January 10, 2024 • 47 mins
How do the theories of special relativity and general relativity apply to satellites? Why is the speed of light constant, but time and distance are not? We get all Einstein up in here!
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Speaker 1 (00:04):
Welcome to Tech Stuff, a production from iHeartRadio. Hey therein
Welcome to Tech Stuff, I'm your host, Jonathan Strickland. I'm
an executive producer with iHeartRadio, and how the tech are you.
We have an episode that originally published on July first,
twenty twenty. It's called It's All Relative And when I
(00:28):
was a kid, I was convinced that Einstein's theories were
these super complicated explanations of the universe that really had
no real intersection with my daily life. But as it
turns out, without an understanding of relativity, a lot of
the technology we rely upon wouldn't work properly. And it's
fascinating stuff. Hope you enjoy. The hertz unit refers to
(00:55):
the number of repeated phenomena over the course of a second.
So well, imagine that you're dribbling a basketball, so that
the ball goes from your hand to the ground back
up to your hand once per second. Well, you could
describe your dribbling as being one hurts in frequency one
full cycle per second, up down, up. Now, if you
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dribbled twice as fast, so that the ball went up, down,
up two full times per second, then it would be
two hurts. Well, we can describe lots of stuff with
the unit hurts. We use it to describe sounds, in
which case we're talking about the frequency at which stuff vibrates.
Typical human hearing spans a range of frequencies that at
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the low end is at twenty hurts. That represents the
lowest pitches of sounds. You get to go those deep
bass notes. That's around the twenty hurts of area, and
then it goes all the way up to twenty kill
a hurts or twenty thousand hurts. That represents the very
highest pitches that people can typically hear, and those frequencies
(02:01):
correlate to how quickly stuff is vibrating back and forth. Now,
when it comes to us hearing things, we usually mean
that we're talking about the vibrations and fluctuation and air pressure,
and those fluctuations and air pressure interact with our ear drums.
But we can use hurts to talk about all sorts
of stuff, including the processor speed of a CPU. In
(02:22):
that case, we're really talking about the number of clock
cycles per second, So you get it. This is a
description of the frequency of the number of times a
certain thing happens like within a second. And I also
explained that we measure the rate at which we can
send data using the term bits. A bit is a
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basic unit of digital information, and when we talk about computers,
we're talking about bits in the form of a zero
or a one binary information, just like your basic two
way physical switch has two positions off or on. So
if you hear a term like kill a bit, that
means one thousand bits, and a megabit is one million bits,
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and a gigabit would be one billion bits. Likewise, megabits
per second tells us how many million bits can move
from one point to another per second over that connection.
So if you've got a one hundred megabit per second connection,
theoretically it would mean that up to one hundred million
bits can transfer across that communication channel per second, though
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that's not how it works out most of the time,
but that's a matter for a different episode. I didn't
mention that this is different from something like megabytes. So
a byte is a unit that consists of eight bits.
And this gets confusing because we often describe stuff like
file sizes in terms of bytes, but transfer speeds in
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terms of bits. So let's say that you do have
that one hundred megabits per second download speed, and you
want to download a one hundred megabyte file, well, that
means it's not going to take one second. It's going
to take eight seconds to download the file, because a
megabyte is eight times larger than a megabit. And actually
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even that is a little bit misleading because in computer
memory terms, we typically look at units of memory based
on powers of two rather than powers of ten. So
instead of a kilobyte being one thousand bytes, it's actually
one thy twenty four bytes. And there's no standardization in
the tech industry, so sometimes people will say a kilobyte
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and they mean one thousand bytes. Sometimes they'll say killobyte
and they mean one thy twenty four bytes, and you
will want to tear your hair out, and then you'll
look like I do, I'm bald if you didn't know.
But this episode isn't about the peculiarities of our naming
conventions and the computer information age. Instead, I wanted to
tackle something else that affects everything really, but in particular,
(04:59):
we really had to suss it out in order to
make certain types of satellites work properly, and this is
the concept of relativity. So in this episode, we're really
going to learn why an understanding of relativity is important
if we want our certain satellite technologies to work, and
it serves as a great reminder that technology is only
really possible through an understanding of science. You can think
(05:22):
of tech as the physical manifestation of our understanding of
scientific principles, and that means if we were wrong in
our understanding of science, the technology shouldn't really work. So
in a way, you can think of technology that works
as evidence that the scientific method is a darn good formula.
Since we're talking about relativity, it means we're going to
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be talking about a real Einstein today. His name was Einstein,
which is convenient. But before we get to Einstein, we
have Galileo Galileo Galileo figure Ro. Wait No, I'm sorry,
wait that's Bohemian Rhapsody. I meant Galileo Galilei. This. Galileo
made an observation that if you've got two observers moving
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at a constant speed and direction, so they're moving at
the same velocity, they will get the same results for
any experiment that involves moving stuff around a mechanical experiment.
This is easier to understand if we use an example,
and I like one that my colleague Robert Lamb used
when he wrote about relativity for HowStuffWorks dot com back
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in the day. He used an example of a train
and a scientific ping pong ball. All right, so imagine
you've got a scientist who's standing in the middle of
an aisle on a moving train, and the train is
moving at a steady speed in a straight line, so
there are no active forces of acceleration going on here. Remember,
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acceleration describes a force that involves a change in velocity,
so that either means a change in direction or a
change in speed, or both. But in this case constant
speed constant direction. Robert used nice round numbers in his examples,
so he suggested that the train is moving at one
hundred miles per hour. Well it's not round. If we
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go to the metric system, that would be one hundred
and sixty one kilometers per hour. If the train stays
steady to the scientist, it will feel as if that
scientist is actually just standing still, just anywhere, and we're
conveniently ignoring an emotion that would happen due to irregularities
with the train's wheels or the train tracks or anything
like that. And if this is hard for you to imagine,
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just think about how you feel when you're standing still
or sitting still or laying down here on Earth. We
know the Earth is moving through space. It is a
body in motion, but when we are still relative to
the Earth itself, we don't feel that motion. Assuming there's
not some other weird event going on, like an earthquake,
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which is something separate. But back to our hypothetical train,
the scientist tosses the ping pong ball down the aisle. Now,
from the scientist's perspective, this ping pong ball will travel
at whatever speed they threw it at. Robert actually suggests
a relatively gentle toss of five miles per hour or
eight kilometers per hour. The ping pong ball would bounce
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down the aisle, just as it would if the scientists
were to toss the ball on a train that isn't
moving at all, or on just flat ground. However, let's
say we have a second observer who's not on the train.
They're standing off to the side, and they can see
through the train. To this person, it will appear as
if the ping pong ball is moving very fast. Indeed,
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relative to this stationary observer, the ping pong ball will
appear to move at the speed at which it was
thrown in addition to the speed of the train itself.
So if we take the two figures, we would get
one hundred five miles per hour or one hundred and
sixty nine per hour. This is called a Galilean transformation. Alternatively,
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if the scientists were throwing the ping pong ball in
the opposite direction of the train's travel, so they're facing
toward the back of the train, it would appear to
this second observer the ping pong ball was moving at
a slightly slower speed than the overall train was, whereas
to the scientist on board, the ping pong ball would
still be traveling at that five mile per hour speed.
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So this is where the term relativity comes into play.
The effects observed are relative to the perspective of the observer.
It's all based on the reference frame of that observer.
If you're on the train, then you're just looking at
a ping pong ball bouncing at a relatively slow speed
down the aisle. If you're not on the train, the
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ping pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
all tracks. I don't know why he talked like that.
In his Laws of Motion, Newton stated that these laws
of motion should hold in an inertial frame as well
as reference frame that was moving at a constant velocity
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relative to the inertial frame. An inertial frame, by the way,
is just a frame of reference in which there are
zero net forces acting upon it, so that there are
no forces of acceleration in play. So in our example,
the train that we talked about, that would be our
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
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the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that.
But hey, what if you're on a train that's traveling
one hundred miles per hour and you're facing forward, you're
facing the direction of travel, and then you have a
flashlight and you turn on the flashlight. Well, doesn't that
mean you should perform a Galileean transformation on this and
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say the light from that flashlight in your hands is
actually traveling at the normal speed of light on board
the train. But also get that boost of the trains travel,
so it should be the speed of light plus one
hundred miles per hour. Doesn't that make sense? While according
to actual experiments performed before Einstein would come around to
explain things, the answer was Nope, doesn't look like it
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works that way. Scientists Edward Morley and Albert A. Michelson
created an experiment to measure the speed of light back
in eighteen eighty seven, and actually they were looking for
something else. They were looking for evidence of a hypothetical
substance called luminiferous ether. Say why, all right, we'll stick
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with me, because in a way this does make sense. Okay,
So on Earth we see waves traveling through a medium, right,
Like if you look out in the ocean, you can
see actual waves in the water, and the water is
a physical medium through which these waves travel. Sound can't
travel in space because space is effect actively a vacuum.
