Aesthetically pleasing formulae involving time?

[ThomasQuinn]

I sincerely hope that I'm posting this in the right place and without violating any etiquette.

I've come here looking for opinions and suggestions from a community of people far more proficient in the field of physics than I am, with a topic that is probably a little unusual. The situation is as follows:

I've been asked to participate in an art project where I have been given a wall-mounted wooden box (roughly 24" high , 12" wide and 6" deep) in which I am to address, in a way of my choosing, the theme of time. I have developed an idea with three sections, and in the middle one I want to put, on a black background, a scientific formula (or possibly formulae) in which time plays a prominent part.

I've been looking at a number of physics articles relating to time in physics and have come across a handful of important formulae involving time, such as Maxwell's equations for electromagnetism and of course several formulae relating to spacetime by Albert Einstein and others. However, I am not especially well at home in serious physics to understand with any depth the meaning of such formulae about the complex mathematics underlying the universe, let alone to find specific formulae that are aesthetically pleasing as well as relevant to the subject.

So, I would like to ask for suggestions: could you suggest any formulae, in which time is an important part, that you find aesthetically pleasing (either because of scientific meaning/implications, or purely visually, or both)?

I am open to all suggestions and not adverse to learning a little more about physics on the side. If you've read all the way to here, thank you for indulging me.

 

[fresh_42]

I would only place a big hourglass in it, one that can be turned by spectators with black velvet as background. Maybe a bit too simple and probably the first thing that comes to mind, though. As a formula with time I like
$$
\Delta E \cdot \Delta t \geqslant \dfrac{\hbar}{2} \text{ or } \Delta E \cdot \Delta t \geqslant \dfrac{h}{4\pi}
$$
as a metaphor to the fundamental uncertainty of life.

 

[anorlunda]

Here's another. The famous Schrödinger equation t stands for time.

But I would also like to see a picture of Devils Tower, and invite people to think about the time passed from when it was created below ground, until the present.

 

[ThomasQuinn]

I would only place a big hourglass in it, one that can be turned by spectators with black velvet as background. Maybe a bit too simple and probably the first thing that comes to mind, though. As a formula with time I like
$$
\Delta E \cdot \Delta t \geqslant \dfrac{\hbar}{2} \text{ or } \Delta E \cdot \Delta t \geqslant \dfrac{h}{4\pi}
$$
as a metaphor to the fundamental uncertainty of life.

Thanks for your reply! I've considered hourglasses in a number of ways, but I'm far from the only participant, and I'm afraid there will be a *lot* of hourglasses around...I'm intending to go with geological strata and a tree growing on the top stratum in the bottom section, identical copper coins in increasing states of corrosion at the top and would like one or more formulae in the middle section. The background is going to be black with scattered watch parts set in it.

I will admit that I had to resort to google a bit to come to some understanding of the formula you gave me. I understand that's the time-energy uncertainty relation, a concrete example of Heisenberg's uncertainty principle, which I seem to gather is an old problem in quantum physics. Is that correct?

 

[ThomasQuinn]

Here's another. The famous Schrödinger equation t stands for time.

View attachment 222466

But I would also like to see a picture of Devils Tower, and invite people to think about the time passed from when it was created below ground, until the present.

View attachment 222468

Thank you for your suggestion. I had never seen Devils Tower before, that is one gorgeous and intriguing picture! I neglected to mention this in the opening post, but I am using geological strata in the bottom section of my object, so that is at least thinking in broadly the same direction. I am gratefully noting the time-dependent Schrödinger equation for a single particle moving in an electric field (I sure hope I got that right...)

 

[fresh_42]

Thanks for your reply! I've considered hourglasses in a number of ways, but I'm far from the only participant, and I'm afraid there will be a *lot* of hourglasses around...I'm intending to go with geological strata and a tree growing on the top stratum in the bottom section, identical copper coins in increasing states of corrosion at the top and would like one or more formulae in the middle section. The background is going to be black with scattered watch parts set in it.

I will admit that I had to resort to google a bit to come to some understanding of the formula you gave me. I understand that's the time-energy uncertainty relation, a concrete example of Heisenberg's uncertainty principle, which I seem to gather is an old problem in quantum physics. Is that correct?

I find it's the most basic principle of quantum physics, the fact that there is an inherent uncertainty to what we can measure (simultaneously). Either we measure the precise energy or the precise time, but not both in one measurement process.

If it is only about time, then basically every physical formula can be used, as physics is about the change of a quantity from one state to another, usually at different times. I thought for a moment about spacetime as topic, but as this is four dimensional, there is no proper realization, resp. image for it. They all are compromises in one way or another. Technically a Lagrange equation could make sense, as it is all around in physics:
$$
\dfrac{d}{dt} \dfrac{\partial L}{\partial \dot{q}_i}-\dfrac{\partial L}{\partial {q}_i} = Q_i
$$
The most natural equation should be motion: either explicitly as parabola $\vec{x}(t)=\frac{1}{2}\vec{a}\cdot t^2+\vec{v}_0\cdot t+\vec{x}_0$ which can be drawn next to it, or more general as $\dot{\vec{p}}=\vec{F}$ or $\dfrac{d\vec{p}}{dt}=\vec{F}$. So maybe Newton's laws can be taken, a kind of starting point of modern physics, a turning point in history.

 

[ThomasQuinn]

Thank you for the explanation and the insightful suggestions. I have to admit, it appeals to me as an historian to involve Newton in this.

 

[Stephenk53]

I don't know about equations but you could create a device that uses a crazy gear ratio so something revolves once every amount of time, the amount of time would be how long it takes for something to occur such as the length of time it takes for the copper coins to corrode.
I second the shrodinger equation however

 

[Stephenk53]

Also when does this need to be done by, because I am wondering if I am a bit late to reply