Does Time Cause Gravity? (Script) (Patreon)

You are currently hurtling through time at the speed of light. But be careful. If even a tiny bit of your breakneck temporal velocity leaks into one of the dimensions of space. And you’re standing in the wrong place at the time, you will rapidly accelerate to your doom. You think I’m kidding? I just described the true source of gravity. Don’t look down.

____INTRO____

Clocks run slow in gravitational fields. Our GPS satellites tick faster by a factor of 1-in-a-billion - enough to thrown their position accuracy off by 11km per day.

In our recent episode, we saw why this gravitational time dilation is inevitable - it follows as surely as 1+1=2 if we accept the two axioms of Einstein’s relativity theory: that the speed of light is constant for all observers, and that the weight induced by acceleration is fundamentally the same as that induced by gravity - the so-called equivalence principle. But none of this is very satisfying.

We know that gravity must cause clocks to run slow on the basis of logical consistency. And we know that gravity DOES cause clocks to run slow based on many brilliant experiments. But  I never explained WHY or HOW gravity causes the flow of time to slow down. And I’m not going to explain it now - because in a sense it’s not true. Gravity does NOT warp the flow of time. It’s the other way around - the warping of time causes gravity. That’s what I’m going to show you right now. If you didn’t watch the previous episode - do it, though it’s also ok if you watch this one first. Just don’t forget. So how is it that time causes gravity?

Let’s start with … a teapot. I lA nice china teapot hanging in space, minding its own business. Absent a gravitational field or any forces, if the teapot starts motionless it stays that way. At least, it stays motionless with respect to the three dimensions of space. Everything is moving through the dimension of time. We can show this with our old friend the spacetime diagram.

Let’s have just two dimensions of space and so we have space … for time. We show progression through time as the object moves up. You could say that it has a positive velocity through time, and zero velocity through space.

OK, now let’s add a second object - something nice and massive … the planet Earth will do. We know that the presence of mass and energy warp spacetime - and the most intense part of that warping is in time - our gravitational time dilation. Things closer to the Earth move through time more slowly. We can show this as a bunch of identical clocks. They tick as they move up. Clocks closer to the Earth take longer to tick for every tick on a distant clock.

“Velocity through time” increases away from the Earth. If we move the clocks according to those velocities - upwards so their ticks stay in sync, we have this sense of time flowing in a gradient - faster streams distant from the Earth, slow stream near it.

Kind of like how water in the center of a stream flows more quickly than the edge, where the shallower stream drags on that flow. It’s almost like Earth’s mass creates a drag on the flow of time around it.

So what happens to an object sitting in this stream of time - parts further away from the Earth age faster, right? Well, yes, but that’s not all. We can think of any object as being made of many tiny clocks. Each atom, each subatomic particle  trying to tick at its own rate. And each of those clocks has a velocity vector in time. So what’s the temporal velocity of the entire object? In Einstein’s relativity you have to remember that time and space are not independent of each other. Objects don’t just have a velocity through space or through time - they have a velocity through spacetime. We call this their 4-velocity. To get at this, let’s move away from our teapot for a second and talk about boats.

Imagine two boats on an actual stream. One near the edge moves slow and one near the center moves fast.

The slow boater reaches out an oar which the fast boater grabs. What happens? Instinct tells us that the fast boat is pulled tow ards the shore.

What’s actually happening is that the two objects become one, and to calculate its final velocity you sum the individual velocities - and the result is that the velocity vector is rotated towards the shore.

It’s the same with the 4-velocity of an object in a gravitational field. The gradient of velocities cause the overall 4-velocity of the object to be rotated. All individual 4-velocities start out being purely in time, but the sum is rotated partially into space. And it’s always rotated in the direction of decreasing flow - which in a gravitational field is downwards.

So this is the motion of any object in a gravitational field - it gradually picks up velocity in the down direction - it accelerates - and it pays for that acceleration by losing velocity - Decelerating in the time direction.

There's a certain way of interpreting the math of relativity that says that everything travels at the speed of light. Light travels at the speed of light through space - obviously enough - and we know that nothing with mass can reach that speed traveling through space. But if we interpret time as a dimension like space, then a stationary mass really is moving at the fastest possible speed in the temporal direction.

This is something we can come back to another time - for now let's go with it.

The 4-velocity of a massive object is pointed almost entirely in the time direction. On the other hand, light itself travels at the speed of light through space only, and not at all through time - a photon’s clock is frozen.

You might imagine it’s 4-velocity is entirely rotated out of the time direction into space - although technically photons and other massless particles don’t have a 4-velocity, which is defined according to the ticking of your own clock - your proper time - which is zero for the timeless photon.

In this picture, a falling object trades some of its enormous velocity through time to pay for a small velocity through space. To us currency exchange looks favorable for space - a teapot gains a rapid plummet to its doom for an imperceptible slowing of its clock. We see the same favorable exchange when we try to convert mass into energy via Einstein’s most famous equation, E=mc^2 - the speed of light is the exchange rate, and the speed of light is very large.

By the way, two of my favorite physics channels have great, slightly different explanations of this effect. Check out Nick Lucid on Science Asylum and Eugene Khutoryansky’s channel to get their takes.

So is that it? Do we now perfectly understand the source of gravity? Well speak for yourself - I’m still confused. This raises thorny questions. Like - what about a particle with no size - supposedly point-like particles like electrons, quarks, etc.

The hydrogen atom should look somewhat like this:

Zooming into the proton should reveal a view like this:

Well, actually, nothing truly occupies only a single, perfectly defined position in space - quantum uncertainty means that everything is always at multiple places at once, and so experiences the gradient of time flow. But actually general relativity doesn’t need quantum mechanics to explain gravity. It’s enough to imagine clocks that are infinitesimally separated and we still have our time gradient.

The other thorny question is about light itself. If photons are already fully rotated into the spatial direction, how is it that they’re also affected by gravitational fields? They have no “velocity through time” to trade. But light DOES bend in a gravitational field - astronomers see it happening all the time in the effect we call gravitational lensing. In fact, the imaginary paths of light rays were one the most important tools that helped Einstein develop both special and general relativity. So we’d better understand the effect of gravity on the path of light. To do so we’re going to need to shift our perspective in a couple of mind-bendy ways to see how the flow of time determines the path of even timeless particles. And with those new perspectives we’ll get a new insight into the source of gravity that seems weirdly at odds with everything I just told you - and yet is simultaneously exactly as correct. But first you’re going to need to some time to think on everything I’ve just told you and let it settle, and we’re going to need some time to make that new episode of space time.