Dear Andrew ~

Forgive me if much of what I shall say is obvious or well-known to you − I’m just trying to be rigorous and hope I don't seem pedantic.

In Newtonian physics and in Einstein’s Special Relativity it is presupposed that 3-dimensional space is Euclidean. The position of an object (idealized as a point) can be labelled by three coordinates (x, y, z). If the object is moving, it’s trajectory can be described by functions x(t), y(t), z(t), where t is time, which is measured by a “clock”. An “event” is something that happens at a particular point, at a particular time: it can be labelled by four coordinates (x, y, z, t). Two events are “simultaneous” if they have the same value of t. The trajectory of a moving object can regarded as a sequence of events − a curve in the four-dimensional “spacetime” called the “worldline” of the object. Now, according to Newton’s first law, an object on which no forces act moves with uniform velocity; the functions for the object’s trajectory x(t), y(t), z(t) are linear - the worldline is a straight line. The coordinate system (x, y, z, t) is then an “inertial frame” (call it K) and t is the time recorded by a clock that is “at rest” relative to K - the coordinates (x, y, z) of the clock are constant.

 It’s not possible to visualize four dimensions; I find it helps me to understand relativity if I concentrate on x and forget about y and z. One can then sketch diagrams and can think in terms of a t-axis and an x-axis in which a wordline is a plot of a function x(t). Light rays are then straight lines parallel to the lines x = ±ct. The worldine of an “inertial observer” (carrying a clock) is a straight line parallel to the t-axis. All the “events” on a line parallel to the x axis are “simultaneous”.

Everything so far applies to Newtonian physics. Einstein’s Special Relativity has not been invoked. Two different “inertial frames” K and K′ are in uniform motion relative to each other. In Newtonian physics a Galilean transformation specifies the transformation from the coordinate system K to the coordinate system K′. Nothing happens to the concept of “simultaneity”. However, the speed of light is not the same in K and in K′. These two propositions are incompatible:

(1)   Simultaneous events are simultaneous in all inertial frames.

(2)   The speed of light is the same in all inertial frames.

The Galilean transformations satisfy (1) but not (2). The Lorentz transformations satisfy (2) but not (1).

 There is no way around that! If the speed of light is the same in all inertial frames, then simultaneity is “relative”. According to the Lorentz transformations two events that occur at the same time t according to a clock at rest in K do not in general occur at the same time t′ according to an identical clock at rest in K′.

 Hence relative simultaneity is not “a computational effect of no consequences to real temporal relations”. It is a very real consequence of the Lorentz transformations.

Your question was also concerned with the length of a rigid rod. I already presented my interpretation of that on another discussion board. For your convenience I’ll copy & paste what I said there:

 “In the attached figure the red line AB represents a “snapshot” of a rod at rest in K (x, t). Its ends have the same value of t.  The grey coordinate system is that of K′ (x′, t′). Event B of K’s snapshot occurs, from the point of view of K′, earlier than A. the two events A and B, simultaneous for K, are not simultaneous for K′. A snapshot taken from K′ will reveal the two ends of the rod at A and B′, which are simultaneous for K′. (This of course, is the origin of so-called “length contraction” − the rod appears shorter to K, but nothing has happened to the rod, it’s moving, that’s all!)”

 That is, I regard so called “length contraction” as an illusory phenomenon, an artifact of the process of observation and measurement and of the “relativity of simultaneity”. If a rod is not in uniform motion but is accelerating, then there will be a time-varying “length contraction” − as you correctly pointed out, to an inertial observer it will seem as if the two ends of the rod are moving relative to each other!

Thank you Eric and Mohamed for taking your time and responding to my question.

I am very interested in this discussion so I will respond after a thorough analysis of your responses. It may not be immediate but it will come for sure. This is what I was expecting posting this question. An honest opinion regarding my claims.

My interest in relative simultaneity is twofold : one, I want to get to the bottom of something claimed by science and utterly illogical to me. The other is the fact that I do not see internal inconsistency in Einstein's model itself.

Talk to you soon

Dear Andrew, I think that a kind of 'answer' to your question is based on:

Johan Prins has also worked on this topic.

Dear Eric Lord:

   In your  nice diagram, how do you determine B'? Geometrically, you need two conditions; however, I see three possible conditions:  1) a parallel to x' axis through A, 2) a parallel to t axis through B, 3) an arc of a circle centered at A, with radius AB. The third alternative implies an a priori belief in the constancy of lengths (which is what we want to disprove).

   I think you forgot to mention that the rod moves in K with some constant speed, so that, in the diagram, rod AB moves parallel to itself along the t axis.  

Dear Raul ~

The rod is at rest in K; Its two ends A and B are permanently at x = 0 and x = 1. I have represented it at some arbitrary time t, by the red line. At some later time it would be represented by a line A′B′ parallel to AB (I didn’t mark A′ in the figure - sorry if its absence confused you…). In K′ (relative to which the rod is moving) AB′ is parallel to the x′ axis; hence A and B′ are simultaneous in K′ (they have the same time coordinate t′). For an observer at rest in K′ the length of the moving rod will seem to be the length AB′. It is shorter than AB. That is “Lorentz contraction”.

Hope it's clearer now. (I habitually think of matters related to Lorentz transformations by translating the algebra into geometrical figures. I tend to forget that others may be less familiar with this approach...)

   Dear Eric,

   On the contrary, I also prefer the geometric graphical approach. Thanks for mentioning A'; I had not thought about it.

   Now, how do we know that the bar A'B' is moving in K'? Just because (and this is not easy to find out) AB' forms with the x' axis an angle different from the one the t' axis makes. That is, AB' is not parallel to the t' axis.

   Any more feedback will be appreciated. 

There is a different way to look at the effects of Special Relativity (SR), including simultaneity.  The "standard" way to look at it is via Minkowski Space, as if each reference frame has a real physical space-time.  The alternate way to look at it is that the measurements of SR are artifacts that appear only after the Einstein synchronization process is performed.

It is easy to demonstrate that this is true.  Take two clocks A and B some distance apart, and stationary in frame X.  Accelerate them simultaneously in X at a high rate over a short time so that they are now traveling at V relative to X, but still not moving with respect to each other.  Immediately after acceleration, A and B, though now moving relative to X, do not exhibit any time skew.  Only after the synchronization is performed can they be used as an Einstein reference frame.

The same is true of the distance between them.  It will, after synchronization, appear too large to them. 

However, quantum mechanical systems perform the resynchronization and length adjustment automatically.  For example, a physical rod will contract (or seem to in the frame of X).  And if an oscillator is formed by resonating something between the two ends of the rod, forming a synchronized pair of clocks in effect, it will appear to be adjusted properly.

In addition to quantum systems, if a system is accelerated infinitely slowly, or if a point observer who has been accelerated makes a measurement of any reference frame which was not accelerated, they will see all of the SR effects.  So it is hard to say that relative simultaneity is a misinterpretation - certainly not with respect to quantum or unaccelerated systems, and that's all SR really deals with anyway.  But there is this caveat that perhaps the interpretation of the physicality of overlapping space-times is over done.

Dear Raul ~

The angles in the figure mean nothing at all (the plane we are thinking about is Minkowskian but that diagram is unavoidably Euclidean). The trajectories of the ends of the rod are the lines x = 0 and x = 1 (that is, the t axis and the line through x = 1 parallel to the t axis). Those trajectories are the “reality”, independent of  whether they are described in the K system or the K′ system. For K, at any instant t the rod is seen as a rod parallel to the x axis. For K′, at any instant t′ is seen as a rod parallel to the x′ axis.

    ____________________________________

 A note about the geometry of the diagram:

the Lorentz transformation K → K′ can be written as

x′ = xcoshχ − wsinhχ, w′ = −xsinhχ + wcoshχ

where w = ct and eχ = √[(1 + v/c)/(1 − v/c)].

This is an expansion eχ along one of the diagonal direction (x − w = const.) and a corresponding contraction e−χ along the other (x + w = const.). That’s how I made the diagram. The "diagonal" lines x ± w = const. are the trajectories of light rays.

Dear Robert ~

I’m not sure whether the following thoughts are related to what you are saying.

Considering Minkowski space purely as a geometry, there are special coordinate systems (x, y, z, w) in which the metric has the form dw2 − dx2 − dy2 − dz2. We can, without implying any physical interpretation, choose to call these special coordinate systems “inertial frames”. The physical interpretation involves the proposition that t = w/c is time recorded on all the clocks located at various fixed positions (x, y, z) relative to the “inertial frame”. To make sense of that, we have to imagine all those clocks synchronized. This involves the assumption that if they are all set to the same identical reading at some value of t, they will continue to give identical readings at all values of t. That is an assumption. Any physical theory whatsoever requires assumptions in passing from the mathematics to physical measurements. Those assumptions are called hypotheses, and have to be tested against experiments and observations.

We are at liberty to choose some other, arbitrary, method of synchronization. Choose a family of spacelike hypersurfaces T = at + f(x, y, z) = const. Then, if the above hypothesis is the “truth about clocks”, it will also be true that, if the clocks at rest in an inertial frame are synchronized on one of these hypersurfaces, they will remain synchronized for all values of T. In this sense, there is considerable arbitrariness in the definition of “simultaneity”. However, all this amounts to nothing more than using a curvilinear coordinate system in Minkowski space. It doesn’t affect the physics that is being described in that coordinate system. So, appealing to Occam’s razor, we may as well stay with the usual very simple interpretation, in which the parameter t of an inertial frame is identified as “clock time”.

Relativity does in fact prescribe a “clock time” for any clock, however it is moving. It is the “proper time” τ, a parameter along the clock’s trajectory. That is an invariant, independent of coordinate systems. For a clock “at rest” relative to an “inertial frame”, it coincides (apart from a constant of integration) with t.

Andrew,

I don't understand your introduction of length contraction to the question of relative simultaneity. Time dilation is about time, length contraction is about space. They are both relativistic effects, but they should be treated independently to avoid needless complication and confusion.

James ~

"length contraction" and "time dilation" are two aspects of the same thing  − the fact that "simultaneity" is frame-dependent. It is instructive, rather than confusing, to consider them together. Then we get the whole picture.

