Einstein’s Train(and the lightning strikes)

Well what can we say about this; one of the most discussed thought experiments conceived by Einstein; yet one of the most misunderstood pieces in all of Relativity.

When I first read chapter IX of Einstein’s wonderful exposition:

Relativity: The Special and General Theory. 1920.

I found it made good sense being straightforward and logical and well reasoned making it relatively (groan) easy to understand.

Einstein’s train

The great man put much thought and effort into describing and explaining this thought experiment, repeatedly emphasising that he was treating it from the perspective of the observer on the Embankment; which is what we would expect as it is all about Relativity.

The experiment can only be described relative to some particular reference frame; in this case it is that of the Embankment.

Chapter IX.       The Relativity of Simultaneity              

“UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every Event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

 

Einstein's Train Fig 1

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment.[1] But the events A and B also correspond to positions A and B on the train. Let M’ be the mid-point of the distance A —> B on the travelling train. Just when the flashes (note1: As judged from the embankment.) of lightning occur, this point M’ naturally coincides with the point M, but it moves toward the right in the diagram with the velocity v of the train.[Fig. 2.] If an observer sitting in the position M’ in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.[Fig. 3.] Now in reality (considered with reference to the railway embankment) [Fig. 2.] he is hastening toward the beam of light coming from B, [2] whilst he is riding on ahead of the beam of light coming from A.[3] Hence the observer will see the beam of light emitted from B earlier [4] than he will see that emitted from A.[5] Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an Event.”

The reference numbers inserted into Einstein’s writing match those in the diagram, Fig. 2. This is Einstein’s Fig. 1. expanded to a Space-Time diagram with the Frame of Reference of the Embankment shewn in blue with the train in red.

Einstein's Train Fig 2

Einstein asks the question “Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train?”

So what exactly is he asking here? It seems to be a straightforward query about how the two lightning strikes are related when considered relative to the train; yet we are dealing with two distinct reference frames here: that of the Embankment and that of the train and the answer will be different for each.

First of all Einstein introduces us to the perspective from the Embankment and only from the Embankment. That this is indeed the case is quite clear when considering his argument point-by-point:

  1. We are dealing, quite explicitly, with lightning strikes that are simultaneous with reference to  (as perceived from/as judged by) the observer on the railway embankment. We know this because it is specifically stated in the description.
  2. We are asked whether they will also be simultaneous  “… relatively to the train.”  It is important to note he says “relatively to the train” and not “relatively from the train”; which tells us it is when considered from the Embankment.
  3. He reminds us: “If an observer sitting in the position M’  in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.”   Now, the only Frame of Reference in Einstein’s thought experiment in which the observer at M’ possesses any velocity, is the Frame of Reference of the embankment.
  4. “Now in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.”   This immediately follows the last quote and quite explicitly confirms from which Frame of Reference that view is taken, for the observer in the train can only be moving toward point B and be “… riding on ahead of the beam of light coming from A.” as viewed from the embankment.
  5. “But the events A and B also correspond to positions A and B on the train.”  The observer on the train will be confident that he is stationary, at the point M’, mid-way between points A and B on the train and that from this perspective it is the embankment that is moving past him.
  6. “Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”   Again it can only be from the perspective of the embankment that the observer at M’ is travelling toward lightning flash B. While in the reference frame of that observer, she is stationary between the points A & B on the train.
  7. “Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.”   It is only from the perspective of the embankment that this sentence makes any sense.  For it is only the embankment observer who could measure the train to be moving. To those who take the railway train as their reference-body it will be stationary and it will be the embankment that is moving. (Surely that is the whole point about Relativity?)
  8. “Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).”   How many times does the great man have to repeat:  “… are simultaneous with reference to the embankment …” ?    (that is simultaneous as measured from the embankment) and  “… are not simultaneous with respect to the train …”  (not simultaneous in relation to the train as measured from the Embankment).
  9. And finally: “… vice versa (relativity of simultaneity).”  Surely this can only be referring to the first part of the sentence, implying it could equally well be written that  “Events which are simultaneous with reference to the train are not simultaneous with respect to the embankment, …”

What else can vice versa mean but that the whole of what has been written above would apply in reverse if considered from the train observer’s point of view in position M’? – “The Relativity of Simultaneity” – then surely it means: “That simultaneity is only relative to the reference frame in which it is measured”.

