Waseem completed his DPhil in physics at the University of Oxford in the UK, where he worked on applied process-relational philosophy and employed string diagrams to study interpretations of quantum theory, constructor theory, wave-based logic, quantum computing and natural language processing. At Oxford, Waseem continues to teach mathematics and physics at Magdalen College, the Mathematical Institute, and the Department of Computer Science.
Waseem has played a key role in organizing the Lahore Science Mela, the largest annual science festival in Pakistan. He also co-founded Spectra, an online magazine dedicated to training popular-science writers in Pakistan. For his work popularizing science he received the 2021 Diana Award, was highly commended at the 2021 SEPnet Public Engagement Awards, and won an impact award in 2024 from Oxford’s Mathematical, Physical and Life Sciences (MPLS) division.
What skills do you use every day in your job?
I’m a theoretical physicist, so if you’re thinking about what I do every day, I use chalk and a blackboard, and maybe a pen and paper. However, for theoretical physics, I believe the most important skill is creativity, and the ability to dream and imagine.
What do you like best and least about your job?
That’s a difficult one because I’ve only been in this job for a few weeks. What I like about my job is the academic freedom and the opportunity to work on both education and research. My role is divided 50/50, so 50% of the time I’m thinking about the structure of natural languages like English and Urdu, and how to use quantum computers for natural language processing. The other half is spent using our diagrammatic formalism called “quantum picturalism” to make quantum physics accessible to everyone in the world. So, I think that’s the best part. On the other hand, when you have a lot of smart people together in the same room or building, there can be interpersonal issues. So, the worst part of my job is dealing with those conflicts.
What do you know today, that you wish you knew when you were starting out in your career?
It’s a cynical view, but I think scientists are not always very rational or fair in their dealings with other people and their work. If I could go back and give myself one piece of advice, it would be that sometimes even rational and smart people make naive mistakes. It’s good to recognize that, at the end of the day, we are all human.
Last year the UK government placed a new cap of £9535 on annual tuition fees, a figure that will likely rise in the coming years as universities tackle a funding crisis. Indeed, shortfalls are already affecting institutions, with some saying they will run out of money in the next few years. The past couple of months alone have seen several universities announce plans to shed academic staff and even shut departments.
Whether you agree with tuition fees or not, the fact is that students will continue to pay a significant sum for a university education. Value for money is part of the university proposition and lecturers can play a role by conveying the excitement of their chosen field. But what are the key requirements to help do so? In the late 1990s we carried out a study aimed at improving the long-term performance of students who initially struggled with university-level physics.
With funding from the Higher Education Funding Council for Wales, the study involved structured interviews with 28 students and 17 staff. An internal report – The Rough Guide to Lecturing – was written which, while not published, informed the teaching strategy of Cardiff University’s physics department for the next quarter of a century.
From the findings we concluded that lecture courses can be significantly enhanced by simply focusing on three principles, which we dub the three “E”s. The first “E” is enthusiasm. If a lecturer appears bored with the subject – perhaps they have given the same course for many years – why should their students be interested? This might sound obvious, but a bit of reading, or examining the latest research, can do wonders to freshen up a lecture that has been given many times before.
For both old and new courses it is usually possible to highlight at least one research current paper in a semester’s lectures. Students are not going to understand all of the paper, but that is not the point – it is the sharing in contemporary progress that will elicit excitement. Commenting on a nifty experiment in the work, or the elegance of the theory, can help to inspire both teacher and student.
As well as freshening up the lecture course’s content, another tip is to mention the wider context of the subject being taught, perhaps by mentioning its history or possible exciting applications. Be inventive –we have evidence of a lecturer “live” translating parts of Louis de Broglie’s classic 1925 paper “La relation du quantum et la relativité” during a lecture. It may seem unlikely, but the students responded rather well to that.
Supporting students
The second “E” is engagement. The role of the lecturer as a guide is obvious, but it should also be emphasized that the learner’s desire is to share the lecturer’s passion for, and mastery of, a subject. Styles of lecturing and visual aids can vary greatly between people, but the important thing is to keep students thinking.
Don’t succumb to the apocryphal definition of a lecture as only a means of transferring the lecturer’s notes to the student’s pad without first passing through the minds of either person. In our study, when the students were asked “What do you expect from a lecture?”, they responded simply to learn something new, but we might extend this to a desire to learn how to do something new.
Simple demonstrations can be effective for engagement. Large foam dice, for example, can illustrate the non-commutation of 3D rotations. Fidget-spinners in the hands of students can help explain the vector nature of angular momentum. Lecturers should also ask rhetorical questions that make students think, but do not expect or demand answers, particularly in large classes.