James,

I do not mention length contraction anywhere. In my examples, I talk about relative distances of parts of rigid structures or points moving synchronously along parallel lines  at the same relative speed.

There is no contraction in K for static structures and no contraction in X direction for objects moving in Y direction. Any apparent changes of distances in system K' that has moved from rest to velocity v, are explained by Lorentz transformation. The assumption that the same clock times in K' determine simultaneous states leads to paradoxical change of relative distances of invariant relative geometric relations in K. A sort of distant analogy is, when you move an irregular shape glass object  front of you eyes you see static objects moving and changing proportions. In this case there is no glass object but wrongly interpreted Lorentz transformations.

I disagree. Given that time dilation can be discussed independent of length contraction, if the question is about simultaneity, contraction is an unnecessary issue. Like the consideration of acceleration, which has also been introduced here, and any other issue that might contribute to a "whole picture", contraction can be deferred without any detriment to the understanding of simultaneity.

James,

Imagine a non relativistic scenario here on Earth.

Imagine a long train on a straight line, which occasionally stops on stations. You monitor the front and end of the train recording their position on tracks and the GMT.. 

You will find that no matter how the train moves, the distance from front to end as determined from their positions on tracks is the same. 

Now for every time of the train's last carriage you subtract 10 seconds and connect new "simultaneous" points on the plot. You find an amusing picture. The train

a. may appear shorter (length contraction)

b.when the train slows to stop it stretches than goes to normal length on the station

c when it mmoves the last carrige goes in front of the engine and gives it "negative length"

The picutre attached.

The illusion of relative simultaneity works similar way

Eric,

In your first comprehensive response I do not find much I would disagree. There are very subtle differences that somehow put us on he opposite side of the fence. I really need more time to figure out the way to highlight this and get to the bottom of it.

 Robert,

Thanks for entering this discussion.

You say:

The alternate way to look at it is that the measurements of SR are artifacts that appear only after the Einstein synchronization process is performed.

I definitely see this way. further more clocks cannot be synchronised at the same instance to more than one frame.

But:

"However, quantum mechanical systems perform the resynchronization and length adjustment automatically."

As far as clock rate is concerned I can agree but the phase shift of the clock has to take place  proportionately to the distance from the origin . How some random clock knows which origin we have selected?

The issue of relative simultaneity does not result from changing clock rate but from the phase shift of the clocks along the x axis which is necessary to make the speed of light the same in both directions.

OK, Eric. Thanks for your explanation.

Valentin,

Good to see you back. Only a short answer as I must go to work to deal with real time problems.

1. there is no third frame there are pints moving on arbitrary paths I do not need to see their clocks and points have 0 dimension so they cannot contract. If this would be a problem than we would not be able to consider any speed of anything  in K'  other than relative 0 and relative c.

2. The same pair of clocks cannot be synchronised to more than one frame because the synchronisation has to be repeated for any new speed system K puts itself in The same inertial System K can be perceived i K' at different speeds v1,v2,v3 etc but can only be one v at a time.

3 It is really a great idea however to analyse multiple clocks side by side at the same location one synchronised to current speed V and the other fot V-i1. It is a bit complex because clocks  automatically adjust to new rate and they have no idea they do.

I have no time right now but I will look into it after I come back from work.

Relative simultaneity is the problem with Relativity.  I can have 3 objects that are at rest with respect to each other but to a third party one is moving and the other is not moving with respect to the third.  This means that all three have different lengths and different masses even though when at rest they have the same mass and the same length.  This proves that the relative motion of something has nothing to do with its mass or its length in reality. 

A planet say earth, has one person standing on the north pole with a satellite that is 10 meters long and its mass is 1000 kgs, one person standing on the equator with a sister satellite that is identical and an other sister satellite in orbit that is stationary above the person on equator but 5000 miles out.  To the person on the north pole and to the person on the equator the satellite is not moving with respect to them.   I move someone in a space ship to the moon and he or she looks back at the situation and they see something different they also measure all the masses differently.  None of the masses have any different mass or length but the person on the moon sees it different.

This is a paradox that can be solved by revising Relativity to show that clocks and the ability to measure things changes as we move them and or they move through gravitational fields not that they actually chance but that our ability to measure them changes as we change our reference frame.     

Andrew, regarding your question: "...but the phase shift of the clock has to take place  proportionately to the distance from the origin . How some random clock knows which origin we have selected?"

 Quantum systems will only adjust themselves to the new reference frame relatively, over the length within which they are coupled.  They won't adjust to the origin of an externally and arbitrarily chosen coordinate system.  For example, take a meter long light clock and accelerate it lengthwise at some time T0 measured by the light clock and in agreement with your local inertial frame before acceleration begins.  Call the ends of the clock A and B.  Let's say you apply the acceleration force only at A (if you apply it at multiple points, you could break apart the quantum system and it would be no longer coupled).

The times (phases really) at each end of the light clock are TA and TB.  Suppose for simplicity the acceleration is instantaneous so that no phase shift occurs during acceleration.  This is highly unrealistic, but easier to calculate.  In theory an elastic light clock would survive it and eventually return to a 1 meter length in its own reference frame.

The point of application of the acceleration impulse, wherever it is, we happened to choose A, becomes a physical "origin" in a sense.  It is the point at which at T0 there is no phase displacement between the A clock (or A end of the clock) and the local clocks of your frame.  Thereafter the clock at TA runs time dilated and phase accumulates due to time dilation.

I'm assuming here that within the light clock, synchronization signals are exchanged between A and B, and that B is entirely slaved to A.  Again, this is only for the purpose of simplifying computation.  An actual quantum system is not so straightforward.  

The clock at B, following acceleration, will find synchronization pulses arriving at unexpected intervals.  Once it has come up to speed, and then had time for a round trip exchange with A, it will make a one time adjustment of its phase, and thereafter run at the correct dilated rate.

If the length of the A-B system is L, then the minimum time from T0 for this to occur is 3L/c.  It takes at least L/c for news of the acceleration to travel from A to B (recall that we constrained the acceleration to be applied at one point), and then 2L/c for the round trip synchronization.  There is actually an additional time factor for B to synchronize its distance.  But you can get rid of it by cheating, i.e. by having B anticipate where it is supposed to be.  

Actually, an analysis of the cheating is quite interesting because it "fills in the gap" of what is happening in the twins problem when a spaceship turns around and heads back to earth.  The clocks at earth do not suddenly advance to the new much greater time in the returning ship's frame.  A figure and analysis giving the answer is on page 13 (figure 7) of the paper linked below.

Hmm... finding the actual coordinate origin of an accelerated material object or clock would be interesting, but I've never seen a paper on this.  The effect of the emphasis on Minkowski space is to avoid asking questions about material objects, as the answers are assumed to be in "space-time."

Article The Twins Clock Paradox History and Perspectives

Dear All,

the issue of simultaneity cannot find an evident and definitive solution till when Anton Zelinger or somebody very expert on quantum entanglement will completely overcome the problem of the finite speed of data transmission (not information) for such a problem.

In such case as for the Canary Islands experiment, one will have the opportunity to measure simultaneous events at a distance.

 For example there will be the opportunity to see in real time the difference of oscillations of the same type of atoms in different position in a gravitational field 

or   oscillators posessing different kinetic energy respect to another, having previously been accelerated from the same position.

Only then will be enlightened, without any reasonable doubt, this issue of simultaneity and time dilation, clarifying if the time dilation depends on how the space-time fabric reacts to the energy content modifying the speed of the signals within it or not.

If we maintain constant the speed of light  Eric Lord cannot be wrong with GRT and SRT.

If we think that the speed of light is not constant and it varies according to the gravitational potential (which is quite possible )and speed, or rather it responds to a principle according to which the greatest the energy content the lowest the local speed of the processes (which is quite reasonable), then GRT and SRT will be  partially wrong.

The experiment of Michaelson Moreley will remain valid in any case because locally there is no way to determine another speed or overcome it. In vacuum, distant from masses, c will be the maximum speed in any case and locally I will Always measure c.

 Maybe one of the reasons why the unification of GRT and QM could not be made is this. Relaxing the boundary of the constancy of the speed of light might allow the merge. 

Two things which are results of GRT and SRT make me think that the speed of light is variable with the ponderable masses and energies, it is the gamma factor which is present in both the gravitational and kinematical time dilation.

dt=dt' (1-beta2)-1/2 where beta=v/c

dt=dt' (1- delta (phi)/c2)-1/2 where delta(phi) is the difference of the gravitational potential.

the two versions can be overlapped.

They testify that in any case the time distance between two events which are fixed as universal events, is measured differently in different reference frames affected by speed or gravitaiton.

 My interpretation of this is:

 the devices used , atomic clocks, are affected/slowed  by the energy content of the space-time compared to a situation of rest and deep space without the presence of masses.

In the first case it is the intrinsic  kinetic energy of the object affecting locally the space time,  in the second case it is  the mass-energy of the big massive body affecting  the space-time in which the objects gravitate.

In such a view it is not the time that is affected but we have the impression that it is affected,  since we use atomic clocks which we see affected.

What is really affected should be the speed of light whose variation affects naturally the pace of oscillating atoms and so locally every material object.

At this point only the intergalactic space, sufficiently far from masses and at rest respect to the CMBR rest frame which is at present used succesfully by astronomers, will posess the reference characteristics to posess the absolute time to which we can refer, the fastest time or fastest relative light speed.

But we will be not anymore in the Newtonian view point of absolute space and time, but something which finds a tradoff between the Newtonian and Einseinian view points and confirms the view of the absolute space-time of Minkowsky and Einstein.

The problem is about geometry : how can we represent the geometry of the Universe, that is the container in which all physical objects live, it is a theory which comes before any anlysis of kinematics, so it does not involve mass or inertia.

