Physicist Mahdi Godazgar on the arrow of time, Schrödinger equation, and Einstein’s relativity theory

Time is something that we experience on a daily basis; characterised by notions such as the past, present and the future. Its progression is embodied in our continued experience of the future becoming the present, while the present becomes the past. In fact, it would be impossible to talk of motion or dynamics without the concept of time and its progression. In this sense, it is very similar to our experience of space. Just as it is natural to ask where a certain event has taken place, it is also natural to ask when it occurred. Therefore, time, along with spatial coordinates, is a marker for deﬁning events. However, it is clear that time is diﬀerent to space in how we experience it in our daily lives. Whereas we feel free to roam in any spatial coordinate that we desire, we feel compelled to follow time forward and always at the same pace. However hard we try the clock will always tick-tock as it always has and will. The future will displace the present, which will itself in turn be driven to the past. This everyday experience of time as possessing a clear (always forward) direction is strangely not borne out in fundamental descriptions of nature and this continues to be one of the biggest puzzles in theoretical fundamental physics.

**Time in Classical and Quantum Mechanics**

In classical physics, time is absolute and invariable. All clocks tick at the same rate and everyone’s experience of time is the same. In this sense, the concept of time here is very similar to our everyday experience of it. However, what is important is that classical physics does not choose an arrow of time. Time-reversing a process or event is just as valid in classical physics as the original process. It makes as much sense to walk forward up a street as it does to walk backwards down the street as far the laws of classical physics are concerned.

Physicist Daniel Kleppner on precise time measurements, gravitational field, and the Global Positioning System

**Time and the Theory of Relativity**

The theory that completely changes our paradigm of what time is is Einstein’s theory of relativity. Relativity asserts that the progression of time is not universal and depends intimately on who is measuring it. In this picture of reality watches tick at diﬀerent rates, depending on who is wearing them. By accelerating at extraordinary rates or being present in the vicinity of strong gravitational forces, such as those around a black hole, one can change the rate at which time ﬂows, even bringing it to a stop or reversing it, at least theo-retically. For example, for a person inside a black hole, space and time seem to interchange. Here, it is the descend into the black hole singularity that becomes inevitable, just as the forward ﬂow of time was outside the black hole. On the other hand, “time” becomes just another direction like left or right.

Relativity puts time on an equal footing with the spatial directions that we are used to; the consequence being that just as spatial directions are not universal and can, for example, be curved, so too can the time direction be “curved.” A measure of this curvature is the rate as which it proceeds. Nevertheless, in relativity too, the equations are time-symmetric; that is they do not favour a particular arrow of time.

**Arrow of Time**

The one feature that classical, quantum and relativistic mechanics share with respect to time is that neither theory designates an arrow of time. Of course, solutions to their equations can break time symmetry, but the theories themselves are time-symmetric. So where does the time asymmetry that we experience around us come from?

Most of the time asymmetry that we experience results from thermodynamics. In particular, the second law of thermodynamics states that the entropy (roughly the amount of disorder) of a system increases with time. A consequence of this law is that, for example, you will never expect to see a puddle of water unmelting in the sun to form a block of ice and hence heat up its surrounding. It must be stressed that this law is a statistical state-ment rather than a rigorous mathematical result derived from the equations of fundamental physics. Why such a statistical law ought to be true and how it is related to the fundamental theories of nature is the “arrow of time problem.”

*Edited by Ksenia Vinogradova*