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The particles that are in space are so far apart
from one another that there's no way for the vibration
of one particle to come into contact and affect another particle.
So sound can't travel. Sound travels through the propagation of
vibrational waves. And if your stuff isn't in contact with
each other, there's no way for them to have that
wave propagate. So there has to be some sort of
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medium like air or solid surfaces or something in order
for sound travel. Well, if that's the case, said the
folks of the time, then stuff like light must need
some sort of medium to travel through, right. I mean
sound has to have something. Light must have something too.
Light can definitely travel through space. I mean, that's how
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we can see anything, because light from the Sun travels
through space to hit the Earth. So the light has
to be moving through some sort of medium we cannot
observe directly. This hypothetical medium was the aforementioned maniferous ether.
But assuming this ether existed at all, it had to
be pretty darn special because we can't feel it, we
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can't detect it, it creates no observable effects, So if
it were real, it had to be unlike pretty much
anything else we had discovered up to that point. Now,
let's assume that the universe is filled with this ether stuff.
The question rises, how the heck does the ether interact
with all the physical stuff that's in the universe, the
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actual matter and also energy. After all, the bodies in
space like stars, planets, moons and all that other stuff.
All of that is moving, none of it is standing still,
and if it is moving, it would presumably disturb this
ether medium, right. I mean, if you move your hand
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through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
the motion of all these elements in space would disturb
the ether in some way, and hypothetically there would be
some sort of ether wind. But if there were a wind,
then presumably the speed of light would be affected depending
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upon the wind's direction in relation to the light's direction.
So think of a really windy day in the real world.
If you're walking against a very very tough wind, like
a gale force wind, you have to power through it
to keep moving forward. Now, if you're walking with the wind,
like the wind is to your back and pushing you,
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then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
and so Mickelson and Morley devised a gadget that would
split light into two beams, directing those beams down different paths,
using mirrors in different directions, and seeing if those two
beams of light would hit an eyepiece at different times.
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The thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
one would be at a cross direction of ether wind,
So we should see a difference in the amount of
time it takes for the light from this one source
that's been split into two to arrive at an eyepiece.
But that's not what they found. They observed no such effect.
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So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
hundred eighty six thousand miles per second or around three
hundred thousand kilometers per second. Now that flew in the
face of classic Newtonian physics clearly. With the example of
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the ping pong ball and the train, the ping pong
ball has to be traveling faster than the train it's on.
I mean, that just makes sense. If you were standing
on the top of the very front of the train
and then you threw the ping pong ball, and we
ignore stuff like wind resistant, the ping pong ball would
land ahead of the train, So it has to be
going faster. So what the heck was so special about
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light and what was going on? Well, this was one
of the great mysteries that Albert Einstein set his mind
to unraveling, and it formed the basis of one of
his great theories of relativity. And this would be the
theory of special relativity, which poses that the laws of
physics are in the same in all inertial frames of references.
And that means the speed of light will be the
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same for all observers, regardless of their relative perspectives. It
doesn't matter the context. The speed of light is the
speed of light. Now, there's an implication to this theory
that really got people scratching their heads. If the speed
of light is absolutely constant, that would mean that stuff
like distance and time are not. And as a heck
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of a brain teaser, when we come back, we'll explore
this more. Let's imagine that you live half a mile
away from a lovely park, and it's a half mile
away in the morning, it's a half mile away. At night,
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it's a half mile away. On a Tuesday, it's a
half mile away. On a Saturday. Half a mile is
half a mile, right, it's a reliable constant in our lives.
If it weren't, we could never give directions to anywhere
because all the measurements and landmarks would change all the time,
and our world wouldn't make sense the way it does
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to us now. So in our individual experiences, in our
day to day lives, stuff like distance seems pretty darn
reliable and fixed. So how dare Einstein come along with
this theory of special relativity at nineteen oh five and say, well, yeah,
but see, the speed of light is really the true constant,
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and for that to work, time and distance or space,
in other word, words, must be somewhat mutable. Einstein positive
that there is no absolute frame of reference in our universe,
which means there is no place in the universe that
is totally stationary. Everything is moving, which means all motion
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is relative. You can't really talk about moving except in
reference to some other moving thing. So even as we
sit still and try to meditate, we do so on
a planet that is hurtling through space. We are in motion.
We're all moving through space and time, and we all
have a frame of reference, and each frame of reference
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is just as legitimate as every other frame of reference,
or I guess you could say, if everybody's super, nobody is.
I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen oh five theory is called special relativity
because Einstein's explanation only covered special cases, that being when
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two inertial frames are in constant motion with regard to
one another, and there can be no acceleration, so the
motion had to be in a straight line at a
constant speed. A change in direction or speed would be
an acceleration, and to cover those instances we would have
to wait a decade for Einstein to work out his
theory of general relativity. We'll get to that, but we've
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got a lot more to say about special relativity. So
Einstein was taking a different approach to the results of
the experiments done by people like Michelson and Morley. The
scientific world at large was essentially saying, well, this can't
be right. These results can't be right. There must be
something wrong with the experiment or the equipment, because we're
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sure this theory is correct and that ether is there.
Einstein was taking a totally different perspective. He was saying,
if we assume the experiments are producing accurate results, then
it stands to reason that the prevailing theory is flawed
and we have to figure out what the real explanation is.
And this is one of those important points in science.
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It's that if your results in your experiment don't meet
your hypothesis, it's very possible that your hypothesis is wrong.
Now you need to do multiple experiments to find out
and to test your equipment make sure there's not any
errors there that could be causing the issues. But it
does mean that you need to re examine that hypothesis,
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and at this time the scientific community wasn't really doing that,
so Einstein did away with the ether. His explanation suggested
that our observable universe has four dimensions, not that there
can only be four dimensions, but rather there are four
dimensions we can detect and observe, and these would be up, down, left, right, forward, backward,
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and then the fourth dimension, which is time. Collectively, those
three dimensions are space. The fourth dimension is time, and
we get the space time continuum, this intrinsic relationship between
space and time or space time continuum, which also gives
us dozens of Star Trek episodes that would use it
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as shorthand, for things are about to get really weird.
Einstein positive that the speed of light is measured as
constant in all frames of reference. And let's think for
a second. What we mean by speed. Speed is a
description of how much distance can be covered per unit
of time. So a speed of one hundred miles per
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hour means that in one hour's time we will cover
a distance of one hundred miles. That's very obvious. But
if the speed of light is constant for all frames
of reference, regardless of how those frames are moving relative
to each other, that must mean something about space and
or time is a little wonky. And let's think about
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our train experiment again. If you are aboard a train
moving at a move one hundred miles per hour in
a straight line, and you toss a ping pong ball
straight up in the air, well, it's gonna go straight
up and come right back down to your hand in
a nice vertical line. From an outside observer who isn't
on the train, it would look a little differently. You
would throw the ball up at one point relative to
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this outside observer, and the ball would appear to move
not just vertically, but horizontally before coming back down. Now,
if we repeat this experiment but we use light, we
really see how it gets confusing. Okay, so now you're
on a train, but it's going really fast, like let's say,
half the speed of light. But the speed and direction
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are constant. So you're on this train. You don't feel
any acceleration forces because you're moving at a constant speed
and in a constant direction, so your velocity remains the same.
In fact, if there were no windows on the train,
you wouldn't even be able to tell that the train
was moving at all. So let's say you've got a
laser pointer and you've got a mirror on the ceiling
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of the train and a foton detector on the floor
of the train. You shoot the laser up at the mirror,
it reflects off the mirror, and then it comes back
down and hits the detector on the floor, and it
registers how long it took the light to travel from
your laser pointer to hit the detector. And to you,
the laser makes a vertical line. All that makes sense, right,
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you can imagine that, But for our outside observer who's
not on the train, it would appear as though the
laser were actually traveling at a diagonal up to that mirror,
and then a diagonal back down toward the detector. So
for one observer, the one on the train, we have
a straight line. It's vertical up down. For the second
observer off the train, we have an angled path, sort
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of like how a billiard ball can hit the side
of a pool table and bounce off at an angle.
But this creates an apparent paradox. The path viewed by
you on the train is a straight line, and by
definition that is the shortest distance between two points. The
path observed by the person who is not on the
train is an angled line, and by definition that has
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to be longer. The speed of light is constant in
both cases, but the distance is different between the two
points of reference. And because speed is distance divided by time,
if the distance is different, the time must also be
different between those two points of reference. Crazy This brings
us to the concept of time dilation. It also, by
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the way, can affect distance. The faster an object gets,
the more squished it gets. So if you had this
train and you were to get up to near the
speed of light, the train to an outside observer would
appear to be shorter than it normally would be to
anyone inside the train, the dimensions would remain exactly the same.
