## Einstein’s quantum clocks and Poincaré’s classical clocks in special relativity

This document contains comments about the document http://arxiv.org/ftp/quant-ph/papers/0101/0101146.pdf Yves Pierseaux
• The text in italics is copied from that url
• Immediate followed by some comments
In the last paragraph I explain my own opinion.

### 1. Principles of relativity and group structure of LT

The article start with the following sentence:
The interest to learn the two approaches of special relativity (SR) has been notably emphasised by John Bell in “How to teach special relativity” (1987):
IMO this is the wrong approach. IMO if you want to understand physics you should start from certain basics and slowly build up a vocabulary of agreed upon concepts. Reflection 1 physics
It is my impression that those [students] with a more classical education [including Fitzgerald contraction], knowing something of the reasoning of Larmor, Lorentz and Poincaré, as well that of Einstein, have stronger and sounder instincts.[
If you want to understand physics you have to study as many scientist, to read as many books and to perform as many experiments as possible.
An essential element of a theory of SR is naturally the formulation of a principle of relativity. Lorentz’s paper of 1904 “Electromagnetic phenomena in a system moving with any velocity less than that of light” is not based on a principle of relativity. Contrary to Lorentz’s approach, Einstein’s and Poincaré’s works are based on a principle of relativity:
What this means that Lorentz’s, Einstein’s and Poincaré’s approach each are different.
But that we should be aware: they all can be wrong.
Henry Poincaré: This impossibility of experimentally demonstrating the absolute motion of the Earth appears to be a general law of the Nature; it is reasonable to assume existence of this law, which we shall call the relativity postulate, and to assume that it is universally valid.
This is a rather tricky sentence because it uses the word absolute. You also have to define the word motion.
The laws by which the states of physical systems undergo change are not affected, whether these changes of state (Zustandänderungen) be referred to the one or the other systems of two systems of co-ordinates in uniform translatory motion
Physical systems don't undergo changes as a result of laws. Laws are the descriptions of these changes.
The physical changes are independent of the coordinate system used.
We insist on the fact that nowhere in Poincaré’s work on SR (from 1900 to 1912) the invariance of the speed of light (second Einstein’s principle) appears to be a basic principle.
The whole question is how important the speed of light is to describe the physical processes within the universe. For example chemical reactions have "nothing" to do with the speed of light.
However (the speed of) light is very important to describe what humans observe.
Next at page 2:
A second essential element for a theory of SR is of course Lorentz’s transformations. (LT)
LT belongs to mathematics. How ever it can also be used to describe physical changes.
For the simplest calculation of the factor gamma see here: Reflection 3
In this document the factor gamma is calculated using a coordinate system at rest.
The interesting point is not in these polemical questions of priority but in the question to know if we must delete the ether because the LT form a group. Let us examine this question in details in Poincaré’s work
This is the first time that the word etheris used. There is no definition. See Reflection 2 - photons, ether and the Higgs particle.
In page 5 we read:
The conception according to which “the absolute space physically exists but it is impossible to measure an absolute speed with respect to it” is not a Poincaré’s conception but a Lorentz’s conception. Lorentz’s point of view is the starting point of Poincaré but not the final point
It is all a measure of definition and a measure of which coordination system is in use. Within a coordination system which includes the whole (visible) universe the concept of absolute does not make to much sense
Poincaré explains in “La relativité de l’espace”(1907)” this fundamental issue of his 1905 work.: the concept absolute space has not got any physical meaning but only a psychological meaning “Whoever speaks of absolute space uses a word devoid of meaning”.
Poincaré is correct. To call the whole visible Universe absolute does not make sense
At page 6 we read:
There are two logical relativistic answers to the negative results of Michelson’s experiment. The first consists to closely associate ether and absolute space and to delete the both. This is Einstein’s well known answer. The second consists to radically dissociate ether and absolute space and to transform the absolute ether into a relativistic ether.
The problem is when you try to understand the outcome of an experiment you should not use therminology which is not clear.
What is the difference between absolute and relativistic ether?
The current understanding is that it can be explained by Length Contraction. The problem is that the whole apparatus is length contracted.

