Special Relativity: “What’s it all about, Albert?”

Special Relativity means different things to different people. From the average ‘man in the street’ to our foremost scientific experts: from something that has the aura of scientific magic, almost akin to alchemy; to the wonderful beauty of Einstein’s great theories explaining how space and time are related.

Many learn the concepts; more merely become familiar with the calculations, a few understand how it works, yet how many understand why it works?

The desire to cling to something familiar, trying to understand Relativity in the context of Classical Newtonian mechanics, has bedevilled Relativity; sowing confusion and doubt, particularly among newcomers to the field, by means of the numerous paradoxes, counter-intuitive descriptions and facts that contradict one another.

Take for instance the fact that experiments prove moving clocks run slow.

Special relativity’s First postulate (principle of Relativity) states:

  1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion. OR: The laws of physics are the same in all inertial frames of reference.

Now a clock moving at a constant rate is also an inertial system and must therefore be governed by the same scientific laws; keeping the same time as any identical clock in another inertial system, in which it is a stationary clock . (i.e. when measured from within that system by an observer at rest in that system)

Yet, measured from another system, relative to which our inertial clock is moving, that same clock is measured to run slow.

The same clock is at once displaying a common time along with all other inertial clocks while, at the same time  running slow as a function of its speed relative to another observer.

Yet we know that both statements are true.

The one clock does keep the common time along with all other inertial clocks and yet also runs slow, as measured by any observer relative to which it is moving.

How can this be so?

 

Light Clocks are commonly used as an aide when describing Time Dilation. Viz.

Sample Explanation of Time Dilation using Light clocks

 

 

 

 

 

 

 

 

Frames of Reference

We measure Space using the same three axes we are used to using to map any space, length, breadth and height, only in Space, we refer to them as x,y,z. We also imagine a standard clock at the Origin, set to zero, upon which we measure time, t. Thus giving us the 4 axes or dimensions of Spacetime.

Because there is no fixed point in space to base a map upon, we use a Frame of Reference based upon whatever location and time suits our needs. Each and every Frame of Reference will have its own map of Spacetime, in which it is stationary and everything else is moving. Yet if that is the case, how do we define two Frames of Reference moving with respect to one another? They cannot both be stationary, can they? So which one would we designate as stationary and which one as moving?

In fact it is the one we are taking taking measurements from that is designated as stationary, and the other to be moving.

Confusing isn’t it? Well, maybe so at first glance, but that is what Special Relativity is all about. Giving a simple, easily understood answer to the conundrum of how everything in Spacetime is stationary and at the same time everything is moving!

The easiest way to explain that, is to take an example and see how it works.

Light clocks

For this ‘thought experiment’ we will use Einstein’s Light Clock. A very simple device. A pulse of light is sent to a distant mirror where it is reflected back to the base of the clock, where it triggers a new pulse of light. So the time in the clock is measured by the speed of light. If we say that in our clock the mirror is one light second away, the light will take one second to reach the mirror and one second to return. It will ‘tick’ every two seconds.

Imagine two identical, synchronized clocks alone in Space so far away from anything else that there is nothing that will affect them. And imagine the two clocks are moving relative to one another, with a relative velocity of 0.6c. Nominal Observers situated at the base of each clock, will measure their local clock as stationary and the other, their remote clock, to be moving away at 0.6c.

                                                          Light clockLight clock Space Station travelling

We will refrain from identifying the individual clocks and merely refer to the local stationary clock and the remote travelling clock.

To the diagram of the simple Stationary clock (in blue), we will add the moving clock (in red).

As measured by our stationary observer, the light in the stationary clock travels 1 light second to arrive at the mirror, while the moving clock’s light path is 1.25 light seconds, to the mirror.

The configuration of the two clocks and the observers upon them are identical and reciprocal; so, as we draw their positions and measurement from the perspective of the stationary observer, each of the two clocks will be both the stationary one and the travelling one, depending on which observer’s view is taken.

The time for the light to reach the mirror in each stationary clock is one second, yet the time when that same clock is moving at 0.6c, is 1.25 seconds.

So, the light in each clock will take both 1 second to reach the mirror, when measured as the stationary clock AND 1.25 seconds when measured as the travelling clock!

Yes both times for the same clock, depending on which observer is measuring!

Time and distance are measured differently due to the movement of the remote system, yet the duration when measured as a stationary clock, remains the same.

So it has to be the measurement scales that change. Time and distances measured locally, within a Frame of Reference, is Proper Time and Proper Distance, while those measured in a remote, moving system are Coordinate Time and Coordinate Distance.

We use the Lorentz Transformation Equations to translate between these two scales of measurement.

This has, unfortunately led to the almost inevitable conclusion that time passes differently and distances measure differently in a system moving at a great proportion of the speed of light.

Whereas, in fact, the times and distances are exactly the same. They do not change. The differences are an effect of the conditions under which the measurements are taken, and it is the measurement scales that change.

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“Stupid NTs”

A very thoughtful and thought provoking piece that has much truth it its premises.