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You would not suddenly see a shorter train. It wouldn't
be like you were in that compressor scene in Star Wars.
The train would appear to be normal only from an
outside observer who is not traveling at that speed, when
it appeared that the train itself was getting squished shorter. Likewise,
the faster something goes with respect to some other point
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of reference that's important, the more quickly time appears to
pass for those at the other point of reference. Or alternatively,
the more slowly time seems to pass for the fast
moving thing from the frame of reference of the person
who's not moving fast. This gets really clunky. I know,
it gets confusing. So let's talk about space travels some more,
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because examples actually make this way easier to explain. All right,
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eighty percent of the speed
of light, and you're gonna go on a year long
jaunt out in space, and your best friend is hanging
back on Earth. Now we now have our two frames
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of reference. We have the spaceship, and then we have
the person on Earth. So let's ignore accelerative forces for
the moment because we're gonna have to just focus on
special relativity. We'll get to general relativity in a moment.
So you're in your spaceship. You're zooming around at eighty
percent the speed of light, and for you, time is
passing normally. The seconds feel like seconds, minutes feel like minutes,
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hours feel like hours, et cetera. And you're on there
for a full year. Back on Earth, time is passing normally.
For your best friend who's just hanging out on Earth,
they feel their seconds pass like seconds. They're minutes passing minutes,
and so on. However, when we look at the two
of you in reference to one another, something unusual happens.
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So to your best friend on Earth, it looks like
time is passing very slowly for you aboard your spaceship.
To you on your spaceship, it looks like time is
passing super fast for your friend back on Earth. So
when you do get back to Earth a year later
than the two of you enter the same point of reference,
things are weird. From your perspective, you've only aged a
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year because you spend a year aboard your SPA ship,
but a little more than a year and a half
has passed on Earth while you were gone. Your calendars
wouldn't line up anymore. The faster you go relative to
your frame of reference, the more pronounced the time dilation. Now,
I do want to be clear about this, it's not
really correct to say that as speed increases time slows down.
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You have to always relay this in terms of having
another frame of reference, because within a single frame of reference,
time just passes normally. There's no difference. By the way,
This is also why star dates in the Star Trek
universe don't make a whole lot of sense. They tried
to retroactively make it make sense. But keeping time when
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you're on a ship that can travel at the speed
of light or in the case of Star Trek, magically
going faster than the speed of light and we won't
even get into warp speed at all, is crazy. But
being able to use that and somehow relate it to
making sense on time passing on planets or space stations
or whatever. That's a huge mess. But it's also outside
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of our episode, so we'll just leave it at that.
We don't notice the effects of special relativity in most
of our day to day lives, because we are not
traveling fast enough relative to each other for it to
be a real factor most of the time. But it
does get even more weird. Were it possible to build
a spaceship that could travel at the speed of light,
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and you were to take this sort of trip to
an outside observer, time would appear to stop for you
aboard your spaceship. Now if assuming this was even possible,
you would still experience time in your own frame of
reference as per normal, but your friend back on Earth
would see that it looked like you were frozen in time. However,
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this is a moot point. Matter cannot travel at the
speed of light, so it's more of a thought experiment anyway. However,
we can actually detect time dilation with extremely accurate time
measurement device like atomic clocks. In fact, we've done it
in experiments. Scientists have synchronized two atomic clocks, and these
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atomic clocks keep incredibly accurate time down to a matter
of nanoseconds, and a nanosecond is one billionth of a second,
So one clock was kept stationary, you know, relatively speaking,
here on Earth. The other traveled aboard a high speed aircraft,
and at the end of the experiment they compared the
two clocks against each other, and the one that was
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aboard the aircraft had measured less time than the one
that stayed on the ground on Earth. Less time passed
on that aircraft relative to the amount of time passing
on the ground. It wasn't just that one clock was
moving more slowly than the other. Literally less time was
passing in reference to the other point of from the
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perspective of the other point of reference, that is, the
difference was right in line with Einstein's calculations. Now, as
we'll see, this ends up being an important point when
we get to satellites. But we can't just jump on
that yet. We do need to take into consideration general relativity. So,
as i mentioned, special relativity only looks at frames of
reference that are in a constant and consistent motion with
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regard to one another. There could be no change in
direction or speed because that introduces accelerative forces and that
changes things. So to take acceleration into account. Einstein proposed
his theory of general relativity ten years after his theory
of special relativity, so this would be nineteen fifteen For
those who are keeping track, This theory would incorporate the
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force of gravity into Einstein's work, which means factoring in acceleration.
So in this theory, Einstein introduced the equivalence principle, which
says that gravity pulling in one direction is equivalent to
acceleration in another direction. So we can actually experience this.
It's easy to remember and imagine. Imagine getting on an
elevator and it's going up, and as it goes up,
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you feel that sense of increased gravity pulling down on
you as the elevator accelerates. When the elevator is going down,
you feel a sense of decreased gravity as the elevator
accelerates downward. So gravity and acceleration are equivalent, which means
that it can also affect our measurements of space and time.
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Einstein hypothesized that gravity was warping space time itself. Take
something that's really massive, like a huge dense star, that
would warp space time around it through its gravity, and
we can even observe this scientifically, scientists have measured light
that has curved around massive stars. This is called gravitational lensing.
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Now here's another thing that gets a bit confusing. The
effects of gravity on time mean that time passes differently
for objects in orbit when taken in reference to time
passing on Earth itself, time pass this is faster in
orbit than it does on Earth. Now, again, this is
a frame of reference thing, because if you were on
(32:07):
a spaceship in orbit, your experience of time would feel
exactly the way it does when you are on Earth.
It's only when we look at this from two frames
of reference that we see how it doesn't match up.
So what does this all mean for satellites. Well, it
means that satellites in orbit have a couple of different
relativistic effects going on. In our frame of reference here
(32:30):
on Earth, satellites are traveling faster than we are to
maintain orbit, which means that if we compare the passing
of time in each frame of reference, time would pass
faster for us than for the satellite. However, due to
the gravitational effect on space time, we also know that
something in orbit will have time pass faster for that
(32:52):
thing than we would experience here on Earth. So it's
the opposite of the effect of special relativity in a way,
and the effects of special relie relativity and general relativity
don't actually cancel each other out, which means ultimately that
time on a satellite and time down here on Earth
are not syncd up with reference to one another. And
for some types of satellites that's a problem. I'll explain
(33:15):
more after we take this quick break to understand why
relativity is important with certain satellites, let's talk about the
Global Positioning System or GPS. Now, this is the satellite
system that provides data back to Earth that makes it
(33:37):
possible to get precise coordinates using a GPS receiver. So
how does that work? Well, here on Earth, you could
get a very imprecise idea of your general coordinates through
a trilateration using signals from cell phone towers. This works
on a fairly simple principle. So we know that the
(33:58):
radio signals sent to and from cell phones travel at
essentially the speed of light. So if a cell phone
tower broadcasts out a short command that just requests your
phone to respond back with a quick response a ping.
In other words, the amount of time it would take
for the ping to reach the cell tower could be
(34:19):
used to work backward and figure out how far away
the phone is from that cell phone tower. Because you
know the speed of travel, right is the speed of light,
so you also know how much time it took. That
means you can work backward to figure out the distance
between those two points. However, that's just a distance, there's
no direction there. Now, if you did this with multiple
(34:41):
cell towers, the collective data from those towers could be
used to get a rough estimate of where the phone is.
So let's imagine we've got a map, and on that
map we've got three cell towers A, B, and C.
You can see exactly where each one is. And let's
say that you've got a phone that located somewhere within
(35:01):
the broadcast range of those three cell towers. Each tower
sends a ping to your phone, Your phone responds with
a ping back, and you are given the amount of
distance between your phone and each of those three towers. Well,
Tower a's result says that you are a mile away
from Tower A, so you actually have to draw a
(35:24):
full circle around Tower A to represent all the possible
points you could be that are one mile away from
Tower A, So you're drawing a mile radius around Tower A.
Tower B responds that you're within one point five miles
of Tower B, so you have to draw a circle
around Tower B to represent all the points where you
(35:44):
could be that are a mile and a half away
from it. Now, the circle from tower B in the
circle from Tower A should intersect each other at two points,
but that means you could be at either of those
two points. Right, you could be at either overlap, so
you don't have enough information yet. By coordinating with tower C,
and let's say that one tells you you're within two miles,
(36:05):
you can draw a third circle, and the point where
all three circles would meet would be your general location.
