### What's Up

### Most Read Articles

#### Welcome to Einstein Relatively Easy!

This web site is aimed at the general reader who is keen to discover Einstein's theories of special and general relativity, and who may also like to tackle the essential underlying mathematics.

Einstein's Relativity is too beautiful and too engaging to be restricted to the professionals!

Have fun!

*"I have no special talents*

* I am only passionately curious" *

Albert Einstein

If you like this content, you can help maintaining this website with a small tip on my tipeee page

## Deutsch Algorithm with Google Cirq API

- Details
- Category: Quantum Mechanics
- Hits: 232

This article will walk through on how to implement the **Deutsch algorithm** introduced in our previous article The Deutsch-Jozsa algorithm with Google Cirq software library.

##### Quick Start

You can find all the technical details on how to run this program at this adress: https://github.com/cyrilondon/quantum-mechanics-python/tree/master/deutsch.

The good news is that **you don't need any python environment installed on your computer**: by following the instructions, you will be able to run the program on your favourite browser (via Python Jupiter notebook).

Run the program (either by clicking Cell -> Run All the first time or just by cliking the last cell afterwards) and you will see the quantum circuit randomly generated (corresponding to a random function to evaluate) as well as the result (0 or 1) of the measurement.

In this case, the program chose randomly the function** f(x) = 1** to be evaluated (<1,1> means <f(0)=1, f(1)=1) , and **measured the final state of the first qubit as 0**, as expected (f(x)=1 means** f is constant** and thus 0 should be measured).

## Advance of the perihelion of Mercury

- Details
- Category: General Relativity
- Hits: 322

Another test that Einstein suggested for testing his gravitational theory was the precession of perihelia. This reflects the fact that noncircular orbits in General Relativity are not perfect closed ellipses; to a good approximation they are ellipses that precess.

The strategy is like as in our previous article about light deflection to describe **the evolution of the radial coordinate r as a function of the angular coordinate Φ**; for a perfect ellipse, r(Φ) would be periodic with period 2π, reflecting the fact that perihelion occured at the same angluar position each orbit.

Using then **perturbation theory**, we can show how General Relativity introduces a slight alteration of the period, giving rise to precession.

We recall from our previous article Gravitational deflection of light the relativistic expression of the Binet's equation (in Newtonian physics, the last term in u^{2} is absent) for a particule with mass (note the presence of the term GM/h^{2} on the right-side of the equation)

If we now consider a circular orbit with constant radius r_{c}: r_{c} should be solution of the previous equation so that, with u_{c}=1/r_{c}:

If we now assume that the solution has the form

### Login Form

### Breadcrumbs

### Quotes

### RSS Feed

### Who is online

We have 173 guests and no members online