July 1, 2020 • 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 tex 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 I love all things tech. And in our last episode,
I explained how communications satellites send information via radio waves,
(00:27):
which is why we talked about signals from such things
in terms like hurts. The hurts unit refers to the
number 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
to your hand once per second. Well, you could describe
(00:49):
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 all went up, down, up,
two full times per second, then it would be two hurts. Well,
we can describe lots of stuff with the unit hurts.
(01:10):
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 base notes.
That's around the twenty hurts of area uh, and then
(01:30):
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,
(01:51):
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 pros sessor 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
(02:12):
a certain thing happens, like within a second. And I
also explained that we measure the rate at which we
can send data using the term bits. A bit is
a 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
(02:32):
basic two way physical switch has two positions off or on.
So if you hear a term like kill a bit,
that means one thousand bits, and a megabit is one
million bits, 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.
(02:56):
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
(03:18):
a byte is a unit that consists of eight bits.
And this gets confusing because we often describe stuff like
file sizes in terms of bytes, but transfer speeds in
terms of bits. So let's say that you do have
that one hundred megabits per second download speed, and you
want to download a one hundred megabyte file, Well, that
(03:40):
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 instead of
(04:03):
a killer bite being one thousand bites, it's actually one
thousand twenty four bites. And there's no standardization in the
tech industry. So sometimes people will say a kill a
bite and they mean one thousand bites. Sometimes they'll say
kill a bite and they mean one thousand, twenty four bites,
And you will want to tear your hair out and
(04:23):
then you'll look like I do, I'm bald if you
didn't know. But this episode isn't about the peculiarities of
our naming conventions and the computer information age. Instead, I
wanted to tackle something else that affects everything really, but
in particular, we really had to suss it out in
order to make certain types of satellites work properly. And
(04:43):
this is the concept of relativity. So in this episode
we're really going to learn why an understanding of relativity
is important if we want our certain satellite technologies to work,
and it serves as a great reminder that technology is
only really possible through an understanding of science. You can
think of tech as the physical manifestation of our understanding
(05:06):
of scientific principles, and that means if we were wrong
in our understanding of science, the technology shouldn't really work.
So in a way, you can think of technology that
works as evidence that the scientific method is a darned
good formula. Since we're talking about relativity, it means we're
gonna be talking about a real Einstein today. His name
(05:28):
was Einstein, which is convenient. But before we 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
(05:48):
a constant speed and direction, so they're moving at the
same velocity, they will get the same results for any
experiment that involves moving stuff around a mechanical experiment. This
is easier to understand if we use an example, and
I like one that my colleague Robert Lamb used when
he wrote about relativity for how Stuff Works dot Com
(06:10):
back in the day. He used an example of a
train and a scientific ping pong ball. All right, so
imagine you've got a scientist who's standing in the middle
of an aisle on a moving train, and the train
is moving at a steady speed in a straight line,
so there are no active forces of acceleration going on here. Remember,
(06:31):
acceleration describes a force that involves a change in velocity,
so that other means a change in direction or a
change in speed or both. But in this case constant
speed constant direction. Robert used nice round numbers in his examples,
so he suggested that the train is moving at one
miles per hour. Well it's not round. If we go
(06:54):
to the metric system, that would be one sixty one
kilometers per hour. If the train stays stead to the scientist,
it will feel as if that scientist is actually just
standing still, just anywhere, and we're conveniently ignoring an emotion
that would happen due to irregularities with the trains wheels
or the train tracks or anything like that. And if
this is hard for you to imagine, just think about
(07:17):
how you feel when you're standing still, or sitting still
or laying down Here on Earth. We know the Earth
is moving through space. It is a body in motion,
but when we are still relative to the Earth itself,
we don't feel that motion. Assuming there's not some other
weird event going on, like an earthquake, which is something separate,
(07:39):
but back to our hypothetical train, the scientist tosses the
ping pong ball down the aisle. Now, from the scientist's perspective,
this ping pong ball will travel at whatever speed they
threw it at. Robert actually suggests a relatively gentle toss
of five miles per hour or eight kilometers per hour.
The ping pong ball would bounce down the aisle, just
(08:02):
as it would if the scientists were to toss the
ball on a train that isn't moving at all, or
on just flat ground. However, let's say we have a
second observer who's not on the train. They're standing off
to the side and they can see through the train.
To this person, it will appear as if the ping
pong ball is moving very fast. Indeed, relative to this
(08:24):
stationary observer, the ping pong ball will appear to move
at the speed at which it was thrown in addition
to the speed of the train itself. So if we
take the two figures, we 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
(08:46):
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 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
(09:07):
is where the term relativity comes into play. The effects
observed are relative to the perspective of the observer. It's
all based on the reference frame of that observer. If
you're on the train, then you're just looking at a
ping pong ball bouncing at a relatively slow speed down
the aisle. If you're not on the train, the ping
(09:28):
pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
all tracks. I don't know why I talked like that.
In his Laws of Motion, Newton stated that these laws
emotions should hold in an inertial frame as well as
a reference frame that was moving at a constant velocity
(09:48):
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
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
(10:11):
the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that.
