### From force to field

The description of forces acting at a distance – e.g., the electrostatic force, by which a particle with electric charge can influence other charged particles – usually involves at least two particles acting on each other, never just one. This isn’t ...

### Time determination with radio signals – from radio-controlled clocks to satellite navigation

Conventional radio-controlled clocks in Germany have a receiver for the time signal of the long-wave transmitter DCF77 in Mainflingen near Frankfurt am Main, which is controlled by the Physikalisch-Technische Bundesanstalt. This is a clock signal – a radio ...

### From light clocks to time dilation

Suppose I am drifting freely through space with a space station, far away from all larger masses. In this case, physicists would consider me an inertial observer, and thus the two basic postulates of special relativity would apply to me. In particular, the ...

### Relativity and satellite navigation

At sea or in the wilderness, precise positioning can be vital. But even in everyday life, there is not always a place or street sign nearby when the question comes up: Where are we now? The answer is readily available these days. A small device, not much ...

### The dialectic of relativity

When first encountered, some of the statements of special relativity sound downright paradoxical. However, in most cases the suspected paradox can be resolved within a framework of a "dialectic of relativity". (Here, the term "dialectic", which is borrowed ...

### Time dilation on the road

For a number of relativistic phenomena, there are helpful geometric analogies. They transplant space-time-phenomena to the more familiar arena of space geometry. Most people might not be familiar with space-time-lines and -projections, but they do know, for ...

### Heat that meets the eye

Physical bodies (or, speaking more generally, physical systems) that are brought into close contact, close enough for them to exchange energy, evolve towards a state known as . In this state, all the systems involved have the same temperature - which is ...

### The shape of space

In three-dimensional space as we know it, geometry is governed, in excellent approximation, by the laws of Euclidean geometry, the standard geometry taught in high school. For instance, all the angles within a triangle always add up to 180 degrees, and ...