More importantly, if a student asks a question, never insult them – there is no such thing as a “stupid” question. After all, what may seem a trivial point could eliminate a major conceptual block for them. If you cannot answer a technical query, admit it and say you will find out for next time – but make sure you do. Indeed, seeing that the lecturer has to work at the subject too can be very encouraging for students.
The final “E” is enablement. Make sure that students have access to supporting material. This could be additional notes; a carefully curated reading list of papers and books; or sets of suitable interesting problems with hints for solutions, worked examples they can follow, and previous exam papers. Explain what amount of self-study will be needed if they are going to benefit from the course.
Have clear and accessible statements concerning the course content and learning outcomes – in particular, what students will be expected to be able to do as a result of their learning. In our study, the general feeling was that a limited amount of continuous assessment (10–20% of the total lecture course mark) encourages both participation and overall achievement, provided students are given good feedback to help them improve.
Next time you are planning to teach a new course, or looking through those decades-old notes, remember enthusiasm, engagement and enablement. It’s not rocket science, but it will certainly help the students learn it.
Sometimes, you just have to follow your instincts and let serendipity take care of the rest.
North Ronaldsay, a remote island north of mainland Orkney, has a population of about 50 and a lot of sheep. In the early 19th century, it thrived on the kelp ash industry, producing sodium carbonate (soda ash), potassium salts and iodine for soap and glass making.
But when cheaper alternatives became available, the island turned to its unique breed of seaweed-eating sheep. In 1832 islanders built a 12-mile-long dry stone wall around the island to keep the sheep on the shore, preserving inland pasture for crops.
My connection with North Ronaldsay began last summer when my partner, Sue Bowler, and I volunteered for the island’s Sheep Festival, where teams of like minded people rebuild sections of the crumbling wall. That experience made us all the more excited when we learned that North Ronaldsay also had a science festival.
This year’s event took place on 14–16 March and getting there was no small undertaking. From our base in Leeds, the journey involved a 500-mile drive to a ferry, a crossing to Orkney mainland, and finally, a flight in a light aircraft. With just 50 inhabitants, we had no idea how many people would turn up but instinct told us it was worth the trip.
Sue, who works for the Royal Astronomical Society (RAS), presented Back to the Moon, while together we ran hands-on maker activities, a geology walk and a trip to the lighthouse, where we explored light beams and Fresnel lenses.
The Yorkshire Branch of the Institute of Physics (IOP) provided laser-cut hoist kits to demonstrate levers and concepts like mechanical advantage, while the RAS shared Connecting the Dots – a modern LED circuit version of a Victorian after-dinner card set illustrating constellations.
Hands-on science Participants get stuck into maker activities at the festival. (Courtesy: @Lazy.Photon on Instagram)
Despite the island’s small size, the festival drew attendees from neighbouring islands, with 56 people participating in person and another 41 joining online. Across multiple events, the total accumulated attendance reached 314.
One thing I’ve always believed in science communication is to listen to your audience and never make assumptions. Orkney has a rich history of radio and maritime communications, shaped in part by the strategic importance of Scapa Flow during the Second World War.
Stars in their eyes Making a constellation board at the North Ronaldsay Science Festival. (Courtesy: @Lazy.Photon on Instagram)
The Orkney Wireless Museum is a testament to this legacy, and one of our festival guests had even reconstructed a working 1930s Baird television receiver for the museum.
Leaving North Ronaldsay was hard. The festival sparked fascinating conversations, and I hope we inspired a few young minds to explore physics and astronomy.
The author would like to thanks Alexandra Wright (festival organizer), Lucinda Offer (education, outreach and events officer at the RAS) and Sue Bowler (editor of Astronomy & Geophysics)
Working with “student LEGO enthusiasts”, they have developed a fully functional LEGO interferometer kit that consists of lasers, mirrors, beamsplitters and, of course, some LEGO bricks.
The set, designed as a teaching aid for secondary-school pupils and older, is aimed at making quantum science more accessible and engaging as well as demonstrating the basic principles of interferometry such as interference patterns.
“Developing this project made me realise just how incredibly similar my work as a quantum scientist is to the hands-on creativity of building with LEGO,” notes Nottingham quantum physicist Patrik Svancara. “It’s an absolute thrill to show the public that cutting-edge research isn’t just complex equations. It’s so much more about curiosity, problem-solving, and gradually bringing ideas to life, brick by brick!”
A team at Cardiff University will now work on the design and develop materials that can be used to train science teachers with the hope that the sets will eventually be made available throughout the UK.