But hey, what if you're on the train that's traveling
one hour and you're facing forward, you're facing the direction
of travel, and then you have a flashlight and you
turn on the flashlight. Well, doesn't that mean you should
perform a Galilean transformation on this and say the light
(10:34):
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 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
(10:57):
Edward Morley and Albert A. Michelson created an experiment to
measure the speed of light back in and actually they
were 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
(11:19):
make sense. Okay, So on Earth we see waves traveling
through a medium, right, Like if you look out in
the ocean, you can see actual waves in the water,
and the water is a physical medium through which these
waves travel. Sound can't travel in space because space is
effectively a vacuum. The particles that are in space are
(11:43):
so far apart from one another that there's no way
for the vibration of one particle to come into contact
and affect another particle. So sound can't travel. Sound travels
through the propagation of vibrational waves. And if your stuff
isn't in contact with each other, there's no way for
them to have that wave propagate. So there has to
be some sort of medium like air or solid surfaces
(12:07):
or something in order for sound travel. Well, if that's
the case, said the folks of the time, then stuff
like light must need some sort of medium to travel through, right,
I mean sound has to have something Light must have
something too. Light can definitely travel through space. I mean,
that's how we can see anything, because light from the
(12:27):
Sun travels through space to hit the Earth. So the
light has to be moving through some sort of medium
we cannot observe directly. This hypothetical medium was the aforementioned
luminiferous ether. But assuming this ether existed at all, it
had to be pretty darn special because we can't feel it,
(12:48):
we can't detect it. It creates no observable effects. So
if it were real, it had to be unlike pretty
much anything else we had discovered up to that point. Now,
let's assume that the universe is filled with this ether stuff.
The question rises, how the heck does the ether interact
with all the physical stuff that's in the universe, the
(13:10):
actual matter and also energy. After all the bodies in
space like stars, planets, moons, and all that other stuff,
all of that is moving, none of it is standing still,
and if it is moving, it would presumably disturb this
ether medium, right. I mean, if you move your hand
(13:31):
through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
the motion of all these elements in space would disturb
the ether in some way, and hypothetically there would be
some sort of ether wind. But if there were a wind,
then presumably the speed of light would be affected depending
(13:53):
upon the wind's direction in relation to the lights direction.
So think of a really windy day in the real world.
If you're walking against a very very tough wind, like
a gale force wind, you have to power through it
to keep moving forward. Now, if you're walking with the wind,
like the wind is to your back and pushing you,
(14:13):
then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
and so Michelson and Morley devised a gadget that would
split light into two beams, directing those beams down different paths,
using mirrors in different directions, and seeing if those two
beams of light would hit an eyepiece at different times.
(14:36):
The thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
one would be at a cross direction of ether wind.
So we should see a difference in the amount of
time it takes for the light from this one source
that's been split into two to arrive at an eyepiece.
But that's not what they found. They observed no such effect.
(15:00):
So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
eighty six thousand miles per second or around three hundred
thousand kilometers per second. Now that flew in the face
of classic Newtonian physics clearly. With the example of the
(15:24):
ping pong ball and the train, the ping pong ball
has to be traveling faster than the train it's on.
I mean, that just makes sense. If you were standing
on the top of the very front of the train
and then you throw 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
(15:46):
light and what was going on? Well, this was one
of the great mysteries that Albert Einstein said his mind
to unraveling, and it formed the basis of one of
his great theories of relativity, and this would be the
theory of special relativity, which poses that the laws of
physics are in the same in all inertial frames of references,
and that means the speed of light will be the
(16:08):
same for all observers, regardless of their relative perspectives. It
doesn't matter the context. The speed of light is the
speed of light. Now, there's an implication to this theory
that really got people scratching their heads. If the speed
of light is absolutely constant, that would mean that stuff
like distance and time are not. And as a heck
(16:30):
of a brain teaser, when we come back, we'll explore
this more. Let's imagine that you live half a mile
away from a lovely park, and it's a half mile away.
In the morning, it's a half mile away. At night,
(16:51):
it's a half mile away. On a Tuesday, it's a
half mile away on a Saturday. Half a mile is
half a mile, right, It's a reliable constant in our lives.
If it weren't, we could never give directions to anywhere
because all the measurements and landmarks would change all the time,
and our world wouldn't make sense the way it does
(17:12):
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,
(17:34):
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
(17:56):
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
(18:19):
is just as legitimate as every other frame of reference.
Or I guess you could say, if everybody's super nobody is.
I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen o five theory is called special relativity
because Einstein's explanation only covered special cases, that being when
(18:40):
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
(19:02):
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
(19:22):
sure this theory is correct and that ether is there.
Einstein was taking a totally different perspective. He was saying,
if we assume the experiments are producing accurate results, then
it stands to reason that the prevailing theory is flawed
and we have to figure out what the real explanation is.
And this is one of those important points in science.
(19:44):
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
error is there that could be causing the issues. But
it does mean that you need to re examine that hypothesis,
(20:06):
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,
(20:31):
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
(20:51):
shorthand for things are about to get really weird. Einstein
posited that the speed of light is measured as constant
in all freems of reference. And let's think for a second.
What we mean by speed. Speed is a description of
how much distance can be covered per unit of time.
So a speed of one hundred miles per hour means
(21:13):
that in one hour's time, we will cover a distance
of one hundred miles. That's very obvious. But if the
speed of light is constant for all frames of reference,
regardless of how those frames are moving relative to each other,
that must mean something about space and or time is
a little wonky. And let's think about our train experiment again.
