There are lots of opportunities to get involved with jIAPS – here we would like to recognise the incredible efforts of our top contributors so far this year.
There is still chance to contribute to jIAPS, whether you would like to write an article, send a photo of an event you participated in, or help with graphic design – just email us at jiaps@iaps.info .
Congratulations to the following jIAPS Staff Members who have reached these milestones:
Author: 🇳🇵 Rabin Thapa, Dolpo Buddha Rural municipality, Dolpa
Rabin has shared his experiences of being a Science teacher in a mountainous region of Nepal with jIAPS:
After completing my Master’s degree in physics, I applied for the post of teacher of mathematics and science in Crystal Mountain School (CMS) which is located in upper Dolpa at an altitude of 4300 meters. Inside me, the answer to the question: ‘why did I apply for this professional vacancy as a late twenties Nepalese citizen , is still an unanswered conflict or chaos tumbling in a wave of thought whenever I close my eyes.
Passing through the physical interview process and orientation, I was ready for an hour flight from Kathmandu to Nepaljung, followed by two days road travel and three days uphill trek to the school. However, my plans were disrupted by a domestic flight cancellation.
Vision Dolpo, an organization managing the seven months academic terms during summer with an ambition to uplift the local literacy potential, can be highly praised. During the six days’ journey, the pressure related to finance and socio economic fluctuation was clearly visible. Meanwhile, we reached our destination on 17th April. A day’s rest was scheduled to face altitude sickness before starting regular teaching on 19th April.
Considering the harsh geographical navigation of CMS coupled with the local living standard, the encounter of limited stationary, student’s uniforms, teaching resources, regular food and IT access was inevitable. In this context, everything apart from basic requirements had to be brought from the capital, to be able to conduct regular academic activity. These supplies were transported from Dolpa’s district headquarters to the school’s location by mules and donkeys. In April, around hundred shacks of school material were on the way to our location. During dinnertime a few days after I arrived, I heard that Dolpo Buddha Rural Municipality was facing official blockage due to political turbulence, which resulted due to per-planned local elections announced by the government. Due to this blockage, whatever its cause, CMS’s administration had to face the scarcity of food for the staff. Most prominently, the 250 students who come to school here are struggling with availability of stationary, learning material, laboratory tools and uniforms. The stark reality, the real image of public education as experienced by me, is really heartbreaking. I can remember wishing that my heartache could be consoled and thinking of the passenger’s song entitled, “Survivor”.
After a long wait of three months, the supplies, including the stationary for the students, finally arrived. However, the staff, along with the administration team, had to overcome the challenge of continuing regular academic activities with limited resources. At a general meeting, I was assigned to initiate the lead in STEAM activities and upgrade the science laboratory. Selecting extracurricular projects was pivotal because I found that very few students in the school were interested in classical or analog projects. Consequently, to motivate interest in modern science and technology, we established a ‘Makers’ Club’. The annual projects selected were: the construction and installation of electric bell, execution of robotics design and designing a smart dustbin. Fifteen students initially enrolled in the ‘Makers’ Club’. In the ‘Maker’s Space’, we came to a mutual agreement with the students that all the members had to contribute two hours to the club every day after their regular class.
These two hours of the school day are the most precious time for the students. They can explore a variety of engineering tools, through regular workshops where they are instructed in practical electronics, magnetism, wiring, working principle of switches, AC, DC, transformers, software coding, hardware and basic design principles, to name a few activities. Sometimes, the students became so enthused by their projects that we used to work for hours, even without sleeping. When all our annual projects were accomplished, after four months of hard work, we showed our finished products to the other students and we were able to attract more students to join the ‘Makers’ Club’. Now, at the altitude of 4100 m, in a remote mountainous region of Nepal, we have a self-made electric bell in operation; an inter-house robotic battle; and smart dustbins with software and hardware developed by the students. In our corner of the world, we are introducing modern science and technology to children in their regular learning environment, in a region where these scientific advances were unknown.
Implications of Relativistic Effects on the Global Positioning System (GPS)
Raghav Sharma, BSc Physical Science with Electronics, University of Delhi
Abstract
Relativity has no obvious consequences in daily life, but one close look at the working of a GPS device is sufficient to highlight the enormous implications of relativistic effects on situations where velocity, gravity, and accuracy are involved. Clocks on a moving satellite do not appear to tick at the same intervals as clocks on Earth. This is especially problematic in high-accuracy systems like the GPS. Understanding the mathematical principles behind these effects allows for a derivation of precise offset values- adjustments that need to be made to satellite clocks to correct any time difference caused by relativity.
