Hi bcs, and thank you so much for the interesting challenge!
First, let's make a basic distinction between special and general
relativity:
Special relativity applies only to objects/systems in uniform motion,
meaning their respective speeds, or velocities, remain constant.
General relativity deals with objects/systems in accelerated motion,
meaning velocity changes over time. (It's important to know that when
talking about relativity, 'accelerated' does not necessarily mean sped
up. An object that is slowing down is also in 'accelerated' motion.
See the formula for calculating accelerated motion at the University
of Illinois at Urbana-Champaign's Physics page,
http://webug.physics.uiuc.edu/courses/phys150/fall98/slides/lect02/sld016.htm
)
Now, to explain the theories:
Special Relativity
Einstein delineated his theory of special relativity in 1905. To quote
the ThinkQuest Internet Challenge Library's page on relativity
( http://library.thinkquest.org/2890/relativ.htm ),"The heart of the
theory is that different observers moving at different rates of speed
will find that the laws of physics and the speed of light remain the
same, even though they will have different perceptions of time and
distance. Because of this, simultaneous events can appear to happen at
different times, or events happening hours apart to one person could
happen at the same time to another. In other words, your reality is
determined by your point of view."
The theory proposes several hypotheses, some of which have become more
widely accepted than others. Among them:
- The speed of light is a constant. For all observers, regardless of
the motion of the observer or of the source of the light, the speed of
light remains the same.
- The speed of light is the fastest achievable speed in the universe.
- Mass and Energy are related.
To quote Virginia Tech's Frequently Asked Questions about Special
Relativity page( http://www.phys.vt.edu/~jhs/faq/sr.html#q3 ), "If you
set up a "black box" (box you can't see into) containing some atoms,
the total mass of the box and its contents will be equal to the sum of
the mass of the box and mass of the individual atoms in the box. If
you heat the box to a high temperature (so the atoms are moving around
at high speed in the box, and thus have high energy), then the total
mass of the box and its contents will be larger than if the
temperature of the box is lower. Why? Because, the higher energy atoms
contribute more mass to the total mass than before the box was heated.
So, if you try to push on the box, you will discover that its inertia
will be larger (it won't accelerate as quickly)...in principle, if the
atoms are made to move at speeds nearing the speed of light, the mass
of the box can be made very large --- even approaching infinity."
- Objects appear to contract in length as they approach the speed of
light.
(See a great example and explanation of length contraction by The
Physics Classroom, a high school physics tutorial, @
http://www.physicsclassroom.com/mmedia/specrel/lc.html )
- The rate of a moving clock seems to decrease as its velocity
increases.
The commonly used 'light clock' example is the best illustration of
this. Imagine that you and I each have a 'clock', made of two mirrors
and a speck of light, and it takes the light exactly one second to
bounce back and forth one time. Now imagine that you are standing
still, and I am on a train that passes you. When I pass you, your
clock will appear as it always has - the light bounces straight up and
down in one second. My clock, however, will look different. Because I
am speeding past you, you will see the light from my clock moving in a
diagonal path, and that path will appear stretched out, longer than
the straight-up-and-down path of your clock. Now, since the speed of
light is constant, and from your position the light had to travel more
distance, it must have taken the light more time to bounce between my
clock's two mirrors. Therefore, to you, my clock appears must be
running slower than yours. To me, just the opposite will be true. My
clock will seem to be running normally, and yours will appear slow.)
- Events that appear to be simultaneous to an observer in one system
may not appear so to an observer in another system. (It's hard to
explain this without pictures... There is an excellent explanation of
this at 'The Dog School of Mathematics' page @
http://members.tripod.com/conduit9SR/SR3.html )
- Therefore, since absolute time cannot be measured, the observations
of observers in different systems are equally correct.
Time as the 4th dimension
Before we move on to General Relativity, it makes sense to address the
question of space-time, or time as the 4th dimension. Remember that
according to special relativity, as an object approaches the speed of
light, it contracts in length, and it's 'clock' moves slower, or takes
more time? To say it another way, space is exchanged for time. Arfur
Dogfrey's site
( http://members.tripod.com/wmhxbigguy/Theory/length.html )provides a
simpler explanation. "An object exists for a certain amount of time at
a particular place, so the four dimensions refer to the fact that an
object or event is described by four quantities, three of which
identify the location in space and one of which specifies the time."
This is the basis for time as the 4th dimension. (When we talk about
the universe in terms of more than 3 dimensions, we are talking about
"hyperspace." For more on hyperspace [specifically in terms of its
relationship to black holes], see the University of Toronto's
individual page on General Relativity @
http://individual.utoronto.ca/ajm/ast199/relativity.html )
General Relativity:
Einstein drew on his theory of special relativity to postulate the
general theory, which, as was mentioned earlier, deals with objects
whose velocities are not constant (like celestial bodies.) To once
again quote the ThinkQuest Internet Challenge Library's page on
relativity,
( http://library.thinkquest.org/2890/relativ.htm )"General Relativity
is an extension of special relativity, but it is mainly a theory of
gravity. It defines gravity as a curvature of the four-dimensional
space-time suggested by special relativity."