(21:36):
If you are aboard a train moving at a smooth
one miles per hour in a straight line, and you
toss a ping pong ball straight up in the air, well,
it's gonna go straight up and come right back down
to your hand in a nice vertical line. From an
outside observer who isn't on the train, it would look
a little differently. You would throw the ball up at
one point relative to this outside observer, and the ball
(21:58):
would appear to move not just vertically, but horizontally before
coming back down. Now, if we repeat this experiment but
we use light, we really see how it gets confusing. Okay,
so now you're on a train, but it's going really fast,
like let's say half the speed of light, but the
speed and direction are constant. So you're on this train.
(22:18):
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 got a laser pointer and you've got a mirror
on the ceiling of the train and a photon detector
(22:39):
on the floor of the train. You shoot the laser
up at the mirror, it reflects off the mirror, and
then it comes back down and hits the detector on
the floor, and it registers how long it took the
light to travel from your laser pointer to hit the detector,
and to you, the laser makes a vertical line. All
that makes sense, right, you can imagine that, But for
(23:00):
are 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
(23:21):
ball can hit the side of a pool table and
bounce off at an angle. But this creates an apparent paradox.
The path viewed by you on the train is a
straight line, and by definition, that is the shortest distance
between two points. The path observed by the person who
is not on the train is an angled line, and
by definition that has to be longer. The speed of
(23:42):
light is constant in both cases, but the distance is
different between the two points of reference, And because speed
is distance divided by time, if the distance is different,
the time must also be different between those two points
of reference. Crazy This brings us to the concept of
time dilation. It also, by the way, can affect distance.
(24:06):
The faster and object gets, the more squished it gets.
So if you had this train and you were to
get up to near the speed of light, the train
to an outside observer would appear to be shorter than
it normally would be. To anyone inside the train, the
dimensions would remain exactly the same. You would not suddenly
(24:28):
see a shorter train. It wouldn't be like you were
in that compressor scene in Star Wars. The train would
appear to be normal. Only from an outside observer who
is not traveling at that speed would it appear that
the train itself was getting squished shorter. Likewise, the faster
something goes with respect to some other point of reference
(24:49):
that's important, the more quickly time appears to pass for
those at the other point of reference, or alternatively, the
more slowly time seems to pass for the fast moving
thing from the frame of reference of the person who's
not moving fast. This gets really clunky. I know, it
gets confusing. So let's talk about space travel some more,
(25:09):
because examples actually make this way easier to explain. All right,
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eight percent of the speed
of light, and you're gonna go on a year long
jaunt out in space, and your best friend is hanging
back on Earth. Now we now have our two frames
(25:30):
of reference. We have the spaceship and then we have
the person on Earth. So let's ignore accelerative forces for
the moment, because we're gonna have to just focus on
special relativity. We'll get to general relativity in a moment.
So you're in your spaceship, You're zooming around at the
speed of light, and for you, time is passing normally.
(25:50):
The seconds feel like seconds, minutes feel like minutes, hours
feel like hours, etcetera. 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.
(26:13):
So to your best friend on Earth, it looks like
time is passing very slowly for you aboard your spaceship.
To you on your spaceship, it looks like time is
passing super fast for your friend back on Earth. So
when you do get back to Earth a year later
than the two of you enter the same point of reference,
things are weird. From your perspective, You've only aged a
(26:36):
year because you spend a year aboard your space ship,
but a little more than a year and a half
has passed on Earth while you were gone. Your calendars
wouldn't line up anymore. The faster you go relative to
your frame of reference, the more pronounced the time dilation. Now,
I do want to be clear about this. It's not
really correct to say that as speed increases, time slows down.
(26:57):
You have to always relay this in terms of having
another frame of reference, because within a single frame of reference,
time just passes normally. There's no difference. By the way.
This is also why star dates in the Star Trek
universe don't make a whole lot of sense. They try
to retroactively make it makes sense. But keeping time when
(27:21):
you're on a ship that can travel at the speed
of light or in the case of Star Trek, magically
going faster than the speed of light, and we won't
even get into warp speed, it all is crazy. But
being able to use that and somehow related to making
sense on time passing on planets or space stations or whatever,
(27:41):
that's a huge mess. But it's also outside of our episode,
so we'll just leave it at that. We don't notice
the effects of special relativity in most of our day
to day lives because we are not traveling fast enough
relative to each other for it to be a real
factor most of the time. But it does get even
more yeared. Were it possible to build a spaceship that
(28:03):
could travel at the speed of light and you were
to take this sort of trip to an outside observer,
time would appear to stop for you aboard your spaceship Now,
if assuming this was even possible, you would still experience
time in your own frame of reference as per normal,
but your friend back on Earth would see that it
(28:23):
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, we
can actually detect 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
(28:49):
keep incredibly accurate time down to a matter of nanoseconds,
and a nanosecond is one billionth of a second. So
one clock was kept stationary a 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
(29:11):
aircraft had measured less time than the one that stayed
on the ground on Earth. Less time passed 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
(29:34):
other point of reference. That is, the difference was right
in line with Einstein's calculations. Now, as we'll see, this
ends up being an important point when we get to satellites.
