To understand Relativity
TO UNDERSTAND RELATIVITY
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One of the amazing aspects of the theory of Relativity is the contrast
between the conceptual and mathematical simplicity on one hand, and the
difficulty of understanding on the other.
Indeed, as the exposition of the theory fills only a few pages, and the
mathematical developments don't exceed the elementary level, this theory
has taken a long time to be accepted by the scientific community, and
is still subject of a countless number of discussions and attempts of
interpretation.
What could be the reason?
Of course, this theory hurts the common sense and asks us to review our
ideas about time and space, but that's not the all explanation.
In fact, I think the basic problem is a lack of clearness and solidity
of the logical basis of the theory.
Those are shortly a few points that may cause some problem:
- The postulates
The principle of Relativity (the equivalence of galilean systems) and
the constancy of the speed of propagation of electromagnetic waves in
empty space are facts which are established by observation and
experimentation.
Einstein made fundamental principles of it, on which he founded his theory.
Consequently, no exception on this principles can be considered.
This creates the unpleasant feeling that the mind imposes his rules to
nature.
- The simultaneity
The problem is to define the simultaneity of events at different places,
in moving reference frames.
Obviously, a procedure has to be used to synchronize the measure of time at
different places.
It seems natural to therefore use light (or other electromagnetic) signals.
It's even difficult to imagine, at the present state of knowledge, to use
any other method.
However, there is no reason to 'a priori' give an exclusivity on
electromagnetism.
The "relativity of simultaneity" is often given as the reason for the
"relativity of time". This assertion is ambiguous.
The definition of simultaneity results from the procedure used to
synchronize (Einstein mentioned it as an agreement). This procedure doesn't
explain the different "time flow" in different systems.
- Time and Space
In the classical theory already, the idea of the Uniformous-Flowing-Universal-
Time was rather hazy. But the definition of time stays abstract and doesn't
influence the laws of the theory.
In Relativity, it's quite different: time and space are considered as
objective entities, who have an own existence and a variable structure,
that reflect in the shape of the objects and in the clock's indications.
Further, each moving system has 'his own time'. So one should consider that
an infinite number of 'times' 'exist' in parallel and 'manage' the working
of moving clocks.
It's vague and rather strange. Anyway, it belongs to philosophy rather
than to physics.
- Spacetime
Shortly after the publication of the Theory of Relativity, the notions of
time and space where replaced by a new idea: the spacetime, which,
however, doesn't make things clearer.
One must indeed realize that this concept is a purely mathematical
construction (it's a structure of four dimensions, one of which being
imaginary).
However, the graphical representation of this structure gives the fallacious
impression that we can imagine it, and this increases the risk of confusion
between the mathematical model and reality.
- The rods and the clocks
The way time can be measured is very vague in the theory of relativity.
There is some talk of clocks "of identical construction" that are
supposed to stay synchronized when not moving. It seems that clocks are
ideal objects that perfectly reflect the "flow of the local time".
Concerning the rulers, they are "perfectly rigid" objects. Besides the
fact that such objects of course don't exist, one must notice that even the
idea of such an object contradicts the principles of the theory.
Indeed, the displacement of a rigid rod would correspond to the emission of
an instantaneous signal from one end to the other.
This problem was subject of many controversies in the first years after
the publication of the special relativity theory, and faded away when
the representation became more abstract.
- Abstraction
Einstein approached the problem of moving bodies in a very abstract manner.
Starting from general principles, the all theory is constructed by the
deduction of pure mathematical formulas.
This very powerful method since was spread over all physics.
However, besides the fact that physics also became unreachable to non
experts, the disadvantage of this method is that it reduces the reality
to a mathematical model. Physics becomes a 'formulas box', in which the
parameters corresponding to observed facts are transformed following the
rules of mathematical logic, with no limitation.
After those transformations, one tries to paste it on reality again,
which is not evident, and sometimes results in some craziness (how can
you, for example, interpret a negative or imaginary time parameter?).
