What is a black hole? Do they really exist? How do they form? How are they related to stars? What would happen if you fell into one? How do you see a black hole if they emit no light? What’s the difference between a black hole and a really dark star? Could a particle accelerator create a black hole? Can a black hole also be a worm hole or a time machine? In Astro 101: Black Holes, you will explore the concepts behind black holes. Using the theme of black holes, you will learn the basic ideas of astronomy, relativity, and quantum physics. After completing this course, you will be able to: • Describe the essential properties of black holes. • Explain recent black hole research using plain language and appropriate analogies. • Compare black holes in popular culture to modern physics to distinguish science fact from science fiction. • Describe the application of fundamental physical concepts including gravity, special and general relativity, and quantum mechanics to reported scientific observations. • Recognize different types of stars and distinguish which stars can potentially become black holes. • Differentiate types of black holes and classify each type as observed or theoretical. • Characterize formation theories associated with each type of black hole. • Identify different ways of detecting black holes, and appropriate technologies associated with each detection method. • Summarize the puzzles facing black hole researchers in modern science.
03.05 – Effects of Special Relativity
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來自 University of Alberta 的課程
Astro 101: Black Holes
9 個評分
從本節課中
The Structure of Spacetime
What happens if you travel close to the speed of light? What happens to the passage of time as you fall towards a black hole? This module will explore relativity. We look at the many ways black holes affect the universe around them from discussions of reference frames through to the change in the passage of time as you approach a black hole.
與講師見面
Sharon MorsinkAssociate Professor
Department of Physics, University of Alberta
[MUSIC]
If you decide to hold a party, you need to tell your guests where and
when they should arrive.
It's not enough to simply tell your friends where the party is
without telling them when it occurs, or vice versa.
Therefore, when we use the word event,
we are using it to describe where and when something is happening.
Events can describe things like your arrival at a party,
the time you spilled your drink.
Or even something as simple as snapping your fingers [SOUND] can be an event.
I could say that I snapped my fingers about five seconds ago at this
location right here.
So an event must include details of both the position and the time.
Our universe has three spatial dimensions.
And so, a defined event could look something like x, y, z, and t.
Where x,y and z define the position, and t defines the time.
A good example of this occurs in popular TV show Big Bang Theory.
In an episode entitled The Cushion Saturation, Dr. Sheldon Cooper explains
the first time he sat on his favorite spot on the couch as follows.
In an ever changing world, it is a single point of consistency.
If my life were expressed as a function on a four
dimensional Cartesian coordinate system, that spot,
at that moment I first sat on it would be 0,0,0,0.
Sheldon feels most comfortable and at home at the x, y,
z coordinates of his spot, or 0, 0, 0.
Although he can return to the spot on the couch many times,
and he does, he can never return to the exact moment
when he first sat on the couch to experience that event again.
The reason for this is that the fourth coordinate in the event is time,
t, and is it always increasing as time passes.
Suppose he originally sat down to enjoy a 40 minute episode of Star Trek.
We can describe the end of the show as an event that happened at 0, 0, 0,
40 minutes.
The only way to return to the original event would be to use a time machine,
such as the one Leonard Hoffsteader took a ride in in Big Bang Theory episode
The Nevada Annihilation.
If we were to return to Sheldon's first time on the couch, and saw Penny riding
a skateboard past the scene, Sheldon would see her in his reference room.
Would Penny see the first moment he sits in that spot followed by
a 40 minute episode of Star Trek in the same order Sheldon experiences it?
Considering our previous discussion about slicing of space-time,
do you think all observers see the two events in the same order, or
with the same time interval between the events?
Let's explore this further using one of Sheldon's favor objects, trains.
Sheldon is preparing for a trip on the Napa Valley Wine Train in his favorite
1915 Pullman standard lounge car.
Ever the physicist, Sheldon would like to conduct an experiment
to test the consequences of a constant speed of light.
To do this, he sets up the light source in the center train car, and
has two of his friends standing in his light detectors in the caboose and
the engine at either ends of the train.
