## Wednesday, February 23, 2011

### Why General Relativity is Easier to Understand than Special

Reason 1:

In General Relativity, the effects on clock rates and rulers have a concrete cause, namely the gravitational field. It's hardly surprising that an all-pervading field can affect the lengths of things or the rates of clocks. One could easily write down equations for other fields that do this same sort of thing.

With Special Relativity, on the other hand, there is no external field causing the effects to moving objects. One then has a puzzle as to "why" the moving objects are affected. The customary explanation is that "spacetime" affects the moving objects, but this just changes to question to why spacetime should affect relativistic matter, when it did not affect Newtonian matter. In fact the difference is field theory, because motion alters the propagation of the fields within the objects, whereas it does not affect the action-at-a-distance forces of Newtonian physics.

Reason 2:

Simultaneity is not an issue in General Relativity. In GR there is no concept of the global reference frame for an observer, hence one does not try to extend an observer's concept of "now" to distant locations.

In Special Relativity, by contrast, one has global inertial frames and one can compare different observers' definitions of "now". One finds that these definitions disagree and this leads to the various "paradoxes" such as the twin paradox.

The twin paradox, for example, arises in SR when one incorrectly applies the inertial frame of the "traveling twin". It does not arise in GR, because one doesn't define an inertial frame for either twin. Of course one could, if one assumes that there is actually no gravitational field (i.e., spacetime is flat), but without gravity one is back to doing Special Relativity.

Reason 3 (really a broader way to state Reason 2):

In GR, one is not concerned with comparing the viewpoints of different observers. Rather, one is concerned with calculating the effects of the gravitational field. An observer at point A is affected by the gravitational field at point A, and likewise for observer B and point B. There is nothing more to say about their viewpoints.

In SR, by contrast, each observer has a global reference frame that encompasses the whole universe and all other observers. One then has questions like how each observer can see the other's clocks to be running slow. In GR one never addresses such questions because a moving clock and a stationary clock are not at the same place to be compared.

Reason 4:

Again this is a variation on the same theme.

In GR, one is not concerned with measurement. There is no discussion about how different observers measure things, and there doesn't need to be. In studying the gravitational red shift, for example, one doesn't get into a big discussion about how the observers at different altitude make their measurements; the issue never even arises.

in SR, by contrast, one has to deal with the question of how moving observers can each see the other's clocks running slow, and rulers shorter. This means discussing the process of measurement and the effects of simultaneity on it. It is a very confusing aspect of SR and does not arise at all in GR, because it has nothing to do with gravity.

I discuss some of these things further in my book Relativity Made Real,

### Shortcomings of the Spacetime View of Special Relativity

One often hears that Special Relativity is a "Spacetime Theory". Indeed, this is the predominant way to view the theory, and has been since Minkowski's famous pronouncements on the subject.

Certainly the spacetime framework is a very elegant one, and summarizes very concisely and graphically the results of the theory. But I want to emphasize that one word very clearly: results. The spacetime framework gives us a good way to visualize what the theory predicts, but it gives us little or no understanding of why the theory predicts such things.

For example, a moving object contracts. Why? In the spacetime paradigm this is "explained" by the differences in coordinate systems used by the two observers, and particularly by their different definitions of simultaneity.

But this is rather circular. Coordinate systems create the appearance of contraction, but what creates the coordinate systems? Well...obviously the observers create them themselves, my measuring things out with their own rulers (and clocks). So actually we need to understand the rulers first, before we can understand the coordinate systems, and not vice versa.

Let me give a specific problem that is hard from the spacetime viewpoint. Consider a spaceship which is accelerating constantly, moving faster and faster. We know that it will be contracting; but exactly how does this happen? Does the nose contract towards the tail, or vice versa, or do both contract towards a point in the center? The question does have a definite answer, because both the nose and tail of the ship have a definite trajectory, fully predictable by physics. But I challenge anyone to produce this answer by drawing spacetime diagrams, or computing Lorentz transformations.

I will give my own answer in a future post. For now I will only point out that, in reality, the contraction of a moving object is caused by changes to its internal forces and fields, most notably the electromagnetic field. Understanding this, one can tackle the problem and it is not particularly hard. One also gets past the circularity described above, because one sees that moving rulers (and clocks) are altered by concrete physical mechanisms, so that observers measuring things with them will naturally build different coordinate systems using them.

The energy/mass relation is also quite mysterious from the spacetime viewpoint. Consider this simple scenario: an electron and proton come together to form a hydrogen atom. This process gives off light, hence the atom has less energy than the electron and proton did separately, hence the atom has less mass than the separate electron plus proton. But why? Why is it harder to accelerate an electron an proton bound into an atom, than to accelerate them when separated? I have no idea how to address this question within the spacetime viewpoint, but it is quite simple if one thinks in terms of the physical mechanisms which give rise to the mass/energy formula.

I discuss these sort of things in more detail in my new book, Relativity Made Real (www.relativitymadereal.com). Indeed, these sorts of questions are the reason I wrote the book (although I don't explicitly answer the first one, because it is a bit too in-depth for a popular book).