# Time travel with memristors

Hey, do you remember that gray-haired professor? The one that at first glance appeared a bit distracted and crazy? They guy that kind of shocked the world coming from “nowhere” and presenting (and demonstrating) a wild idea that would put everything in a new picture? The guy who said that the universe is not that linear and that we can warp the space-time fabric?

Yepp, I am of course talking about the one-and-only Professor Emmett Brown, “Doc Brown”, or “Doc” for short. Great Scott, you say!
Btw, this man is a man of understatements indeed and also a very rigorous scientist and explorer.

## November, 1955

We all remember the 5th of November, 1955, as the date of invention of the flux capacitor. Doc Brown slips in the bathroom and invents the flux capacitor. Here we also have to give Doc Brown cred for being able to take the flux capacitor from idea/invention to fully-functional prototype in just a week, it’s like he was able to travel in time or so.

## A master of timing

One also have to give Doc Brown a big applause for the, with only simple technological tools, be able to accurately time the lightning striking the city hall and at the same time race a stainless-steel deLorean up to (excatly!) 88 miles per hour such that the car hits the flexible lightning rod exactly at the same instant. Very impressive indeed, Heisenberg himself would be impressed by that time-position trade-off.

## The flux capacitor

So, what made time travel possible? The flux-capacitor of course! And what is a flux-capacitor one may ask… From the sketches by Doc Brown, as well as the functional hardware prototype, we see that it is some kind of three-terminal device.

We also get more valueable information on the operation of the flux-capacitor from the literature (i.e. movies…)

• It needs 1.21 GW of power to operate
• It needs to travel at a pace of 88 miles per hour
• and … that’s it… sort of, probably some control and interface circuits are needed too…

Out there, among all the valuable publications (i.e., the internet), we have more theories/proofs on what the flux-capacitor may be:

Oops! What did we just read there in the last bullet!!?!1! The memristor being the inspiration for the flux capacitor. That ties some of the strings together …

## Memristor

The memristor has been coined as the missing element, etc., etc. We have been discussing it slightly before. It is a large field and this single post would not cover the whole story though. Vahid Keshmiri and Joakim Alvbrant at our research group have spent quite some time on memristor studies and will be able to demonstrate for you.

Anyways, let us consider the four basics in the picture below: voltage, current, charge and flow (sorry, couldn’t find the geek letter for flow). If we put these in a mesh like shown below we also find the relations between them.

For example, we have the “static” relationships as:

 $d q = C \cdot d v$ $d v = R \cdot d i$ $d \Phi = L \cdot d i$ $d \Phi = M \cdot d q$

where the last one is the “missing element” according to Leon Chua. Still, the memristor has the unit Ohm. It fills in the last gap in the matrix, sort of.
Further on, the dashed arrows also describe a time-dependent relationship:

 $d \Phi = v \cdot d t$ $d q = i \cdot d t$

A nice symmetry. Also, interestingly, if we for sake of discussion form the product between all relations above:

 $\frac{ d q }{d v} \cdot \frac{ d v }{ d i } \cdot \frac{ d i }{ d \Phi } \cdot \frac{ d \Phi }{ d q } = \frac{ C \cdot R \cdot M }{L } = 1$

and let us be a bit creative and use conductance instead and we get [edit: Thanks, Prateek!]:

${ C \cdot M } = {L \cdot G }$

the products must equal each other (!).

What if we stretch the diagram a bit and use the three components we tend to like most on the corners and see what we get.

Aha! I rest my case. Or something…

## Yeah… so how does 88 mph and 1.21 GW fit into the picture?

Just hang on a few minutes! Once I have solved this mystery, I will go back in time and fix this text and explain.

Have a nice weekend and do not forget to send your paper to the
Special Issue on Computational Structures and Methods with Memristive Devices and Systems in the Elsevier Microelectronics journal. If you miss the March 3, 2014, deadline, just go back in time and submit anyway.

## 4 thoughts on “Time travel with memristors”

1. Using P=F.v gives a force of 30.25×10^6 N to the car. The car (1000kg) would then be accelerated by ~ 3×10^4 ms-2. If you keep accelerating for nearly 3 hours (courtesy the storage capabilities of the flux capacitor), you would reach C and say hello to Einstein (t/sqrt(1-v^2/c^2)).

Also, a small correction:
the equation involving products of the terms in the mesh would be C.M =L.G

• Thanks for the correction, Prateek!

So 1.21 GW might be too little? It does not seem as if he stays in the car three hours between the time jumps… In fact, in the movie they actually say 1.21 JigaWatt. Maybe that’s more than 1.21 GW…

• According to this formulation 1.21Terawatt might be good enough to reach C within 10sec and if JigaWatt is around 10TeraWatt, then you are off within a sec.

2. Joakim