Introduction
The Global Positioning System (GPS) is a highly accurate, satellite-based positioning and navigation system.[1] To maintain that accuracy, time-dilating relativistic effects arising from both the general and special theory of relativity need to be taken into account. This is achieved by adjusting the rates of onboard satellite clocks and incorporating mathematical corrections. This article explores time dilation effects on GPS and describes some calculations and adjustments that are made to account for them. The correction for special relativistic time dilation is derived in detail.
An Overview of Time-Dilation Effects
A handheld GPS receiver can determine the absolute position on the surface of the Earth to within 5 to 10 metres.[1] Achieving a navigational accuracy of 5 metres requires knowing the onboard GPS satellite time to an accuracy of about 17 nanoseconds, which is the time taken by light to travel 5 metres. Because satellites are constantly moving with respect to the Earth-centred (approximately inertial) frame and are further away from the Earth’s gravitational well, one must consider time dilation caused by both special and general relativistic effects. If these effects were left uncompensated, navigational errors would accumulate at a rate in excess of 10 kilometres per day, rendering the system unusable within about 2 minutes.[2]
Special Relativity
GPS Satellites are not geosynchronous because that would limit coverage. They have a time period of about 12 hours (so that any satellite passes over the same location each day) and a corresponding orbital velocity of about 3874 m/s relative to the centre of the Earth.[3]
According to the Special Theory of Relativity, moving clocks run slower.[2] The time dilation amount is determined by Lorentz transformations. The time measured on-board the satellite is reduced by the Lorentz factor γ:
where τ_{Ground} and τ_{GPS} are time intervals measured on the Earth’s surface and by the satellite clock, respectively.
The derivation of the time by which satellite clocks lag behind surface clocks, Δτ, is given below:
Using binomial expansion for small values of (v/c):
Taking v=3874 m/s and c=2.998×108m/s:
For a time-interval of 1 day (86,400s) on the Earth’s surface:
Therefore, GPS clocks lose about 7μs a day due to special relativistic time dilation.
General Relativity
GPS satellites have an orbital altitude of 20,184 km measured from the surface.[3] According to the General Theory of Relativity, a clock in a gravitational field runs slower. This effect is given by:
Where τ_0 is the time interval measured near a mass (i.e., in a gravitational well), and is the time interval measured far away from the mass.
For small values of (M/r):
The clocks on the Earth’s surface are a distance of R_Earth=6378.1 km from the gravitational centre, so the time dilation with respect to GPS satellites is twofold. It is stated without proof that due to general relativistic time dilation effects, clocks onboard the satellites gain about 45μs per day, with respect to ground-based clocks.[1]
Error Correction
The combination of general and special relativistic time dilation means that GPS clocks gain about 38μs a day. As stated before, the desired accuracy can be as high as 17 nanoseconds. Thus, it is crucial to correct any time difference.
A time offset of 38μs corresponds with a fractional change of +4.465×10^-10, i.e. the satellite clocks need to be slowed down by this fraction. The fundamental L-band frequency produced by the atomic clocks on-board is 10.23 MHz. This needs to be offset by the aforementioned fraction. Therefore, the actual frequency of the GPS clocks is set to 10.22999999543 MHz before launch.[3-4]
The variation in these changes due to the eccentricity (deviation from circularity) of the satellite orbit also needs to be taken care of. Built-in microcomputers used in GPS receivers help in any additional timing calculations required using satellite-provided data.[1]
Conclusion
Relativity dictates that clocks aboard GPS satellites do not tick at the same rate as those on the Earth. Both general and special relativistic time dilation effects are at play. Neglecting to adjust for these would render GPS useless in a few minutes. Correcting them involves giving the onboard atomic clocks a slight offset in frequency, so that they may appear to run at the same rate as ground-based clocks. This correction is one of many needed to maintain a navigational accuracy of up to a few metres.
References:
Pogge, Richard W. (2017): Real-World Relativity: The GPS Navigation System
Will, Clifford M.: Einstein’s Relativity and Everyday Life
Nelson, Robert A. (1999): The Global Positioning System- A National Resource
Oxley, Alan (2017): Uncertainties in GPS Positioning- A Mathematical Discourse, Pages 71-80
When talking about the synchronization phenomenon, the most common thing is to think of biological events where it is possible to observe it with our own eyes, for example, when dozens of birds fly in the sky and form various patterns with choreographies that seem very well rehearsed. Also, some types of fish exhibit this type of behavior when swimming; it seems that they do it harmoniously and without colliding with each other [1].
In our case, we will think of the synchronization phenomenon in the following way: it will be a process in which a set of agents interacts, and by allowing a long enough period to pass, then all of them will have the same state, which we will call synchronized state. In the bird example, the synchronized state might be that they are all flying north, and in the fish example, that they are all swimming south.