### 2. Poincaré's principles and Einsteinís principles of SR

In 1904 Poincaré, in his conference on “the principles of mathematical physics”, just after his first formulation of principle of relativity, Poincaré underlines the necessity to admit another principles:
Unhappily, that does not suffice, and complementary hypotheses are necessary. It is necessary to admit that bodies in motion undergo a uniform contraction in the sense of the motion.
Why length contraction? From a physical point of view the energy to increase your own speed has to come from something.
In his fundamental 1905 work, he determines this force:
But in the Lorentz hypothesis [LH], also, the agreement between the formulas does not occur just by itself; it is obtained together with a possible explanation of the compression of the electron under the assumption that the deformed and compressed electron is subject to constant external pressure, the work done by which is proportional to the variation of volume of this electron.
This is a physical exlanation of Length contraction.
According to Poincaré, the principle of relativity and the principle of real contraction are dynamically complementary. It is however true that Poincaré 1905 work is not presented on an axiomatic basis as Einstein’s kinematics.
It is important that Poincaré uses the word real
We read at page 8:
1) There is an underlying kinematics “of Poincaré’s deformable rods”, based, as Einstein’s kinematics, on “fundamental principles”.
2) The important concept in Einstein’s kinematics is not the rigidity of rods but the identity of the rods within both inertial frames.
Point (1): kinematics and deformable rods, imply physics.
Point (2): both inertial frames, imply mathematics.
Let us develop firstly this second point. A superficial analysis could let think that Poincaré presentation is more coherent than Einstein presentation because it is well known that classical rigidity (instantaneous action-at-a-distance, à la Descartes) is incompatible with Einstein’s SR (ESR) as well than Poincaré’s SR (PSR). But the important concept according the spirit of the text is not the rigidity but the identity:
The problem is that it is not defined clearly what rigidity physical means. A rotating disc will be influenced by stress. That means to try to rotate large discs will become more and more difficult. To reach a constant large speed is very difficult.
For a very large rod the same problems arise. Ofcourse when you accept instantaneous action-at-a-distance the whole problem is mathematically solved. However that is incompatible with physical experiments.
Max Born, who was a specialist of rigidity in Einstein’s special relativity wrote in 1921 in his book on relativity that Einstein introduces a tacit assumption:
A fixed rod that is at rest in the system S and is of length 1 cm, will, of course, also have the length 1 cm, when it is at rest in the system S’, provided that the remaining physical conditions are the same in S’ as in S. Exactly the same would be postulated of the clocks.
The issue is if this is mathematics or physics.
To demonstrate this you have to measure both conditions of a moving object in a frame at rest independent of each other without any moving observer.
What happens with the above assertions if the remaining physical conditions are never the same ? Any way what are these physical conditions?

### 3. Poincaré's use and Einsteinís use of LT

It is well known that the compatibility with the null-results of the Michelson's experiment is based on real contraction of lengths in Lorentz-Poincaré's point of view.
Real contraction of what?
When it is the earth itself also the apparatus is length contracted. So what does this solve.
Next at page 10:
Poincaré writes, in his sixth "paragraph" of his 1905 work, on LH:
In accordance with LH, moving electrons are deformed in such a manner that the real electron becomes an ellipsoid, while the ideal electron at rest is always a sphere of radius r (...) The LT replaces thus a moving real electron by a motionless ideal electron.
For Poincaré the whole issue of length contraction is physical.
IMO as such you only need one reference frame.

