Ch 14. Down the Rabbit Hole
What was the "luminiferous aether" believed to be, and why did physicists propose that it existed?
"Luminiferous aether" was believed to be the material through which light waves propagated. Scientists thought all waves needed a material in which to propagate.
What is a frame of reference? What and who currently share your frame of reference?
A frame of reference is the perspective of a person making observations. Any object or person who is experiencing the same motion as you shares your frame of reference.
black hole
A region of space-time whose strong gravitational distortion prevents anything, including light, from escaping.
Quantam gravity
A theory (yet to be fully worked out) that unifies general relativity and quantum mechanics, describing how space-time becomes granular ("quantized") at the smallest scales.
What happens inside the horizon?
According to Einstein's equations, space and time reverse roles in a very strange way. Just as we can only travel into the future in normal space-time, now there is only one direction in space you can travel and that is into the singularity. Thus your journey ends as you are drawn toward the giant mystery that is singularity.
How does the detection of muons on the surface of Earth, after they are created high in Earth's atmosphere, provide evidence of special relativity?
After creation muons speed toward the Earth at 99 percent of the speed of light. Muons are expected to decay in less than one-millionth of one second after they are created and so should not be detected. But scientists do find muons in their ground-based detectors, suggesting that these particles are not decaying at their normal rate. The reason for this surprising finding is relativistic time dilation.
special theory of relativity
Albert Einstein's first theory of relativity, stating that the laws of physics are the same for all observers that are in uniform motion relative to one another, and that the speed of light in a vacuum is the same for all observers, regardless of their relative motion.
general theory of relativity
Albert Einstein's second theory of relativity, which extends to the special theory of relativity by incorporating gravity. 1. Matter-energy tells space-time how to bend 2. Space-time tells matter-energy how to move
Massive Stellar Cinders
Astronomers currently estimate that stars greater than 20-30 MSun become black holes. A high-mass star burns through a sequence of elements up to iron after its core hydrogen is exhausted. The star collapses on itself. With nothing to restrain the inward crush of gravity, it collapses further toward an ever-smaller radius. Because a zero radius gives a zero volume, the stellar density shoots toward infinity as the radius shrinks to nothing.
What evidence suggests that massive black holes exist in galaxies?
Astronomers have detected Doppler-shifted material falling toward the centers of galaxies. From these measurements they have been able to determine the mass of the central object. The mass is so large and packed into such a small region of space that the only possible explanation is a black hole.
Pulsars and Gravity Waves
Astronomers used the binary pulsar PSR 1913+16 to infer the existence of gravity waves, ripples in the fabric of space-time Concluded that two pulsars were slowly spinning inward toward each other. Their orbit was shrinking as energy was lost to the elusive gravity waves. The exact amount of orbital decay matched perfectly the predictions of gravity wave generation. First time gravity waves were directly detected.
Two spaceships are moving in opposite directions, spaceship A traveling at 0.9c and spaceship B traveling at 0.95c. Which of the following statements is true?
Both measure light passing them at c.
How do astronomers determine the mass of these central objects?
By analyzing the lights doppler shift astronomers determined the speed of the orbiting gas and therefore could derive the mass of the central object.
Why did Einstein conclude that space and time must be unified and measurements of each depend on an observer's frame of reference?
Einstein concluded that measurements of space and time must depend on an observer's frame of reference because the speed of light does not vary from one reference frame to another. Length (Δx) and time duration (Δt) have to change from one frame of reference to another so that the speed of light Δx/Δt that you measure and the speed that I measure remain the same.
Gravity and Acceleration
Einstein realized that moving in an accelerating frame of reference feels equivalent to the presence of gravity. The astronaut and tools in the spacecraft moving at a constant velocity seem to be weightless. But when the astronaut is in an accelerating spacecraft or experiencing the gravity on the surface of a world, he and his tools react similarly.
What were some of Einstein's thought experiments?
