I would argue as follows: in the mathematical framework, we have no problem: basic entities are points in a four dimensional continuum, where the distance is pseudo-euclidean, singling out one timelike direction and three spacelike ones.

To describe these points in numerical terms we arbitrarily introduce reference frames, with respect to which each point is now described by a set of coordinates. The reference frames are arbitrary, and the coordinates inherit this arbitrariness. To transform from one reference frame to another implies changing coordinates, using well-defined rules (Lorentz transformations).

All this is similar to what happens in geometry, where we use rotations to go from one coordinate system to another.

As for physics, we call such spacetime points events in order to emphasize that they are not, like ordinary points,  lasting structures, but that they are essentially instantaneous.

You are of course correct to say that Minkowski did not use the word event: he uses the word ``Raum-Zeitpunkt'' (see p. 57). Terminology changes. Events in that sense should, indeed, not be confused with events in the usual sense, though it seems to me the problem is not great: any event that can be idealised as pointlike (that is, it is spatially not very extended nor lasts very long) can be well described by a spacetime point. I do not see the problem here. If nothing happens, at all, at a given spacetime point, it might be hard to determine that it is the same, but that can be remedied by making something happen.

A more important confusion arises between spacetime points themselves and their coordinates: the former are, in a sense, objective (and there an event, say a collision between two particles, is useful to call attention to the invariable and objective nature of the spacetime point). The latter, on the other hand, are quite conventional and depend on the choice of a coordinate system. That is why the transformations in the coordinates should not be assigned the significance they often are, as being something that actually happens to an object. Rather, we have a pair of events which, observed in one frame are simultaneous and separated by a given distance, whereas in another frame, they are not simultaneous, and the distance differs.

Another important issue concerning events is that they are usually much simpler to handle and to understand than objects. Extended objects cause all sorts of paradoxes, because in each reference frame we see a different three dimensional projection of the object's history. Thus, if an object at rest is becoming warmer but has all the time a constant temperature, a moving observer observes temperature gradients. In my opinion, this means that it is risky to say that we see ``the same'' extended objects in all reference frames. At the very least, such beliefs can lead to serious misunderstandings.

Best wishes

Francois

Francois

Thank you for the balanced answer. I hope there will be more to see what others think.

One more problem I see with event terminology is that:

if  we have E=(x,y,z,t) and call it an event and have E'= (x'y'z't') another event as per description in the reference source, it is not possible to tell if this is one or two events without additional description. This is because you need to know the physical context or single out Lorentz transformation out of all possible transformations to say it is one the same event designated by .... what.. event E and event E'?

In Euclidean geometry every linear transformation between two coordinate systems is about finding coordinates of the same point in two frames. There is nothing suggesting that in some transformations the two sets of coordinates mean one and sometimes two points.

It is possible to defend poor terminology used for some reason, but you cannot prove it is a better choice. Like in the court of law it is possible to defend a crime but you cannot prove the actions of the defendant benefited the victims.

But at the end, the consensus prevails whether terminology is good or bad.

A little known Copernicus law postulated the principle that bad money drives out good money.

Yes Andrew, it is right to say that the "space-time" is the set of all "events". This means that we can call the set R^4 "space-time" and its elements "events". However, through the "event" (x,y,z,t) one has continuously many lines of universe and every of them has its own "time" t' if considered to be an observer. We can also speak of the fact that any of them has infinitely many linear parametrizations, corresponding to different 4-speeds. Lorentz busts applied in (around) 0 are an interpretation of movement, but the lines of universe are also interpretations of moving points, and the parametrizations of those lines are interpretations of movements as well. And so on. So it is better to use the names "space-time" and "event" just as conventions.

To your remark concerning telling spacetime points apart. Yes, I agree, and whenever such an issue arises, we should take care that something happens at (x, y, z, t), in other words, we should associate an event (usual meaning) to that spacetime point. Whether the terminology is good or bad is not clear to me: saying that events (usual meaning) are described by spacetime points seems OK to me. And since it is often convenient to have an event (usual meaning) for the description of any spacetime point, I do not think there is a major problem.

Also, whenever you describe a paradox, say barn pole, it is very useful to fix one's attention on actual (usual) events, and to determine their coordinates. We should not say: the barn pole is here. But rather: the event: the first end of the barn pole is crossing the entrance of the barn has such and such coordinates (x, y, z, t). Hence the insistence on events

I would say basic elements are physical events and space and time (together with other magnitudes) are physico-mathematical variables that we have chosen for describing those events. Because there isn't only one observer, but many different observers, in various situations of relative motion, then the reference frame (O,x,y,z,t) becomes necessary for the description of the same physical event by different observers. Different observers will discover they describe otherwise the same physical event because of different causes that distinguish different physical situations of every observer that change the physical event for those observers. Only for observers with inertial relative motion, the Principle of Relativity garantuees the invariance of physical laws and consequently the same description with one same mathematical model.

I insist to consider the use of words to convey precise meaning.

English language is riddled with words having multiple meaning and the verb 'set', has set the record of 430 meanings listed in the Second Edition of the Oxford English Dictionary. Language of science should be more precise than the natural language.

If I  was to implement event in software, I would make it a class with attributes:

x,y,z,t,s1,s2...sn and a Boolean method operating on a subset of the attributes which has a true value if the event happens.

For example an event where an element of water in a lake reaches its triple point can be described as:

E ≡ H(x,y,z,t,T,Pp)=(T=273.16 K  ∧ Pp=611.657 pascals  ∧x=1∧y=2 ∧z=3 ∧t=4 )

How much more useful is the event  (x=1∧y=2 ∧z=3 ∧t=4)?

In order to show that I am not the only insane requesting clear distinction between events and their coordinates:

Relativity Physics

W. H. McCREA: An " event " will be taken to mean something happening at a certain place at a certain time, for example the emission of a light-signal at a given place

and time, or, say, the passage of a moving particle at  a certain instant through some marked position.

Introductory Relativity

W. G. V. ROSSER

The co-ordinate system ∑' willbe considered as having its own series of imaginary rulers so that the co-ordinates of an event can be measured relative to ∑' . By an event is meant something which happens independently of any co-ordinate system,

The Theory of Space Time  and Gravitation

V. Fock

By " event " we mean an instantaneous occurrence that can be characterized by a point in space and a corresponding moment of time.To have a concrete picture, we shall imagine that the " events " consist of

the instantaneous flashing of light signals.

I agree,, language of science has to be precise and simple. I agree still that an event is "something which happens independently of any co-ordinate system", but co-ordinate systems or reference frames become necessary when from the simple observation we pass to the description. Then every observer discovers his description can be different from the other

That no one should say, unless as a short cut, that an event is described by coordinates is something I fully agree with. On the other hand, the confusion between an event and a spacetime point does not seem so bad to me: a point, in geometry, and also in spacetime geometry, is always defined as something having an absolute identity independent of any coordinates. But overall I have no problem with the points raised by Andrew.

You capture the gist very well, Francois - not only for the specialist but also for the layperson - in your insightful comment: "As for physics, we call such spacetime points events in order to emphasize that they are not, like ordinary points, lasting structures, but that they are essentially instantaneous."

My only question is this. How does one distinguish between "lasting" and "instantaneous"? Is there an agreed upon criterion here? Paul

I fully agree that language in science needs to be precise to avoid misunderstandings. As an example we have the noun "definition" and its verb "to define". We therefore can "deifine a point in space to be . . . " - to be what? Well, there seems to be two options: (1) we can define the "concept" of a point in space ("a point has location but not extension") or we can define a point by citing its location with respect to a coordinate system. We also use the concept of "point" as a "point in time." In spacetime the concept of a "point" conveniently encompasses both location and time and with this doble usage of "point" it strikes me as useful to label this "point" compactly as an "event" which conveys both the notions of "location" and "time".

And in the comment above by F. Leyvraz we have a another use of "point", to wit: "But overall I have no problem with the points raised by Andrew" (italics addedd).

@ Paul: a point is always an approximation. The point of contact between two colliding billiard balls may be a relevant concept in some cases, in others you need to look in detail at the shape of the contact area. In relativity, as well, whether an (ordinary) event can be described by a spacetime point depends on whether it is short enough, in the relevant context.

