The space mates by Rebecca Minniti

Our first class on relativity:

letizia_marasco — 2018-05-04 13:08:45 UTC

The theory of relativity is a topic which has been studied since 1900. In particular, Albert Einstein is well-known to have illustrated two different theories: a special and a general one. The first one was published in 1905, and it is about the retilineal uniform motion; the general theory, published in 1916, describes gravity as a geometric property of space and time. We can introduce a very important key word about the study of relativity, which is "reference frame", also called by A. Einstein himself "body of reference", made by an intersection between three axes (x, y, z), into this space every point can be located by its coordinates. In relativity, if we want to find out the exact moment in which something happens, we can talk about the meaning of event and scene. The scene is where the event takes place, so its definition depends on the coordinates x,y,z plus the time t. A particular reference frame which has a privileged role in physics is the inertial reference frame, which is a not accelerated system. Some years earlier, Maxwell in 1864 published some famous questions which describe the weird lights behaviour. Light is an electromagnetic wave which velocity is expressed by this formula.

The ether is where light propagates.

Just to make an idea about a light wave, let's watch this video made by TED education! Enjoy :)

re_minniti — 2018-05-16 14:14:46 UTC

Galileo was the first scientist ever who formulated the principle of relativity: all the natural phenomena run their counts in exactly the same way in all the inertial reference frames. Let's make an example: when flying it is not possible to understand if we are moving or if we are still when the plane moves at costant speed and direction. At the end of his experiments Galileo was able to postulate his relativity hypothesis: "any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments". So he understood that kinematic phenomena depend on the different inertial reference frames; let's consider an inertial reference frame in which there is a body who is moving with a u velocity. This inertial frame is also moving with a V velocity. If we take in example another system, which is not moving, the velocity v reffered to the stationary system will be described by the formula: v= Vo + u'

Does ether exist?

re_minniti — 2018-05-16 15:03:08 UTC

In 1900, scientists started thinking and discussing about the real existence of ether, a hypothetical medium in which light and sound waves can propagate. In 1905 Einstein said that ether doesn't exist and that light can be propagated also in vacuum; he formulated two postulates: the Galilean principle of relativity and Constancy of speed of light. The consequence was that time was seen as simultaneity: if a physical quantity like a fire-cracker blow up at 5 o'clock, we can say that the event is completely simultaneus to the position of the clock hands. We can detect this conclusion observing a common and natural phenomenon: taking in example two points on the ground A and B, we can imagine that two lighting bolts will strike exactly the two points at the same time. Let's call M the point which is in the middle between A and B. If the rays of the lighting bolts meet in that middle point, it means that they are simultaneous.

What is time dilation?

re_minniti — 2018-05-18 15:47:22 UTC

According to what we said before, time is connected with simultaneity. Let's make an example to make this more clear: supposing that we have two ideal clocks placed with a distant D between them, we can see the first clock which emits a flash of light at a fixed time, t=to and the second one is able to take over the same flash. This phenomenon is described by the formula: (t-to)=D/c (where c is the velocity of light). The events recorded refer to the definition of simultaneity: if there is an external observer in the two clocks reference frame, and he's placed at the midpoint between their positions, he will be able to get the two light flashes at the same time. Now imagine that one of the clocks is on a carriage that is moving with a V velocity, and on the same carriage there is also an observer who receives the flash light at the time expressed by the formula DT(t-to)=D/c. At the same time on the ground there's a second observer who describes the same phenomenon by his point of view. Since light runs across the distance D, the carriage keeps moving. So for the second observer the flash light crosses a distant represented by the triangle's cathets AB, BC. So now we can apply Pitagora's theoreme and obtain this fundamental relation:

To make it easier we can replace with symbol β the relationship between the velocity of the object and the velocity of light.
And also the values that are under the root square can be replaced by the Lorentz factor γ (it expresses the amount of time and motion). And so the formula Dt = γ Dto expresses time dilation. When β is 0,999, for example, γ grows of 70%, and when β is 1, γ cannot be measured and it tends to infinity.
A lot of experiments tested that the space around the heart is filled by radiations emitted by stars and so on. We are protected from this radiations by the atmosphere, but if we are at 6km of altitude some particles called muons, charged negative, produce radiations. this muons have an average lifetime of 2.2 microsec. At the velocity of 6km/h they have to go on 700 m before decade, and their life-time To is expandend of 7%. This is an another proof of time validity.

Hope you'll enjoy this interesting video about muons and how they reach our planet :)

The twin paradox

re_minniti — 2018-05-31 13:22:54 UTC

The Einstein's theory of time dilation can be applied to every natural phenomena. Let's make an example: there are two twins Bruno and Carlo and they are bp. Bruno decides to leave on a spacecraft and to travel through the space with a C velocity. The journey takes 24 light years to run across the distance of the nearest star system. After 48 Ly Bruno has come back to the ground and he had found his brother, Carlo, who stayed on Earth, older. This paradox is explained by the asymmetrical reference frame in which both twins are. Carlo remains on a inertial reference frame, while Bruno's travelling on an accelerated reference frame.

BUT WHAT IS THE REAL AGE?

Clearly is Carlo's one because he has lived on an inertial reference frame.
Observing that, we can pay attention to one peculiar phenomenon of the special relativity's theory by Einstein: the lenght contraction. The lenght of a moving object is measured to be shorter than its own lenght. Of this event can be seen just a substantial fraction of the speed of light and it becomes important only when the object that is moving interferes with an observer. So when the velocity get faster the object get smaller.
The last point of Einstein theory is the value of the light speed.
E=mc^2 but it would be better to write this as E0=mc^2 because it refers at the energy at rest of a mass m; when it's moving we can introduce the constant γ and writing the formula as: E= γmc^2

I hope you'll enjoy this space-trip

re_minniti — 2018-05-31 15:06:42 UTC

         
          Let yourself accompanied by this soundtrack

...and now we just have to thank you for your time.

letizia_marasco — 2018-05-31 15:32:31 UTC

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