- Reciprocity
Reciprocity is an essential concept in (special) relativity theory, as
it justifies the equality of the equations of electromagnetic waves
propagation in moving systems: x+y+z-ct=x'+y'+z'-ct', from which the
transformation formulas are deduced.
This notion, however, causes serious comprehension problems.
Indeed, if - as Einstein always said - the time and space transformations
are very real in each referential system (and can not be considered as
a sort of illusion due to observation), one comes to have to consider
the idea of sorts of "parallel realities" where it's true that a is smaller
than b as well as b is smaller than a.
An exemple
can make this clearer.
- The twins paradox
The story of the twins, one of them coming back from a journey being
younger than his brother, is wrongly called a paradox.
Indeed, if the situation is not reciprocal, we have just a rather
dramatic consequence of the modification of "time flow" in a moving system
(speaking in the terms of the theory).
Otherwise, if their situation is reciprocal, it isn't a paradox but a
real incoherence.
So the problem is generally solved by denying the reciprocity: the traveler,
as he went thru accelerations, lost his status of an inertial system.
Thus, it is "logic" that the time measured by his brother will be verified
when they meet again.
The explanation is a little simple.
Indeed, the reciprocity is one of the bases of the relativity theory, which,
besides, doesn't deal with accelerations.
So you see that, as soon as you try to apply the theory in reality,
you are in a situation that fundamentally differs from that where the
theory is based on.
And, although the relativity proclaims "all" the inertial systems to be
equivalent, it seems that, really, only one such a system exists, being
that which never had any acceleration.
All those points - the above list can be enlarged - which make the theory
hard to understand, are generally hushed in publications that pretend to
explain relativity to a large audience.
So one should not wonder that this theory isn't accepted or is interpreted in
the most bizarre way.
Does the Theory of Relativity therefore have to be rejected? Surely not.
One must simply try to interpret it correctly.
First, you should remind that the Theory of Relativity belongs to physics
and not to philosophy.
Consequently, its first aim is to describe coherently the results of measures
and to anticipate correctly on future results.
The fundamental idea of Relativity is that straight and uniform movement
does not influence the formulation of physical laws, despite the constancy
of light speed.
In other terms, the laws can be expressed in such a way that the value of c
will stay the same, whatever may be the speed of the system.
The transformations imposed by this hypothesis on time, space, mass etc.
parameters, indicates that the MEASURE of these parameters concerning one
specific phenomenon will be different, when performed in different referential
frames.
Of course, because these transformations are imperceptible to the
observer in the moving frame, he can consider himself as being at rest, and
if he didn't noticed the accelerations, he will never be able to determine
the speed of his own system.
One can, for example, very well consider that the earth is motionless in space
(not taking in account the non uniform aspect of its movement) and that
the stars are moving relative to us. But actually, we know very well that
this probability is small.
But why does the measure of the light speed not vary in spite of the
displacement of the system on one hand, and the independence of light
propagation from the source on the other?
It's very simple:
BECAUSE YOU MEASURE THE SPEED OF LIGHT WITH LIGHT.
All the interactions inside the matter, that determine the dimensions and the
inner movement of all measuring tools, are electromagnetic waves, or at least,
follow the same propagation rules as light.
In other words, the structure of the rods and the clocks, but also of all
objects, from the atoms to the stars passing the human body, vary
depending on his speed. This variation reflects the fact that the propagation
of the interactions does participate no more on the system movement as the
other electromagnetic signals do.
It is thus obvious that the rods and the clocks will behave differently
(will indicate other measures) according to their reciprocal speed, but will
give the same results when measuring the propagation of electromagnetic waves.
There is no need to use concepts of "variable time and space", which are just
creations of our mind (The Time doesn't make the clocks work, but the
movement of the clocks - and other objects - induces in our mind the concept
of Time).
It seems usefull, for better understanding, to see how some parameters behave
at the speed of 'c':
- Length contraction:
The shape of the objects results from electromagnetic interactions between
the particles. Remember that the diameter of the nucleus is only 1/100,000
that of the whole atom.
If the body is moving, the speed of the particles influences the
propagation of the interactions.