Many thanks for that helpful explanation, Francois. Best wishes, Paul

Dear Andrew,

I agree on the definition of event as something that really happens and not as something that is observed via a coordinate system, whatever is that.

After all I have fed up with all that S and S' industry.

Enough!

Sorry, but the "happening" of an event can only be specified with respect to a coordinate system and a clock. You may observe the event but you cannot communicate your obeservation without using a location and specifying the time. Try calling 911 and saying only "There is a fire."

Dear Dwight

We have to separate concerns. The happening of an event may not be related to where/when it has happened, although the location may be useful.

With your fire example we need to say only about "fire broke out" not about "being on fire", which is a state not an event. If two fires broke out due to children playing with matches the positions of the houses play no role in the event but the position of matches whether in or outside the flamable area within. The time of events play no role either. The event " match has been lit" while coinciding with the curtain in the house is sufficient.

The fire investigators would find from the damaged clock when it happened and the position on earth where the house was built but if the clock had no date or it is 12 hours clock the day or the am or pm couldn't be established without the additional data.

On the other hand if an arsonist plans to set a fure have been revealed and place and tinme wewe known, the event could have been prevented.

Time and position is important to know and manage events but insufficient so my case is to use terminology making distinction between events and their coordinates.

As I said before, one can do a lot to defend unfortunate terminology but one cannot prove ambiguity is better than the lack of thereof unless this is politics.

Dear Andrew Wutke,... I have same perception like Demetris Christopoulos  *I agree on the definition of event as something that really happens and not as something that is observed via a coordinate system, whatever is that.* 

Today, in time of walking to work, had arisen idea how we could demonstrate easily that our solar system formation theory, GR, are false reflection back of reality... Why... Take a piece of rock... Same rock exist in rocky planet surface and in Inner Asteroid Belt... They build up from minerals... Such of minerals form a very well defined and known *event*... In case of asteroid stage does not exist such a condition... So we can affirm that these asteroid from Inner asteroid Belt was formed in a pre-existed rocky planet condition...

I fully agree that an event is something real that takes place - but it takes place somewhere and at some time. How do we communicate or record that information without using a coordinate system, however, rudimentary, and some kind of time reckoning - "it occurred this morning over by that tree yonder". We specify the time of occurrence with a tieme reckoning system of "morning, noon, night, etc. and a spatial coordinate system with its origin at "that tree over yonder."

You call the fire department to report a house on fire. The fire is an event. You tell the fire department "there's a fire". You have reported an event. But don't you want the fire department to extinguish the fire? You have to tell them the location of the fire and you have to use some kind of common spatial reckoning system, aka "coordinate system", to tell them the location of the fire. 

Of course events happen all of the time everywhere in the universe without coordinate systems and clocks.  It is when we wish to communicate, record or otherwise study an event that we use coordinate systems and clocks.

Dear Dwight

I'm not saying coordinates are useless but they may be quite separate thing and may not contribute to the event. But kinematic events are different. You can legitimately define an event as an arrival of a point objest to a particular place and time. And there is nothing more needed for duch events to happen. But this is one of many types of events.

So what is wrong in calling a space time point a space time point or or point for short?

May be because as Minkowski puts it:

"It came as a tremendous surprise, for in his student days Einstein had been a lazy dog...He never bothered about mathematics at all.

as quoted in a conversation with Max Born about the development of the theory of relativity, by Carl Seelig, Albert Einstein: A Documentary Biography (1956)

Dear Armit

Motion is not an event. A particular position of the photon and time can be. A special case kinematics eve t when happening is fully described by coordinates.

If somebody called coordinates xyzt a happening, I would not object. This could be appropriate and common to say for three events:

Arrival of gamma photon 

Arrival of atom nucleus

Production of electron positron pair

Three events, same position and time, one happening

And there is no wrong question. Only answers.

It seems to me quite number of people like the term events instead their coordinates perhaps due to the same mechanism most people prefer qwerty keybord designed to slow typing down.

Dear F. Leyvraz

Your answer that has attracted many likes puts everything in the correct perspective and someone who understand the shortcut "event" the way you do has no problem. 

This becomes a personal preference. As I come from engineering background even a subtle ambiguity matters. There are some consequences of crippling simplifications and generalisations in the SR.

After using reference frames and thought experiments for more than a century, I think we have lost connection to the common sense.

Fact:

A boat is leaving from the port.

Question:

What is the event?

Try to answer that small question and you will find all the fallacies that have inserted in our life in Physics last 100+ years.

I wish everyone to enjoy the summer (Northern Hemisphere) or the Olympics Rio 2016 (Southern Hemisphere).

I am not sure that the question is meaningful. In general, mathematics represents a succinct language for communication. In the special theory of relativity, STR, the Lorentz transformation, axiomatically derived from the postulates of relativity, translates "information" between inertial systems that are travelling at constant speeds in relation to each other. Space-time imparts that (x,y,z,t) is needed to identify something that is "reported" in one particular privileged system – not (x,y,z) at time t.

A mathematical point is of course not a relevant physical abstraction, but this is not the reason to abandon STR as unreasonable, since it serves its fundamental purpose as an important deductive step in the evolution of scientific understanding.

If the "event", necessitates, i.e. a QM-description one needs to add the postulates of that theory and then proceed from there and so on.

Landau anf Lifshitz (The Classical Theory of Fields, Pergamon Press, 1975, p. 3) define an "event" as follows: "An event is described by the place where it occurred and the time when it occurred." They apply this definition in their presentation of the epecial theory of relativity (STR). Thus space in STR is populated by "events".

Of course one can quibble but I think that this succinct, clear definition suffices for the purposes required of it in elucidating STR.

Erki, 

There is no intention to abandon the STR becayse of the misuse of a word, but to discuss the re-use of  the common linguistic term associated with a physical change.

I think my question is meaningful because names should be chosen wisely to help not to confuse, avoiding ambiguity if possible. 

In my student's years, fascinated with the freedom of expression in software but not in political reality I lived in, I toyed with my Algol programs giving variables some silly names like Lenin for temperature and Stalin for pressure. As expected, programs were working correctly, but an engineer could have problems in guessing what the programs were about.

You say:

"A mathematical point is of course not a relevant physical abstraction"f

Why not?

On one side, you have -according to the  lecture of Bernhard Riemann in 1854 - every mathematical object parametrized by n real numbers may be treated as a point of the n-dimensional space of all such objects.[1]

On the other side you have Minkowski saying: "I shall call a point in space at a definite time, that is, a system of values, x, y, z, t, a world-point ( Weltpunkt). The multiplicity of all possible systems of values x, y, z, t I shall call the world"[2]

Ignoring the pompous yet restricted scope of Minkowski's "world", you can see the intent to retain the core point in the name. In his previous work Minkowski was more modest:

An individual system of values of x, y, z t, i. e., of x1, x2, x3, x4,shall be called a space-time point(Raum-Zeitpunkt).[3]

If mathematical point is not a relevant physical abstraction then what is spacetime?

"In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum." - Wikipedia

[1]Bourbaki, Nicolas (1994), Elements of the history of mathematics, Masson (original), Springer (translation).according to https://en.wikipedia.org/wiki/Space_(mathematics)

[2] H Minkowski Time and Space

[3H.Minkowski ]The Fundamental Equations for Electromagnetic Processes in Moving Bodies (1908) https://en.wikisource.org/wiki/Translation:The_Fundamental_Equations_for_Electromagnetic_Processes_in_Moving_Bodies

Dear Demetris,

I don't understand your problem. The "event" is "the boat leaving from a port" conceived as something "happening" in which the boat and the port have a location and the boat presumably leaves at a specifiable time.  However, the abstract concept of a "boat leaving a port" is not an "event" because it is not put in a context of something that is "happening". An event as defined in my comment above "happens" by presumption. Suppose that I am giving a physics lecture and I say: "Consider a boat leaving a port." For the purposes of the lecture this is an "event". In the context of the lecture there is a port with an implied location, there is a boat located at the port and "leaving" implies an occurrence in time. Hence an "event" albeit fictional.