In Fig. 3. the same events are drawn using the Train’s Frame of Reference. The Train is of course now stationary while the Embankment is moving with the velocity -v. The reflected lights meet at [1]. M’ meets the light from A [2] first at time tA [4], then the light from B [3] later at time tB [5].

(After some debate I have retained the convention of making the moving frame the primed frame, so M’ is mid-point between A and B on the Embankment as it is the Embankment that is moving in the Train’s Frame of Reference.

Einstein's Train Fig 3

For the observer, sitting in the middle of the train, his frame is at rest and point M, mid-way between A and B, is permanently located in his Frame of Reference; and the embankment would have mid-point M’, moving toward strike A. Leading to the inevitable conclusion that the observer at M in the train would see the strikes simultaneously, while the Embankment observer at M’ would see strike A before strike B.

The constant events that will be the same from whichever Frame they are observed are the two pulses of light meeting at the midpoint of the line AB. The question we must ask is: what are the coordinates of that location in the individual Frames of Reference?

Now within each Frame of Reference we have to consider what is at that mid-point of AB at the time the pulses of light meet.  And that this could be either M or M’ depending on which frame is stationary for the particular observer. M for the embankment and M’ for the train.

Summary

That is the Relativity of Simultaneity; each observer will see it within his own Frame of Reference but deny that it happens in any Frame of Reference that he observes to be moving.

Which is exactly what Einstein was saying when he wrote:

“People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every Event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment [my emphasis].”

 

How much clearer and more explicit can he possibly have stated it? Repeating the principle in his conclusion where he states:

“Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).”

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A new simpler view of Relativity

This is an introduction to a new simpler way to conceptualize the essential mechanism at the heart of Special Relativity. This can be done using only simple cartesian constructs and a different way of understanding Time as the fourth dimension.

We are all familiar, I am sure, with Cartesian axes; whether we know them as x,y,z; length,width and height; or latitude, longitude and altitude. They are the common way we have of viewing the 3D Universe we live in.

Time, on the other hand, is more difficult as it has no physical direction but is the same anywhere from wherever or whenever we view it. This does not mean that any two people will measure it the same in all circumstances, yet to any one observer the time in their Frame of Reference is the same everywhere .

The best way we have of measuring time is by timing the passage of light in a vacuum, because Einstein’s second  Postulate that Relativity is that the speed of light in a vacuum is  ‘c’ a fundamental physical constant.

Time has no direction, it expands in all directions. Imagine it as an sphere expanding at the speed of light. The whole of that sphere constitutes a point in time. Its measure is the length of any radius drawn to the surface of that sphere. Thus the time axis can be considered to be any radius of that sphere and it is profitable to use whichever radius best suits one’s purpose.

 

Fig 15 Four Dimensional axes

Fig 1

We see this in Fig. 1. where the time axis labelled ct could lie in any direction. Because the time is the same throughout that sphere it is in effect a point in time that does not move but expands.

Also, as our fourth dimension, the surface of our expanding point in time crosses each of the other three dimensions at right angles!

The Duality of Time

How then do we resolve the spherical expansion of time with the traditional idea of the linear nature of time, with concepts like the arrow of time?

We measure time in two ways: with a clock as the background time that passes everyday, or with a stop watch to measure the duration of any activity or process.

One can see the effect of this disparity in Fig. 2. where diagram A demonstrates this difference, with red lines of the expanding point of local time from the event at  (0,0), in contrast to the blue lines which are part of a much wider circle centred on whatever point in the distant past one is measuring from – to give a feel for this I have included diagram B where the blue circle is centred on a point 1 minute in the past; and in diagram B, centred on 1 hour in the past. Yet the background time as we think of it is centred at some vague point in the distant past, which could be anything from the start of the day, or right back to the Big Bang! So one can see just how big that blue circle would be and why in diagram A  , the divisions form straight lines.

duality of time.png

Fig. 2

Frame of Reference

A Frame of Reference is the way that Spacetime is mapped relative to a real or imaginary location. As mapped in a Frame of Reference, spacetime will, a priori, be at rest relative to that Frame of Reference.

In a Space time diagram (plotting time against the x axis) the world-line of any stationary body or particle will be vertical, for as time progresses that body will remain at the same point on the x axis.

