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ASTRO 130 - NIEL BRANDT
QUESTIONS FROM THE STUDENTS
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If you find errors in the questions or answers below, please let me
know. I'll work to improve them.
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What is an inertial frame? What is an inertial force?
Inertial frames are the "arena" in which special relativity can
correctly describe Nature.
In special relativity (where there is no spacetime curvature),
an inertial frame is one where
* A free particle released from rest stays at rest.
* A particle launched with a given velocity maintains
the magnitude and direction of that velocity.
Thus, in special relativity, a frame where there is gravity
would _not_ be an inertial frame. However, a frame moving
with constant velocity out in isolated space would be an
inertial frame.
You can think of the word "inertial" as meaning "freely
floating."
An inertial force is a force arising from the acceleration
of an observer's frame of reference.
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Given that light is the fastest thing to exist in the Universe, how fast
do other wavelengths of light move in proportion to it? In a vacuum will
gamma-rays travel faster or slower than visible light?
All types of light travel at the same speed, c, in a vacuum. This includes
Radio waves
Microwaves
Infrared radiation
Visible light
Ultraviolet light
X-rays
Gamma-rays
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According to special relativity, is the speed of light the only thing that
is not relative?
No, there are other things that are not relative too. Some examples
include...
The Minkowski absolute interval (see Chapter 2 of the Thorne book)
The underlying mathematical form of the laws of physics (for example,
Maxwell's laws of electromagnetism)
Some physical constants, such as Planck's constant
For another interesting possible example, see the short article by Giovanni
Amelino-Camelia in Nature 418, 34 (4 July 2002). This should be available
from the library on the second floor of Davey Lab.
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What special and general relativity effects need to be taken into account
for Global Positioning System (GPS) satellites?
Some examples include...
The satellites are moving relative to a person on the Earth. This has a
"slowing" effect on their atomic clocks.
The satellites are high up above the surface of the Earth. The gravitational
potential there is less. This has a "speeding up" effect on the satellites'
atomic clocks.
The satellites move through Earth's gravitational field, and this changes
the rate at which the atomic clocks on them run. The Earth is not a
perfect sphere, and its gravitational field is actually complex.
In total, relativistic effects are about 10,000 times too large to ignore.
When you fly in an airplane during bad weather, the GPS is one of the
key things that lets the pilots fly safely. So thank Einstein the next
time you make a safe landing. Thank the pilots too, of course!
For a detailed discussion of this topic, see the article by Neil Ashby on
page 41 of the May 2002 issue of Physics Today. This should be available
from the library on the second floor of Davey Lab. Also see Project A in
the book _Exploring Black Holes_ by E.F. Taylor and J.A. Wheeler.
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In the book by Begelman & Rees, they say that "Nowhere is gravity stronger
than near the objects we call black holes." Is this statement absolutely
conclusive? How do they know that even when we haven't explored all of space?
We have not been able to prove this strictly in an observational sense,
since as commented above we have not explored all of space. However, we
have good evidence that general relativity applies throughout the
entire Universe. Since we think it is universal, we theoretically expect
that the statement by Begelman & Rees is correct.
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Do photons of light have mass? If not, what implications does this have?
Photons of light have no rest mass. One implication from special relativity
is that any particle without rest mass _must_ move at the speed of light.
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Why is the speed of light 300,000 km/s? Why does the speed of light not have
some other numerical value?
Nobody knows the full answer to this deep question. Someday, when we know
all the laws of physics, we hope to be able to calculate the speed of
light from first principles. For some further discussion on this see the
book _The Life of the Cosmos_ by Lee Smolin (chapter 7 is the most
relevant one to my knowledge).
One could imagine a universe where the speed of light has a different
numerical value, say 200 miles per hour. Einstein's laws of relativity
could still hold in such a universe, although the mathematical equations
would contain a different numerical value for the speed of light (all
velocities in Einstein's relativity enter the equations only relative to
the speed of light). If we could exist in such a universe, we would see
relativistic effects when we drive our cars!
Also see
http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/fast_light.html
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You mentioned that we've known about the aberration of light for quite some
time now. How and when did the first signs of this come to light? Was this
pre-relativity?
Aberration of light was discovered in 1725 by James Bradley. He found that
all distant stars displayed an apparent systematic movement related to the
direction of the motion of the Earth in its orbit. This stellar aberration
is analogous to the well-known falling-raindrop situation. A raindrop,
although falling vertically with respect to an observer at rest on the
Earth, will appear to change its incident angle when the observer is in
motion. Special relativity effects make the real situation more complex
than the falling-raindrop analogy. For further discussion see
http://www.fourmilab.ch/cship/aberration.html.
Aberration of light was known well before Einstein's relativity.
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If I travel at 87% the speed of light and I see everyone on Earth's clock
slowed, why when I return to Earth from my journey is everyone so much
older than me?
In your journey away from Earth and back to Earth, this is not actually
what you will "see." You need to take into account the "standard" Doppler
shift effect as well as relativistic time dilation. This issue is
often discussed as part of the "twin paradox." For full discussion see
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html
and the associated World Wide Web pages.
Take the twins in the twin paradox to be named
Stella = Flying in the spaceship
Terrence = At home on Earth
The situations of Stella and Terrence are not "symmetric." Stella felt the
acceleration on her trip outward as well as when she fired her thrusters to
turn around and return to Earth. Terrence did not feel this acceleration.
More technically, special relativity does not declare that all frames of
reference are equivalent, only so-called "inertial frames." Stella's frame
is not inertial while she is accelerating.
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