Our speed through spacetime is constant. The more we move through space, the less through time and vice versa.
Everything travels through spacetime at the speed of light. Me, you, the cat (even Schrödinger’s cat), the Earth, the sun, bits and bytes, and any particles including photons (light particles).
Note that I said spacetime. Of course, we travel at different speeds through space, we might even be standing still in our frame of reference. This frame of reference is moving relatively in other frames of reference, for example you might be sitting still while reading this, but you are on Earth (I’m guessing), which is spinning at 1,600 km/h at the equator, and Earth is also moving around the Sun (107,000 km/h), and the Sun is moving around the center of the Milky Way (828,000 km/h). Milky Way is also moving in relation to any other galaxy at 600 km/s or 2,160,000 km/h.
But none of the above mentioned, except for photons, travel at the speed of light through space (which is 300,000 km/s or 1,080,000,000 km/h for comparison). Our motion through spacetime, on the other hand, is different.
We all travel at exactly the speed of light through spacetime.
Spacetime is a 4-dimensional concept, the three spatial dimensions, also called space, and one temporal dimension. Our speed is spread between the four components, and since the speed has a direction, we call it velocity. The 4-velocity is the vector U = γ(𝑐,𝑣_𝑥,𝑣_𝑦,𝑣_𝑧) where γ is the Lorentz factor.
It doesn’t matter for the equations, how we spread our movements through the 3 space-dimensions x, y, and z, we only care about the speed, not the velocity with a specific direction, so we say that the movement is broken in two components, space and time.
When we are still, e.g. don’t move through space (as seen in our own frame of reference), then we move through time at the maximum speed. When a photon moves at the maximum speed, c, then it doesn’t move through time at all. For a photon there is no time component.
We could draw the coordinate system like this, with space on the x-axis and time t, on the y-axis.
A movement through spacetime is shown in the coordinate system as a vector (the arrow) from the origin (0,0) to the dashed arch.
Someone or something standing still in their frame of reference would only be traveling along the y-axis (time), not using any part of the space-component. Someone traveling faster would have a component on the x-axis (space) and a component on the y-axis (time), but the time-component would be smaller, than the person standing still in space.
The faster we move through space, the smaller our time-component will be. This is called the time-dilation in relativity and the time-component on the y-axis is called the proper time. This is the time measured by a clock in the moving frame of reference.
The fastest objects through space are the massless photons (electromagnetic force carrier and what we see as light) and gluons (strong nuclear force carriers). Those particles only use the space component, and for them, the proper time is zero.
This means that a photon doesn’t experience time. The photons we measure from the big bang are captured by our detectors in the same instance (form their point of view) that they come into existence although it for us was 13.8 billion years ago.
For a photon, the beginning and the end of the Universe, and everything in between, happens at the same point in time.
When the photons move through space at the maximum speed of light with no part in the time-component, they will also experience a maximum length contraction. All the distance they travel through will be contracted down to a single point.
Thus, if you travel through only space in spacetime, your speed will be maximum in space, you will have no experience in time and distance will be a singularity. The acceleration of a mass for this speed would require an infinite amount of energy, which is why only massless particles can travel this speed through space.
If you travel only through time, your proper time (time measured on your clock) will be maximized. It’s also the laziest thing to do — no energy required.
Minkowski spacetime diagram
A better coordinate system would be using ct on the time-axis instead of just t since the units would then be comparable: ct is the speed of light times time, so meters per second times seconds, which gives us a unit of meters, just like the space-coordinate.
This kind of coordinate system is called the Minkowski diagram.
Now, a person standing still in their frame of reference have moved the distance ct on the y-axis. Since they spent time t on traveling that distance, they are traveling at the speed c through spacetime. (Speed is distance divided by time: ct/t = c).
They are of course not traveling through space at the speed of light, which would require a movement on the x-axis. It’s the speed in the combination of space and time that is c for the person standing still.
Light would be a diagonal line through the spacetime coordinate, traveling at the speed of c.
Your movement through spacetime can be drawn in the Minkowski diagram as your worldline. The diagram can also be drawn with two space-dimensions in a 3D-diagram, as seen below (unfortunately we cannot draw a 4D diagram with the three space-axis). The light wordline will then become a lightcone. Anything on the other side of the light cone is inaccessible to us since it would require information traveling faster than light through spacetime.
In total, we all move at the total speed of light, c, through spacetime, with the speed spread between space and time. We can’t go faster than light through space. And we neither can go faster nor slower than light through spacetime. It’s the constant speed of everything in the fabric of spacetime.
In the words of Lewis Carroll Epstein:
“You can’t go faster than the speed of light, because you can’t go slower than the speed of light. You are always going the speed of light through spacetime. If you use some of your speed to go through space then there is less speed through time.”