The norm or magnitude of the four-velocity is always exactly equal
to the speed of light. Thus all objects can be thought of as moving through
spacetime at the speed of light. This provides a way of understanding
time-dilation: as an object like a rocket accelerates from our perspective, it
moves faster through space, but slower through time in order to keep the
four-velocity constant. Thus to an observer, a clock on the rocket moves
slower, as do the clocks in any reference frame that is not comoving with them.
Light itself provides a special case- all of its motion is through space, so it
does not have any “left over” four-velocity to move through time. Therefore
light, and anything else traveling at light speed, does not experience the
“flow” of time.
The Reddit community has written a number of easy to understand
illustrations of this phenomena. The first is from a thread called __Why does light travel?__:
Everything, by nature of simply existing, is “moving” at the speed
of light (which really has nothing to do with light: more on that later). Yes,
that does include you.
Our understanding of the universe is that the way that we perceive
space and time as separate things is, to be frank, wrong. They aren’t separate:
the universe is made of “spacetime,” all one word. A year and a lightyear
describe different things in our day to day lives, but from a physicist’s point
of view, they’re actually the exact same thing (depending on what kind of
physics you’re doing).
In our day to day lives, we define motion as a distance traveled
over some amount of time. However, if distances and intervals of time are the
exact same thing, that suddenly becomes completely meaningless. “I traveled one
foot for every foot that I traveled” is an absolutely absurd statement!
The way it works is that everything in the universe travels through
spacetime at some speed which I’ll call “c” for the sake of brevity. Remember,
motion in spacetime is meaningless, so it makes sense that nothing could be
“faster” or “slower” through spacetime than anything else. Everybody and
everything travels at one foot per foot, that’s just… how it works.
Obviously, though, things do seem to have different speeds. The
reason that happens is that time and
space are orthogonal, which is sort of a fancy term for “at right angles to
each other.” North and east, for example, are orthogonal: you can travel as far
as you want directly to the north, but it’s not going to affect where you are
in terms of east/west at all.
Just like how you can
travel north without traveling east, you can travel through time without it
affecting where you are in space. Conversely, you can travel through space
without it affecting where you are in time.
You’re (presumably)
sitting in your chair right now, which means you’re not traveling through space
at all. Since you have to travel through spacetime at c (speed of light),
though, that means all of your motion is through time.
By the way, this is why time dilation happens: something that’s
moving very fast relative to you is moving through space, but since they can
only travel through spacetime at c, they have to be moving more slowly through
time to compensate (from your point of view).
Light, on the other hand, doesn’t travel through time at all. The
reason it doesn’t is somewhat complicated, but it has to do with the fact that
it has no mass.
Something that isn’t moving that has mass can have energy: that’s
what E = mc2 means. Light has no mass, but it does have energy. If we plug the
mass of light into E=mc2, we get 0, which makes no sense because light has
energy. Hence, light can never be stationary.
Not only that, but light can never be stationary from anybody’s
perspective. Since, like everything else, it travels at c through spacetime,
that means all of its “spacetime speed” must be through space, and none of it
is through time.
So, light travels at c. Not at all by coincidence, you’ll often hear
c referred to as the “speed of light in a vacuum.” Really, though, it’s the
speed that everything travels at, and it happens to be the speed that light
travels through space at because it has no mass.
edit: By the way, this also covers the common ELI5 question of why
nothing can ever travel faster than light, and why things with mass cannot
travel at the speed of light. Since everything moves through spacetime at c,
nothing can ever exceed it (and no, traveling backwards in time would not fix
that). Also, things with mass can always be “stationary” from someone’s
perspective (like their own), so they always have to move through time at least
a little bit, meaning they can never travel through space as fast as light
does. They’d have to travel through spacetime faster than c to do that, which,
again, is not possible.
First, let’s talk about
directions, just to get ourselves oriented. “Downward” is a direction. It’s
defined as the direction in which things fall when you drop them. “Upward” is
also a direction; it’s the opposite of downward. If you have a compass handy,
we can define additional directions: northward, southward, eastward and
westward. These directions are all defined in terms of something — something
that we in the business would call an “orthonormal basis” — but let’s forget
that right now. Let’s pretend these six directions are absolute, because for
what we’re about to do, they might as well be.
I’m going to ask you now
to imagine two more directions: futureward and pastward. You can’t point in
those directions, obviously, but it shouldn’t be too hard for you to understand
them intuitively. Futureward is the direction in which tomorrow lies; pastward
is the direction in which yesterday lies.
