Relativity

Premisses

Universality : In physics, it has been taught since Newton that all reference systems are equivalent, i.e. Newton propagated a universality of physics.

In other words: The same laws of nature apply everywhere in the universe and we are free to choose our coordinate system for our mathematical descriptions of the world. The laws of nature apply in every case – regardless of whether we place the origin of the coordinates in the sun or in the earth or on alpha Centauri.

What does that mean?

This knowledge has been latently anchored in astronomy for centuries. We use several different coordinate systems that move relative to each other: the horizon system and the equator system are the most important of these.

In the horizon system , the origin of all coordinates lies in the observer himself. The basic plane of the system is its local horizon. The star coordinate ‘azimuth’ (angle) is then measured as the distance from south to west, i.e. in the direction of the daily apparent rotation of the sky. As a result of this rotation, the height h of the star above the observer’s local horizon also changes.

Equator systems

If you want to specify long-term stable star coordinates, it is better to measure their relative distance to each other or to a (fictitious) co-rotated line in the sky. This can be done by projecting the earth’s equator onto the imaginary celestial sphere as the celestial equator:

You can then define a fictitious point on the celestial equator as the prime meridian. There are two excellent points for this, namely the intersection of the celestial equator with the apparent path of the sun, the ecliptic. Neither of them is marked by bright stars, but the sun is there once a year. The vernal equinox was chosen as the starting point for the count. From then on, one counts in the direction of the apparent annual course of the sun, i.e. from the vernal equinox to the east and calls this coordinate ‘right ascension’ α (Latin for ‘correct ascent’), i.e. the actual/true/ correct direction of ascent of the sun in the course of the year.

You can transform the local azimuth angle into the equatorial system and then obtain the hour angle τ as a coordinate, which is counted from south to west. The sidereal time θ is the sum of right ascension and hour angle, as you can easily see from the vectors in the drawing above.

We learn:

Because of the equivalence of reference frames (both are allowed, neither is physically ‘preferred’), it is permissible in some contexts to think geocentrically.

Every single observer on earth has the feeling of being the centre of the celestial sphere, but everyone sees it a little differently.

If we take a step away from the earth and look at it from the outside, then the centre of the earth appears to us as the centre of the celestial sphere.

This does not mean that the heliocentric view of our solar system is wrong, nor does it mean that the universe has a centre, but it only means that we cannot tell from the earth that any one point is more distinguished as a centre than another. (philosophers have been thinking about this since ancient times).

Principle of Equivalence

Weak …

Strong …

What is “relative”?

Relativity in everyday life means that something depends on the observer. In physics, it means that the exact form of the formula is different depending on whether you describe everything in the same or in different coordinate systems.
If you want to solve a problem, you should first define the coordinate system. In this system, the same laws always apply (i.e. the equivalence principle: no matter which system you choose, it is always the same physics). BUT if you look at another coordinate system from your own chosen coordinate system, then the formula changes a little: Astronomers have known this for centuries, because they are constantly transforming from the equatorial system to the horizon system, so instead of the right ascension from the printed star catalogue, they need the hour angle to set it on the telescope.

We are familiar with this phenomenon from everyday life:

When we travelled on the Trans-Siberian Railway from Krasnoyarsk to Omsk, we were allocated a seat by the railway company. In the railway company’s ‘coordinate system’, for example, I had the same seat the whole time during the one-day journey, e.g. seat 14 in carriage 31 of this particular train.

From the point of view of our friends in Krasnoyarsk, however, I did indeed change my location coordinate: I was no longer on planet Earth in their city (56° N, 92° 56‘ E), but in Omsk (54° 58’ N, 73° 23′ E) further to the west.