While the train is in the station, we say that it is at rest.
Here in the station, Sheldon conducts his first experiment by flashing the light and
recording the arrival times that his friends measure at each end of the train.
Since the distance to the light source is the same from the both friends,
they each detect the light at the same time.
We call this a Simultaneous Detection.
The train then leaves the station and begins its journey,
traveling at a constant speed through the mountains.
Sheldon prepares the experiment again, this time with the train in motion.
Since the train is traveling at a constant speed, once again,
the flash of light arrives at each of his friends at precisely the same time.
In both the stationary case and the one with the moving train,
the observers are at rest with respect to Sheldon and the light source.
As a result, they observe the pulses arriving simultaneously on each occasion.
Sheldon wants to know what his experiment would look like if he was stationary
with respect to a moving train, so he gets off at the next stop.
He gets ahead of the train, and
gets set up to redo his experiment as the train passes at a constant velocity.
This time, the light source flashes the moment that it passes Sheldon.
Since the train is moving from left to right,
Sheldon observes the light pulse arrive at the caboose of the train first.
Followed by the arrival of the pulse at the engine of the train second.
Sheldon is puzzled.
He observed the light pulse arrive at the back of the train first, but
his friends onboard report that the light pulse arrives simultaneously.
In Sheldon's frame of reference, the light pulses do not arrive simultaneously,
even though his friends' frame of reference, they do.
This disagreement between observers is a result of light traveling at
a constant speed no matter how quickly the source of light moves.
This is called the relativity of simultaneity.
And it describes that stationary and moving observers will report the order
of events differently depending on their proper motion with respect to one another.
As strange as it seems, both Sheldon and his friends on the train are right.
In some cases, the order of events depends on the motion of the observer.
Einstein explained this through the concepts of length contraction and
time dilation.
So why don't observers in different reference frames
agree on the order of events?
Well, think back to our block of cheese space-time analogy.
A moving observer, relative to another observer,
actually slices up space-time differently.
Not only can they potentially see events in different order than other observers,
but they also measure length and time differently.
Have a look at this graph, which represents space-time for
a stationary observer.
A stationary observer sees objects as they naturally are, and clocks run as expected.
However, a moving observer sees space-time through a different slice.
Here's what space-time looks like to a moving observer.
Both the moving observers time axis and distance axis have shifted.
Physicists say that the time and
space coordinates are rotated due to the motion of the observer.
This is a convenient picture to paint.
But what are the real observable effects of this skewed reference frame?
Well, earlier we mentioned that moving observers measure changes in
length and time.
Length contraction is given by the equation L is equal to L zero tomes
the square root of 1 minus the velocity of the observer divided
by the speed of light squared.
What this equation describes is how the length of
the object appears to a moving observer.
If I jump into a spacecraft, and I'm moving at nearly the speed of light,
objects I observe will appear to shrink in my direction of motion.
Something like the planet Earth would pass by the ship appearing to be
almost as flat as a pancake.
It's not just length that changes, though, time also changes.
Time dilation is given by the equation
t is equal to t zero divided by the square root of 1,
minus the velocity of the observer, divided by the speed of light squared.
In this case, time is modified by dividing by these terms under the square root sign.
So instead of decreasing, the time observed by the moving observer increases.
So the moving observers see all external clocks slowing down the faster they move.
Both length contraction and
time dilation are effects that are measured by a moving observer.
The faster the observer moves with respect to any object such as a clock,
the thinner it appears and the slower it takes.
Hopefully, your head isn't spinning too much yet.
Because we have to discuss an important issue with Special Relativity.
Since a moving observer appears to be stationary in their own frame of
reference, who can we trust when say that the lengths have been contracted and
the clocks have been slowed?
To illustrate this problem, we need to introduce you to the twin paradox.
Let's imagine that twins named Leah and
Luke are preparing for a interstellar voyage.
Leah will stay behind on Earth to monitor the journey.
While Luke, the adventurous one,
takes off in his spaceship capable of reaching nearly the speed of light.