Dwight,

This indeed is what L&L say, but:

1. "event is described by"  not "event is" in contrast with negligent definition  of Feynman in Lecture IV: "A given point (x,y,z,t) in space-time is called an event". Now you know why a generation of physicist absorbed this kind of notion.

2. "the place where it occurred and the time when it occurred" implies it is no the place or/and time but something else - the same way as a house address is not a house.

Further down L&L say:

"It is frequently useful for reasons of presentation to use a fictitious four-dimensional space, on the axes of which are marked three space coordinates and the time. In this space, events are represented by points, called world points. In this fictitious four-dimensional space there corresponds to each particle a certain line, called a world line."

It is clear L&L respect Minkowski's terminology. I remind; here is no word event used in any form in Mnkowski's Time and Space.

In physics, and in particular relativity, an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it.[wikipedia]

Andrew,

I agree that the abstraction of a mathematical point is very relevant as a basis for Newton's classical mechanics – position, momentum, trajectories etc., but as soon as we enter QM we know that a reasonable physical interpretation necessitates going beyond ...!

An excellent book concerning these questions is "IS NATURE SUPERNATURAL? – a Philosophical Exploration of Science and Nature" by Simon L. Altmann.

Thanks Erkki

I will find this book.

Dear Andrew,

Just when I think that I have an issue completely under control somebody comes along and bursts my bubble. Thank you for your comment on my comment and now I offer a few responses (italics) to your comment.

"This indeed is what L&L say, but:

1.  An "event is described by"  not "event is" in contrast with negligent definition  of Feynman in Lecture IV: "A given point (x,y,z,t) in space-time is called an event". Now you know why a generation of physicist absorbed this kind of notion.

RESPONSE: Feynman according to your quote above doesn’t say “an event is” he says “an event is called”, i.e., defined  by a point in spacetime, this is a definition of an “event” not an equivalence. But from the above I can make a single statement with many variations “[For the purposes of STR] A point in spacetime is called an event/describes an event/is considered to be an event/designates an event, etc all of which statements are equivalent definitions of an event for the purposes of STR.

2. "the place where it occurred and the time when it occurred" implies it is no the place or/and time but something else - the same way as a house address is not a house.

RESPONSE: I don’t understand your statement here. The address of a house denotes a location in space, which location is occupied by the house. I don’t see the problem here.

Further down L&L say:

"It is frequently useful for reasons of presentation to use a fictitious four-dimensional space, on the axes of which are marked three space coordinates and the time. In this space, events are represented by points, called world points. In this fictitious four-dimensional space there corresponds to each particle a certain line, called a world line."

RESPONSE; I would quibble here with the use of the would “fictitious”  and would prefer a word like “idealized” that avoids the connotation of fiction in the sense of  being a “Alice in Wonderland” kind of fantasy fiction (although some may argue that that is exactly what STR is – “fantasy fiction”).

It is clear L&L respect Minkowski's terminology. I remind; here is no word event used in any form in Mnkowski's Time and Space.

In physics, and in particular relativity, an event is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it.[wikipedia]"

Is it right to say that basic elements of spacetime are events? - ResearchGate. Available from: https://www.researchgate.net/post/Is_it_right_to_say_that_basic_elements_of_spacetime_are_events#view=57ae81b093553b99f041f25e [accessed Aug 13, 2016].

Using of the event term in the theory of relativity rather has the opposite meaning. This is an opportunity to uniquely identify event thanks to a 4-vector spacetime. It is like to the point which indicates the state of the system in the extended phase space, but not in the full sense, since changes, which corresponds to event, involves system transition from one point of phase space to another.

In general, event is a change in the state of the world (in topology of some local region of its structure).

The theory of relativity deals with non-periodic processes. Time and space are not independent in it. Any changes in this system involve the evolution of the entire system.

Quantum mechanics (and periodic orbits in dynamic systems) involve periodic processes. Strict periodic can be viewed outside of the system as a constant state of a system like unitary object, i.e. as the absence of events, although within the system will be a process of periodical changing the state in which you can recognize events.

If we go back to the phase space, the biggest problem is how to interpret the system, changes of which corresponds to a transition from point to point along the degree of freedom, associated with the time axis (may be more correct to say coherent evolution parameter or lifetime). Formally, it can be considered as events, but in fact such system is not evolving system. Conception of time for such closed system is senseless.

The event is a change, not a state.

Dear Vasilly,

In the context of relativity I would maintain that an "event" is neither a "change" nor a "state" - it is a "happening" with a specifiable location and time of occurrence, "Change" implies a before and after and "state" implies a condition of a pre-existing entity. A "change of state", however, may be an "event".

To capture a broader class of changes as events we should include a change of state or the change in position, where the operator "or" does not mean an exclusive "or".

Events where no change of state of an object is taken into account can be called kinematic events. For such events the spatial coordinates change is sufficient  information. Time is also useful to establish the relationship to other events.

Der Dwight

Thanks for the detailed analysis of my post. This is good when somebody's statements are dissected so lessons can be learnt how to precisely express thoughts.

1. An "event is described by" not "event is"  vs “an event is called”,

 The "is called" relation can be one of the two kinds

a. A synonymic relation that is having an identical or similar meaning e.g. "likelyhood of something (usually an event) happening is called the probability". 

b. A mistaken Identity when the synonimic relationship is erroneous, e.g. "mass is called weight in common language"

2. "the place where it occurred and the time when it occurred" implies it is no the place or/and time but something else - the same way as a house address is not a house.RESPONSE: I don’t understand your statement

What I poorly expressed is  that:

because "it" (event) occurred in place and time as said by L&L means: "it" is not identical with "it"'s place and time of occurrence however related.

There is many ways you can designate an object by name or by other reference.

I said that the reference such as the house's address is not the same as the house itself. Typically you can kick the house but you cannot kick the abstract address.

In software, a variable which has a numerical content is not the same as the variable containing address of that numeric content (pointer), and it is extremely dangerous in safety critical application to mix up the two.

Dear Andrew,

I think that we are in agreement but maybe not. Let us focus on the term "event" as it used in Einstein's Theory of Relativity (STR). The term "event" is defined specifically in STR as a "point" in spacetime and the term is used as a convenient way to visualize a point in a 4-dimesional psuedo-Euclidean space. It is easy to think of an "event" like a birthday party which nominally has a location and a time just as does a "point" in spacetime. "Event" in STR has no fundamental signifigance, it is a label.

On to the house. Neither the house nor its address qualify as "events" in STR because an event is a "happening" with a specific location and time of occurrence like a birthday party. The house is located where it is for all time and the address is just a label by which to locate the house. If the house burns down the time and location of the fire is an "event".

Dear Dwight,

I think we better understand each other. The event analysis starts to look like a bible study sometimes, but we seek common ground to see the limits of the definition of an event in the STR. I think the summary of F. Leyvraz captures most of the subtleties of the problem.

The term "event" is defined specifically in STR differently by different people but we can agree it is commonly used as a shortcut linking physical event with its coordiantes in spacetime. This is not my preference to have shortcut names leading to ambiguity. You may agree that one physical event can be located by an infinite number of coordinate sets, and some people call a set of four coordinates an event.

I can explain where ambiguity in counting and locating events may lead to confusion by presenting a small use case attached to this post.

You are right that the house is not event in my example but it only serves as an illustration that something that is a reference to a tangible object is not identical with the object.

I would like to add two observations to Francois' first contribution.

1. Instead of Lorentz transformations and rotations one should probably consider inhomogeneous Lorentz transformations (forming the Poincaré-group) and motions (forming the Euclidean group).

