UNDERSTANDING RELATIVITY

By David A. Cooper:-

Relativity came out of the simple idea that you can never tell whether you are moving or not. When you think you are walking past a tree, it is quite possible that the tree is actually moving past you and that you are having to walk along just to stay still. However, because the Earth is moving as well, it is much more likely that you and the tree are both moving, though there is still a question as to whether you might be moving faster or slower than the tree.
indentAlbert Einstein's theory of relativity says that it is impossible to work out whether anything is really moving or not, and that does indeed seem to be the case (though he wasn't the first person to say this), but he went on to claim that it is perfectly correct to say that everything is both stationary and moving at the same time: you can claim that you are stationary while everything moving relative to you is moving, but it is also right for someone else to claim that they are stationary while everything moving relative to them is moving, including you: it's all relative! Both beliefs are valid not just because neither can be proved or disproved, but because he asserts that both claims are true, and that both claims are equally true.
indentSome people have no trouble accepting Einstein's claim, but others reject it as nonsense because it offends their sense of reason. We're going to have to look carefully at the evidence to see if we can work out who's right. My main objective in writing this though is to arm you with a robust understanding of the main details of relativity so that you don't fall victim to the bombardment of misinformation which will assail you almost everywhere else. We really need to start at the beginning of the story though by looking at an older theory which came out of the stable of good old common sense. This old theory said that things like planets, stars and light move through a substance of some kind called aether (or ether; both are pronounced "eether"), and the aether was imagined to restrict light to travelling at a particular speed which we call, unsurprisingly, the speed of light.

Now, it occured to a couple of scientists, Albert Michelson and Edward Morley, that they might be able to carry out an experiment to reveal which direction the Earth was moving in through the aether. They came up with the apparatus shown in the diagram above. The idea is that a laser (at the bottom) sends light up into a semi-silvered mirror to split the beam and send it along two paths to mirrors at the ends of long arms. From those mirrors, the light is reflected back to meet up again at the semi-silvered mirror before being sent on into a detector (shown as a yellow box in the diagram). They reckoned that the light would take longer to complete the trip along one arm than the other if the apparatus was moving, so they built it and tried it out to see.
indentHere is how they expected things to happen, though in the diagram below I've got the apparatus moving at a ridiculously fast 86.6% of the speed of light to exagerate things enough to make the difference show up really clearly. The red dots represent pulses of light, and the speed at which they cross the screen obviously represents the speed of light through the aether, with the screen serving as that aether. It is important to understand that the red dots move across the screen at the same speed all the time (except when waiting to start in the bottom of the laser and after they've been captured by the detector) - you can check that they really do move at a constant speed by clicking on the "hide" button to remove the distraction of the moving Michelson-Morley apparatus.

