The origin of the concept of matter waves started by de Broglie, leading to the explosive development of modern science and quantum mechanics.

1. © ABCC Australia 2015 new-physics.com
DE BROGLIE'S THEORY
Matter-Waves [001]

2. © ABCC Australia 2015 new-physics.com
Wave Particle Duality of Light
After fighting over hundreds of years, the issue of
weather light is a particle or a wave is finally settled,
or rather, compromised in the early twentieth
century. It is now generally accepted that light is a
particle as well as a wave. It is a hybrid called a
wave-particle.

3. © ABCC Australia 2015 new-physics.com
Wavicles
Some clever people coined the word
‘wavicle’ for a particle that is wave
and at the same time as particle. The
composite particles have dual
characteristics, like the mythical
hybrids in ancient Greek mythology.

4. © ABCC Australia 2015 new-physics.com
Light imitates material
particles and becomes a
wavicle. But what about
the material particles
themselves?
There are many micro-
particles such as
electrons, neutrons, and
protons and even quarks
and gluons. Do they
behave like waves as
well?
Material Particles?

5. © ABCC Australia 2015 new-physics.com
Matter Waves
Photons are different from
matter particles in that they
are singularly characterized.
Matter particles are
traditionally believed to be
solid, localized and unwavy –
even when they are in
motion.
The idea of matter particles
that waves like a photon was
not known until 1924.
Photon = Particle + Wave
Matter particles and objects

6. © ABCC Australia 2015 new-physics.com
de Broglie Hypothesis
In 1924, a young French
nobleman named Louis de Broglie
(1892-1987) submitted his
doctoral thesis to the University
of Paris under the title “Research
in the Quantum Theory”[1].
It contained a new message that
seemed to have the potential to
completely revolutionize the
classical view of matter.
[1] Louis de Broglie: ‘Recherches sur la théorie
des quanta (Researches on the quantum
theory)’ Thesis (Paris), 1924; L. de Broglie, Ann.
Phys. (Paris) 3, 22 (1925).
Louis de Broglie (1892-1987)

7. © ABCC Australia 2015 new-physics.com
Particle Waves
Based on the work of Max
Planck (1858-1947)[2] and
Albert Einstein (1879-1955)[3],
de Broglie proposed in his
thesis that material particles
such as electrons should have
both wave and particle
properties, just like photons.
[2] Max Planck: Energy of radiation [Link]
[3] Albert Einstein: Relativistic energy [Link]
Photon = Particle + Wave
Matter particles

8. © ABCC Australia 2015 new-physics.com
Early Days of the Theory
His thesis was so original that it was
easily recognized. But there was not
any experimental evidence of such a
kind of wave at the time. So this
new idea of matter-wave was not
considered to have any physical
reality.
However, Paul Langevin (1872-1946)
drew the attention of Albert Einstein
(1879-1955) to the matter.
Einstein immediately recognized its
significance and promoted it to the
attention of other physicists.
Good
stuff!
[Because it
came from my
formula!]

9. © ABCC Australia 2015 new-physics.com
Nobel Prize Award
Three years later in 1927, de
Broglie’s idea was confirmed
by experiments and he
received the Nobel Prize for
his discovery of the wave
nature of electrons in 1929.
This made him the first
person to receive a Nobel
Prize on a PhD thesis.
Nobel Prize Medal

10. © ABCC Australia 2015 new-physics.com
Debut of Matter Waves
de Broglie said in 1929:
“We thus find that in order to
describe the properties of Matter,
as well as those of Light, we must
employ waves and corpuscles
simultaneously. We can no longer
imagine the electron as being just
a minute corpuscle of electricity:
we must associate a wave with
it.” [4].
[4] Louis de Broglie: Nobel prize speech 1929.
Classical picture of an
electron in motion
Matter wave picture
of an electron particle
in motion

11. © ABCC Australia 2015 new-physics.com
Significance
With this new discovery, de
Broglie opened the gateway
to the development of wave
and quantum mechanics in
the early 19th century.
Although in the later stage of
development, the precision
descriptions of a particle in
motion no longer prevailed
and gave way to probabilistic
interpretations, the discovery
of de Broglie remained a
historic landmark in physics.

12. © ABCC Australia 2015 new-physics.com
RELATIVISTIC ENERGY
Aoppendix : Einstein’s

13. © ABCC Australia 2015 new-physics.com
Relativistic Energy
The momentum 𝑝𝑝 in relativistic
expression is:
𝑝𝑝 =
𝑚𝑚𝑜𝑜 𝑣𝑣
1 −
𝑣𝑣2
𝑐𝑐2
𝑚𝑚𝑜𝑜 is the rest mass of the particle; 𝑣𝑣
the velocity of the particle; 𝑐𝑐 the speed
of light.
Squaring both sides:
(𝑝𝑝)2
=
𝑚𝑚𝑜𝑜 𝑣𝑣
1 −
𝑣𝑣2
𝑐𝑐2
2
We arrive at:
𝑝𝑝2
=
𝑚𝑚𝑜𝑜
2
𝑣𝑣2
1 −
𝑣𝑣2
𝑐𝑐2

14. © ABCC Australia 2015 new-physics.com
Multiplying both sides by 𝑐𝑐2
:
𝑝𝑝2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2
𝑣𝑣2
𝑐𝑐2
1 −
𝑣𝑣2
𝑐𝑐2
Or:
𝑝𝑝2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2 𝑣𝑣2
𝑐𝑐2 𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
By adding and subtracting a term it
can be put in the form:
𝑝𝑝2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2 𝑣𝑣2
𝑐𝑐2 𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
=
𝑚𝑚𝑜𝑜
2
𝑐𝑐4 𝑣𝑣2
𝑐𝑐2 − 1
1 −
𝑣𝑣2
𝑐𝑐2
+
𝑚𝑚𝑜𝑜
2
𝑐𝑐4
1 −
𝑣𝑣2
𝑐𝑐2
= −𝑚𝑚𝑜𝑜
2
𝑐𝑐4
+ 𝑚𝑚2
𝑐𝑐4

15. © ABCC Australia 2015 new-physics.com
The term
𝑚𝑚𝑜𝑜
2 𝑐𝑐4
1−
𝑣𝑣2
𝑐𝑐2
is just the
relativistic mass m. So:
𝑝𝑝2
𝑐𝑐2
+ 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
= 𝑚𝑚2
𝑐𝑐4
Or
𝑚𝑚2
𝑐𝑐4
= 𝑝𝑝2
𝑐𝑐2
+ 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
which may be rearranged to give
the expression for relativistic energy
𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟:
𝑚𝑚𝑚𝑚 = 𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + 𝑚𝑚𝑜𝑜
2
𝑐𝑐4
= 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2

16. © ABCC Australia 2015 new-physics.com
At the same time, Einstein's
theory of relativity pointed
out that for a particle like a
photon of zero rest mass
𝑚𝑚𝑜𝑜 = 0. So the relativistic
energy becomes:
𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝2 𝑐𝑐2 + (𝑚𝑚𝑜𝑜 𝑐𝑐2)2
= 𝑝𝑝𝑝𝑝
𝐸𝐸𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑝𝑝𝑝𝑝

17. © ABCC Australia 2015 new-physics.com
THE EQUATION DERIVED BY DE BROGLIE
To be continued in : Matter-Waves [002]
ABCC