The fact that we need 4 coordinates to locate an event in the universe implies that the universe must be a 4 dimensional manifold. In Newtonian and SR geometries this is an affine space. The fact that a material body occupies a spatial location at each time implies that it travels on a line on this manifold. We assume that any observer can, at least locally, build his chart of the manifold : he can assign a time to the events, which represennt his present, and as a consequence there is a folliation of the manifold by 3 dimensional hypersurfaces. But this chart and follitaion are specific to each observer. There is a fundamental symmetry breakdown : the four dimensions are not equivalent, we cannot travel in time and its measure is done by different ways as lengths.  As a consequence time is also the coordinate with respect to which one measures the rate of change of phenomena. This leads to consider derivatives, and the tangent space to the manifold, in which we have frames and vectors. In particular the velocity which is the tangent to the world line (the path traveled by material bodies and observers). In the tangent space, using frames, one can define metrics. It must be a 4 dimensional metric. Accounting for the dissymetry a metric, a physical metric must distinguish the time coordinate, and there are only 2 solutions with the signature (3,1) and (1,3). So we are lead to assume that such a metric exists. And the most natural assumption about the motion of material bodies and observers on their world line is that the length of their velocity is the same : which is equivalent to say that their clocks run at the same rate (their proper time). With these assumptions it is not difficult to prove the usual Lorentz formulas for a change of coordinates between orthonormal frames of two observers located at the same point (no need to make any assumption if they are inertial or not : it is always true). One needs a constant to go from the measure of lengths to themeasure of times, it has the dimension of a spatial speed, and experiment shows that this is the speed of light.

The key points are that in the universe a location is absolute (there only one physical point) but its measure is relative (it depends on the observer), and this is the same for the velocity : there is only one vector which is tangent to the world line, and only one parameter (the proper time) for which the world line is traveled at constant speed. So the velocity and the proper time do not depend on coordinates. The proper times (which is the biological time) flows at the same rate for all observers, but the elapsed time since an event depends on the trajectories of the observers : this is the twins paradox : because they do not follow the same path in the manifold, there is no reason why the length (measured with the Lorentz metric) of their path should be the same.

As one can see there is no need to involve complicated physics : just the implementation of classic mathematical tools to the representation of phenomena that anybody can experiment. And this is more obvious in the GR context, when we are free from the usual cartesian coordinates.

Regarding Stefano's comment on simultaneity relative to entanglement ... I just want to point out a duality. 

In classical SR you have an inability to detect absolute simultaneity because everything is relative and the best you can do is communicate at the speed of light.

In QM entanglement you have instantaneous communication, but it is concealed by randomness and can only be detected when the "key" has been transported from the other location and a correlation performed.

Neither one suggests than an absolute simultaneity does not exist, only that it is undetectable, i.e. nature carefully hides it.  An interesting philosophical problem.

Beautifully expressed, Jean Claude!   (-:  (-:

Thnks you Eric

I just want to add some thoughts which I beliieve are aimed at the core of Relativty.

We use concepts such as location, space, time, speed, to denote phenomena that we perceive, and to build narratives which are the frames of our theories. We use the mathematical formalism, attaching variables with precise properties, to the concepts,  to  go from a narrative to a predictive tool (we require computation) and to organise the collection of our data. The formalism is one representation of the real world. It enables us to imagine (at least in the properties of the variables and the equations) more than we can perceive, or even measure. For instance if we accept the representation of the universe by a manifold, we can imagine an object that extends in the past and the future. When you denote a function x(t) you imagine that t goes beyond your present time (even to infinity). This is not new in Physics : even in the Newtonian Geometry one assumes a universe which is infinite in space (and does not change with time). What is really new with Relativity is that it compells us to acknowledge that one can imagine, mathematically or with words, what we want, but the real world which is accessible, to measures and to scientific check, is specific to each observer. Relativity has introduced a new object in Physics : the observer, with specific properties. One cannot speak freely about speed of light, or any other measure, without labeling the measure with when, where and how the measure has been done. This not new, but it becomes mandatory. Speaking about the speed of light (this is the topic of another thread) has no meaning without telling with respect to what the speed is measured.

There is an inevitable discrepancy between our imagination and representation of the world on one hand, and the world which is accessible to our measures on the other hand. What we can do is try to patch the bits which are accessible to get a larger picture. We have a simiilar fact with QM :we can imagine a continuous variable representing the evolution of a phenomenon over a period of time (the state of the phenomenon) but we can make only a finite number of mesures to estimate the function, so there is a discrepancy, which appears between the continuous representation and the discontinuous experiments. Tell that the time does not exist (as some claim) is similar to claim that the world is random : we cannot attribute to the real world what comes from our limitations.

Andrew,

It seems you offer here to discuss again “the Wutke rod problem” -?

- yea, that is a next problem for the SR, since in the reality, independently on the K’ [inertial] reference frame clocks’ showing, the rod [rail here] will fall on the X’ axis flatwise, i.e. simultaneously by all its points. But that is only one of many other examples – since the SR contains (evidently – as that Dingle had shown) illogical postulate that all inertial reference frames are totally equivalent.

If some mathematical/logical construction has at least one illogical postulate, then this construction has infinite number of absurd consequences – that is very well known; and, again – your example is only a next example of this number.

But from the discussion here seems that there is some necessity in more detailed discussion of the notion “simultaneity” .

So – the simultaneity is, first of all, some usual common a human’s characteristic of processes in the external World. For example – if a cowboy is on equal distances from some bad boys and simultaneously shoots the boys, then bullets simultaneously hit in both boys; and that is evident for a non-physicist in any case – are the cowboy and the boys in a saloon or all of them are in a wagon, which moves with the speed V;

though in the second case the bullet’s distance for the boy that is in front end of the wagon is evidently larger then for the boy that is in back end. The explanation is simple – for the front end boy the bullet speed is equal to (its "Colt’s speed" +V), for the back end boy the bullet speed is equal to (its "Colt’s speed" –V). (Note, though, that if the wagon moves with very high speed, the “Colt’s speed” and V sum must be summed according the “SR speed sum” equation.)

As well as until near 1900 practically any human thought that the Colt flashes hit the boys simultaneously also. If the cowboy and the boys are in the caloon, that is indeed so.

But near end of 19 century it was shown, that nothing can add its speed to the speed of light, so the flashes’ hits in the wagon must be non-simultaneous – when according to the relativity principle this situation doesn’t differ from the situation in the saloon.

“To save the relativity principle” in the SR the “relativity of the simultaneity” was introduced – when on the platform the flashes’ hits aren’t simultaneous (since the speed of light is constant) when in the wagon and in the saloon they are simultaneous. As well as in the SR the speed of light was declared as some fundamental constant and “Einstein synchronization method” for distant clocks was introduced, which is in the consistence with the Lorentz transformations.

Besides the Lorentz transformations evidently allow to use an other method – “the low clocks transport”, when the gamma-factor of transported clocks is practically equal to 1.

That’s all – the convention about clocks’ synchronizations is no more then a convention that is necessary for observers for correct depiction of the external World. Sometimes it works well, sometimes – as in this “Wutke rod example” – it is wrong.

But in rigid systems it works mostly well, for example – an observer on the platform observes, say, that the distance between corresponding flash’ photons and the back end boy decreases with the speed (c+V), i.e – more then the speed of light; when everything in Matter move with the speed of light only, the observed speed is in this case “physically unreal” – but if the observer wants only to know – how much time is necessary for the hit – this speed value is useful…

Cheers

Robert ~

Just my thoughts arising from the philosophical point you raised:

Isaac Newton once said

“If it were possible to know the position and velocity of every particle in the universe, then we could predict with utter precision the future of those particles and, therefore, the future of the universe.”

Of course, we all know, from the advent of quantum physics, that the universe doesn’t work like that! The idea of a totally deterministic universe is in any case in conflict with the day-to-day experience of what it is like to be a living creature − we make decisions, we plan for the future, etc (we have what we call “free will”...). The universe seems to be an evolving process, which has a “past” that is fixed and cannot undergo any further change, and a “future”, which is a realm of possibilities and probabilities where events are not inevitable.

This suggests a continually changing spacelike hypersurface, which can be called the  “absolute now” or the “absolute present”, separating “the absolute past” from “the absolute future” − metaphorically, a kind of leading wavefront where “things happen”. It may even be a thin slice (how long does “the present” last?...).

At first, this view of things seems to be in conflict with the “relative simultaneity” of SR, whereby each observer has a his own personal “now” − an event in the past for an observer can be in the future for another observer. Indeed, an event that is in the “absolute” future may be in the past according to an observer’s “now”. There is, however, no conflict − no "paradox" − because for an observer at a particular instant a distant event occurring at that same instant is not observable – the observer has to wait until information, traveling at a finite speed, reaches him. Only then is it observed. A little thought (involving the principles of SR) leads to the conclusion that any observed event is in the observer's past as well as in the “absolute past”.

I hope what I’ve said is clear and makes sense. The conclusion I draw is that yes, the logic of QM and the logic of ordinary life experience suggests that there is an “absolute simultaneity”, but that, as you said, it is in principle undetectable! (Analogous, perhaps, to wave functions in QM, which are also in principle undetectable?)

George E.,

Thank you for joining the discussion.

 I can have 3 objects that are at rest with respect to each other but to a third party one is moving and the other is not moving with respect to the third. 

This means that all three have different lengths and different masses even though when at rest they have the same mass and the same length.

It seems to be the case based on simple calculations in the example attached to the question. the mass of the object in motion wile the other is still resting must differ. It is not inconsistent within relativity in itself, but defies logic when we know from the stationary system that all objects in question are either all at rest or moving together and at all times their structure is invariant i.e. they are at the same distance to each other

I am not solving the problem of how to set up multiple points in motion so they synchronously start. It is a different problem, but the same problem applies, to  the moving system :K': How can this system and all its clocks at relative rest can be accelerated to velocity v.

This proves that the relative motion of something has nothing to do with its mass or its length in reality. 

"Nothing to do with reality" is probably too strong. It is an image of reality that may be used for certain purposes. Like lenses in your camera giving inverted scaled and a bit distorted 2D image of the 3D real landscape in front of you.

But would anyone argue based on this image that the railway tracks in front of you are not parallel therefore intersecting in some point?. The discussion I have started may go through similar claims regarding relative simultaneity.

Valentine,

It looks like my example did not make certain things crystal clear because it has caused some misunderstanding.

But the 2 points are on that bar and the whole bar is in motion from K, right?

