What is Matter?What is Matter?

A Classical IntroductionA Classical Introductionto theto the

Physical UniversePhysical Universe

bybyRobert Close, PhD.Robert Close, PhD.

Copyright © 2006 Robert Close

Early Theories of LightEarly Theories of Light

Early theories of light were based on Early theories of light were based on analogy with sound waves. The medium of analogy with sound waves. The medium of propagation was called the ‘luminous propagation was called the ‘luminous aether’. Nowadays it is called ‘the vacuum’ aether’. Nowadays it is called ‘the vacuum’ or ‘empty space’ to emphasize that it is not or ‘empty space’ to emphasize that it is not made of matter.made of matter.

PolarizationPolarization

1600’s: Christian Huygens used 1600’s: Christian Huygens used birefringent crystals to separate light into birefringent crystals to separate light into two components, called ‘polarizations’.two components, called ‘polarizations’.

Light

Light polarization is easily demonstrated using polarizers.

Light: Waves or Particles?Light: Waves or Particles?

1600’s: Isaac Newton observed a similarity 1600’s: Isaac Newton observed a similarity between colors of light and tones of sound between colors of light and tones of sound but criticized the wave theory of light but criticized the wave theory of light because sound waves do not have two because sound waves do not have two polarizations. He thought that light might polarizations. He thought that light might consist of particles which could have consist of particles which could have different orientations.different orientations.

Speed of LightSpeed of Light

1675: Olaf Roemer observed that the time 1675: Olaf Roemer observed that the time between eclipses of the first moon of between eclipses of the first moon of Jupiter (moon moving behind Jupiter) Jupiter (moon moving behind Jupiter) lengthened as Earth and Jupiter moved lengthened as Earth and Jupiter moved farther apart. He deduced that it takes light farther apart. He deduced that it takes light 11 minutes (actually about 8 min 20 sec) 11 minutes (actually about 8 min 20 sec) to travel between the Sun and Earth.to travel between the Sun and Earth.

CassiniCassini1672: Giovanni Domenico Cassini 1672: Giovanni Domenico Cassini

measured the Earth-Sun distance to be measured the Earth-Sun distance to be 140,000,000 km using parallax methods. 140,000,000 km using parallax methods.

Mars

Paris FrenchGuiana

Speed of LightSpeed of Light

From Roemer’s and Cassini’s measurements the From Roemer’s and Cassini’s measurements the speed of light can be calculated to be:speed of light can be calculated to be:

●This result established a uniform speed for light waves in vacuum. ●The presently accepted value is:

The Aether as an Elastic SolidThe Aether as an Elastic Solid

1817 Thomas Young believed light to be waves 1817 Thomas Young believed light to be waves because it had a characteristic speed. He because it had a characteristic speed. He suggested that light consists of transverse suggested that light consists of transverse vibrations such as occur in an elastic solid. vibrations such as occur in an elastic solid.

Direction of vibration Direction of propagation

The Aether as an Elastic SolidThe Aether as an Elastic Solid

Young’s ideas were used successfully by Young’s ideas were used successfully by scientists such as Augustin Fresnel, scientists such as Augustin Fresnel, James MacCullagh, and Joseph James MacCullagh, and Joseph Boussinesq to explain the properties of Boussinesq to explain the properties of light. light.

Light WavesLight Waves

Waves combine with interference: Waves combine with interference: ‘‘In-phase’ waves add (In-phase’ waves add (____________ + + -------)-------)

‘‘Out-of-phaseOut-of-phase’ waves cancel’ waves cancel

Light WavesLight WavesGradual variation of propagation time results in

interference fringes.

Path Difference (d)

1 wavelength (bright)½ wavelength (dark)0 (bright)- ½ wavelength (dark)-1 wavelength (bright)

Light

Slits

d

DiffractionDiffraction

The two-slit interference pattern persists even if there is no division between the two slits (two halves of one slit).

You can observe this ‘diffraction’ pattern in a small slit between two pencils.