Einstein's thought experiments involved imagining a person in an accelerating rocket. The person is accelerated toward the floor. He realized that a person inside an accelerating rocket has the same experience as a person in a rocket at rest sitting on a planet's surface. In another thought experiment Einstein imagined a person in a rocket free-falling in orbit around the Earth and a person in a rocket with the engine turned off. In both cases the person would float freely in the capsule, and the conditions would be indistinguishable from a state of constant motion.
(T/F) The theory of general relativity has no experimental evidence supporting its predictions.
False
True/False: The 1919 solar eclipse provided support for relativistic length contraction
False
regarding special relativity and general relativity, which of the following is true?
General relativity alone deals with gravity
What credentials did Albert Einstein hold at the time he submitted his manuscript on special relativity to the most famous physics journal of the time?
He had a degree in physics. But was simply a clerk working at the Swiss patent office.
Black Holes Gravitational pull
If our sun turned into a black hole Earth would still go on its orbit just in darkness. It's only relatively close to the event horizon that the strange general relativistic effects appear.
Think about any movies or TV shows in which black holes have been portrayed. According to what you now know about black holes, were they reasonably accurate?
In TV and movies black holes are depicted as portals to other parts of space. However, real black holes would tear any spacecraft to pieces with tidal forces and destroy any spacecraft with radiation from an accretion disk or jets. However, supermassive black holes (those at galactic centers) will not have extreme tidal effects until the observer is within the event horizon.
Black Holes Merging
In the process, the structure of space and time around the black holes is distorted as predicted by Einstein's general theory of relativity. Moving from left to right we see gravity waves (red) emitted more intensely as the two black holes spiral inwards towards each other. Eventually the holes merge into a single object.
Would you want to catch the mailbag while standing inside of the train or while standing on a platform outside the train?
Inside the train. Outside the train would be the velocity of the bag moving plus the velocity of the train moving.
Imagine that you are standing on a shore watching a boat move on a river. How would you measure the velocity of the boat you are observing?
It is the velocity of the water compared to you plus the velocity of the boat compared to the water.
Which of the following is true about gravitationally induced motion, according to general relativity?
It occurs as objects fall freely following the curvature of space-time
Which of the following statements about Einstein's theory of gravity, compared with Newton's law of gravity, is true?
It showed that Newton's laws were a "limiting case" of general relativity that applied only when velocity and gravity were relatively low.
What are some of the effects that occur near black holes?
Near a black hole time is dilated, light is shifted to longer wavelengths, and light is lensed so that objects directly behind the hole would appear to a distant observer as a bright band that runs around the edge of the event horizon. Tidal forces will tear any object apart as it gets near the black hole event horizon. However, supermassive black holes (those at galactic centers) will not have extreme tidal effects the observer is within the event horizon.
spaghettification
Near a black hole, space-time is so distorted that your feet are being stretched toward the black hole much more strongly than your head.
describe a situation in which the "addition of velocities" gives a correct result.
One situation in which the "addition of velocities" gives a correct result is if a friend tosses a ball to you from a moving car. The ball's velocity is the addition of the car's velocity and the velocity at which it was thrown.
For what kinds of situations is special relativity relevant? For what kinds is general relativity relevant?
Only when objects are in motion at a significant fraction of the speed of light (10 percent of c) do the predictions of special relativity come into play in any sort of noticeable way. General relativity effects will become significant in the presence of large concentrations of mass.
The formula to determine the Schwarzschild radius
Rs = 2GM/c^2
string theory and loop quantum gravity
Some of this work indicates that the collapse may be halted at the smallest scales, as the tiny quanta of space-time resist further compression. But without a complete description of a quantized space-time, the singularity remains a fundamental mystery--a tear in the fabric of reality.
Curved Space-Time
Space-time can be thought of as stretched or curved toward the center of Earth by Earth's mass. The general theory of relativity states that matter-energy tells space-time how to bend, and space-time tells matter-energy how to move.
What are the differences between supermassive black holes and stellar-mass black holes in terms of how they form?
Stellar mass black holes form from the collapse of a single high-mass star, whereas supermassive black holes form in the centers of galaxies.