But we can't just jump on that yet. We do
need to take into consideration general relativity. So, as I mentioned,
special relativity only looks at frames of reference that are
in a constant and consistent motion with regard to one another.
(29:57):
There could be no change in direction or speed because
that introduces accelerative forces and that changes things. So to
take acceleration into account, Einstein proposed his theory of general
relativity ten years after his theory of special relativity, so
this would be nineteen fifteen for those who are keeping track.
This theory would incorporate the force of gravity into Einstein's work,
(30:19):
which means factoring in acceleration. So in this theory, Einstein
introduced the equivalence principle, which says that gravity pulling in
one direction is equivalent to acceleration in another direction. So
we can actually experience this. It's easy to remember and imagine.
Imagine getting on an elevator and it's going up, and
as it goes up, you feel that sense of increased
(30:42):
gravity pulling down on you as the elevator accelerates. When
the elevator is going down, you feel a sense of
decreased gravity as the elevator accelerates downward. So gravity and
acceleration are equivalent, which means that it can also affect
our measurements of space and time. Einstein hypothesized that gravity
(31:02):
was warping spacetime itself. Take something that's really massive, like
a huge dense star, that would warp spacetime 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
(31:25):
gets a bit confusing. The effects of gravity on time
mean that time passes differently for objects in orbit when
taken into 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
(31:49):
would feel exactly the way it does when you are
on Earth. It's only when we look at this from
two frames of reference that we see how it doesn't
match up. So what does this all mean for satellites, Well,
it means that satellites in orbit have a couple of
different relativistic effects going on. In our frame of reference
here on Earth, satellites are traveling faster than we are
(32:12):
to maintain orbit, which means that if we compare the
passing of time in each frame of reference, time would
pass faster for us than for the satellite. However, due
to the gravitational effect on space time, we also know
that something in orbit will have time passed faster for
that thing than we would experience here on Earth. So
(32:33):
it's the opposite 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
(33:04):
why relativity is important with certain satellites, let's talk about
the Global Positioning System or GPS. Now, this is the
satellite system that provides data back to Earth that makes
it 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
(33:27):
through UH trilateration 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.
(33:50):
In other words, the amount of time it would take
for the pain 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
(34:11):
between those 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
(34:32):
can see 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,
(34:54):
Tower as 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
(35:16):
of Tower B, 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 at either overlap, So
you don't have enough information yet. By coordinating with Tower C,
(35:40):
and let's 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
(36:00):
in 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.
(36:22):
So 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.
(36:45):
The satellite beams out of 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,
(37:08):
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
(37:30):
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
y four and not three, and I gave the three
cell phone tower examples. Well, it's because the clocks on
(37:51):
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 synchrono eyes 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
(38:16):
the only place they could all intersect. So if a
GPS receiver's clock is not matching up to the clocks
on the satellites, there will be no intersection at all,
and the receiver will say, well, I can't find an intersection,
so that I know that means my clock is off
from all the other clocks, and it will then adjust
its own clock to be an alignment so that the
(38:37):
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 a Downding
(39:00):
level 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
(39:23):
surface 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 the 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.
(39:47):
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
(40:09):
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 o 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
(40:31):
more time having passed 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
(40:52):
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 microsecond lag due to special relativity,
(41:16):
but we have the forty five microsecond surge due to
general relativity. So in the end, we're looking at a
thirty eight microsecond difference per day between a clock on
a satellite and a clock here on Earth. The clocks
on the satellites will get ahead of similar clocks here
on Earth by thirty eight microseconds every single day. And
(41:38):
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 to thirty nanoseconds. This
(41:59):
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 in the effects of relativity, our
(42:20):
GPS wouldn't work for very long at all. Our technology
proves that the science is real, or else the tech
would fail at what it needs to do now. In general,
I think that's a great lesson to take home. There
are a lot of voices out there that call science
into question, and some of them are more outlandish than others.
A person who is passionately and sincerely arguing that the
(42:43):
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 do experience on a day to day basis is
(43:06):
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 positioning information for government and military, but specifically
(43:28):
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 position of various military units to people who
didn't belong to those divisions. So, as a matter of
(43:51):
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 degradation of public GPS signals. They were introducing
(44:15):
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 GPS receiver as a turn by turn directions
(44:36):
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 get accurate data. And that's what made the
(44:59):
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 that wraps up this episode about relativity and why
(45:21):
it's important with technology, and it's not just satellite tech,
but that's a big one, and it also ends up
being a big thorn in the side for science fiction
authors who want to write about interstellar travel at faster
than light speeds because you have to start finding alternative
explanations for how that's possible, because we we've come up
(45:41):
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 betweening your point of origin and your destination. It
(46:03):
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,
because it's the only way you can get around the
(46:24):
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 tech stuff hs W and I'll talk
to you again really soon. Text Stuff is an I
(46:47):
heart Radio production. For more podcasts from my heart Radio,
visit the i heart Radio app, Apple Podcasts, or wherever
you listen to your favorite shows. Two
Welcome to tex 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 I love all things tech. And in our last episode,
I explained how communications satellites send information via radio waves,
(00:27):
which is why we talked about signals from such things
in terms like hurts. The hurts unit refers to the
number 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
to your hand once per second. Well, you could describe
(00:49):
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 all went up, down, up,
two full times per second, then it would be two hurts. Well,
we can describe lots of stuff with the unit hurts.
