Author Archives: anuj - Page 24
Examples of Hilbert Spaces
Hilbert Spaces can be FINITE dimensional or INFINITE Dimensional Finite Dimensional Hilbert Spaces n-Tuples of real numbers - $R^n$ - $R^5$ Inner Product would be just the dot product of…
Subspaces of Vector Spaces, Invariant Subspaces
The idea is to create a RESTRICTED space within the given vector space. Within R3 $\R^3$: $\{ \vec{i}, \vec{j}, \vec{k} \}$ we can define a space that is far more…
The cosmological constant
Einstein did not have the benefit of knowing that a) There were other galaxies besides our own (Hubble found Andromeda in 1923) b) These 'other galaxies' were receding from us…
Local neighborhood of Galaxies
Andromeda is about million light years away, and is far from the nearest galaxy to our own. Nearest Galaxies by Type Title Galaxy Date Distance Notes Nearest galaxy Milky…
How to think of complex numbers
Think of it as a duo - there's actually TWO (real) numbers wrapped up in a single complex number. Think of it as a regular vector , but with a…
How many particles are in the Universe? How many Gravitons in all?
$10^{90}$ This includes photons, but doesn't include gravitons
Vector Spaces Examples
The set of functions that take in a natural number n and return a REAL number. \ Functions of ONE Real Variable ( REAL to REAL) \ Of what use…
The nowhere continuous function
For example, the nowhere continuous function \
True Randomness in Quantum Computing
Truly Random Numbers? If you have a Computer Science background, you may be aware that truly (100% ) random numbers simply do not exist. Random number generation algorithms using classical…
Dark Energy or Multiple Universes
There's a mystery as to why the Universe's expansion is accelerating. As per all our educated guesswork, the first 9 billion years found the Universe in a decelerating mode. The…