“We are sharing our experiences, LEGO interferometer blueprints, and instruction manuals across various online platforms to ensure our activities have a lasting impact and reach their full potential,” adds Svancara.
If you want to see the LEGO interferometer in action for yourself then it is being showcased at the Cosmic Titans: Art, Science, and the Quantum Universe exhibition at Nottingham’s Djanogly Art Gallery, which runs until 27 April.
Imagine you have been transported to another universe with four spatial dimensions. What would the colour of the Sun be in this four-dimensional universe? You may assume that the surface temperature of the Sun is the same as in our universe and is approximately T = 6 × 103 K. [10 marks]
Boltzmann constant, kB = 1.38 × 10−23 J K−1
Speed of light, c = 3 × 108 m s−1
Solution
Black body radiation, spectral density: ε (ν) dν = hνρ (ν) n (ν)
The photon energy, E = hν where h is Planck’s constant and ν is the photon frequency.
The density of states, ρ (ν) = Aνn−1 where A is a constant independent of the frequency and the frequency term is the scaling of surface area of an n-dimensional sphere.
The Bose–Einstein distribution,
n(v)
where k is the Boltzmann constant and T is the temperature.
We let
and get
ε(x)
We do not need the constant of proportionality (which is not simple to calculate in 4D) to find the maximum of ε (x). Working out the constant just tells us how tall the peak is, but we are interested in where the peak is, not the total radiation.
We set this equal to zero for the maximum of the distribution,
This yields x = n (1 − e−x) where
and we can relate
and c being the speed of light.
This equation has the solution x = n +W (−ne−n) where W is the Lambert W function z = W (y) that solves zez = y (although there is a subtlety about which branch of the function). This is kind of useless to do anything with, though. One can numerically solve this equation using bisection/Newton–Raphson/iteration. Alternatively, one could notice that as the number of dimensions increases, e−x is small, so to leading approximation x ≈ n. One can do a little better iterating this, x ≈ n − ne−n which is what we will use. Note the second iteration yields
Number of dimensions, n
Numerical solution
Approximation
2
1.594
1.729
3
2.821
2.851
4 (the one we want)
3.921
3.927
5
4.965
4.966
6
5.985
5.985
Using the result above,
616 nm is middle of the spectrum, so it will look white with a green-blue tint. Note, we have used T = 6000 K for the temperature here, as given in the question.
It would also be valid to look at ε (λ) dλ instead of ε (ν) dν.
Question 2: Heavy stuff
In a parallel universe, two point masses, each of 1 kg, start at rest a distance of 1 m apart. The only force on them is their mutual gravitational attraction, F = –Gm1m2/r2. If it takes 26 hours and 42 minutes for the two masses to meet in the middle, calculate the value of the gravitational constant G in this universe. [10 marks]
Solution
First we will set up the equations of motion for our system. We will set one mass to be at position −x and the other to be at x, so the masses are at a distance of 2x from each other. Starting from Newton’s law of gravity:
we can then use Newton’s second law to rewrite the LHS,
which we can simplify to
It is important that you get the right factor here depending on your choice for the particle coordinates at the start. Note there are other methods of getting this point, e.g. reduced mass.
We can now solve the second order ODE above. We will not show the whole process here but present the starting point and key results. We can write the acceleration in terms of the velocity. The initial velocity is zero and the initial position
So,
and once the integrals are solved we can rearrange for the velocity,
Now we can form an expression for the total time taken for the masses to meet in the middle,
There are quite a few steps involved in solving this integral, for these solutions, we shall make use of the following (but do attempt to solve it for yourselves in full).
Hence,
We can now rearrange for G and substitute in the values given in the question, don’t forget to convert the time into seconds.
This is the generally accepted value for the gravitational constant of our universe as well.
Question 3: Just like clockwork
Consider a pendulum clock that is accurate on the Earth’s surface. Figure 1 shows a simplified view of this mechanism.
1 Tick tock Simplified schematic of a pendulum clock mechanism. When the pendulum swings one way (a), the escapement releases the gear attached to the hanging mass and allows it to fall. When the pendulum swings the other way (b) the escapement stops the gear attached to the mass moving so the mass stays in place. (Courtesy: Katherine Skipper/IOP Publishing)
A pendulum clock runs on the gravitational potential energy from a hanging mass (1). The other components of the clock mechanism regulate the speed at which the mass falls so that it releases its gravitational potential energy over the course of a day. This is achieved using a swinging pendulum of length l (2), whose period is given by
where g is the acceleration due to gravity.
