Imagine the Earth were to shrink to the size of a marble. We might be in trouble, but the planet would continue its smooth course around the Sun while the Moon would maintain its orbit, circling Earth once a month. Isaac Newton proved that the Earth’s gravitational pull would be the same even if all … Continue reading The Future of Physics may be Surreal
Tag: Physics
Quantum Physics, a Century Old, still Passes Understanding
This is the International Year of the Quantum, celebrating quantum science and its many applications. This year marks the centenary of Werner Heisenberg’s seminal work in modern physics. In recent years, there have been dramatic developments in quantum communications, cryptography and computing, and quantum science is key to solving pressing problems in clean energy, climate … Continue reading Quantum Physics, a Century Old, still Passes Understanding
The Doppler Effect: Simple but Remarkably Useful
We have all noticed how the horn of a speeding car changes as it approaches: each wave-peak is emitted from a closer point, so the wave is “squeezed” and the pitch increases. As the car recedes, the reverse effect stretches the wave, making it sound lower. The changing pitch of the note is called the … Continue reading The Doppler Effect: Simple but Remarkably Useful
Mileva Marić and the Special Theory of Relativity
The year 1905 was Albert Einstein’s “miracle year”. In that year, he published four papers in the renowned scientific journal Annalen der Physik. The first, on the photoelectric effect, established the quantum nature of light, and led to the award of a Nobel Prize some 17 years later. The second, on Brownian motion, confirmed the … Continue reading Mileva Marić and the Special Theory of Relativity
Retroreflectors: Right Angles Save Lives
As everyone knows, left and right are swapped in a mirror image. Or are they? It is really front and back that are reversed, but that's a story for another day. During a visit to the Science and Industry Museum in Paris some years ago, I stood facing a spinning mirror. Lifting one arm, I … Continue reading Retroreflectors: Right Angles Save Lives
The Potency of Pattern: Mind the Gap
In his book A Mathematician’s Apology, leading British mathematician G H Hardy wrote “A mathematician, like a painter or poet, is a maker of patterns.” He observed that the mathematician's patterns, like the painter's or the poet's, must be beautiful; beauty is the acid test [TM245 or search for “thatsmaths” at irishtimes.com]. Everyone is familiar with the concept of … Continue reading The Potency of Pattern: Mind the Gap
From Wave Equations to Modern Telecoms
Mathematics has an amazing capacity to help us to understand the physical world. Just consider the profound implications of Einstein's simple equation $latex {E = m c^2}&fg=000000$. Another example is the wave equation derived by Scottish mathematical physicist James Clerk Maxwell. Our modern world would not exist without the knowledge encapsulated in Maxwell's equations. Observation … Continue reading From Wave Equations to Modern Telecoms
Convergence of mathematics and physics
The connexions between mathematics and physics are manifold, and each enriches the other. But the relationship between the disciplines fluctuates between intimate harmony and cool indifference. Numerous examples show how mathematics, developed for its inherent interest in beauty, later played a central role in physical theory. A well-known case is the multi-dimensional geometry formulated by … Continue reading Convergence of mathematics and physics
From Sub-atomic to Cosmic Strings
The two great pillars of modern physics are quantum mechanics and general relativity. These theories describe small-scale and large-scale phenomena, respectively. While quantum mechanics predicts the shape of a hydrogen atom, general relativity explains the properties of the visible universe on the largest scales. A longstanding goal of physics is to construct a new theory … Continue reading From Sub-atomic to Cosmic Strings
All Numbers Great and Small
Is space continuous or discrete? Is it smooth, without gaps or discontinuities, or granular with a limit on how small a distance can be? What about time? Can time be repeatedly divided into smaller periods without any limit, or is there a shortest interval of time? We don’t know the answers. There is much we … Continue reading All Numbers Great and Small
Entropy and the Relentless Drift from Order to Chaos
In a famous lecture in 1959, scientist and author C P Snow spoke of a gulf of comprehension between science and the humanities, which had become split into “two cultures”. Many people in each group had a lack of appreciation of the concerns of the other group, causing grave misunderstandings and making the world's problems … Continue reading Entropy and the Relentless Drift from Order to Chaos
A New Mathematical Discovery from Neutrino Physics
Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com]. Neutrinos are sub-atomic particles that interact only weakly with matter, so that they … Continue reading A New Mathematical Discovery from Neutrino Physics
The curious behaviour of the Wilberforce Spring.
