PEP Conceptual PhysicsClass Notes

Unit 4 – Matter and EnergyChapter 11 – Relativity

Relationship Between Matter and Energy

• Section 11.1• Einstein’s Formula

• The Speed of Light

• Antimatter

• Strange Particles

Einstein’s Formula• Einstein’s formula is well-known

• 𝐸 = 𝑚𝑐2 (Energy = mass times speed of light squared)

• It is used in nuclear reactions• In a nuclear reaction (section 10.3), some of the mass is

converted from nuclear matter into energy

• The amount of energy released is tremendous

• 1 𝑘𝑔 of mass is equivalent to 9 × 1016 𝐽

• Comparison to chemical reactions• In chemical reactions, energy release is small and mass

difference is too small to measure

• In nuclear reactions, energy release is large, and mass difference is large enough to measure

The Speed of Light• Light and gravity move at the speed of light

• c = 300,000,000 𝑚/𝑠

• Light takes 8 𝑚𝑖𝑛𝑢𝑡𝑒𝑠, 19 𝑠𝑒𝑐𝑜𝑛𝑑𝑠 to travel from the sun to the earth

• If the sun were to suddenly vanish• Earth would still see sunlight and feel gravitational pull in orbit

for that amount of time

• After that, earth would be in darkness and would go flying off into space

• By contrast, sound travels at about 340 𝑚/𝑠, which is about one million times slower that light• That’s why it takes about 5 seconds after seeing a flash

of lightning before you hear its thunder

Antimatter• Until the 1930s, scientists thought all matter was

made of atoms consisting of protons, neutrons, and electrons• First, they discovered antimatter

• Antimatter – matter which has the opposite charge and other properties from normal matter• The antiproton is like a proton, but with a negative charge

• The antielectron (positron) is like an electron, but with a positive charge

• Pure energy can create a particle and antiparticle

• When a particle and antiparticle meet, they are “annihilated” and create pure energy

Strange Particles• Shortly after antimatter was discovered, other

fundamental particles were discovered

• Neutrinos, neutrally-charged, lighter than electrons, and hard to detect, also occur during beta decay• Trillions pass through your body every second

• Neutrinos do not react with ordinary matter except through the weak nuclear force

• There are heavier elementary particles that have been and are being discovered in high energy accelerators• Fermilab near Chicago, Illinois

• CERN’s Large Hadron Collider near Geneva, Switzerland

Strange Particles• Protons and neutrons are made of even smaller

particles called quarks• Lightest quarks are “up” and “down”

• “Up” quarks have a +2/3 charge

• “Down” quarks have a −1/3 charge

• There are also “strange”, “charm”, “top”, and “bottom”

• Protons consist of 2 “up” and 1 “down” quark

• Neutrons consist of 2 “down” and 1 “up” quark

• Heavier particles are made up of other quarks

Special Relativity• Section 11.2

• Matter, Energy, Time and Space

• Speed of Light Problem

• Speed, Time, and Clocks

• The Twin Paradox

Matter, Energy, Time and Space• Theory of Special Relativity – Einstein’s theory

describing what happens to matter, energy, time, and space at speeds close to the speed of light

• Time dilation – a result whereby time runs slower for objects in motion than for objects at rest

• Mass increase – a result whereby increasing kinetic energy of a moving object results in greater mass rather than faster speed

• Length contraction – a result whereby distance measured for objects in motion is shorter than for objects at rest

Speed of Light Problem• At low, common, everyday speeds, two speeds in

different reference frames will …• Add if both frames are traveling in the same direction

• Subtract if both frames are traveling in different direction

• Look at Figure 11.7 on page 279• Girl on train traveling at 10 𝑚/𝑠 throws a ball at 10 𝑚/𝑠

• Observer sees the ball traveling at 20 𝑚/𝑠

• Light is always observed to travel at the same speed regardless of reference frames• Look at Figure 11.8 on page 279

• Girl on train traveling at 1𝑥108 𝑚/𝑠 shines a flashlight

• Observer sees light at 3𝑥108 𝑚/𝑠, not 4𝑥108 𝑚/𝑠

Speed of Light Problem• Michelson-Morley experiment – 1887

• Arguably the most famous “failed” experiment in history

• The earth orbits the sun at 29,800 𝑚/𝑠

• They built a very sensitive instrument to measure the speed of light• First, they measured the speed of light parallel to the

direction of orbital motion

• Next, they measured the speed of light perpendicular to the direction of orbital motion

