Space, time and Einstein

Published : May 20, 2005 00:00 IST

What exactly did Einstein do? Why was it important for physics then? Why does it continue to be of lasting significance for physics today?

IT is somewhat ironic to pinpoint the moment of birth of an idea that has reshaped our very notions of time and space. Even its originator, Albert Einstein, could not have anticipated that his discovery of the Special Theory of Relativity would itself become a marker in historical time. As we celebrate its centenary this year, let us revisit Einstein's discovery, viewing it also in the context of history, through three questions:

What exactly did Einstein do? Why was it important for physics then? Why does it continue to be of lasting significance for physics today?

It is conventional to state that relativity completely altered our concepts of space and time. So what exactly did Einstein do in 1905 which was so radical? In one sentence, the answer is: he placed the physically measured notion of time on essentially the same footing as that of space.

To understand more fully what that means, let us look closer at our notion of space. From early childhood, we apprehend the three-dimensionality of the space around us. Though "up" may look different from "right" and "down" from "left", we do not think of the various directions in space as intrinsically different. Especially in an age of visuals from outer space, we can readily imagine even the terrestrial distinctions between "up", "down" and so on disappearing. In other words, we take it for granted that the three dimensions of space are on the same footing. This fact has some immediate consequences in our day-to-day experience, which we do not often appreciate.

In particular, when observing objects or events around us, we can orient ourselves in any arbitrary way in these three dimensions. For instance, we might be standing upright, lying down or performing a yogic asana on our heads. In all these cases, we realise that our visual perspective of any given object will differ depending on the orientation we have chosen. At the same time (and this is very important), we also know how to take into account this effect of perspective. We do not get confused looking at a table from different angles; we know it is the same table.

What we can abstract from these facts of our everyday experience is the following. First, we can "mix" up different directions in space by changing our orientation so that what is up for me may be to your left. More generally, this manifests itself in altered perspectives of objects. Second, though there can be these differences in perspective, we nevertheless have a certain mental apprehension of objects which is invariant under changes of orientation.

Einstein's radical advance, as we have said, was to propose that time is also, essentially, on the same footing as these three dimensions of space. Hence the notion of a four-dimensional combined space-time. This is not something rooted in our daily experience (and for a very good reason as we shall come to soon).

We shall later describe the background for arriving at this postulate. For the moment, let us just accept this proposal at face value and describe some of its striking consequences by analogy with our understanding of space. Just as we can move freely in the three directions of space by orienting ourselves differently, let us assume that there can be observers who can be "oriented" differently in space and time. Hence, the notions of space and time can also get "mixed" with each other, just as the different directions in space could mix up when changing orientation. This is a startling consequence simply of accepting that space and time can be on the same footing.

One immediate casualty of this proposal is the notion of an absolute time, which is the same for all observers. Observers oriented differently in space-time would measure time intervals, by their respective clocks, differently from each other. This is the effect known as relativistic time dilation. It is analogous to a difference in spatial perspective whereby objects can appear contracted along any one spatial direction depending on orientation.

More surprisingly, the notion of one event occurring first and another later in time can also be something dependent on the observer's orientation in space-time.

In particular, events measured to be simultaneous by one observer would not necessarily be so for another. As a rough spatial analogy, consider several people sitting around a circular table. There is no absolute notion of who is farthest or closest. Someone may be closest as measured from the wall, while another may be closest as measured from the door. Two persons may be sitting at equal distance from one observer but not from another. It all depends on where you choose to view the table from. Similarly, there can be events in time whose ordering depends on the orientation of the observer in space-time. There is no contradiction here as long as it applies to those events that can have no causal influence on each other. If one event can causally influence a second event, it actually turns out that the first will always be before the other for all observers however differently oriented they might be in space-time. In other words, the notion of being able to causally affect another event is something invariant, as it should be. In any case, by viewing time on the same footing as space, Einstein's proposal upset deep-seated notions of time such as the absolute nature of simultaneity.

It affected certain notions of space as well. Another consequence of treating space and time on the same footing is that lengths (such as those of a rigid rod), too, would be measured differently by observers differently oriented in space-time. This would be so since distances in space alone (like intervals in time) are not something invariant in space-time as a whole. While we can readily visualise two observers who are differently oriented in space, how are we to think of two observers who are differently oriented in space-time? It was Einstein's insight that two observers who are moving with respect to each other with a uniform velocity should be thought of as oriented differently in space-time. We do not, however, see very much mixing up of space and time when we move on a train or even a plane. The reason is that with the small terrestrial velocities that we experience, we do not alter our orientation in space-time by too much. Only when velocities become comparable to the speed of light, which is 300,000 kilometres a second, do the effects of different orientation in space-time become noticeable.

This new situation in space-time can once again be understood by analogy. If we were fixed to a particular position and orientation in space and could only just nod our head ever so slightly from side to side, we would not have to take into account at all the effects of different perspectives in space. It would then be initially quite disorienting for us to learn that perspectives can differ dramatically if we were able to shift our orientation more than the tiny amount we were used to. The notion that we can be very differently oriented in space-time and view events in very different perspectives is similarly a radical departure from what was known before through our limited experience.

At this stage a warning is appropriate. "Everything is Relative" is often the profoundly misleading conclusion drawn from the above observations on space and time. It is important to realise that just as we can deal with different spatial perspectives and yet apprehend the invariant nature of an object like a table, the same can be done with events in space-time. Different observers in relative uniform motion may thus view events in space-time from different orientations, but nevertheless arrive at invariant conclusions about physical phenomena. Everything is not relative.