Since Leah stays on the Earth as Luke speeds away,
Luke's clock appears to slow down the faster he zooms off in his ship.
But to Luke, Leah appears to be speeding away.
So to Luke, Leah's clocks have slowed down.
Both observers see the other clock as being slow,
while their own clocks are at regular speed.
How can that be?
Surely, both observers can't be right.
Welcome to the twin paradox proposed by Einstein.
Not as a paradox, but as a peculiarity of Special Relativity.
In Einstein's 1905 paper, he reasoned that if two clocks were synchronized,
and one of them were to go on a lengthy journey, the traveling clock would return
to the original location with its time lagging behind the stationary clock.
However, since Relativity says that either clocks could view the other as being
the one in motion, that is the traveling clock could consider itself at rest and
the stationary clock would therefore be the one moving away, shouldn't
the stationary clock be the one lagging behind when the other returns again?
Most explanation of the twin paradox talk about the acceleration of
the traveling twin.
It's the traveling twin that experiences the effects of time dilation,
returning to Earth much younger than the twin who stayed behind.
However, the twin paradox can be explained without accelerations at all.
Let's watch as Luke flies to a nearby star system six light-years away
while Leah stays behind on the Earth.
Luke can travel at a significant fraction of the speed of light, say 0.6c.
When we say that something is traveling at 1c,
it is the same as saying that it goes one lightyear per year.
So if Luke travels at 0.6c,
he will travel 0.6 of a lightyear, for each year of travel.
As such, Leia will say that Luke's journey takes 10 years.
However, let's carefully assess what Luke observes on his particular journey.
Luke sets his spaceship to travel at 0.6c.
In doing so, the distance to his destination changes.
At 0.6 C, the length between the Earth and
the destination has shortened by 25%.
So instead of six lightyears,
the star appears to be only 4.8 light years away from Luke's perspective.
At 0.6c, Luke's time of arrival is only eight
years after his departure from the Earth.
To Leah, this is compounded by the fact that she cannot receive any signal
from Luke marking his arrival in the nearby star system as any signal Luke
sends will come back to Leah on the Earth will travel at the speed of light.
This means that Leah doesn't even get Luke's arrival note
until 16 years after departure.
Meanwhile, Luke has turned his ship around and begins his journey back to the Earth.
Again, at 0.6c.
So the same length contraction applies.
Instead of flying across six lightyears of space,
Luke only flies the length contracted 4.8 light years.
And he is back from his distant star system after another 8 year journey.
For Leah, Luke has been gone for 20 years.
But from Luke's perspective, he has only been gone 16 years.
Luke is now four years younger than Leah.
Hopefully, you can now see why Einstein said this was a peculiarity and
not a paradox.
Luke as the moving observer, sees space itself foreshortened.
But in Leah's reference frame,
the distances haven't changed, merely the shape of Luke's ship.
We've seen the square root equation come up twice already.
So, what is it?
Well, this is a useful little equation that represents the strength
of the time dilation or length contraction based on the speed of the moving observer.
It's more commonly found in this form, called the Lorentz factor or
the Gamma factor.
The Lorentz factor is a convenient tool when discussing length contraction and
time dilation because it converts these equations into these vastly simpler forms.
So someone traveling at 10% of the speed of light, or 0.1c,
sees a 0.5% shortening in the length of a stationary object.
And a 0.5 increase in the flow of time.
That's not that much.
And even at half the speed of light, it's only a 15% change.
You need to be traveling at almost the speed of light to see significant changes.
At 90% of the speed of light, the Lorentz factor is more than 2.
Here's a graph illustrating how quickly
the Lorentz factor changes at very high speeds.
We should note that Einstein develops Special Relativity to describe physics for
observers who are not experiencing a strong gravitational force.
But what happens near an object with strong gravitational field,
such as a black hole?
Einstein realized that he had to modify his theory of Special Relativity
to make it more general and to allow for gravity.
Einstein called this relativistic theory of gravity General Relativity.
In order to understand the theory of General Relativity,
we'll begin with Einstein's first ponderings on the subject,
something called the equivalence principle.
