# Temperature and Time

By Daniel Tarade

Time. The fourth dimension. In popular science, time travel is a recurrent theme. Travel through time, in either direction, features prominently in novels, films, and imagination. But, in reality, we are all time travellers. It is just that we can only travel in one direction at a (fairly) fixed pace. And, of course, time is a useful co-ordinate. Arranging to meet someone at a particular street corner is useless if you don’t also provide a date and time. Hence, time as the fourth dimension. The fourth co-ordinate. But is our use of time as the fourth co-ordinate arbitrary? Can we simply use another property to create a new co-ordinate system, one that does not require time? This is the topic that a group of biochemistry students stumbled upon on the bus ride back from our annual retreat. A lack of sleep may have played a role. Some participants in this conversation may have been hungover. Regardless, it was a heated discussion, where two sides emerged; those who figured that our co-ordinate system is arbitrary, that time is substitutable, and those that said nah.

Very quickly, the topic of conversation solidified as one individual argued that temperature is as logical a candidate as time is for status as the fourth dimension. Their argument had multiple components. Weaker adjuvant arguments referenced that temperature has absolute zero, whereas our methods of keeping track of time (calendar, 24-hour day, etc) are arbitrary. Further, the infinitesimal increments of temperature relate to discrete quanta of energy. However, the focus of our conversation narrowed on two ideas. The first I found quite silly but here we go anyways. They argued that any particular temperature, to the infinite decimal place, has occurred only once in the universe, thus making temperature a potentially useful co-ordinate. It took a while to find a suitable answer. However, by establishing that some arbitrary point with x, y, z co-ordinates has experienced fluctuation around some arbitrary temperature (say 298 k) multiple times, then it became clear that upon transiting from a temperature higher than 298 k to a temperature lower than 298 k, the temperature must have, at one point, been exactly 298 k. Once the temperature rises above 298 k the exact same temperature would have occurred for the second time. This counter-argument already eliminates the use of temperature as a co-ordinate because co-ordinates must be unique.

Now, my friend also argued that time and temperature are linked. The idea is also worth discussing. They alluded to the idea that time can be thought of in terms of fundamental interactions between atomic and sub-atomic particles. Or rather, that time can be defined in terms of atomic vibrations. Hence, the atomic clock. As per wikipedia, “the international definition of time is 9,192,631,770 cycles of radiation corresponding to the transition between two energy levels of the ground state of the caesium-133 atom.” However, the definition has been amended to clarify temperature; namely, 9 trillion or so cycles of radiation at absolute zero. This is of importance because atomic behaviour speeds up at higher temperature. After all, temperature is a measure of average kinetic motion of particles. None of this means that time speeds up with increasing temperature or vice versa. Just that a definition of time on the basis of atomic vibrations needs to specify a temperature. More esoteric, and completely beyond my training as a biochemist, is the idea that temperature and (imaginary) time have a fundamental relationship in quantum field theory. This, of course, did not come up during our bus ride.

On occasion, substituting temperature for time does work at a macroscopic level in the real world. When a group of friends decides to have a barbecue the first warm weekend of spring. Or, waiting for a oven to pre-heat. In these instances, we are not waiting for time but for temperature. Limitations are that temperature is not continuous but rather a fluctuating property of a particular co-ordinate on longer time* *scales. Ultimately, that is why temperature cannot substitute as a co-ordinate. Rather than extending linearly from a central point, temperature ambles about, in both positive and negative directions. Co-ordinates of space and time are unique and continuous. And I guess that’s that.

**Post-script on arbitrary measures of time keeping**

Although the same time does not occur at the same point with x, y, z co-ordinates more than once (unlike temperature) our arbitrary measures of time have created some confusion. One anecdote features the Russian olympic shooting team arriving eleven days late to the 1908 competition, as they were following the Julian Calendar while the UK hosts had already transitioned to the Gregorian calendar.