A good way of demonstrating this is by looking at light clocks – where each ‘tick’ of the clock is the passage of a pulse of light between two mirrors set 1 light second apart, where the position of the light flash corresponds to the time. (Fig. 3)

Simple Relativity Blog Fig.1a.png           Simple Relativity Blog Fig.1b

Fig. 3                                                                                                    Fig. 4

Clock B  is an identical inertial clock, synchronized with Clock A, their light flashes each reaching their mirror after 1 second. This is how it would be measured in the reference frame of either clock. (Fig. 4)

But when Clock B’s Frame of Reference is measured relative to clock A,  Clock B’s measurements are transformed; from a stationary observer in Frame B, to a moving observer in Frame A.

The travelling clock

The movement of Clock B away from Clock A reveals a very different – and perhaps surprising difference in the measurements of the light path in Clock B.

Simple Relativity Blog Fig.1d.png

Fig. 5

As observed from Clock A,  when the light in Clock B has travelled 1 light second along the time axis of clock B (in red), Clock B has travelled 0.6 light years from Clock A. The light will then be at point (0.6,0.8) in A’s Frame of Reference. Fig. 5. The time axis of Clock B being rotated through angle β, where sin β = vt/ct (the ratio of the clock’s speed, v to the speed of light, c.

To Summarize; measured in Clock B’s Frame, the light in Clock B travels 1 second to the mirror, Fig.4. But when Clock A measures the movement of the light in clock B, it takes 1.25 seconds.

That is Time dilation. The measurement of the light’s movement in Clock B, 1 light second in one second, is  transformed by the Lorentz factor, γ = formula14which at 0.6c = 1.25, to 1.25 light seconds in 1.25 seconds relative to Clock A.

It is important to understand the inceased time measured for the travelling clock is to factor in the time taken for the clock to travel in addition to the time accrued on the clock.

Be aware too, that the use of light clocks is only to make the visualization easier. With the light clocks we can see the passing time measured by the light’s movement. One light second takes one second.

It would be just as valid to have drawn a round clock with a face, or a digital watch, travelling. Only in that case it would only be the time increasing without the light path to measure.

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Newtonian vs Relativistic Mechanics

Einstein’s Theories of Relativity led to a revolution in our understanding of the movement of bodies, particularly at speeds approaching that of light in an empty medium. The mathematics of which are unassailable, having been proven in so many practical applications such as the ubiquitous GPS systems, by the Perihelion precession of Mercury and by the deflection of light by the sun.

Yet it seems difficult to visualise these effects without being confronted with paradoxes or counter-intuitive phenomena.

For the most part these seemingly irrational consequences seem to derive from the inability to abandon classical Newtonian Mechanics and embrace Einstein’s second postulate, when drawing diagrams of relativistic phenomena; viz. “that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”

A prime example of this is seen in the following diagram of two Light Clocks with the relative speed of 0.6c. The diagram on the left is drawn of the perspective from Clock A, using Newtonian mechanics. We see the light flash travel both 1 light second within clock B and 0.6 light seconds with clock B.

So after one second using Newtonian Mechanics, the light flash has travelled

√(0.62 + 1.02) = 1.166 light seconds which contradicts the second Postulate.

The diagram on the right is drawn from the perspective of clock B, using Relativistic mechanics. The light in clock A has travelled 0.6 light seconds from clock B when that same light has travelled 1 light second from the light source in clock B.

Mechanics compared(large for blog)

After 1 second the light has reached (0.6,0.8), clock A’s Frame of Reference, while it has travelled 1 light second along clock B’s time axis which is rotated through angle β.

The time in the moving clock A t’ = 𝜸t where the Lorentz factor 𝜸 for 0.6c = 1.25, in accord with Time Dilation.

We see this same discrepancy in so many diagrams that are drawn to show features of relativity, where the Maths is right, yet the diagrams still hold fast to Newtonian Mechanics because that is the way we have been taught to think.

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older aspies group

In the European Union some things are going on that are targeted against autistics. So, we drafted an Open Letter (I made the English translation, hopefully without major mistakes). It would be good if those of you who live in the EU, forward it to their local EU Parliament Members. Here it is:

—————————–

Open Letter to the European Ombudsman and the European Parliament Members

Dear Sirs,

with great astonishment, we have heard that to the Information Day for the Declaration on Autism, autistics themselves were not invited. Already during the vote, we were not asked whether we want to be typed in all of Europe, and what our stance towards a Europe-wide introduction of evidence-based therapy is.

In times of the “Convention on the Rights of Persons with Disabilities” of the UN this is not acceptable, because, after all, this deals with our matters. According to Article 4 (3) and Article 29 of the UN CRPD we want to be heard on this topic and actively be involved in the further steps. According to the motto: “Not about us, but together with us”.

