Theoretical Thursday - week 2

NOTE: anyone not interested in how my brain works does not have to read this. It is a bit drier than I would have liked, but hey, it’s physics.

Week 2– of me reading RELATIVITY the Special and General Theory, A Clear Explanation that Anyone Can Understand, by Albert Einsten, (1916)

Part 1 The Special Theory of Relativity,
Chapter one – Physical Meaning of Geometrical Propositions.

I was a little worried when I began chapter 1 when the first sentence talked about being “chased about for uncounted hours by conscientious teachers” on the “lofty staircase” in the “noble building of Euclid’s geometry. I don’t remember my geometry teacher, Mr. Fritz, becoming animated enough to chase any student anywhere. But I pressed on. Here is what I learned –

Geometry is filled with lots of ‘truths’ about a straight line, a plane, a point, etc. We think that these things are all true, but truth is limited. Geometry is not concerned with how axioms relate to real experiences. Geometry makes connections between one geometric idea and another. I thought this was interesting because when I took geometry I remember lots of word problems with real stuff like balls and tables and trains. But apparently, real geometry-ettes, - ites, -ists (?) don’t care about real stuff.

However, Physics is concerned with real stuff - how geometry relates to the real world. The catch is – the ‘truth’ of a geometrical proposition is founded on incomplete experience. (Isn’t all truth based on incomplete experience??) There for – “truth is limited.”

Ta Da! I got through the first chapter!! Do I dare move on to chapter 2? You bet.

The System of Co-ordinates.

In this chapter Albert gets pretty basic. Distance between two points is measured by a standard of measurement (ROD S). You can locate any point (or event as he calls it, which is confusing, but I’m getting used to it) in relation to other points on a rigid body (like Earth) by means of measuring these distances. And to explain things on a third plane, he uses the analogy of a cloud flying over Potsdamer Platz, Berlin. We can calculate that clouds position by knowing the location of Potsdamer Platz on Earth and the distance the cloud is from the ground. We have located an object in space.

Rather than using names, mathematicians prefer numbers and the Cartesian system of co-coordinates of x, y, and z three planes perpendicular to each other. I think of it as the corner of a see-through box. In pottery, to measure the size of a pot before firing, we would place it in the corner of a gridded box to measure the pots, height, width, how much space it would take up in the kiln.

But like Albert says, “in practice, the rigid surfaces which constitute the system of co-ordinates are generally not available,” meaning that we don’t live in a big gridded box. We have to imagine it. He concludes: “Every description of events in space involves the use of a rigid body to which such events have to be referred. The resulting relationship takes for granted that the laws of Euclidean geometry hold for “distances,” the “distance” being represented physically by means of the convention of two marks on a rigid body.”

Chapter 3 – I’m on a roll and I can’t stop now – Space and Time in Classical Mechanics.

I’m still on board the physics train, but not sure why Albert says, “In the first place we entirely shun the vague word “space,” …. and we replace it by “motion relative to a practically rigid body of reference.” When I look at the space in my living room, I'm not thinking it relative to the coach, but I will from now on. Here he uses the classic illustration of the stone dropped off a train. From the droppee the stone appears to fall in a straight line. To a person on the ground the stone appears to fall in a curve. The fall is ‘relative’ to whom ever sees it. Got it. However, to me, the stone does not occupy two different locations. So, to me, the stone is not relative – the measurement is relative. I’m sure somebody would have a problem with that, but that’s how it works for me.

But then he says – “for every point on the trajectory it must be stated at what time the body is situated there.” WHY MUST WE? Don’t give me a must and not explain why.

And THEN he says – “In this connection we have not taken account of the inaccuracy involved by the finiteness of the velocity of propagation of light." ???? But he assures me we will later.

Okay. Better go before my head explodes.