The bar marked blue is a static long reference line from which the points originate and start from. It does not move in K. The other rail also does not move. It is another reference structure. The line segment between the two points can be filled with a rigid moving rod but this is not essential in this discussion because it may raise unnecessary complications such as contraction in the Y direction. May be I should not have mentioned it at all.

I have updated the description to make it clear what the rails are and where the rod could be if someone wants.

So the points are at rest from each other as they are at rest on the bar, while they (and the bar) move from both frames K and K' respectively, which means they are not at rest in either K or K', so they are not part of either K or K' reference frames.

Yes but they should be in relative rest all together.

The frame K and the bar constitute the same situation as in Einstein's example of a rod moving from a "stationary" system. He considered that as having 2 different frames, and so is this: the frame K and the frame of the bar. The only difference is the orientation of the bar and its direction of motion as seen in K.

I agree there is a third frame but it does not enter the discussion. Any moving point is another rest frame to itself but we do not mention it unless we want to see its clock and its relative view.

In my case I do not want to know anything about point 1 and 2 clocks neither what is the world from their perspective. it is enough trouble with the two frames already.

Stefano,

Thank you for joining the discussion and bringing practical aspects of synchronisation.

Relative simultaneity only exists because some people believe there is no greater speed than light and therefore it cannot be experimentally established. I have more than one problem with it.

1 There is no speed limit in mathematical model and you can exercise the concept of instantaneous synchronisation. Science use non realistic conditions for legitimate purposes. Recall thermodynamic  definition of entropy."The change in entropy (ΔS) of a system was originally defined for a thermodynamically reversible process" . The process is infinitely slow at thermodynamic equilibrium at all time. How does it stop entropy from being used?

2.There is more than one example when the speed of light limit can be broken for synchronisation purposes without new physics. One is a laser beam sweep from large distances. In theory you can approach instantaneous synchronisation asymptotically. You still cannot transfer information faster from point A to point B but you can synchronise clocks almost instantaneously. Another method is a humble rigid rod falling on X axis in a parallell descent. Two enf points would synchronise corresponding clocks instantaneously, This method however has no chance to be practical, but theoretical significance of it cannot be understated.

the issue of simultaneity cannot find an evident and definitive solution till when Anton Zelinger or somebody very expert on quantum entanglement will completely overcome the problem of the finite speed of data transmission (not information) for such a problem.

That is a great chance instantaneous distant clock synchronisation be practically realised withiin acceptable experimental error.

Jean Claude,

Thank your for joining the discussion. It is an impressive summary how one can approach modelling of the spatio-temporal relations. I have to say however that there may be more than one valid representations in particular when simple scenarios are involved.

I cannot immediately resolve my problem based on your response. My problem is whether the demonstrated spatio-temporal relation anomalies resulting from a particular set of Lorentz transformations are sufficient to declare relative simultaneity as a computational artefact being the source of distortion of stationary system structural integrity in the moving system.

You say:

The fact that we need 4 coordinates to locate an event in the universe implies that the universe must be a 4 dimensional manifold.

I am not sure this implication is formally true. The universe is not a manifold but can be modelled by one.

I can equally see the universe through 3 dimensional space and time being a scalar parameter (or perhaps a scalar field).

What is wrong about this? I can and I do use a 4th spatial coordinate w as an abstract coordinate for computational convenience. I consider it an instrument of the model but the spatial 4th dimension as a useful fiction. The "motion" in this fourth coordinate is also a function of a scalar parameter t viz w=ct.

Dear Eric

I agree with the first part of your post, not with the suggestion that…< there is an “absolute simultaneity”>

Absolute simultaneity only happens if the event occurs at the same space point (example: crash car).

By the way, are you sure that your first phrase belongs to Newton? I always thought that it was Laplace thinking.

What is the problem with relativity of simultaneity?

Andrew, please, may be clarified this proposal?

I can have 3 objects that are at rest with respect to each other but to a third party one is moving and the other is not moving with respect to the third.

Regards

Thierry

Thank you for the interesting reply. Will need to think a bit about all the aspects of it.

You say:

The rate decrease of clocks with velocity is also wrongly equated with the idea of elongation of time itself that would result in a longer longevity due to velocity.

At this moment I have no reason to question slowing down clocks with velocity.

For example, finding the μ-Mesons’ lifetime extended due to their relative motion in the atmosphere  is very convincing that particles behave as if time “has slowed

down” for them, but there is nothing inherently illogical in the fact that some processes may run slower in different conditions. Relative simultaneity is not explicit at this level of STR practical application, but  slowing down processes may be. This is based on:

D. H. Frish and J. H. Smith, "Measurement of the Relativistic Time Dilation Using μ-Mesons," American Journal of Physics, no. 31, 1963.

Sergey,

Thank you very much for joining this discussion.

It seems you offer here to discuss again “the Wutke rod problem” -?

My friends will be laughing at this name but it is a funnier one than "Kerr black hole":),

This discussion is indeed related to the rod discussed in my other post. The rod is a particular instance of the problem while here I want to focus on more general issue of relative simultaneity.

- yea, that is a next problem for the SR, since in the reality, independently on the K’ [inertial] reference frame clocks’ showing, the rod [rail here] will fall on the X’ axis flatwise, i.e. simultaneously by all its points.

You are right about"  fall on the X’ axis flatwise" but the rails in my example are a fixed references not moving in K. I have corrected the description to be more specific about it because Valentin has read my example the same way contrary to my intentions.

The rod in K is the straight line segment between points 1 and 2 at all times.

In K' during the initial phase of the process of non simultaneous take off, a part of this "rod" would be still on the first rail while the other will be pulled by point one thereby having the rod bent with the bend point moving towards point 2 until it eventually moves.

If some mathematical/logical construction has at least one illogical postulate, then this construction has infinite number of absurd consequences – that is very well known; and, again – your example is only a next example of this number.

I know what you are trying to say but postulate bay be logical mathematically but at odds with reality. So mathematical result are consistent wile reality of such mathematics may be questionable.

The example of simultaneous relations being distorted by wrong wording can be seen even without relativity. If simultaneous emissions at distant point on x are propagated to the origin at x=0 they arrive in sequence. The close one first, then the more distance one. From that image no one should call the events not simultaneous if you have other evidence they were.

That’s all – the convention about clocks’ synchronizations is no more then a convention that is necessary for observers for correct depiction of the external World. Sometimes it works well, sometimes – as in this “Wutke rod example” – it is wrong.

Well said Sergey, I fully agree. In this case it is a pity all the fantasies about parallel temporal realities in different inertial systems were developed and propagated.

Hugo,

Thank you very much for joining this discussion

Eric's quote does not seem to come from Newton himself but it is a consequence of Newton's system. The quote seems to be from "The Limits of Knowledge" By Paul O'Hara page 125.

Unlike you I concur with the comments of Eric on absolute simultaneity. The concept is may be a little obscure since it has been largely abandoned after 1905. Some who tried to defend it were publicly humiliated like philosopher and Nobel Prize laureate Henri Bergson - the author of" Duration and Simultaneity"

What is the problem with relativity of simultaneity?

There are multiple problems from my point of view. 

I could probably throw in a few more but the three are sufficient to illustrate my point of view.

Andrew, please, may be clarified this proposal?

I can have 3 objects that are at rest with respect to each other but to a third party one is moving and the other is not moving with respect to the third.

The quote is mostly from  Gerge''s post who introduces a third object. In my analysis of the example scenario,  the third point is not absolutely necessary .

But it  clear from initial conditions and relevant equations of motion after Lorentz transformation, that one point  (1) at x'=0 on line y'=-Dy moves first due to relative simultaneity, while other points between x'=0 and x'=-Dx on  line y'=-Dy remain at rest until their turn to move. This agrees with Sergey's statement.

So ,some two points in the neighbourhood of a point (-Dx, -Dy) on y'=-Dy  remain at rest for the moving observer until their time to move out comes. In reality in the stationary system all these points move together at once and thy are not attached to an initial object (rail) they were on. There may be two distant rails where two points touch together but no such rails exist in the stationary system because the two points may only be a part of one rail at a time.

The effect is bizarre relations between real points at fixed distance to each other appearing relatively moving. You get the same effect when you collect the position vs time data of a train for the engine and the last carriage and plot it shifted by say tten second. I described this example in my earlier response here ,but I attach the plots of last carriage versus engine shifted in time here for convenience.

Dear Hugo ~

Perhaps I was being too dogmatic in saying “there is [emphasized by italics!] an absolute simultaneity”. But I can’t see a way around that conclusion if one accepts the first part of my post − that the “future” (for a spatially extended process such as “the universe", not just the future of a single “event”) consists only of probabilities, while the “past” is already “determined”.

Unfortunately, the terms “present”, “past”, and “future” are used ambiguously in SR. With reference to a single “event” the “present” is the vertex of a light cone and “past” and “future” are the interiors of the two parts of the light cone. With reference to an observer in an inertial frame the “present” is a hyperplane t = const. and “past” and “future” are the two regions into which it partitions spacetime. “Relative simultaneity”, of course, refers to the fact that those concepts are frame-dependent.

“What is the problem with relativity of simultaneity?”

No problem at all, within the context of classical SR. But it seems to me to be inconsistent with QM.

“By the way, are you sure that your first phrase belongs to Newton? I always thought that it was Laplace thinking.”

You may be right. (The problem with well-known quotes is that they get attributed to more than one person!) I need to google it…

Eric, I just noticed a question on here that appears to be addressed to me.  It is a ways back.  I'm having trouble summarizing your question, since I don't see how it relates to anything I said.  : )

You are talking about inertial frames where nothing ever changes.  As far as I know, you can use the mathematics of Minkowski space without thought or restriction in those circumstances and never make a mistake in computing the answer to a problem.  Nor can you run any experiment to determine if the Minkowski 4-space exists all at once and forever like 3-space (sorry, I'm not being very precise here, and don't really care to be - it's a philosophical question).