2. " in the mathematical framework, we have no problem:" Of course this is right, in a sense. However, it is also misleading in a sense that is closely related to the question under consideration. The mathematical framework ( differential manifolds) works by assuming a set X on which there are defined R^n- valued functions which need not be defined on the whole set X but satisfy consistency requirements in the regions of overlap. This looks innocent enough but for a physicist this is asking for much more than is fair: As a set, X carries a strict definition of equality. On the other hand, if it would not be a set, what would it mean to have functions defined on X?. In 3-dimensional space in real live (where we may sit in a train which not only rolls over land but is carried by mother Earth around the Sun) there is no notion of equality of space points unless we agree on some reference system (e.g. a set of three digital cameras; for the present argument it is not the point that these associate numbers with points but that they decide whether to observations referring to points at different times refer to the same points or not). We thus have the situation that we need a reference system (and, in effect, also the coordinate functions) to define our set X. So from an axiomatic mathematical point of view there is no problem with 3-dimensional manifolds but there application to physics is not as straightforward as the text books suggest.

The situation in space-time is much easier in this respect. Here the concept of a physical process of ignorable (for the purpose under consideration) duration and spatial extension ('event') has a direct meaning independent (up to accuracy questions the ignorance of which is a reasonable idealization) of the motion state of the observer. So the space-time continuum is the only kind of space for which the model of a differentiable manifold fits without ado.

Dear Ulrich,

The most general view is that of Differentiable Manifolds, see Figure 2 of publication, also attached here as png.

But anyone is using the sub-case that best fits to his/her task to prove, see for example Figure 3 which is exactly the 'FIG. 1. Construction of the spacetime manifold.' of 

http://arxiv.org/pdf/gr-qc/0106015v2.pdf

So, by accepting that reality can be described by such a big hypothesis (reality is continuum) we have made a first 'jump' that cannot be legitimated easy.

After that we have also many problems that come from reference frames way of defining, but I don't want to write more on those.

Data A detailed critical review of reported event GW150914 that L...

Dear Demetris,

I intended to breed doubts whether "The most general view is that of Differentiable Manifolds"  at least in their present standard axiomatization. When I started studying physics one spoke about relativity in the language of the Ricci calculus (as Einstein did) where there is no set X on which the coordinate systems define functions.  As it appears to me, a calculus is a deeper and more useful structure than an axiomatic theory. My hope is that a generation of scientists who are more experienced with formal systems like programming languages will come up with a language for physics and mathematics which will avoid much of the ambiguity and unnecessary complexity of our todays's notions and notational systems.

Recently I became aware of the book:

Karl Menger: Calculus, A Modern Approach, Dover 2007 (Originally published Boston: Gin 1955)

where I found formulated much of my personal uneasiness with notational practices of mathematics particularly at its interface to physics. Reading the book convinced me that good insight in the problem is not sufficient for coming up with a good solution.  My impression was that following Menger's presentation is not more enjoyable and enlightening than the more conventional presentations. This supported my expectation that much experience and ingeniosity has to go into such an endeavour in order to make it a success.

Dear Ulrich,

I just copy from page 181 here:

"...Example 1. Is the gas volume v a function of the gas pressure p?

(Both domains consist of the instantaneous gas samples, and the

identity pairing is tacitly understood.) The answer is negative.

Indeed, there are gas samples such that

p y = p y' and yet v y # v y' -samples with different temperatures.

Confining the question to gas samples of one and the same temperature,

however, Boyle not only discovered that the answer is affirmative but

succeeded in identifying the function connecting, say, v (on G 100) and

p (on.G 100 )' namely, with 100 r j-1..."

As we see many of our accepted Physics laws are ill defined...

 I am a bit confused about the statement that "As it appears to me, a calculus is a deeper and more useful structure than an axiomatic theory". I do not think that "calculus"  in any way is "immune" to axiomatics – on the contrary it is fundamentally dependent on it!

Dear Andrew,

Here I offer my solution to the problem you sent me the other day (see below) as I interpret it:

We have a rod of length L fixed in reference frame K’ that is moving with speed v along the x-axis of the stationary reference frame K. The observer is at the origin of a Cartesian coordinate system in the stationary frame K with a precisión timer (clock). He watches the rod, its reference frame K’ and the K’ Cartesian coordinate system approach along the x-axis in K.

I will use the subscripts 1 and 2 (instead of 0 and1) to denote the events.

Event E1 for the observer occurs at the observer’s  origin in K just as the leading edge of the rod reaches the origin in K. The observer triggers his timer and an identical timer in K’ just as the rod reaches the origin in K and for which we have coordinates in K and K': x1 = x1’ = 0 and t1 = t1' = 0. This is event E1.

The observer at the origin in K stops his timer just as the trailing end of the rod passes the origin in K. We then have the coordinates of this occurrence in K and K’: x2  = ?, x2 ’= -L, t2’ = ? with t2 being the time recorded on the timer in K. This is event E2 . There are just these two events, E1 and E2.

Applying the Lorentz transformations for this situation for the unkown coordinate values t2' and x2 we have

            t2’ = βt2 – vx2’/c**2         and     x2 = βx2' +  vt2

where t2 and x2’ = -L are known giving x2 -x1= x2 = vt2 –βL, which is the length of the rod as measured in K.   β = (1 – v2/c2)**1/2

Your specific questions:

a)    With my definition of E1 and E2 all of the coordinate values are given above.

b)    None of these are events. Only E1 and E2 are events; the events are the two observations made by the observer in K.

c)    E1 and E2 are events for the purposes of STR because they are both “happenings” with locations and times of the “happenings” which are the two acts of observation and collecting data made by the observer. Events are tailroed to the problem at hand.

d)    The problem is to determine the length as measured in K of the rod of fixed length L in K’ moving with speed v relative to K. The “events” of interest for STR are the two acts of measurement performed by the observer in K. The two sets of coordinates in K and K’ are used to detrmine the length of the rod in K. We are interested only in the two endpoint measurements. These are the events of interest to us for this problem.

Dear Dwight

Thank you for your interpretation.

You have changed the scenario presented in my use case not only the indices.

I agree with b) they are multiple sets of coordiantes not events per se

I agree with c) but the actual question was why then people call the set of coordinates events. We seem to converge that calling a set of coordinates an event is a bad idea

Your reference to d) is not to my question d) but it is not needed to be answered because you said in b) Only E1 and E2 are events

as for a) I give you my interpretation of the case depicted on the graph. I prefer numbers so we see the scale and γ=2 for v = .8660254040*c.

I will retain my numbering to be consistent wit the graph

(x'0=0,t'0=0), (x'1=2L,t'1=-2vL/c2) while 

(x0=0,t0=0), (x1=L,t1=0) 

And that is why it is another reason to say that referring to coordinates sets as events is a bad idea. 

Dear Andrew,

Yes, I simplified your original problem as you posed it but we both are addressing the same problem. If I set v = (0.866 . . . )c in my result for the coordinate x2 in K:  x2 = -Lβ + vt2 , I get x2 = (1/2)L, which is the coordinate on the x-axis in K of the leading edge of the rod when its trailing edge is at the origin in K.

The proper length of the rod is measured and defined only in K', the reference frame in which the rod is at rest.

Is not the problem you pose to predict the length of the rod that will be observed in K of a rod fixed in moving frame K'?

Dwight,

You present one "event" as E1 corresponding to the space-time point (0,0) in K and (0,0)' in K'. "Event" E2 corresponds to the space time-point (0, L/v) in K which under LT translates to the space-time point (𝜸L, 𝜸L/v)' in K' – here 𝜸 = 𝜷-1. What is the problem?

Dear Dwight,

I have got slightly confused, because in my scenario there is no eqivalent event: E1 where as you write the leading edge of the rod reaches the origin in K. I ignore this one ,but it does not mean your case is not correct.

Your event E2 is a successive event after E1 in the same place in K, while in my case E0 and E1 are simultaneous events at distant points in K. The time and length values match but in a different context. In both cases we have two events and four coordinate sets to identify them, so the coordinate sets should not carry the name "events" unless someone loves ambiguities. As I said before, English langue is ambiguous with the word "set" reaching 36 meanings in Meriam Websrer dictionary but some says it has 430 meanings (http://www.guinnessworldrecords.com/world-records/english-word-with-the-most-meanings/). Language of science should avoid ambiguity.

