An object does not have to move to have energy. Einstein’s equation connects its mass, m, with its rest energy, E₀. The factor c², the speed of light squared, gives the relationship between them. Even when an object is completely at rest, its mass corresponds to an enormous amount of energy.

This connection also changes how we understand the mass of a whole system. Heat a sealed container of gas, and the energy added increases its mass by a tiny amount, even though no particles have been added. The mass of a system reflects its total energy in its rest frame, including the motion and interactions of its constituents.

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The closer you get to the speed of light, the slower time passes for you relative to someone on Earth.

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Quadric Surfaces: Standard Forms and Formulas

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How does a rocket work perfectly well in the vacuum of space?

In a vacuum, there is no air for a rocket to push against in order to move forward.

But a rocket carries its own propellant with it. It accelerates exhaust gases backward at high speed, causing the rocket to accelerate forward. This follows the principle of conservation of momentum: as the exhaust gains momentum backward, the rocket gains momentum forward

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A passing siren can change pitch while emitting a steady tone. As the source approaches, successive wavefronts arrive closer together in time, raising the frequency heard. As it recedes, they arrive farther apart, lowering it.

The Doppler effect turns wave timing into a measure of motion. Radar uses frequency shifts in reflected waves to measure speed toward or away from the detector.

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These wells illustrate how gravity becomes more extreme near compact objects.

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The 2026 Nobel Prize in Physics has been awarded to Francis Halzen for his decisive contributions to the IceCube Neutrino Observatory and the discovery of high-energy neutrinos of astrophysical origin.

So what exactly did Halzen’s Nobel-winning work reveal?

Not neutrinos. They were discovered decades ago.

The breakthrough was finding high-energy neutrinos coming from beyond our Solar System and using them as a new way to study the most violent places in the universe.

Neutrinos are almost impossible to detect. Trillions pass through your body every second, barely interacting with matter. But because they are electrically neutral, they can travel across the universe without being deflected by magnetic fields.

That makes them extraordinary cosmic messengers.

In 1988, Halzen proposed using the Antarctic ice as a gigantic neutrino detector. His idea eventually became IceCube, a cubic kilometre of ice containing thousands of light sensors.

When a neutrino finally collides with matter in the ice, it can produce a tiny flash of Cherenkov light. IceCube detects that flash and reconstructs where the neutrino came from and how much energy it carried.

In 2013, IceCube announced the first compelling evidence for a population of high-energy neutrinos originating far beyond our Solar System.

Then came another remarkable result. In 2017, an IceCube neutrino helped astronomers identify a distant blazar as a likely source of high-energy neutrinos and cosmic rays.

Halzen’s work effectively opened a new window onto the universe. Instead of observing the cosmos only through light, we could now use neutrinos to investigate some of its most extreme environments. A cubic kilometre of Antarctic ice became a telescope for the most elusive particles in nature.

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Division for kids

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Resonance occurs when a periodic drive acts near a system's natural frequency. Each cycle then adds energy with favorable timing, so the amplitude builds. Damping limits the peak and broadens the response; weaker damping produces a taller, narrower resonance.

The same principle amplifies a playground swing, selects frequencies in a radio circuit, and shapes musical instruments. It can also damage machines or bridges when forcing aligns with a structural mode.

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A year’s tidal predictions could be drawn in about four hours by this mechanical computer.

William Thomson, later Lord Kelvin, designed it to combine ten tidal components. Rotating shafts drove pulleys through periodic motions. A cord running over them added their displacements, allowing a pen to trace the predicted rise and fall of the tide.

The amplitudes and phases had to be set for each harbour using measurements of its tides.

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Water can survive longer on a hotter surface.

Above the Leidenfrost temperature, the bottom of a droplet vaporizes so rapidly that a continuous gas cushion forms beneath it. This insulating layer reduces direct contact with the pan and lets the droplet glide with far less heat transfer than during ordinary nucleate boiling.

The threshold is not one universal temperature. It depends on the liquid, surface texture, contamination, pressure, and heating history.

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