Bruce Harvey's Alternative Physics site

Relativity and the nature of time


simultaneity - no specific entry point: the whole article is relevant.

Taking photographs

The camera is very useful tool because its optics imitate the human eye with which we observe the world. The camera has one distinguishing feature that the eye lacks, it takes a snapshot in time, while the eye sees the world as a moving panorama over an interval of time. The eye cannot distinguish the difference in time of events it sees to less than a few tenths of a second. Mechanical camera shutters can do better than this achieving speeds of a thousandth of a second and less. Shutters made from liquid crystals and operated by computers can better this by a factor approaching a million times faster. We can imagine an electronic camera of the near future with a shutter speed of 1 nano second. A shutter speed so fast that light can only travel only 30cm in the time it is open.

When we turn our futuristic camera of on a scene, and take a single snapshot in time, what the camera actually sees is not one snap shot in time, but a host of snapshots in time of different objects which are out of synchronisation with each other. If I photograph a row of 13 people each half a meter apart from a distance of four metres, the light from the two people on the ends of the row has to travel five metres to the camera while that from the centre person travels only four metres. The person in the centre is 3 nanoseconds in the future of the two on the outside because the light captured by the camera had to travel an extra metre. But I can remedy this situation quite simply by taking out my long range telephoto lens and retreating to a distance of 150 metres. Now the light reaching the camera from the two people at the ends of the line only has to travel an extra 3cm which takes it only one tenth of the time that the camera shutter is open.

But now imagine that I have been called in to photograph a larger group of people sitting in 2 rows of chairs. No matter how far I go back with my telephoto lens, the light from the back row will still take several nanoseconds longer to reach the camera. It is clear that the ability of the camera to capture images of objects at the same moment in time is affected by the geometry of the scene and by the position of the camera. In the normal course of events, all this is quite meaningless because the time intervals involved are of little practical importance. But we could imagine some physics experiment in which we were observing two events and wanted to show that one event was caused by the other. We know that the two events happen almost simultaneously, but which happens first. Well we can take a photograph and see. But if the events are so close together in time that light could not travel between them that fast, we are in trouble. It all depends where we position the camera. In fact if members of the research team were in disagreement about which event caused which, each rival camp could set their camera up in a position that prove themselves right.

What is the answer to this problem? Will the scientists have the intelligence to understand the simple geometry. Will they be able to do the calculations of how long the light takes to travel from each event to each camera? Will they then be able to apply corrections to the observations and come up with a definitive answer? On balance, I am tempted to answer no. They are far more likely to retreat into the doctrine that simultaneity is meaningless!

Train Spotting

Well actually, photographing moving trains.

I want to move now into the imaginary world which Einstein used in explaining the special theory of relativity. I want to photograph a high speed train as it hurtles through a station. The dangers inherent in setting my camera up on the very edge of the platform are obvious, but in the interests of science, I will take the risk. Unfortunately, when the photographs comes come back from the processors, my fine picture is a blue blur. Never mind, I get out my supper fast camera and try again. Wow, what a picture, it is in focus and it is clear. Every little bit of dirt on the blue paint is visible, and yes, there, I can see a screw head covered by the blue paint. New concepts come very slowly to the human mind and on the third day, the spotty faced anorak clad youth called Wayne finally gets me to understand that I have to get away from the platform and up onto the road bridge in order to get good photographs of the train.

To take clear pictures of the train, I need to get back from the track. If I want to photograph the engine, I need to be 100 metres away from it, If I want to photograph the whole train, I need a vantage point half a mile away. The best photographs are taken as the train approaches so that the front of the engine can be seen. Imagine that I have never been allowed close to an engine and I want to measure it. I should be able to take a photograph of it. I want to make the maths simple, so I arrange for my camera to be triggered by the interruption of a laser beam timed so that the light ray caught by my camera travelling from the front of the train is at right angles to the track. Say the engine and tender is 30 metres long and I am 40 metres from the track. The light ray from the end of the tender which my camera captures has to travel an extra 10 metres and that means that it had to leave the train 33 nanoseconds before the light ray from the front of the engine. In that time, my 125 mph train travels a distance of 0.00186 mm. My photograph will show the train to be 30.00000186 metres long.

