The way we measure the world

Probably the way we measure the world would seem so obvious than any attempt to perform those measurements on a different way would be simply ignored and discarded, without any more prove on its fundamentals than the “common sense”. This is easily observable on any aspect of our daily life, let's suppose as an example that a man must cut a stick of a given metal in some way that its length will adjust as much as possible to the length of a side of a rectangular metal body, the most “obvious” way would be of course to take a tape and perform a measurement of the reference body and then transfer the measurement to the stick of metal, a process so simple that does not require any more explanation.

In a similar way, we can point out the way on which the classic mechanics bases the measurements of positions using a euclidean system with the implication and limitations that this measurement system contracts and that they are revealed by the relativity theory by Einstein.

However the measurements we perform and the way we perform them condition the kind of results we obtain, this does not imply that the results are wrong or right, but it conditions the complications we will have to derive over those basis the theories that will explain the world we irremediably try to explain, in order to be more verbose on this (and explain) we can take as an example the theory of the general relativity and how it changed the fundamentals of measurements of reality by proposing the equivalency between non-euclidean systems of coordinates, it simplifies and unifies several hypothesis that previously where not clearly related.

At this point it is necessary to introduce an specific example to allow me to explain what this is about: let's suppose that we have a pool table in the center of a room, on its surface we draw (an imaginary Gaussian system where the ʋ curves are parallel in between them and separated by a distance of an arbitrarily chosen unit; the ʊ curves will be perpendicular to the ʋ curves and they will be parallel in between them and separated by the same unit chosen.

As you can see the system of coordinates could be an euclidean system, however we define it as an specific case of the Gaussian system to solve the implications that the first system will bring to a surface as is described by the general theory of relativity for those systems.

Now let's assume that we have a ball on the table which we will locate it on an arbitrarily point A of the table and we send it with a constant speed to an arbitrarily point B on the table, this movement implies however ignoring the breaking action that the table will apply on the ball and of course any change of direction that an irregularity on the table will generate on the ball.

This is, the ball will obey the laws of movement on which the ball on a resting state will begin to move with an uniform movement determined by the force that broke its initial state. To perform the measurement of the position of the ball we will locate a video camera hanging on top of the table in a way that we can observe at any given instant on time where is the ball located.

Once we have this experimental table we turn on the lights on the room in a way that the table is completely illuminated y we can clearly see it as well as the initial position of the ball; we start recording with the video camera and we perform the experiment, this is, we hit the ball to move it around from A to B. Once the trajectory have been finished we stop the video camera and with the video recorded we can know the precise position and the speed of the ball at any given instant of time. This experiment is so simple that does not have any mayor complications to prove and use the results.

Now, let's assume for a moment that there's no light on the room (and the video camera is not able to provide it or record what's happening on those conditions), let's assume also that the only or more evident way to solve this issue is:

In some way we can determine (say arbitrarily) the four corners of the table so we can (as well as in the previous example) draw a Gaussian system to help us to identify the position of the ball. Now, to “see” the ball we assume that it has on its surface a substance X which we are not interested on what it is only on the fact that when it crash with another ball covered with the same substance it generates a small spark that can be observed and captured by the video camera.

We are ready to execute the experiment again to send the ball from an arbitrarily point A to a point B, however we still need to consider some problems we need to solve. First, we should realize that in order to observe the position of the ball, we need intercept it with another ball, this is, hit it with other ball so it will generate an spark which will indicate us its position, however this position is not exact anymore, because the second ball can hit our experimental ball on different parts of its surface depending on the direction the second ball is traveling.

As we can see, we cannot (not even closely) know the real position of the ball, however let's assume that to obtain a more satisfactory result we send a third ball which will hit our ball under study, this approach will give us two sparks that will allow us to know better the position of the ball.

Now we have two points (or set of coordinates) and the position of the ball should be closely in between those, however as we realized previously the result does not necessarily needs to be the same every time we perform the experiment, this is, there's “uncertainty” on the position of the ball, in the way that we can only obtain a series of points on which the ball can be on a given instant of time, without being able to determine with precision the position of it.

Once the ball is hit with other ball its trajectory is modified significantly as well as its speed. Given that in the first place the third ball should hit our target on a position which does not correspond to its original trajectory because it has already been modified by the second ball, increasing with this the uncertainty on the measurements.

