Dario de Judicibus - Einstein’s Relativity Theory can survive ultrafast neutrinos - The Independent.

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A recent experiment by OPERA (*Oscillation Project with Emulsion-tRacking Apparatus*) seems to suggest the possibility that **neutrinos can travel faster than light**. The Italian researchers claimed to have measured the 730-kilometer trip between CERN and its detector to within 20 centimeters and the resulting time to within 10 nanoseconds. They have detected more than 16,000 events measured over the past two years where neutrinos have been faster than light by 60 nanoseconds on the mentioned distance.

In case such evidence should be confirmed by other experiments, should we rethink the Einstein’s *Theory of Special Relativity*? In my opinion, not necessarily.

First of all, the Special Relativity assumes that there is **a maximum threshold** for the speed of matter, energy, and information in the universe. Such a speed is called c and it is assumed to be the speed of light in empty space, that is, vacuum. However the **space is never empty**. Even where the density of matter is mostly zero, there are many fields in space, especially gravitational and electromagnetic ones. Furthermore, vacuum is polarized because of **virtual pair production**, that is, the creation and immediate annihilation of pair of fermions (particle and anti-particle) in space.

Second, we know that the speed of light in a mean is lower than c. In fact, when light pass through a material medium, its speed is diminished because of electro-magnetic interaction with the particles composing that material. The ratio between c and the speed v at which light travels in a material is called the **refractive index** n of the material, and is calculated as the ratio n = c / v.

Third, photons interact with the electro-magnetic field, one of the four fundamental forces in the Universe, as well as with weak nuclear and gravitational fields. On the other hand, neutrinos interact **only** with the weak nuclear and gravitational field. At the energies of the experiment, weak forces operate only on the extremely short distance scales found in an atomic nucleus. In actuality, that force is stronger than the electromagnetic one, but its messenger particles (W and Z bosons) are so massive and sluggish that they do not faithfully transmit its intrinsic strength.

So, let us assume that there is a maximum speed in universe and call it c. Since there is nothing like a real vacuum, we have to suppose that both photons and neutrinos do not really reach that speed, although there are very close to it. Furthermore, since photons have more probabilities to interact with fields and matter in space, we may assume that light is slowed a little bit more with respect neutrinos. That would explain the results of Opera experiment without breaking the Special Relativity of Einstein.

Of course, this is just a **conjecture**, not a real theory. A new realistic model of space should be developed and simulations have to be performed to verify if such a conjecture might explain the resulting data. Anyway, it is worth a try, isn’t it?

Dario de Judicibus - Einstein’s Relativity Theory can survive ultrafast neutrinos - The Independent.

]]>Warning: this article is available in English language only by automatic translation (Google Translate).

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Non so quanti di voi conoscano il metodo della **conversione fonetica** per ricordare numeri molto lunghi. In pratica si tratta di sostituire a ogni numero un suono consonantico, aggiungere liberamente vocali per formare parole di senso compiuto, legare fra loro queste parole in una frase e scegliere la frase in modo da collegarla logicamente al numero che si cerca di ricordare.

Ad esempio, la parola defuntoè formata dalle seguenti consonanti: D, F, N e T. La D e la T sono entrambe consonanti dentali e rappresentano lo stesso numero, ovvero 1, mentre la N è una consonante nasale e rappresenta il 2, mentre la F una consonante labiodentale e rappresenta l’8, per cui il numero corrispondente è il 1821, ovvero la data della morte di Napoleone.

Come si può vedere ogni numero è associato a più suoni consonantici che fanno parte della stessa famiglia. Se si aggiunge il fatto che le vocali servono unicamente a formare parole di senso compiuto, si ha abbastanza flessibilità per creare frasi che abbiano un significato. Lo schema di riferimento è il seguente, in italiano:

Cifra | Famiglia | Suono consonantico |
---|---|---|

1 | dentale | T, D |

2 | nasale | N, GN |

3 | mugolante | M |

4 | vibrante | R |

5 | liquida | L, GL |

6 | palatale | C, G [dolci] |

7 | gutturale | K, CH, GH [dure] |

8 | labiodentale | F, V |

9 | labiale | P, B |

0 | sibilante | S, SC, Z |

Una tipica applicazione di questa tecnica mnemonica è quella di ricordare le costanti fisiche e matematiche fino a un certo decimale. È molto importante riuscire in questo caso a costruire frasi che abbiano un legame logico con l’oggetto che si vuole ricordare, altrimenti si rischia di non ricordare neppure la frase menmonica. L’alfabeto è sostanzialmente lo stesso per tutte le lingue se facciamo riferimento, più che alle lettere, alle famiglie di suoni ma, ovviamente, ognuno cerca di sviluppare frasi nella propria lingua. Da notare che in italiano le consonanti doppie valgono una, ovvero scrivere NN è la stessa cosa che scrivere solo N. Analogamente CCH, CH e K sono tutte forme equivalenti.