Einstein on the other hand never met Wayne, his approach to the problem was quite different, he used two cameras mounted right on the edge of the platform separated by a distance which he believes to be the length of the train. He then attempted to take two photographs of the two ends of the train at the same instant. His conclusion is that his measurement of the length of the train is actually shorter than it really is.

It is not hard for me to get the same result. All I have to do is to turn my camera, move my laser a little and photograph the train just as it has passed me. This time it is the light ray from the front of the engine which has to travel an extra 10 metres and the train appears 0.00186 mm shorter than it actually is.

I can move further away and use my telephoto lens to eliminate the problem. But I can still alter the measured length of the engine and tender by taking photographs of the train, from different angles as it approaches, is level with me, and then is departing into the distance.

Of mathematics, time and distance

We assume mathematics to be an absolute. Mathematics cannot lie. If we form an equation, then its solutions must correspond to reality. This is wrong. Mathematics is totally flexible and algebras and calculi can be created at will. What we then do is to select which one fits a given real situation best. We only have to consider the different sets of rules we might make up for combining ordered pairs of numbers. One set has served us well for thousands of years in the arithmetic of fractions, but those rules are of no use with two dimensional vectors. For vectors, we need a much simpler set of rules.

When we use mathematics to try to understand nature, we have to be aware that mathematics is not an absolute. We need to understand the relationship between the physical situation and the mathematics. Good educationalists will see that little children play with sand and water. It is only through this play that the principle of conservation of volume will be understood. Our understanding of counting, adding, subtracting and multiplying depend on an understanding of conservation. Three buckets of sand plus four buckets of sand equals seven buckets of sand. Take three pint bottles full of water from an eight pint bucket and you have five left. Count sheep into a pen and you expect to count the same number out. In these situations, we have a good sound one to one correspondence between the mathematics and the real world.

Grow up and become a mathematician and everything is simple. Grow up and become a builder and you will find that three buckets of sand plus four buckets stones + two buckets of water does not equal nine buckets of concrete. Grow up and become a train spotter and you will find that one full cup of railway cafe tea plus two spoons of salt equals one full cup of railway cafe tea: the expected overflow can be avoided with slow sprinkling and careful stirring. (Most train spotters have met this trick of putting the salt in a bowl and hiding the sugar) What we have to do is to get a one to one correspondence between the mathematics and the natural process. Once we understand the fact that sand can fill the spaces between the stones, water can fill the spaces between the sand grains and salt can fill the spaces between the water molecules, then we can adapt the mathematics to predict the results. (And it will not work with sugar.)

What we have to realise is that there is very little difference between photographing groups of people and photographing trains. The optics of the camera and the geometry of the light rays is exactly the same even if the personal qualities of steam engines and people are different. The fact that the train is moving makes no difference to the camera. It captures pictures of people and trains in the same way and with the same time differences. The train is not really longer or shorter. So far as our attempts to photograph it go, it has an absolute length. If photographs from different angles give different lengths, then that is a property of the geometry of the situation. All we need is to know is the geometry and we can compensate for the finite speed of light and calculate the actual velocity of the train. (The train does not have an absolute length in that it changes with temperature, with the passage of longitudinal sound waves through its metal and possible with other as yet uncharted phenomena) Einstein sets his cameras at the track side almost touching the passing train and looks perpendicular to the track with two cameras. However, we can use one camera to produce whatever result we want by moving the camera to a location which will give the right geometry. If we take the geometry and the finite speed of light into account, we can always calculate the true length of the train. If I take my camera with its telephoto lens and move away from the track at right angles to it from a point mid way between Einstein's two cameras, as he takes two pictures simultaneously, I should be able to time it so that I take a single picture from which I can make two enlargements absolutely identical to his two pictures. There is a way in which I can still cheat and get Einstein's result. If I take my photograph in the dark with a somewhat longer exposure time and allow the train to illuminate itself with a single flash of light at its centre.

Einstein's method of deducing the Lorentz transforms is based on a particular geometry. There is no reason to select that geometry other than the fact that it gives the correct result. My argument is that other geometries give other results. Therefore only an overview which allows the same result to be calculated from each geometry is valid. Any argument based on a single geometry is nothing more than a fiddle.