<1mm

Aether DriftAether Drift

If the aether were solid, then how did Earth If the aether were solid, then how did Earth and planets move through it?and planets move through it?

Scientists supposed that the aether behaved Scientists supposed that the aether behaved as a solid for light but as a rarified fluid for as a solid for light but as a rarified fluid for Earth (compare with putty or wax which can Earth (compare with putty or wax which can bounce like a solid ball or be squeezed bounce like a solid ball or be squeezed through a hole like a liquid).through a hole like a liquid).

As Earth moved through this ‘fluid’, the speed As Earth moved through this ‘fluid’, the speed of light should depend on its direction.of light should depend on its direction.

Aether Drift ExperimentsAether Drift Experiments

1881-1887 Albert Michelson and E. W. 1881-1887 Albert Michelson and E. W. Morley performed experiments which Morley performed experiments which seemed to indicate a lack of relative motion seemed to indicate a lack of relative motion between the earth and the aether. Looking between the earth and the aether. Looking at interference fringes between light at interference fringes between light propagating East-West and North-South, propagating East-West and North-South, they measured zero difference in light speed they measured zero difference in light speed parallel and perpendicular to the earth’s parallel and perpendicular to the earth’s motion. Therefore the aether is not a fluid.motion. Therefore the aether is not a fluid.

The Theory of RelativityThe Theory of Relativity

1903 Hendrik Lorentz determined that 1903 Hendrik Lorentz determined that inability to detect drift through the aether inability to detect drift through the aether requires the difference between the requires the difference between the squared distance and the squared squared distance and the squared propagation time between two events to propagation time between two events to be independent of observer motion, i.e.be independent of observer motion, i.e.

xx22++yy22++zz22--cc22tt2 2 = constant= constant. .

The Theory of RelativityThe Theory of Relativity

If the constant is zero, then:If the constant is zero, then:

xx22++yy22++zz22==cc22tt22

Notice that this equation simply means:Notice that this equation simply means:

(Distance) = (Distance) = cc(Propagation Time)(Propagation Time)This means that distance and light This means that distance and light

propagation time cannot be measured propagation time cannot be measured independently! It is as if all matter independently! It is as if all matter consisted of light waves.consisted of light waves.

Distance and TimeDistance and Time

The interdependence of distance The interdependence of distance and time measurements is explicit and time measurements is explicit today. The meter is today. The meter is defineddefined as the as the length of the path traveled by light length of the path traveled by light in vacuum during a time interval in vacuum during a time interval 1/1/cc =1/299,792,458 of a second. =1/299,792,458 of a second.

1904 Henri Poincare gave the name 1904 Henri Poincare gave the name ‘Principle of Relativity’ to the doctrine that ‘Principle of Relativity’ to the doctrine that absolute motion is undetectable. He also absolute motion is undetectable. He also deduced from this principle that no velocity deduced from this principle that no velocity can exceed the speed of light.can exceed the speed of light.

1905 Albert Einstein reformulated relativity 1905 Albert Einstein reformulated relativity theory with the more positive assertion theory with the more positive assertion that the speed of light is a universal that the speed of light is a universal constant independent of observer motion.constant independent of observer motion.

The Theory of RelativityThe Theory of Relativity

The Theory of RelativityThe Theory of Relativity A key result of Einstein’s analysis is the A key result of Einstein’s analysis is the

relationship between mass (relationship between mass (mm), energy (), energy (EE), ), and the light speed (and the light speed (cc):):

E=mcE=mc22

This equation is not as simple as it seems This equation is not as simple as it seems because Einstein made up a new definition of because Einstein made up a new definition of moving mass. In terms of the ordinary ‘rest moving mass. In terms of the ordinary ‘rest mass’ mass’ mm00: :

mm==mm00

(( is the Greek letter gamma) is the Greek letter gamma)

The Theory of RelativityThe Theory of Relativity

The factor The factor is a relationship between is a relationship between particle velocity and the speed of light.particle velocity and the speed of light.