(01:10):
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 base notes.
That's around the twenty hurts of area uh, and then
(01:30):
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,
(01:51):
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 pros sessor 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
(02:12):
a certain thing happens, like within a second. And I
also explained that we measure the rate at which we
can send data using the term bits. A bit is
a 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
(02:32):
basic two way physical switch has two positions off or on.
So if you hear a term like kill a bit,
that means one thousand bits, and a megabit is one
million bits, 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.
(02:56):
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
(03:18):
a byte is a unit that consists of eight bits.
And this gets confusing because we often describe stuff like
file sizes in terms of bytes, but transfer speeds in
terms of bits. So let's say that you do have
that one hundred megabits per second download speed, and you
want to download a one hundred megabyte file, Well, that
(03:40):
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 instead of
(04:03):
a killer bite being one thousand bites, it's actually one
thousand twenty four bites. And there's no standardization in the
tech industry. So sometimes people will say a kill a
bite and they mean one thousand bites. Sometimes they'll say
kill a bite and they mean one thousand, twenty four bites,
And you will want to tear your hair out and
(04:23):
then you'll look like I do, I'm bald if you
didn't know. But this episode isn't about the peculiarities of
our naming conventions and the computer information age. Instead, I
wanted to tackle something else that affects everything really, but
in particular, we really had to suss it out in
order to make certain types of satellites work properly. And
(04:43):
this is the concept of relativity. So in this episode
we're really going to learn why an understanding of relativity
is important if we want our certain satellite technologies to work,
and it serves as a great reminder that technology is
only really possible through an understanding of science. You can
think of tech as the physical manifestation of our understanding
(05:06):
of scientific principles, and that means if we were wrong
in our understanding of science, the technology shouldn't really work.
So in a way, you can think of technology that
works as evidence that the scientific method is a darned
good formula. Since we're talking about relativity, it means we're
gonna be talking about a real Einstein today. His name
(05:28):
was Einstein, which is convenient. But before we 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
(05:48):
a constant speed and direction, so they're moving at the
same velocity, they will get the same results for any
experiment that involves moving stuff around a mechanical experiment. This
is easier to understand if we use an example, and
I like one that my colleague Robert Lamb used when
he wrote about relativity for how Stuff Works dot Com
(06:10):
back in the day. He used an example of a
train and a scientific ping pong ball. All right, so
imagine you've got a scientist who's standing in the middle
of an aisle on a moving train, and the train
is moving at a steady speed in a straight line,
so there are no active forces of acceleration going on here. Remember,
(06:31):
acceleration describes a force that involves a change in velocity,
so that other means a change in direction or a
change in speed or both. But in this case constant
speed constant direction. Robert used nice round numbers in his examples,
so he suggested that the train is moving at one
miles per hour. Well it's not round. If we go
(06:54):
to the metric system, that would be one sixty one
kilometers per hour. If the train stays stead to the scientist,
it will feel as if that scientist is actually just
standing still, just anywhere, and we're conveniently ignoring an emotion
that would happen due to irregularities with the trains wheels
or the train tracks or anything like that. And if
this is hard for you to imagine, just think about
(07:17):
how you feel when you're standing still, or sitting still
or laying down Here on Earth. We know the Earth
is moving through space. It is a body in motion,
but when we are still relative to the Earth itself,
we don't feel that motion. Assuming there's not some other
weird event going on, like an earthquake, which is something separate,
(07:39):
but back to our hypothetical train, the scientist tosses the
ping pong ball down the aisle. Now, from the scientist's perspective,
this ping pong ball will travel at whatever speed they
threw it at. Robert actually suggests a relatively gentle toss
of five miles per hour or eight kilometers per hour.
The ping pong ball would bounce down the aisle, just
(08:02):
as it would if the scientists were to toss the
ball on a train that isn't moving at all, or
on just flat ground. However, let's say we have a
second observer who's not on the train. They're standing off
to the side and they can see through the train.
To this person, it will appear as if the ping
pong ball is moving very fast. Indeed, relative to this
(08:24):
stationary observer, the ping pong ball will appear to move
at the speed at which it was thrown in addition
to the speed of the train itself. So if we
take the two figures, we 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
(08:46):
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 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
(09:07):
is where the term relativity comes into play. The effects
observed are relative to the perspective of the observer. It's
all based on the reference frame of that observer. If
you're on the train, then you're just looking at a
ping pong ball bouncing at a relatively slow speed down
the aisle. If you're not on the train, the ping
(09:28):
pong ball is moving quite fast, so it's all relative.
Isaac Newton would follow along and say, yeah, mate, this
all tracks. I don't know why I talked like that.
In his Laws of Motion, Newton stated that these laws
emotions should hold in an inertial frame as well as
a reference frame that was moving at a constant velocity
(09:48):
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
inertial frame. All of this is fairly intuitive, but then
we get to something really tricky. Einstein would establish that
(10:11):
the speed of light in a vacuum is the fastest
speed in our universe. Nothing can go faster than that.