Each time the pendulum swings, it rocks a mechanism called an “escapement” (3). When the escapement moves, the gear attached to the mass (4) is released. The mass falls freely until the pendulum swings back and the escapement catches the gear again. The motion of the falling mass transfers energy to the escapement, which gives a “kick” to the pendulum that keeps it moving throughout the day.
Radius of the Earth, R = 6.3781 × 106 m
Period of one Earth day, τ0 = 8.64 × 104 s
How slow will the clock be over the course of a day if it is lifted to the hundredth floor of a skyscraper? Assume the height of each storey is 3 m. [4 marks]
Solution
We will write the period of oscillation of the pendulum at the surface of the Earth to be
.
At a height h above the surface of the Earth the period of oscillation will be
,
where g0 and gh are the acceleration due to gravity at the surface of the Earth and a height h above it respectively.
We can define τ0 to be the total duration of the day which is 8.64 × 104 seconds and equal to N complete oscillations of the pendulum at the surface. The lag is then τh which will equal N times the difference in one period of the two clocks, τh = NΔT, where ΔT = (Th − T0). We can now take a ratio of the lag over the day and the total duration of the day:
Then by substituting in the expressions we have for the period of a pendulum at the surface and height h we can write this in terms of the gravitational constant,
[Award 1 mark for finding the ratio of the lag over the day and the total period of the day.]
The acceleration due to gravity at the Earth’s surface is
where G is the universal gravitational constant, M is the mass of the Earth and R is the radius of the Earth. At an altitude h, it will be
[Award 1 mark for finding the expression for the acceleration due to gravity at height h.]
Substituting into our expression for the lag, we get:
This simplifies to an expression for the lag over a day. We can then substitute in the given values to find,
[Award 2 marks for completing the simplification of the ratio and finding the lag to be ≈ 4 s.]
Question 4: Quantum stick
Imagine an infinitely thin stick of length 1 m and mass 1 kg that is balanced on its end. Classically this is an unstable equilibrium, although the stick will stay there forever if it is perfectly balanced. However, in quantum mechanics there is no such thing as perfectly balanced due to the uncertainty principle – you cannot have the stick perfectly upright and not moving at the same time. One could argue that the quantum mechanical effects of the uncertainty principle on the system are overpowered by others, such as air molecules and photons hitting it or the thermal excitation of the stick. Therefore, to investigate we would need ideal conditions such as a dark vacuum, and cooling to a few millikelvins, so the stick is in its ground state.
Moment of inertia for a rod,
where m is the mass and l is the length.
Uncertainty principle,
There are several possible approximations and simplifications you could make in solving this problem, including:
sinθ ≈ θ for small θ
and
Calculate the maximum time it would take such a stick to fall over and hit the ground if it is placed in a state compatible with the uncertainty principle. Assume that you are on the Earth’s surface. [10 marks]
Hint: Consider the two possible initial conditions that arise from the uncertainty principle.
Solution
We can imagine this as an inverted pendulum, with gravity acting from the centre of mass and at an angle θ from the unstable equilibrium point.
[Award 1 mark for a suitable diagram of the system.]
We must now find the equations of motion of the system. For this we can use Newton’s second law in its rotational form τ = Iα (torque = moment of inertia × angular acceleration). We have another equation for torque we can use as well
where r is the distance from the pivot to the centre of mass and F is the force, which in this case is gravity mg. We can then equate these giving
Substituting in the given moment of inertia of the stick and that the angular acceleration
We can cancel a few things and rearrange to get a differential equation of the form:
we then can take the small angle approximation sin θ ≈ θ, resulting in
[Award 2 marks for finding the equation of motion for the system and using the small angle approximation.]
Solve with ansatz of θ = Aeωt + Be−ωt, where we have chosen
We can clearly see that this will satisfy the differential equation
Now we can apply initial conditions to find A and B, by looking at the two cases from the uncertainty principle
Case 1: The stick is at an angle but not moving
At t = 0, θ = Δθ
θ = Δθ = A + B
At t = 0,
, A=B
This implies Δθ = 2A and we can then find
So we can now write
or
Case 2: The stick is at upright but moving
At t = 0, θ = 0
This condition gives us A = −B.
At t = 0,
This initial condition has come from the relationship between the tangential velocity, Δv which equals the distance to the centre of mass from the pivot point, and the angular velocity . Using the above initial condition gives us where
We can now write
[Award 4 marks for finding the two expressions for θ by using the two cases of the uncertainty principle.]
Now there are a few ways we can finish off this problem, we shall look at three different ways. In each case when the stick has fallen on the ground .