With this concept of synchronization that has just been defined, we can now think of another type of phenomenon, in particular, the following: consider an empty, impermeable box, without a lid (to be able to observe what happens inside), in which we will pour a liquid (none in particular, we can think of water or oil), with a volume large enough to cover the entire surface of the box. Intuition tells us that when we finish pouring the liquid, each unit of surface area of the box will be the basis of the same volume of liquid. This would be the synchronized state, and this process is more commonly called diffusion.
Figure One: Impermeable box, with markings on each area unit. Drops of different sizes and the place where the liquid is poured are shown, as well as the circular neighbourhood formed by pouring the liquid into the box.
The way in which the liquid fills the box is not a very surprising mechanism; that is, if the liquid begins to pour at a point, then a circular neighborhood around that point is expected to fill uniformly at the same time, until the entire area of the box is covered, and then, we will see how its volume increases, until the liquid runs out.
On the other hand, what happens if the box is not initially empty? Suppose that on the surface of the box there are drops of different volumes, and the liquid begins to pour at a point where there is no drop. Diffusion occurs as in the case of the empty box, but when the liquid interacts with a drop, then the circular neighborhood changes its shape to become a kind of deformed number 8, and so on with the drops that it finds in its path. What happens is a kind of agglutination phenomenon, that is, how one drop sticks to another, just before the area of the box fills up and begins to increase in volume until the liquid runs out.
So, for the case where there are drops, how could we describe the way the box is filled? First, we can identify that this phenomenon depends on some factors, the first, how many drops there are in the box at the beginning and what volume each of them has. You can even think of the effect if the box is not square or has holes inside it (without considering liquid losses, each of the holes would have a barrier that would prevent liquid loss).
Despite these new obstacles, the ways in which the synchronized state is reached are accurately described using mathematics, thanks to a new combinatorial approach. In this approach, the configurations of the droplets are encoded together with their volume and the total volume of the liquid. In this way, its route towards synchronization is fully determined [2].
The kind of mathematical objects that are used to describe and code the paths to synchronization are very simple to understand. They are called discrete increasing functions that go above the diagonal and below the constant. They take a list of length N, considering that in each place a number greater than or equal to the one on the left and less than the one on the right is placed. For example, when N=5, the diagonal is (1,2,3,4,5), the constant is (5,5,5,5,5) and two functions between them would be (2,2,3,4,5) and (2,2,4,4,5). These mathematical objects have been extensively studied; multiple characteristics and properties of them are known.
In physics, knowing how to use the tools provided by mathematics, which usually focus on calculus, differential equations, probability, and statistics, have allowed us to solve many problems in an elegant, useful, and educational way. In this case, using combinatorial and number theory tools allowed us to make an exact description of what happens before reaching synchronization, which in turn is a widely observed and studied phenomenon. No tool is left over, one day it could help us to graduate with a doctorate.
References:
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization – a universal concept in nonlinear sciences, in: Cambridge Nonlinear Science Series, 2001.
A. España, X. Leoncini, E. Ugalde, Combinatorics of the paths towards synchronization, 2022. doi:10.48550/ARXIV.2205.05948. URL: https://arxiv.org/abs/2205.05948
Author: Aikaterini Nikou, University of Edinburgh, UK
Happy New Year! This is the first article in an exciting new series. Every month we hope to showcase a scientific article written by an undergraduate or postgraduate physics student. Is there a topic you would like to write about? Just email your article to jiaps@iaps.info .
In the orbits of stars, in particle collisions, in chemical reactions, in vehicles’ machines… physics is everywhere. Notoriously, physics is also in human behaviours, human interactions, and social dynamics. Have you ever considered how elegantly physics could describe social phenomena?
Figure 1: Human behaviour forms patterns that can be described by mathematical models just like the laws of physics (from pixabay)
There is a particularly graceful beauty in the notion that social phenomena could be modelled, explained, analysed and predicted using mathematics in a way similar to physical phenomena. This could have a great spectrum of applications including economy (econophysics), pedagogy, tackling pandemics or even… dating. Social physics experiments conducted in the MIT media laboratory have investigated dating and found that it is possible to predict the outcome merely by analysing non-linguistic social signals such as the tone of voice [1]. A similar view could be used to analyse and predict other societal aspects including negotiating.
Social physics is a revolutionising topic in science; however, studying social phenomena through a scientific scope has existed for centuries. The English philosopher Thomas Hobbes mentioned this concept before the term Social Physics or Sociophysics was coined for the first time. He expressed the notion that social phenomena could be represented in terms of the laws of motion of physics and therefore explained through the lens of physics. In his book “De Corpore” (“On the Body”), he described the idea that the behaviour of “material bodies” can be expressed mathematically through the laws of motion invented by Galileo [2]. It seems almost natural to stop for a second and admire the beautiful diachronism of physics, as well as its interdisciplinarity in examining society from a scientific point of view.