It's not incredibly precise, but it does give you an
idea of where you are. The GPS constellation of satellites
does something similar, only we have to think of this
in terms of three dimensional space rather than a two
(36:26):
dimensional map. So a satellite sends out a high frequency,
low power radio signal and receivers pick that signal up.
The receiver, let's say it's your smartphone, doesn't have to
send data back up to the satellite, which is good
because i'd be an enormous drain on your smartphone's power.
So really it's just listening for these signals. Now, the
(36:48):
receiver and satellite both run the same digital pattern relative
to a specific time stamp. It's easy if we think
of this as midnight. So let's say that midnight hits
and and this particular digital pattern starts both on the
satellite and the receiver, so they're both running the exact
same pattern. The satellite beams out a signal carrying this
(37:10):
digital pattern. The satellite is far away, so it takes
a little time, you know, not much, but a little
time for that signal to get to your receiver. And
the lag between the pattern that's playing on your receiver
and the signal of that same pattern coming in from
the satellite tells the receiver how far away it is
from that particular satellite, because again we know that the
(37:32):
signal is moving at the speed of the transmission itself,
and that's the speed of light, and that's a constant.
So now the receiver knows how far away it is
from that one satellite. And because the orbits of these
satellites are predictable, the receiver has a record of where
that satellite should be relative to your surface. Occasionally we
have to tweak that record because stuff like gravity can
(37:55):
pull a satellite slightly out of position over time, so
that actually is something that has to be a rest
on occasion. Now, this receiver will do this with at
least four satellites the Y four and not three, and
I gave the three cell phone tower examples. Well, it's
because the clocks on satellites and the clock that's running
(38:16):
on the device that the receiver is built into may
not be and really aren't truly synchronized. And the intersection
of for spheres of distance like these four spheres representing
the various ranges that these satellites are finding themselves in
with regard to this receiver can only intersect at one point.
(38:39):
That's the only place they could all intersect. So if
a GPS receiver's clock is not matching up to the
clocks on the satellites, there will be no intersection at all.
And the receiver will say, well, I can't find an intersection,
so that I know that means my clock is off
from all the other clocks, and it will then adjust
its own clock to be an alignment so that the
(39:00):
or spheres have a point of intersection and that is
your location on Earth. Now, in order for our receivers
to be able to do this, the accuracy of the
atomic clocks aboard those GPS satellites has to be accurate
within twenty to thirty nanoseconds. And remember a nanosecond is
one billionth of a second. That is an astounding level
(39:23):
of accuracy. And because these satellites are in motion and
they are also affected by Earth's gravity, they are subject
to the effects of special and general relativity, and this
means we actually have to make calculations to take that
into account. Now, according to special relativity and the relative
speeds of satellites to a fixed point on the surface
(39:46):
of the Earth, we would expect the atomic clock aboard
that satellite to register seven fewer microseconds per day than
a clock on Earth because these satellites are moving through
space faster than we are, relatively speaking, so that means
from our frame of reference, time is passing more slowly
on that satellite than it does here on Earth. Ah.
(40:09):
But general relativity comes into play too, and general relativity
tells us that the Earth's gravity warps space time around
our planet. And one of general relativity's predictions is that
a clock closer to a massive object, so like a
clock here on Earth, will tick more slowly than a
(40:31):
clock that is further out from that same massive object.
So the closer the clock is to the massive object,
the less time it will experience it will measure compared
to a clock that's further away, which is crazy, right.
So taking only general relativity into account, we would see
that a clock aboard one of these satellites would register
(40:54):
more time having passed on that satellite than a clock
here on Earth, meaning for our frame of reference, time
is actually passing faster on those satellites than it does
here for us. This would come out to about forty
five microseconds a day, meaning that at the end of
day one, the clock aboard that satellite would be ahead
(41:15):
of a clock here on Earth by forty five microseconds,
and this would continue day after day, with the gap
growing wider every single day. Now, when we bring both
special and general relativity together into consideration, we see that
they don't just cancel each other out right, because we've
got that seven microsecond lag due to special relativity, but
(41:39):
we have the forty five microsecond surge due to general relativity.
So in the end, we're looking at a thirty eight
microsecond difference per day between a clock on a satellite
and a clock here on Earth. The clocks on the
satellites will get ahead of similar clocks here on Earth
by thirty eight microseconds every single day. And while a
(42:01):
microsecond is a very small amount of time, I mean
we're talking at a level that we don't typically experience.
We don't think of time in microseconds for our day
to day lives. However, thirty eight microseconds is equal to
thirty eight thousand nanoseconds, and if you're looking for an
accuracy of around twenty to thirty nanoseconds, this becomes an
(42:22):
enormous problem if we don't take it into account. And
this brings us back round to something I mentioned at
the top of the show. We know that Einstein was
right about relativity because we have to account for it
with technology like GPS. If we didn't take it into account,
if we didn't factor in the effects of relativity, our
(42:43):
GPS wouldn't work for very long at all. Our technology
proves that the science is real, or else the tech
would fail at what it needs to do now. In general,
I think that's a great lesson to take home. There
are a lot of voices out there that call science
into questions, and some of them are more outlandish than others,
a person who's passionately and sincerely arguing that the Earth
(43:06):
is flat seems pretty far out there for me, because
so much of our technology we've built upon and we
rely upon wouldn't work if that were true. Even if
you can't experience something directly, such as having a meaningful
experience of time dilation, a ton of the stuff we
do experience on a day to day basis is affected
(43:29):
by this stuff, and it proves the existence and also
the benefits of having the scientific method. Now I'll give
a little side note on GPS to kind of wrap
this up. The original GPS configuration came out of a
United States Department a defense project. The original purpose was
to provide positioning information for government and military, but specifically
(43:51):
the United States and its allies, and for that reason,
the US government wished to restrict access to this technology.
The general line of thought was that it be better
if the US didn't allow tech that could, you know,
give precise coordinates for stuff like military bases or the
position of various military units to people who didn't belong
(44:11):
to those divisions. So, as a matter of national security,
the US guarded this technology civilian receivers. So if you
went out and you bought a GPS receiver, you could
get public GPS signals, but the United States was purposefully
instituting a policy called selective availability, which was an intentional
(44:32):
degradation of public GPS signals. They were introducing errors on
purpose so that GPS receivers couldn't get an accurate location.
It limited accuracy to around fifty meters horizontally and one
hundred meters vertically, and effectively that meant that you wouldn't
really know your precise coordinates. You certainly couldn't use a
(44:55):
GPS receiver as a turn by turn directions tool because
you wouldn't even necessarily show up on the right street.
You wouldn't know if you were approaching your turn or
if you had already passed it. It was it was
not practical for that. It was only in the year
two thousand, when US President Bill Clinton directed the government
to end selective availability, that civilian GPS receivers could actually
(45:19):
get accurate data. And that's what made the modern GPS
receivers and stuff like our phones possible. So before two thousand,
GPS receivers didn't work very well for the average person,
but it wasn't because the technology was bad, or that
the science was wrong it worked that way, or if
you prefer it, it didn't work properly on purpose. And
(45:40):
that wraps up this episode about relativity and why it's
important with technology, and it's not just satellite tech, but
that's a big one, and it also ends up being
a big thorn in the side for science fiction authors
who want to write about interstellar travel at faster than
light speeds, because you have to start finding alternative X
nations for how that's possible, because we've come up against
(46:04):
these limits that Einstein predicted, and so far his predictions
have held true. So in order to travel faster than
the speed of light, you do have to create something
like warp drive, which theoretically warps space around you. So
rather than traveling faster than light, you're decreasing the distance
between your point of origin and your destination. It would
(46:26):
be kind of like taking a map of the United
States and saying I'm going to travel from Atlanta to
Los Angeles, from one coast to the other, but instead
of drawing a line from Atlanta to LA you just
fold the map so that the two dots are next
to each other, and then you draw a line that way.
That's how warp speed is supposed to work, because it's
the only way you can get around the fact that
(46:47):
you can't really go faster than the speed of light.
But that's a topic for another show. If you guys
have suggestions for future topics I should tackle, please let
me know. Send me a message on Twitter. The handle
is text hsw and I'll talk to you again really soon.
(47:10):
Tech Stuff is an iHeartRadio production. For more podcasts from iHeartRadio,
visit the iHeartRadio app, Apple Podcasts, or wherever you listen
to your favorite shows.
Welcome to Tech Stuff, a production from iHeartRadio. Hey therein
Welcome to Tech Stuff, I'm your host, Jonathan Strickland. I'm
an executive producer with iHeartRadio, and how the tech are you.