Where it makes a difference is in things like the twins problem and the Bell spaceship paradox (so-called), and acceleration enters into all of those.  But acceleration is not the problem.  There are also distances which are not rigid rods.  Again it is a philosophical question.  But look at the 3-space component.  That is geometry, and you know it as such.  If you restrict to rigid rods, you can move the rod (gently enough that you don't break it) into another reference frame, and it is still whatever length it is, say one meter.  Even if it no longer is in a relatively moving frame, or when viewed from another gravitational potential.  Oddly, in a gravitational field, you can just change the orientation from tangential to radial, and the length changes for distant observers.  So this all could be geometry.  No one has ever proved it has to be, by the way.  That is just what Cliff Will calls a "convincing argument".

If you take a measured distance, or a string (not rigid, and let's presume so weak it breaks easily), or a pair of synchronized clocks, and move those into another reference frame (let's say another state of motion, keeping it to SR), then in general they will not be synchronized or at the correct distance in the new frame.  You have to do something to it to get a valid frame.  Even if the clocks are affixed to a rigid rod, then they will be the correct distance apart, but will not show the correct times.  If "time" were geometry, they would, I believe. 

I have a friend, Vesselyn Petkov, whose papers I like very much, he writes very clearly about things like the Bell spaceships, but I do not agree with him philosophically.  He seems to believe (and of course I risk misrepresenting him) that Minkowski space is as real as a brick or a block of salt that is just "there" and you can move around in it or cut it with a knife.  To me the problem that reference frames, unlike rigid rods, do not conform to the new geometry they find themselves in after, say, a change of motion, is evidence otherwise.  I first realized this when reading an old 1960ish paper by Swan, where he points this out at some length.

Philosophically, most early 21st century physicists, I suspect, I haven't taken a formal poll, agree more or less with Petkov.  There is a reason.  This interpretation of Minkowski space supports the usual "interpretation" of GR.  This does not in any way affect the math of GR or its validity (which I consider entirely an empirical question), only its philosophical interpretation.  However, with the more conservative interpretation (that it's not geometry unless all aspects of systems conform spontaneously to the new geometry they find themselves in) might suggest some boundary conditions on GR that would let out esoterica like wormholes and time travel.

Valentin

Einstein's relativity states clearly a real time dilation which has been trumpeted for a century now, and so that automatically excludes an absolute simultaneity - and that unfortunately has always suppressed any opinions and any research in the direction of absolute simultaneity (or absolute space).

I agree that anyone mentioning absolute simultaneity or absolute space risks a crackpot tag. As much as  Einstein insists on relativity of simultaneity, he was not so clear about space when he says: 

• According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media.

And so the concept of "relative simultaneity" is nothing more than a confusion between the concept (of simultaneity) and the observation method (of simultaneity), as a consequence of a poor measurement practice.

I quite agree although we seem  to have different views what exactly is being confused.

I say this is only clock phase shift due to synchronisation method not the relative rate it may change to.

Eric,

The quote does not seem to come from Newton himself but it is a consequence of Newton's system. The quote seems to be from "The Limits of Knowledge" By Paul O'Hara page 125.

Robert,

Thanks for your replies

Back to the same issue:

"...but the phase shift of the clock has to take place  proportionately to the distance from the origin . How some random clock knows which origin we have selected?"

I mean that you can accelerate any clock from a pool of initially synchronised clocks totally independent from each other by applying the same acceleration for the period programmed identically by each clock after which it disables accelerating module. all clocks accelerated this way end up in the same frame. Based on SR we may believe their rate becomes the same. This is what you call automatic adjustment.  But each clock launched at different periods would have different period spent in the fast ticking (initial rest) frame. They end up being unsynchronised in the new frame having the same rate. They have no idea where the intended origin is going to be.

Einstein synchronisation from different points will give the clocks synchronised differently as it is clear from Lorentz transformation that phase shift depends on distance from the origin and clocks have no idea where it is and who is synchronising them

Robert,

You give quantum mechanic references and other people refer to GR.

My point of view is as follows.

It is important that relative or absolute simultaneity are investigated from those and any other relevant perspectives.

But I take the stand from the point of view of the state of knowledge before 1916 when there was no General Theory and quantum theory was in its infancy.(Copenhagen interpretation came to light in 1930 after Heisenberg's book "The Physical Principles of the Quantum Theory")

Well before this, relative simultaneity has been proposed and propagated to public domain. At that time, they were explaining it with rigid rods, clocks that had hands, and light beams emanating from trains. And I question the foundations of relative simultaneity in those terms of reference.

My position is that using this tool set and common understanding of reality there is no reason to say that relative simultaneity reflects the reality. This is because it may distort the structural integrity of the stationary systems that is assumed well known. 

You cannot have relatively stationary points in their own frame and some other reference frame (K), and have them changing their relative position in the moving K'. I clearly prove it with elementary calculations believed to be correct.

We can see shadows changing geometric relations of the original objects depending on light source characteristics and projection angles, but no one claims that shadows are the objects and their proportions are the proportions in real objects. You can however find out a lot about object's shape by collecting multiple shadows from different angles.

I believe that having wrong understanding of fundamental concepts may not reflect well on later developed more advanced theories.

I also want to make a point that I have no urge to qualify whether SR is or is not valid or internally consistent.

I see however quite clearly that popular claims/interpretations based on it are at odds with reality and the common sense.

Andrew,

There are not problems or contradictions with SR.

There are multiple problems from my point of view.

1 - First, is cannot exist in nature being only a result of a particular conventional clock synchronization which sole purpose was to make the computational speed of light the same in all direction for a moving system (which is a fair method to connect distant clock inductions).

The use of clocks and sticks (Einstein's method) are unnecessary. It was used in the beginning, before Emmy Noether theorem (1913). Modern formulation of SR (Logunov, 2002) only requires certain space-time symmetries.

Actually, the acceptance of the Universal Conservation Principles gave validation to SRT, because both have the same fundaments (postulates).

If SR fails, then the Universal Principles (and the Electrodynamics) will also be wrong.

2 - Second, when you assume it as a particular interpretation of special relativity the image of the reality assumed in a stationary system becomes so unrealistic that I do not hesitate to call it paradoxical.

I don’t understand what you are talking about.

The claimed contradictions usually are consequence of inadequate treatment in resolving the problem. This case (a moving rod) involves time, positions and velocities. It would not be surprising to have mistakes.

Try analyzing the movement of two separated points (x1, x2) with constant velocity (vy).

The trajectories (right lines) are perpendicular to x axe for O1 and inclined (but parallel) for O2.

There are no contradictions

To Andrew,

Sorry, I missed your question, the discussion is going fast. Of course, we do not know what is the real world, what we do is just to try to build an efficient representation. Efficient from two points of view : it must be intelligible, easy to understand in words, and provide accurate predictions. About the manifold : this is a mathematical structure that is not always well understood. At the  beginning are charts : there are bijective maps from some vector space to a set : they enable to locate a point of the set with a collection of scalars. And obviously this what we do when we locate an event. Say "see you next year at Stonehedge at the spring equinox" and you will be understood. Notice that a clock measure the elapsed time since an event : it does not locate an event by itself (for this you need clocks which run at the same rate, and choose a common initial event. The Ancients did well by choosing to locate events by comparison with stars configurations). An atlas is a collection of compatible charts which cover the set : there bijective maps betxeen the vector spaces such that one can go from the coordinates of one chart to the coordinates of another chart. Two atlas are equivalent if the reunion of their chart is still an atlas. And a manifold is a class of equivalence of atlas. So there is no assumption at all about the structure of the set (not even topologicalor algebraic).which is the universe This underlines the fact that one cannot play with points as if they were vectors or coordinates : a location = a point is absolute. The formalism covers all usual geometries.The assumption in SR or newtonian geometry is that the universe is an affine space, which is a special manifold (the maps for going from one chart to another are affine).  Notice that the existence of a manifold structure says only that there are ways to compare two charts, it does not tell how to do it. One of the problem is to find a way to compare the time used by different charts. The issue of simultaneity can be summed up by : a given observer can tell if an event exist in his present. The common assumption is that there is a map which can assign a time to each point of the manifold (at least locally), but this map is specific to each observer.

Because there is instantaneous communication in newtonian geometry, any observer can synchronise his clock with another observer. With this assumption in newtonian geometry the vector space over which the manifold is modelled is the direct product of R3 by R (there is a canonical projection from the set of coordinates on the manifold to R = the time is common to all observers), meanwhile this is not possible in Relativity and then one must find a way to compare the charts and this is the purpose of the celebrated formulas,through additional assumptions about the way material bodies travel in the universe, and the existence of a metric. These assumptions are checked by the predictions made through the formulas..

A last point, related to your question. In cosmology it is usual to assume that the universe can be represented as the product of a 3 dimensional manifold with R (a warped universe), so there is some kind of universal time, and moreover it is generally assumed that everything stays on the same 3 dimensional hypersurface (the image of the expanding balloon). But these are additional assumptions : what one can do is build a consistent GR theory at our scale (say accessible by astronomy).

Hugo,

Thank you for responding. I have noticed a few typos in my statements which can make it hard to read, but I hope the content is not distorted.

There are no contradictions within the SR as the postulates are consistent with the derived linear transformation. I do not attempt to prove such thing. The discovery of clocks slowing down when set in motion seems to be confirmed experimentally. The problem I am discussing is relative simultaneity not having much to do with reality.

Point 1 says that synchronisation of clocks by Einstein method had an objective to make the speed of light constant to retain the appearance of a system in absolute rest for any inertial system. Simultaneity of events for the same clock indication is not self evident at least.

In aerodynamics we talk about aircraft speeds using Mach number but it does not mean two aircraft would be flying at constant distance to each other while having the same Mach number. The purpose of such speed in Mach units is to calculate lift and drag not navigation. The fact that SR model solves some problems does not automatically mean it can be uncritically projected to other things.

Point 2 refers to particular cases when Lorentz Transformation of trajectories produces result that cannot be considered realistic while mathematically is still correct. I am referring to an example given in a paper attached to the question at the beginning of this thread. The motion of two equidistant points can transform to a bizarre case where those points relatively at rest change relative distance widely.

If you consider this realistic then there is no point to discuss relativity but the definition of realistic.

The trajectories of two points after Lorentz transformation and including initial conditions are given in the paper attached and approximate plots of  relevant trajectories show distance of equidistant points changing. I would welcome your equations and plots proving your point of view rather than stipulating I made a mistake (which is of course theoretically possible).

