We saw last time how the development of accurate clocks in the 18 th and 19 th centuries transformed human cultures over the world.

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1 We saw last time how the development of accurate clocks in the 18 th and 19 th centuries transformed human cultures over the world. They also allowed for the precise physical measurements of time needed to drive the scientific revolutions occurring in physics, including experiments with electricity and magnetism. This work eventually led to another major change in timekeeping devices the invention of the quartz clock. In 1880, Pierre and Marie Curie discovered that quartz crystals produce electricity when they are deformed by pressure. Pierre and Marie Curie in their lab, ca

2 Further research showed that applying an electric current to the quartz could make it deform and in a remarkably regular manner, allowing the crystal to serve as the regulator for a clock. Such a quartz clock first appeared in 1927, and by the late 1960 s, thanks to their small size and high level of accuracy, they gave us our fist digital watches. 2

3 But the most accurate clocks to emerge from the new physics were so-called atomic clocks, which used the cyclic behavior found in atoms themselves to keep track of time. In particular, when electrons in atoms gain energy, they lose that energy in a very predictable and reliable way, and as early as 1879 the physicist William Thomson (Lord Kelvin) suggested using such energy transitions to keep time. Because of the difficulties involved, these clocks did not really become practical until the mid-20 th century, but now they represent the pinnacle of modern timekeeping. Atomic clocks typically use atoms of Cesium 133, a stable isotope that is bombarded with a microwave laser to excite the atom s electrons. 3

4 These clocks can keep time to within 1 part in one 10 billionth of a second, and in fact represent the fundamental measurement of time in our modern world. Time servers around the world use standard atomic clocks to measure and provide us with the shared now that we call the current moment. Atomic clock at the National Institute of Standards and Technology the clock that determines when leap seconds get added to our days! And it s that now that we ll turn our attention to today by backing up a bit to those early pendulum clocks not only did they revolutionize our means of keeping track of time, but the analysis of their movements by Galileo and others eventually did far more than that. 4

5 For Galileo s work involved taking the motion of the pendulum out of time, and describing its movement mathematically. Rene Descartes he of I think, therefore I am fame was a contemporary of Galileo, and developed a system for recording the position and movement of objects in time which we still call the Cartesian coordinate system. This was another great revolution in our thinking about time and space it suggested a uniform, measurable space around us that could be contained within this coordinate system, and the flow of time could then be represented by timeless mathematical curves within that space. 5

6 A basic spacetime diagram showing the orbit of the Earth around the Sun. Further, time itself could be assigned to a coordinate giving us our first mathematical view of time as a space-like dimension. These mathematical tools, invented in the 1600 s, were critical to the work of Newton in the formulation of his laws of motion, and fundamentally shaped his views on space and time. Space itself was absolute and infinite, and the objects in it moved in perfectly predictable ways as time passed. 6

7 Time itself, according to Newton, was absolute, true and mathematical time, [which] of itself, and from its own nature, flows equably without relation to anything external. Any object at any point in space experiences that same universal and absolute time including a shared present moment. This notion of a constant and universal time allowed Newton s laws to be extended into the infinite future and past given a set of initial conditions, the laws of motion seemed able to describe all future (and past!) behaviors of objects in space. This so-called clockwork universe was a key development in the philosophy of determinism, an idea we ll return to later. 7

8 However, our issue at the present is Newton s view on the universal nature of time. By the late 19 th century, this view had begun to be seriously questioned by scientists like Hendrik Lorentz and our old friend Henri Poincaré. Hendrik Lorentz, Henri Poincaré, Poincaré was working for the French government on ways to synchronize clocks across the newly developed time zones by using beams of light. In the process, he and Lorentz had begun developing the mathematics necessary to describe how light would appear to move through the universe if its speed were constant to all observers in some particular state of motion, or reference frame. 8

9 But their work was soon deeply extended by a young German physicist, Albert Einstein, who argued that the speed of light really was constant to all observers, regardless of their state of motion. Light arrives at v+c? Einstein had long been troubled by a simple idea imagine riding a bicycle with a headlight shining out of its front. Is the light from your bike moving faster because of the speed at which you are riding? If you could ride your bicycle at the speed of light, would you catch up to the light in some way? 9

10 No! Einstein postulated that the answer was no that all observers would see light moving at the same speed regardless of their own relative motion. That demanded that observers in relative motion must measure space and time intervals (the components of speed) differently space and time were not absolute, but relative! Einstein s bicycle rider can never catch up to the light from the flashlight, because his clock runs slower and slower as he approaches the speed of light! This difference in the rate at which time runs is an effect often referred to as relativistic time dilation, and is one of the most fundamental and besttested! outcomes of what Einstein would call his theory of special relativity. In particular, special relativity demands that clocks in motion measure time moving more slowly than clocks at rest. 10

11 One way to visualize how this might work is to imagine a laser reflecting off of a mirror in a moving spaceship. The astronaut only sees the beam go back and forth but the observer on Earth sees the beam take a much longer path. The only way that the beam can be moving at the speed of light for both observers is if time is running slower on the spaceship than on the Earth! This is a profound effect and one that we ll explore in some more detail next time when we discuss the role of time in space travel. But the impact of special relativity on our notions of time runs far deeper, and ultimately reveal a central flaw in our notion of the present moment. 11

12 An insightful illustration of this deeper issue is Einstein s famous moving train thought experiment. Imagine you are observing a train car as it passes directly in front of you. Now suppose at precisely the moment that the car is front of you, lightning strikes just in front of and just behind the train car. You observe the two lightning strikes to take place simultaneously. 12

13 However, an observer on the moving train car will experience something very different. Because of her motion, light from the strike at the front of the car along with all other possible physical effects caused by that strike will reach her before light from the back of the car will. Back-to-back lightning strikes cool! Two lightning strikes at once cool! So the two observers here report something very different about how the events occurred in time the stationary observer says both strikes occurred at the same time, while the moving observer says that one occurred before the other! 13

14 And what if there are two cars, moving in opposite directions? In that case the situation really gets strange indeed! The strikes are simultaneous. 14

15 The strike on the left happened first, then the one the right. The strike on the right happened first, then the one on the left. 15

16 The two observers on the train, despite being in almost exactly the same place, experience a completely reversed sense of the past, present, and future! This neatly illustrates the Relativity of Simultaneity the simple fact that observers in motion relative to each other experience a completely (and potentially radically) different version of now unfolding. Holy Crap! Think about what this does to the traditional vision of 4-dimensional spacetime. Newton had thought that time was a universal absolute, and that all observers experienced the same now as time passed. The present was like a wave passing through time and as such had a meaningful physical reality, even if it wasn t clear from the laws of motion which way the future or past lay. 16

17 Special relativity does away with even this aspect of time not only is there no clear distinction between the past and future, there is no meaningful definition of the present either. Observers in motion (as we all are!) experience different versions of now, along with different versions of the past and future! This way of thinking about the universe is often referred to as block time or the block universe. Because there is no distinction between past, present, and future in the block universe, there is arguably no passage of time at all just a collection of configurations in space-time, whose relationships depend entirely on the changing positions of objects within the universe. 17

18 Is our universe really like this? Does time not really exist? Many modern physicists believe so, and Einstein himself would have agreed in some ways. But what about those arrows of time? What about our conscious awareness of time, or concepts like free will? Is the relativistic universe as deterministic as the Newtonian universe? If all moments are equally real, why do I only experience now? We ll pick up on those topics again in a couple of weeks first we ll need to explore the universe a bit more carefully, and we ll start next week with a trip to the stars! 18