Without Zero it would be impossible to measure anything.
Pi is only constant in Euclidean Geometry, it is not the same in other Geometries. In the non-Euclidean geometry that Relativity theory uses the difference between PiE and PiNE is extremely small, approaching zero.
Relativity theory breaks down at a singularity, such as in a black hole, because the equations of General Relativity give nonsensical results when dealing with infinite density and curvature. At the singularity, the laws of physics as we currently understand them cease to provide meaningful predictions, leading to a breakdown in our ability to describe the physical phenomena occurring there.
Relativity: The Special and the General Theory; Sidelights on Relativity; Relativity: Einstein's Theory of Spacetime, Time Dilation, Gravity and Cosmology; Investigations on the Theory of the Brownian Movement
When an object is travelling at the speed of light in a vacuum, relativity theory says that time stops for that object. Relativity theory also says that it is not possible for any object with a non-zero mass to accelerate to that speed. So, except in the trivial case of massless particles (which, in a vacuum, already travel at the speed of light), time does not ever freeze.
Newton's Theory of Gravity is simpler and easier to use for most space missions because the speeds and gravitational forces involved are not extreme enough to require the precision of Einstein's General Theory of Relativity. Newton's theory is also more computationally efficient for many practical applications, making it a convenient choice for mission planning.
Just as matter is defined by having mass, there cannot be matter with zero mass. Current theories all define the "photon" (energy quantum) as having zero rest mass, although it can be treated as both a "particle" and a wave.
In simple, average Joe terms, string theory says that all the particles in the universe are really little "strings", rather then the conventional ball-shape they are normally thought of. Unlike the balls (or more accurately, points) which are zero-dimensional, strings are one-dimensional. This has some very interesting implications, but to explain them would evolve out stepping a "simple definition". String theory is known for uniting both the physical laws of the large (Einsteins general relativity- stars, planets, and people) and the small (quantum mechanics- subatomic particles), which were previously incompatible. Short for super sting theory, now known as M-theory. This answer explains only the very basics of string theory.
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According to Einstein's theory of relativity, an object cannot travel at the speed of light due to infinite energy required. Therefore, the length of a train moving at the speed of light is an undefined concept.
The difference between theory and natural law is that a theory is a framework, while a natural law is a single rule, usually expressed in mathematics. They are not two different stages of acceptance among scientists (as it is sometimes claimed in error); they are two completely different things; a theory does not evolve into a law with when sufficient evidence for a theory has been gathered for example. For example consider: The Theory of Special Relativity <-- Theory Speed of light is constant <-- Law Theory of Electromagnetism <-- Theory Divergence of the Magnetic field is zero <-- Law Quantum Field Theory <-- Theory Conservation of Energy <-- Law
The zero theory, or null hypothesis, is the assumption that there is nothing extraordinary in a set of data; this is to contrast to the alternative hypothesis, that there is a certain pattern in the data.