So please present the equations showing that after Lorentz transformation of two points that simultaneously start motion in K perpendicular to X, also start the motion simultaneously in K' and therefore remain equidistant at all times or they start the motion in a sequence but still retain constant distance to each other.

You have to admit that it is an impossible request. 

Hello Robert ~

“Eric, I just noticed a question on here that appears to be addressed to me.  It is a ways back.  I'm having trouble summarizing your question, since I don't see how it relates to anything I said.  : )

I’m surprised by your saying that what I said doesn’t relate to anything you said. What I posted was the train of thought sparked off by what you said. (“In classical SR you have an inability to detect absolute simultaneity because everything is relative and the best you can do is communicate at the speed of light” and “Neither one [by which I presumed you meant QM and SR] suggests than an absolute simultaneity does not exist, only that it is undetectable, i.e. nature carefully hides it.”) I felt that I was doing little more than expressing that, from my own viewpoint!. Anyway, no matter (-:

This thread is growing far too fast − it took me a while to actually find the post I’d responded to (on page 3), and my response (on page 4)!

 Jean Claude,

Thank your for interesting description of manifolds. I need to learn more before I will be able to fully understand your messages. I recall you have written a book which I have download in a hope to study it some time. For now I am stuck with traditional tools used initially to derive and present special relativity.

My question to you is whether the manifold approach can make any difference to the fact that mapping two relatively equidistant points which were set in motion, to points varying in distance can be considered reality as opposed to mathematically valid image (abstraction).

My problem is not with mathematics but with physical semantics. 

Thierry,

Thanks for the explanation I need to look up the sources you mention. But I still try not to get involved in assessment of special relativity but want to maintain focus on incorrect  interpretation of the SR given that it is correct.

To Andrew,

Yes, actually it helps. When you are stuck with frames and coordinates in affine space there are too many interfering factors, as one can see on this thread. In the manifold framework  material bodies (say material points) travel independantly on lines. Their path is a map x(t) which does not depend on coordinates, but a single parameter, the proper time, which is not a coordinate (it is similar to the milage in the road). The quastion of simultaneity is then : how an observer can follow  the trajectories of different material points which travel independantly. The answer is that there is a relation between the proper time and the time of the observers. To cut a long story short : the possibility to follow simultaneously the trajectories of different material points implies that their proper times are related. And the basic relation can be formulated using the relative velocities of the material points. This is quite simple and more illuminating in the GR context. And helps to understand something which is quite puzzling : if the material points have independant trajectories in a 4 dimensional universe what makes that on can see them continuously ?

Andrew,

It seems be useful here to write about the “simultaneity problem” again.

Again – that is a convention/ a claim when people describe external World – as that is true for any other theory, which describes the World. And this convention indeed works well in cases when all interacting material objects constitute a rigid system; when for “the rigidity” not too strong bonds in macro World is necessary. An example – if some force accelerates a rod along the rod’s axis along the X-axis, the rod rotates in the (X,ct) plain, but practically all work that is made by  the force transforms into the rod’s kinetic energy and only very small part – on the rotation.

At that – indeed all parts of the rod have slowed down processes (in 1/gamma times) and relative positions having different temporal coordinates – all in full accordance with the Lorentz transformations.

But (1) – at that nothing happens with the spacetime, it by any means doesn’t rotate – as that the SR postulates; and (2) - if the system’s objects are free, then even they were accelerated by identical different forces and so have identical speeds and so are in the same “inertial reference frame” (and so, as that the SR claims, “rotated with/by spacetime in the moving reference frame relatively to the stationary frame”) - the objects 4D coordinates will not be in accordance with the Lorentz transformations.

An example more. Let two bad boys in the back and front ends of the wagon (see SS post on 4 page) were born on the wagon before its motion simultaneously, say – inside a time interval 10-30 s. After the train reaches the inertial speed, just because of the wagon rotation in the (X,ct) plain the two bad boys rotated with all wagon so, the front end boy indeed occurred in the past relating to the back end boy and so became be younger then the back front one on the Voigt-Lorentz decrement –VL/c2 (L- is the wagon’s length).

So let the cowboy in the wagon’s middle shots by very short pulses from some laser; then the light evidently moves to the front end bad boy the  larger distance, then to the back end bad boy. But just because of the front end boy at that was younger then the back end one, at the moments, when they were shot, they have equal ages – with the same accuracy 10-30 s – as well as the boys clocks show at that identical times (so the boys are shot in this sense indeed simultaneously)– all in accordance with the Lorentz transformations. When, of course, in a stationary reference frame the front end boy is shot later.

But not with the SR, since at that nothing happens with the spacetime – no “rotations”, no “contractions”, no “dilations”, etc.

But if before the cowboy shoots the both boys were in back end and one of them moved slowly by some free way in the front end having, at that, some clock, then he remans in the same time coordinate as the back end boy’s time and will be older relating to his fellow when be shot…

Cheers

Eric, oh, I see what you were getting at. 

Andrew, re:

You cannot have relatively stationary points in their own frame and some other reference frame (K), and have them changing their relative position in the moving K'

Sorry, as Eric noted, the thread is so popular we are missing notes.  I just noticed this.

If you only accelerate observers, not frames (i.e. systems of objects and observers), then you never actually have any changing of relative position in the moving K'.  Let K be a reference frame with clocks A and B in sync, separated by L.  Make these measurements while stationary in  K.  Then accelerate yourself (a point) but not the frame, and make measurements.  Things appear different, but they haven't actually moved.  It is only when one tries to accelerate the frames (systems of objects) that difficulties in interpretation arise.

This thread is going too fast for me. It would be convenient discuss the different aspects and questions one by one.

In this post I will refer to modern formulation of SR (Logunov - 2002), answering Valentin Danci.

In a next post I will share a file with the calculus requested by Andrew Wutke.

Valentin,

If you agree let's try one by one. Now is "simultaneity" time

< I don't think Noether's theorem is a reformulation of SR…>

You are right. I was not as clear as needed in my last post.

Emmy Noether showed that the conservation laws are only consequence of space-time symmetries.

Logunov showed that SR only requires the same space-time symmetries. It is no necessary another requirement. Einstein’s Postulates (maximum constant velocity and Relativity Principle) are deducted.

< Practically Logunov blames those who consider "Minkowski space [...] to be only some formal geometrical interpretation of SRT within A.Einstein’s approach, instead of a revelation of the geometry of space-time.">

I agree with Logunov's ideas about SR, but it should be recognized too that he was a controversial person.

What you call the “revelation of the geometry of space-time” is as valid as any other postulate in physics and is common to all Modern Physics theories, excepting GR.

The conservation laws, which require such geometry of space-time, have been tested without contradictions over more than 300 years.

I can’t imagine a postulate with better verifications than symmetries of physical space and physical time.

Every physical theory requires at least one postulate and often admits several different treatments. The deeper formulation is one that has fewer postulates. Logunov formulation needs only one postulate, so it is the deepest possible formulation.

< That is a wrong way to do science. No one can ask anybody to believe that an abstract representation (of a theory) is actually something real, without any real proof.>

I do not agree with this subjective statement. If so, we should reject all Modern Physics.

The brilliant Logunov formulation of SR (2002, last version 2005) may be downloading from:

http://arxiv.org/pdf/physics/0408077v4.pdf

Hugo reminds us above "Emmy Noether showed that the conservation laws are only consequence of space-time symmetries.  Logunov showed that SR only requires the same space-time symmetries."

I just want to quibble with the word consequence.  I'm not sure how Hugo meant it.  The real implication is probably "each implies the other" or something like that.

We don't know which came first, or is more fundamental, if indeed the question has an answer, physical or even philosophical.  I tend to think of the conservation laws as primary, and the symmetries as symptoms, or indicators.  Perhaps just a matter of preference.

If we take seriously the idea that SR is entirely a consequence of the conservation of energy, which is the implication of Hugo's comment, then physics has not explored all the ramifications.  In thinking about E=mc2, we know that it can be entirely electromagnetic energy, as from the annihilation of a particle pair.  We know that c is the universal communication speed limit.  But Lorentz, Poincare, et. al. abandoned the idea of an electromagnetic theory of matter upon the difficulty of confining charge, and only a few people have considered it since.  But is it really possible to have any other "kind" of energy and still have it conserved?

I suspect not, the difficulties of formulating it aside.  But if everything is light, then the relativistic effects become not geometry at all, but just the mechanics of making things, including measurement instruments, with light. 

Dear Robert:,

I agree with something like that.

You are focusing into the medullar question. I think that Logunov’s formulation of SR means the most important integration of different branches of physics.

The alluded symmetries are present in almost every modern theory (excepting GR).

Regards

Not GR, really?  Can you tell me more about that?  I at first added to my post "but then we have gravity," and deleted it because I wasn't sure why I had thought it or where my mind had been going with it.

For better understanding how a simple synchronous motion of a rigid rod along the y axis in K is distorted in K', the following explicit plot is helpful.

Note the boxed area where the right end moves and drags some parts of the rod with it while the other part remains motionless. See the point where rod bends moving towards far end until the whole rod moves at an angle to X

But it is only an illusion not the true picture of the simultaneous process.

Hugo,

“The brilliant Logunov formulation of SR (2002, last version 2005) may be downloading from”; and [Logunov]:

“According to Poincare and Minkowski, the essence of relativity theory consists in the following: the special theory of relativity is the pseudo-Euclidean geometry of space-time. All physical processes take place just in such a space-time.”

- yea,   Logunov, in fact, only re-formulated the SR – that is indeed true.

 But from the fact that somebody re-formulated the SR  by any means doesn’t  follow that this (and further – the GR) theory is correct; there were a lot of the “reformulations of the SR” – though the SR is nothing more – till the SR is adequate to the reality – then a re-formulation of the Voigt-FitzGerald-Larrmor… Lorentz theory.

 Including the SR is adequate  till the pseudo-Euclidian formalism remains be only a version of the Lorentz transformations and till the transformations themselves are adequate – when they are adequate not in any physical situation.