To understand the meaning of this factor, To understand the meaning of this factor, consider the geometry of triangles…consider the geometry of triangles…

TrianglesTriangles

Base

Height

(Cut and Paste to make rectangle)

The Pythagorean TheoremThe Pythagorean Theorem

b

a

c

Start with a right triangle with short sides a and b and

hypotenuse c.

The Pythagorean TheoremThe Pythagorean Theorem

A

a

b

Insert four such

triangles into a square with

side length (a+b). The area of the

outlined blue square is c2.

c

c

c

c

a

a

a b

b

b

The Pythagorean TheoremThe Pythagorean Theorem

A

a

b

Rearrange the triangles. The area of

the blue region is now

clearly a2+b2.

Therefore: a2+b2 =c2

c

c

a

a

ab

b

b

The Gamma (The Gamma () Factor) FactorAccording to the Pythagorean Theorem, According to the Pythagorean Theorem, is the is the

ratio between the hypotenuse of a right ratio between the hypotenuse of a right triangle and one of its sides.triangle and one of its sides. This is the This is the velocity triangle: velocity triangle:

cv

Interpretation of MassInterpretation of Mass

Suppose that matter propagation has two components:Suppose that matter propagation has two components:

1.1. Circular motion (oscillating motion is also possible)Circular motion (oscillating motion is also possible)

2.2. Linear motionLinear motion

If the circular motion is in a plane perpendicular to the If the circular motion is in a plane perpendicular to the linear motion then the path is a helix (spiral).linear motion then the path is a helix (spiral).

If one component of the circular motion is aligned with If one component of the circular motion is aligned with the linear motion then the path is called a cycloid. the linear motion then the path is called a cycloid. The circular and linear components still satisfy the The circular and linear components still satisfy the Pythagorean relation.Pythagorean relation.

Helical & Cycloidal MotionHelical & Cycloidal Motion

D=ctdC=2r dT=vt

+ =

Velocity TriangleVelocity Triangle

is the ratio between the total wave speed and the circulation speed.

Relate total speed c and circulation speed vC:

Energy TriangleEnergy TriangleConsider the right triangle representing a Consider the right triangle representing a spiral wave: the three sides are average spiral wave: the three sides are average velocity, circulating velocity, and the speed of velocity, circulating velocity, and the speed of light.light.

Multiply each side by Multiply each side by mm00c.c.

cv

€

c2 − v2

Energy TriangleEnergy TriangleEnergy is proportional to the speed of light.Energy is proportional to the speed of light.Momentum is proportional to average velocity.Momentum is proportional to average velocity.Rest Mass is proportional to circulating velocity.Rest Mass is proportional to circulating velocity.

Energy (E =m0c2)Momentum

(pc =m0cv)

Rest Mass

Energy EquationEnergy Equation

We can therefore write this equation for energy:We can therefore write this equation for energy:

This is another form of Einstein’s equation.This is another form of Einstein’s equation.

Twin ParadoxTwin Paradox

Relativity theory predicts that if one twin Relativity theory predicts that if one twin stays put while the other goes on a high-stays put while the other goes on a high-speed voyage, the traveling twin will be speed voyage, the traveling twin will be younger (ages less) than the stationary younger (ages less) than the stationary twin. twin.

Twin ParadoxTwin Paradox A clock counts the number of circular orbits A clock counts the number of circular orbits

executed by a circulating matter wave. executed by a circulating matter wave. A matter wave with translational motion travels A matter wave with translational motion travels

farther (at the same speed of light) than a farther (at the same speed of light) than a stationary matter wave during each rotation cycle. stationary matter wave during each rotation cycle. Therefore a moving clock ticks slower than a Therefore a moving clock ticks slower than a stationary one, and a moving twin ages slower stationary one, and a moving twin ages slower than a stationary one.than a stationary one.