At the limit, if the particles reach the speed c, the length of the object
becomes zero, as the interactions couldn't go from one particle to the
other.
- Time dilation:
The movement of an object is influenced by the motion of the system in
which it is moving.
It's easy to understand that a clock made of a light signal that oscillates
between two mirrors would be influenced by their motion.
But in any other clock, exactly the same happens: the inner movement depends
on the interactions between the particles. Due to the electromagnetic
nature of those interactions, all motion becomes impossible in a system
that moves at the speed of c, thus time stops.
- The increase of the mass
The mass of a body intervenes when you want to interact with it. This
interaction is electromagnetic. On the speed of c, no interaction can
influence the body, thus its mass becomes infinite.
So we can say that, although the fundamental principles of the Relativity
Theory are only valid in a theoretical universe that isn't that in which
we are living, all the formulas of the theory apply on reality, due to the
electromagnetic nature of it.
So let's review, from this point of view, the questionable points we listed
before:
- The postulates:
Can be suppressed.
The relativistic transformations result from the nature of the phenomena
and not from some kind of prejudice.
- Simultaneity
The definition of the simultaneity of distant events depends on the
synchronization procedure you use. In the current state of knowledge,
the procedure described by Einstein is the only usefull. However, if new
kind of signals where found, which would propagate differently from light,
one would have to take in account which kind of signals were used in any
experiments.
Einstein's Relativity a priori excludes the existence of such signals, since
those would make possible to know the proper movement of inertial systems.
- Time and Space
are abstract concepts. Their definition is a matter of metaphysics, not
of physics.
- Spacetime
is very helpful as a mathematical instrument. But it's neither necessary,
nor acceptable to give a reality sense to this concept.
- The rods and the clocks
We can use only one sort of instruments: rods and clocks which structure's
depends on interactions that propagate according to the laws of
electromagnetism.
For example, Michelson-Morley's interferometer wasn't made of rigid arms.
At the atomic level, the distance between the nuclei is immense and the all
structure 'stands' by the exchange of signals that are comparable to those
one pretends to measure.
- Abstraction
The abstraction is usefull when it permits to deal with the power of
mathematics. But the physicists often tend to forget that we do not
live on paper. In no case one must lose the link between the formulas and
the reality they are presumed to represent.
- Reciprocity
We saw that when you measure lengths in different systems, the contraction
compensates the desynchronization, so that reciprocity is kept.
Also, in time measurements, the slowdown of the clocks compensates the
asymmetrical propagation of the signals.
However, this reciprocity is virtual, because considering it real results
in contradictions.
Each observer can consider himself as being at rest during his measures;
this won't change the results. But it doesn't mean everybody IS at rest
because this assertion is absurd.
This exemple
can make this clearer.
- The twins paradox
When the traveler leaves his brother, his system goes thru tremendous
modifications. The direction of all the interactions between particles
changes. All the inner movements of the system slow down to find a new
balance between transversal and longitudinal interactions.
On the particles level, this adaptation is experienced as a reaction to
movement, i.e. as inertial mass.
These modifications are very real and surely not reciprocal; they take place
during the "change of velocity", in other words during the acceleration.
Given that every movement is the sum of accelerations, which are real
phenomena that can be observed and quantified, it is justified to give
a absolute sense at the system's movement.
The "proper speed" is the result of all the changes in velocity of the
system since its origin.
The fact that, in practice, one hasn't knowledge of all the past
accelerations don't change anything of this principle.
I would finally remark that this more "concrete" approach of physics can
also be applied on the General Relativity.
You can see, for example, that the change of mass of the planets, due to
the changes in distance to the sun and the to the variable speed on an
elliptic orbit, will influence this orbit: the "faster" part will be located
on a lightly smaller ellipse than the "slower" part, so the axis of the
ellipse will rotate. This explains the precession of mercury's perihelion,
as predicted by General Relativity.
I am sure that this approach would allow not only to better understand
modern physics and to get rid of many misunderstandings, but also to open
new ways for development of the theory.