These eight directions
together — upward, downward, northward, southward, eastward, westward,
pastward, futureward — describe the fundamental geometry of the universe. Each
pair of directions we can call a “dimension,” so the universe we live in is
four-dimensional. Another term for this four-dimensional way of thinking about
the universe is “spacetime.” I’ll try to avoid using that word whenever
necessary, but if I slip up, just remember that in this context “spacetime”
basically means “the universe.”
So that’s the stage. Now let’s consider the players.
You, sitting there right now, are in motion. It doesn’t feel like
you’re moving. It feels like you’re at rest. But that’s only because everything
around you is also in motion. No, I’m not talking about the fact that the Earth
is spinning or that our sun is moving through the galaxy and dragging us along
with it. Those things are true, but we’re ignoring that kind of stuff right
now. The motion I’m referring to is motion in the futureward direction.
Imagine you’re in a train car, and the shades are pulled over the
windows. You can’t see outside, and let’s further imagine (just for sake of
argument) that the rails are so flawless and the wheels so perfect that you
can’t feel it at all when the train is in motion. So just sitting there, you
can’t tell whether you’re moving or not. If you looked out the window you could
tell — you’d either see the landscape sitting still, or rolling past you. But
with the shades drawn over the windows, that’s not an option, so you really
just can’t tell whether or not you’re in motion.
But there is one way to know, conclusively, whether you’re moving.
That’s just to sit there patiently and wait. If the train’s sitting at the
station, nothing will happen. But if it’s moving, then sooner or later you’re
going to arrive at the next station.
In this metaphor, the train car is everything that you can see
around you in the universe — your house, your pet hedgehog Jeremy, the most
distant stars in the sky, all of it. And the “next station” is tomorrow.
Just sitting there, it doesn’t feel like you’re moving. It feels
like you’re sitting still. But if you sit there and do nothing, you will
inevitably arrive at tomorrow. That’s what it means to be in motion in the
futureward direction. You, and everything around you, is currently moving in
the futureward direction, toward tomorrow. You can’t feel it, but if you just
sit and wait for a bit, you’ll know that it’s true.
So far, I think this has all been pretty easy to visualize. A little
challenging maybe; it might not be intuitive to think of time as a direction
and yourself as moving through it. But I don’t think any of this has been too
difficult so far. Well, that’s about to change. Because I’m going to have to
ask you to exercise your imagination a bit from this point on.
Imagine you’re driving in
your car when something terrible happens: the brakes fail. By a bizarre
coincidence, at the exact same moment your throttle and gearshift lever both
get stuck. You can neither speed up nor slow down. The only thing that works is
the steering wheel. You can turn, changing your direction, but you can’t change
your speed at all.
Of course, the first
thing you do is turn toward the softest thing you can see in an effort to stop
the car. But let’s ignore that right now. Let’s just focus on the peculiar
characteristics of your malfunctioning car. You can change your direction, but you
cannot change your speed.
That’s how it is to move
through our universe. You’ve got a steering wheel, but no throttle. When you
sit there at apparent rest, you’re really careening toward the future at top
speed. But when you get up to put the kettle on, you change your direction of
motion through spacetime, but not your speed of motion through spacetime. So as
you move through space a bit more quickly, you find yourself moving through
time a bit more slowly.
You can visualize this by imagining a pair of axes drawn on a sheet
of paper. The axis that runs up and down is the time axis, and the upward
direction points toward the future. The horizontal axis represents space. We’re
only considering one dimension of space, because a piece of paper only has two
dimensions total and we’re all out, but just bear in mind that the basic idea
applies to all three dimensions of space.
Draw an arrow starting at the origin, where the axes cross, pointing
upward along the vertical axis. It doesn’t matter how long the arrow is; just
know that it can be only one length. This arrow, which right now points toward
the future, represents a quantity physicists call four-velocity. It’s your
velocity through spacetime. Right now, it shows you not moving in space at all,
so it’s pointing straight in the futureward direction.
If you want to move through space — say, to the right along the
horizontal axis — you need to change your four-velocity to include some
horizontal component. That is, you need to rotate the arrow. But as you do,
notice that the arrow now points less in the futureward direction — upward
along the vertical axis — than it did before. You’re now moving through space,
as evidenced by the fact that your four-velocity now has a space component, but
you have to give up some of your motion toward the future, since the
four-velocity arrow can only rotate and never stretch or shrink.