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Clearly if the apparatus was stationary (as shown on the left) both light beams would complete the journey in the same length of time as each other, but if the apparatus was moving fast through space (as on the right) it would take longer for the light to follow both paths because it would have to travel a lot further through the aether (or across the screen) in order to complete the trip along the arms and back: twice as long on the vertical arm in this case where the apparatus is moving at 86.6% the speed of light, and four times as long on the horizontal path. I have chosen this particular speed because it results in the light following the line of the blue dots which slope at 60 degrees to the vertical, and this leads to the light taking exactly twice as long to complete the trip through the vertical part of the apparatus. If you type the "sin" key (sine) on a calcuclator followed by 60 and then "=", you will find the number 0.866 appears on the screen. (On an older calculator you may need to type 60 first followed by "sin" and "=".)
indentBecause the light following the side-to-side arm of the apparatus takes longer to complete the trip than the light following the up-and-down arm, it arrives later at the detector: two separate pulses of light are detected at the finish line instead of a single one. You should be able to imagine now that whenever one arm is lined up more than the other arm in the direction in which the whole apparatus is travelling through space, it will take longer for the light to complete the trip on that path than it would on the other path, and the difference between the two pathways could have been used by the scientists to work out which direction the apparatus was moving in relative to the aether, in addition to telling them how fast it was going. What actually happened though was a huge surprise to everyone, because no matter which way they lined up the equipment, and regardless of the direction the Earth was moving at the time in its orbit round the sun, they never saw any difference between the two paths at all - the two beams somehow always reached the detector at exactly the same moment. They concluded from this that the Earth always behaved as if it was stationary, even though it couldn't be stationary all the time as it was known to be going round and round the sun at sufficient speed that little timing differences should have shown up. [Note: in reality, they weren't able to time different arrival times for the light pulses because the difference would have been too short to measure by that method, so instead they were looking for a change in the interference pattern where the two beams met up again on a screen, and no change ever appeared.]
indentA Dutch physicist by the name of Hendrik Lorentz initially tried to account for this result by suggesting that there might be aether drag, this idea being that the Earth could be dragging a bubble of aether around with it, so it would not be moving relative to that aether at all and the experiment would thus show no movement of the apparatus through it, but other experiments quickly ruled this idea out. He then began to think of the aether as being more like a fixed fabric of space and explored the possibility that the very act of moving through this fabric might somehow cause the arm of the apparatus pointing in the direction of travel to become physically shorter, thereby allowing the light to complete the trip along it and back in the same amount of time as the light takes on the other pathway. He came up with a formula which related the speed of travel to the necessary amount of shortening, though he had great difficulty trying to explain why things should actually contract in this way. You don't really need to use Lorentz's formula though to work out length contraction as you can simply take the speed of travel of an object (based on the speed of light being 1, half the speed of light being 0.5, etc.) and then type that speed into a calculator followed by the "inv" (inverse) and "sin" (sine) keys [or on newer calculators you may have to press "shift" then "sin" before typing in the speed] to work out the angle which light actually has to go at if it's to travel along the vertical arm and back. The cosine (cos) of that angle will then tell you how much the apparatus will be contracted in the direction of travel, and this same figure also gives you the rate at which a clock moving at that speed will tick (because moving clocks run slow, but I will say more about that later). In the diagram below, the red dots are all travelling at the same speed as each other across the screen as before, but this time the horizontal dimensions of the moving apparatus have all been halved, as the formula dictates that they should be with the apparatus travelling through space at 86.6% the speed of light.

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So, the light now takes twice as long to complete the round trip on the moving apparatus as it does on the stationary apparatus, and it does this on both of the paths through it. At 86.6% the speed of light, the length of a moving object will halve, but time will also seem to be slowed to half the normal rate. This apparent slowing of time occurs because it takes twice as long for light to travel backwards and forwards between two points: twice as long for an electron to orbit its atom's nucleus, twice as long for forces to be sent between particles of matter, twice as long for electricity to flow round a circuit, and twice as long for any clock to tick. All of these things take exactly twice as long at this speed because everything has to travel exactly twice as far through the fabric of space to get the same work done. What Lorentz had done was to correct an incorrect assumption of common sense and to create a more accurate version of the old theory of how the universe works, and his version of that theory remains a viable contender to this day, although it gets very little attention: Wikipedia's entry on Lorentz Ether Theory.

It's worth stopping here for a moment to look at an objection that intelligent readers often make when they see the diagram with the contracted MM apparatus - the angle of the semi-silvered mirror looks wrong, so how is it going to reflect the light in the right direction to send it along the arms or into the detector? The key to understanding this is to realise that the movement of the mirror will make it behave as if it is set at a different angle from the one it is actually set to. If the mirror is moving at 86.6% the speed of light, as in the diagram above, it will be physically angled not at the 45 degrees it would be at for the stationary apparatus, but at 63.4 degrees to the horizontal. Now I want you to imagine a wavefront of the light coming up from the laser below, it will obviously hit the lower part of the mirror first, with the rest of the wavefront progressively hitting higher parts of the mirror as the mirror moves to the right - this results in the mirror acting as if it is actually at 85 degrees to the horizontal. You then have to take into account that the light coming up to the mirror from the laser will not be coming up to it vertically, but at 60 degrees to the vertical, so you can now see that the light will reflect off it to move precisely horizontally to the left as required. It's a similar story for the light coming down from the top mirror to the angled semi-silvered mirror, but this time the wavefront of the light will hit the top of the mirror first, and then it will progressively hit lower parts of the mirror as the mirror moves to the right, the result being an effective angle for the mirror of only 15 degrees to the horizontal. The light coming down from the top mirror is again not coming down vertically, but at 30 degrees to the horizontal, so when it hits the mirror which is behaving as if it's at 15 degrees to the horizontal, the light will again reflect off it to travel exactly horizontally, directing it straight into the detector.

