September 29, 2022 • 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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Episode Transcript
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Speaker 1 (00:04):
Welcome to tech Stuff, a production from I Heart Radio.
Hey there, and welcome to tech Stuff. I'm your host,
Jonathan Strickland. I'm an executive producer with I Heart Radio.
And how the tech are you. Well, I'm still on vacation, y'all.
I'll be back soon. But in the meantime, we have
(00:25):
an episode that originally published on July one, twenty. It's
called It's All Relative. And when I was a kid,
I was convinced that Einstein's theories were the 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
(00:49):
we rely upon wouldn't work properly. It's fascinating stuff. I
hope you enjoy. The hurts unit refers to the numb
or of repeated phenomena over the course of a second.
So imagine that you're dribbling a basketball, so that the
ball goes from your hand to the ground back up
(01:11):
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 dribbled
twice as fast, so that the ball went up down
up two full times per second, then there would be
two hurts. Well, we can describe lots of stuff with
(01:33):
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
the low end is that twenty hurts. That represents the
lowest pitches of sounds. So you can think of those
deep bass notes. That's around the twenty hurts of area uh,
(01:54):
and then it goes all the way up to twenty
killer hurts or twenty thousand hurts. That represents the very
highest pitches that people can typically here, And those frequencies
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,
(02:16):
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
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
(02:37):
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
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
(02:58):
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,
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.
(03:21):
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
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
(03:43):
a bite is a unit that consists of eight bits,
and this gets confusing because we often describe stuff like
file sizes in terms of bites, but transfer speeds in
terms of bits. So let's say that you do have
that one hundred megabits person, I can download speed, and
you want to download a one hundred megabyte file, Well,
(04:05):
that means it's not going to take one second. It's
gonna take eight seconds to download the file, because a
megabyte is eight times larger than a megabit. And actually
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
(04:27):
instead of a killer byte being one thousand bytes, it's
actually one thousand twenty four bytes. And there's no standardization
in the tech industry, so sometimes people will say a
kill a byte and they mean one thousand bytes. Sometimes
they'll say kill a byte and they mean one thousand
twenty four bytes, and you will want to tear your
hair out, and then you'll look like I do, I'm
(04:50):
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. It affects everything, really,
but in particular 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
(05:11):
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 of tech as the physical manifestation of
our understanding of scientific principles, and that means if we
(05:34):
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 darned good formula. Since we're talking about relativity, it
means we're gonna be talking about a real Einstein today.
His name was Einstein, which is convenient. But before we
(05:57):
get to Einstein, we have Galileo Galileo, Galileo Figaro. Wait no,
I'm sorry, Wait that's Bohemian Rhapsody. I meant Galileo galile This.
Galileo made an observation that if you've got two observers
moving at a constant speed and direction, so they're moving
at the same velocity, they will get the same results
(06:19):
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 how Stuff Works dot
Com back in the day. He used an example of
a train and a scientific ping pong ball. Alright, so
(06:42):
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,
acceleration describes a force that involves a chain and velocities.
That other means a change in direction or a change
(07:04):
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
miles per hour. Well it's not round. If we go
to the metric system, that would be one kilometers per hour.
If the train stays steady to the scientist, it will
(07:26):
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 trains wheels or the
train tracks or anything like that. And if this is
hard for you to imagine, 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.
(07:50):
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 mother weird event going on like an earthquake,
which is something separate. But back to our hypothetical train,
the scientist tosses the ping pong ball down the aisle. Now,
(08:11):
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
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
(08:35):
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,
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.
(08:58):
So if we take the two figures, we get one
hundred five miles per hour or a hundred sixty nine
kilometers per hour. This is called a Galilean transformation. Alternatively,
if the scientists were throwing the ping pong ball in
the opposite direction of the trains travel, so they're facing
towards the back of the train, it would appear to
this second observer that the ping pong ball was moving
(09:21):
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.
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.
(09:45):
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
ping pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
old tracks. I don't know why I talked like that.