How is the bending of starlight used to test general relativity?
Studying the positions of stars in a night sky comparing them with their apparent positions during a solar eclipse. When starlight passes near the position of the Sun its path should be deflected by the massive object's curvature of space--an effect called gravitational lensing. When observing the eclipse they could see even light is subject to the bending of space-time by a massive object.
singularity
The central point of a black hole, where density and space-time curvature is infinite.
Describe the evidence for the existence of black holes
The discovery of Cygnus X-1 was the first strong evidence for the existence of black holes. Cygnus X-1 is a binary system with an invisible 10 solar mass companion that emits X-rays. The X-rays originate from an accretion disk around the black hole. In addition, the large amounts of energy emitted from the centers of active galaxies could only be produced by material falling into the black hole.
Which of the following does/do not represent a successful test of relativity? Choose all that apply
The discovery of the wave nature of light weightlessness experienced by astronauts in space
Schwarzschild radius
The distance from a black-hole singularity where the escape velocity equals the speed of light Defines a point of no return for all objects falling into a black hole The Schwarzschild radius equals about 3 km for each solar mass in the black hole.
What phenomenon defines the event horizon of a black hole?
The event horizon of a black hole is defined by the radius at which the escape velocity equals the speed of light.
Geometric points have no volume, so how can the entire mass of a star occupy zero volume?
The fact that quantities like density and temperature approach infinity at the singularity really tells us that the physics we do understand--Einstein's general theory of relativity--must break down at the center of a black hole. In that way, the singularity is a road block for physicists. all reality must be described by quantum physics, on the smallest sizes nature always becomes granular. "nothing quantam about it and thats the problem"
What happens when a singularity is forming at the center of a black hole, and the collapsing material reaches its Planck length?
The laws of quantum gravity should begin to operate, modifying the collapse. Unfortunately a theory of quantum gravity does not exist.
Plunging into a Black Hole
The nature of a black hole will change if it is rotating or carries an electric charge. Black holes distort space-time. As you get closer, your path becomes a long spiral towards the event horizon. The effects of gravitational time dilation and gravitational redshift become apparent to an observer far from the black hole. If you were near a black hole, you would be able to see stars in the background gravitationally lensed into a ring around the event horizon. The blackness of the event horizon fills your field of view. You are now plunging into a black hole!
Black Hole Models
The problem that astrophysicists have with building models of black holes is that the density, temperature, and curvature of space-time become infinite at the singularity. The singularity is essentially a geometric point.
How do muons become a test of special relativity?
The time it takes one to decay takes longer then the time they are sent down to Earth. Since Scientists can find them in their ground-based detectors it suggests that these particles are not decaying at their normal rate.
Explain the difference between core mass and main-sequence mass in determining the end product of star depth.
The total mass of a star may be described as its "main sequence mass." However, stars lose mass through a number of processes after they leave the main sequence. The mass of the star's core will determine exactly what happens in the last moments of the star's life. A black hole, neutron star, or white dwarf may form depending on the mass of the core. The core will collapse into one of the above stellar remnants.
How do electromagnetic waves travel across space?
The transfer of energy by electromagnetic waves is called electromagnetic radiation. ... When it travels through space, it doesn't lose energy to a medium as a mechanical wave does.
What is the twin paradox?
The twin paradox describes how the time passes differently for two twins when one twin travels at 99.9 percent of the speed of light. The traveling twin travels to a star 30 light years away and returns to Earth. Her Earth twin experiences 60 years of time while the traveling twin is only three years older.
True/False: Spaghettification upon approaching the event horizon of a black hole occurs because gravity varies with distance from its source.
True
What was the name of one of the first X-ray space telescopes launched by NASA?