Figure 2: Venn diagram showing the interdisciplinary of Social Physics, and its relationship with Physics, Mathematics, Social Science and Computer Science
Social Physics in Today’s Society
We live in a society where data collection is easier than ever, while there is a great number of datasets that are incredibly large and complex to analyse. Such datasets could be phone call records, web activity and credit card transactions. These datasets hold in their arms mathematical patterns that could reveal behavioural changes and patterns. Social physics can… deal with all – the so called “big-data”. It is a powerful tool that could be used for the blooming of our society. Evidently, data science is at the heart of social physics. Wonderfully, it can also help tackle world issues like the Covid-19 pandemic. A study showed that the multi-wave dynamics of Covid-19 outbreaks was dependent on the differences in responses to social stress [3].
A great benefit of social physics is that big data and exact mathematical tools can be applied in order to, in great accuracy, reflect on human behaviour as well as changes in it. It allows us to notice behavioural patterns and to therefore predict future social trends. These trends could include purchase preferences, shopping behaviour, communication behaviour, mobility or even Covid-19 cases spikes. These can then help us come up with more efficient plans to tackle climate change or urban development and traffic. It is worth noting that we could also observe and mathematically model connections between innovation and patterns of habits and communication which could greatly benefit the evolution of society. In other words, social physics can provide us with a way to more profoundly and accurately understand the mechanism of change of society. This could signal the birth of a new and innovative theory for society.
Social Physics and Machine Learning?
A question worth addressing is whether this analysis could be achieved using machine learning. Machine learning is a great tool for analysing mechanical and physical-driven data. For example, it can be invaluable in monitoring oil drill pumps control data and helping engineers prevent a possible malfunction. What about analysing financial transactions and therefore predicting customers’ preferences? Which type of customer would opt for a specific service for example? Social physics can help here as an appropriate tool for analysing human behaviour data.
Social Physics and human development
Moreover, social physics can also help in furthering our understanding of human development processes. Social physics has revealed a connection between the communication of a child and its brain development. The level of engagement (communication with people close to them such as parents or caretakers, inside of the red circle as seen in Fig.3) greatly affects the brain development of a child. Children that have a higher level of engagement and exploration (communication with people not in their close circle) have more developed brains and these children become more successful [4].
Figure 3: Patterns of Success. The inner of the red circle includes the “engagement”, anything outside comprises the “exploration” (from [4])
Conclusion
Recently, more and more social and societal phenomena are being studied through the lens of physics and mathematics. This interdisciplinary of social physics is particularly powerful. A great number of social physics studies have been conducted bringing to the surface revolutionising ideas, and so many more have yet to be conducted by the next generation of social physicists that could contribute to the blooming of our society.
Introducing the jIAPS Article of the Month, a new feature of jIAPS for 2023:
Every month we will showcase a scientific article written by an undergraduate or postgraduate physics student. Read the first article in this new series here. Is there a topic you would like to write about? Just email jiaps@iaps.info .
The IAPS Music Group has recorded a new song to celebrate the holiday season – check it out here.
What will 2023 bring? What will you contribute to jIAPS in 2023?
The jIAPS Advent Calendar is still going for the next few days. Today’s post includes Juan Ignacio Iribarren’s description of a traditional Christmas or New Year in Argentina – read more here.
There are lots of opportunities for you to be a part of jIAPS in 2023. The Article Contest and Creative Contest are now open with amazing prizes to be won. We’re always looking for Physics-related news stories too – just email us at jiaps@iaps.info – and don’t forget the jIAPS Monthly Photography Competition.
In the company of the reports from your favorite past, present and future events (to the Philippines, ICPS 2023!), you’ll also read some unusual and unique articles. Among them, an enticing interview with a new member of IAPS, a call for action to resolve long-standing problems in academia, and a detailed review of an extraordinary general meeting. It probably doesn’t get more interesting than a comic strip involving physics students, can you find it?
As the ICPS 2022 comes closer, so does the jIAPS 2022 edition. As it is already traditional, there will be jIAPS contests open for student submissions. Besides having their submissions published in jIAPS, the winners will also receive IAPS merch as a special prize!
We have two contests this year, about which you can read more on their respective pages:
Along with the Worldwide Grant, there is another opportunity for attending the ICPS for free while developing your scientific work skills: the jIAPS Article Contest.
The contest is a great opportunity to write about any Physics-related topic you like and have your article published in jIAPS, the IAPS journal!