We have an episode that originally published on July first,
twenty twenty. It's called It's All Relative And when I
(00:28):
was a kid, I was convinced that Einstein's theories were
these super complicated explanations of the universe that really had
no real intersection with my daily life. But as it
turns out, without an understanding of relativity, a lot of
the technology we rely upon wouldn't work properly. And it's
fascinating stuff. Hope you enjoy. The hertz unit refers to
(00:55):
the number of repeated phenomena over the course of a second.
So well, imagine that you're dribbling a basketball, so that
the ball goes from your hand to the ground back
up to your hand once per second. Well, you could
describe your dribbling as being one hurts in frequency one
full cycle per second, up down, up. Now, if you
(01:18):
dribbled twice as fast, so that the ball went up, down,
up two full times per second, then it would be
two hurts. Well, we can describe lots of stuff with
the unit hurts. We use it to describe sounds, in
which case we're talking about the frequency at which stuff vibrates.
Typical human hearing spans a range of frequencies that at
(01:40):
the low end is at twenty hurts. That represents the
lowest pitches of sounds. You get to go those deep
bass notes. That's around the twenty hurts of area, and
then it goes all the way up to twenty kill
a hurts or twenty thousand hurts. That represents the very
highest pitches that people can typically hear, and those frequencies
(02:01):
correlate to how quickly stuff is vibrating back and forth. Now,
when it comes to us hearing things, we usually mean
that we're talking about the vibrations and fluctuation and air pressure,
and those fluctuations and air pressure interact with our ear drums.
But we can use hurts to talk about all sorts
of stuff, including the processor speed of a CPU. In
(02:22):
that case, we're really talking about the number of clock
cycles per second, So you get it. This is a
description of the frequency of the number of times a
certain thing happens like within a second. And I also
explained that we measure the rate at which we can
send data using the term bits. A bit is a
(02:43):
basic unit of digital information, and when we talk about computers,
we're talking about bits in the form of a zero
or a one binary information, just like your basic two
way physical switch has two positions off or on. So
if you hear a term like kill a bit, that
means one thousand bits, and a megabit is one million bits,
(03:04):
and a gigabit would be one billion bits. Likewise, megabits
per second tells us how many million bits can move
from one point to another per second over that connection.
So if you've got a one hundred megabit per second connection,
theoretically it would mean that up to one hundred million
bits can transfer across that communication channel per second, though
(03:29):
that's not how it works out most of the time,
but that's a matter for a different episode. I didn't
mention that this is different from something like megabytes. So
a byte is a unit that consists of eight bits.
And this gets confusing because we often describe stuff like
file sizes in terms of bytes, but transfer speeds in
(03:50):
terms of bits. So let's say that you do have
that one hundred megabits per second download speed, and you
want to download a one hundred megabyte file, well, that
means it's not going to take one second. It's going
to take eight seconds to download the file, because a
megabyte is eight times larger than a megabit. And actually
(04:12):
even that is a little bit misleading because in computer
memory terms, we typically look at units of memory based
on powers of two rather than powers of ten. So
instead of a kilobyte being one thousand bytes, it's actually
one thy twenty four bytes. And there's no standardization in
the tech industry, so sometimes people will say a kilobyte
(04:35):
and they mean one thousand bytes. Sometimes they'll say killobyte
and they mean one thy twenty four bytes, and you
will want to tear your hair out, and then you'll
look like I do, I'm bald if you didn't know.
But this episode isn't about the peculiarities of our naming
conventions and the computer information age. Instead, I wanted to
tackle something else that affects everything really, but in particular,
(04:59):
we really had to suss it out in order to
make certain types of satellites work properly, and this is
the concept of relativity. So in this episode, we're really
going to learn why an understanding of relativity is important
if we want our certain satellite technologies to work, and
it serves as a great reminder that technology is only
really possible through an understanding of science. You can think
(05:22):
of tech as the physical manifestation of our understanding of
scientific principles, and that means if we were wrong in
our understanding of science, the technology shouldn't really work. So
in a way, you can think of technology that works
as evidence that the scientific method is a darn good formula.
Since we're talking about relativity, it means we're going to
(05:45):
be talking about a real Einstein today. His name was Einstein,
which is convenient. But before we get to Einstein, we
have Galileo Galileo Galileo figure Ro. Wait No, I'm sorry,
wait that's Bohemian Rhapsody. I meant Galileo Galilei. This. Galileo
made an observation that if you've got two observers moving
(06:08):
at a constant speed and direction, so they're moving at
the same velocity, they will get the same results for
any experiment that involves moving stuff around a mechanical experiment.
This is easier to understand if we use an example,
and I like one that my colleague Robert Lamb used
when he wrote about relativity for HowStuffWorks dot com back
(06:31):
in the day. He used an example of a train
and a scientific ping pong ball. All right, so imagine
you've got a scientist who's standing in the middle of
an aisle on a moving train, and the train is
moving at a steady speed in a straight line, so
there are no active forces of acceleration going on here. Remember,
(06:52):
acceleration describes a force that involves a change in velocity,
so that either means a change in direction or a
change in speed, or both. But in this case constant
speed constant direction. Robert used nice round numbers in his examples,
so he suggested that the train is moving at one
hundred miles per hour. Well it's not round. If we
(07:14):
go to the metric system, that would be one hundred
and sixty one kilometers per hour. If the train stays
steady to the scientist, it will feel as if that
scientist is actually just standing still, just anywhere, and we're
conveniently ignoring an emotion that would happen due to irregularities
with the train's wheels or the train tracks or anything
like that. And if this is hard for you to imagine,
(07:36):
just think about how you feel when you're standing still
or sitting still or laying down here on Earth. We
know the Earth is moving through space. It is a
body in motion, but when we are still relative to
the Earth itself, we don't feel that motion. Assuming there's
not some other weird event going on, like an earthquake,
(07:58):
which is something separate. But back to our hypothetical train,
the scientist tosses the ping pong ball down the aisle. Now,
from the scientist's perspective, this ping pong ball will travel
at whatever speed they threw it at. Robert actually suggests
a relatively gentle toss of five miles per hour or
eight kilometers per hour. The ping pong ball would bounce
(08:21):
down the aisle, just as it would if the scientists
were to toss the ball on a train that isn't
moving at all, or on just flat ground. However, let's
say we have a second observer who's not on the train.
They're standing off to the side, and they can see
through the train. To this person, it will appear as
if the ping pong ball is moving very fast. Indeed,
(08:43):
relative to this stationary observer, the ping pong ball will
appear to move at the speed at which it was
thrown in addition to the speed of the train itself.
So if we take the two figures, we would get
one hundred five miles per hour or one hundred and
sixty nine per hour. This is called a Galilean transformation. Alternatively,
(09:05):
if the scientists were throwing the ping pong ball in
the opposite direction of the train's travel, so they're facing
toward the back of the train, it would appear to
this second observer the ping pong ball was moving at
a slightly slower speed than the overall train was, whereas
to the scientist on board, the ping pong ball would
still be traveling at that five mile per hour speed.
(09:26):
So this is where the term relativity comes into play.
The effects observed are relative to the perspective of the observer.
It's all based on the reference frame of that observer.
If you're on the train, then you're just looking at
a ping pong ball bouncing at a relatively slow speed
down the aisle. If you're not on the train, the
(09:48):
ping pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
all tracks. I don't know why he talked like that.
In his Laws of Motion, Newton stated that these laws
of motion should hold in an inertial frame as well
as reference frame that was moving at a constant velocity
(10:09):
relative to the inertial frame. An inertial frame, by the way,
is just a frame of reference in which there are
zero net forces acting upon it, so that there are
no forces of acceleration in play. So in our example,
the train that we talked about, that would be our
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
(10:32):
the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that.
But hey, what if you're on a train that's traveling
one hundred miles per hour and you're facing forward, you're
facing the direction of travel, and then you have a
flashlight and you turn on the flashlight. Well, doesn't that
mean you should perform a Galileean transformation on this and
(10:53):
say the light from that flashlight in your hands is
actually traveling at the normal speed of light on board
the train. But also get that boost of the trains travel,
so it should be the speed of light plus one
hundred miles per hour. Doesn't that make sense? While according
to actual experiments performed before Einstein would come around to
explain things, the answer was Nope, doesn't look like it
(11:16):
works that way. Scientists Edward Morley and Albert A. Michelson
created an experiment to measure the speed of light back
in eighteen eighty seven, and actually they were looking for
something else. They were looking for evidence of a hypothetical
substance called luminiferous ether. Say why, all right, we'll stick
(11:37):
with me, because in a way this does make sense. Okay,
So on Earth we see waves traveling through a medium, right,
Like if you look out in the ocean, you can
see actual waves in the water, and the water is
a physical medium through which these waves travel. Sound can't
travel in space because space is effect actively a vacuum.
(12:01):
The particles that are in space are so far apart
from one another that there's no way for the vibration
of one particle to come into contact and affect another particle.
