Relativity and space-time

Introduction

Relativity is one of the most famous scientific theories of the 20th century, but while Einstein and some of the predictions of the theory like the existence of black holes are indeed very popular, the public's ignorance about the most important implication of the theory on reality is unfortunately very great.

The theory of special relativity enunciated by Einstein in 1905 was a response to the experimental fact that the speed of light is a universal constant independent of the observer. This has the consequence that there is not an universal time as our intuition and classical physics have always considered, but each observer in motion measures his own time in his own frame of reference.

It was Hermann Minkowski who realized the deeper implications of the theory's postulates. If two observers in relative motion have different times, consequently they must have different sets of simultaneous events, and this in turn implies that they must also have different spaces or "worlds". Space and time are related in a geometric structure which Minkowski called space-time. He announced it this way in 1908:

The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

At first Einstein considered Minkowski's work a mere mathematical trick, but he finally understood that the geometrical interpretation of space-time was fundamental to incorporate gravity into the theory. In 1915 he published his theory of general relativity, where gravity appears as a consequence of the curvature of space-time.

The space-time described by Minkowski and that emerges from the postulates of relativity is a structure of four dimensions, a continuum that contains all space and all time. It is known in the philosophy of time as the block universe. It is the observer who decomposes this four-dimensional continuum into time and three-dimensional space in its own frame of reference. In Einstein's own words:

Since there exists in this four dimensional structure no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.

And in his famous letter of condolence to the Besso family:

For we convinced physicists the distinction between past, present, and future is only an illusion, however persistent.

And this is no doubt the most important consecuence of relativity: the existence of space-time as a continuum that includes all space and all time. It's certainly counter-intuitive and presents a difficulty that seems insurmountable to many (physicists included): it leads to eternalism, that is, all events that we view as past, present or future coexist in the block universe. Space-time must have been "created" in an instant and events have't been sequentially evolving from an origin, but rather all exist right from the beginning: space-time does not evolve, it simply exists. The Big Bang is therefore located at the beginning of space-time but it's not the cause that created it.

Presentism is a philosophy that opposes relativity affirming that only the present ("now") exists. Its contradiction with relativity is most evident in its affirmation that there exists an absolute simultaneity: only the present exists. This implies that all observers in relative motion should share the same set of simultaneous events. The problem is that by contradicting relativity, it contradicts the experimental evidence that led to the theory. A consequence of the relativity of simultaneity is the phenomenon known as time dilation, which has been empirically verified (particle accelerators, atomic clocks carried on aircrafts, GPS navigation systems, the experiment of the muons, etc). Presentism contradicts experimental evidence and is therefore false.

In short, space-time is a geometric structure that contains all space and all time. The phenomena associated with relativity can only be interpreted correctly from this geometric point of view. A good illustration for this is the well-known example of the light clock. Although it is relatively simple to understand, it poses a paradox: all observers notice that clocks in motion slow in relation to their own clocks, since motion is relative. How is that possible? We'll analyze it in Diagram 11: reciprocal time dilation.

Relativity and space-time

Introduction

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