- This episode was made
possible by Curiosity Stream. I'm gonna level with you. I can't hold a lot of
information in my head at once. Sometimes I feel like when
I learn something new, it pushes something else out. Oh, I have so much in my brain already that new ideas just won't go in. So in today's video, we're
going to solve a paradox which proves Einstein's
special theory of relativity using only two laws of physics. Then we'll just follow the trails of logic all the way to the solution. If you happen to like this
video, please subscribe so you don't miss other
videos similar to this one. Here's the paradox. This is a subatomic
particle called a muon. The muon is like the awkward
cousin of the electron, much bigger and much more unstable. They have an average lifetime
of just 2.2 microseconds. This means that if you
take a bunch of muons and measure how long they last from the time they're created
to the time they decay, the average lifetime
will be 2.2 microseconds. Now muons are created by
high energy collisions in the Earth's atmosphere, about 15 kilometers
above the earth surface. They make their way down to earth at speeds of up to 99% the speed of light. But because of their short lifetime, they should only travel about
660 meters before dying. So how many would you
expect to detect on earth? Well, almost none, right? There might be some ambitious
ones that make the journey, but most of them would never get here. It'd be like us traveling to a planet that takes over 2000 years to get to. We die long before we reached it. But here's the thing. This is a muon detector
built by my friend, Grady from the channel, Practical Engineering. Every time it flashes, that's
a muon on being detected. And I'm pretty sure Grady
was on earth surface when he used this. In fact, if you hold out
the palm of your hand, approximately one muon passes
through it every second. That is a lot more than expected. So how do muons make
the impossible journey down to earth surface, a
journey 22 times their lifespan? And if muons can cheat time,
does that mean we can too? This is called the muon paradox and it was one of the
first pieces of evidence supporting Einstein's
special theory of relativity. As promised, we're going to solve it using just two laws of physics. The first is this. (gentle music) Every time I see this some part
of me expects the trampoline will keep moving forward without the guy and he'll miss it when he
lands, but it never happens because the laws of physics are the same in all inertial frames of reference. This sentence sounds more
complicated than it is. So let's break it down. What is an inertial frame of reference? A frame of reference is
a fancy way of saying a point of view. Imagine this is you,
from your point of view or a frame of reference
as we're now calling it, this is what you see. (gentle music) From my frame of reference
this is what I see. So that's all a frame of reference means, different points of views
from different observers. The word inertial just
means not accelerating. So either moving at constant
velocity or stationary. We'll soon see that there's no such thing as absolutely stationary,
but just go with it for now. This is an inertial frame of reference. This is an inertial frame of reference. This is not an inertial
frame of reference. You probably have a rough idea of what the laws of physics means. Motion, matter, energy, all the equations that
govern the universe. So what does it mean to
say the laws of physics are the same in all inertial
frames of reference? Well, I could tell you,
but I'd rather show you. Imagine you're standing on the ground throwing a ball in the air. It's only moving in
the vertical direction, straight up and down. You then see me move past you
with some constant velocity also throwing a ball in the air. You see my ball trace out an
arc or upside down parabola, if you're feeling fancy. You conclude that because my ball is moving both vertically
and horizontally, you must be standing still and
I must be moving to the left. But let's look at things
from my reference frame. Here I am happily throwing a
ball on the back of a vehicle, watching it go up and down
in the vertical direction. I see you. And this time it's your ball
that's tracing out a parabola. I therefore conclude
that because your ball is moving both vertically
and horizontally, I'm the one who's standing still and it's you in the ground
that are moving to my left. The laws of physics in this case, motion, work the exact same way for both of us. There is no experiment
we can perform to tell us who is standing still and who is moving. You might be thinking
Jade, that's outrageous. You can play your physics tricks, but I know the ground
isn't actually moving. And I'd reply, why do we
have day and night then? The earth is rotating at roughly
1,700 kilometers per hour. So the surface of the earth is also moving at 1,700
kilometers per hour. Not only that, but we're orbiting the sun at about 30 kilometers per second. And the Milky Way galaxy is
moving through the universe at around 230 kilometers per second. So you are definitely not standing still. In fact nothing and no one is. Everything in the universe is moving. The closest we can get to stillness is to say that we are
moving with zero speed relative to something else. So coming back to the muon paradox. From our frame of reference, we are stationary and the
muon is traveling toward us. But the muon also has a frame of reference and it can just as easily
say that it is still and earth is the one traveling toward it. But that still doesn't explain how it's able to travel a
distance 22 times its lifetime. For that, we need our second law. The speed of light is the same in all inertial frames of reference. Okay, so this is one of the weirdest ideas in all the physics. I still cannot wrap my head around it. It may sound innocent, but it is not. If you don't see why yet, don't worry. I literally went my entire physics degree without really getting
why this is so weird. So to understand, we need to take a drive. Here I am parked on the side of the road totally not creepily filming cars go by. It's a 60 zone. So let's say everyone is
a good law abiding citizen and driving exactly 60
kilometers per hour. Not surprisingly from
my frame of reference, all cars appear to be
traveling exactly that speed. Now let's drive. It's still a 60 zone, but I'm
being a rebel in doing 40. This guy's odometer we'll read 60 and an observer on the street
will view him as going 60. But from my frame of reference, they appear to be traveling
at 20 kilometers per hour. Similarly, for the cars going
in the opposite direction an observer on the street sees them as doing 60 kilometers per hour, but I see them as doing 100. (gentle music) This is a demonstration of relative speed. Speed being dependent on