We've seen then with the Michelson Morley experiment why clocks are slowed down by movement, but in LET (Lorentz Ether Theory) it is important to understand that it is not time that is slowing - everything continues to move in normal time, but the communication distances for light and for all forces between atoms and particles increases and results in a slowing of apparent time. The simplest kind of clock is the light clock: this is a device which sends a pulse of light out to a mirror which then reflects it straight back again to a sensor from where the light was originally emitted, and the round trip of the light pulse counts as a tick. If a light clock is aligned with the movement of travel, the whole device will be length-contracted, so it will keep perfect time against another light clock moving with it but angled in any other direction. Moving clocks of this kind, and of any other, will be slowed down in terms of their ticking rate by their movement through the fabric of space, and the Michelson Morley apparatus is really just a pair of light clocks set up at 90 degrees to each other, so you can see the slowing of apparent time just as clearly there. A mechanical clock may seem quite different, but the way the atoms behave is affected by the increased communication distances for forces between its atoms in the same way: all the forces involved are transmitted at the speed of light, so it will slow to exactly the same degree as a light clock. Clocks are slowed by movement, but importantly, Lorentz Ether Theory says that actual time is not slowed at all: you can see that this must be the case because the light is still travelling through the fabric of space at its full normal speed. (Einstein's theory makes very different claims about all this, but we'll look at that in detail later.)
indentBy the way, if the Michelson Morley apparatus was to move through space at the speed of light, light would then be incapable of completing either trip along the arms at all, not just because it would be unable to make any progress in the direction of travel of the apparatus, but because time would appear to stop for the apparatus completely and the laser wouldn't even be able to generate any light, never mind send it anywhere. Furthermore, the apparatus would be contracted in length to the point where the arrangement of the atoms would be lost because they'd all be pushed into a two-dimensional plane which would destroy the structural arrangement of the equipment. In practice though, it wouldn't be possible to get the apparatus up to the speed of light because it would need to have an infinite amount of energy put into it to get it to go that fast, and that could never be done.

The most surprising thing that comes out of all this is that it's impossible to tell whether things are moving or not by looking at how other things are behaving: it always looks as if you're stationary regardless of how fast you may be moving through the fabric of space. The Michelson Morley experiment was an attempt to pin down which way the Earth was moving through this fabric (or through an aether), but it turned out that it was incapable of doing any such thing because of the length contraction which had not been predicted: this length contraction hid the movement completely and no experiment has ever been devised that can get round it. There was still no obvious reason why length contraction should occur, but it hinted at a deep, hidden mechanism that causes things to contract such that the communication distances of forces in the direction of travel will always take the same length of time to complete a round trip as forces expressed sideways - certainly, if something is already moving at close to the speed of light and also wants to wobble around a bit in different directions, no part of it can be allowed to exceed the speed of light, so the wobble in the direction of travel must automatically be reduced. (Be aware though that light and radio waves are not length-contracted in this way: their lengths are not maintained by forces travelling between any of their component parts at the speed of light, so there is no inner mechanism capable of contracting them.) To explore this further, you may benefit from spending some time playing with my Reference-Frame Camera.
indentYou may still not be convinced that it should be so impossible to tell whether you're moving or stationary, because if moving clocks run slower and moving rockets are contracted in length, you might imagine that you can simply compare clocks moving in different directions and see which ones are running fastest, or look at the lengths of rockets to see if they're shorter than they normally would be, but it turns out that it isn't so easy - if you're in a moving rocket, the stationary rocket will appear to you as if it has been length-contracted and its clocks will also appear to be running slow. Feel free to skip the rest of this section if you already understand all that: you should continue reading from the heading "Enter Uncle Albert" instead because that's where things begin to happen. If you have a really poor attention span, run down to the interactive diagram half way down the page and explore it carefully, because once you've done that it may just begin to dawn on you that this might be the most important page about relativity that you will ever encounter.
indentIt's easy to demonstrate why this happens with clocks. Imagine two rockets, one of which is stationary and the other which is moving along at the usual 86.6% the speed of light (because that gives us nice round numbers to work with). If we assume that rocket A is stationary and rocket B is moving, then the clocks in rocket B will be running at half the rate of the clocks in rocket A. These clocks could be connected up to radio transmitters to send out a beep for each tick. When the crew of rocket A listen to the beeps coming from rocket B, they may hear the beeps comming in at one beep every two seconds. When the crew of rocket B listen to the beeps coming from rocket A though, they too will hear one beep every two seconds. It isn't quite that simple though, because there are awkward Doppler effect complications, so let's start by looking at an extreme case first where a moving rocket is racing directly away from a stationary one. In the diagram below, you can count the rate at which beeps from a stationary clock arrive at a rocket moving at 86.6% of the speed of light, and you can also see the rate at which beeps from a clock in the moving rocket reach the stationary rocket. Remember that ticks are emitted by the moving rocket at half the rate of the stationary one because the speed it is travelling at forces its clock to run at exactly half the normal rate.