This is the origin of the famous “time dilation” effect everybody
talks about when they discuss special relativity. If you’re moving through
space, then you’re not moving through time as fast as you would be if you were
sitting still. Your clock will tick slower than the clock of a person who isn’t
moving.
This also explains why the phrase “faster than light” has no meaning
in our universe. See, what happens if you want to move through space as fast as
possible? Well, obviously you rotate the arrow — your four-velocity — until it
points straight along the horizontal axis. But wait. The arrow cannot stretch,
remember. It can only rotate. So you’ve increased your velocity through space
as far as it can go. There’s no way to go faster through space. There’s no
rotation you can apply to that arrow to make it point more in the horizontal
direction. It’s pointing as horizontally as it can. It isn’t even really
meaningful to think about something as being “more horizontal than horizontal.”
Viewed in this light, the whole idea seems rather silly. Either the arrow
points straight to the right or it doesn’t, and once it does, it can’t be made
to point any straighter. It’s as straight as it can ever be.
That’s why nothing in our universe can go faster than light. Because
the phrase “faster than light,” in our universe, is exactly equivalent to the
phrase “straighter than straight,” or “more horizontal than horizontal.” It
doesn’t mean anything.
Now, there are some mysteries here. Why can four-velocity vectors
only rotate, and never stretch or shrink? There is an answer to that question,
and it has to do with the invariance of the speed of light. But I’ve rambled on
quite enough here, and so I think we’ll save that for another time. For right
now, if you just believe that four-velocities can never stretch or shrink
because that’s just the way it is, then you’ll only be slightly less informed
on the subject than the most brilliant physicists who’ve ever lived.
Not sure the source on this one
The reason
why the speed of light is a hard limit on the universe is that everything is travelling within this
four-dimensional thing called spacetime, with the same amount of speed.
When a
photon (a particle
of light) travels through spacetime at the speed of light,
That’s how
it is to move through our universe. You can steer, but you can't accelerate.
When you sit at apparent rest, you’re really careening toward the future at top
speed. But when you get up to go to the fridge, you change your direction of
motion through spacetime, but not your speed of motion through spacetime. So as
you move through space a bit more quickly, you find yourself moving through
time a bit more slowly.
To
reiterate that last point, as it is important: The faster you travel through
space, the more you have to give up your movement through time. At the speeds
that we're used to on Earth, the effect is negligible. To give you some idea of
how fast we need to be talking before time dialation starts to happen, lets
look at GPS satellites. A GPS satellite orbits the Earth at 14,000 km/h (8,700
mph). Once every sixty years their
clocks will be ahead by one second due
to the effects of time dialation.
The
fastest object every built by human beings thus far is the Voyager 1
Spacecraft, having flown past Saturn and is now travelling through interstellar
space. It is travelling at speeds of about 62,140 km/h (38,610 mph), or 17
kilometres (10.5 miles) per second. That is so fast that it could:
At these
speeds, Voyager 1 experiences one second of time dialation every 13.7 years.
Voyager
1's speed is just 0.00006% of the speed of light. Once you reach the speed of
light, that time dialation becomes total. You
stop experiencing time.
Time and space are orthogonal, which is sort of a fancy term for “at right angles to each other.” North and east, for example, are orthogonal: you can travel as far
as you want directly to the north, but it’s not going to affect where you are
in terms of east/west at all. Just like how you can travel north without
traveling east, you can travel through time without it affecting where you are
in space. Conversely, you can travel through space without it affecting where
you are in time.
You’re (presumably) sitting in your chair right now, which means you’re not traveling through space at all. Since you have to travel through spacetime at c (speed of light), though, that means all of your motion is through time.
Particles with mass (everything made out of atoms) and particles without mass (like light and other electromagnetic radiation) travel through the dimensions of spacetime in different
allocations. For particles with mass, it can vary. Particles that do not have
mass have maxed out their speed in the direction of space, and don't travel
through time at all.
All matter is travelling same speed through the totality of all dimensions, but each dimension in a different allocation.
Human beings are made up of particles, atoms, that have mass and therefore we, nor anything else made of atoms, will be able to travel at the speed of light.
//As human beings have mass, we will never be able to approach the speed of light.
//To go faster than the speed of light, you'd need to go backwards in time. This seems impossible. - Can't be right.