And any reference on any “[more then 300 years] experimental confirmations of the SR” doesn’t mean that the experiments confirm validity of the SR only – they confirm validity of the VFL...L theory also; till now both theories are experimentally non- distinguishable.

But the “fundamental” difference of the SR and the VFL...L theory just is that when the VFL...L theory was developed for the absolute Euclidian 4D spacetime – what is indeed true, when in the SR just the “the REAL pseudo-Euclidean geometry of space-time” is postulated, and just for this postulate in the SR once more postulate was introduced – the postulate  that all inertial reference frames are totally equivalent.

Just provided that this postulate is correct it turns out to be possible to formulate further such a “strange” “relativistic effects” as the “space contraction”, the “time dilation”; further – in the GR – the “spacetime curvature”, etc.

 When a very simple logical analysis of this postulate immediately, and undoubtedly  shows  that from the postulate follow  evidently absurd sequences – see the Dingle problem of the SR as an example; though there exist many others. And, correspondingly, from that follow that the postulate about real  pseudo-Euclidean spacetime in Matter isn’t correct also; the real spacetime is 4D Euclidian manifold, where t-axis is always orthogonal to any 3D spatial line.

 As well as it can be shown that there is no, say,  either the “space contraction” – in the reality  there is contractions of spatial projections of concrete  material objects in the 4D Euclidian spacetime;  or “time dilation” – in the reality there is the slowing down of internal processes’ rates in the concrete spatially moving material objects, when this rate is maximal when an object is at 3D spatial [absolute] rest; it is possible to measure the absolute speed; etc., etc., etc.

 More – see, again, the SS posts and the Net/RG links in the posts.

 Cheers

Andrew, your proposal is wrong. The rod, moving along x axis, will be always parallel to x' axis

I will write the file (.doc) with the solution according with SR and attach to the next post

Hugo,

I am looking forward to see your interpretation. I have shown the transformed rod the way Lorentz transformation appear to position it.

I disagree with it but most people who appear to be interpreting the SR in a traditional way insist it travels at an angle. I have even been banned from a public discussion forum for maintaining my opposition to this belief.

If your solution shows the rod travelling is parallel to X' I would be delighted.

I appreciate your and other's involvement in solving this riddle.

SRT has a particular characteristic: it has simple calculus and very difficult hidden concepts. As I said:

It is always possible to make mistakes but one should learn from them. So please Hugo show my mistakes.

Dear Andrew,

  The abundance of answers to your question shows that you have touched a problem of broad interest. Actually, all points raised by you have already been addressed in these answers, therefore I will only formulate briefly the basic results:    

1)  Relativity of simultaneity is not a computational effect - it is a real physical phenomenon.                                                                                                                          

 2) Time is a local characteristic depending on position when considered from another reference frame.  

3)  Length of an object is its relative characteristic whose numerical value may be different in different frames.                                                                                                   4)  Time dilation and length contraction are observable physical effects.                              I also want to mention that many aspects of your question regarding accelerating rods have been discussed in details in my publications:      

"The dynamics of relativistic length contraction and the Ehrenfest paradox ", arXiv:0712.3891 [physics.class-ph];                                                                                        "Two permanently congruent rods may have different proper length" ,  arXiv:0807.0881 [physics.class-ph]        

You can also find them in my book "Special Relativity and How It Works," Wiley-VCH, 2008 , Ch. 7 (I think, the addressed topics must be, at least partially, presented in its e-version)    

Moses Fayngold,                                                                                                                NJIT

I will try to answer the questions in a more detailed way.

Let us consider a collection of material points (particles) which together constitute a material body. They travel on the 4 dimensional manifold on wolrd lines with their proper time. Because the world lines do not cross, one can represent the set of world line by a vector field, V future oriented and Lorentz length -1 (with signature 3,1 and c=1). The proper time is defined up to an additive constant. We assume that at a time t=0 all the points are on a 3 dimensional hypersurface S(0). Then the location at t of any particle is given by the flow F(t,a) of V where a is the location of the material point at t=0.. This is similar to what we have in fluid dynamics. It defines a function f(m)=t which gives the time t at which any particle is at m. This function defines a family of hypersurface S(t), diffeomorphic to S(0), which can be seen as the material body at t.

For an observer who sees a given material point at his proper time T , he continues to see it if there is a relation between T and t (given by the usual formula involving the spatial speed of the particle with respect to the observer). But he will observe something which is not exactly the material body but the intersection of the 3 dimensional hypersurface representing his space at T, with the family of hypersurfaces S(t). This is a distorsion of the material body.

Now if we are in SR, and if S(0) is a hyperplane then S(t) will be a hyperplane if and only if the vector field V is orthogonal to S(0). Then the material body is a solid (with constant distance betwee the material points) only for the observer whose velocity is parallel to V. For any other observer the material body looks as a dstorsion.

Because usually the 4 dimensional velocities are all closed of each other the physical phenomenon is not signficant.

Moses,

Thank you very much for joining this discussion.

I am glad your extend the resource basis which I can explore to study this problem in depth. I need some time to reflect on your answer because I need to look up all the sources you are pointing to.

But I need to align myself with your understanding of  "real physical phenomenon" when you say:

Relativity of simultaneity is not a computational effect - it is a real physical phenomenon.  

Before I go any further, I need some confirmation about the behaviour of the hypothetical rigid rod mentioned in my writing supporting the main question and illustrated by the attached plots.

I attach all relevant sources below for quick reference.

Jean Claude,

Thank you for detailing the answer from your perspective. I only have some problem with your last statement.

Because usually the 4 dimensional velocities are all closed of each other the physical phenomenon is not significant.

I simply do not understand "velocities are all closed of each other".  

Andrew,

I will use an image to help to understand. Imagine that you are an asttronomer looking at Jupiter. It is a hige planet, so the time it takes for the light to go from a point on the equator to you is smaller that the time it takes for the light to go from the pole to you. So the image of Jupiter that you get is not exactly Jupiter as it is at a given time. And of course this is worse when you look at the stars.

Thank you Jean Claude

I understand the difference between observation of distant positions and instantaneous position within a coordinate system.

I particularly avoid using words like "observer who sees  something" so commonly used in relativity presentations, because seeing includes projection of points by light through the lenses onto the retina of the observer hence your Jupiter effect.

Despite the declared impossibility of instantaneous communication the coordinate systems using time instantaneously connecting all points to infinity is still in use. (Minkowski Space-Time). Until this approach is abandoned I am free to use coordinate systems and infer 3d geometric relations of objects based on trajectories of their parts.

All my speculations here never include observation in order to avoid unnecessary complication of already messy problem. The uncontaminated by observation geometric relations of an object acknowledged in the coordinates of the stationary system K are distorted in K' as you seem to agree in your previous message. The distortion exists and it does not matter if it is minuscule or scrambled by observation.

My example shows piling off the rod bit by bit from its original rest state which has no place in reality and indicates non-physical nature of such image. It is just similar to representing two trajectories shifted in time as I previously demonstrated on a train example where trajectories of the engine and the last carriage are shifted by 10 seconds. In extreme the last carriage seems to in front of the engine when the train accelerates from stop.

Sadly most of people here seem to agree that old anomaly is a new normal.

I have a really simple explanation of all of this but I should not even attempt to explain if the problem I am presenting is seen as non existent.

Andrew,

The problem is that we are too used to coordinates systems, solid, ...and mixing lorentz transformations with QM and what else. We have to come back to some basic, nonsensical ideas and concepts. A material body is comprised of material points. Each of them is located at a geometric point and travels independantly on a world line in a 4 dimensional universe. Actually this is not very different from what we see as the motion of a material body in the 3 dimensional space. Because the material points travel independantly we have to make some additional assumptions in order to make sense of the concept of material body : there are lnks between the material points. In Classic Mechanics we have the concept of solid based on fixed distance, it does not hold any more in relativity (but even without any relativist effect solid are deformable). The simplest assumptions that we can make are : i) the world lines can be represented by a vector field (which means that they look alike = a steady flow) ii) at some time all the material points are together in an area of 3 dimensional hypersurface. Then this is just a bit of differential geometry to show that one can define at any time the material body as a 3 dimensional hypersurface. The key point is that this sensible definition is arbitrary. Another example is in fluid mechanics : you can always single out a slice of water flowing in a pipe and follow it along.

In the usual 3 dimensional space, if you represent all the successive locations of the material points which comprise a material body, you have a cloud, in which you single out some of them by saying that they represent the body at some time. In relativity we have 4 coordinates, the choice is still possible, it just looks more arbitrary, and of course it depends on the observer.

I tried to trace through the follow up on comments or questions about whether length contraction of a rod, and by implication time effects on clocks at each end of the rod, are a "real" or "computational" effect.  I didn't see it, but maybe the discussion is too abstract to process quickly.

First, I have no idea what is meant by "computational" effect.  Are there computers involved?  I might have used the term "measurement" effect, but I don't know if that is what is meant.

There is a very simple test for a real effect and an apparent (or measurement) effect, both of which are present in SR.

Let there be a group of observers A, B, C, ... in inertial frames, all with rods and clocks.  Let then all make measurements of each others' rods and clocks.  Then let ONE of them accelerate.  Say, A, it is arbitrary. 

Everyone except A will agree that A's rod has changed in length, though they may disagree on whether it is shorter or longer.  So we conclude something has "really" changed about A's rod.

Everyone except A will agree that their rods and clocks are unchanged, so the changes in B, C, etc. noticed by A are attributed to changes in A's measurements, not in B, C, etc.

Robert,

Thanks for continuing the discussion. Every bit matters.

Language: 

It is important to use proper terms so other people understand. My weak point is non English speaking background.

"computational" comes from the verb compute. 

The term pre-dates computers: ((17th century).  from Latin computare (“sum up, reckon) In Webster dictionary "to determine especially by mathematical means" and this is my understanding. I acknowledge that today compute  means more like nuerical calculation. I will think of a better word then.

Ultimately everything boils down to computations of positions of objects which may be real or not whatever theword "real" means.

Language is a tricky thing. I also use term "apparent",  while this word carries two opposite meanings

one is "obvious", the other :

manifest to the senses or mind as real or true on the basis of evidence that may or may not be factually valid.

