the opposite direction showed that most of the mass of
the atom was concentrated in a very small volume, the nucleus.
The discovery of the proton
Experiments similar to those with cathode rays
could be done with ions accelerated and allowed to pass electric and magnetic
fields, eventually to hit some material where they would produce a visible
reaction. For most ions, two or more different q/m-values could be found, which
were simple multiples of each other (e.g. for helium the doubly ionised He2+
has twice the q/m-value of the singly ionised He+). For hydrogen
ions only one q/m-value was ever found, and since hydrogen also is the lightest
element (which was known from chemistry) it was in the 1910s suggested that the
hydrogen atom was a combination of an electron and a much heavier particle with
an equal positive charge, a proton.
Chadwick's
discovery of the neutron
One problem with the model of the atom so far
concerned the number of protons in an atom which affected the charge of the
nucleus and therefore the number of electrons required to keep it neutral, and
through that the chemical properties of the atom. If the mass of the proton was
the same as that of a hydrogen ion and the electrons much lighter, then the
mass of most atoms was too large to be explained. A He-atom could not contain
more than two protons, but its mass was about 4 times that of H, for larger
atoms the difference was even bigger.
One possible explanation was that there were
electrons in the nucleus as well as in the outer regions of the atom; then
there could be additional protons in the nucleus which contributed mass but
whose electric charge was cancelled out by these nuclear electrons. Another
possibility was that there was a yet unknown third fundamental particle present
in most nuclei, heavy enough to explain the mass but electrically neutral.
James Chadwick ca 1930 provided support for the
idea of a neutral particle - the neutron - by bombarding beryllium with
alpha particles. The beryllium did not emit any known particles which could be
detected like electrons or proton, but paraffin placed in the vicinity would
start to emit protons when the beryllium was irradiated by alphas. Electric and
magnetic field did not affect whatever it was that carried the energy and
momentum from the beryllium to the paraffin. It was first suggested that it
could be some kind of electromagnetic radiation, photons, like light or X-rays.
It was known from the photoelectric effect that light could strike out electron
from a piece of metal. But electrons needed very little to be set in motion,
the protons in the paraffin were much heavier. And these mysterious neutral
rays or particles did not discharge electroscopes, as gamma rays would.
Calculations of the conservation of momentum and kinetic energy showed that an
incoming particle with about the same mass as a proton but no charge would
explain the ejection of protons from the paraffin, thus supporting the idea of
the neutron.
(To complicate things a bit, it was later found
that although neutrons are rather stable inside a nucleus, free neutrons decay
with a half-life of 10-11 min. to a proton, a neutron and neutrino. If the
decay takes place while the neutron is in a nucleus, we call it beta decay).
10.8 Models of the atom
Much of this part of the Historical physics
option repeats issues presented in the Atomic, Nuclear and Quantum physics
topic.
Atomic spectrum of hydrogen
When hydrogen in a gas tube is heated, it emits
light of certain discrete wavelengths (emission spectrum) and when light of all
wavelengths (white) passes trough the H-gas, the same wavelengths are absorbed
(absorption spectrum).