Method 1
Take and , use then rearrange for tf in both cases. We have
Look at the expression for cosh−1x and sinh−1x given in the question. They are almost identical, we can then approximate the two arguments to each other and we find,
we can then substitute in the uncertainty principle as and then write an expression of , which we can put back into our arccosh expression (or do it for Δv and put into arcsinh).
where and .
Method 2
In this next method, when you get to the inverse hyperbolic functions, you can take an expansion of their natural log forms in the tending to infinity limit. To first order both functions give ln 2x, we can then equate the arguments and find Δx or Δv in terms of the other and use the uncertainty principle. This would give the time taken as,
where and .
Method 3
Rather than using hyperbolic functions, you could do something like above and do an expansion of the exponentials in the two expressions for tf or we could make life even easier and do the following.
Disregard the e−ωt terms as they will be much smaller than the eωt terms. Equate the two expressions for and then take the natural logs, once again arriving at an expression of
where and .
This method efficiently sets B = 0 when applying the initial conditions.
[Award 2 marks for reaching an expression for t using one of the methods above or a suitable alternative that gives the correct units for time.]
Then, by using one of the expressions above for time, substitute in the values and find that t = 10.58 seconds.
[Award 1 mark for finding the correct time value of t = 10.58 seconds.]
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Several years ago I was sitting at the back of a classroom supporting a newly qualified science teacher. The lesson was going well, a pretty standard class on Hooke’s law, when a student leaned over to me and asked “Why are we doing this? What’s the point?”.
Having taught myself, this was a question I had been asked many times before. I suspect that when I was a teacher, I went for the knee-jerk “it’s useful if you want to be an engineer” response, or something similar. This isn’t a very satisfying answer, but I never really had the time to formulate a real justification for studying Hooke’s law, or physics in general for that matter.
Who is the physics curriculum designed for? Should it be designed for the small number of students who will pursue the subject, or subjects allied to it, at the post-16 and post-18 level? Or should we be reflecting on the needs of the overwhelming majority who will never use most of the curriculum content again? Only about 10% of students pursue physics or physics-rich subjects post-16 in England, and at degree level, only around 4000 students graduate with physics degrees in the UK each year.
One argument often levelled at me is that learning this is “useful”, to which I retort – in a similar vein to the student from the first paragraph – “In what way?” In the 40 years or so since first learning Hooke’s law, I can’t remember ever explicitly using it in my everyday life, despite being a physicist. Whenever I give a talk on this subject, someone often pipes up with a tenuous example, but I suspect they are in the minority. An audience member once said they consider the elastic behaviour of wire when hanging pictures, but I suspect that many thousands of pictures have been successfully hung with no recourse to F = –kx.
Hooke’s law is incredibly important in engineering but, again, most students will not become engineers or rely on a knowledge of the properties of springs, unless they get themselves a job in a mattress factory.
From a personal perspective, Hooke’s law fascinates me. I find it remarkable that we can see the macroscopic properties of materials being governed by microscopic interactions and that this can be expressed in a simple linear form. There is no utilitarianism in this, simply awe, wonder and aesthetics. I would always share this “joy of physics” with my students, and it was incredibly rewarding when this was reciprocated. But for many, if not most, my personal perspective was largely irrelevant, and they knew that the curriculum content would not directly support them in their future careers.
At this point, I should declare my position – I don’t think we should take Hooke’s law, or physics, off the curriculum, but my reason is not the one often given to students.
A series of lessons on Hooke’s law is likely to include: experimental design; setting up and using equipment; collecting numerical data using a range of devices; recording and presenting data, including graphs; interpreting data; modelling data and testing theories; devising evidence-based explanations; communicating ideas; evaluating procedures; critically appraising data; collaborating with others; and working safely.
Science education must be about preparing young people to be active and critical members of a democracy, equipped with the skills and confidence to engage with complex arguments that will shape their lives. For most students, this is the most valuable lesson they will take away from Hooke’s law. We should encourage students to find our subject fascinating and relevant, and in doing so make them receptive to the acquisition of scientific knowledge throughout their lives.
At a time when pressures on the education system are greater than ever, we must be able to articulate and justify our position within a crowded curriculum. I don’t believe that students should simply accept that they should learn something because it is on a specification. But they do deserve a coherent reason that relates to their lives and their careers. As science educators, we owe it to our students to have an authentic justification for what we are asking them to do. As physicists, even those who don’t have to field tricky questions from bored teenagers, I think it’s worthwhile for all of us to ask ourselves how we would answer the question “What is the point of this?”.