I may consider not using this word as well.

Robert,

You have touched the real essence of the problem by saying:

"the changes in B, C, etc. noticed by A are attributed to changes in A's measurements, not in B, C"

We cannot ignore that we have clear knowledge which one has actually moved.

There must be consequences of that move. 

The first order effect is that the whole world with no exception appears to be moving relative to A (from his perspective):

two friendly observers B and C, the Sun, the Moon, Venus and Mars etc. 

Observer A with two bits of memory  would be insane to claim the whole world has moved while he stays in place (which is theoretically possible albeit unlikely)

The second order effect is that A's clocks runs differently (some question it but I do not)

Lorenz transformation for this case allow to compute and draw the trajectories of  two points which could be ends of a rigid rod moving relative to Kin the direction perpendicular to X, in the K' coordinates .

Trajectories are equations that cover infinite range, so one needs initial conditions of the beginning of the motion.

Relative simultaneity doctrine insists one point must start moving after another so while one end moves the distance between the two must be changing.

If we use rigid rod example it must be progressively bending with discontinuity on its body travelling towards the stationary end (a funny kind of dynamic bending).

The relative distances between two points differ progressively where no such thing takes place in reality. 

In such case I call the transformations result is some image of reality but not fthe faithful representation of it.

A map of the globe reflects most of its features except overhangs, and as useful as it might be, it does not make the earth flat and distorted geometry of objects real.

It is easy to prove me wrong by simply finding errors in my calculations presented on the attached pictures and providing alternative proper calculations with the correct plots.

Andrew, re: "Relative simultaneity doctrine insists one point must start moving after another so while one end moves the distance between the two must be changing..."

I tried to explain this earlier, talking about how quantum systems automatically re-synchronize after acceleration, and macro systems do not.  But it is confusing and I think you missed the relevance to your method of inquiry.  If you are trying to construct the changes as artifacts of acceleration, this will ultimately not work.  I realize you are excited about your discovery and will probably ignore me, but I have pursued similar ideas in the past.

Without getting into the quantum systems, there are two ways you get the proper distances and clock phases for relativistic effects.  One is to accelerate the objects in a reference frame infinitely slowly.  The simultaneity issue kind of goes away.  But this doesn't much interest me.  

The other is to re-construct the reference frame after acceleration, to mark off the distances with quantum objects, like meter sticks, and to follow the Einstein synchronization procedure with the clocks.  Note that you can stack the meter sticks sideways while accelerating them, so that their length cannot have changed from that cause.  Then you only turn them 90 degrees while they are inertial.

Valentin, it is quite acceptable for A to eject part of itself as reaction mass to account for its acceleration.  If you'd like for both A and B to accelerate, fine, but you will not learn anything unless you compare their observations with C, D, E, ... etc.  In physics one tries to explain any legitimate observations, not some restricted set intended to enforce some preconceived limitations.

Valentin, probably you should ask a specific question and start your own thread.  There are many on here who will answer.  I have other things on my mind right now, and after looking at your posts, I think it would take a bit of time.  These questions tend to recur on RG over and over, with new people asking them.  I just think if my approach didn't register with you, then maybe let someone else try.

Dear Andrew,

I apologize because I don’t read all the thread. I misunderstand the question about the rod, believing that it was moving along x axis.

I attached (.doc) the resolution of the rod problem considering two different movements (parallel and transversal to x axis).

This problem, analyzed in SR framework, involves a conceptually difficult phenomenon which challenges common logic.

Two inertial RFs in relative motion have the same space-time geometry, which means that have identical symmetries (homogeneity and isotropy of space and uniformity of time).

However, they have different spatial length measurements along the direction of relative velocity of RFs and also different time rate. Of course, these peculiar aspects are linked with the length contraction and time dilation. So, moving bodies have different size than at rest

Another consequence is that two simultaneous events at different points in a RF will not be simultaneous in any other RF having relative motion. Absolute simultaneity only happens when two events occur at the same spatial point

"Is relative simultaneity a misinterpretation of Special Relativity?"

No.

Robert,

I have no intention to ignore you. I said in response to you post:

"It is important that relative or absolute simultaneity are investigated from those and any other relevant perspectives."

Bu ihave to clear the issue from my own perspective and critique I brought upon myself in this thread. But that is as it should be. The ideas should be forged in fire.

Hugo,

Thank you for the document. I thought you have forgotten. It looks really neat and I will digest it as soon as I can. I like when discussions enter this stage where we can make verifiable statements.

Valentin and others:

Here is a simple representation of how two observers in relative motion will each see the other's clock moving more slowly due to their different orientations in spacetime.

Hugo,

“Another consequence is that two simultaneous events at different points in a RF will not be simultaneous in any other RF having relative motion. Absolute simultaneity only happens when two events occur at the same spatial point”; and

“the spatial configuration of moving bodies in a RF is not the detected configuration picture by any observer.”

- that isn’t so.

“The Wutke rod problem” is a good example, when, in a simple case of two relatively moving inertial reference frames K and K’ along X,X’-axes,  the using of the Lorentz transformations as the something absolute is evidently wrong. Though that was already in the corresponding thread, I repeat the result – this deviation from the SR prediction is simply observable:

So – in the problem a [parallel to X-axis] rod moves along Y-axis in the stationary frame K;

- yea, when the rod crosses the X’-axis,   the K’ the reference’s clocks indeed will show – in full accordance with the Lorentz transformations – that the rod’s ends cross the X’ axis in different times – so an SR observer in the K’ must think, that the rod crossed the axis at a angle φ, Cos(φ) =1/gamma; if the K’ speed is very high – practically orthogonally to the X’-axis.

But if the K’ observer places a bathtub  with plasticine on the place where the rod falls, the observer purely experimentally will observe that the rod doesn’t stick out the plasticine, it has fell flatwise – the plasticine doesn’t know the Lorentz transformations and so show real experimental result in contrast to the observer’s illusions.

 Again – there aren’t in the reality the “relativistic effects” as “the space contraction”, “the time dilation”, etc. – nothing can change anything in the Matter’s spacetime. But moreover even the Lorentz transformations aren’t valid totally.

Cheers

Hugo,

You have independently verified my calculations which I do in a different way. What you describe is the same anomaly in a slightly different regime. Since there is no error in calculations there is only interpretation of the effect left to be discussed.

I have followed up your train of thoughts and used your document to insert my maths and a few comments. I attach it for the record. If you do not your work to be altered by my annotations let me know and I will remove it.

Thank you.

I have given a look at the computations. Of course the Lorentz transformations are exact, what is not exact is the definition of the rod : it is observer dependant. The rod itself, is a collection of material points which follow velocities which can be represented as a vector field of velocities, from which we can define a common proper time for the rod. With respect to this proper time the rod keeps its shape (and even its length), but what the observers observes is a collection of material points which belong to the state of the rod at different proper times (of the rod). You define the rod by its extremities, this is right but the extremities which are observed do not correspond to the same proper time of the rod. So the rod looks as if it was distorded (and probably not linearly).

Re: Valentin "I am well used to the many proclamations - often contradictory - coming from those who use or who support the theory of relativity."  How ironic that I am now perceived as establishment.  If you only knew.  My example with ABCD... is quite correct, but an argument not a proof based on the idea preponderance of evidence from many observers.  It is not actually accepted by strict establishment relativists, so your accusation shows you neither understand my example nor relativity.  It is wise to understand something before criticizing it.  I read one of your papers.  You have exerted a lot of effort but missed something ... I think something about the nature of aberration, to which I also once assigned too much importance.  In a few years you will see it.

Dear Andrew

I agree with your formulation (it is equivalent to mine), but I disagree with your last comment.

< This plot uncovers an interesting distortion of reality by which it moves prior the moment of coincidence of the coordinate system potentially prior to its existence. Additionally since both ends are not on parallel line, one end must start its motion from where it has never been.>

There is not a distortion of reality because both descriptions are the “reality”.

Each observer has its own unique reality, different from any other observer with relative motion.

If not so, how would one explain that we are in the center of the Universe? Casually?

No chance, the spherical symmetry of the observable Universe is an invariant within the SR.

A few years ago I gave a talk on the Cosmological Principle and its demonstration in the framework of the SRT. If you want I can send you my notes (in Spanish) with the mathematical proof (unpublished).

It must be emphasized that SRT modifies the classical notion of experimental measurements.

Before SR you need a “physical object” and an “instrument” to get a physical measurement.

After SR you should add the observer to the measurement method.

By the way, the rod problem assumes that movements are always uniform.

Sergey Shevchenko,

Excuse my delay in responding.

A few days ago you wrote an extensive post about inconsistencies in SR and referring to the "problem of Dingle". Also named alternatives theories and finally you indicated .

It is impossible to try so many different subjects.

I agree to discuss issues, but one at a time. Make your choice

Regards

Valentin, you've made several assertions:

"geometrical constructions are only abstract representations of suppositions about reality (i.e. the Lorentz transformations), and they do not reflect anything of what time is as a fundamental concept of physics."

The spacetime diagram I offered is a two-dimensional projection, abstracting from the two spatial dimensions that are irrelevant to uniform relative motion, which proceeds in one dimension relative to an observer. You may not like the idea of spacetime as a continuum, and you may not like the idea of relativity, but the diagram displays the rationality of what you and others have described in various ways as nonsense, and a simple assertive rejection is without value. The diagram's elaboration allows (exclusively) an explanation of why light is invariant and a limit, and explanatory power is a scientific value that isn't refuted with a dogmatic dismissal.

"You cannot simply plot time values on 2 separate axes and then bring the axes together in an angle as if they pertain to the same plane. Time is not a 2-dimensional concept."

The diagram treats time as one-dimensional. In doing so, it represents relative uniform motion without exception. A flat denial is the verbal equivalent of shutting one's eyes.

"there is no evidence in reality that time has geometrical properties. So there is nothing that justifies the claim that in reality time would be oriented at 90o from the 3D space, or that it would be observed at an angle from another reference frame."

The evidence is the diagram's fidelity to physical relationships. When motion in time is represented as perpendicular to space, the "illogical", "nonsensical" properties of SR are shown to be valid, like it or not.