By the so-called early, intensive assistance that is supposed to bring about mitigation, as they say nicely paraphrased in the Declaration, can only be meant a specific therapy.

What was just a guess until then, is certainty now at the very latest after an examination of the invited guests to the Information Day. This is about ABA (Applied Behavior Analysis) and therapies based thereon.

The core of these therapy and early intervention programs are time-consuming controls of the behavior of the autistic children, a performance mainly by the parents and in the premises of the family. The behavior of autistic children – it is recommended – is controlled and conditioned for 40 hours and more (per week). By involving the parents as co-therapists, these children do not have trusted contacts and caregivers in the family environment any more. The possibility to escape to the nursery or in general from therapy at home, is not given. For autistics, safety is an important factor in their lives. That safety is revoked and denied to these children on several levels. It is our opinion that here already in the core basic human rights such as the right to personal development and mental integrity (Article 17 UN CRPD) are violated.

The aim of the targeted therapies is that autistic children unlearn their autistic behavior and learn normative behavior. This contradicts the idea of inclusion, the right to self-determination, and the general principle of ‘respect for the diversity of people with disabilities and the acceptance of these people as a part of human diversity and humanity’, formulated in Article 3 of the UN CRPD.

Proponents of ABA like to cite as reasons that ABA would be medically accepted and be the only evidence-based treatment for autism, and thus there would be no alternative. This is not true. There are alternatives that are not based on conditioning and re-education of the children, but support them in their needs. Here, autism is not educated away, but for autistic people there is created an environment that meets their requirements in the best possible way and enables them to share in everyday life. The basic advantage over strict conditioning consists in a sustainable participation with a simultaneous acceptance of the autistic personality as a part of the diversity of life.

Conditioning certainly brings about faster visible results, but these are bought at the expense of the autistic personality and its needs. This is, however, not visible and goes unnoticed as an investigative point in studies on conditioning autistics by behaviorism. Ignoring these circumstances and the associated long-term consequences for autistics, presents a clear indication to us as autistics, that here it is not acted in favor of autistic people but against their will and to their detriment.

The success rates referred to in the study by Lovaas came about only by the massive and ethically and morally very questionable use of aversives, physical punishment, and psychological abuse. In recent studies, without the use of methods infringing human rights, these success rates of supposedly up to 47% were neither confirmed nor achieved even partially.

On the contrary. Studies like e.g. Smith, Groen und Wynn (Randomized trial of intensive early intervention for children with pervasive developmental disorder, 2000) show that ABA is less successful in the long run than methods like e.g. TEACCH., which are geared to the needs of the client.

Added to this are the demands of the respective treatment providers for a comprehensive application of ABA as the sole method of therapy for autism. This objective is, however, justified by the questionable success rates of the study by Lovaas. The claim alone to recognition of ABA as the only applicable form of therapy for autistics is massively violating the rights of people affected here. They shall be robbed of any right to self-determination through such a declaration. Here, through intensive lobbying is sought a unique position of ABA as a therapy for autistics. An access to alternative therapies building upon other methods would thus be prevented.

Another point that must be addressed by autistics, is the systematic collection of genetic material required Europe-wide. Here, an extensive gene pool is created, which will make it possible to develop preventive measures to diagnose autism as early as possible. What is not pointed out is the option that genome information is used to develop a prenatal genetic test on autism. This interest undoubtedly exists, as the participation of large and well-known pharmaceutical companies (Roche, EliLilly, Servier, Janssen Pharmaceutica, Pfizer, and Vifor Pharma) in the EU-AIMS project makes clear. Furthermore, also AutismSpeaks from the USA participates in EU-AIMS, and AutismSpeaks also aims at such prenatal tests and the collection of genome information. AutismSpeaks is seen highly controversial among autistics worldwide. Here, by means of commercials – e.g.. “I’m Autism” – statements about autism are issued which are generally hostile towards disabled persons and inhumane.