It goes on to use the example of a lead ball dropped on a rubber sheet
(where the rubber sheet is space-time, and the ball is an object... a
planet, for instance.) The ball will cause the sheet to curve
downwards, and that downward curve is the object's gravitational
field. The more massive the object, the greater it's field.
Furthermore, if you were to drop a less massive object on to the
sheet, it would roll towards the more massive object - in effect,
pulled in by its gravitational field.
General relativity also says that gravitational fields affect light by
bending it. (In that way, some of the stars we 'see' would not be
visible to us if their light traveled in a straight path, unaffected
by gravity... But the gravity of the sun has bent that light such that
we can see it.) One of the most researched aspects of general
relativity is the black hole - a collapsed star so massive, with so
strong a gravitational field, that nothing can escape it... not even
light.
(See ThinkQuest's page on black holes for more information.
http://library.thinkquest.org/2890/blahol.htm )
Of course, in our every day lives, we consider time a constant. Races
are run and won based on the assumption that time applied equally to
all runners. We schedule our lives based on the idea that an hour
means the same thing to everyone. We think of ourselves as living in
a 3-dimensional universe, not in hyperspace. In fact, no person or
thing in our everyday lives is moving at a speed close enough to the
speed of light for the relativity of time to have much effect on us.
But it’s fascinating and important to consider that the aspects of our
lives that we consider constant may not be… and that those same
inconstant forces are at work, on both galactic and sub-atomic levels,
all around us.
I really hope this answer provides the kind of information you are
looking for. I certainly had a ball doing the research! If you’re
interested, take a look at the additional information below, and
please, please feel free to request clarification if I can be of
further help.
Best,
Rebecca
Additional resources:
Relativity: The Special and the General Theory, by Albert Einstein
( http://www.amazon.com/exec/obidos/ASIN/0517884410/qid=1025051980/sr=2-1/ref=sr_2_1/002-5143495-5702412
)
Evolution of Physics, by Albert Einstein, Leopold Infeld
( http://www.amazon.com/exec/obidos/ASIN/0671201565/qid=1025052039/sr=1-6/ref=sr_1_6/002-5143495-5702412
)
Black Holes and Time Warps: Einstein's Outrageous Legacy
by Kip S. Thorne, Frederick Seitz (Introduction), Stephen Hawking
( http://www.amazon.com/exec/obidos/ASIN/0393312763/qid=1025052039/sr=1-1/ref=sr_1_1/002-5143495-5702412
)
Six Not-So-Easy Pieces: Einstein's Relativity, Symmetry and Space-Time
by Richard Phillips Feynman, Roger Penrose (Introduction)
( http://www.amazon.com/exec/obidos/ASIN/0201328410/qid=1025052039/sr=1-2/ref=sr_1_2/002-5143495-5702412
)
Relativity Visualized, by Lewis Carroll Epstein
( http://www.amazon.com/exec/obidos/ASIN/093521805X/qid=1025052039/sr=1-3/ref=sr_1_3/002-5143495-5702412
)
Black Holes, Wormholes & Time Machines, by Jim Al-Khalili
( http://www.amazon.com/exec/obidos/ASIN/0750305606/qid=1025052039/sr=1-5/ref=sr_1_5/002-5143495-5702412
)
Understanding Relativity: A Simplified Approach to Einstein's Theories
by Leo Sartori
( http://www.amazon.com/exec/obidos/ASIN/0520200292/qid=1025052266/sr=1-1/ref=sr_1_1/002-5143495-5702412
)
The following sites were particularly helpful in answering this
question, and are sure to be great further resources:
University of Virginia's course entitled 'Galileo and Einstein'
(Lecture Notes by Michael Fowler)
( http://galileoandeinstein.phys.virginia.edu/ )
Encyclopedia.com's section on Relativity
( http://www.encyclopedia.com/html/r1/relativi.asp )
'Arfur Dogfrey's page called Special Relativity Doggy Style
( http://members.tripod.com/conduit9SR/SR0.html )
'Autotheists' page at Geocities called 'Advanced Physics Made Simple'
( http://www.geocities.com/autotheist/Physics/sr.htm )
ThinkQuest Internet Challenge Library's page on relativity
( http://library.thinkquest.org/2890/relativ.htm )
I searched for:
what does "uniform motion" mean?
( ://www.google.com/search?sourceid=navclient&q=what+does+%22uniform+motion%22+mean%3F
)
special relativity clock
( ://www.google.com/search?sourceid=navclient&q=special+relativity+clock
)
special relativity contraction
( ://www.google.com/search?sourceid=navclient&q=special+relativity+contraction
)
special relativity mass
( ://www.google.com/search?sourceid=navclient&q=special+relativity+mass)
"time the fourth dimension"
( ://www.google.com/search?sourceid=navclient&q=%22time+the+fourth+dimension%22
) |