My example shows a case, where some reasoning may lead to coordinates that do not correspond to physical events that really happen. In my example:

the Lorentz transformation gives the two events coordinates:

(x'0=0,t'0=0), (x'1=2L,t'1=-2vL/c2) but the system K' using traditional interpretation cannot say that (x'1=2L,t'1=-2vL/c2) happened simultaneously with t'=0. It must be (x'1=2L,t'1=0), and as I have shown (x'1=2L,t'1=0) cannot be associated with the only events that happened:E0 and E1 so it is a fake one.

Dear all,

It is difficult to give a precise view of relativity.

If you might take time to look at this summary of 3 different interpretations of relativity, I would be thankful to you.

https://www.researchgate.net/publication/306117984_Answer_to_relativists

Article Answer to relativists

Dear Erkki,

I respond to your comment below:

"You present one "event" as E1 corresponding to the space-time point (0,0) in K and (0,0)' in K'. "Event" E2 corresponds to the space time-point (0, L/v) in K which under LT translates to the space-time point (𝜸L, 𝜸L/v)' in K' – here 𝜸 = 𝜷-1. What is the problem?"

No, we set in K the time t1 = 0 and location x1 = 0 as the leading edge of the rod that is fixed in K' and is moving with velociy v with respect to K arrives at our origin in K. At the same time the clock in K' can be set to zero as well as the location of the leading edge of the rod x1' in K'.

We in K await the arrival of the traling end of the rod at our origin and when it arrives we stop the clock in K to give us the time interval t2 - t1 = t2 in K. We do not know where the leading edge of the rod is in K and denote this location as x2 = ?. In K' we know that x2' = - L because L is fixed in K'. But we don't know the time t2' registered by the clock in K' when the trailing edge passes our origin in K because the clock in K' is attached to the leading edge of the rod in K' and we can't see it from our vantage point at the origin in K. Thus we have t2' = ?.

So we now apply the Lorentz transformations and solve for x2 and t2'.

Is it right to say that basic elements of spacetime are events? - ResearchGate. Available from: https://www.researchgate.net/post/Is_it_right_to_say_that_basic_elements_of_spacetime_are_events#view=57b479363d7f4bef433a421c [accessed Aug 17, 2016].

Dear Andrew,

I think you'll find interesting the term 'primary event' of Johan Prins here:

https://www.linkedin.com/pulse/absurd-physics-relativity-blunders-20th-century-johan-prins

Dear Dwight,

You ask for the time in K' when the trailing edge of a rod of length L in K', passes the origin in K, i.e. an event E2, see explanation below, corresponding to the space time-point (0, 𝜷L/v), (𝜷=𝜸-1) in K. This "event" corresponds to the space-time point (–L, L/v)' in K'. Hence t2' = L/v.

 Note that x2’= –L in K’ corresponds to x2= –𝜷L at t2=0 in K. Hence (–𝜷L,0) in K corresponds to (–L, vL/c2)’ in K’. Finally the space-time coordinate in K when the trailing edge of the rod of length L in K’ passes origin of K, becomes x2=0 and t2= 𝜷L/v, i.e. the event L2 is defined by (0, 𝜷L/v) in K.

Your answer is that the time in K' when the rod's trailing end passes origin in K is L/v.

The Top secret of relativity is how to keep on the objectivity same as in classical physics. That means how to keep on the phenomenon observer independent. That means keeping on materialism same as in classical physics. In classical physics, when t'=t same as in Galilean transformation, then objectivity exists, and thus the phenomenon is observer independent, and thus materialism is working good. If t'not=t same as in LT, in this case there is no way to keep on materialism, but Einstein kept on it by the reciprocity and thus by the Paradoxes of SRT.  IN this case he kept on materialism in gravity by Geometry.

The only solution of  the problems of relativity is removing materialism, and that means removing objectivity BY REMOVING RECIPROCITY. In this case the phenomenon is observer dependent same as in the Copenhagen school. That means the death of materialism. In this it is resulted the transformation is gauge theory and thus by the equivalence principle gravity is gauge theory, and thus gravity is completely quantized. All the problems in physics are solved from Higgs to Galaxies, but that means the death of materialism!!!

And review the simple way of time dilation and length contraction.

https://www.researchgate.net/publication/299781761_Time_dilation_and_length_contraction_in_SRT_in_a_simple_way

Research Proposal Time dilation and length contraction in SRT in a simple way

Is it right to say that basic elements of spacetime are events?

No. The reason is because events tell us nothing about there being behaviors of either space or time. Events inevitably involve changes of velocities of objects. The empirical evidence of physics consists of patterns in changes of velocities of objects. Neither space not time is an object. there is no specimen of either one in any laboratory. There is no empirical evidence from experimentation on either space or time. There are no known space events. There are no known time events.  By known I mean documented experimental results upon both space and time.  There is a lot of empirically unsupported guesses by theoretical physicists. Those guesses are not sitting on the sideline. Some of them have been been bullied into being received into physics equations so that they now give the appearance of being staples of physics knowledge. This problem needs corrected as soon as physicists will allow it to occur. 

Has the dilation of the property of time been confirmed by empirical evidence to be physically real? - ResearchGate. Available from: https://www.researchgate.net/post/Has_the_dilation_of_the_property_of_time_been_confirmed_by_empirical_evidence_to_be_physically_real#57b67a1393553bf0fb54e302 [accessed Aug 18, 2016].

read this paper

http://physicsessays.org/browse-journal-2/product/1490-18-azzam-almosallami-reinterpretation-of-lorentz-transformation-according-to-the-copenhagen-school-and-the-quantization-of-gravity.html

Dear James,

You have misunderstood the question which is about "spacetime" not about "space" and "time'. "Spacetime" is an abstract (mathematical) construct used in Einstein's Special Theory of Relativity (STR). It is a four-dimensional "space" in which the three-dimensional space coordinates and time are the four-dimensional coordinates of "spacetime". An "event" as used in STR is a label applied to a "point" in four-dimensional spacetime and has nothing to do with "real" events as we experience them here on earth.

Dear Andrew,

Einsteinian "events" in spacetime are labels applied to points in spacetime they are not the "ponts" themselves. Remembering that "spacetime" is an abstract concept, "events" in spacetime are also abstract entities. There is a "happening" in spacetime, for example, I mike a measurement of something. I do this at a specific time and place, "point", in "abstract" spacetime and I label the equally abstract space and time coordinates to be the site of an "event" in spacetime, no more, no less.

Dear Dwight Hoxie,

Hermann Minkowski, developed a new scheme for thinking about space and time that emphasized its geometric qualities. In his famous quotation delivered at a public lecture on relativity, he announced that,

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."

So in order to prove the reality or the phenomenon is observer independent, then you must prove the reciprocity or the paradoxes of SRT and that means you must prove the twin paradox. 

The problem of physics now is how to understand physics without the reciprocity principle. In this case continuum exists only locally. But globally it is depending on the vacuum energy where it is  gauge theory, and in this case the phenomenon or the reality observer dependent. The speed of light is locally constant and equals to the speed of light in vacuum, but globally it is vacuum energy dependent (gauge). So here in the math of physics we must distinguish between global and local. That is very important in physics now, because of that the uncertainty principle plays the rule in this case. The local and the global principles in SRT are logically independent, and relativists say that the local version is more important. That is not true, and now we can understand why? 

Local versions of the (special) principle of relativity say that if the same type of experiment is conducted in two isolated, unaccelerated laboratories, then the outcomes of those experiments must be the same. Global versions of the principle say that if you take a physically possible world and boost the entire material content of that world, you get another physically possible world. Local and global in SRT are independent.

Hi Dwight,

 I did misunderstand the use of the meaning of event if it was intended by the questioner in the manner that you describe.  I thought that Andrew Wutke was pointing out that the use of the word 'event' lacked clarity. I understood him to mean that that word doesn't serve well as a name or description of an abstract construct. With regard to my own view, I do not see relativity theory as being put forward as an abstract construct. I see it as being put forward as a physical description of the universe. For example, relativity's space-time shapes the universe. With regard to your valid point that "...An "event" as used in STR is a label applied to a "point" in four-dimensional spacetime and has nothing to do with "real" events as we experience them here on earth.", I see relativity theory being credited with describing real events here on Earth and throughout the universe. My view is that its underpinnings must be physically real for its effects to be physically real. However, I do understand that my response was not relevant for the question meant in the manner that you have described. Thank you for raising this issue. 