To give you an insight into this spot and the mindset of AutismSpeaks, the original text follows now:

“I am autism. I’m visible in your children, but if I can help it, I am invisible to you until it’s too late. I know where you live. And guess what? I live there too. I hover around all of you. I know no color barrier, no religion, no morality, no currency. I speak your language fluently. And with every voice I take away, I acquire yet another language. I work very quickly. I work faster than pediatric aids, cancer, and diabetes combined. And if you’re happily married, I will make sure that your marriage fails. Your money will fall into my hands, and I will bankrupt you for my own self-gain. I don’t sleep, so I make sure you don’t either. I will make it virtually impossible for your family to easily attend a temple, birthdayparty, or public park without a struggle, without embarrassment, without pain. You have no cure for me. Your scientists don’t have the resources, and I relish their desperation. Your neighbors are happier to pretend that I don’t exist – of course, until it’s their child. I am autism. I have no interest in right or wrong. I derive great pleasure out of your loneliness. I will fight to take away your hope. I will plot to rob you of your children and your dreams. I will make sure that every day you wake up you will cry, wondering who will take care of my child after I die? And the truth is, I am still winning, and you are scared. And you should be. I am autism. You ignored me. That was a mistake.”

It creates massive fears of autism here. Autism is something that destroys the family in the eyes of AutismSpeaks, families are driving into bankruptcy and parents robbed of the children. Can you imagine that such an organization would like to help autistics? This inhuman picture must not cause, from fear and from misinformation about autism, that genetic material is collected to register autistics, and to work in the future towards the aim that autistic people can be sorted out already prenatally. Please also ask what such a registry of autistics triggers in society. Autistics are humans and have done nothing wrong. We want to live in an inclusive society and not be captured through a gene database, registered, and made identifiable. We have a right to live like any other respectable person, too. Autistics also have a right to have their disability not be known against their will, for example, by a data leak.

We are people like you all and do not live, as is often claimed, in our own world. We are, like everyone else, an asset to the society. If one supports us, we can do our part to societal life. By agreeing to methods such as ABA or the gene database, you create an exclusionary framework for the future life of autistic people in Europe and disregard the UN CRPD significantly. Autistics are not people of a lower class.

Autism can be a severe disability. But this does not justify unethical therapies and early interventions that are contrary to human rights and work against the autistics by re-educating them towards an externally defined standard. We advocate here again for the support of autistic people to enable them to participate in everyday life. We advocate for diversity in society and speak out against a re-education. We stand by our way of perceiving and do not want to be sorted out in the future by means of genetic testing.

We are humans!

We ask you for the following:

Inform yourselves about treatment options, and check them, as well as the Europe-wide registration, especially under human rights aspects. Keep in mind, please, the situation of the autistics and their inherent inner perspective on autism. Invite autistic people, experience the diversity, and make your own impression, detached from lobbying and association work.

We, the autistics, will happily be available for you.

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Time – what is it?

Time – What is time? Time is, strictly speaking, not a dimension; so much as it is the rational ordering of events; It is an effect, an effect produced by the process of change.

Time is a mysterious amorphous entity whose presence is everywhere, yet its definition has eluded man ever since he started to question his understanding of the world.

So what is time? To determine that, we could start with defining what we know the Fundamentals of time. And yet, how can we determine the fundamentals of time, without defining what time is?

Newton wrote:

“Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or inequable) measure of duration by the means of motion, which is commonly used instead of true time …”

Which seems to be a very sensible and concrete definition.  It is something that agrees well with our own perception.  That time flows equably, without regard to anything external, all we can do is to choose the background, or coordinate scale, against which to measure time.  We can change the units we measure by, we can change their dimension but time moves inexorably on.

It is said, in a somewhat light-hearted way, that: “Time is what stops everything happening at once”; yet I would venture to declare that it is, in fact, the very opposite, that Time is created because changes don’t happen ‘in an instant’. Time is an effect of change.

Time Happens. It accumulates.

A Time Interval, is the temporal separation of two Events, that may, or may not, be at the same location.

System is a set of interacting or interdependent components forming an integrated whole.

Any System has an Absolute time. That is the time measured from the start of that system. It stops at the end of that system. The Universe is one such system, where time began at the Big Bang.

Then time is being created by many systems at the same time, I hear you say, so what happens to it all?

The time created by each system is independent and created in parallel and can only be measured by comparison to other generated times.

And how is it absolute?

Because it can only be measured against another time. All times are measured against whatever timescale we choose.

And one time scale, the life of the Universe, encompasses all others. Every event occurs at one individual specific point on that scale.

So again What is time? A good question. For it is not easy to determine the fundamentals of time without defining what time is. Let us begin by examining what we do know about a strange entity that has a presence, with no physical form, yet is described as the fourth dimension.

How do we detect time? How does it interact with the physical world as we know it and with the other three dimensions?

Anything but an instantaneous change (if such a thing is even possible) has a duration. A period of time that lasts from the start of the process of change until the end of that change. Time is the label that we give to the interval between the start and the end of a change, or to the interval between Events.