Come spesso capita, di frasi in italiano non se ne trovano tante, per cui ne ho sviluppate alcune che ho deciso di condividere qui:

Pi greco (π) arrotondato alla settima cifra decimale, ovvero 3,1415927:

Immagine mentale : cercare di ricordare un numero come pi greco fa paura, quindi Frase mnemonica : MeTTeR TaLe PaNiCo Cifre equivalenti : 3 1 4 1 5 9 2 7

Il numero di Eulero (e) arrotondato alla dodicesima cifra decimale, ovvero 2,718281828459:

Immagine mentale : un numero del genere finisce che uno ci mette tutta la notte a ricordarselo Frase mnemonica : Né CHi DeVe, Ne Voi, DeVoN FaRe aLBe Cifre equivalenti : 2 7 1 8 2 8 1 8 2 8 4 59

La velocità della luce (c) in chilometri al secondo, ovvero 299.792,458:

Immagine mentale : è la velocità massima a cui può andare la luce e nessuna particella reale va altrettanto veloce Frase mnemonica : Nè Può PoCo Più, Né ReaL Va Cifre equivalenti : 2 9 9 7 9 2 4 5 8

La costante di Dirac (ħ) in Joule secondi, detta anche *acca tagliato*, ovvero 1,054571629×10^{-34}:

Immagine mentale : la costante indica la dimensione più piccola fra due quanti, che posson esser visti come tasselli nei vari campi (mari) Frase mnemonica : TaSSeLLi ReaLi CHe aDaGi iN Più MaRi Cifre equivalenti : 1 0 5 4 5 7 1 6 2 9 - 3 4

A voi trovarne altre… mettetele pure nei commenti.

Dario de Judicibus - Phonetic convertions - The Independent.

]]>Dario de Judicibus - Dark Universe: just an idea - The Independent.

]]> I was a physicist. I said "*was*" since I am no more. When I got my degree, in fact, I joined IBM and began a completely different career in the information technology sector. Since being a physicist is a vocation, anyway, not a job, I continued to get in touch with the most recent discoveries of scientific community by reading various specialized magazines and journals. At the beginning I was reading only articles about high energies particles, because I worked in that area at CERN, SLAC, and DESY, but later on I began more and more to read mostly everything, from astronomy to anthropology, from archeology to psychology. By the way, I am subscribed to "*Le Scienze*", the Italian version of "*Scientific American*", since 1978.

I was a physicist, but not a theoretical one: I was a researcher. So, even if I had good math foundations, I was more oriented to observation and testing, rather than filling sheets of paper by formulas. Anyway, after 22 years, my ability to play with integrals and derivatives is dramatically decreased to pre-scholar levels. So, I have no more the elements to represents ideas and hypotheses by using mathematics.

One of the subjects I am very interested too in this period is cosmology. In particular how the Universe is shaped and why, its behaviour, its structure, everything related to the Cosmos. As you probably know, two intriguing areas that are currently investigated by scientists are about the existence of **dark energy** and **dark matter**.

*Dark energy* is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. According to theoreticians, it accounts for **74%** of the total mass-energy of the universe.

On the other hand, *dark matter* is hypothetical matter that does not interact with the electromagnetic force, but whose presence can be inferred from gravitational effects on visible matter. According to theoreticians, it accounts for **22%** of the total mass-energy of the universe.

So, **96% of Cosmos is dark**, that is, made of matter and energy that hardly interact with the matter and energy that for centuries we thought were the components of our Universe, the visible one.

Is there a relationship between dark energy and dark matter? Is there a model of such a *hidden universe*? Well, here is why I am writing this article. I had an idea, or if you prefer, an **intuition**. As I said, I am **not** able to elaborate it to make a real scientific theory. It is just a flash. So I had two possibilities: forget it, or expose it. The first one presents no risk at all, but generates no value too. The second one would lay myself open to criticism by experts, even bitter ones. In the worst of cases my idea could be considered insubstantial, maybe even ridiculous.