Twin ParadoxTwin Paradox

The twin paradox is not just hypothetical.The twin paradox is not just hypothetical. Unstable particles moving nearly the Unstable particles moving nearly the

speed of light have significantly longer speed of light have significantly longer lifetimes than otherwise identical particles lifetimes than otherwise identical particles with slower motion.with slower motion.

GPS navigational systems must adjust GPS navigational systems must adjust clocks for relative motion.clocks for relative motion.

One More QuestionOne More Question

Why does matter appear to propagate Why does matter appear to propagate at the speed of light?at the speed of light?

Matter as WavesMatter as Waves

1900 Max Planck explained the distribution of 1900 Max Planck explained the distribution of thermal radiation by supposing light to be thermal radiation by supposing light to be emitted by vibrators whose energy (emitted by vibrators whose energy (EE) can ) can only have integer multiples (only have integer multiples (nn) of the vibration ) of the vibration frequency (frequency (ff) multiplied by a universal ) multiplied by a universal constant (constant (hh).).

E= nhfE= nhf

Such a restriction is called ‘quantization’.Such a restriction is called ‘quantization’.

Photo-Electric EffectPhoto-Electric Effect

1905 Einstein used quantization of 1905 Einstein used quantization of radiation to explain the photo-electric radiation to explain the photo-electric effect, in which the frequency of light effect, in which the frequency of light (rather than the brightness) must exceed a (rather than the brightness) must exceed a certain threshold in order to liberate certain threshold in order to liberate electrons from a metal. electrons from a metal.

QuantizationQuantization

19131913 Niels Bohr used quantization of Niels Bohr used quantization of angular momentum and energy to derive angular momentum and energy to derive energy levels and spectral frequencies of energy levels and spectral frequencies of the hydrogen atomthe hydrogen atom..

Electron WavesElectron Waves

1924 Louis Victor de Broglie proposed in 1924 Louis Victor de Broglie proposed in his doctoral thesis that electrons have a his doctoral thesis that electrons have a wave-like character with the same relation wave-like character with the same relation between momentum and frequency as for between momentum and frequency as for light waves. light waves.

Electron WavesElectron Waves

1927 Clinton Davisson and Lester Germer 1927 Clinton Davisson and Lester Germer (and independently George Thomson and (and independently George Thomson and Alexander Reid) confirmed the wave nature of Alexander Reid) confirmed the wave nature of electrons by demonstrating diffraction of electrons by demonstrating diffraction of electrons by crystals.electrons by crystals.

Matter as WavesMatter as Waves

Electron scattering from crystals yields a diffraction pattern characteristic of waves. A similar diffraction pattern can be obtained using x-rays of the same wavelength.

Patrick Blackett discovers opposing spiral Patrick Blackett discovers opposing spiral tracks in a magnetized cloud chamber, tracks in a magnetized cloud chamber, indicating positron/electron pair production indicating positron/electron pair production from cosmic gamma rays. This conversion from cosmic gamma rays. This conversion of electromagnetic wave energy to matter of electromagnetic wave energy to matter confirms de Broglie’s wave hypothesis.confirms de Broglie’s wave hypothesis.

Matter, like light, evidently consists of Matter, like light, evidently consists of “affections” of the aether as envisioned by “affections” of the aether as envisioned by Maxwell.Maxwell.

ELECTROMAGNETISM1933

http://teachers.web.cern.ch/teachers/archiv/HST2002/Bubblech/mbitu/ELECTRON-POSITRON2-piece.jpg

Matter as WavesMatter as Waves

Experiments indicate that Experiments indicate that matter consists of waves!matter consists of waves!

Matter as WavesMatter as Waves

• de Broglie used the wave model of de Broglie used the wave model of electrons to derive Bohr’s angular electrons to derive Bohr’s angular momentum and energy levels of the momentum and energy levels of the Hydrogen atom.Hydrogen atom.

Matter as Waves

de Broglie used the wave model of electrons de Broglie used the wave model of electrons to derive Bohr’s angular momentum and to derive Bohr’s angular momentum and energy levels of the Hydrogen atom.energy levels of the Hydrogen atom.