(Remember; an Event is a specific point in space at a particular instant in time).

Whenever and however we measure time, we are measuring change. How long it takes to change from a ‘Before’ state to an ‘After’ state. Time is the Duration of that change.

If there existed a volume of Spacetime, of even a Spacetime, in which there were no change: a completely empty vacuum, not affected by any kind of radiation, for example; no time could pass within that volume.

(Think about it; if that space were visited at 1,000 year intervals, as measured by an outside observer, within that space nothing could have changed so, within that space, no time could be measured to have passed).

I believe it is valid therefore, to aver that time is generated by change. Intervals between Events are measured within a global or absolute time that has existed from the Big Bang since which there has been a single ongoing change – the expansion of the Universe.

If we keep two identical clocks, in identical systems, or in the same system, they would keep identical time. Viz. Einsteins First Postulate.

If we imagined them as the finest Swiss mechanical watches, or indeed as atomic clocks, it would mean that when synchronized, they would always read the same time but if one were to be set running slow then the time created by that clock would be less; e.g. it might read 59 secs when the other watch read a full minute. Or it could be stated just as correctly that one watch was running fast, reaching 60 seconds while the other read only 59 seconds. Each would be creating its own local time and standard or absolute time could be whichever time, whichever clock, we selected for our standard.

Durations

Time: that constitutes the intervals between events.

Event: a location in Spacetime; i.e. a point in space at an instant in time.

Interval:

As Processes progress, so time accumulates.

The past cannot be changed, as it has already happened.

The present is where we are and it always will be, just where we are.

Future time does not exist, it has yet to be created.

Can time’s rate of progression vary?

Time is measured by comparison of the duration of a process against a standard. That standard may be one ongoing process of change, such as the expansion of the Universe, or it may be a count of a regular repeated change, such as an atomic clock. But all it is is a line along which events may be placed. All events then will have a specific place in that timeframe; time cannot run faster nor slower, for it defined by scale against which it is measured.

However time can be measured, to run faster or slower, for that is exactly what happens when a clock runs faster or slower, when a process is measured to run faster or slower due to the conditions under which those measurements are made.

The time created/measured by one clock would be a four dimensional Spacetime Sphere centred on the Origin of that clock’s Frame of Reference. And identically so, for any other clock.

Each clock would create Time according to its own dial, over the same period and, depending upon their accuracy, at the same rate!

So yes, time IS what is measured by a clock

Any time that we measure, however we measure it, is, in essence, only a comparison to a scale of measurement, in this case another measure of time, to another measure of ongoing or repetitive change; whether that be the slow background movement of the stars, constellations and Galaxies on the grand scale of our Universe, or the tiniest changes in a subatomic clock. Time is but a concept generated by change.  Processes have duration. The speed of a process can change, subject to the conditions under which it happens, and we may measure different times depending on how, that is under what conditions, we measure it, but Time, as an individual entity, cannot vary because it is only a standard that we define to measure against.

Time is an effect created by change; It is no more than a measurement, against a scale.

Time does not pass at a rate, time cannot pass slowly or quickly. Time is merely something that is observed.

Processes may be fast or slow and this may affect the duration of an event; that is the time that has passed between the start and the end of a process, measured against some scale, but that does not mean that more or less time has passed, only how it is measured.

Only how many units of time have been counted, but the total amount of time measured is also dependent on the magnitude of those units of time.

Time is absolute. It may be considered to have started with the Big Bang and can, logically, be measured against the expansion of the Universe. Every event has happened at some point in that expansion of the Universe. At some point on a simple, single, straight-line scale. And each point marks how long after the Big-Bang that event occurred. If two events have the same separation from the Big-Bang then they must be simultaneous measured against the life of the Universe! It is as simple as that.

Different observers may perceive Time differently, but that is only because of the conditions under which they measure Time.

If we say that time passes more slowly when observed by a speeding observer, all we are identifying, is the interval in which a certain amount of change has accrued; i.e. How we measure that quantity of time. It is the processes of change rather than time that pass more slowly.  And as we measure the passage of time by events (e.g. the ticking of a clock), then the clock will ‘tick’ more quickly (a shorter duration for each ‘tick’), that is more ‘ticks’ will be counted, when measured by a moving observer, giving the impression that more time has passed.  The movement of the observer is affecting the measurement of time passing rather than the passage of time.  It cannot be the passage of time, for that, when measured in the clock’s own Frame of Reference, is unchanged; and again, when measured against a wider scope, such as the expanding Universe, the same time will have passed.

