Relativity & ThermodynamicsOur Understanding of Space and Time Credits: www.phy.mtu.edu/~akantamn/Physics/lec3/Special_Relativity%20III.ppt www.few.vu.nl/~ptn900/teaching_files/Relativity.ppt www.serendip.brynmawr.edu/local/scisoc/time/7arrows.ppt www.astro.ufl.edu/~vicki/AST3019/General_Relativity.ppt
The Relativity Principle The Ptolemaic Model The Copernican Model Galileo Galilei 1564 - 1642 Problem: If the earth were moving wouldn’t we feel it? – No
The Relativity Principle v A coordinate system moving at a constant velocity is called an inertial reference frame. Galileo Galilei 1564 - 1642 The Galilean Relativity Principle: All physical laws are the same in all inertial reference frames.
The Relativity Principle Other Examples: Galileo Galilei 1564 - 1642 As long as you move at constant velocity you are in an inertial reference frame.
Electromagnetism A wave solution traveling at the speed of light c = 3.00 x 108 m/s Maxwell: Light is an EM wave! James Clerk Maxwell 1831 - 1879 Problem: The equations don’t tell what light is traveling with respect to
Einstein’s Approach to Physics 1. Gedanken (Thought) Experiments E.g., if we could travel next to a light wave, what would we see? 2. “The Einstein Principle”: If two phenomena are indistinguishable by experiments then they are the same thing. Albert Einstein 1879 - 1955
Einstein’s Approach to Physics 2. “The Einstein Principle”: If two phenomena are indistinguishable by experiments then they are the same thing. current current Albert Einstein 1879 - 1955 A magnet moving A coil moving towards a magnet towards a coil Both produce the same current Implies that they are the same phenomenon
Einstein’s Approach to Physics 1. Gedanken (Thought) Experiments E.g., if we could travel next to a light wave, what would we see? c c Albert Einstein 1879 - 1955 We would see an EM wave frozen in space next to us Problem: EM equations don’t predict stationary waves
Electromagnetism Another Problem: Every experiment measured the speed of light to be c regardless of motion The observer on the ground should measure the speed of this wave as c + 15 m/s Conundrum: Both observers actually measure the speed of this wave as c!
Special Relativity Postulates Einstein: Start with 2 assumptions & deduce all else • The Relativity Postulate: The laws of physics are the same in every inertial reference frame. • The Speed of Light Postulate: The speed of light in vacuum, measured in any inertial reference frame, always has the same value of c. This is a literal interpretation of the EM equations
Special Relativity Postulates Looking through Einstein’s eyes: Both observers (by the postulates) should measure the speed of this wave as c • Consequences: • Time behaves very differently than expected • Space behaves very differently than expected
Time Dilation One consequence: Time Changes Equipment needed: a light clock and a fast space ship.
Time Dilation In Bob’s reference frame the time between A & B is Δt0 Δt0 Ending Event B Bob Beginning Event A Sally on earth
Time Dilation In Sally’s reference frame the time between A & B is Δt Bob Bob Δt Sally A B on earth Length of path for the light ray: and
Time Dilation Length of path for the light ray: and Solve for Δt: Time measured by Bob
Time Dilation Δt0= the time between A & B measured by Bob Δt= the time between A & B measured by Sally v= the speed of one observer relative to the other If Δt0 = 1s, v = .999 c then: Time Dilation = Moving clocks slow down
Time Dilation How do we define time? The flow of time each observer experiences is measured by their watch – we call this the proper time • Sally’s watch always displays her proper time • Bob’s watch always displays his proper time • If they are moving relative to each other they will not agree
Time Dilation A Real Life Example: Lifetime of muons Muon’s rest lifetime = 2.2x10-6 seconds Many muons in the upper atmosphere (or in the laboratory) travel at high speed. If v = 0.999 c. What will be its average lifetime as seen by an observer at rest?
Length Contraction The distance measured by the spacecraft is shorter Sally’s reference frame: Bob’s reference frame: Sally Bob The relative speed v is the same for both observers:
Twirling Pole Paradox You hold a really long pole. You hold one end firmly and twirl the pole so that the free end goes around in a big circle. Can the free end go faster than c? • No. Every physical object must travel less than c. • Yes, for a long enough pole twirled fast enough, the free end must go faster than c. • Where's the barn? I heard this paradox had a barn.
Twirling Pole Paradox 1. No. Every physical object must travel less than c. The pole end is real and cannot move at v > c. The problem is that such a pole cannot be perfectly rigid. Information cannot move ALONG the pole at v > c so that the end of the pole cannot know that the inner parts of the pole are twirling. A perfectly rigid pole would break. A very elastic pole would twist into a spiral pattern with the free end constrained to move at v < c.
