General_relativity

Space and Time Can Warp Your Mind

Space

What is space? Gridwork for

measuring distances

Everything – planets, stars, galaxies, and the universe

Is space infinite?

Time

What is time? The constant drumbeat of existence “Time is what happens when nothing else

does.”

Measured with atomic clocks to one part in 1015

One second since the demise of the dinosaurs

Does time have a beginning? An end?

Motion

Change of position in space over time Change in space Change in time

Motion through space variableMotion through time constantChange within fixed framework

Motion is Relative

Motion measured compared to fixed frame of reference Which frame is fixed? Which is moving?Why you can’t sit still Earth’s rotation – 800 mph Earth’s orbit – 65,000 mph Sun’s orbit – 450,000 mph Milky Way’s motion – 1,300,000 mph

Speed of Light

Speed of Light

Finite186,000 miles per second 670 million mph

Light travel distances Earth-Sun distance is 93 million miles 500 seconds of light travel time 1 light-year = 6 trillion miles

Time-Warped View

Proxima Centauri – 4.2 lyCenter of Milky Way – 27 thousand lyAndromeda galaxy – 2.5 million lyFornax cluster – 65 million lyMost distant objects – 13 billion ly

Looking out in space = back in time

Observable Universe

Finite speed of lightFinite age of the universeFinite volume observableProperties Spherical Centered on the observer Horizon, not edge

Special Theory of Relativity


Speed of light is an absolute - cPhysics is the same to all observers Observer at rest Observer in motion Inertial reference frame Our reference frame has considerable

motion

Non-relativistic Motion

Velocities add together

20 mph

2 mph

Total 22 mph

Relativistic Motion

Motions don’t add linearly

0.95 c

0.1 c

Total 1.05 c - WRONG

Relativistic sum = 0.96 c(0.1 + 0.95) c(1 + 0.1*0.95)


Thought experiments Deduce relativistic behavior Observer at rest vs. observer in motion

Speed of light is constant Change in space different Change in time different

Thought Experiment - rest

light

mirror

Measure distanceMeasure timeCalculate speed of light

Thought Experiment - motionmirror

light

Measure distanceMeasure timeCalculate speed of light

Shrinking Space

Length contraction The length of an object appears shorter

when measured by a moving observerSpaceship pilot flying at 0.99c would measure football field as 14 yards longCrowd would measure spaceship to be 1/7 as long as pilot thinksRelativistic diet tip: If you move fast, other people think you’re thinner

Stretching Time

Time dialation Time appears to slow down when

measured by a moving observer

Travel to Proxima Centauri at 0.99 c would take 4.25 yearsPilot would only age (4.25/7) years, about 7 monthsOne way time travel to the future

Light doesn’t exist?

At speed of light, lengths go to zeroAt speed of light, time stands stillPhoton of light doesn’t experience space or time Emitted Instantaneously crosses any amount of space Absorbed

In its own frame of reference, light doesn’t exist in space or time


One’s view of space and time depends on one’s motion

General Theory of Relativity


Matter warps spaceRe-interpret gravity as geometry Straight paths, but in curved space Geodesic

Extends special relativity to handle non-inertial frames of reference

Warped Space

Warped Space

Matter tells space how to curve

Curved space tells matter how to move

Gravitational Lenses

More mass, more warpWarped space can act like a glass lens

Slowing Time

Gravitational time dilation Clocks run slower in a larger gravitational

fieldTested by flying atomic clock in plane Slower due to special relativity Faster due to general relativityToday’s atomic clocks can measure altitude difference of 1 yard


One’s view of space and time depends on how much matter is around and how it is distributed

Expansion of Space

Einstein’s Greatest Mistake

Equations for the universe unstableEinstein added an energy of space (cosmological constant) term to create stable solutionMissed predicting the expansion of the universe

Energy of motion

Energy of matter

Energy of space

= +

Expansion of Space

Hubble measured motions of galaxies All appear to move away from us Cosmic cooties?

Expansion through space - WRONG Galaxies moving away from center No measurements show a center Copernican hypothesis underlies

astronomy, and all science

Expansion of Space

• Expansion of space Galaxies at rest Space between galaxies expanding All galaxies see every other galaxy moving

away No centerDifferent kind of relative motion Observers at rest Reference frame in motion

Big Bang

The Universe has expanded … from small to big from hot to cold from dense to rarified

Standard framework of cosmology Only hypothesis that fits observations Scientific theory

Big Bang Observation

Cosmic Microwave Background Remnant glow from hot early universe Seen in every direction on the sky\ Perfect thermal spectrum Time: half a million years after big bang Temperature: 3000 degrees Size: 1/1000th present size

Observational evidence that the universe was smaller, denser, and hotter in the past

Expansion of Space

One’s view of space and time depends on when in the history of the universe one is observing

SOME say the world will end in fire,

Some say in ice.

From what I’ve tasted of desire

I hold with those who favor fire.

But if it had to perish twice,

I think I know enough of hate

To know that for destruction ice

Is also great

And would suffice.

Fire and Ice - Robert Frost

“Thank You”

Education

General_relativity