From the largest … to the smallest Fundamental length scales: The Planck length

1. Length Scales • From the largest … to the smallest • Fundamental length scales: The Planck length • Nanometer length scale: Nanotechnology Ch. 2.4, 2.5

2. Universe (observable part) 1027 Exponent 1027 = 1000000000000000000000000000(27 zeros) 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”) Fig. 2.12 Exponent = Number of zeros = Order of magnitude

3. 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.

4. The largest: The horizon The universe expands: Distant galaxies move away faster. Classical physicstells 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.

5. 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.

6. 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 0.0004billion years after the Big Bang.

7. The smallest: The Planck length • All measurable quantities are measured in units. For example, length lis measured in meters, time tin seconds, and so on. • Most units are related to each other by the laws of physics, such as E=mc2. 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 ћin quantum theory, and the gravitational constant G. • The Planck lengthis 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).

8. Universe (observable part) 1027 10–35 Planck Length (space falls apart into “quantum foam”) Kilo 103 = thousandMega 106 = millionGiga 109 = billionMilli 103= 1/103Micro 106 = 1/106Nano 109 = 1/109 Micrometer to nanometer,the realm of high technology (microelectronics, biochemistry) 10–3 mm 10–6 m 10–9 nm

9. Getting down to the nanometer scale Hewlett- Packard molecular memory Each panel is 10x magnified. Each time we see something new.

10. Gate Source Drain Nanotechnology on the desktop Transistor Hard Disk Sensor Medium Quantum Well 6 nm Gate oxide 2 nm Switching layer 5 nm Magnetic grain 10 nm

11. Nanotechnology in daily life Iridescent car paint, based on interference colors of mica flakes coated with nanoparticles (like butterfly colors). No bleaching.

12. Nanocrystals Quantum physics begins at the nanometer scale. Electrons start behaving like waves. Crystal size determines the color (blue when small).