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Watch what happens around the points in time where the radio beeps either disappear or emerge from behind the rocket they're passing and keep notes of the exact times of these events on the counter underneath (the key points to look out for being, for example, the points where the first and last of the blue beeps appear from behind the stationary rocket and the points where the first and last of the red beeps appear from behind the moving rocket). Subtract the smaller number from the bigger one each time to get the duration. The numbers vary for different browsers so you'll need to note down the numbers you get on your screen. In some browsers it's also a bit hit or miss as to the exact timings of things disappearing or appearing - errors creep in due to the way HTML parts of the program are handled, but some of the timings do tie in exactly with what they should be (and you can check the maths in the source code). You can see that twice as many ticks reach the stationary rocket as the moving one in a given length of time, but you have to remember that time is running at half the normal rate in the moving rocket, so those ticks will be perceived as arriving there at exactly the same rate as in the stationary rocket. Of course, if the moving rocket is travelling in the opposite direction and towards the stationary one, then the ticks arrive at both rockets at a much faster rate, as you can see below, but again when you allow for the slowed time in the moving ship, the perceived tick rates received by each ship are identical, and so there is absolutely no way to determine from these situations which ship is really moving.

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Again both rockets will perceive the beeps arriving at the same rate, regardless of which one is actually moving. If you were to average out the tick rates for a rocket approaching you and then moving away at 86.6% the speed of light, that average perceived tick rate would be one tick every two seconds from the two rockets, each one hearing two of its own ticks for each tick of the other, thereby making it look as if the other must be running with slowed clocks.
indentNow, you might still think that you could spot the difference in tick rate when one rocket goes right past the other, but if there is any space between them it is impossible to determine when that point occurs because there is a delay in relaying that information caused by the speed of light not being infinite, and even if one rocket was to go right through the middle of the other it wouldn't help, because then there would be no stretch of time during which the moving ship was going past rather than coming towards or moving away: you'd need it to be going past for more than an instant to measure the gap between two ticks. Let's just take a bit of time to think our way through an experiment where the two rockets pass each other at some distance though: when the crew of Rocket A see rocket B reach the point of closest approach, at that point the beeps should be coming in from it at one tick every two seconds. That is indeed the tick rate they will observe, and the crew of rocket B will actually hear two beeps per second coming from rocket A at that moment because the beeps are being produced twice as fast by rocket A and time is running at half speed in rocket B. So, have we found a way then to tell which rocket is actually moving? Unfortunately not. At the point when rocket B appears to be at its point of closest approach to rocket A (from the point of view of the crew of rocket A), it doesn't look that way at all to the crew of rocket B because rocket A still appears to them to be 60 degrees ahead of the point where it actually is: they won't see rocket A as being at the point of closest approach to rocket B until much later on, by which point they will be receiving one beep every two seconds from rocket A. What's actually happening is that if the crew of rocket A decide where the point of closest approach is, they will determine that they are not moving and that rocket B is racing past them, but if the crew of rocket B decide where the point of closest approach is, it is they who will determine that they are not moving and that it is rocket A that is racing past them. Not only that, but the crew of each rocket will see the other rocket as being contracted to half its normal length, so that doesn't provide any useful answers either. No matter how you try to analyse things, it turns out that the absolute truth of any such situation can never be worked out.