The empirical Rydberg formula
Johannes (Janne) Rydberg (1854-1919) suggested a
formula which gives the wavelengths emitted/absorbed based on the experimental
data, without any deeper theoretical foundation:
1/l = RH(1/n2 -
1/m2) [DB p 11]
where n = the number of the shell the electron
falls to, m = number it falls from and RH = the Rydberg constant =
1.097 x 107 m-1 (not the gas constant R, not in data
booklet, given when needed). This constant is valid for atoms or ions with one
electron (H and He+). Different n-values give:
The Bohr model
Problem: Why is the atom stable, although an
accelerated charge should emit energy, and the centripetally accelerated
electrons therefore lose energy and spiral down into the nucleus? Niels Bohr
(1885-1962) suggested these postulates in ca 1913:
If this arbitrary assumption is made, then the
Rydberg formula follows (the proof is also in the ANQ topic where it is not
required):
[Outline of the proof, not in IB:
First, for
the possible radii of the orbits of electrons in an H-atom where the nucleus
and the electron have the same charge q (=e) though with opposite signs:
·
the centripetal force
on an electron = the Coulomb force so mv2/r = kqq/r2 = kq2/r2
where k = the Coulomb constant
·
solving for r gives r
= kq2/mv2 and using mvr = nh' with h' = h/2p which gives v = nh'/mr we get:
·
r = kq2/(m(nh'/mr)2) which becomes r = kq2mr2/n2h'2,
solving for r gives:
·
r = h'2n2/(mkq2) or for shell n : rn =
constant A * n2
Then to
find the energy levels we note that an electron, like a satellite in orbit
around a planet, has both a kinetic and a potential energy which is negative:
·
E = Ek + Ep
= ½mv2 + (- kqq/r) = ½mv2 - kq2/r into which
we put v = nh'/mr so
·
E = ½m(nh'/mr)2
- kq2/r = (n2h'2/2mr2) - kq2/r
and using r = h'2n2/[mkq2] then
·
E = (n2h'2/2m(h'2n2/[mkq2])2)
- ( kq2/(h'2n2/[mkq2]) )
which will give
·
E = - mk2q4/2h'2n2
or for shell n : En = - constant B / n2
·
here we have const.B =
mk2q4/2h'2
For n = 1
it turns out that E = - 13.6 electronvolts, the energy needed to ionise a
hydrogen atom with its electron originally in the lowest shell. To get towards
the Rydberg formula we look at an electron falling from shell m to shell n (or
being raised from n to m), where m > n :
·
the change in energy =
En - Em =
-constB/n2 - (-constB/m2) which is
·
constB (1/m2
- 1/n2). When the atom loses this energy, a photon with the energy E
= hf is emitted. The change in energy of the atom is negative and that of the
photon is positive (so totally the energy is conserved). We can equate them
after adjusting the sign:
·
- hf = constB*(1/m2
- 1/n2) or hf = constB*(1/n2 - 1/m2). Combining
with c = fl giving hf = hc/l we then have:
·
hc/l = const.B*(1/n2 - 1/m2)
or dividing with hc then
· 1/l = (const.B/hc)*(1/n2 -
1/m2)
Finally we
note that:
·
(const.B/hc) = (mk2q4/2h'2)/hc.
Inserting the values gives the same value for this expression as that of the
experimentally found Rydberg constant RH. ]
Commonly used is the formula
En = -13.6/n2 [not in DB]
which gives the energy in electronvolts for an
electron in shell n of a one-electron atom or ion.
De Broglie's matter waves
Louis de Broglie (1892-1987) in ca 1924
suggested an explanation for the arbitrary Bohr postulate L = mvrn = nh/2p by suggesting that all material
(and here especially electrons) would be particles and waves at the same time,
just like light had been found to be particles (photons) and waves in a
complementary way. The de Broglie wavelength of
a particle is (see ANQ and Relativity for an explanation of why this
formula is used: E2 = m02c4
+p2c2 for massless
photons becomes E2 = p2c2 or E = pc which with
the photon energy E = hf = gives pc = hc/l so p = h/l or l = h/p. The same is then used for
materia)
l = h/p [DB
p. 8]
where h = the Planck constant and p = mv
(classically) = the momentum of the electron or other particle. De Broglie's
reason for this development was that since energy and momentum in various
events (e.g. emissions and absorptions) are exchanged between the world of
materia and the world of waves then we cannot have a completely different
physics for these two worlds. Again, repetition from the ANQ topic: To fit in
the electron wave as a stationary wave around the nucleus it must follow the
condition nl = 2pr => nh/p = 2pr => nh/mv = 2pr => mvr = nh/2p which was Bohr's assumption (originally made
only because it happened to lead to a formula which fits Rydberg's
experiments).
Schrödinger's wave functions and Heisenberg's
uncertainty principle
See section 6.5. of the ANQ topic.
Mechanical determinism
The Heisenberg uncertainty principles (some
pairs of quantities cannot be known with infinite precision simultaneously) and
the quantum model of the atom (only a probability for finding a particle in a
certain orbit can be given) impose fundamental limits on our ability to predict
the future of a system of objects: we cannot know its initial state precisely,
and even if we could we could not predict is future. This means that the idea
in classical physics that one at least in theory could know everything about
the universe has been found to be incorrect.