According to Einstein, if you are sitting in your chair, you are moving more through time and less through space, so time is moving faster for you than it is for a speeding jet. Unlike you, the jet is moving more through space and less through time. If a particle is completely at rest, it moves exclusively through time. If a particle is propagating at the speed of light, it is moving exclusively through space. Below is a Minkowski diagram illustrating the point. The vertical arrow represents the particle at rest and the horizontal line represents a photon. The diagonal arrow could be anything going less than light speed but not at rest.
Now, think about how we humans measure time. We see repeating patterns like day and night, the four seasons, the moon's phases. We then assign time units to these patterns. But imagine a universe where there are no patterns or events, where everything is at rest. How could time be measured? Who would do the measuring?
According to Einstein, everything in that universe is moving through time only, but how can we verify that? There are no clocks to track the alleged passing time. Consider his thought experiment where he has a clock consisting of a light beam oscillating in a boxcar. In the diagram below we mimic that thought experiment with an imaginary photon oscillating vertically inside a box:
The photon is moving at light speed, so special relativity says it experiences no time, but we do. Why? Because we see something happening. We see something that is not at rest. We decided to make that moving photon our clock. Ironically, in order to have time or know time exists, we need something to move through space.
Here's another irony: If all the particles in our imaginary universe were to change to a new overall state, we would say time has moved forward. If all the particles returned to a previous state, we'd say time has gone backwards. If you grow older, time is progressing; if you grow younger, time is regressing. Now, suppose you didn't age or grow younger? Suppose all particles stopped changing states? We would no doubt say time has stopped.
But how can that be? Didn't Einstein say when particles are at rest they move through time?
What gives a sense of time is ongoing change and/or repeated patterns. Time feels real when stuff is happening. When nothing happens, it is as if time has stopped. When things happen faster, it's as if time has sped up, when things slow down, time seems slower. However, if the photon box moves through space, the photon does not appear to complete the cycle as fast, so from our point of view, time has slowed:
But here's the thing: do all clocks slow down when they move faster through space? We will demonstrate the answer to this question is definitely NOT a "yes." First, let's define the variables we will be using:
Here's a new thought experiment: We take a photon clock like the one illustrated above. We have it oscillate in a larger box at velocity u. The larger box is moving at velocity v. Let's assume both velocities are well below the speed of light. We use the Pythagorean theorem to calculate the combined velocity. Below is a diagram for visual reference:
Of course the photon in the smaller box is still moving at velocity c, but this is no longer the clock we want to track time with. We decide to use the larger clock with the small box ticking off the time at a steady rate of velocity u. The question is, what happens to this new rate of time when velocity v is increased? To figure this out requires a little math. We start with equation 1 below which gives the relative mass of the entire system. From there we derive equation 9:
Equation 9 is just Einstein's full energy equation. Let's assume energy is conserved and the combined velocity of v and u is held constant. If we increase velocity v, u must decrease accordingly. So far, our new clock is consistent with relativity's prediction that time slows when velocity v is increased.
Now suppose we add energy to the system. Since both v ad u are well below light speed, we can use the additional energy to increase v without decreasing u! The system mass will increase, but time stays the same!
And what of the photon clock? It slows down as expected. What we now have are three time rates: t', t, and u. We can relate them as follows:
If we only change velocity v, velocity u can remain steady while time t' changes. However, if the combined velocity of u and v is light speed, when v increases, u must decrease.
So to keep our new clock ticking at the same rate, we must keep our combined velocity below light speed. That shouldn't be too hard.
Below we derive equations 16 and 17. These equations express u in terms of time rather than velocity:
Thus when when something moves through space it doesn't necessarily move less through time, and vice versa.