• No difference was observed – the speed of light was the same in both directions

• Einstein explained the reason in 1905

Speed, Time, and Clocks• Einstein postulated that these effects of special

relativity were not just appearances but were real• Time does not just appear to be different in different

reference frames but is different

• Consider a “clock” made of two mirrors and a “tick” is a beam of light bouncing between them• On a moving object, the light travels in a straight line

• Look at Figure 11.9 on page 280

• On a stationary observation deck, the light travels in a zigzag – it travels farther• Look at Figure 11.10 on page 280

• If the speed of light is constant, then the moving clock must “tick” slower than the stationary clock

The Twin Paradox• This results in an apparent paradox that is famous

in relativistic discussions• The actual statement and solution to this paradox is

more complicated than what the textbook presents

• Two twins – one travels to a distant star at nearly the speed of light and the other stays home• The astronaut twin’s clock (spaceship and biological)

runs slower and she only ages 2 years

• The homebound twin’s clock runs at a “normal” speed, and he ages 20 years

• The astronaut has traveled 18 years into the future!

General Relativity• Section 11.3

• Reference Frames

• Acceleration and Gravity

• Curved Space-Time

• Black Holes

• The Big Bang

Reference Frames• Reference frame – a perspective from which the

position and motion of a system can be described

• In Newtonian and Galilean environments• Reference frames are equivalent

• You cannot detect uniform motion, but you can detect acceleration

• The girl on the train sees the boy on the platform moving toward her at 10 𝑚/𝑠

• The boy on the platform sees the girl on the train moving toward him at 10 𝑚/𝑠

Acceleration and Gravity• General relativity – Einstein’s theory in which

gravity is an effect created by the curvature of space-time

• With general relativity, acceleration and gravity are indistinguishable• Suppose you’re standing on a pair of scales inside an

elevator and you notice you’re feeling heavier• Are you stationary but starting to move up?

• Are you moving up but starting to slow down?

• Are you stationary but the force of gravity increased?

• You cannot experimentally differentiate between these three situations

Curved Space-Time• Einstein deduced two results

• Space must be curved

• Light will be deflected by gravity, even though it has no mass

• Flat space is like a sheet of graph paper out in deep space and away from all massive objects• Objects can travel in straight lines with no effects

• Curved space is like a sheet of graph paper made of rubber where a mass creates a well• Smaller masses create shallower wells

• Larger masses create deeper wells

Curved Space-Time• An object traveling in a straight line in curved space

will be deflected toward the well just like an object traveling in a straight line in flat space would be deflected by a nearby mass• Look at Figure 11.13 on page 283

• The effect of curved space is identical to the force of gravity!

• Einstein’s theory was proven in 1919 when light from distant stars was observed to have bent around the sun during a total solar eclipse

Black Holes• For an object to escape Earth’s gravity, it must be

faster than the escape speed of 40,000 𝑘𝑝ℎ

• Black hole – a compact, astronomical object with such strong gravity that its escape velocity equals or exceeds the speed of light• Since no light can escape, the object appears “black”

• If the Earth were to become a black hole, it would have to collapse to the size of a marble

• You cannot see a black hole, but you can see what happens near and around a black hole• As an object fall into a black hole, they emit intense

radiation

The Big Bang• There are 200 billion stars estimated to be in our

own Milky Way galaxy

• There are billions of other galaxies as large as ours

• What caused it all?• Secular scientists, like the authors of the textbook,

believe that an incredible amount of energy in a space smaller than an atom exploded in a “Big Bang” and made the universe and it is still expanding

• Creation scientists, like your tutor, believe that God created the universe several thousand years ago by the word of His power just like Genesis 1-2 and Hebrews 1 tell us and with the appearance of old age

Creation3 When I look at your heavens, the work of your fingers, themoon and the stars, which you have set in place, 4 what isman that you are mindful of him, and the son of man that youcare for him?

Psalm 8:3-4, ESV