Of mathematical fiddles

I know of three mathematical derivations of the Lorentz transforms, the light clock, the railway carriage and the K calculus. All of these are fiddles but they are accepted by hundreds of thousands of students some of whom go on to teach them. I do not attribute this phenomena to any lack of personal integrity, but rather to the human condition. We are good at learning, but not so good at understanding. When it comes to developing new concepts, we are extremely obtuse. Discovering how poor my own mental abilities are in this respect has been a revelation. In my work on alternative theories and laws of physics, I have discovered just how easy it is conjure up a bit of algebraic manipulation to justify a given theory. But try to go beyond our present understanding and the concepts take months to come. If your starting point is someone else's incorrect work, then the chances of doing anything other than simply learning subsequent work by rote are very remote.

Einstein had an experimental fact and was looking for an explanation. What he stumbled upon was a homomorphism. An area in which there is a one to one correspondence between two systems. It is an experimental fact that any measurement of the speed of light on the surface of the earth gives the same result. The speed of light is a constant. The answer we get is not affected by the motion of the earth through space. The historical context of Einstein's investigation into that experimental result is that the answer was expected to depend on the velocity of the earth. Space was thought to be pervaded by an incompressible, mass-less fluid called the aether. Magnetism was believed to be a movement of the aether. Light was believed to be a form of electromagnetic wave. The observed position of the stars in some areas of the sky altered very slightly over the course of a year because the light from the star travels in a straight line, which the telescope based on the earth moving around the sun intercepts. These were all good reasons for believing that light travelled through the aether at a constant speed and the Michelson-Morley experiment was designed to detect the earth's velocity through the aether. When their experiment failed to detect any variation in the speed of light Lorentz suggested that the earth's movement through space causes matter to contract in the direction of motion. All the geometry of the Michelson-Morley experiment and the algebra of the Lorentz contraction had already been worked out when Einstein looked at the problem. Einstein looked for an alternative explanation which did not require the earth and everything on it to shrink slightly in the direction of motion. By assuming that the speed of light would always be the same to every observer no matter what their velocity, he hit upon an alternative explanation. Einstein said that instead of matter shrinking, clocks run slow. But having said that clocks run slow, he then runs into problems with moving trains and deduces that the train will appear to shrink when viewed from the station platform and that the station platform will appear to have shrunk when viewed from the train. Now all of these effects are quantifiable in terms of the fraction

and since the fraction was first calculated by Lorentz, we call the resulting equations the Lorentz transforms. The important thing for us to note here is that this formula has a similarity with two others from the world of trigonometry.
This is not just a coincidence, it happens because in deriving the the Lorentz transform, we get a triangle in which both the sine and cosine of an angle are involved and we use one of the two trigonometry equations. But if we now draw two velocity time graphs of the train going through the station, on such a scale that the speed of light is represented by a line at 45°ree; to the axes, one from the point of view of the train spotter and the other from the point of view of a passenger on the train, we find that lines in one seem to be rotated compared with the other. To calculate such a rotation requires both the sine and cosine of the angle of rotation to be used. Hence the term in the Lorentz transforms fits the idea of rotation, Einstein says that we should leave the lines where they are and rotate the axes. He then makes one great leap of faith and says that the real world is in fact four dimensional with time, on a suitable scale such that the speed of light is 1, as the fourth dimension. To change the view of the world as seen by one observer to that of another travelling at a different velocity, the axes of the four dimensional space are rotated.

The beauty of a rotation is that it does not distort a picture. The numbers stored in the computers memory are changed, but the picture is still the same and tilting one's head will reoriented it. Because the Lorentz transforms are a rotation, they have this property of leaving the fundamental geometry of the situation in four dimensional space time unaltered. Consequently they produce consistent results. Two observers in relative motion observe the light spreading out from a flash. Both see an expanding sphere. Carry out a Lorentz transform and one observer's sphere turns into an ellipsoid. But it is what I call a time shifted ellipsoid because one end of it is in the past and the other is in the future. Now take any point on the ellipsoid and draw a line through it and the observed site of the flash. Now move along that line so as to eliminate the time distortion and we find ourselves on the surface of the sphere which the other observer sees. That this works is a property of the geometry of rotation. Does it imply that this is how nature is working. There might be any number of possible natural mechanisms which would produce the same experimental result.

