Imagine being a time traveler, desiring to witness dinosaurs during the Cretaceous period. Are these creatures located somewhere in the past, or is it necessary to revert the world to its previous state to visit them? According to Einstein's theory, all moments in time coexist within our spacetime. Despite quantum mechanics presenting challenges to determinism, we'll inevitably experience the future as it unfolds into the past. With a century's worth of supporting evidence, his theory seems indisputable.
However, delving deeper into Einstein's theory reveals how his philosophical ideas about space and time have shaped our understanding for the past 100 years.
In 1905, while working at a Swiss patent office, Einstein introduced his special relativity theory that demonstrated how our perception of time and space depends on our motion. The theory states that as an object approaches the speed of light, it appears to slow down, and its length contracts. Although Einstein didn't connect special relativity to spacetime geometry at the time, we now observe these effects in particle accelerators.
Years later, mathematician Minkowski expanded on Einstein's ideas, proposing that time dilation and length contraction result from our relative motion in a four-dimensional spacetime. Einstein embraced this concept and integrated gravity into it, forming his general relativity theory. In this model, spacetime is curved, and the curvature manifests as gravity. Supported by observations from a solar eclipse in 1919, Einstein's theory presents the universe as a four-dimensional variety with specific properties.
In Einstein's universe, there is an unbreakable rule: nothing can travel faster than the speed of light. Regrettably, this is the only apparent method to travel back in time in Minkowski's universe. However, Einstein offers a solution: by modeling spacetime so that certain paths are shorter than others, travel between two points could be reduced without exceeding the speed of light. Theoretically, it could even be possible to connect a future point to a past point through a spacetime bridge.
Another feature of Einstein's multidimensional universe is the absence of universal time. Instead, every entity experiences its unique time as it navigates the dimensions.
Objects that are close to each other and in a similar state of motion tend to experience similar flows of time, which is why all of us on Earth experience almost the same flow of time. The variations for ordinary velocities on Earth and small differences in gravitational fields are small to the point that only super-accurate atomic clocks can measure the differences.
It seems that all this discussion about bridges between times and places and no universal time means that time works like a highway. We all move around in our cars, experiencing our own flow. There are exit ramps and you can go back in time if you can find an exit that takes you to the opposite road. All this supports the idea that those dinosaurs we want to see are "down there" only 65 million exits behind us. A time traveler just needs to "get unstuck" in this stream of time, take a shortcut back to the past by taking an instant vacation to the Cretaceous (watch out for meteors!).
But wait, things are not so simple and straightforward.
The truth is that General Relativity is formulated according to Einstein's philosophy. He proposes that space and time have a geometry, and physicists and mathematicians usually present it that way, as he did. If something has a geometry, it must have every point existing somewhere. There is no evidence for this part of the theory because all the tests of the theory have been done on a very small area of the universe, on Earth and its immediate surroundings. Even observations of deep space have been made by looking at the "old light" that has traveled millions or billions of years to reach us.
There is a problem with Einstein's formula.
The problem is that Einstein makes a jump from spacetime having a geometry to something in "free fall," that is, something that does not experience an external force, following a "geodesic" in that spacetime. A geodesic is a shorter linear path in a curved geometry. It comes from the Greek geodaisia , ge-, the Earth, and daio-, "to divide." On Earth, a geodesic is a "great circle" path between two points; therefore, it always divides the Earth into two halves.
We all know that if you were to go out on the ocean and follow a constant direction, you would not follow a great circle path except under forced circumstances. Instead, you would have to follow a "rhumb line" path, which is not the shortest line path at all.
To follow a great circular path, you have to make periodic course corrections. In Einstein's curved spacetime, there is a mechanism for making these course corrections and that is gravity. But now we seem to have two separate pieces of the theory: a curved spacetime, like the Earth, and a force that makes us obey that curvature, gravity.
Ockham's razor tells us that we shouldn't invent things that serve no purpose, so it seems reasonable that if we want to explain gravity, we could just get rid of curved spacetime and keep gravity. But then we end up with everything happening at the same time in the same place. We need a coordinate system to keep things separate, but we don't need Einstein's ideas about geometry so much.
In 1950, Utiyama created a version of general relativity that more or less matched this perspective, called gauge theoretic gravity. The gauge theory then took off and explained all the other forces: weak, strong and electromagnetic, becoming what is now known as the Standard Model of quantum physics.
All gauge theories have a geometric interpretation, but for other forces it is not seen as fundamental (the geometries of other forces exist in spaces made of complex numbers, so they are not so intuitive). However, most presentations of gravity used the geometric approach. Gauge's theory of gravity has the advantage of presenting gravity as a force, which is what it is, and not as a geometry that needs gravity to order phenomena according to geodesics.
Let us now return to our analogy with the highway. In our Einsteinian theory of curved variety, we travel on a highway and the past is "back there" and the future is "further ahead." In a theoretical version of the indicator, however, we could be on a treadmill with screens around us showing scenarios as a kind of racing simulator.
The forces exerted on us are the same in both cases (they are mathematically equivalent). A space-time coordinate, rather than representing a point on a variety, is an artificial construct that helps us label events as distinct from each other. When I travel from one place to another, gauge theory tells me what will happen as I travel that "distance." It also tells me how different people ("observers" in the jargon of relativity) will have different experiences depending on how they interact with the gauge force of gravity.
Suppose the universe is not a manifold of dimensions. Suppose that you, in fact, are experiencing neither motion in space nor in time according to Einstein's ideas, but you are interacting with a measurement force that makes it appear that you are moving. This means that, not only is the past not "over there" somewhere, but other places are not exactly "over there" either. Rather, to move from place to place or time to time, you interact with the force of gravity that translates, rotates, rotates and accelerates you like the treadmill. Like in the movie Matrix, other people experience their own versions of reality that they reconcile by communicating with each other and sharing observations through forces.
The universe does not need to be a computer simulation to be like The Matrix (this would simply invoke another universe that is as "real" as the variety we just got rid of and would send Willem of Ockham into a tailspin). Gauge theory works in precisely this way.
Although gauge theory has few implications for physical measurements at this time because it is mathematically equivalent to the geometric form of general relativity, it has philosophical implications. If the past and future do not exist "out there," then they could be created by the interaction between ourselves and the universe, especially when we add quantum indeterminacy into the mix. Our choices could, in fact, profoundly affect what we experience because the future has not been written and the past has been erased. I say could because we do not know.
In this regard, let us remember to take a look at the many-worlds interpretation of quantum mechanics.
It is dangerous to draw philosophical conclusions from physics, even more dangerous to present one interpretation of a physical theory as the only one. If the history of philosophy is a guide, people will choose sides depending on what they want to be true. I, for example, like the idea that my choices matter and that the future is mine to choose. Those like Einstein will desire a universe in which they have no responsibility for their actions. If the history of physics is any guide, just when we think we have made sense of the universe, it will reveal that we still have no idea.
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