Everyday Asperger's

Author’s note:
NT is the abbreviation for the word neurotypical. It is a familiar term to those on the autistic spectrum and was originally used to describe those individuals who do not have neurological brain differences when compared to members of the mainstream society. NT is generally accepted as a substitution for the word ‘normal,’ as the word ‘normal’ is subjective. For some, utilizing the word ‘neurotypical’ is an active choice, for the act of using the word ‘normal,’ in reference to those not on the autistic spectrum, implies that those on the spectrum are not normal.

On numerous accounts members of the autistic and/or Aspergers community have been alienated, ostracized, and pointed out by the majority as inherently flawed or wrong. Individuals on the spectrum continue to site feelings of extreme isolation from mainstream society and times of repeated criticism in which observers offer out measures in which the…

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Time – the 4th Dimension

Setting the scene; a fourth dimension.

Space the Final Frontier

Before we start, let us begin by considering where we are. Yes, we ought to define what just what we mean by Space.

We know that it is all around us; that it stretches away to infinity, in every direction and that it is the same everywhere.

Einstein used two main tenets or Postulates as they are known:
that the laws of science apply equally everywhere and in every direction, and
that the speed of light, in a vacuum, ‘c’ is a constant.

To the average layman this seems quite reasonable. It appears quite logical common sense, to aver that Space is the same everywhere and that the Light travels at a constant speed we know as ‘c’.

Spacetime.

We are all familiar with the concept of 3 dimensional space. It is the way we think and the way that we view our world. Everything we relate to can be seen as having height, width and depth. And position, for example, a location anywhere on the Earth, can be defined by its three coordinates, Latitude and Longitude and its height above Sea Level. But Einstein and Minkowski insisted that we should consider time as a fourth dimension, by adding a fourth coordinate, t, to our three familiar coordinates, x,y,z.

These three are the scientists way of referring to any physical location, relative to a given point. By adding the time coordinate we can define not only an individual point in Space (x,y,z) but that point at a particular time.

This combination of a point in Space at a specific moment in Time, is unique and is labelled as an Event. This means that we can follow how the content or properties of any location in Space change over time. Yet for for those of us who think in pictures, visual thinkers, the question remains: how do we conceptualize or visualize this fourth dimension?

In fact it can be considered in a very straightforward way.

Dimensions

Fig. 1

Start with a single dimension; all the points in that dimension, taken together as a continuum, comprise a straight line; let us term this the x axis. Any point on this axis can be defined by a single coordinate (x) denoting how far it is from the start of the line.

Adding a second dimension, normal, that is at right angles, to our x axis means that at each and every point on this y axis we may imagine straight lines, parallel to the x axis, giving us the y coordinate. Thus any point on such a plane can be defined or referenced by our two coordinates (x,y).

Now we will add a third dimension, normal to our two dimensional x,y plane. At each and every point on this z axis we can imagine another plane, parallel to our x,y plane, representing our z coordinate. This addition gives us a three dimensional volume, any point in which may be defined or referenced as x,y,z, our old familiar Cartesian Coordinates.

Now, to follow this pattern, the fourth axis must be normal to each of the existing axes, x,y and z. The only construction that will achieve this is a sphere, centred on the given point at the Origin of our 3D space, or Frame of Reference. For the surface of a sphere always approximates to a plane, normal to any radius of that sphere.

Our t coordinate may be measured along any radius of that sphere; this is compatible with the fact that time has no spatial direction. As a consequence of this a moment in time will exist throughout the whole of our sphere, and include every location within that sphere.

If, all the points in one dimension constitute a line, and all the points in two dimensions constitute a plane, and all the points in three dimensions constitute a volume, then it is reasonable to suggest that all the points in four dimensions will constitute nothing less than the total existence of that volume of Space. That Time started with the Big Bang, and has expanded at the speed of light with the expanding Universe.

Imagine then that a point on this t axis will be the time coordinate for the whole of that volume of Space within the Time Sphere, as it expands.

But, hold hard a moment, surely each moment in time is no more than a representation of the 3D space, as we would have with a simple Cartesian diagram or indeed with a photograph of the space. Each successive moment would be no more than a copy of that representation including any changes occurring in the very brief time period between one moment and the next.

In real time this could be no more than watching the hands move round a clock face, or indeed whatever we are looking at!

Thus a Four Dimensional diagram could be effected by the (relatively) simple device of an animated 3D diagram. But then, are we not saying that by adding the fourth dimension, Time, to a 3D representation of space, such as a photograph, is merely progressing from still photography to a moving film?

That is essentially what we are doing when we see the world changing around us, we are seeing the same representation of three dimensional space changing moment by moment. All we need now is a way to map all those changes against time. Mapping all of space at each moment of time to give us a map of Spacetime.

As an aid to visualizing this progression, one could picture time as the colour of the Universe; as if we were observing it through a coloured glass. Let us say that it began as a single wavelength in the red part of the spectrum and that, for each successive instant of time, another wavelength is used or added. Then the colour of Spacetime would progress through the rainbow as time increases. An instant at a point in space, which we would call an event, could be seen as 3 spatial coordinates for the position and a colour coordinate for the time. (Note: this is merely a way to visualize it).