Ladder Paradox or ? Also called the "Barn and the Pole" paradox. You hold a long ladder and run toward a short garage. If you run fast, can you trap the ladder in the garage?
Ladder Paradox Yes, you can trap the ladder in the garage. The information that the front end of the ladder has hit the back end of the garage can only move along the ladder at v < c. As this information moves, the back end of the ladder can pass into the garage and the garage door can be closed. We then get to see if the ladder is stronger than the door.
TwinParadox One twin stays home. One twin rockets away and then comes back. Special relativity implies time dilation for moving objects, but each moved only as seen by the other. Which twin is older? • The twin who stayed home is older. • The twin who rocketed away and came back is older. • Symmetry demands they are the same age.
Twin Paradox 2. The twin who rocketed away & came back is younger. The symmetry is broken because the leaving twin had to accelerate to come back, whereas the staying twin experienced no acceleration. Is this a way to travel into the future? Yes. Time travel this way is permissible. There is no way to use the twin paradox to travel BACK in time.
General Relativity • GR is Einstein’s theory of gravitation that builds on the geometric concept of space-time introduced in SR. • Is there a more fundamental explanation of gravity than Newton’s law? • GR makes specific predictions of deviations from Newtonian gravity.
Curved space-time • Gravitational fields alter the rules of geometry in space-time producing “curved” space • For example the geometry of a simple triangle on the surface of sphere is different than on a flat plane (Euclidean) • On small regions of a sphere, the geometry is close to Euclidean
No gravity gravity t t x x • How does gravity curve space-time? • With no gravity, a ball thrown upward continues upward and the worldline is a straight line. • With gravity, the ball’s worldline is curved. • It follows this path because the spacetime surface on which it must stay is curved. • To fully represent the trajectory, need all 4 space-time dimensions curving into a 5th dimension(!) • Hard to visualize, but still possible to measure
Principle of Equivalence • A uniform gravitational field in some direction is indistinguishable from a uniform acceleration in the opposite direction • Keep in mind that an accelerating frame introduces pseudo-forces in the direction opposite to the true acceleration of the frame (e.g. inside a car when brakes are applied)
Elevator experiment • First, elevator is supported and not moving, but gravity is present. Equate forces on the person to ma (=0 since a=0) • Fs - mg = 0 so Fs = mg • Fs gives the weight of the person. • Second, no gravity, but an upward acceleration a. The only force on the person is Fs and so • Fs = ma or Fs = mg if “a” value is the same as “g” • Person in elevator cannot tell the difference between gravitational field and accelerating frame • Third, there is gravity and the elevator is also in free-fall • Fs - mg = -mg or Fs = 0 • “Weightless” Let upward forces be positive, thus gravity is -g See also http://www.pbs.org/wgbh/nova/einstein/relativity/
Einstein was bothered by what he saw as a dichotomy in the concept of "mass." On one hand, by Newton's second law (F=ma), "mass" is treated as a measure of an object’s resistance to changes in movement. This is called inertial mass. On the other hand, by Newton's Law of Universal Gravitation, an object's mass measures its response to gravitational attraction. This is called gravitational mass. As we will see, Einstein resolved this dichotomy by putting gravity and acceleration on an equal footing. The principle of equivalence is really a statement that inertial and gravitational masses are the same for any object. This also explains why all objects have the same acceleration in a gravitational field (e.g. a feather and bowling ball fall with the same acceleration in the absence of air friction).
Tests of General Relativity • Orbiting bodies - GR predicts slightly different paths than Newtonian gravitation • Gravitational Lensing • Gravitational Red shifting • Gravitational Waves
Arrows of Time Memory Arrow Cosmological Arrow Entropy Arrow
Memory only works backwards (We don't remember the future) 1. Memory Arrow
2. Cosmological Arrow We live in an expanding universe, not a contracting one. Would time change direction if universe started contracting?
3. Entropy Arrow Entropy always increases (second law of thermodynamics)
Entropy Entropy can be thought of as waste heat generated in any realistic process “Disorder” in a system
Second Law:Entropy of a system always increases under realistic (“irreversible”) process Only law of nature that exhibits direction of time!
Question: Are arrows independent? Hawking: Memory and entropy arrows linked (Requires energy to read one bit, increases entropy by certain amount)
“Thermodynamic system”:System with lots of particles(Gas)Obeys second law But individual particles obey Newtonian physics
Central Paradox:Gas is a thermodynamic system;obeys second law.But if gas particles individually obey time-symmetric Newtonian physics, how canarrow of time arise?
Prigogine’s Solution: Second Law is fundamental. Can’t derive. Chaotic systems manifest irreversible Behavior. Entropy increase tied up with chaos
Core Questions Do time and space exist independently of the mind? Do they exist independently of one another? What accounts for time's apparently unidirectional flow ? Do times other than the present moment exist? What do these say about divine action in the world?