### 4. Poincaré's and Einstein’s conventions of synchronisation

In this paragraph it is important to see that the letter k is used in two diffent ways. As a capital letter K and as a small letter k. They identify two systems which are in relative motion.
At page 12 we read:
Poincaré explains: 1- (Two observers are at rest relative to ether, System K)
The most ingenious idea has been that of local time. Imagine two observers [A and B] who wish to adjust their watches by optical signals; they exchange signals, (...) And in fact, they [The clocks of A and B] mark the same hour at the same physical instant, but on one condition, namely, that the stations are fixed.
What would be very nice if someone would rewrite this whole paragraph without mentioning ether
The issue is not that the staions are fixed but that the difference between all the clocks in the frame is the same (fixed). As such what you get is a global time.
At page 13 we read:
1 - (Einstein’s “stationary time of a stationary system K”)
But it is not possible without further assumption to compare, in respect to time, an event at A with an event at B. We have so far defined only an “A time” and a “B time”. We have not defined a common “time” for A and B, for the latter cannot be defined at all unless to establish by definition that the time it required by light to travel from A to B equals the time it requires to travel from B to A.
Of course you can define that but physical that maybe is not correct.
 ``` ^ \ .. / / \| \ x / / | \ .. / / |\ \. . / / | \ . . / | \ . \/. / | \ . /\ . / | \ . / \./ | \ ./ B | \./ | A t=0 ---------------------- Figure 1 ``` The physical issue is that photons are created from a source independent of the speed of its source. For example if you have two lightsources A and B which are a certain distance appart the lightwave of light flash A will never interfer which the lightwave of the other light flash B. independent of the speed of A and B at the moment of the lightflash of each Figure 1 demonstrates this. The \ / lines represents the lightwave (light flash) which propagates through space. The points above A show the path of lightsource A. The same for the points above lightsource B. The point x is the meetingpoint of both lightsources, but this point is not in the center of the two lightwaves.
Let a ray light start at the “A time tA” from A towards B, let it at the “B time” tB be reflected at B in the direction of A, and arrive again at A at the A time t'A. In accordance with definition the two clocks synchronize if
tB - tA = t’A - tB
It is essential to have time defined by means of stationary clocks in stationary system
or tB = (t'A - tA) / 2.
The issue is to what extend you can also do that for a different stationary system in relative motion with above i.e. system k, discussed next.
At page 14 we read:
2 - (Einstein’s “stationary time of a stationary system k”)
The synchronisation of identical clocks within the second system k is exactly the same than the synchronisation in the first system because the speed of light is of course exactly the same. In Einstein’s own terms “as demanded by the principle of relativity and the constancy of the speed of light also propagates with velocity c in the moving system”.
What this means that in Einstein's philosophy the laws in both systems K and k are completely identical.
The question is how do you measure the speed of light in a system at rest versus a moving system using the same equipment.
At page 15 we read:
It is indeed easy to see that Einstein’s synchronisation and Einstein’s identity of units are exactly the same concept. With identical rods and with the (one-way) speed of light c numerically identical within the two systems, we have of course the same internal duration.
Einstein’s concept of “synchronous clocks” is very subtle because the repetition of the process of synchronisation (sometimes called Einstein’s light clock) provides an identical rhythm (unit of time) for the clocks.
 This seems to indicate that if you perform the experiment as outlined in Figure 2 it does not matter if you perform this test with a train at rest or when moving. As indicated in the text the rhythm or frequency of the clock pulses should be identical. ``` | | | t2 . | | . . | | . . | | . . | | . . | t1. .t3 | . . | | . . | | . . | | . . | t0| Y | ------------------------- X Figure 2 v=0 ```

### 5. Einstein's preparation of identical isolated stationary systems and the adiabatical hypothesis

Einstein: first stage. The preparation of the two systems in state of rest:
“Let us consider K et k two equivalent systems of reference; we may say that the systems have measuring- rod of same length and clocks giving the same indications, the comparison between this objects being made when they are in state of relative rest ”
What this means that rods and clock's in both systems are identical.
Second stage: the “launching of the boost”:
“Now let a constant velocity v (Es werde nun dem Anfangspunkte ... erteilt) to the origin of one of two systems (k)”
The issue is how is this speed v measured. IMO this is a speed measured in a frame at rest.
The young specialist of statistical thermodynamics Einstein formulates explicitly in 1907 the hypothesis (I discuss this adiabatical hypothesis in my book) that his identical clocks and his “rigid” rods are not modified by the passage from the velocity to the velocity v.