It is unfortunate that we cannot tell if we're stationary or not, but this doesn't actually get in the way of making calculations about what will happen when we send rockets around - we can simply imagine that we are stationary and thus assume that we are not moving through the fabric of space, and then we can calculate how much other things will appear to be length-contracted and how much their clocks will appear to be slowed on the basis of how fast they appear to be moving through the fabric of space. Other people who are moving relative to us can do the same thing and assume that they are stationary while we are moving, and although their accounts of events will disagree with ours in many ways, the most useful details will always match up.
indentFor example, if a rocket leaves the Earth and flies away into space for a year at 0.866 of the speed of light, then turns round and comes back at 0.866 of the speed of light, that trip will take two years from the point of view of the people in the rocket, but four years will have run through on the Earth before the rocket comes back. If we do our analysis from the "frame of reference" in which the Earth is considered to be stationary, then the rocket was moving and its clocks were ticking at half the normal rate throughout both legs of its voyage. However, if we use a different frame of reference instead, we could then imagine that it's the rocket that is stationary during the first leg of its voyage while the Earth is moving away from it at 0.866 of the speed of light, and that would mean that the clocks on the rocket can now be thought to be ticking twice as fast as the clocks on the Earth throughout this half of its trip. During the second half of the rocket's journey though, the rocket will be calculated to be chasing the Earth at 0.99 of the speed of light to catch up with it, and its clocks will be reckoned to be ticking about three and a half times as slowly as clocks on the Earth. The end result will still be that the whole journey will take two years for the rocket (as recorded by its clocks) while four years will still have gone by on the Earth (as recorded by clocks there). So, while we have accounts of events that contradict each other as to when the different clocks were running faster or slower than each other, the most important numbers about how long the whole trip takes will always agree at the end of the process when the two parties are reunited - all accounts determine that the rocket records two years while the Earth records four.
indentThe contradictions in the accounts of events from different frames of reference are still important though, for they demonstrate that not all the accounts of events can be true. There is only one frame of reference which can be tied to the fabric of space, so its accounts are the ones which are true while all the other accounts are false. We cannot tell which frame of reference is tied to the fabric of space, so we cannot tell which accounts are true and which are false, but we are allowed to pick whichever frame of reference is the most convenient for us to work with, and then we can use it for our calculations exactly as if it is the special, absolute frame of reference. The accounts of events describing the different rates at which clocks tick relative to each other can never be trusted to be true, but we can trust the average differences in tick rates for clocks which are separated and then reunited (like the rocket leaving and returning to the Earth) because we will always get the same answers for that no matter which frame of reference we use as our base for the calculations. We will look more closely at the issue of the contradictions later on because they are extremely important: if there are contradictions in rival accounts generated within a theory, that theory cannot be valid.