But hey, what if you're on the train that's traveling
one hour and you're facing forward, you're facing the direction
of travel, and then you have a flashlight and you
turn on the flashlight. Well, doesn't that mean you should
perform a Galilean transformation on this and say the light
(10:34):
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 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
(10:57):
Edward Morley and Albert A. Michelson created an experiment to
measure the speed of light back in and actually they
were 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
(11:19):
make sense. Okay, So on Earth we see waves traveling
through a medium, right, Like if you look out in
the ocean, you can see actual waves in the water,
and the water is a physical medium through which these
waves travel. Sound can't travel in space because space is
effectively a vacuum. The particles that are in space are
(11:43):
so far apart from one another that there's no way
for the vibration of one particle to come into contact
and affect another particle. So sound can't travel. Sound travels
through the propagation of vibrational waves. And if your stuff
isn't in contact with each other, there's no way for
them to have that wave propagate. So there has to
be some sort of medium like air or solid surfaces
(12:07):
or something in order for sound travel. Well, if that's
the case, said the folks of the time, then stuff
like light must need some sort of medium to travel through, right,
I mean sound has to have something Light must have
something too. Light can definitely travel through space. I mean,
that's how we can see anything, because light from the
(12:27):
Sun travels through space to hit the Earth. So the
light has to be moving through some sort of medium
we cannot observe directly. This hypothetical medium was the aforementioned
luminiferous ether. But assuming this ether existed at all, it
had to be pretty darn special because we can't feel it,
(12:48):
we can't detect it. It creates no observable effects. So
if it were real, it had to be unlike pretty
much anything else we had discovered up to that point. Now,
let's assume that the universe is filled with this ether stuff.
The question rises, how the heck does the ether interact
with all the physical stuff that's in the universe, the
(13:10):
actual matter and also energy. After all the bodies in
space like stars, planets, moons, and all that other stuff,
all of that is moving, none of it is standing still,
and if it is moving, it would presumably disturb this
ether medium, right. I mean, if you move your hand
(13:31):
through a pool of water, you are disturbing that water.
You're making currents and eddies. So it was thought that
the motion of all these elements in space would disturb
the ether in some way, and hypothetically there would be
some sort of ether wind. But if there were a wind,
then presumably the speed of light would be affected depending
(13:53):
upon the wind's direction in relation to the lights direction.
So think of a really windy day in the real world.
If you're walking against a very very tough wind, like
a gale force wind, you have to power through it
to keep moving forward. Now, if you're walking with the wind,
like the wind is to your back and pushing you,
(14:13):
then you get a big boost. Well, the same thing
should be happening with light if ether wind were real,
and so Michelson and Morley devised a gadget that would
split light into two beams, directing those beams down different paths,
using mirrors in different directions, and seeing if those two
beams of light would hit an eyepiece at different times.
(14:36):
The thought being well, one of these directions would theoretically
be in the same direction as the ether wind, and
one would be at a cross direction of ether wind.
So we should see a difference in the amount of
time it takes for the light from this one source
that's been split into two to arrive at an eyepiece.
But that's not what they found. They observed no such effect.
(15:00):
So if there were such a thing as ether, the
stuff wasn't giving either a boost or a drag on
light itself. No matter what. The light was traveling at
a constant speed, which turned out to be approximately one
eighty six thousand miles per second or around three hundred
thousand kilometers per second. Now that flew in the face
of classic Newtonian physics clearly. With the example of the
(15:24):
ping pong ball and the train, the ping pong ball
has to be traveling faster than the train it's on.
I mean, that just makes sense. If you were standing
on the top of the very front of the train
and then you throw 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
(15:46):
light and what was going on? Well, this was one
of the great mysteries that Albert Einstein said his mind
to unraveling, and it formed the basis of one of
his great theories of relativity, and this would be the
theory of special relativity, which poses that the laws of
physics are in the same in all inertial frames of references,
and that means the speed of light will be the
(16:08):
same for all observers, regardless of their relative perspectives. It
doesn't matter the context. The speed of light is the
speed of light. Now, there's an implication to this theory
that really got people scratching their heads. If the speed
of light is absolutely constant, that would mean that stuff
like distance and time are not. And as a heck
(16:30):
of a brain teaser, when we come back, we'll explore
this more. Let's imagine that you live half a mile
away from a lovely park, and it's a half mile away.
In the morning, it's a half mile away. At night,
(16:51):
it's a half mile away. On a Tuesday, it's a
half mile away on a Saturday. Half a mile is
half a mile, right, It's a reliable constant in our lives.
If it weren't, we could never give directions to anywhere
because all the measurements and landmarks would change all the time,
and our world wouldn't make sense the way it does
(17:12):
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,
(17:34):
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
(17:56):
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
(18:19):
is just as legitimate as every other frame of reference.
Or I guess you could say, if everybody's super nobody is.
I guess I've watched The Incredibles too many times. Well, anyway,
this particular nineteen o five theory is called special relativity
because Einstein's explanation only covered special cases, that being when
(18:40):
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
(19:02):
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
(19:22):
sure this theory is correct and that ether is there.
Einstein was taking a totally different perspective. He was saying,
if we assume the experiments are producing accurate results, then
it stands to reason that the prevailing theory is flawed
and we have to figure out what the real explanation is.
And this is one of those important points in science.
(19:44):
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
error is there that could be causing the issues. But
it does mean that you need to re examine that hypothesis,
(20:06):
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,
(20:31):
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
(20:51):
shorthand for things are about to get really weird. Einstein
posited that the speed of light is measured as constant
in all freems of reference. And let's think for a second.