The issue is how does he know that? You have to perform at least some tests that this is true.
Many authors think that the problem of rigidity in young Einstein’s text can only be solved in general relativity (GR) because the concept of rigidity is deeply connected with Euclidean geometry.
IMO rigidity is typical a physical problem.

### 6. Einstein's quantum clocks and the spectral identity of atoms

The young Einstein identifies explicitly “clock and atom” in his second fundamental synthesis on SR in 1907:
Since the oscillatory process that corresponds to a spectral line is to be considered as a intra-atomic process, whose frequency nu is determined by the ion alone, we can consider such an ion as a clock of definite frequency nu0; this frequency is given, for example, by the light emitted by identically constituted ions at rest with respect to the observer.
You can start from the assumption that an atom clock has a certain frequeny f as measured by an observer (at rest) in the same frame as the atom clock.
• The first question is how is this frequency measured?
You do that by a "counter" also at rest with the atom clock. The distance between the clock and the counter is fixed.
• A second issue is what happens with the frequency if the atom clock has a speed v away from the observer at rest.
In that case you need atom clocks and two counters. You can set up two experiments:
1. In the first experiment the moving clock first has a speed v away from the observer. After a certain time stops and immediate returns with a speed v towards the observer at rest.
The difference in clock counts informs the observer about the average behaviour of the moving clock.
2. This experiment is the same as the first with the only difference that the observer at rest also has a second counter to count the frequency of the moving atom clock. This counter should give the same counts as the moving counter when the atom clock returns back home.
The importance of the second counter is that the frequency of the incoming counts will be different. The frequency of the out going counter will be low and of the incoming counts will be high. This allows the observer to detect a frequency change and to test if the moving counter has the same frequency in both directions.
 ``` xb.y4 x5| , xa. . | . . x4. y3 | . . | . . x3| . . | y2 | . x2. . | . . | y1 x1. . | . | . A Figure 3 ``` ``` | . | y2. | , | / . | . / . | . | / . | . | / ./ | . | / . / x2. | , . / | . | ,/ . / | . | , / . / | . | , / . / | . /. / | . |y1. / | . | / . / | . |/ . / x1. / . | . /| ./ | . / | . / | /. | . / | / . / | / . | / | / . | / |/. |/ A B Figure 3A ``` ```y4. B |\. |\ | \ . | \ x5. \ . | \ | . \ . \ | .\ | . \ | \ | . \ | . .\ | . . | . |\ . \ | . | \ . \ x4. |y3\. \ | . | \ . \ | . | \ . \ | . | \ . \ | . \ . \ | . | \ . \ | . | \ .\ | . | \ . x3. | \ . \ | . | \ . A . B y2\. Figure 3B ```
Figure 3 shows the two atom clocks.
The vertical line shows the atom clock at rest. At x1 this clock counts 1. At x2 this clock counts 2. At x5 this clock shows 5. When the moving clock return the atom clock shows b ( b= 5.333)
The dots at 45 degree angle show the moving clock. At y1 the m-clock counts 1. At y2 the m-clock counts 2 and then returns. At y3 the m-clock counts 3. At y4 the m-clock counts 4 and is than back base. This implies that the moving clock runs slower (4 counts versus 5.33 counts).
Near the observer at rest at x2 the second clock counts 1. At x4 the second clock counts 2. That means the frequency of clock counts received of the moving clock is very low.
At xa with a=4.66 the second clock counts 3. At xb with b=5.33 the second clock counts 4. That means after the point of return, the frequency of the clock counts received is high.
In this particular example the speed in both directions is the same.
At page 19 we read:
In “La mesure du temps” , The great specialist Poincaré of Celestial Mechanics writes in 1998:
“In fact the best clocks have to be corrected from time to time, and corrections are made with the astronomical observations; (...) In other terms, it is the sidereal day or the duration of rotation of the Earth, that is the constant unit of time.
The rotation of the Earth is maybe very practical but not very scientific.
In the same text Poincaré writes:
“When we use the pendulum to measure time, which is the postulate that we admit implicitly? It is that duration of two identical phenomena is the same. Watch out one moment. Is it possible that experiment denies our postulate.? If experiment made us the observers of such a spectacle our postulate would be contradicted.”
What is the reason to write: "that duration of two identical phenomena is the same"?
This seems completely physical logical. When two phenomena are identical they should have the same duration.
Two phenomena are not identical if one is performed at rest and a second one moving.
In a paper in 1910 on his SR Einstein affirms explicitly his postulate:
(1) Thus, we postulate that two identical phenomena are of the same duration.
(2) The perfect clock so defined plays a role in the measurement of time that is analogous to the role played by the perfect solid in the measurement of lengths.
Postulate item (1) smells like common sense
Postulate item (2): If you use a concept like a perfect clock than you should also define what is a not-perfect clock.
It is only possible to define a perfect clock and a perfect solid if measurements are made from one reference frame.

