What is relativistic covariance?
Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. In particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e., they transform under the trivial representation).
Who almost beat Einstein to general relativity?
Actually, the German mathematician David Hilbert submitted an article containing the correct field equations for general relativity five days before Einstein. Hilbert never claimed priority for this theory.
What are the three consequences of general relativity?
Some of the consequences of general relativity are: Gravitational time dilation: Clocks run slower in deeper gravitational wells. Precession: Orbits precess in a way unexpected in Newton’s theory of gravity. (This has been observed in the orbit of Mercury and in binary pulsars).
What is the principle of general covariance?
In the context of special relativity, the principle of general covariance states that the spacetime metric ηab, is the only quantity pertaining to spacetime structure which can appear in any physical law.
What is difference between invariant and covariant?
Invariant: Any physical quantity is invariant when its value remains unchanged under coordinate or symmetry transformations. Covariant: The term covariant is usually used when the equations of physical systems are unchanged under coordinate transformations.
Who helped Einstein with maths?
Marcel Grossmann
Two friends from Einstein’s student days — Marcel Grossmann and Michele Besso — were particularly important. Grossmann was a gifted mathematician and organized student who helped the more visionary and fanciful Einstein at crucial moments.
Did Einstein steal his research?
As was typical of Einstein, he did not discover theories; he merely commandeered them. He took an existing body of knowledge, picked and chose the ideas he liked, then wove them into a tale about his contribution to special relativity.
Why is a black hole black?
A black hole is a region of spacetime where gravity is so strong that nothing — no particles or even electromagnetic radiation such as light — can escape from it. In many ways, a black hole acts like an ideal black body, as it reflects no light.
What did Einstein mean by time is relative?
In the Special Theory of Relativity, Einstein determined that time is relative—in other words, the rate at which time passes depends on your frame of reference. The effect of time slowing down is negligible at speeds of everyday life, but it becomes very pronounced at speeds approaching that of light.
What does it mean for an equation to be covariant?
Covariance means form invariant. Eg: Maxwell’s covariant field equation ∂αGαβ=0. takes the same form under lorentz transformation.
What is covariant equation?
In general relativity, a manifestly covariant equation is one in which all expressions are tensors. The operations of addition, tensor multiplication, tensor contraction, raising and lowering indices, and covariant differentiation may appear in the equation.
What is general covariance in physics?
General covariance. In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical laws under arbitrary differentiable coordinate transformations.
What is the formula for covariance in statistics?
Cov(X,Y)=E[(X−E[X])(Y−E[Y])]. Now, instead of measuring the fluctuation of a single variable, the covariance measures how two variables fluctuate together. For the covariance to be large, both X−E[X] X – E[X] X−E[X] and Y−E[Y] Y – E[Y] Y−E[Y] must be large at the same time or, in other words, change together.
What did Einstein mean by ‘general covariance’?
Einstein described both demands by a single phrase, “general covariance.”. The “no prior geometry” demand actually fathered general relativity, but by doing so anonymously, disguised as “general covariance”, it also fathered half a century of confusion.
What does it mean when the covariance is positive?
If the covariance for any two variables is positive, that means, both the variables move in the same direction. Here, the variables show similar behaviour. That means, if the values (greater or lesser) of one variable corresponds to the values of another variable, then they are said to be in positive covariance.