In his Laws of Motion, Newton stated that these laws
(10:07):
emotions should hold in an inertial frame as well as
a reference frame that was moving at a constant velocity
relative to the inertial frame. And 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
(10:28):
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that. Hey,
what if you're on the train that's traveling one per
hour and you're facing forward, you're facing the direction of travel,
(10:49):
and then you have a flashlight and you turn on
the flashlight. Well, doesn't that mean you should perform a
Galilean transformation on this and 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 miles per hour. Doesn't
(11:11):
that make sense? Well, according to actual experiments performed before
Einstein would come around to explain things, the answer was Nope,
doesn't look like it works that way. Scientists Edward Morley
and Albert A. Michelson created an experiment to measure the
speed of light back in seven and actually they were
(11:31):
looking for something else. They were looking for evidence of
a hypothetical substance called luminiferous ether. Say what, all right,
We'll stick 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
(11:52):
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
effectively a vacuum. The particles that are in space are
so far apart from one another there's no way for
the vibration of one particle to come into contact and
(12:14):
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 medium like air or solid surfaces or
something in order for sound travel. Well, if that's the case,
(12:37):
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 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
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we cannot observe directly. This hypothetical medium was the aforementioned
luminiferous ether. But assuming this ether existed at all, it
had to be pretty darn special because we can't feel it,
we can't detect it, it creates no observable effects, So
if it were real, it had to be unlike pretty
(13:20):
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
actual matter and also energy. After all, the bodies in
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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
through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
(14:02):
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
upon the wind's direction in relation to the lights direction.
So think of a really windy day in the real world.
(14:25):
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,
then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
(14:45):
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,
the thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
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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.
So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
(15:31):
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
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 the ping
pong ball and the train, the ping pong ball has
(15:52):
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 through the ping pong ball, and we ignore stuff
like wind resistance, 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 light and
(16:12):
what was going on? Well, this was one of the
great mysteries that Albert Einstein's that is mine 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 same
(16:33):
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 of
(16:55):
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, it's
(17:17):
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 in nineteen o 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 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 is super,
nobody is. I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen o 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
(19:48):
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 result, 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 spacetime continuum, which also gives us
dozens of Star Trek episodes that would use it as
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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 miles per hour means that
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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 our train experiment again.
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If you are aboard a train moving at a smooth
one 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 this outside observer, and the ball would
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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 are constant. So you're on this train.
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You don't feel any acceleration forces because you're moving at
a constant speed and 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 a laser pointer and you've got a mirror on
the ceiling of the train and a photon detector on
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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, you can imagine that, But for our
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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
towards 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 of like how a billiard ball can
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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 to be longer. The speed of light is constant
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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 the way, can affect distance. The faster and object gets,
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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.
You would not suddenly see a shorter train. It wouldn't
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be like you were in that compressor scene in Star Wars.
The train would a to be normal. Only from an
outside observer who is not traveling at that speed would
it appear that the train itself was getting squished shorter. Likewise,
the faster something goes with respect to some other point
of reference that's important, the more quickly time appears to
(25:18):
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 travel some more,
because examples actually make this way easier to explain. All right,
(25:39):
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eight 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 of reference. We
have the spaceship and then we have the person on Earth.
(26:00):
So let's ignore accelerative forces for the moment, because we're
going to 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 the speed of light,
and for you, time is passing normally. The seconds feel
like seconds, minutes feel like minutes, hours feel like hours, etcetera.
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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 passed like seconds,
their minutes passing minutes, and so on. However, when we
look at the two of you in reference to one another,
something unusual happens. So to your best friend on Earth,
it looks like time is passing very slowly for you
(26:44):
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. Your perspective, you've
only aged a year because you spend a year aboard
your spaceship, but a little more than a year and
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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. You have to always relay this in
terms of having another frame of reference, because within a
(27:29):
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 try to retroactively make it makes sense. But keeping
time when you're on a ship that can travel at
the speed of light or in the case of Star Trek,
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magically going faster than the speed of light, and we
won't even get into warp speed. It all is crazy.
But and being able to use that and somehow related
to making sense on time passing on planets or space
stations or whatever, that's a huge mess. But it's also
outside of our episode, so we'll just leave it at that.