Following is a list with "Comments in Wikipedia" about related subjects

### Reflection 1 - physics

If you want to understand physics than you have to start from simple agreed upon concepts and slowly build up more complex concepts.
1. One of the first concepts is to start from: is that there exists only one Universe (which encapsulates all of space)
2. What exists are objects (entities). objects are different. Some are simple and some can be very complex. Some of these objects (entities) are visible for humans but other objects are not. But this is totally unimportant for our understanding.
3. The most important concept is that the objects are not static but dynamic. That means the objects change in position and constitution in time. As such the whole universe evolves in time.
4. It is the endavour to study these changes, to describe these changes, what caused these changes and how they evolve in time.
5. Newton's Law, SR and GR are some of the laws that describe similar changes.
6. All these changes (the universe) should be described in one coordinate system or reference frame. Within this coordinate system they are called absolute (motions). Changes can also be described relative to each other. As such they are called relative (motions).
7. All the changes (events) that happen in the unverse at the same time are called symultaneous.
8. Changes within objects are subject of what is called stress and can never happen instantaneous. That means they slowly propagate within the objects.

### Reflection 2 - photons, ether and the Higgs particle.

Photons, ether and Higgs particles are called objects in Reflection 1 physics. Photons are the building blocks of (visible) light. The most important parameter of light is what is called the speed of light .
The speed of light is considerd constant but that is the question if you consider the behaviour of photons throughout the whole of the Universe.
You can consider the speed of light constant in a vacume or empty space, but that is already tricky because empty space is by definition not empty when there are photons.
A different question is to what extend the speed of light is constant throughout the universe if they cannot escape from a blackhole. One possible solution could be to consider the speed of light only locally (close to earth) a constant (but not globally)

A whole different question is to what extend the behaviour of the photons which exists around our earth are not effected by a fluid, the so called ether. This fluid inturn is influenced by (the gravitational field) our Earth or by (the gravitational field) the Sun.

For the Higgs particle and the so called Higgs field the same issues arise.

The whole issue around ether is in a certain sense outdated. The whole issue is to what the speed of photons is everywhere the same in all directions within our Galaxy, the stars and the planets.

### Reflection 3 - Different clocks at rest

Figure 4 (blow) shows the behaviour of two clocks:
• One clock at rest. The counts of this clock are identified with the points x1,x2,x3,x4,x5 and xb
• One moving clock. The counts of this clock are identified with the points y1,y2,y3 and y4.
What figure 4 shows is that the moving clock counts slower as the clock at rest. 4 counts versus 5.333 counts.

 ``` xb.y4 x5| , xa. . | . . x4. y3 | . . | . . x3| . . | y2 | . x2. . | . . C | y1 , x1. . , | . , | . , A Figure 4 ``` ``` | . | / / t4. | ,t5 / | . | ,/ / | . | , / / | . | , / / | . / / | L3 . | .t3 / | . | / . / | . |/ . / t1. L1 / .t2 | . /| ./ | . / | . / | /. | . / | / . / | / . | / | / . | / |/. |/ A L Figure 5 ``` Figure 5 shows the bottom part of Figure 4 t1 is the duration of one count of the stay at home clock. t1 = 2 * L / c t3 is the duration of one count of the moving clock. L + v * t2 = c * t2 : t2 = L / (c-v) L = c * t3' + v * t3' : t3' = L / (c+v) t3 = t3' + t2 = L / (c+v) + L / (c-v) = 2Lc/(c^2-v^2) = t1 / (1 - v^2/c^2) t4 is the time when the observer at rest receives the first count of the moving clock t4 = L3/c + t3 : v*t3/c + t3 = (v+c) * t3 /c = t1 * c / (c-v) L3 = v*t3 = (t4-t3)*c : t4*c = (v+c) * t3 : t4 = t1 * c/(c-v) t5 is the time when the moving observer receives the first count of the clock at rest t5 = L1/(c-v) + t1 : L1 = v* t1: t5 = v * t1/(c-v) + t1 = (v*t1 + (c-v)*t1)/(c-v) = t1 * c / (c-v) Using this information the following two fractions can be calculated: f1 = t4/t1: This is the fraction of the clock at rest. f2 = t5/t3: This is the fraction of the moving clock.

 v/c t1 t2 t3 t4 t5 f1 f2 f1/f2 f2/f1 0.666 2 3 3.6 6 6 3 1.666 1.8 0.555 0.5 2 2 2.666 4 4 2 1.5 1.333 0.75 0.333 2 1.5 2.25 3 3 1.5 1.333 1.125 0.8889 0.166 2 1.2 2.057 2.4 2.4 1.2 1.1667 1.028 0.9722
What the table shows is that there is a clear difference between the frame that is at rest and which is not.
• In the frame at rest (relative) the fraction f1/f2 is larger than 1.
• In the frame not at rest (relative) the fraction f2/f1 is smaller than 1.

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