What we mean by speed. Speed is a description of
how much distance can be covered per unit of time.
So a speed of one hundred miles per hour means
(21:13):
that in one hour's time, we will cover a distance
of one hundred miles. That's very obvious. But if the
speed of light is constant for all frames of reference,
regardless of how those frames are moving relative to each other,
that must mean something about space and or time is
a little wonky. And let's think about our train experiment again.
(21:36):
If you are aboard a train moving at a smooth
one miles per hour in a straight line, and you
toss a ping pong ball straight up in the air, well,
it's gonna go straight up and come right back down
to your hand in a nice vertical line. From an
outside observer who isn't on the train, it would look
a little differently. You would throw the ball up at
one point relative to this outside observer, and the ball
(21:58):
would appear to move not just vertically, but horizontally before
coming back down. Now, if we repeat this experiment but
we use light, we really see how it gets confusing. Okay,
so now you're on a train, but it's going really fast,
like let's say half the speed of light, but the
speed and direction are constant. So you're on this train.
(22:18):
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 got a laser pointer and you've got a mirror
on the ceiling of the train and a photon detector
(22:39):
on the floor of the train. You shoot the laser
up at the mirror, it reflects off the mirror, and
then it comes back down and hits the detector on
the floor, and it registers how long it took the
light to travel from your laser pointer to hit the detector,
and to you, the laser makes a vertical line. All
that makes sense, right, you can imagine that, But for
(23:00):
are 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
(23:21):
ball can hit the side of a pool table and
bounce off at an angle. But this creates an apparent paradox.
The path viewed by you on the train is a
straight line, and by definition, that is the shortest distance
between two points. The path observed by the person who
is not on the train is an angled line, and
by definition that has to be longer. The speed of
(23:42):
light is constant in both cases, but the distance is
different between the two points of reference, And because speed
is distance divided by time, if the distance is different,
the time must also be different between those two points
of reference. Crazy This brings us to the concept of
time dilation. It also, by the way, can affect distance.
(24:06):
The faster and object gets, the more squished it gets.
So if you had this train and you were to
get up to near the speed of light, the train
to an outside observer would appear to be shorter than
it normally would be. To anyone inside the train, the
dimensions would remain exactly the same. You would not suddenly
(24:28):
see a shorter train. It wouldn't be like you were
in that compressor scene in Star Wars. The train would
appear to be normal. Only from an outside observer who
is not traveling at that speed would it appear that
the train itself was getting squished shorter. Likewise, the faster
something goes with respect to some other point of reference
(24:49):
that's important, the more quickly time appears to pass for
those at the other point of reference, or alternatively, the
more slowly time seems to pass for the fast moving
thing from the frame of reference of the person who's
not moving fast. This gets really clunky. I know, it
gets confusing. So let's talk about space travel some more,
(25:09):
because examples actually make this way easier to explain. All right,
So let's say you've built a spaceship and this spaceship
can go wicked fast, like eight percent of the speed
of light, and you're gonna go on a year long
jaunt out in space, and your best friend is hanging
back on Earth. Now we now have our two frames
(25:30):
of reference. We have the spaceship and then we have
the person on Earth. So let's ignore accelerative forces for
the moment, because we're gonna have to just focus on
special relativity. We'll get to general relativity in a moment.
So you're in your spaceship, You're zooming around at the
speed of light, and for you, time is passing normally.
(25:50):
The seconds feel like seconds, minutes feel like minutes, hours
feel like hours, etcetera. 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.
(26:13):
So to your best friend on Earth, it looks like
time is passing very slowly for you aboard your spaceship.
To you on your spaceship, it looks like time is
passing super fast for your friend back on Earth. So
when you do get back to Earth a year later
than the two of you enter the same point of reference,
things are weird. From your perspective, You've only aged a
(26:36):
year because you spend a year aboard your space ship,
but a little more than a year and a half
has passed on Earth while you were gone. Your calendars
wouldn't line up anymore. The faster you go relative to
your frame of reference, the more pronounced the time dilation. Now,
I do want to be clear about this. It's not
really correct to say that as speed increases, time slows down.
(26:57):
You have to always relay this in terms of having
another frame of reference, because within a single frame of reference,
time just passes normally. There's no difference. By the way.
This is also why star dates in the Star Trek
universe don't make a whole lot of sense. They try
to retroactively make it makes sense. But keeping time when
(27:21):
you're on a ship that can travel at the speed
of light or in the case of Star Trek, magically
going faster than the speed of light, and we won't
even get into warp speed, it all is crazy. But
being able to use that and somehow related to making
sense on time passing on planets or space stations or whatever,
(27:41):
that's a huge mess. But it's also outside of our episode,
so we'll just leave it at that. We don't notice
the effects of special relativity in most of our day
to day lives because we are not traveling fast enough
relative to each other for it to be a real
factor most of the time. But it does get even
more yeared. Were it possible to build a spaceship that
(28:03):
could travel at the speed of light and you were
to take this sort of trip to an outside observer,
time would appear to stop for you aboard your spaceship Now,
if assuming this was even possible, you would still experience
time in your own frame of reference as per normal,
but your friend back on Earth would see that it
(28:23):
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, we
can actually detect 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
(28:49):
keep incredibly accurate time down to a matter of nanoseconds,
and a nanosecond is one billionth of a second. So
one clock was kept stationary a 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
(29:11):
aircraft had measured less time than the one that stayed
on the ground on Earth. Less time passed 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
(29:34):
other point of reference. That is, the difference was right
in line with Einstein's calculations. Now, as we'll see, this
ends up being an important point when we get to satellites.