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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,
and you were to take this sort of trip to
(28:34):
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,
this is a mood point. Matter cannot travel at the
speed of light, so it's more of a thought experiment anyway. However,
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we can actually det time dilation with extremely accurate time
measurement devices like atomic clocks. In fact, we've done it
in experiments. Scientists have synchronized two atomic clocks, and these
atomic clocks keep incredibly accurate time down to a matter
of nanoseconds, and a nanosecond is one billion of a second.
(29:23):
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
aboard the aircraft had measured less time than the one
that stayed on the ground on Earth, less time passed
(29:45):
on that aircraft relatively 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 perspective
of the other point of reference, that is, the difference
was right in line with Einstein's calculations. Now, as we'll see,
(30:07):
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
regard to one another. There could be no change in
direction or speed because that introduces accelerative forces and that
(30:28):
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
force of gravity into Einstein's work, which means factoring in acceleration.
So in this theory, Einstein introduced the equivalence principle, which
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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,
you feel that sense of increased gravity pulling down on
you as the elevator accelerates. When the elevator is going down,
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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.
Einstein hypothesized that gravity was warping space time itself. Take
something that's really massive, like a huge dense star, that
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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.
Now here's another thing that gets a bit confusing. The
effects of gravity on time mean that time passes differently
(31:57):
for objects in orbit when taken in reference to time
passing on Earth itself. Time passes faster in orbit than
it does on Earth. Now, again, this is a frame
of reference thing, because if you were on a spaceship
in orbit, your experience of time would feel exactly the
way it does when you are on Earth. It's only
(32:19):
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 on Earth,
satellites are traveling faster than we are to maintain orbit,
(32:39):
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 passed faster for that thing then
we would experience here on Earth. So it's the opposite
(33:00):
of the effect of special relativity in a way, and
the effects of special 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 more after
we take this quick break. To understand why relativity is
(33:32):
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 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 uh trilateration
(33:56):
using signals from cell phone towers. This works on a
fairly simple principle. So we know that the 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,
(34:18):
the amount of time it would take for the ping
to reach the cell tower could be 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
(34:38):
two points. However, that's just a distance, there's no direction there. Now,
if you did this with multiple 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, n C. You can see
(35:00):
exactly where each one is. And let's say that you've
got a phone that's located somewhere within 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 as
(35:22):
result says that you are a mile away from Tower A,
so you actually have to draw a 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,
(35:44):
so you have to draw a circle around Tower B
to represent all the points where you 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 an either overlap, So you don't have
enough information yet. By coordinating with tower C, and let's
(36:07):
say that one tells you you're within two miles, 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
(36:27):
terms of three dimensional space rather than a two 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
would be an enormous drain on your smartphones power. So
(36:49):
really it's just listening for these signals. Now, the 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
this particular digital pattern starts both on the satellite and
the receiver, so they're both running the exact same pattern.
(37:12):
The satellite beams out a signal carrying this 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.
(37:34):
Because again we know that the 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 the your surface. Occasionally we have to tweak
(37:56):
that record because stuff like gravity can pull a satellite
slightly out of position over time, so that actually is
something that has to be addressed on occasion. Now this
receiver will do this with at least four satellites. The
why four and not three, and I gave the three
cell phone tower examples. Well, it's because the clocks on
(38:18):
satellites and the clock that's running on the device that
the receiver is built into may not be in and
really aren't truly synchronized. And the intersection of four spheres
of distance like these four spheres represent the various ranges
that these satellites are finding themselves in. With regard to
this receiver can only intersect at one point. That's the
(38:43):
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
(39:04):
four 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 astiunding level
(39:28):
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
(39:50):
of the Earth, we would expect the atomic clock aboard
that satellite to register seven fewer micro seconds 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.