So, what is to be done? No doubt: I decided to run the risk and to publish my intuition. In the worst of cases it will be ignored, but it is also possible that it might become the starting point for further considerations. So here it is.

As you know, the universe is a *space-time continuum* which is curved by the presence of matter. You can imagine it as a wide elastic membrane on which balls of various masses are placed. The larger is the mass, the stronger is the deformation of the membrane. The amount of deformation is called *strain*. If a ball moves on that membrane its path will depend on the shape of the surface. Passing close to an heavy mass, the small ball will deviate towards it, like in a whirlpool, giving the appearance to be attracted by the other mass. That is *gravity*.

Now, what if that membrane is not just a mass-less and energy-less geometrical element? What if **the space itself has a mass**? And what if we could consider it really as an elastic membrane, a physical one, with a linear relationship between stress and strain? For a spring, the relationship between strain and applied force, is ruled by the *Hooke’s law*, that is,

F = -kx

where x is the *displacement*, F is really the *force* exerted by the spring – notice the negative sign – and k is the *spring constant*. Therefore, the larger is the spring constant, the more elastic is the spring.

In a three-dimensional space, the law is a little bit more complicated, since the proportionality constant between stress and strain is a 4th order tensor, but the principle is the same. The strain tensor is a matrix of 81 elements based on 21 independent elastic coefficient. Furthermore, if the membrane is made of an isotropic materials, whose properties are independent of direction in space – and we can assume that space continuum is isotropic – the strain tensor is a symmetric one. In such a case all coefficient may depend only on two scalar constants: **E**, called *modulus of elasticity*, and **ν**, known as *Poisson’s ratio*.

When we deform a spring, we store in it a potential energy that is released when the spring is relieved. That amount of energy is given by

V = ½ kx2

This is true for the membrane too, even if the formula is much more complicated. In such a case the potential energy will depend on E and ν, of course. If an heavy ball is removed from the surface, in fact, assuming that the membrane has no *hysteresis*, that is, exhibits no memory of deformation, the surface will take again the original shape.

My first hypothesis is that the **dark energy is the total amount of potential energy** associated to the strain of space generated by all the visible matter. It practically would depend on the overall visible mass of universe and the elasticity coefficients of space.

Let us go back to the membrane representing the space, now. Let us assume it has a thickness and a uniform density, that is, let us suppose that **space has a finite mass** itself. Let us also assume that when a mass warps the space, the thickness of membrane decreases so that the total mass of deformed zone does not change. Since gravity is determined by the strain, the mass of the membrane itself has no effect on the individual balls, but has to be considered when we think the Universe as a whole.

So, my second hypothesis is that **dark matter is due to the membrane itself, that is, to the mass of space**. It is a constant, because while the Universe is expanding, the space becomes thinner and thinner, that is, the membrane density uniformly decreases. By the way, we know that Universe is not infinite. So it is not the space mass.

But what happens to a real membrane if we stretch it? Well, the strain caused by balls decreases too but also the coefficients of elasticity would change. So it is very possible that the density of dark energy will remain the same. This is the typical case where **intuition fails** and I would have to perform some calculation.

And why dark energy is responsible for the acceleration of expansion of Universe? Why does it oppose to gravity? According to current theories, **a positive density of dark energy generates a negative pressure**, and therefore accelerate the expansion of Universe.

In the model I am proposing, the dark energy is associated to the potential energy related to the deformation due to visible masses. Imagine now that our membrane is really a *balloon*. What is happening to that potential energy as the balloon is inflated? The membrane is getting thinner and thinner, I said. Locally it is also getting flatter and flatter and the tension reduces the strain, that is, the deformation due to a certain mass is decreased. In theory we could say that gravity force is weakening. But if gravity is weakening, the clusters of visible matters tend to spread. Maybe the structure of the space itself is weakening. So, whatever caused the expansion of Universe is finding less and less resistance to expansion. Is it this an explanation? **I do not know.** At this point, it is necessary to define a mathematical model based on my intuition and see if it works or not.

If anybody is willing to work on this, he/she is welcome.

Dario de Judicibus - Dark Universe: just an idea - The Independent.

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