Uluru launched in 1970
Massive Stellar Cinders
When the hydrogen-burning phase ends for intermediate-mass stars (M < 8 Msun) the cores contract enough to initiate helium fusion. Once the helium is gone, core fusion ends. From that point on, only the quantum mechanical degeneracy pressure of electrons keeps the burned-out stellar cinder alive as a white dwarf. Higher-mass stars (M > 8 Msun) burn through a sequence of elements up to iron after their core hydrogen is exhausted. But since iron requires more energy to fuse than it gives back, the star collapses on itself, creating a solid neutron core in some cases. The ultra dense neutron star is another kind of stellar cinder that, like white dwarfs, is supported against gravity by the quantum physics of degeneracy pressure, though this time it's the neutrons that are degenerate. Since a zero radius gives a zero volume, the stellar density (mass divided by volume) shoots toward infinity as the radius shrinks to nothing. Physicists call this kind of infinite limit a singularity and its creation is the black hole. Many factors including the rate of rotation, determine whether a newly formed neutron star will be stable or will survive for just a brief time before collapsing into a black hole. Truly massive stars may even form a black hole at their center before a neutron core can form.
Simple math of time dilation
You can calculate how long a sneeze takes as experienced by the sneezer by using the round trip of a laser pulse, according to Δty = 2 H/c, where Δty is the sneeze duration, H is the capsule height, and c is the speed of light.
A baseball player is traveling away from you at a speed of 140 km/h. He throws a baseball that, according to him, is traveling at 90 km/h in your direction. What do you see the ball doing?
You see the ball traveling away from you at 50 km/h.
How does your cell phone use GPS technology to keep time?
Your cell phone compares its own clock with the time measured by the satellites. It then uses the difference between the times to calculate your distance from each satellite. Since light travels at 300,000 km/s a time difference of one-thousandth of a second implies that the ground-based receiver must be 300 km from the satellite. This comparison of the receivers time and the time signal sent by the four satellites enables accurate determinations of the receiver's position.
supermassive black holes
a black hole of millions or billions of solar masses that is found in the center of a galaxy. Masses between 10^6 and 10^9 Msun.
Two spacecraft (X101 and X102) with different velocities relative to each other pass in interstellar space. Which of the following cannot be true?
a distant observer measures zero velocities for both
cosmic ray
a high-speed subatomic particle (atomic nucleus) from space.
In the twin paradox, the twin who travels in the spaceship experiences
a normal flow of time in her frame of reference
which of the following shares your reference frame while you're reading this book in your room?
a person in an adjacent room of your residence
E=mc^2
a statement that mass can no longer be seen as something unchanging and unchangeable. Einstein's relativity showed that mass is a form of energy. The terrible power of atomic weapons and the gift of light from the Sun are both testaments of how through this equation, Einstein's relativity captured new fundamental truths about the world.
space-time
a unified, four-dimensional geometry of the Universe that incorporates both space and time. (three dimensions of space and one dimension of time)
galaxy
a vast collection of stars, gas, and dust with a total average mass of approximately 10^12 MSun. At the center of many galaxies are supermassive black holes.
muon
an elementary, extremely short-lived particle that is heavier than an electron.
frame of reference
an individual perspective from which observations are made.
Microquasars
binaries in which one of the companions is a black hole or a neutron star. Jets of material can move at velocities of 0.99 c and are seen hurtling away from microquasars.
an observer moving at 90 percent of the speed of light (0.9c) would observe light around him to be moving at
c.
John Mitchell
discovered that if the mass M of a central object was large enough, or its radius R was small enough, then the escape velocity would be greater than the speed of light: Ve > c.
Which of the following is/are not measurable properties of black holes? Choose all that apply
elemental composition color
Which force or process is primarily responsible for creating a black hole?
gravity
The Twin paradox
illustrates the effect of "time dilation" in special relativity. For the twin who rockets away on a spaceship traveling at a substantial portion of the speed of light. Time flows more slowly relative to the twin who stays home on Earth. Although each sister feels her own time passing at a normal rate. It's only the relative flow of time between the two frames of reference that changes. The acceleration of the spaceship is what breaks the symmetry between the sisters. while the length seemed the same for both, due to time flowing faster for the sister on Earth their durations were different.
Binary black hole
is a system consisting of two black holes in close orbit around each other. ... As the orbiting black holes give off these waves, the orbit decays, and the orbital period decreases. This stage is called binary black hole inspiral.