(40:14):
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 take more slowly than a
(40:36):
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 this 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
(40:58):
more time having past on that satellite than a clock
here on Earth, meaning from 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 micro seconds a day, meaning that at the end
of day one, the clock aboard that satellite would be
(41:19):
ahead of a clock here on Earth by forty five
micro seconds, 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 micro second lag due to
(41:42):
special relativity, but we have the forty five micro second
surge due to general relativity. So in the end we're
looking at a thirty eight micro second difference per day
between a clock on a satellite and a clock here
on Earth. The clocks on the satellites will get a
head of similar clocks here on Earth by thirty eight
(42:02):
microseconds every single day. And while a 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
(42:24):
to thirty nanoseconds, this becomes an enormous problem if we
don't take it into account. And this brings us background
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
(42:45):
in the effects of relativity, our 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 let us And to take home, there are
a lot of voices out there that call science into question,
and some of them are more outlandish than others. A
(43:07):
person who is passionately and sincerely arguing that the Earth
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
(43:30):
do experience on a day to day basis is affected
by this stuff, and it proves the existence and also
the benefits of having the scientific method. Now 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
(43:51):
positioning information for government and military, but specifically the United
States and its allies, and for that reason, the U
S Government wished to restrict access to this technology. The
general line of thought was that it would be better
if the U. S didn't allow tech that could, you know,
give precise coordinates for stuff like military bases or the
(44:12):
position of various military units to people who didn't belong
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
(44:37):
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 in a
hundred meters vertically, and effectively, that meant that you wouldn't
really know your precise coordinates. You certainly couldn't use a
(45:00):
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
(45:23):
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
(45:44):
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 ser than
light speeds, because you have to start finding alternative explanations
(46:04):
for how that's possible, because we we've come up against
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
(46:26):
between your point of origin and your destination. It would
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 l A, 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,
(46:49):
because it's the only way you can get around the
fact that 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 stuff H s W and I'll
talk to you again really soon y. Text Stuff is
(47:15):
an I Heart Radio production. For more podcasts from I
Heart Radio, visit the i heart Radio app, Apple Podcasts,
or wherever you listen to your favorite shows.
Welcome to tech Stuff, a production from I Heart Radio.
Hey there, and welcome to tech Stuff. I'm your host,
Jonathan Strickland. I'm an executive producer with I Heart Radio.
And how the tech are you. Well, I'm still on vacation, y'all.
I'll be back soon. But in the meantime, we have
(00:25):
an episode that originally published on July one, twenty. It's
called It's All Relative. And when I was a kid,
I was convinced that Einstein's theories were the 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
(00:49):
we rely upon wouldn't work properly. It's fascinating stuff. I
hope you enjoy. The hurts unit refers to the numb
or of repeated phenomena over the course of a second.
So imagine that you're dribbling a basketball, so that the
ball goes from your hand to the ground back up
(01:11):
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 dribbled
twice as fast, so that the ball went up down
up two full times per second, then there would be
two hurts. Well, we can describe lots of stuff with
(01:33):
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
the low end is that twenty hurts. That represents the
lowest pitches of sounds. So you can think of those
deep bass notes. That's around the twenty hurts of area uh,
(01:54):
and then it goes all the way up to twenty
killer hurts or twenty thousand hurts. That represents the very
highest pitches that people can typically here, And those frequencies
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,
(02:16):
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
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
(02:37):
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
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
(02:58):
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,
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.
(03:21):
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
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
(03:43):
a bite is a unit that consists of eight bits,
and this gets confusing because we often describe stuff like
file sizes in terms of bites, but transfer speeds in
terms of bits. So let's say that you do have
that one hundred megabits person, I can download speed, and
you want to download a one hundred megabyte file, Well,
(04:05):
that means it's not going to take one second. It's
gonna take eight seconds to download the file, because a
megabyte is eight times larger than a megabit. And actually
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
(04:27):
instead of a killer byte being one thousand bytes, it's
actually one thousand twenty four bytes. And there's no standardization
in the tech industry, so sometimes people will say a
kill a byte and they mean one thousand bytes. Sometimes
they'll say kill a byte and they mean one thousand
twenty four bytes, and you will want to tear your
hair out, and then you'll look like I do, I'm
(04:50):
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. It affects everything, really,
but in particular 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
(05:11):
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 of tech as the physical manifestation of
our understanding of scientific principles, and that means if we
(05:34):
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 darned good formula. Since we're talking about relativity, it
means we're gonna be talking about a real Einstein today.