Is it right to say that basic elements of spacetime are events? - ResearchGate. Available from: https://www.researchgate.net/post/Is_it_right_to_say_that_basic_elements_of_spacetime_are_events#view=57b6b79e3d7f4b617e05c821 [accessed Aug 19, 2016].

Dear Dwight,

I have answered your question: what is the time in K’ when the trailing end of a rod of length L in K’ passes origin in K. It is t2’= L/v.

I do not understand your comments: But we don't know the time t2' registered by the clock in K' when the trailing edge passes our origin in K because the clock in K' is attached to the leading edge of the rod in K' and we can't see it from our vantage point at the origin in K. Thus we have t2' = ?.

The position of the clocks are fixed in K and K’, but the clock in K’ moves with respect to the clock in K and vice versa, but this has no bearing on what they display, since all you need to do is to identify given space-time points as defined by the “event” in question.

Dear Erkki J. Brändas,

SIAD: "The position of the clocks are fixed in K and K’, but the clock in K’ moves with respect to the clock in K and vice versa, but this has no bearing on what they display, since all you need to do is to identify given space-time points as defined by the “event” in question."

Because of that global and local are independent in SRT. In your case you do not consider t'2=L/v, you consider only time registered in K' in real at the moment t'2=R^-1 (L/v) where R is Lorentz factor, and the light path from back to front inside the moving train for the observer on the moving at this time is R^-1L, where at this time the light beam still not arrived the front or the back yet for the observer in K'. While the equivalent time in K is L/v at this moment, and in this case you can compute the time dilation. If you want to consider the time t'2=L/v, in this case if you want to consider time dilation, the clock on K must read t=R(L/v). Read this paper. That explained in Fig. 1.

Research Proposal Time dilation and length contraction in SRT in a simple way

Dear Erkki,

"what is the time in K’ when the trailing end of a rod of length L in K’ passes origin in K. It is t2’= L/v."

It may be that we have a problem with nomenclature. In my rendering of the problem the time t'2 is the time in K' when the trailing end of the rod passes the origin in K. The clock in K' is fixed in K' and thus is moving with the rod in K'. The observer at the origin in K with his clock fixed in K cannot "see" the moving clock in K' that has moved away from him with the leading edge of the rod. Thus the observer in K does not know what be the itme t'2 as would be registered by a clock in K' when the trailing end of the rod in K' crosses the origin in K. Thus as the rod moves away from the origin in K the observer in K knows only the time interval in K required for the length of the rod to pass his origin in K and that in K' the length of the rod is L. He knows neither the x-coordinate in K at which the leading end of the rod was located when the trailing end passed the origin in K nor the time t'2  in K' when the trailing end of the rod passed the origin in K.

Dear Dwight,

You say: 

The observer at the origin in K with his clock fixed in K cannot "see" the moving clock in K' that has moved away from him with the leading edge of the rod.

Any observer in K can determine from LT what the moving clock in K' should measure.

Further:

Thus the observer in K does not know what would be the time t'2 as would be registered by a clock in K' when the trailing end of the rod (with length L) in K' crosses the origin in K.

That an observer in K will know what the clock in K' will register is the strength of STR when associating events with space-time points!

Dear Erkki,

Below are your comments on  on my comments regarding the problem of the moving rod. I want to understand whether we agree or not so I offer some responses in bold assuming that "LT" means "Lorentz transformation":

The observer at the origin in K with his clock fixed in K cannot "see" the moving clock in K' that has moved away from him with the leading edge of the rod.

Any observer in K can determine from LT what the moving clock in K' should measure.

I don't think that there is a problem here because that is what I did to arrive at the time t'2 in K' with respect to the observer in K:  t'2  = Υt2 - vx'2/c2.

Further:

Thus the observer in K does not know what would be the time t'2 as would be registered by a clock in K' when the trailing end of the rod (with length L) in K' crosses the origin in K.

That an observer in K will know what the clock in K' will register is the strength of STR when associating events with space-time points!

I agree with this statement as long as the requisite conditions are met. If we are dealing solely with clocks, the observer in K needs two clocks in K' since it is a time interval in K' that will differ from the same time interval recorded by the one clock in K.

Is it right to say that basic elements of spacetime are events? - ResearchGate. Available from: https://www.researchgate.net/post/Is_it_right_to_say_that_basic_elements_of_spacetime_are_events#view=57b7116dcbd5c29b315eed2d [accessed Aug 20, 2016].

Dear Dwight,

You say "If we are dealing solely with clocks". This is a dangerous statement since we can never in STR "isolate" time and space. You also receive a different time in K' for the end of the rod passing origin in K. I maintain that my result is in accordance with LT.

Dear Erkki said "Thus the observer in K does not know what would be the time t'2 as would be registered by a clock in K' when the trailing end of the rod (with length L) in K' crosses the origin in K."

Yes that true, but why? Because the clock on the moving frame K' exists locally on the moving frame K' not on the stationary frame on the ground K. The clock on the ground exists locally on the ground. And since by the uncertainty principle there is no way the observer on the ground on K and the observer on the moving frame K' are agreed at the same location of the moving frame K' on the ground at the same time where here we have t' not equal to t because of time dilation. In this case if the observer on the ground sees the location of the moving frame K' now on Paris according to his time t on K. At this time the moving frame K' for the observer on the moving frame K' is not on Paris now according to his clock time t' on K'. At this time t'=R-1taccording to the clock on K' because of time dilation, and at this time the moving frame is at distance x'=R-1x from London for the observer on the moving frame K'. In this case in order to the observer on K  knows what is t'2, that required the moving frame k' must be on Paris too for the observer on K' and that means t' must=t same as in Galilean transformation. And that is impossible because of time dilation where here t' not=t. That means the reality is not observer independent, and that against materialism. In this case the reality is observer dependent same as in the Copenhagen school. There is one way to prove the phenomenon is observer independent and then proving materialism by physics. That is we must prove the paradoxes of SRT, and that means proving the twin paradox. Otherwise, there is no way the reality to be observer independent, and then keeping on the materialism according to physics.

Erkki said "This is a dangerous statement since we can never in STR "isolate" time and space."

Also he said " I maintain that my result is in accordance with LT."

Yes that is true!! Because in this case space must be invariant and it is only time because of time dilation.  In this case it is resulted the reality observer dependent which is against materialism as I explained before. So if we want to accept materialism according to LT, in this case we must prove the twin Paradox  in SRT or we back to Ether theory and prove Ether theory which is resulted from LT

Data Incorrect relativistic comparisons hide Special Relativity's...

Dear Dwight,

For the event E2 (we can skip the index 2 here and only indicate primed coordinates for K’ and un-primed for system K) you say that the time t’ in K’ (when the end of the rod of length L in K’ passes the origin in K) with respect to the observer in K becomes (*) t’= 𝜸t-vx’/c2. This not correct, see below:

The correct LT form is of course t’= 𝜸(t-vx/c2). The starred equation above is only true when x’= 𝜸x, i.e. when t=0. Since we want to know the time in K when the end of the rod (length L in K’) passes origin in K, the time in K (x=0 for this event) when this happens must be t= 𝜷L/v which imparts that t≠0 and (*) is wrong.

From this follows that x=0, t= 𝜷L/v in K corresponds to x’=–L, t’=L/v in K’. This makes sense since the origin in K’ has moved so that the origin in K now corresponds to x’=–L in K’ and the time for this to happen becomes t’=L/v.

Dear Erkki, 

The time t'2 in the problem that I solved is the time that would have been registered on the clock fixed at the leading edge of the rod in K' as it would have appeared to the observer at the origin in K. This is not the time that would have been registered by a moving clock in K'. The problem to be solved is the apparent length in K of the moving rod of proper length L in K'  The data available to the observer at the origin in K is the  time in K' and K when the leading end of the rod is at the origin K (times t1 = t'1 = 0), the time t2 when the trailing end of the rod passes the origin in K, and that the proper length of rod in K' is L. All calculations are to be performed by the observer at the origin in K given the available data in K as cited above.