The Wilberforce Spring (often called the Wilberforce pendulum) is a simple mechanical device that illustrates the conversion of energy between two forms. It comprises a weight attached to a spring that is free to stretch up and down and to twist about its axis. In equilibrium, the spring hangs down with the pull of gravity … Continue reading The curious behaviour of the Wilberforce Spring.
Stokes’s 200th Birthday Anniversary
Next Tuesday, the 30th of August, is the 200th anniversary of the birth of George Gabriel Stokes. This extended blog post is to mark that occasion. See also an article in The Irish Times. Whether we are designing aircraft, modelling blood flow, studying propulsion, lubrication or the dynamics of swimming, constructing wind turbines or forecasting … Continue reading Stokes’s 200th Birthday Anniversary
Symplectic Geometry
For many decades, a search has been under way to find a theory of everything, that accounts for all the fundamental physical forces, including gravity. The dictum ``physics is geometry'' is a guiding principle of modern theoretical physics. Einstein's General Theory of Relativity, which emerged just one hundred years ago, is a crowning example of … Continue reading Symplectic Geometry
Plateau’s Problem and Double Bubbles
Bubbles floating in the air strive to achieve a spherical form. Large bubbles may oscillate widely about this ideal whereas small bubbles quickly achieve their equilibrium shape. The sphere is optimal: it encloses maximum volume for any surface of a given area. This was stated by Archimedes, but he did not have the mathematical techniques … Continue reading Plateau’s Problem and Double Bubbles
El Niño likely this Winter
This week’s That’s Maths column in The Irish Times (TM056 or search for “thatsmaths” at irishtimes.com) is about El Niño and the ENSO phenomenon. In 1997-98, abnormally high ocean temperatures off South America caused a collapse of the anchovy fisheries. Anchovies are a vital link in the food-chain and shortages can bring great hardship. Weather … Continue reading El Niño likely this Winter
Light Weight (*)
Does light have weight? Newton thought that light was influenced by gravity and, using his laws of motion, we can calculate how gravity bends a light beam. The effect is observable during a total eclipse of the sun: photographs of the sky are compared with the same region when the sun is elsewhere and a … Continue reading Light Weight (*)
How Big was the Bomb?
By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s That’s Maths column in The Irish Times, TM053, or search for “thatsmaths” at irishtimes.com). Physicists, engineers and applied mathematicians have an arsenal of problem-solving techniques. Computers crunch out numerical solutions in short … Continue reading How Big was the Bomb?
“Come See the Spinning Globe”
That’s Maths in The Irish Times this week (TM050, or Search for “thatsmaths” at irishtimes.com) is about how a simple pendulum can demonstrate the rotation of the Earth. Spectators gathered in Paris in March 1851 were astonished to witness visible evidence of the Earth's rotation. With a simple apparatus comprising a heavy ball swinging on … Continue reading “Come See the Spinning Globe”
Rollercoaster Loops
We all know the feeling when a car takes a corner too fast and we are thrown outward by the centrifugal force. This effect is deliberately exploited, and accentuated, in designing rollercoasters: rapid twists and turns, surges and plunges thrill the willing riders. Many modern rollercoasters have vertical loops that take the trains through 360 … Continue reading Rollercoaster Loops
White Holes in the Kitchen Sink
A tidal bore is a wall of water about a metre high travelling rapidly upstream as the tide floods in. It occurs where the tidal range is large and the estuary is funnel-shaped (see previous post on this blog). The nearest river to Ireland where bores can be regularly seen is the Severn, where favourable … Continue reading White Holes in the Kitchen Sink
New Estimate of the Speed of Light
A team of German scientists have recently discovered a new method of measuring the speed of light using Einstein's famous equation E = m c2 Scientists from SFZ, the Spätenheim Forschungszentrum in Bavaria, assembled a group of twenty volunteer climbers at a local mountain, Schmerzenberg. Using high-precision Mettler balance equipment, each climber was weighed at … Continue reading New Estimate of the Speed of Light
The Pitch Drop Experiment
Later this year a big black blob of sticky pitch will plummet from a funnel and plop into a beaker. The story is recounted in this week's That's Maths ( TM017 ) column in the Irish Times. In one of the longest-running physics experiments, the slow-flowing pitch, under a bell-jar in the University of Queensland … Continue reading The Pitch Drop Experiment
Packing & Stacking
In That's Maths this week (TM004), we look at the problem of packing goods of fixed size and shape in the most efficient way. Packing problems, concerned with storing objects as densely as possible in a container, have a long history, and have broad applications in engineering and industry. Johannes Kepler conjectured that the standard … Continue reading Packing & Stacking
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