His name was Einstein, which is convenient. But before we
(05:57):
get to Einstein, we have Galileo Galileo, Galileo Figaro. Wait no,
I'm sorry, Wait that's Bohemian Rhapsody. I meant Galileo galile This.
Galileo made an observation that if you've got two observers
moving at a constant speed and direction, so they're moving
at the same velocity, they will get the same results
(06:19):
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 how Stuff Works dot
Com back in the day. He used an example of
a train and a scientific ping pong ball. Alright, so
(06:42):
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,
acceleration describes a force that involves a chain and velocities.
That other means a change in direction or a change
(07:04):
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
miles per hour. Well it's not round. If we go
to the metric system, that would be one kilometers per hour.
If the train stays steady to the scientist, it will
(07:26):
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 trains wheels or the
train tracks or anything like that. And if this is
hard for you to imagine, 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.
(07:50):
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 mother weird event going on like an earthquake,
which is something separate. But back to our hypothetical train,
the scientist tosses the ping pong ball down the aisle. Now,
(08:11):
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
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
(08:35):
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,
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.
(08:58):
So if we take the two figures, we get one
hundred five miles per hour or a hundred sixty nine
kilometers per hour. This is called a Galilean transformation. Alternatively,
if the scientists were throwing the ping pong ball in
the opposite direction of the trains travel, so they're facing
towards the back of the train, it would appear to
this second observer that the ping pong ball was moving
(09:21):
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.
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.
(09:45):
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
ping pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
old tracks. I don't know why I talked like that.
In his Laws of Motion, Newton stated that these laws
(10:07):
emotions should hold in an inertial frame as well as
a reference frame that was moving at a constant velocity
relative to the inertial frame. And 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
(10:28):
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that. Hey,
what if you're on the train that's traveling one per
hour and you're facing forward, you're facing the direction of travel,
(10:49):
and then you have a flashlight and you turn on
the flashlight. Well, doesn't that mean you should perform a
Galilean transformation on this and 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 miles per hour. Doesn't
(11:11):
that make sense? Well, according to actual experiments performed before
Einstein would come around to explain things, the answer was Nope,
doesn't look like it works that way. Scientists Edward Morley
and Albert A. Michelson created an experiment to measure the
speed of light back in seven and actually they were
(11:31):
looking for something else. They were looking for evidence of
a hypothetical substance called luminiferous ether. Say what, all right,
We'll stick 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
(11:52):
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
effectively a vacuum. The particles that are in space are
so far apart from one another there's no way for
the vibration of one particle to come into contact and
(12:14):
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 medium like air or solid surfaces or
something in order for sound travel. Well, if that's the case,
(12:37):
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 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
(12:58):
we cannot observe directly. This hypothetical medium was the aforementioned
luminiferous ether. But assuming this ether existed at all, it
had to be pretty darn special because we can't feel it,
we can't detect it, it creates no observable effects, So
if it were real, it had to be unlike pretty
(13:20):
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
actual matter and also energy. After all, the bodies in
(13:40):
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
through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
(14:02):
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
upon the wind's direction in relation to the lights direction.
So think of a really windy day in the real world.
(14:25):
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,
then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
(14:45):
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,
the thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
(15:08):
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.
So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
(15:31):
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
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 the ping
pong ball and the train, the ping pong ball has
(15:52):
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 through the ping pong ball, and we ignore stuff
like wind resistance, 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 light and
(16:12):
what was going on? Well, this was one of the
great mysteries that Albert Einstein's that is mine 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 same
(16:33):
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 of
(16:55):
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, it's
(17:17):
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
(17:38):
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 in nineteen o five and say, well, yeah,
but see, the speed of light is really the true constant,
(18:00):
and for that to work, time and distance or space
in other 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
(18:22):
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
(18:45):
is just as legitimate as every other frame of reference
or I guess you could say, if everybody is super,
nobody is. I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen o five theory is called special relativity
because Einstein's explanation only covered special cases, that being when
(19:06):
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
(19:28):
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
(19:48):
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 result, 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.