Matter as WavesMatter as Waves It just so happens that the frequencies of light It just so happens that the frequencies of light

in the hydrogen spectrum satisfy the relation:in the hydrogen spectrum satisfy the relation:

• Assuming that energy of a light wave is Assuming that energy of a light wave is proportional to frequency yields the difference proportional to frequency yields the difference between two of de Broglie’s orbit energies:between two of de Broglie’s orbit energies:

GravityGravityGravity is a reduction of wave speed in the Gravity is a reduction of wave speed in the

vicinity of massive objects (a prediction of vicinity of massive objects (a prediction of General Relativity).General Relativity).

For example, compression of a solid aether For example, compression of a solid aether would reduce the wave speed.would reduce the wave speed.

GravityGravityWaves refract (bend) toward regions of Waves refract (bend) toward regions of

slower wave speed.slower wave speed.

Fast

Slow

GravityGravity During a solar eclipse, the positions of stars During a solar eclipse, the positions of stars

near the direction of the sun are observed to be near the direction of the sun are observed to be shifted. This confirms that the light rays from shifted. This confirms that the light rays from those stars are bent as they pass near the sun.those stars are bent as they pass near the sun.

SunEarth

Light from star

Apparent directionof star

Moon

SummarySummaryMatter consists of wave packets Matter consists of wave packets

which propagate along curved paths which propagate along curved paths at the speed of light. at the speed of light.

Mass represents circular or oscillating Mass represents circular or oscillating motion. motion.

Momentum represents linear motion. Momentum represents linear motion. Energy represents total motion.Energy represents total motion.Gravity represents wave refraction.Gravity represents wave refraction.

BibliographyBibliography Louis de Broglie, Louis de Broglie, Recherches sur la Théorie des QuantaRecherches sur la Théorie des Quanta (Researches on (Researches on

the quantum theory), PhD Thesis, (University of Sorbonne, Paris, 1924).the quantum theory), PhD Thesis, (University of Sorbonne, Paris, 1924). Clinton Davisson and Lester Germer, “Diffraction of Electrons by a Crystal Clinton Davisson and Lester Germer, “Diffraction of Electrons by a Crystal

of Nickel,” of Nickel,” Phys. Rev.Phys. Rev. 3030 705–40, 1927 705–40, 1927 Albert Einstein, Albert Einstein, The Meaning of RelativityThe Meaning of Relativity, (Princeton University Press, , (Princeton University Press,

Princeton, 1956) Fifth Edition, pp. 29-37.Princeton, 1956) Fifth Edition, pp. 29-37. Albert A. Michelson and Edward W. Morley, “On the Relative Motion of the Albert A. Michelson and Edward W. Morley, “On the Relative Motion of the

Earth and the Luminiferous Ether,” Am. J. Sci. (3rd series) 34, 333-345 Earth and the Luminiferous Ether,” Am. J. Sci. (3rd series) 34, 333-345 (1887).(1887).

Barry N. Taylor, Barry N. Taylor, Guide for the Use of the International System of Units (SI)Guide for the Use of the International System of Units (SI), , NIST Special Publication 811 (National Institute of Standards and NIST Special Publication 811 (National Institute of Standards and Technology, Gaithersburg, MD, 1995), Appendix A.Technology, Gaithersburg, MD, 1995), Appendix A.

George P. Thomson GP and Alexander Reid, “Diffraction of cathode rays by George P. Thomson GP and Alexander Reid, “Diffraction of cathode rays by a thin film,”  a thin film,”  NatureNature 119119 890-5, 1927. 890-5, 1927.

Edmund Whittaker, Edmund Whittaker, A History of the Theories of Aether and ElectricityA History of the Theories of Aether and Electricity, , (Edinburgh: Thomas Nelson and Sons Ltd.) 1951.(Edinburgh: Thomas Nelson and Sons Ltd.) 1951.