But we can't just jump on that yet. We do
need to take into consideration general relativity. So, as I mentioned,
special relativity only looks at frames of reference that are
in a constant and consistent motion with regard to one another.
(29:57):
There could be no change in direction or speed because
that introduces accelerative forces and that changes things. So to
take acceleration into account, Einstein proposed his theory of general
relativity ten years after his theory of special relativity, so
this would be nineteen fifteen for those who are keeping track.
This theory would incorporate the force of gravity into Einstein's work,
(30:19):
which means factoring in acceleration. So in this theory, Einstein
introduced the equivalence principle, which says that gravity pulling in
one direction is equivalent to acceleration in another direction. So
we can actually experience this. It's easy to remember and imagine.
Imagine getting on an elevator and it's going up, and
as it goes up, you feel that sense of increased
(30:42):
gravity pulling down on you as the elevator accelerates. When
the elevator is going down, you feel a sense of
decreased gravity as the elevator accelerates downward. So gravity and
acceleration are equivalent, which means that it can also affect
our measurements of space and time. Einstein hypothesized that gravity
(31:02):
was warping spacetime itself. Take something that's really massive, like
a huge dense star, that would warp spacetime 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
(31:25):
gets a bit confusing. The effects of gravity on time
mean that time passes differently for objects in orbit when
taken into 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
(31:49):
would feel exactly the way it does when you are
on Earth. It's only when we look at this from
two frames of reference that we see how it doesn't
match up. So what does this all mean for satellites, Well,
it means that satellites in orbit have a couple of
different relativistic effects going on. In our frame of reference
here on Earth, satellites are traveling faster than we are
(32:12):
to maintain orbit, which means that if we compare the
passing of time in each frame of reference, time would
pass faster for us than for the satellite. However, due
to the gravitational effect on space time, we also know
that something in orbit will have time passed faster for
that thing than we would experience here on Earth. So
(32:33):
it's the opposite 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
(33:04):
why relativity is important with certain satellites, let's talk about
the Global Positioning System or GPS. Now, this is the
satellite system that provides data back to Earth that makes
it 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
(33:27):
through UH trilateration 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.
(33:50):
In other words, the amount of time it would take
for the pain 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
(34:11):
between those 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
(34:32):
can see 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,
(34:54):
Tower as 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
(35:16):
of Tower B, 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 at either overlap, So
you don't have enough information yet. By coordinating with Tower C,
(35:40):
and let's 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
(36:00):
in 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.
(36:22):
So 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.
(36:45):
The satellite beams out of 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,
(37:08):
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
(37:30):
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
y four and not three, and I gave the three
cell phone tower examples. Well, it's because the clocks on
(37:51):
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 synchrono eyes 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
(38:16):
the only place they could all intersect. So if a
GPS receiver's clock is not matching up to the clocks
on the satellites, there will be no intersection at all,
and the receiver will say, well, I can't find an intersection,
so that I know that means my clock is off
from all the other clocks, and it will then adjust
its own clock to be an alignment so that the
(38:37):
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 a Downding
(39:00):
level 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
(39:23):
surface 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 the 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.
(39:47):
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
(40:09):
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 o 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
(40:31):
more time having passed 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
(40:52):
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 microsecond lag due to special relativity,
(41:16):
but we have the forty five microsecond surge due to
general relativity. So in the end, we're looking at a
thirty eight microsecond difference per day between a clock on
a satellite and a clock here on Earth. The clocks
on the satellites will get ahead of similar clocks here
on Earth by thirty eight microseconds every single day. And
(41:38):
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 to thirty nanoseconds. This
(41:59):
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 in the effects of relativity, our
(42:20):
GPS wouldn't work for very long at all. Our technology
proves that the science is real, or else the tech
would fail at what it needs to do now. In general,
I think that's a great lesson to take home. There
are a lot of voices out there that call science
into question, and some of them are more outlandish than others.
A person who is passionately and sincerely arguing that the
(42:43):
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 do experience on a day to day basis is
(43:06):
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 positioning information for government and military, but specifically
(43:28):
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 position of various military units to people who
didn't belong to those divisions. So, as a matter of
(43:51):
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 degradation of public GPS signals. They were introducing
(44:15):
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 GPS receiver as a turn by turn directions
(44:36):
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 get accurate data. And that's what made the
(44:59):
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 that wraps up this episode about relativity and why
(45:21):
it's important with technology, and it's not just satellite tech,
but that's a big one, and it also ends up
being a big thorn in the side for science fiction
authors who want to write about interstellar travel at faster
than light speeds because you have to start finding alternative
explanations for how that's possible, because we we've come up
(45:41):
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 betweening your point of origin and your destination. It
(46:03):
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,
because it's the only way you can get around the
(46:24):
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 tech stuff hs W and I'll talk
to you again really soon. Text Stuff is an I
(46:47):
heart Radio production. For more podcasts from my heart Radio,
visit the i heart Radio app, Apple Podcasts, or wherever
you listen to your favorite shows. Two
TechStuff News
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