(20:10):
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,
(20:32):
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,
(20:57):
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 spacetime continuum, which also gives us
dozens of Star Trek episodes that would use it as
(21:17):
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 miles per hour means that
(21:39):
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 our train experiment again.
(22:01):
If you are aboard a train moving at a smooth
one 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 this outside observer, and the ball would
(22:24):
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 are constant. So you're on this train.
(22:44):
You don't feel any acceleration forces because you're moving at
a constant speed and 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 a laser pointer and you've got a mirror on
the ceiling of the train and a photon detector on
(23:05):
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, you can imagine that, But for our
(23:26):
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
towards 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 of like how a billiard ball can
(23:48):
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 to be longer. The speed of light is constant
(24:09):
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 the way, can affect distance. The faster and object gets,
(24:34):
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.
You would not suddenly see a shorter train. It wouldn't
(24:56):
be like you were in that compressor scene in Star Wars.
The train would a to be normal. Only from an
outside observer who is not traveling at that speed would
it appear that the train itself was getting squished shorter. Likewise,
the faster something goes with respect to some other point
of reference that's important, the more quickly time appears to
(25:18):
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 travel some more,
because examples actually make this way easier to explain. All right,
(25:39):
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eight 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 of reference. We
have the spaceship and then we have the person on Earth.
(26:00):
So let's ignore accelerative forces for the moment, because we're
going to 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 the speed of light,
and for you, time is passing normally. The seconds feel
like seconds, minutes feel like minutes, hours feel like hours, etcetera.
(26:21):
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 passed like seconds,
their minutes passing minutes, and so on. However, when we
look at the two of you in reference to one another,
something unusual happens. So to your best friend on Earth,
it looks like time is passing very slowly for you
(26:44):
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. Your perspective, you've
only aged a year because you spend a year aboard
your spaceship, but a little more than a year and
(27:06):
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. You have to always relay this in
terms of having another frame of reference, because within a
(27:29):
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 try to retroactively make it makes sense. But keeping
time when you're on a ship that can travel at
the speed of light or in the case of Star Trek,
(27:51):
magically going faster than the speed of light, and we
won't even get into warp speed. It all is crazy.
But and being able to use that and somehow related
to making sense on time passing on planets or space
stations or whatever, that's a huge mess. But it's also
outside of our episode, so we'll just leave it at that.
(28:12):
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,
and you were to take this sort of trip to
(28:34):
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,
this is a mood point. Matter cannot travel at the
speed of light, so it's more of a thought experiment anyway. However,
(28:59):
we can actually det time dilation with extremely accurate time
measurement devices like atomic clocks. In fact, we've done it
in experiments. Scientists have synchronized two atomic clocks, and these
atomic clocks keep incredibly accurate time down to a matter
of nanoseconds, and a nanosecond is one billion of a second.
(29:23):
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
aboard the aircraft had measured less time than the one
that stayed on the ground on Earth, less time passed
(29:45):
on that aircraft relatively 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 perspective
of the other point of reference, that is, the difference
was right in line with Einstein's calculations. Now, as we'll see,
(30:07):
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
regard to one another. There could be no change in
direction or speed because that introduces accelerative forces and that
(30:28):
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
force of gravity into Einstein's work, which means factoring in acceleration.
So in this theory, Einstein introduced the equivalence principle, which
(30:51):
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,
you feel that sense of increased gravity pulling down on
you as the elevator accelerates. When the elevator is going down,
(31:14):
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.
Einstein hypothesized that gravity was warping space time itself. Take
something that's really massive, like a huge dense star, that
(31:36):
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.