This may seem like ‘nit picking’ the terminology; but it is much more than that, for it is bringing us into line with Minkowski’s Spacetime, where there is one time axis, one time dimension which is drawn as the vertical axis, the ordinate, in Minkowski diagrams with respect to the observer’s Frame of Reference in which the Observer is stationary. It is every other Frame that is moving and whose time axis is angled with respect to the drawn Frame; which reflects the changes to the scales against which the other Frame’s times are measured.

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Reciprocality of Relativity

A Frame of Reference then, maps the whole of Spacetime relative to a single, specific, Spacetime Point, or Event, that we care to define, real or imaginary. And, as a single specific Event in Spacetime is a moment in time, it cannot, therefore, be moving; Spacetime must be fixed relative to that Frame of Reference, i.e. relative to that Event.

Consider Space as we see it from the Earth. It moves in relation to us. The night sky changes throughout the year, while at night the stars, constellations and the moon rise and set. So relative to our Frame of Reference, here on the earth, everything else in the Universe is moving.

Similarly, if we were mapping space from Saturn’s moon, Titan, the whole of the universe, including the Earth, would be moving relative to Titan’s Frame of Reference.

It follows from this that if the whole of Spacetime can be considered static, relative to any individual Frame of Reference, then the relative movement of two Frames of Reference will each be the reciprocal of the other; i.e. as A moves with respect to B, so B moves with respect to A.

Imagine two Kings on a chess board, facing one another three spaces apart. If either one is moved one space forward, the distance between them, will be reduced to two spaces from either perspective; similarly, if white moves one space to the right, Black will be three spaces away and one space to the left; similarly black will now see white three spaces away and one space to its left. For any such movement, the participants can be reversed and the record of movements will still be valid.

Chess Pieces

From this it follows that position and movement can only be relative; there can be no absolute position nor movement, for any entity, real or imaginary, may be considered to be stationary. (As it is within its own Frame of Reference. i.e. the Frame of reference centred on that entity).

This raises an interesting conundrum for how may a body possess properties due to its speed or velocity if it is at rest relative to Spacetime? If such attributes or properties can only be measured from within Frames of Reference in which that entity is moving?

Specifically, those two old phantoms, Time Dilation and Length Contraction, only materialize where the entity affected is measured to be moving. They cannot materialize in that entity’s own Frame of Reference in which there is no movement, the entity being at rest.

Suffice it to say that Time Dilation and Length Contraction (which are the same phenomenon viewed from different perspectives) are real enough, yet only when measured by a moving observer.

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More on Frames of Reference

More on Frames of Reference

The Origin of the Frame of Reference, has the coordinates 0,0,0,0 and it is the location of the Nominal Observer and his clock.

There are at least three ways of viewing a Frame of Reference:
From the perspective of a Nominal Observer (real or imaginary) located at the Origin, holding, or at least adjacent to, a standard clock. This clock will be measuring Proper Time, as the clock is at all times, at the Origin, with that Frame’s Nominal Observer and so will be tracing the path of that Frame of Reference.
From the perspective of an Observer, elsewhere in that Frame of Reference, carrying a clock synchronized with the Nominal Observer’s Clock. Measurements, made using a synchronized clock and standard ruler, will also be Proper Times and Proper Lengths.
From the perspective of a remote Observer who is moving with respect to that Frame of Reference, rather than in it. All measurements are taken by the Frame’s Nominal Observer and are then converted (Transformed) by that remote observer to cater for the relative velocity. This is done using the Lorentz Transformation Equations. These Transformed measurements are Coordinate Measurements.

It is immediately apparent that an observer, on any body or at any location in Spacetime, will measure time on his local clock and measure lengths, in his frame of Reference, with his standard ruler and that those measurements will be in Proper units.

Spacetime is Homogeneous and Isotropic. It is the same everywhere, in any direction. It obeys the same basic scientific laws throughout. Therefore, if we place an object within a Frame of Reference, its properties will be the same as they would be in any Frame of Reference. This is one way of stating Einstein’s First Postulate of his Theory of Special Relativity.

Let us consider what this means by taking an Event, a flash of light, and examining how it appears from different points of view.

If we take the time and location of that flash of light as the origin of a Frame of Reference it will have the coordinates 0,0,0,0. Light travels away from that event at ‘c’ in every direction.