So sound can't travel. Sound travels through the propagation of
vibrational waves. And if your stuff isn't in contact with
each other, there's no way for them to have that
wave propagate. So there has to be some sort of
(12:24):
medium like air or solid surfaces or something in order
for sound travel. Well, if that's the case, said the
folks of the time, then stuff like light must need
some sort of medium to travel through, right. I mean
sound has to have something. Light must have something too.
Light can definitely travel through space. I mean, that's how
(12:46):
we can see anything, because light from the Sun travels
through space to hit the Earth. So the light has
to be moving through some sort of medium we cannot
observe directly. This hypothetical medium was the aforementioned maniferous ether.
But assuming this ether existed at all, it had to
be pretty darn special because we can't feel it, we
(13:09):
can't detect it, it creates no observable effects, So if
it were real, it had to be unlike pretty much
anything else we had discovered up to that point. Now,
let's assume that the universe is filled with this ether stuff.
The question rises, how the heck does the ether interact
with all the physical stuff that's in the universe, the
(13:31):
actual matter and also energy. After all, the bodies in
space like stars, planets, moons and all that other stuff.
All of that is moving, none of it is standing still,
and if it is moving, it would presumably disturb this
ether medium, right. I mean, if you move your hand
(13:52):
through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
the motion of all these elements in space would disturb
the ether in some way, and hypothetically there would be
some sort of ether wind. But if there were a wind,
then presumably the speed of light would be affected depending
(14:13):
upon the wind's direction in relation to the light's direction.
So think of a really windy day in the real world.
If you're walking against a very very tough wind, like
a gale force wind, you have to power through it
to keep moving forward. Now, if you're walking with the wind,
like the wind is to your back and pushing you,
(14:34):
then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
and so Mickelson and Morley devised a gadget that would
split light into two beams, directing those beams down different paths,
using mirrors in different directions, and seeing if those two
beams of light would hit an eyepiece at different times.
(14:56):
The thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
one would be at a cross direction of ether wind,
So we should see a difference in the amount of
time it takes for the light from this one source
that's been split into two to arrive at an eyepiece.
But that's not what they found. They observed no such effect.
(15:21):
So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
hundred eighty six thousand miles per second or around three
hundred thousand kilometers per second. Now that flew in the
face of classic Newtonian physics clearly. With the example of
(15:44):
the ping pong ball and the train, the ping pong
ball has to be traveling faster than the train it's on.
I mean, that just makes sense. If you were standing
on the top of the very front of the train
and then you threw the ping pong ball, and we
ignore stuff like wind resistant, the ping pong ball would
land ahead of the train, So it has to be
going faster. So what the heck was so special about
(16:07):
light and what was going on? Well, this was one
of the great mysteries that Albert Einstein set his mind
to unraveling, and it formed the basis of one of
his great theories of relativity. And this would be the
theory of special relativity, which poses that the laws of
physics are in the same in all inertial frames of references.
And that means the speed of light will be the
(16:28):
same for all observers, regardless of their relative perspectives. It
doesn't matter the context. The speed of light is the
speed of light. Now, there's an implication to this theory
that really got people scratching their heads. If the speed
of light is absolutely constant, that would mean that stuff
like distance and time are not. And as a heck
(16:51):
of a brain teaser, when we come back, we'll explore
this more. Let's imagine that you live half a mile
away from a lovely park, and it's a half mile
away in the morning, it's a half mile away. At night,
(17:13):
it's a half mile away. On a Tuesday, it's a
half mile away. On a Saturday. Half a mile is
half a mile, right, it's a reliable constant in our lives.
If it weren't, we could never give directions to anywhere
because all the measurements and landmarks would change all the time,
and our world wouldn't make sense the way it does
(17:34):
to us now. So in our individual experiences, in our
day to day lives, stuff like distance seems pretty darn
reliable and fixed. So how dare Einstein come along with
this theory of special relativity at nineteen oh five and say, well, yeah,
but see, the speed of light is really the true constant,
(17:55):
and for that to work, time and distance or space,
in other word, words, must be somewhat mutable. Einstein positive
that there is no absolute frame of reference in our universe,
which means there is no place in the universe that
is totally stationary. Everything is moving, which means all motion
(18:17):
is relative. You can't really talk about moving except in
reference to some other moving thing. So even as we
sit still and try to meditate, we do so on
a planet that is hurtling through space. We are in motion.
We're all moving through space and time, and we all
have a frame of reference, and each frame of reference
(18:40):
is just as legitimate as every other frame of reference,
or I guess you could say, if everybody's super, nobody is.
I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen oh five theory is called special relativity
because Einstein's explanation only covered special cases, that being when
(19:02):
two inertial frames are in constant motion with regard to
one another, and there can be no acceleration, so the
motion had to be in a straight line at a
constant speed. A change in direction or speed would be
an acceleration, and to cover those instances we would have
to wait a decade for Einstein to work out his
theory of general relativity. We'll get to that, but we've
(19:24):
got a lot more to say about special relativity. So
Einstein was taking a different approach to the results of
the experiments done by people like Michelson and Morley. The
scientific world at large was essentially saying, well, this can't
be right. These results can't be right. There must be
something wrong with the experiment or the equipment, because we're
(19:44):
sure this theory is correct and that ether is there.
Einstein was taking a totally different perspective. He was saying,
if we assume the experiments are producing accurate results, then
it stands to reason that the prevailing theory is flawed
and we have to figure out what the real explanation is.
And this is one of those important points in science.
(20:05):
It's that if your results in your experiment don't meet
your hypothesis, it's very possible that your hypothesis is wrong.
Now you need to do multiple experiments to find out
and to test your equipment make sure there's not any
errors there that could be causing the issues. But it
does mean that you need to re examine that hypothesis,
(20:27):
and at this time the scientific community wasn't really doing that,
so Einstein did away with the ether. His explanation suggested
that our observable universe has four dimensions, not that there
can only be four dimensions, but rather there are four
dimensions we can detect and observe, and these would be up, down, left, right, forward, backward,
(20:52):
and then the fourth dimension, which is time. Collectively, those
three dimensions are space. The fourth dimension is time, and
we get the space time continuum, this intrinsic relationship between
space and time or space time continuum, which also gives
us dozens of Star Trek episodes that would use it
(21:13):
as shorthand, for things are about to get really weird.
Einstein positive that the speed of light is measured as
constant in all frames of reference. And let's think for
a second. What we mean by speed. Speed is a
description of how much distance can be covered per unit
of time. So a speed of one hundred miles per
(21:34):
hour means that in one hour's time we will cover
a distance of one hundred miles. That's very obvious. But
if the speed of light is constant for all frames
of reference, regardless of how those frames are moving relative
to each other, that must mean something about space and
or time is a little wonky. And let's think about
(21:55):
our train experiment again. If you are aboard a train
moving at a move one hundred miles per hour in
a straight line, and you toss a ping pong ball
straight up in the air, well, it's gonna go straight
up and come right back down to your hand in
a nice vertical line. From an outside observer who isn't
on the train, it would look a little differently. You
would throw the ball up at one point relative to
(22:18):
this outside observer, and the ball would appear to move
not just vertically, but horizontally before coming back down. Now,
if we repeat this experiment but we use light, we
really see how it gets confusing. Okay, so now you're
on a train, but it's going really fast, like let's say,
half the speed of light. But the speed and direction
(22:38):
are constant. So you're on this train. You don't feel
any acceleration forces because you're moving at a constant speed
and in a constant direction, so your velocity remains the same.
In fact, if there were no windows on the train,
you wouldn't even be able to tell that the train
was moving at all. So let's say you've got a
laser pointer and you've got a mirror on the ceiling
(22:58):
of the train and a foton detector on the floor
of the train. You shoot the laser up at the mirror,
it reflects off the mirror, and then it comes back
down and hits the detector on the floor, and it
registers how long it took the light to travel from
your laser pointer to hit the detector. And to you,
the laser makes a vertical line. All that makes sense, right,
(23:19):
you can imagine that, But for our outside observer who's
not on the train, it would appear as though the
laser were actually traveling at a diagonal up to that mirror,
and then a diagonal back down toward the detector. So
for one observer, the one on the train, we have
a straight line. It's vertical up down. For the second
observer off the train, we have an angled path, sort
(23:42):
of like how a billiard ball can hit the side
of a pool table and bounce off at an angle.
But this creates an apparent paradox. The path viewed by
you on the train is a straight line, and by
definition that is the shortest distance between two points. The
path observed by the person who is not on the
train is an angled line, and by definition that has
(24:02):
to be longer. The speed of light is constant in
both cases, but the distance is different between the two
points of reference. And because speed is distance divided by time,
if the distance is different, the time must also be
different between those two points of reference. Crazy This brings
us to the concept of time dilation. It also, by
(24:25):
the way, can affect distance. The faster an object gets,
the more squished it gets. So if you had this
train and you were to get up to near the
speed of light, the train to an outside observer would
appear to be shorter than it normally would be to
anyone inside the train, the dimensions would remain exactly the same.