Now here's another thing that gets a bit confusing. The
effects of gravity on time mean that time passes differently
(31:57):
for objects in orbit when taken in reference to time
passing on Earth itself. Time passes faster in orbit than
it does on Earth. Now, again, this is a frame
of reference thing, because if you were on a spaceship
in orbit, your experience of time would feel exactly the
way it does when you are on Earth. It's only
(32:19):
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 on Earth,
satellites are traveling faster than we are to maintain orbit,
(32:39):
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 passed faster for that thing then
we would experience here on Earth. So it's the opposite
(33:00):
of the effect of special relativity in a way, and
the effects of special 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 more after
we take this quick break. To understand why relativity is
(33:32):
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 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 uh trilateration
(33:56):
using signals from cell phone towers. This works on a
fairly simple principle. So we know that the 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,
(34:18):
the amount of time it would take for the ping
to reach the cell tower could be 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
(34:38):
two points. However, that's just a distance, there's no direction there. Now,
if you did this with multiple 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, n C. You can see
(35:00):
exactly where each one is. And let's say that you've
got a phone that's located somewhere within 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 as
(35:22):
result says that you are a mile away from Tower A,
so you actually have to draw a 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,
(35:44):
so you have to draw a circle around Tower B
to represent all the points where you 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 an either overlap, So you don't have
enough information yet. By coordinating with tower C, and let's
(36:07):
say that one tells you you're within two miles, 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
(36:27):
terms of three dimensional space rather than a two 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
would be an enormous drain on your smartphones power. So
(36:49):
really it's just listening for these signals. Now, the 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
this particular digital pattern starts both on the satellite and
the receiver, so they're both running the exact same pattern.
(37:12):
The satellite beams out a signal carrying this 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.
(37:34):
Because again we know that the 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 the your surface. Occasionally we have to tweak
(37:56):
that record because stuff like gravity can pull a satellite
slightly out of position over time, so that actually is
something that has to be addressed on occasion. Now this
receiver will do this with at least four satellites. The
why four and not three, and I gave the three
cell phone tower examples. Well, it's because the clocks on
(38:18):
satellites and the clock that's running on the device that
the receiver is built into may not be in and
really aren't truly synchronized. And the intersection of four spheres
of distance like these four spheres represent the various ranges
that these satellites are finding themselves in. With regard to
this receiver can only intersect at one point. That's the
(38:43):
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
(39:04):
four 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 astiunding level
(39:28):
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
(39:50):
of the Earth, we would expect the atomic clock aboard
that satellite to register seven fewer micro seconds 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.
(40:14):
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 take more slowly than a
(40:36):
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 this 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
(40:58):
more time having past on that satellite than a clock
here on Earth, meaning from 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 micro seconds a day, meaning that at the end
of day one, the clock aboard that satellite would be
(41:19):
ahead of a clock here on Earth by forty five
micro seconds, 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 micro second lag due to
(41:42):
special relativity, but we have the forty five micro second
surge due to general relativity. So in the end we're
looking at a thirty eight micro second difference per day
between a clock on a satellite and a clock here
on Earth. The clocks on the satellites will get a
head of similar clocks here on Earth by thirty eight
(42:02):
microseconds every single day. And while a 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
(42:24):
to thirty nanoseconds, this becomes an enormous problem if we
don't take it into account. And this brings us background
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
(42:45):
in the effects of relativity, our 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 let us And to take home, there are
a lot of voices out there that call science into question,
and some of them are more outlandish than others. A
(43:07):
person who is passionately and sincerely arguing that the Earth
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
(43:30):
do experience on a day to day basis is affected
by this stuff, and it proves the existence and also
the benefits of having the scientific method. Now 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
(43:51):
positioning information for government and military, but specifically the United
States and its allies, and for that reason, the U
S Government wished to restrict access to this technology. The
general line of thought was that it would be better
if the U. S didn't allow tech that could, you know,
give precise coordinates for stuff like military bases or the
(44:12):
position of various military units to people who didn't belong
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
(44:37):
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 in a
hundred meters vertically, and effectively, that meant that you wouldn't
really know your precise coordinates. You certainly couldn't use a
(45:00):
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
(45:23):
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
(45:44):
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 ser than
light speeds, because you have to start finding alternative explanations
(46:04):
for how that's possible, because we we've come up against
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
(46:26):
between your point of origin and your destination. It would
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 l A, 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,
(46:49):
because it's the only way you can get around the
fact that 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 stuff H s W and I'll
talk to you again really soon y. Text Stuff is
(47:15):
an I Heart Radio production. For more podcasts from I
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