I picture the Big Bang as a spherical wave of light coming from one point that is the Universe at the beginning. That sphere being the limit of the universe at any one moment, expanding at the speed of light and the colour changing continuously.

So if time is represented as an expanding sphere encompassing more and more space moment by moment, (Why does the Big Bang constantly intrude upon my thoughts?) where does the Time axis lay? In which direction should we draw it?

The time axis exists everywhere in every direction running from the origin of whatever Frame of reference we are using. So, to be mathematical for a moment, Pythagoras tells us that the radius of a sphere equals √(x2+y2+z2) giving us t2 = x2+y2+z2 or t2-x2-y2-z2 = 0, the signature of Spacetime.

Fig 15 Four Dimensional axes

Fig. 2

It is interesting to note that this formula, arrived at by reasoning and simple logic, is identical to that found by the best mathematicians; giving this visualization a level of credibility.

(If the other axes are also scaled in light second times, any of the three space axes may also represent, or be replaced by, a time axis if one is appropriate to what is depicted, e.g. in a diagram using only one or two spatial dimensions).

(The surface of the Future Time Sphere denotes the limits of Space, that could be affected, by an Event at the Origin; or, for a negative value, the Past Time Sphere is, for that time, the volume of Space in which a change, at that moment in Time, could affect an event at the Origin).

(It is important to understand that the time coordinate, that is the ‘now’ of an event does not apply only to the surface of the sphere, but to everywhere within it).

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An Autistic layman’s approach to a Theory of Autism aligns with the Intense World Theory

An Autistic layman’s approach to a Theory of Autism aligns with the Intense World Theory.

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Defining Time

So that is what Time is!

Now I get it it!

A Eureka moment!

In an absolutely sterile, environment time does not exist.

Time doesn’t exist of itself, it is created as an effect by processes.

The interval between the start and the end of a process, its Duration is the time created by that process.

Time cannot exist on its own, there has to be something happening, i.e. some kind of process to create time.

Time can only be measured by comparison to other times created by other processes.

That is why we set standards on the Macro scale, e.g. the life of the universe, since the Big Bang, or on the Pico scale, e.g. regular nuclear processes.

 

Every Event in Spacetime occurs at some unique point in time within the life of the Universe that contains the whole of Spacetime.

 

If two events occur at the same point in time but at different locations they will be simultaneous wherever they are observed from. That must be an inevitable conclusion from Minkowski’s theory of Spacetime.

 

Time cannot speed up nor slow down, it is the processes that create time that are measured to run faster or slower, yet the total time they create is still the same.

 

The measure of Time, the magnitude of the units multiplied by the quantity of the units, what I would call the Absolute Time of a process is constant and unchanging; yet the magnitude of each unit will vary depending on how and from where and by whom it is measured.

 

Processes create change. Time is created by change. Therefore Time travel back in time cannot be possible; once a time has passed change has occurred and the only way that time might exist to travel back to is for every change to be undone, to be reversed.

 

So, Time does not exist as a self contained entity, but only as a product of change and is only measured by comparison to other times.

 

Time cannot vary, yet every observer may measure time differently depending on their perspective and the conditions under which they measure it.

 

And the irrefutable logic that proves backward time travel impossible is that recreating exactly a former time is in itself a change, in the same way that the return of a pendulum might be considered. Only the count of swings of the pendulum would increase meaning further change rather than change undone.

The very act of time travel being a process would create more time not undo it, so the process of time travel would inevitably take one forward rather than backward in time.

 

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Why I Refuse To Light It Blue for Autism

Why I Refuse To Light It Blue for Autism.

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Visualizing 4 dimensions.

Four Dimensions – How do we envisage a 4-dimensional space? Not easy is it?
Let us take a simple approach and identify how the fourth dimension would connect or interface with three the dimensions that we are so familiar with. The first principle that most people would identify is that it must be at right angles (normal) to our three existing dimensions, the axes of a Cartesian diagram; and the only way that can be done is by a sphere centred on the origin of three equal scaled axes that cuts each axis at the equivalent points, for then the surface of the sphere will be to all intents and puposes, in the limiting case a flat surface normal to each axis.

But where then is the fourth axis? Which direction does it lie in? Well it doesn’t because it cannot lie in any mapped orientation within our three existing axes. So let us say that it has no direction but lies in all directions, that it may be represented by any line drawn from the origin to the surface of our sphere. And that if we say its coordinate scale is ct, light seconds for example, then we have added time as our fourth dimension, which fits quite well as time has no direction.

How though can we mark the passage of time, our movement along this fourth dimension, or even denote a specific point on that coordinate in relation to our other three coordinates? I would suggest that it must be something other than by adding new lines yet it must be visible across the whole three dimensional space; and so I would turn to colour.

Let us say that as time passes it is represented by a changing colour of our three dimensional drawing of space, so a particular time and the associated spatial 3D diagram would be given a specific colour.

Then we would have the time axis that could be drawn anywhere on the diagram as a line from the origin to a particular point in a particular colour and we would have:
c²t²=x²+y²+z² or c²t²-x²-y²-z²=0

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