IAPS 2022-2023 jIAPS

Article of the Month – March 2023

Implications of Relativistic Effects on the Global Positioning System (GPS)

Raghav Sharma, BSc Physical Science with Electronics, University of Delhi


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.


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.

  1. 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] 

  1. 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.

  1. 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]

  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]


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.


  1. Pogge, Richard W. (2017): Real-World Relativity: The GPS Navigation System
  2. Will, Clifford M.: Einstein’s Relativity and Everyday Life
  3. Nelson, Robert A. (1999): The Global Positioning System- A National Resource
  4. Oxley, Alan (2017): Uncertainties in GPS Positioning- A Mathematical Discourse, Pages 71-80

Article of the Month IAPS 2022-2023 jIAPS

February 2023 – Another way to see the synchronization

Author: Andrea Arlette ESPAÑA-TINAJERO

Universidad Autónoma de San Luis Potosí, México

Aix-Marseille Université, France

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.

Imagen que contiene Dibujo de ingeniería

Descripción generada automáticamente
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.


  1. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization – a universal concept in nonlinear sciences, in: Cambridge Nonlinear Science Series, 2001.
  2. A. España, X. Leoncini, E. Ugalde, Combinatorics of the paths towards synchronization, 2022. doi:10.48550/ARXIV.2205.05948. URL:

Article of the Month IAPS 2022-2023 jIAPS

January 2023 – Social Physics

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

(Word limit – 1000 words. For guidance on how to write an article, see and )


Social Sciences; Let’s get… physical!

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])


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. 


  1. Madan A, Caneel R.  Pentland A”S”. Voices of Attraction. MIT Media Laboratory Technical Note 2004 Sep; No. 584. Available from:
  2. Social Phyics/ Wikipedia [Internet]. Available from 
  3. Kastalskiy AI, Pankratova VE, Mirkes ME, Kazantsev BV, Gorban NA. Social stress drives the multi-wave dynamics of COVID-19 outbreaks. Sci Rep. 2021 Nov18;11(1):22497. 
  4. MIT TEDxTalk [Intenet] Success through Social Physics Alex “Sandy”; 2014 Dec 13. Available from 

jIAPS Article of the Month

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 . 

For guidance on how to write an article, see and

The only rule is that there is a word limit of 1000 words. We are looking forward to seeing your articles.


Happy New Year 2023!

Happy New Year 2023! from jIAPS

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 – and don’t forget the jIAPS Monthly Photography Competition.

IAPS 2022-2023

Have you seen jIAPS’ Advent Calendar 2022?

jIAPS has created an online Advent Calendar, featuring contributions from Physics students from over twenty countries across five continents. Find it at:

IAPS 2022-2023

jIAPS Advent Calendar 2022

This year, we have created an online Advent Calendar, featuring contributions from Physics students from over twenty countries across five continents. We will be posting the Advent Calendar on our Instagram (@j.iaps, each day in December.

Learn about festive traditions across the globe, create Physics-themed Christmas tree decorations and listen to music played by our own international music group of Physics students. With puzzles, and recipes to try, there is something for everyone.

jIAPS also organises a monthly photography competition. During December, the theme will be photos of the Festive Season. We would love to see your photos – just email us or tag us on social media. You don’t have to be a current physics student to enter. If you would like to learn more about jIAPS, please email us at

IAPS 2022-2023

jIAPS Article Contest 2023 is now open

Do you love to write? Put your writing skills to the test for the chance to win a free place at ICPS 2023 Philippines! Your article will also be published in jIAPS 2023, the journal of IAPS. The runner-ups will receive certificates and a small prize. 

All you have to do is write a physics related article of 600-800 words. You can find more details at jIAPS Article Contest.

The Article Contest will be open for submissions until 28th February 2023.

IAPS 2022-2023

Happy 35th anniversary of IAPS

12th September 2022 is the 35th Anniversary of IAPS! Join us to continue building a larger and more inclusive community.

In 1986, four Hungarian physics students, Levai, Horváth, Budai and Van had the idea of creating an international association of physics students and in 1987, their proposal was formally accepted at the 2nd International Conference of Students of Physics (ICSP, or as it is now renamed, ICPS).

35th Anniversary Competition

How will you celebrate IAPS’ 35th Anniversary?

Will you host a party with your local Physics society or LC? Could you bake a cake or sample traditional dishes from around the world? You could do something related to the number 35 – anything from making a list of 35 Physicists to doing 35 press-ups… in this competition, any entries are accepted, whether they are simple or creative or extraordinary. You can think out-of-the-box or just say ‘happy birthday’ in your native language. Whatever you do, we would love to hear from you. Just email your entry (in any format) to . The winning entries will be featured in jIAPS 2023 (prizes and deadline TBC).

Read more about the History of IAPS in ‘Made In Hungary’ and look out for future events over the next year, to celebrate this special anniversary.

Feliz cumpleaños Gabriel

IAPS 2022-2023 News

Welcome to the new IAPS year 2022-23!

Authors:  Jeet Shannigrahi,  Harvey Sapigao, Alexia Beale

Nearly four decades ago, a group of like-minded individuals came together to form an organization for students who come from a variety of backgrounds around the world but are united by a shared love for physics. The International Association for Physics Students (IAPS) is now globally the largest organization for students of physics, regardless of age, ethnicity or economic background. IAPS has formally been accepted into IUPAP and continues to represent physics students worldwide. 

jIAPS (the Journal of IAPS) is an integral part of IAPS, expressing its ethos and goals through articles, blogs, creative entries and newsletters. Over the years, jIAPS has been led by diverse individuals; this year’s editorial team includes IAPS members from around the world (from Mexico and the Dominican Republic to India and beyond), demonstrating the inclusivity and diversity that IAPS has come to embody. jIAPS 2023 echoes this spirit with a fresh commitment to expand on the horizon of physics for students from every corner of the globe. Here are some highlights to look out for in the coming year:

  1. PLANCKS 2023 – PLANCKS is an exciting physics competition for teams of Bachelor’s and Master’s students, with guest lectures and social activities to attend too. Now is a good time to start thinking about organising a Preliminary in your country. IAPS can support you with the organisation of Preliminaries.  You may be selected to represent your country at the final of PLANCKS 2023 in Milan. 
  2. ICPS 2023 – Next summer, ICPS (the International Conference for Physics Students) will be held in Baguio and Manila, Philippines. It is the first time ICPS shall be hosted in Southeast Asia!  
  3. Article Contest and Creative Competitions – Preparations for jIAPS 2023 are underway. Watch this space for the announcement of the Article Contest and Creative Competitions with amazing IAPS Merchandise and waived entry fees to ICPS for the winning entries. 
  4. Sunday Discord Sessions – IAPS has several informal groups which meet on Sundays, usually at 1pm UTC. Come and listen, play, and discuss international music in the newly formed Music Group; try different recipes at the Cooking Day sessions; and seek support in the Mental Health Check-Ins.
  5. Coming soon: Learn more about the range of Working Groups within IAPS and how to join them.

and finally… jIAPS is always looking for more Contributors – do you want to write articles about physics or help scout for new stories? Just send us a message at to join the team.