The reader has not been given any inkling so far as to why Einstein conceived these new concepts of space-time and how it helped transform the physics of his time. It is thus important to have some appreciation of this to avoid the misconception that these notions arose purely as a flight of the imagination.

On the contrary, Einstein arrived at (or one might say, was forced into) his conclusions by seeking a resolution to a major physical puzzle of the early 20th century. This concerned the propagation of light. Michael Faraday and J.C. Maxwell's studies of electromagnetism in the late 19th century had culminated in the prediction that light was a disturbance (or wave) of the electromagnetic field. Heinrich Hertz had experimentally verified this by producing electromagnetic waves. This was to lead to the radio and other inventions.

However, from prior experience with other waves, such as waves in water or those of sound in air, it was felt that light too needed a medium to propagate in. In the case of electromagnetism, the candidate was dubbed the `ether'. However, a problem with this proposal was that the ether was not directly observed. Also it would seem as if the speed of light would depend on one's motion with respect to the ether. In particular, in its motion around the sun, the earth would be moving with respect to the ether. However, no experiment detected any change in the speed of light either when it propagated in the direction of the earth's motion or perpendicular to it. To account for these puzzling results, people tried to attribute unusual dynamical properties to the ether whereby it could cause lengths to shrink in its direction of motion.

To appreciate Einstein's marvellous and far-reaching solution to this conundrum, we need to distinguish between kinematics and dynamics. Kinematics is simply about describing the basic aspects of motion such as the positions of objects and how these change with time. It is not concerned with the causes of motion. Dynamics, on the other hand, addresses the forces that are involved in such motion and thereby tries to explain the motion. Kinematics therefore involves (implicitly or explicitly) assumptions about the geometry of space and its relation to time. These assumptions, abstracted from our perception of the world, rarely need changing. The laws of dynamics (like those of gravitation, for example) deal with specific forces and are built on these kinematic assumptions. These laws are being continually refined and modified as we learn more about the causes of different kinds of motion. To give a rough analogy, kinematics is akin to the basic note structure in any particular system of music. Dynamics is more akin to the different ragas and compositions that can be built on that underlying framework. The latter evolves over the course of history while the former rarely changes.

The basic kinematic assumption underlying physics since Isaac Newton had been that of an Absolute (three-dimensional) Space and a separate Absolute Time which is the same for all observers, whatever their individual state of motion. Einstein's genius was in recognising that this kinematic assumption was flawed, and only approximately valid in circumstances where the velocities are small compared to the velocity of light. He proposed a new kinematical rule that told one how measurements of space and time by one observer would be related to another in uniform motion with respect to the first. This rule put space and time on the same footing in the sense that has been explained earlier, namely that the two observers are merely oriented differently in four-dimensional space-time.

With this rule, all observers in uniform motion would measure the same speed of light. Thus Einstein proposed a kinematical solution to what seemed like a problem of the dynamics of light's propagation in the ether. In fact, Einstein's solution showed that there was no need to propose this unobserved medium. All the facts about electromagnetism fitted in neatly with his new kinematical rules. Moreover, as mentioned earlier, when relative velocities of observers are small compared to that of light, these rules reduce to what we expect from the Newtonian kinematic assumption of a separate space and time.

The new kinematics had a number of other immediate consequences. Among the most famous is the equivalence of energy and mass encapsulated in the E = mc2 relation. Again, because the origin of this relation is kinematical, it applies to all objects, whatever be their constitution or the nature of the forces acting on them. Thus Einstein's solution of the ether puzzle had an impact far beyond the particular dynamical context in which that puzzle had arisen.

The kinematic framework of physics rarely changes. The year 1905 is thus quite a unique occasion, which is why Einstein's discovery continues to be a lasting legacy to this day. In the intervening century, while there have been other upheavals in physics such as quantum mechanics and many new discoveries from the sub-nuclear regime to intergalactic scales, we have yet to see a need for a modification to the kinematic framework proposed by Einstein. On the contrary, we have much greater access to velocity regimes close to the speed of light where Einstein's mixing of space and time is dramatically validated. The scientific observer, while viewing space-time, can do far more than, figuratively speaking, being able to nod one's head just a little bit.

As far as we know, the kinematic rules proposed by Einstein are satisfied by all dynamical laws of nature. In fact, because of the absence of any evidence to the contrary, the consistency of any fundamental dynamical law with Einstein's kinematics is essential. Thus the postulates of the Special Theory of Relativity have become guiding principles in the formulation of new dynamical laws.

More generally, Einstein's emphasis on the role of symmetries and invariance percolated through the physics of the last century. It has proved immensely fruitful both in the discovery of new laws and in the deeper appreciation of existing ones.

Einstein's later discoveries in his study of gravitation further deepened the physicist's conception of space and time. It changed the idea of space-time as a passive arena for all events and rather made space-time itself a participant. The cosmological expansion of the universe is the most striking demonstration of this idea.

To get a sense of how monumental Einstein's legacy to physics is, we merely need to recall that while we have described here one of his colossal achievements, we have not even touched on any of his other seminal contributions in quantum theory and statistical mechanics. We, the inheritors of his legacy, can only stand in quiet humility even a century afterwards.

Rajesh Gopakumar, a theoretical physicist, is at the Harish Chandra Research Institute, Allahabad.

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