(24:49):
You would not suddenly see a shorter train. It wouldn't
be like you were in that compressor scene in Star Wars.
The train would appear to be normal only from an
outside observer who is not traveling at that speed, when
it appeared that the train itself was getting squished shorter. Likewise,
the faster something goes with respect to some other point
(25:09):
of reference that's important, the more quickly time appears to
pass for those at the other point of reference. Or alternatively,
the more slowly time seems to pass for the fast
moving thing from the frame of reference of the person
who's not moving fast. This gets really clunky. I know,
it gets confusing. So let's talk about space travels some more,
(25:31):
because examples actually make this way easier to explain. All right,
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eighty percent of the speed
of light, and you're gonna go on a year long
jaunt out in space, and your best friend is hanging
back on Earth. Now we now have our two frames
(25:51):
of reference. We have the spaceship, and then we have
the person on Earth. So let's ignore accelerative forces for
the moment because we're gonna have to just focus on
special relativity. We'll get to general relativity in a moment.
So you're in your spaceship. You're zooming around at eighty
percent the speed of light, and for you, time is
passing normally. The seconds feel like seconds, minutes feel like minutes,
(26:15):
hours feel like hours, et cetera. And you're on there
for a full year. Back on Earth, time is passing normally.
For your best friend who's just hanging out on Earth,
they feel their seconds pass like seconds. They're minutes passing minutes,
and so on. However, when we look at the two
of you in reference to one another, something unusual happens.
(26:35):
So to your best friend on Earth, it looks like
time is passing very slowly for you aboard your spaceship.
To you on your spaceship, it looks like time is
passing super fast for your friend back on Earth. So
when you do get back to Earth a year later
than the two of you enter the same point of reference,
things are weird. From your perspective, you've only aged a
(26:57):
year because you spend a year aboard your SPA ship,
but a little more than a year and a half
has passed on Earth while you were gone. Your calendars
wouldn't line up anymore. The faster you go relative to
your frame of reference, the more pronounced the time dilation. Now,
I do want to be clear about this, it's not
really correct to say that as speed increases time slows down.
(27:19):
You have to always relay this in terms of having
another frame of reference, because within a single frame of reference,
time just passes normally. There's no difference. By the way,
This is also why star dates in the Star Trek
universe don't make a whole lot of sense. They tried
to retroactively make it make sense. But keeping time when
(27:42):
you're on a ship that can travel at the speed
of light or in the case of Star Trek, magically
going faster than the speed of light and we won't
even get into warp speed at all, is crazy. But
being able to use that and somehow relate it to
making sense on time passing on planets or space stations
or whatever. That's a huge mess. But it's also outside
(28:05):
of our episode, so we'll just leave it at that.
We don't notice the effects of special relativity in most
of our day to day lives, because we are not
traveling fast enough relative to each other for it to
be a real factor most of the time. But it
does get even more weird. Were it possible to build
a spaceship that could travel at the speed of light,
(28:27):
and you were to take this sort of trip to
an outside observer, time would appear to stop for you
aboard your spaceship. Now if assuming this was even possible,
you would still experience time in your own frame of
reference as per normal, but your friend back on Earth
would see that it looked like you were frozen in time. However,
(28:47):
this is a moot point. Matter cannot travel at the
speed of light, so it's more of a thought experiment anyway. However,
we can actually detect time dilation with extremely accurate time
measurement device like atomic clocks. In fact, we've done it
in experiments. Scientists have synchronized two atomic clocks, and these
(29:09):
atomic clocks keep incredibly accurate time down to a matter
of nanoseconds, and a nanosecond is one billionth of a second,
So one clock was kept stationary, you know, relatively speaking,
here on Earth. The other traveled aboard a high speed aircraft,
and at the end of the experiment they compared the
two clocks against each other, and the one that was
(29:33):
aboard the aircraft had measured less time than the one
that stayed on the ground on Earth. Less time passed
on that aircraft relative to the amount of time passing
on the ground. It wasn't just that one clock was
moving more slowly than the other. Literally less time was
passing in reference to the other point of from the
(29:54):
perspective of the other point of reference, that is, the
difference was right in line with Einstein's calculations. Now, as
we'll see, this ends up being an important point when
we get to satellites. But we can't just jump on
that yet. We do need to take into consideration general relativity. So,
as i mentioned, special relativity only looks at frames of
reference that are in a constant and consistent motion with
(30:17):
regard to one another. There could be no change in
direction or speed because that introduces accelerative forces and that
changes things. So to take acceleration into account. Einstein proposed
his theory of general relativity ten years after his theory
of special relativity, so this would be nineteen fifteen For
those who are keeping track, This theory would incorporate the
(30:38):
force of gravity into Einstein's work, which means factoring in acceleration.
So in this theory, Einstein introduced the equivalence principle, which
says that gravity pulling in one direction is equivalent to
acceleration in another direction. So we can actually experience this.
It's easy to remember and imagine. Imagine getting on an
elevator and it's going up, and as it goes up,
(31:01):
you feel that sense of increased gravity pulling down on
you as the elevator accelerates. When the elevator is going down,
you feel a sense of decreased gravity as the elevator
accelerates downward. So gravity and acceleration are equivalent, which means
that it can also affect our measurements of space and time.
(31:21):
Einstein hypothesized that gravity was warping space time itself. Take
something that's really massive, like a huge dense star, that
would warp space time around it through its gravity, and
we can even observe this scientifically, scientists have measured light
that has curved around massive stars. This is called gravitational lensing.
(31:46):
Now here's another thing that gets a bit confusing. The
effects of gravity on time mean that time passes differently
for objects in orbit when taken in reference to time
passing on Earth itself, time pass this is faster in
orbit than it does on Earth. Now, again, this is
a frame of reference thing, because if you were on
(32:07):
a spaceship in orbit, your experience of time would feel
exactly the way it does when you are on Earth.
It's only when we look at this from two frames
of reference that we see how it doesn't match up.
So what does this all mean for satellites. Well, it
means that satellites in orbit have a couple of different
relativistic effects going on. In our frame of reference here
(32:30):
on Earth, satellites are traveling faster than we are to
maintain orbit, which means that if we compare the passing
of time in each frame of reference, time would pass
faster for us than for the satellite. However, due to
the gravitational effect on space time, we also know that
something in orbit will have time pass faster for that
(32:52):
thing than we would experience here on Earth. So it's
the opposite of the effect of special relativity in a way,
and the effects of special relie relativity and general relativity
don't actually cancel each other out, which means ultimately that
time on a satellite and time down here on Earth
are not syncd up with reference to one another. And
for some types of satellites that's a problem. I'll explain
(33:15):
more after we take this quick break to understand why
relativity is important with certain satellites, let's talk about the
Global Positioning System or GPS. Now, this is the satellite
system that provides data back to Earth that makes it
(33:37):
possible to get precise coordinates using a GPS receiver. So
how does that work? Well, here on Earth, you could
get a very imprecise idea of your general coordinates through
a trilateration using signals from cell phone towers. This works
on a fairly simple principle. So we know that the
(33:58):
radio signals sent to and from cell phones travel at
essentially the speed of light. So if a cell phone
tower broadcasts out a short command that just requests your
phone to respond back with a quick response a ping.
In other words, the amount of time it would take
for the ping to reach the cell tower could be
(34:19):
used to work backward and figure out how far away
the phone is from that cell phone tower. Because you
know the speed of travel, right is the speed of light,
so you also know how much time it took. That
means you can work backward to figure out the distance
between those two points. However, that's just a distance, there's
no direction there. Now, if you did this with multiple
(34:41):
cell towers, the collective data from those towers could be
used to get a rough estimate of where the phone is.
So let's imagine we've got a map, and on that
map we've got three cell towers A, B, and C.
You can see exactly where each one is. And let's
say that you've got a phone that located somewhere within
(35:01):
the broadcast range of those three cell towers. Each tower
sends a ping to your phone, Your phone responds with
a ping back, and you are given the amount of
distance between your phone and each of those three towers. Well,
Tower a's result says that you are a mile away
from Tower A, so you actually have to draw a
(35:24):
full circle around Tower A to represent all the possible
points you could be that are one mile away from
Tower A, So you're drawing a mile radius around Tower A.
