Over the last hundred years or so, scientists
have pushed our understanding of the universe into some extreme conditions, for example
the world of the very small, the realm of very high speeds and the under the frigid
conditions of near absolute zero. While each of us have developed an intuition
about how the world works, it’s very important to remember that this intuition only applies
to a very limited set of conditions. For instance, there’s absolutely no reason
to expect that matter will act the same in the center of the sun as it does here on Earth
on a bright and sunny day. However, that last statement is hard for some
people to accept and, judging by my email inbox, the extreme realm that causes people
the most difficulty is what happens when things are going super-fast. In 1905, Albert Einstein published his theory
of special relativity. It predicts all sorts of mind-blowing things,
for instance distance shorten and clocks slow down. I made another video about how clocks act
at high speed. It turns out that all of those seemingly crazy
implications originate from a single cause, or maybe two if we take it slow. So, first, let me tell you what this video
isn’t. It doesn’t tell you about the postulates
that Einstein used to build his intuition and it certainly doesn’t derive his equations. Instead, this video tries to tell you the
key insights that make it easier to develop a relativistic intuition. I hope to teach you why it is impossible to
go faster than the speed of light. If you’re not a physics groupie, hearing
that there is a maximum speed in the universe might surprise you, but it’s true. And, if you are a groupie, you’ve probably
heard that the reason that you can’t go faster than light is due to the fact that
mass increases when you speed up. It turns out that the explanation of mass
changing as you go faster is a wrong one. I know that statement is going to confuse
some people- including those with fairly sophisticated understandings of relativity, but it’s true. However, that then leaves an open question. Just why is it that you can’t go faster
than the speed of light? It turns out to be due to a combination of
a deep and fundamental property of the universe and fairly simple geometry. So, let me explain how that all works. The first of the two crucial insights is that
Einstein taught us that space and time were not separate entities, but rather they are
two components of a bigger idea, called spacetime. I’ll give you a helpful visual way to think
of this in a moment, but for right now, just trust me on this. Then we need to combine that insight with
the observation that everybody sees the speed of light to be the same, no matter how fast
they are moving with respect to one another. Let’s start with an analogy and then come
back to relativity. To understand the analogy, you need to imagine
a car driving on a huge flat surface. Further, you need to imagine that the car
can only move at one speed, say 60 miles per hour. Or, so the comments don’t fill up with metric-snobbery
hate mail, 100 kilometers per hour. Now let’s put a couple arrows on the screen
to point out north and east. While we know the overall speed the car is
going, we don’t know how much of it is in the east direction and how much of it is in
the north direction. So let’s take a closer look at that. The car can move entirely in the eastward
direction, which means that it has no motion in the northward direction. Or, the car can move entirely northward and
not at all eastward. Or we can live dangerously and move towards
the northeast. In this case, we see that the car is moving
in both the east and north directions, with neither direction getting all of the motion. So that’s the core analogy and hopefully
it’s very clear. Now, let’s bring in relativity. In relativity, we don’t have the east and
north directions. Instead, we have spacetime. Let’s imagine that the horizontal direction
is space and the vertical direction is time. So suppose that there is a single and fixed
speed that we can travel through spacetime. This happens to be true, so it’s not a ridiculous
supposition. We can therefore mix these ideas with our
earlier analogy. An object can move vertically. In that case, they are not moving through
space and they're moving entirely through time. That’s probably what you’re doing right
now. You’re sitting and watching this video,
so your position in space isn’t changing. However, you are experiencing time. You aren’t moving through space, but you're
moving through time. On the other hand, what happens as you start
moving through space? That’s a fancy way to say that you gain
some velocity. Well we see here that what starts to happen
is that as you begin to move through space, you move less through time. And eventually, when you move only through
space, you don’t move through time at all. And this is basically what relativity says. As you move faster and faster, your clocks
slow down. And, as you get very close to the speed of
light, your clocks very nearly stop. We’ve scientifically proven that this is
what happens and I direct you to my video on time dilation so you can see one way that
we’ve tested that. So, this brings us to our fundamental realization
of relativity. The reason that we can’t move through space
faster than the speed of light is because we are constantly moving through spacetime
at a single speed- the speed of light. If we aren’t moving through space, we experience
time in the fastest way; and if we start moving through space, we experience time slower and
slower. Finally, since we're moving through spacetime
at a single speed, that means that when we're moving only through space, there is no more
speed to gain. We move through space at the speed of light
and that’s it. This observation wasn’t made by Einstein. It was made by his mentor, Herman Minkowski. Minkowski was one of Einstein’s mentors
and he was a better mathematician. Two years after Einstein’s seminal 1905
paper, Minkowski appreciated the geometrical underpinnings of special relativity and had
determined this deep and fundamental explanation why we can’t travel faster than light through
space. There are two final important points. First, while Minkowski showed why light speed
is the maximum speed through space, what he didn't explain was why we move only at one
speed through spacetime. To this day, nobody really knows. It seems to be a fundamental property of spacetime. Maybe it will take another person as smart
as Einstein to figure out that particular conundrum. The second point is more technical and I mention
it only for the real physics nerds. In my analogy, I connected space and time
as being similar to east and north and there is a lot of merit in that. Morphing from motion through time to motion
through space was like turning a car from moving north to moving east. However, this analogy is also technically
inaccurate. From a mathematical point of view, it uses
the geometry of circles, while the proper geometry is that of hyperbolas. I only bring this up because I want you to
know my analogy is imperfect and you shouldn’t push it too far. Otherwise you might come to a numerically
incorrect conclusion and think that you’ve made a new discovery. If you want to dig into this more deeply,
be sure to use the full and proper Minkowski mathematics. Still, even with the limitations I’ve mentioned,
the core point is valid. The reason that you can’t move faster through
space than the speed of light is because that every object moves through spacetime at one
and only one speed- the speed of light. Once you’ve embraced that central idea and
the fact that space and time are just like two directions of spacetime, then all of those
seemingly weird observations of relativity just click into place and special relativity
makes total sense. So I don't know about you, but I think this
insight about relativity is just about the coolest thing ever. If you liked this video, be sure to like,
subscribe, and share- let's get those numbers up. And let me know what you think in the comments. I'll see you next time, and keep on physics-ing.
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what i want to understand is, whats the distincition with space inflation? if matter can distance itself faster then the speed of light with inflation, is the implication that it cant then inflate space in the reverse direction faster then the speed of light? because we always say nothing can go faster then light, but we also say the universe seems to have expanded further then it could in the time believed to have elapsed since the big bang. If that distance could then be covered/caught up to, then whats the distinction?
Server tick rate won’t allow it. Lazy ass programming if you ask me
Me? Personally? You know, I've never really thought about it. I guess I've never really applied myself. I mean I could blame my upbringing or my culture, focusing on intelligence and not perserverance, but one really should take responsibility for one's own life. Some day though, when I don't have this pervasive sense of hopelessness holding me back, I'll break that barrier.
So in my Modern Physics course our professor told us that you can get c from Maxwell’s relations and you get an equation that depends on the permittivity and permeability of free space. Can you make the assumption that since these constants determine how electromagnetic waves can propagate through space (with some modifications depending on the media) and since all matter is technically somewhat of an electromagnetic wave that’s why c is the cosmic limit? It squares up in my head, and would explain why light travels at different speeds through different media, since permittivity and permeability changes depending on the media. The flaw I can see in this hypothesis is that matter is both a particle and a wave at the quantum level, but I guess the closer it gets to a wave, the closer it can get to c, with only true electromagnetic waves being capable of traveling at c.