What does it mean when we say nothing is faster than light?

Hello Lena942820,

The astonishing thing isn't how fast light travels, but that its propagation speed is finite. Even Descartes believed that light doesn't need any time at all, which would mean that even events arbitrarily far away could be seen as they happened.

In the same (17th) century, however, RØMER was able to roughly determine the speed of light propagation c based on observations of Jupiter's moons. It turned out to be quite large by human standards, but quite small by cosmic standards. Today, the value is known more precisely: c = 299,792,458 m⁄s.

So when you look into the distance, you're automatically looking into the past: For the Moon, 1.3 seconds; for the Sun, about 8 minutes; for Saturn at opposition, just under 1.5 hours; for stars other than the Sun, years to centuries. And it goes even further:

In the constellation Andromeda, there is a patch of light visible to the naked eye under good visibility conditions, the so-called Andromeda Nebula. This is actually a galaxy similar to the Milky Way; light takes 2.5 million years to reach it.

However, I would like to address the wording of your question:

What does it mean when we say nothing is faster than light?

It means that (relative to a reference body considered to be at rest, such as a clock U) no body or particle can move faster than c. A body or particle with mass m or rest energy E₀ = mc² cannot even reach c, but can only approach it arbitrarily, for which its kinetic energy Eₖ must be so large that E₀ can be neglected.

The deeper reason lies in the geometric structure of spacetime : two events can

• be separated in time , ie there is a coordinate system in which they are co-local , ie take place at the same place,
• be separated in a light-like manner , such as the transmission and reception of the same radio signal, and
• be spatially separated , i.e. there is a coordinate system in which the events take place simultaneously in different places.

In a spatial plane, which we will call the zx-plane, there is a distance Δs between two points, for which the Pythagorean theorem applies:

(1) Δs² = Δz² + Δx²

Fig. 1: A rotation of the coordinate system does not change the distance between two points in the zx-plane.

Something similar exists in spacetime or for two events in the tx-plane, MINKOWSKI's distance square

(2.1) Δτ² = Δt² − Δx²⁄c²

for a pair of temporally separated and

(2.2) Δς² = Δx² − c²Δt²

for a pair of spatially separated events. Obviously, Δτ is a time span and Δς a spatial distance.

Fig. 2: The change from U as reference clock to a clock U' moving uniformly in a straight line relative to U as reference clock (LORENTZ transformation) does not change the MINKOWSKI distance between two events.

In fact, Δτ is the time span that a local clock Ώ would measure directly, the proper time , while Δt is the time span between the same two events determined from U, the U coordinate time .