Tower B responds that you're within one point five miles
of Tower B, so you have to draw a circle
around Tower B to represent all the points where you
(35:44):
could be that are a mile and a half away
from it. Now, the circle from tower B in the
circle from Tower A should intersect each other at two points,
but that means you could be at either of those
two points. Right, you could be at either overlap, so
you don't have enough information yet. By coordinating with tower C,
and let's say that one tells you you're within two miles,
(36:05):
you can draw a third circle, and the point where
all three circles would meet would be your general location.
It's not incredibly precise, but it does give you an
idea of where you are. The GPS constellation of satellites
does something similar, only we have to think of this
in terms of three dimensional space rather than a two
(36:26):
dimensional map. So a satellite sends out a high frequency,
low power radio signal and receivers pick that signal up.
The receiver, let's say it's your smartphone, doesn't have to
send data back up to the satellite, which is good
because i'd be an enormous drain on your smartphone's power.
So really it's just listening for these signals. Now, the
(36:48):
receiver and satellite both run the same digital pattern relative
to a specific time stamp. It's easy if we think
of this as midnight. So let's say that midnight hits
and and this particular digital pattern starts both on the
satellite and the receiver, so they're both running the exact
same pattern. The satellite beams out a signal carrying this
(37:10):
digital pattern. The satellite is far away, so it takes
a little time, you know, not much, but a little
time for that signal to get to your receiver. And
the lag between the pattern that's playing on your receiver
and the signal of that same pattern coming in from
the satellite tells the receiver how far away it is
from that particular satellite, because again we know that the
(37:32):
signal is moving at the speed of the transmission itself,
and that's the speed of light, and that's a constant.
So now the receiver knows how far away it is
from that one satellite. And because the orbits of these
satellites are predictable, the receiver has a record of where
that satellite should be relative to your surface. Occasionally we
have to tweak that record because stuff like gravity can
(37:55):
pull a satellite slightly out of position over time, so
that actually is something that has to be a rest
on occasion. Now, this receiver will do this with at
least four satellites the Y four and not three, and
I gave the three cell phone tower examples. Well, it's
because the clocks on satellites and the clock that's running
(38:16):
on the device that the receiver is built into may
not be and really aren't truly synchronized. And the intersection
of for spheres of distance like these four spheres representing
the various ranges that these satellites are finding themselves in
with regard to this receiver can only intersect at one point.
(38:39):
That's the only place they could all intersect. So if
a GPS receiver's clock is not matching up to the
clocks on the satellites, there will be no intersection at all.
And the receiver will say, well, I can't find an intersection,
so that I know that means my clock is off
from all the other clocks, and it will then adjust
its own clock to be an alignment so that the
(39:00):
or spheres have a point of intersection and that is
your location on Earth. Now, in order for our receivers
to be able to do this, the accuracy of the
atomic clocks aboard those GPS satellites has to be accurate
within twenty to thirty nanoseconds. And remember a nanosecond is
one billionth of a second. That is an astounding level
(39:23):
of accuracy. And because these satellites are in motion and
they are also affected by Earth's gravity, they are subject
to the effects of special and general relativity, and this
means we actually have to make calculations to take that
into account. Now, according to special relativity and the relative
speeds of satellites to a fixed point on the surface
(39:46):
of the Earth, we would expect the atomic clock aboard
that satellite to register seven fewer microseconds per day than
a clock on Earth because these satellites are moving through
space faster than we are, relatively speaking, so that means
from our frame of reference, time is passing more slowly
on that satellite than it does here on Earth. Ah.
(40:09):
But general relativity comes into play too, and general relativity
tells us that the Earth's gravity warps space time around
our planet. And one of general relativity's predictions is that
a clock closer to a massive object, so like a
clock here on Earth, will tick more slowly than a
(40:31):
clock that is further out from that same massive object.
So the closer the clock is to the massive object,
the less time it will experience it will measure compared
to a clock that's further away, which is crazy, right.
So taking only general relativity into account, we would see
that a clock aboard one of these satellites would register
(40:54):
more time having passed on that satellite than a clock
here on Earth, meaning for our frame of reference, time
is actually passing faster on those satellites than it does
here for us. This would come out to about forty
five microseconds a day, meaning that at the end of
day one, the clock aboard that satellite would be ahead
(41:15):
of a clock here on Earth by forty five microseconds,
and this would continue day after day, with the gap
growing wider every single day. Now, when we bring both
special and general relativity together into consideration, we see that
they don't just cancel each other out right, because we've
got that seven microsecond lag due to special relativity, but
(41:39):
we have the forty five microsecond surge due to general relativity.
So in the end, we're looking at a thirty eight
microsecond difference per day between a clock on a satellite
and a clock here on Earth. The clocks on the
satellites will get ahead of similar clocks here on Earth
by thirty eight microseconds every single day. And while a
(42:01):
microsecond is a very small amount of time, I mean
we're talking at a level that we don't typically experience.
We don't think of time in microseconds for our day
to day lives. However, thirty eight microseconds is equal to
thirty eight thousand nanoseconds, and if you're looking for an
accuracy of around twenty to thirty nanoseconds, this becomes an
(42:22):
enormous problem if we don't take it into account. And
this brings us back round to something I mentioned at
the top of the show. We know that Einstein was
right about relativity because we have to account for it
with technology like GPS. If we didn't take it into account,
if we didn't factor in the effects of relativity, our
(42:43):
GPS wouldn't work for very long at all. Our technology
proves that the science is real, or else the tech
would fail at what it needs to do now. In general,
I think that's a great lesson to take home. There
are a lot of voices out there that call science
into questions, and some of them are more outlandish than others,
a person who's passionately and sincerely arguing that the Earth
(43:06):
is flat seems pretty far out there for me, because
so much of our technology we've built upon and we
rely upon wouldn't work if that were true. Even if
you can't experience something directly, such as having a meaningful
experience of time dilation, a ton of the stuff we
do experience on a day to day basis is affected
(43:29):
by this stuff, and it proves the existence and also
the benefits of having the scientific method. Now I'll give
a little side note on GPS to kind of wrap
this up. The original GPS configuration came out of a
United States Department a defense project. The original purpose was
to provide positioning information for government and military, but specifically
(43:51):
the United States and its allies, and for that reason,
the US government wished to restrict access to this technology.
The general line of thought was that it be better
if the US didn't allow tech that could, you know,
give precise coordinates for stuff like military bases or the
position of various military units to people who didn't belong
(44:11):
to those divisions. So, as a matter of national security,
the US guarded this technology civilian receivers. So if you
went out and you bought a GPS receiver, you could
get public GPS signals, but the United States was purposefully
instituting a policy called selective availability, which was an intentional
(44:32):
degradation of public GPS signals. They were introducing errors on
purpose so that GPS receivers couldn't get an accurate location.
It limited accuracy to around fifty meters horizontally and one
hundred meters vertically, and effectively that meant that you wouldn't
really know your precise coordinates. You certainly couldn't use a
(44:55):
GPS receiver as a turn by turn directions tool because
you wouldn't even necessarily show up on the right street.
You wouldn't know if you were approaching your turn or
if you had already passed it. It was it was
not practical for that. It was only in the year
two thousand, when US President Bill Clinton directed the government
to end selective availability, that civilian GPS receivers could actually
(45:19):
get accurate data. And that's what made the modern GPS
receivers and stuff like our phones possible. So before two thousand,
GPS receivers didn't work very well for the average person,
but it wasn't because the technology was bad, or that
the science was wrong it worked that way, or if
you prefer it, it didn't work properly on purpose. And
(45:40):
that wraps up this episode about relativity and why it's
important with technology, and it's not just satellite tech, but
that's a big one, and it also ends up being
a big thorn in the side for science fiction authors
who want to write about interstellar travel at faster than
light speeds, because you have to start finding alternative X
nations for how that's possible, because we've come up against
(46:04):
these limits that Einstein predicted, and so far his predictions
have held true. So in order to travel faster than
the speed of light, you do have to create something
like warp drive, which theoretically warps space around you. So
rather than traveling faster than light, you're decreasing the distance
between your point of origin and your destination. It would
(46:26):
be kind of like taking a map of the United
States and saying I'm going to travel from Atlanta to
Los Angeles, from one coast to the other, but instead
of drawing a line from Atlanta to LA you just
fold the map so that the two dots are next
to each other, and then you draw a line that way.
That's how warp speed is supposed to work, because it's
the only way you can get around the fact that
(46:47):
you can't really go faster than the speed of light.
But that's a topic for another show. If you guys
have suggestions for future topics I should tackle, please let
me know. Send me a message on Twitter. The handle
is text hsw and I'll talk to you again really soon.
(47:10):
Tech Stuff is an iHeartRadio production. For more podcasts from iHeartRadio,
visit the iHeartRadio app, Apple Podcasts, or wherever you listen
to your favorite shows.
TechStuff News
Host
Jonathan Strickland
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