Ingredients

Dough for double-crust pie
1/3 cup sugar
1/3 cup packed brown sugar
1/4 cup all-purpose flour
1 teaspoon ground cinnamon
1/4 teaspoon ground ginger
1/4 teaspoon ground nutmeg
6 to 7 cups thinly sliced peeled tart apples
1 tablespoon lemon juice
1 tablespoon butter
1 large egg white
Optional: Turbinado or coarse sugar, ground cinnamon, vanilla bean ice cream and caramel sauce



1. Preheat oven to 375°. On a lightly floured surface, roll half of the dough to a 1/8-in.-thick circle; transfer to a 9-in. pie plate. In a small bowl, combine sugars, flour and spices. In a large bowl, toss apples with lemon juice. Add sugar mixture; toss to coat. Add filling; dot with butter.

2. Roll remaining dough to a 1/8-in.-thick circle. Place over filling. Trim, seal and flute edge. Cut slits in top. Beat egg white until foamy; brush over crust. If desired, sprinkle with turbinado sugar and ground cinnamon. Cover edge loosely with foil.

3. Bake 25 minutes. Remove foil; bake until crust is golden brown and filling is bubbly, 20-25 minutes longer. Cool on a wire rack. If desired, serve with ice cream and caramel sauce.

The speed of light in vacuum, commonly denoted c, is a universal physical constant that is important in many areas of physics. Its exact value is defined as 299792458 metres per second (approximately 300000 km/s or 186000 mi/s).[Note 3] According to the special theory of relativity, c is the upper limit for the speed at which conventional matter, energy or any signal carrying information can travel through space.

All forms of electromagnetic radiation – not just visible light – travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for a message to travel between Earth and the spacecraft. In computing, the speed of light fixes the ultimate minimum communication delay between computers, to computer memory, and within a CPU. The speed of light can be used with time of flight measurements to measure large distances to high precision.

Ole Rømer first demonstrated in 1676 that light travels at a finite speed (non-instantaneously) by studying the apparent motion of Jupiter's moon Io. Progressively more accurate measurements of its speed came over the following centuries. In a paper published in 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c.[4] In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source.[5] He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism.

Massless particles and field perturbations such as gravitational waves also travel at the speed c in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. Particles with nonzero rest mass can approach c, but can never actually reach it, regardless of the frame of reference in which their speed is measured. In the special and general theories of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence, E = mc2.[6] In some cases objects or waves may appear to travel faster than light (e.g. phase velocities of waves, the appearance of certain high-speed astronomical objects, and particular quantum effects). The expansion of the universe is understood to exceed the speed of light beyond a certain boundary.

The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of electromagnetic waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material (n = c/v). For example, for visible light, the refractive index of glass is typically around 1.5, meaning that light in glass travels at c/1.5 ≈ 200000 km/s (124000 mi/s); the refractive index of air for visible light is about 1.0003, so the speed of light in air is about 90 km/s (56 mi/s) slower than c. Numerical value, notation, and units

The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin celeritas (meaning 'swiftness, celerity'). In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant that was later shown to equal √2 times the speed of light in vacuum. Historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by then had become the standard symbol for the speed of light.[7][8]

Sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum.[9] This subscripted notation, which is endorsed in official SI literature,[10] has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, and Z0 for the impedance of free space. This article uses c exclusively for the speed of light in vacuum.

Since 1983, the metre has been defined in the International System of Units (SI) as the distance light travels in vacuum in 1⁄299792458 of a second. This definition fixes the speed of light in vacuum at exactly 299792458 m/s.[11] As a dimensional physical constant, the numerical value of c is different for different unit systems. For example, in imperial units, the speed of light is approximately 186282 miles per second,[Note 4] or roughly 1 foot per nanosecond.[12][13] In branches of physics in which c appears often, such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1.[14][15] Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result. Its unit of light-second per second is still relevant, even if omitted.
Fundamental role in physics
See also: Special relativity and One-way speed of light

The speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer.[Note 5] This invariance of the speed of light was postulated by Einstein in 1905,[5] after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether;[16] it has since been consistently confirmed by many experiments.[Note 6] It is only possible to verify experimentally that the two-way speed of light (for example, from a source to a mirror and back again) is frame-independent, because it is impossible to measure the one-way speed of light (for example, from a source to a distant detector) without some convention as to how clocks at the source and at the detector should be synchronized. However, by adopting Einstein synchronization for the clocks, the one-way speed of light becomes equal to the two-way speed of light by definition.[17][18] The special theory of relativity explores the consequences of this invariance of c with the assumption that the laws of physics are the same in all inertial frames of reference.[19][20] One consequence is that c is the speed at which all massless particles and waves, including light, must travel in vacuum. Special relativity has many counterintuitive and experimentally verified implications.[23] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 8] and time dilation (moving clocks run more slowly). The factor γ by which lengths contract and times dilate is known as the Lorentz factor and is given by γ = (1 − v2/c2)−1/2, where v is the speed of the object. The difference of γ from 1 is negligible for speeds much slower than c, such as most everyday speeds—in which case special relativity is closely approximated by Galilean relativity—but it increases at relativistic speeds and diverges to infinity as v approaches c. For example, a time dilation factor of γ = 2 occurs at a relative velocity of 86.6% of the speed of light (v = 0.866 c). Similarly, a time dilation factor of γ = 10 occurs at v = 99.5% c.

The results of special relativity can be summarized by treating space and time as a unified structure known as spacetime (with c relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c.[26]

Press W.