This effect could be minimized if the speed of the balls two and three is increased, achieving with this that that the interception from the third ball will happen as soon as possible, on this way the trajectory and speed of the initial ball will be modified the the less possible amount of time decreasing with this the error of the measurement.

However, this takes is to our second problem: an increase on the force used to send the balls two and three will increase the amount of disturbance in the original position and speed of the ball.

We should clarify on this matter that the speed or the force applied to the balls two and three should be the always the same for both balls, this consideration is quite important for following considerations. As you can see and analyze with the vectors, an attempt to to reduce the first problem, will increase in the same amount the error on the measurements.

It can be clearly observable that the uncertainty on the measurements cannot be avoided, leading that we can only obtain a set of possible places where the ball can be and statistically, if we expand the number of measurements, the probability that the ball will be on any of those places.

We could even generate equations and theories which could predict the probability of happening; however it will still exist an aleatory factor which will prevent us to know with certainly the position of the ball, we could only know the probability of the ball being on a certain place, which as we can appreciate by increasing the precision of the measurements the probability will decrease consequently.

Now let's try to imagine the problems we would have to fight if we had to base the theories that explain the world under these kind of measurements. Probably we will reach something close to the theories we have in the present day, but clearly with a big amount of problems and limitations that we would have to fight on the way; or maybe we would keep on an initial state tying to solve those problems and limitations a measurements system like this will impose on us.

However, at this point let's make a consideration about this problem (example) we've been working with, it might seem absurd frankly to move from the original problem to the second one when we know beforehand the first way to approach it. In this direction the second approach seems absurd and unnecessary, given that the first approach is clearly more reliable and simple (not simplistic) not only to solve this particular problem but to define with this kind of measurements the base to create, prove and measure the theories that explain the world.

But this idea seems less (or not at all) absurd if for a moment we assume that we are not aware of the first approach to the problem, if we only know the second approach it will acquire validity and by not having any reason to doubt about it, it will then get general acceptance and become the base for the creation, prove and measurement of all the theories.

Seeing from this perspective the situation, it does not seem so absurd a measurements system like that. However it can be clearly observable that discovering a new approach like the initial one would be a revolution which will completely change the way to see the world and more important it would be a step forward on simplifying and obtaining the theories we are interested in.

Up to this point, the present essay is not more than an imaginative story without any real meaning, however it necessary to reveal the considerations behind this example and present the conclusion of it. We'll do that by modifying the problem we've been using on the following way:

Assume now that our pool table is a portion of the space, the ball a particle which we want to know its position and speed, balls two and three are the light used to illuminate the particle and given the wave-particle duality if the light we represent them as balls as well. The particle moves from a point A in space to a point B, the speed of balls two and three is the wave length of the light used to illuminate the particle.

As you can see, the problem just described is the way the quantum mechanics used to measure the position and speed of particles, and as you can see it implies a big quantity of obstacles and by finding a way to perform the measurements similar or equivalent to the first approach of our problem (this is a way that does not require to interfere with the object of study) would be a great advance for the measurement and understanding of the universe.

Probably finding such a way of measuring under the quantum mechanics which will simplify its contents would be far less than impossible and we will not be even close to imagine it; however this is not true, however we just have in the theory of fields from relativity the solution we are looking for.

Let me explain a bit why is this: the theory of fields will allow to define a particle's position (and speed as well) by measuring how the particle disturbs its environment, we can “see” the particle on the same way we can define the position of a planet on the space (by the disturbance and curvature of the space it generates), this approach is closer to our first approach on our example as we don't disturb our object of measurement but perceive its effects on the space.

We could argue that the environment will also disturb our object of measurement, but let's analyze how it will work: on the assumption that a particle is also a wave we can define an artifact that given several sensors places strategically would allow is to sense the waves and define the position of the origin of those waves (similar to an earthquake), those sensors can be placed on a way that they do not disturb our particle on an irregular way and will allow is to take the required measurements.

Einstein believed on this possibility, and in case we could prove its capacity to explain the world of quantum mechanics as a field, it will imply on a natural and practically transparent way the solution to a unified theory of the world.

First draft originally written in Spanish during Jan-Feb 2006