Velocity time graphs

The error in this great leap of faith is simple, Einstein was looking for too much symmetry. Rotation is a beautifully symmetric transformation, but it is not the only one possible. Let us look at a simple situation and keep the scales of our velocity time graphs to reasonable proportions. Our train spotter is some platforms away from the train armed with a video camera as is the passenger on the train. A porter is walking down one of the platforms between them and the station has some form of roofing above the platforms which enables distances to be measured from the video pictures. Both the train spotter and the passenger latter analyse their video pictures frame by frame and draw velocity time graphs.

At first their seems no possible connection between these graphs, but we need to understand that each has omitted a line from the his graph. The train spotter hardly though it necessary to record the movement of the station because it did not move and the passenger likewise omitted to draw a line for the train which so far as he was concerned did not move. These two lines should be drawn on top of the time axis, so we will make a modification and draw the time axis somewhere harmless and put in the omitted lines for the station and train.
Now the situation is obvious, each graph has three lines labelled train, porter and station and the way to transform one graph into the other is to shear the diagram vertically. Every point stays in the same vertical line, and the vertical distance between points on the same vertical line remains unaltered and straight lines remain straight. To make things clear, here is a little picture of a steam engine which has been subject to such a shear.
This is the correct way of converting from the velocity time graph of the traveller to the velocity time graph of the train spotter and back again. Mathematicians find it quite easy to extend vector concepts from 1 to 2 to 3 to more dimensions and it makes little difference to the mathematics whether or not these dimensions exist in the real world. Minkowski space is a mathematical representation in four dimension's of the three dimensions of space plus time as the forth dimension. Is this the way the universe behaves? Well it does and it does not. If the train spotters video camera had broken down before the the train reached the porter, then it would still be possible for him to construct his velocity time graph and extend the lines until they met thus determining when and where the train caught up with the porter. Finding a new owner of a video camera on the station who just happened to be videoing everything, he could verify that his graph gave the right answer. The universe did behave in the way the the graph predicts, but the train, the station and the porter really exist while the graph is only an abstract representation on a piece of paper. We do not know whether or not the universe has the four dimensional form of Minkowski space, but we can be certain that if we try to represent it in a diagram on a sheet of paper, what we have in front of us is a velocity time graph even if do turn the page through 90°, call it a world line diagram, and use a strange scale on the time axis. If the correct transformation for the velocity time graph is a shear, then that is also the correct transformation of Minkowski space. We can transform from one frame of reference to another by making a shear in Minkowski space perpendicular to the time direction and in a plane containing their relative velocity and the time axis.

The nature of time

At the heart of Einstein's theory is his belief in the equal status of all observers. The null result of the Michelson Morley experiment is accounted for by believing that every experiment will give the same result: that every observer will obtain the same answer for the speed of light. At the heart of my theory is an equally unfounded belief that time is an absolute. I can still hold to this pre-Michelson Morley belief because I can explain the null result with my stasis theory which is derived from my understanding of the laws of electricity and magnetism.

Time is an absolute because the universe only exists in the present. The universe is in a state of flux, so we can map the movement of objects onto the mathematical artefact which we call time. We cannot observe the present. We cannot see the universe as it is. We can only focus on light waves which were emitted in the past. In the case of my computer screen, my eyes see it as it was 2 nanoseconds ago. In the case of some distant galaxies we see as stars in the night sky, we might be seeing them as they were 10 billion years ago. We see only the past and what we see is a record of what happened. We might watch a television program in which someone on the other side of the world is interviewed. What we see on the screen is a record of what they said two or three words ago. Those pictures will be recorded on tape and shown again in a few hours now more obviously a record of the past.

Time (almost) only exists in our recording of the past and our mapping of events onto a system of numbers. The Greeks understood this, but did not discover the almost. Time does exist within now. Now is not an instant in time, but an infinitely small length of time. This is a distinction which is hard to understand, but it is necessary to allow motion within the universe. If now was instantaneous, then nothing could change. The fact that now is an infinitely small length of time allows infinitely small movement within that length of time and an infinite number of these infinitely small movements add up to give us motion and change in the universe.

Clocks do not measure time, they attempt to measure time. The new theories of electricity and magnetism which explain why matter has what we call inertial mass give us every reason to believe that the pendulum bob on a grandfather clock and the quarts crystal in a digital watch will increase in mass as they increase in velocity. This affects the speed of the clock just as does temperature. We do not say that time slows in hot weather because the pendulum has expanded in the heat slowing the clock. Clocks may slow, but time remains an absolute.

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© Copyright Bruce Harvey 1997.