Dwight,

The time t’=L/v that I have given is precisely the time that would have been registered on the clock in K' fixed at the leading edge of the rod K' as it would have appeared to the observer at the origin in K. Note that when the end of the rod of length L in K' passes the spatial origin in K the clock in K is not zero – it is t= 𝜷L/v.

The clock in K' is of course fixed, but the clock in K is moving relative K'.

Hence in summary the the problem that " the apparent length in K of the moving rod of proper length L in K' " is simple, as already stated, 𝜷L, the coordinates for the the leading end of the rod passes origin in K is x=x'=t=t'=0. This imparts according to LT that x=0, t= 𝜷L/v in K corresponds to x’=–L, t’=L/v in K’. Again I think that the space-time coordinates are the simplest way to disentangle "events" in STR.

Dear Erkki,

We are talking past each other. Actually the clock in K' on the moving rod is irrelevant to the problem as I posed it. The observer is fixed at the origin in the stationary frame K with his clock at the origin in K. He knows the proper length of the rod in K'. I am looking  at the problem from the point of view of the observer in K. From his point of view it is the rod and K' that are moving while he is staionary. His clock in K is set to t1 = 0 when the leading end of the rod passes his origin and the clock will read t2 when the trailing end of the rod passes the origin in K. Thus the total time interval for the rod to pass the origin in K as measured in K is t2 - t1 = t2 since t1 = 0.

To obtain the length of the rod in K the observer needs the coordinate x2  in K of the leading edge of the rod when the trailing end of the rod passes the origin in K; then the length LK of the rod in K will be LK = x2 - x1 = x2 since x1 is the origin x1 = 0 in K. By STR the observer in K does know that LK = αL where α is a number between 0 and 1.

Is this how you analized the problem?

"we can never in STR "isolate" time and space"

There is no meaning in that statement.

The space 3 coordinates sets in a static case of an inertial systems can be materialised by a 3D grid - a fixed wire-frame. Time is the state of synchronised clocks1 - special purpose devices, if we chose to have any in some or all nodes of the grid. The clocks tick the grid stays there. You can see the grid at all times you cannot see time without clocks there. You see fixed grid, and time is just passing by. You can fix the grid, you cnnot stop time. You can rotate the grid so X becomes Z but you can never expose T  to see and make Y disappear. Yes, you can isolate time and space.

Only a child can believe time and space is the same.

1 The local times of all space points taken together are the “time” which belongs to the selected system of inertia, if a means is given to “set” these clocks relative to each other. One sees that a priori it is not at all necessary that the “times” thus defined in different inertial systems agree with one another.

A.Einstein

Dwight,

You say: 

His clock in K is set to t1 = 0 when the leading end of the rod passes his origin and the clock will read t2 when the trailing end of the rod passes the origin in K. Thus the total time interval for the rod to pass the origin in K as measured in K is t2 - t1 = t2 since t1 = 0.

Correct and this time is 𝜷L/v and the space-time point in K corresponds to (0, 𝜷L/v) in K, since the clock in K is fixed at x=0. An observer with the clock at x=0 in K measures the length of the rod (measured to be L in K') to be 𝜷L.

This is easily obtained from LT: x'=𝜸(x-vt) by inserting x'= L at t=0 in K, to be 𝜷L, i.e. the rod of length L in K' is contracted in K as it should be according to STR.   

I am not sure what is your problem. What time do you get according to your analysis for the time t' in K' corresponding to the end of the rod, with length L in K', passing x=0 in K?

Andrew,

In STR the only "synchronization" possible is to put x'=t*=x=t=0 when the spatial origin in K' passes the spatial origin in K.

Dear Erkki,

I think we agree. Thank you for your patience.

Dear Erkki,

It is true that x'=t*=x=t=0  is a symbolic summary of origins synchronisation used to create two coordinate systems alignment for the STR transformations in the usual form.

It is also a sufficient synchronisation for many scenarios where one clock is sufficient. With one clock we can measure distances assuming c is constant and even velocities of  uniformly moving objects consistent with the STR.

But this is not the only synchronisation needed. The STR is derived under  the assumption that time indication at any point is related with the origin clock by applying Einstein's synchronisation method. If you use Lorentz transformation this synchronisation is implicit. 

If you have a uniformly moving point you can determine its velocity with one clock and two round trip measurements using light signals. If you want to verify the speed is the same using two points in space and clock times there, the clocks have to be synchronised by Einstein method otherwise the results would be different.

Assuming that physics of moving bodies conforms to the STR, yet you chose different sycnchronisation of clocks the whole new world opens. But it would be a subject of another story.

Dear Erkki,

Calculating the ensuing travel times of light round the interferometer we find that the LT – due to its linear term x v/c2 – does not predict any Sagnac Effect, but results in c = const also in a rotating system as it does in an inertial system. This explains then why Ashby [6], e.g., uses the Newtonian or Galilean time transformation t’ = t rather than t’ = γ (t - x v/c2 ) when he calculates the Sagnac Effect in the GPS-System. This was also observed by Carroll Alley in a comment at the end of an engineering presentation on GPS and Relativity [7].

IN this case Sagnac can be explained according to the Ether theory only not SRT. Because in this case you must explain Sagnac effect in case of t'=t, and in this case you can keep on the reality is observer independent, and thus keeping on materialism.

If you want to propose time dilation same as in SRT. In this case Sagnac effect can't be explained by SRT and LT if you want to propose the reality observer independent as proposed by SRT and the reciprocity. In this case if you want to propose the moving plane is in Paris now for both the two observers according to your interpretation by the reciprocity in SRT and the Paradoxes in SRT, we have here t' not equal to t at Paris by time dilation. In order to explain Sagnac effect by proposing time dilation according to SRT, in this case we must propose the retardation, and that means the plane must arrive Paris at first for the observer stationary on the ground according to his  time t according to his ground clock, and after that the moving plane will leave Paris for him, and after that the plane will arrive Paris too for the observer on the moving plane according to his time t' of  the clock of the moving plane. According to that we get at this time the moving plane arrives Paris at time t for the observer on the ground  according to his ground clock, and also it arrives Paris at time t' for the observer on the moving plane according to his  moving plane clock,  and in this case at the same point  in space on Paris on the ground in both cases we have t'=t. But in reality t'not = t because at the time t' according to the clock on the moving plane, the ground clock reads now t=Rt' for the observer on the ground, and the plane left Paris at this time for the observer on the ground, the plane now at distance from London x=Rx0 where x0 is the real distance between London and Paris. That is against the reality is observer independent. It agrees completely with the Copenhagen school and the reality is observer dependent, and that against materialism. The real transformation can explain that is not LT, it is the transformation

x=R2(x'-vt') t=R2(t'-vx'/c2) y=Ry' z=Rz' and In this case by taking the time term, we have t-=R2(t'-vx'/c2)  and t+=t=R2(t'+vx'/c2)  Thus from that we get

delta (t)=R2(2x'v/c2) and since space is invariant, then we get x'=L0 

Thus we get delta (t)=R2(2 L0v/c2) and R is the Lorentz factor.

Now that explains the Saganc effect in the same way of explaining Sagnac effect in the framework of Ether theory, but instead of the Ether, it is vacuum energy dependent. and in this case we have t'=t same as in the experimental result.That explains, if you want to consider time dilation same as in SRT, there is no way to keep on materialism. If you want to prove materialism according to your explanation, in this case you must prove the reciprocity, and in this case you must prove the twin paradox experimentally, and that is impossible. Show us according to your explanation the reciprocity. You must do your calculations according to the reciprocity and show us how to explain the paradoxes. Can you explain the Paradoxes and prove them experimentally???

Read this paper for Sagnac effect.

http://arxiv.org/pdf/1404.4075v1.pdf

Also that explains completely the H&K experiment.

Andrew,

Strictly speaking one can only make the "symbolic summary of origins synchronisation" in STR to get the usual form of LT. All other synchronization methods do in one way or the other go beyond STR.

Erkki

Yes and no. The SRT brought the necessity of change of process rates and length variaton by just changing from one constant speed to another. Different clock synchronisation but if course not rate opens a different view of the same which may be quite interesting.

