Download The Planck length

Length Scales
• From the largest … to the smallest
• Fundamental length scales: The Planck length
• Nanometer length scale: Nanotechnology
Ch. 2.4, 2.5
1027
Fig. 2.12
Universe (observable part)
Exponent
1027 =
1000000000000000000000000000
(27 zeros)
Exponent = Number of zeros
= Order of magnitude
Logarithmic scale:
Each tickmark is a factor of 10.
Useful for covering a large range.
10–35
Planck Length (space falls apart into “quantum foam”)
The largest and the smallest
Ch. 18.6
Ch. 11.3
Horizon:
Velocity=c
Earth
Distant objects (galaxies) move away from
us faster and faster, turning redder and
dimmer. When they reach the speed of
light, they turn black. That is the horizon.
String theorist’s view of space
becoming quantum foam at lPlanck.
The largest: The horizon
The universe expands: Distant galaxies move away faster.
Classical physics tells us that something special happens
when galaxies move away from us with the speed of light c.
The outward velocity of a galaxy compensates the velocity
of its light going towards us. The light cannot reach us.
Einstein’s theory of relativity says that light always moves
with the same velocity c. It cannot stand still, like classical
physics would predict. Instead, the light from a receding
galaxy turns red and becomes darker. At the horizon the
galaxy is completely dark.
Quantum physics says that light can be viewed as a stream
of particles (the photons). As the light turns red, the energy
of the photons is reduced. At the horizon the energy vanishes.
What is outside the horizon ?
Since we cannot see beyond the horizon, we can only make theories
about what might be there. There is no way to prove or disprove such
theories experimentally. This is not part of physics.
Nevertheless, there is a theory named “cosmic inflation” which does
rather well in explaining observations of the early universe (Lect. 18).
It allows an educated guess: Early in its life, the universe expanded
faster than the speed of light. During that period we lost contact with
the part of the universe outside our horizon.
Einstein’s equations of gravity allow space itself to expand faster than
the speed of light. Only the objects in space (galaxies, particles,…)
are subject to Einstein’s speed limit. Think of space as a rubber sheet,
and of galaxies as stickers attached to it. The sheet can be stretched
very fast, while the galaxies are moving around slowly on the sheet.
A second explanation of the horizon
By looking outward, we also look back in time. The light of
distant objects takes time to get to us. Looking all the way
out to the horizon, we see the beginning of the universe.
There is no reason to look farther, because the universe did
not yet exist.
The universe started 13.7 billion years ago with an explosion
(the Big Bang, Lect. 17). We can look back almost that far,
to a time only 0.0004 billion years after the Big Bang .
The smallest: The Planck length
• All measurable quantities are measured in units . For example,
length l is measured in meters, time t in seconds, and so on.
• Most units are related to each other by the laws of physics,
such as E = m c2 . Only three fundamental units are needed.
• These three units are defined by three fundamental constants:
The velocity of light c in Einstein’s theory of relativity, Planck’s
constant ћ in quantum theory, and the gravitational constant G.
• The Planck length is obtained from these three constants:
lPlanck = ћG/c3
• Below the Planck length, quantum theory affects space itself.
Space becomes fuzzy due to the uncertainty relation (Lect.23).
• We are very far from reaching the Planck length (a factor of 1014 ).
1027
Universe (observable part)
Kilo 103 = thousand
Mega 106 = million
Giga 109 = billion
Milli 103 = 1/103
Micro 106 = 1/106
Nano 109 = 1/109
10–3
mm
10–6
m
10–9
nm
Micrometer to nanometer,
the realm of high technology
(microelectronics, biochemistry)
10–35
Planck Length (space falls apart into “quantum foam”)
Getting down to the nanometer scale
HewlettPackard
molecular
memory
Each panel is 10x magnified. Each time we see something new.
Nanotechnology on the desktop
Transistor
Hard Disk
Gate
Sensor
Source
Quantum Well
6 nm
Medium
Drain
Gate oxide
2 nm
Switching layer
5 nm
Magnetic grain
10 nm
Nanotechnology in daily life
Iridescent car paint, based on interference colors of mica flakes
coated with nanoparticles (like butterfly colors). No bleaching.
Nanocrystals
Quantum physics begins at the nanometer scale.
Electrons start behaving like waves.
Crystal size determines the color (blue when small).