your frame of reference. In other words, the speed of normal things is different from different
inertial frames of reference. Now let's contrast this
with our second law. The speed of light is the same in all inertial frames of reference. The speed of light is about
300 million meters per second. This means that if we
were measuring the light coming from the cars headlights, in all scenarios, both me and the observer would measure it to be
the exact same speed. It doesn't matter if the light beams are traveling toward me, away from me, doesn't matter how fast I'm going, we will always measure the speed of light to be 300 million meters per second. I cannot stress how weird and
counter-intuitive this is. It goes against all of our
experience of relative speed. Now we've learn the two of laws of physics needed to solve the muon paradox. We just need to see what happens when these two laws work together. We're going to do our
ball experiment again except at this time
we're going to use light. As we can't exactly
throw light up and down, we're going to bounce it
between these two mirrors, okay. So light moves way too fast for us to actually do a real
demonstration with light. So we're going to animate it instead. But this is what would really happen if we could do the demo. In my frame of reference, I see the light beam bounce like this, straight up and down between the mirrors. From your frame of reference,
you see it bounce like this, tracing out a diagonal path as it bounces between the mirrors. From your frame of reference, the light beam traveled a longer distance. We can show it with some simple trig. We simply make a right angle triangle with this side being the light beam I saw from my reference frame, and the hypotenuse being the light beam you saw from your reference frame. And we all know that the
hypotenuse is the longest side of any right-angle triangle. Now speed is just a measure of distance covered per unit time. Usually if the distance covered in the same amount of time
increases, the speed increases, but the speed of light is a constant. It doesn't change under any circumstance, even when it covers a greater distance. How is this possible? The only way this logically makes sense is if the light beam takes
a longer amount of time to get from one mirror to the other in one reference frame
than it does in the other. That's right. The time between two events pauses at different rates for
different observers. Time is not absolute, but depends
on how fast you're moving. This is summed up by the expression, moving clocks run slowly. This effect is called time dilation. The dilating or stretching of time. I know it sounds crazy and the effect is much too small to observe at our everyday speeds, but it's one of the insane consequences of the two postulates
of special relativity. Oh yeah, out two laws of physics they're Einstein's two
postulates of special relativity. I probably should have mentioned that, but I didn't wanna give everything away. So how do our muons reach earth surface? Well, time dilation may be too small to observe at our everyday speeds, but muons travel at up to
99% the speed of lights. They are all about time dilating. From our frame of reference on earth, we are stationary and the
muon is traveling toward us. And because of time dilation, they experience time more slowly. Remember, moving clocks run slow. So to us they last longer and can travel a further distance. So time dilation explains how the muons make it down to earth. But something's off. We said that the muons
were moving toward us and moving clocks run slow, that's why they're time dilated. But the first postulate
of special relativity says that there is no
special frame of reference. So a muon can equally
say, hey, I'm not moving, it's the earth surface
that's moving toward me. Your clocks are running slow. You're being timed dilated, not me. From the muon's perspective, it still has an average lifetime
of just 2.2 microseconds. So it still can't make the 15
kilometer journey to earth. It can't reach earth in
one frame of reference and not in another. So what gives? Here's where one of
the most famous results of special relativity comes into play. The realization that space and time are not separate entities, but are in fact two sides
of the same coin, spacetime. We said that the muon is traveling toward the earth at
99% the speed of light. And likewise, the muon says the
earth is traveling toward it at 99% the speed of light. The speed of travel does not change depending on the reference frame. So in the muon's frame of reference, the only way it can travel the same speed in a shorter amount of time is if it travels a shorter distance. This is called length contraction, and is another crazy consequence
of special relativity. Distances actually shrink
depending on how fast an observer is moving. So to sum up, from our
frame of reference on earth, the muons reach earth surface because they experience time dilation. And from the muon's frame of reference, the Earth's atmosphere
experiences length contraction. Oh yeah, and to answer the question from the beginning of the video, if muons can travel distances
many times their lifetime, does that mean that we can too? Could we ever travel to galaxies
thousands of years away? Yes we could, but we need to invent rockets
that could travel at speeds close to the speed of light. So far the fastest spacecraft ever built travels at around 0.05%
the speed of light. So yeah, we've got a long
way to go, but I have faith. The cool thing about special relativity is that you only need
to know these two laws and you can just derive
everything else from them. It's great for people like
me with terrible memory and limited brain capacity. Speaking of limited brain capacity, some of you have noticed
that it takes me a while to make these videos. And it's because physics is not something that comes very naturally to me. It takes me a really long
time to digest these concepts. And in fact, the whole
reason I started this channel was to help people like me, people who want to understand
the secrets of our universe, but find the information hard to digest. Someone that shares this passion for enlightening and
inspiring is today's sponsor, Curiosity Stream. They make award-winning
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Sure to be precise it is evidence for Einsteins theory in the first place, but that does kinda disprove FE... Anyhow I would really be interested in FE theorys about this phenomenon!
Here's another way to confirm relativity, and hence gravity and hence disprove flat earth.
https://www.youtube.com/watch?v=2Vrhk5OjBP8