Just like seeing the same landscape in different spectra despite the fact  it has its specific colours.

Dear All,

Andrew Wutke succinctly pointed out the flaw in the statement "we can never in STR "isolate" time and space". Let us probe what he is saying at a bit deeper level.

Central to the special theory of relativity (STR) is the concept of an “interval” between two spacetime “events”. According to STR this interval is invariant, that is, it is the same to all observers each of whom may be situated on any one of a multitude of inertial reference frames all moving with respect to each other. In one of these reference frames the two events are happenings occurring in that reference frame (and thus are at rest with respect to that reference frame) but which can be observed by observers in all of the other moving reference frames. A succinct way to express an interval is to think of a a very small interval ds whose square can expressed symbolically in STR as ds2  =  dx2 – dy2  - dz2, where t is time, c is the speed of light, and x,y,z are the three (Euclidean) space coordinates. The space coordinates can be interchanged at will so STR can be divided into space and time elements as long as the square of the interval ds2 is unchanged.

In GR the elementary interval is defined by Einstein like this

                             ds2 = - dx12- dx22 - dx32 + dx42

Minkowski instead defined the elementary interval

                          ds2 =  dx12+ dx22 + dx32- c2dt2

Anyway whether Einsten's or Minkowski's version there is a big problem: in fact in both versions it is accepted that the elementary interval ds can assume imaginary values according to values of variations of coordinates. From my viewpoint it cannot be accepted and consequently that mathematical model.presents important problems already from the start.

Dear Daniele,

There really are no problems with imaginary intervals in relativity - such an interval between two events is said to be "spacelike" in which case there is a reference frame in which the events occur simultaneously. If the interval is real It is called "timelike" in which case there is a reference frame in which the two events occur in the same place.

Dear Dwight,

I respect your interpretation, but mathematics of those models says different things.

Andrew,

I do not understand your point, since to me there is only one "synchronization" when x=x'=t=t'=0. To do something else is going beyond STR. 

Daniele,

Dwight is right! Mathematics is a language to formulate your ideas. It is only wrong if you make a mathematical error in your derivations.

Dear Erkki,

Quantum is not working with SRT  according to the reciprocity or the symmetry of LT. 

If you are right in that, then can you tell me is LT exact or approximate??? It is approximation and I showed you that many times.  Or Is Loretnz symmetry conserved for all velocity ranges? Can you answer this question

https://www.researchgate.net/post/Is_Loretnz_symmetry_conserved_for_all_velocity_ranges

There are a lot of problems in quantum physics with LT same as the huge problems in gravity!!! You can't solve any of these problems!!! All of what you want to keep on the reality is observer independent in order to keep on materialism!!! That is not true in physics!!!

Erkii,

Mathematics isn't a personal or national language. It is an universal language and consequently doesn't represent a personal interpretation. Physics is different, it is based on initial interpretations of experimental facts that then are structured in the Mathematical Language. Therefore errors in  physics are connected also with wrong initial interpretations besides with wrong derivations.

Daniele,

I do not agree. Mathematics like english, german etc., universal or personal, is our way to communicate our ideas. Interpretations are based on consensus – there is no absolute truth. Provided the math is not in error one has to go back to the assumptions if the consequences to an interpretation appears unsound and the predictions come out wrong.

Dear Erkki,

The synchronisation x=x'=t=t'=0 is more or less an alignment of two coordinate system origins. This is independent from any theory as it would be the same for hypothetical Galilean systems.

What distinguishes the STR from other potential theories is the synchronisation of distant clocks within the inertial system. The derivation of Lorentz transformation in Einstein's 1905 work is a direct consequence of the assumed synchronisation. To use two the same remote clock indications a simultaneous requires definition of simultaneity.

From the practical point of view alignment of origins is possible and necessary, however how do you synchronise a moving clock just above x=1 at t=0?: t'=0?, I don't think so.

If the STR is correct for physical systems you should perform Einstein's synchronisation of clocks to get consistent resultss. But in practical experiments and theoretical analysis, nothing stops me from synchronising clocks in a different way. Depending on synchronisation method interesting observations can be made. This is however out of scope of this thread.

But if you ask me why, I can only say that some synchronisation methods at least in theory lead to true absolute simultaneity which is not what Einstein calls simultaneity.

That also has nothing to do with validity of the STR. The misleading terminology where arbitrary clock sybchroneity is called simultaneity is the source of all paradoxes. That is why I am trying to be picky to call things what they are not what they appear to be or to shortcut things (coordinates of events called events for example)

The statement: in reality, physics is causal, is not meaningful. Nature appears to be causal and this feature rewards successful evolution with survival. However, physical theories concerning e.g. microscopic processes seems not to be rooted in causality and as a result the mathematical formulation of such physical laws exhibit time reversibility and other invariances. This has nothing to do with what mathematicians do to develop the language of math., except that their development is highly beneficial for scientists to communicate new physical knowledge.

Mathematics provide the language for the laws of nature based on physical assumptions and it is necessary to have excellent relations between natural science and math.

Andrew,

The synchronisation x=x'=t=t'=0 is is indeed the only alignment and its importance in STR, in contrast to the Galilean transformation, is its fundamental dependence on space-time points that must be considered in discussing physical events as they appear in different reference frames. 

Dear Thierry,

A statement like: “in reality, physics is causal" is perhaps something said casually in the bus to work, but in a serious discussion on the fundamental laws of nature, I would expect better. For instance what reality means has been discussed since Plato and later Kant and we know today that whatever “objective reality” would be out there, we can only deduce what is projected on our minds.

Furthermore, since ‘physics’ means knowledge of nature, this knowledge may be non-causal in the microscopic domain and becomes causal macroscopically. I can only conclude that defending such a statement imparts muddled thinking and confusion.

I will not comment the rest of your litany since it corroborates what I already said above.

@Thierry,

what is your causal view of the microscopic world? Physicists don't 'believe in a non-causal microscopic world'  but they know that no logically satisfying causal theory of the microscopic world has been proposed so far in spite of intensive efforts (e.g. by E. Schrödinger, D. Bohm and G. 't Hooft).

Of course, also physicists have their believes, (for instance, I believe in a causal microscopic world) but since these concern things that we don't know, they should not considered as parts of physics.

Dear Thierry,

I want to understand your point of view. Beta decay was known for some time and, I believe, neutrinos were "invented" to preserve conservation of energy and momentum not as evidence for E = mc2. Are space and time "inventions" or, as I would maintain, are simply there as given elements that endow structure to the Universe. And you say that the expansion of the Universe is an "invention" and so the observations of increasing red-shift in apparently distant objects is not due to the Doppler effect? And the "Standard Model of Particle Physics" was "invented" as a tribute to Einstein? It has little that is attributalbe directly Einstein. Neutrinos don't exist?  So what do you make of experiments that reveal their existence?

Thierry,

The phenomenon ‘dropping the coin on the edge of the glass’ is not a microscopic phenomenon – do you understand?

Your example seems to be an unsophisticated copy of the super deterministic approach of Manuel Morales. I did analyse his “coin in cup experiment” in detail in Stefano’s Doppler thread some time ago. Although Morales’ assumptions may seem consistent I showed it to be wrong in relation to the findings of modern physics.

Your statement ‘physics is deterministic but the description is statistical by the lack of knowledge’ again displays your muddled thinking. In classical physics we may derive statistical relations based on lack of knowledge, but this is nothing but subjective ignorance, since there is here in principle no limit in prescribing accurate initial conditions. ‘Objective ignorance’ is commensurate with QM.

Further you say: ‘Believing in a non-causal microscopic world is naïve, with or without Kant’ displays utter confusion. Theoretical descriptions in the microscopic domain appear to exhibit time reversibility, while our macroscopically evolved world violates time-symmetry and appears causal. These inconsistencies concerning micro-macro correlates are of fundamental importance and should not be swept under the carpet with simpleminded abrasive statements.

I know that you will go on and on and on … trying to find any piece of droppings that could be used to advance your ignorant and ill-informed critique of modern science.