As an object approaches the event horizon of a black hole, the light from it is observed to become
longer in wavelength
The Event Horizon calculation
pg. 367
X-Ray Binaries
pg. 371
Stephen Hawking
proposed the principle of cosmic censorship in which naked singularities (singularities lacking an event horizon) would never occur.
James Clerk Maxwell
provided an explanation of light as an electromagnetic wave before Einstein was born. According to this explanation, the visible light our eyes respond to is nothing more than waves of oscillating electric and magnetic fields traveling through space at the tremendous speed of 300,000 kilometers per second, or 670 million miles per hour.
A patent clerk in a spaceship observes that time on the clock of an astronaut on a spaceship passing at 0.25c runs slower than does time on his own clock. This phenomenon is called
relativistic time dilation
Which of the following is the densest?
singularity of a black hole
What did scientists detect with this X-ray telescope?
strong signals emerging from a region associated with a blue giant star (of spectral class B) located in the constellation Cygnus. Tagged as a candidate for a black-hole binary system when analysis of the B star's motion showed it in orbit with a massive but unseen object.
The event horizon
the boundary of a black hole, located one Schwarzschild radius (Rs) out from the singularity. Inside a black hole-- is a region of space-time that is entirely cut off from the rest of the cosmos.
What do astronomers mean by the singularity of a black hole?
the center of the black hole, where density and space-time curvature are infinite
gravitational lensing
the change in the path of light passing a massive object produced by the curvature of space-time
Cosmic censorship
the conjecture that the Universe will not allow the existence of a singularity without an event horizon.
The no-hair theorem
the description of a black hole as having only three properties—mass, spin, and electric charge—that never get erased when matter crosses the event horizon.
Time dilation
the effect of relativity in which time runs slower for objects near a strong gravitational source or for objects that are moving at relativistic speeds in the reference frame of distant observers. the fact that time flows more slowly in some reference frames than in others.
Frame dragging
the process by which a massive, spinning object pulls the surrounding space-time around with it, such as a black hole. Once the material spirals into the inner regions of the accretion disk, frame dragging forces it to plunge directly into the event horizon
The Planck length
the size scale at which space-time should begin showing its quantum nature, about 10-44 meters (a hundred million billion billion billion billionth of a meter); smaller than the nuclei of atoms.
Which of the following statements is/are consistent with Einstein's special theory of relativity? Choose all that apply
there is no privileged frame of reference the speed of light is an upper bound to motion in the universe time is not the same in all frames of reference
How do scientists explain the creation and composition of these relativistic jets?
they are composed of material that has been lifted off the inner regions of an accretion disk surrounding a black hole. Magnetic fields tied to the rapidly spinning disk fling material out into space in a process resembling the way jets are created from young stars. Plasma tied to those field lines gets whipped around with the disk's rotation at relativistic speeds. When the gas eventually gets flung out into space, its already moving close to the speed of light. The relativistic speeds tell astronomers that the launching must occur in the inner regions of the disk, where the orbital speeds are also relativistic. Gas rotating at 200 km from a 10-Msun black hole moves at about 81,000 km/s or 27% of light speed.
If GPS satellites orbited higher, which of the following would be true regarding the general relativistic adjustments currently required for accuracy of positioning on Earth's surface?
they would be greater because of the greater difference in the curvature of space-time between the ground and satellite.
What is true about a black hole?
time runs slower near a black hole
relative motion
watching a boat move on a river from the shore, you would measure its velocity to be the velocity of the water relative to you plus the velocity of the boat relative to water.
The Chandrasekhar limit applies to which kinds of objects?
white dwarfs
stellar-mass black holes
with masses from 1 MSun to 100 MSun
Does frame dragging happen on Earth? If so, how?
yes it is caused by any massive rotating object just to a weaker affect. pg. 372
If you could be 475 km from the center of a 200-Msun black hole, which of the following would be true?
you would no longer be able to communicate with the rest of the universe