After 1 second the light emitted will be measured to have travelled 1 light second in every direction and will have traced out a sphere in Spacetime, radius 1 light second. And it will be a sphere, radius 1 light second in each and every Frame of Reference, only the coordinates of that Event will be different.

There is one rather surprising outcome from these considerations however. For when we define our Frame of Reference, Spacetime is fixed and at rest from our perspective, then surely, one would think, Spacetime must be moving for every other Frame of Reference, that is moving with respect to our ‘fixed’ Frame of Reference.

Yet as soon as one thinks this way, one has fallen into the trap, and failed to grasp the essential meaning of Relativity. Everything is Relative. No Frame of Reference is fixed and at rest absolutely; yet each and every Frame of Reference is fixed and at rest from its own perspective.

No, there is not, nor ever can be any one preferential Frame of Reference. For if Spacetime were at rest in only one Frame that Frame would take precedence having simpler Laws of Science than other Frames of Reference.

Again I say No! For the simple reason that Spacetime is at rest as observed from any Frame of Reference.

Each and every Frame of Reference is a Map of Spacetime, with the origin of that Frame of Reference as the fixed centre of that Map.

From the perspective of any observer, at rest in any Frame of reference, every other entity or Frame of Reference is moving, in Spacetime, relative to that Frame of Reference! That is each and every Frame of reference is moving relative to every other Frame of Reference or Map of Spacetime (for if they are not moving they are different parts of the same Frame of Reference).

I have repeated myself, ad nauseam, in the passage above, because it is describing the fundamental principle of Relativity: Everything is Relative.

This is the most fundamental and I may say surprising facet of Relativity, and one that so many eminent scientists, indeed the whole scientific establishment have, as yet, failed to grasp; determined as they still are to see everything relative to some particular Frame of Reference, thereby failing to recognize that that particular Frame too, must also interact in exactly the same way relative to other Frames as those Frames interact with it.

AS A IS TO B, SO B IS TO A

So let us try and picture this, shall we?

Let us take for an example a train moving along a railway track. A lightning strike hits the track, as the very centre of the train is passing that point on the track. How is the flash of the lightning observed from the track and from the middle of the train. Fig. 1

Train on track landscape 1

Fig. 1

This is a practical example of our original event the flash of light and two frames of reference, the track and the train, that are moving relative to one another.

Now as we saw in the earlier discussion, each will see the light travel at ‘c’ relative to their Frame of Reference, so the observer on the track will measure the light travel equal distances, in the each direction, along the track as the train moves away. Fig. 2

Train on track landscape 2

Fig. 2

while the observer on the train will measure the light travel equal distances, in each direction along the train, as the track moves away from the train. That same observer on the train, will see the light reach both ends of the train at the same time; although when that happens, the two ends of the train will no longer be equidistant from the observer on the track. Fig. 3

Train on track landscape 3

Fig. 3

So which one is correct, the observer on the train or the one on the track?

As we have just seen, they both are, hence the need for Einstein to explain it!

Think about it! At the moment of the flash of light both B and B’ are coincident at the flash of light.

The two Observers are located, one at B on the Track and one at B’ on the Train, which coincide when the flash of light occurs. So each Observer, at rest in Spacetime as they Map it, will observe the light travel at ‘c’ in all directions in their Frame of Reference. The light will, therefore, reach the points, A and C on the track, and A’ and C’ on the train, at the same time. It is the observers B and B’ who are each moving away from the other and so are no longer at the location of the flash of light,  AS MEASURED IN THE OTHER FRAME.

The important fact to realize here is that every observer will measure the light expanding evenly from the initial event, the flash of light, within his own Frame of Reference! But that every other Frame of reference, will be moving away from him. Exactly as we see in our ‘thought experiment’ with the train .

A paradox, or a conundrum at the very least, one might think, yet the answer is a simple one: there is only one expanding sphere of light that is mapped as being at rest in each and every observer’s view of Spacetime!

For each and every observer the light expands evenly in their Spacetime, while all other observers are moving through that expanding Sphere of light; thus the stationary observer’s inevitable conclusion that the moving observer cannot see the light travelling evenly in both directions.

Note: that it is only in the measurement, relative to a stationary observer, that the space and time of the moving observer, is distorted.

So how is this distortion, of the moving observer’s view and measurements of Spacetime, experienced by those concerned, how do we relate the stationary observer’s measurements with those of the moving observer?

At which point we ask those two venerable old rogues, Time Dilation and Length Contraction to step forth and take a bow!

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