Enter Uncle Albert

So far we've been looking at events through the lens of Lorentz Ether Theory (LET), but it's now time to bring Albert Einstein into the picture to find out how he stamped his name all over relativity. The way things work in LET results in it being impossible to tell if anything is moving or not: there is an absolute frame of reference which is tied to the fabric of space itself, but it cannot be identified because from where we are (inside the universe) all frames behave as if they might be that frame. Einstein decided that if you can't pin it down, you might as well just assume that there is no such absolute frame of reference. He declared that all frames of reference are equally valid instead, though he had a good excuse for making this claim as he believed it was possible to eliminate all the contradictions in the rival accounts of events from different frames of reference, and we'll look into that in detail later on. Much more interesting though is what Einstein did with the nature of time, because he changed it into a dimension and in doing so turned the fabric of space into a four dimensional fabric called Spacetime. In LET the universe has three space dimensions running under a Newtonian time (which is not considered to be a dimension), but Einstein decided it was more similar in nature to the three space dimensions. Many people will tell you that time doesn't run in Einstein's model: time has become more of an arrow pointing from past to future, but this cannot be the case as it would prevent the future of a universe from being generated out of its past. Such generation depends on a rolling, ordered process which is completely impossible if time doesn't run. Some people actually believe that the whole past and future of the universe simply exist eternally in a block of frozen events and that none of these events ever run at all, but they completely fail to account for how such a universe could come into being in the first place without having to introduce an earlier construction phase which would need to operate under different laws of physics in which time is able to run. But before we get bogged down in that issue, we must try to get our heads round how this time dimension works so that we can understand the main difference between it and the Newtonian time used in LET.
indentIn Einstein's Spacetime, there is no real length contraction, meaning that objects aren't physically contracted by their movement through the fabric of space, and this clearly has to be the case because they can always validly be thought of as being completely stationary as all frames of reference are really equally valid. When you observe objects from a frame of reference in which they appear to be length contracted, they will act in every way as if they are length-contracted, and so the length contraction is in practical terms fully real, but it is ultimately just a kind of illusion. Einstein manages this trick by allowing objects to hide some of their length in the time dimension. He plays a similar trick with time, getting rid of the slowing of moving clocks too. Because all frames of reference are equally valid, a moving clock isn't really moving, so it can't actually be running slow: this too is just an illusion. While a clock which is moving past you appears to be running slow, it may actually be taking a shortcut into the future instead, or you could be taking a shortcut into the future while it isn't doing so. If we look at our earlier thought experiment with a rocket leaving the Earth at very high speed and then returning home again, in our LET explanation (Lorentz Ether Theory) we had moving clocks running slower than stationary clocks, but in Einstein's model it is different: the rocket and its clocks which looked as if they were running slow were actually functioning at their fully normal rate, but the rocket was taking a shortcut into the future (travelling a shorter distance through the time dimension), and that made it look as if its clocks were running slow when they weren't. The travelling rocket made its trip in two years while the Earth took four years to travel the same distance into the future, but it did so without its clocks running slow, and this means that the rocket has jumped two years ahead of the Earth into the future to be reunited with a future version of the Earth rather than the current version (which will still have to wait another two years before it experiences that same event of the rocket meeting up with it). Now, you might wonder how there can be a future version of the Earth ready for the rocket to land on two years early, but we can fix this by going back to the idea of the universe being an eternal block in which the entire future already exists (and in which the past continues to exist eternally too): this allows fast moving objects to jump ahead into the future where they can interact with slower moving things which have taken more time to get there. The downside to this is that such a universe could never have had its future events generated out of its past events under these rules because many of its events would have failed to mesh together properly during the generation phase (when the block was originally being constructed): a rocket which has taken a shortcut would have been unable to land on a planet which has not taken a shortcut as there wouldn't be a future version of that planet there yet for the rocket to interact with. (There is actually one way round this, but it's messy so we'll look at it later.) There is an easy way to avoid event-meshing failures, but it involves allowing time to run at different relative rates for objects moving at different relative speeds, but that requires adding a second kind of time into the model to enable this, as we will soon see (and indeed it turns out that a second kind of time must be added to the model to allow time to run at all, because the "time" dimension is not sufficient to allow this by itself).
indentLet's just think our way through the thought experiment with the rocket again though, because it's important to see if there is an issue with contradictions here under Einstein's theory in relation to his claim that all frames of reference are equally valid (and that there is no special frame of reference akin to the absolute frame in LET). If we decide that the Earth is not moving and is therefore not taking a shortcut into the future, when the rocket sets out on its journey at 0.866 of lightspeed, the rocket will be taking a shortcut into the future during the first leg of its journey, and on the return leg of its journey it will again be taking a shortcut into the future. However, if we use a different frame of reference for our analysis, we can then decide that the Earth is taking a shortcut into the future the whole time because it is the one that's moving at 0.866 of lightspeed, so when the rocket makes the first leg of its journey it is now regarded as stopping for a year while the Earth speeds away from it, and that means the rocket has stopped taking a shortcut into the future during this leg of its journey. During the second leg though, the rocket is taking a much bigger shortcut into the future than the Earth, and so it will still end up taking an overall shortcut into the future for the trip as a whole (when compared with the constant shortcut being taken by the Earth). We therefore again have accounts which contradict each other: one account says that the rocket is taking a shortcut into the future over the Earth during the first leg, while another account says the exact opposite. So, not all the accounts can be true as they directly contradict each other on some points. There must again be a special frame of reference which would provide us with a true account of events (if only we could identify it) while the accounts from all other frames of reference must be wrong. A theory which generates contradictions is automatically invalidated by those contradictions, so Einstein's assertion that all frames of reference are equally valid is beginning to look highly doubtful.
indentWhy then has that claim ever been allowed to be part of his theory when it looks as if it must be wrong? Well, the answer is something called "Lorentz invariance". This invariance means that if you view the universe at any point in time under one frame of reference and then switch to using a different frame of reference to view it again, you will not change anything at all in terms of the events that have happened or the events that have yet to happen, so if an event has taken place as calculated under one frame of reference, it will be calculated as having happened under all other frames of reference too, while an event which has not taken place yet, as calculated under one frame of reference, cannot be calculated to have happened yet under any other frame of reference either. If you view events through the static block universe model, the contradictions thus disappear, but the downside of this is that events will no longer mesh together properly during the construction phase as you have to run time at the same rate on all paths in order to maintain the Lorentz invariance. After the block universe is complete it is certainly possible for events to mesh together successfully with things taking shortcuts and meeting up with future versions of other objects which have not taken such shortcuts through time, but a proper theory must also be able to account for the construction phase and not merely restrict itself to the post-construction, static block phase. That means that events have to be made to mesh together correctly during the construction phase by applying different rules while growing the block (or events are allowed to fail to mesh during the construction phase, which is messy), and during that construction phase it is not possible to maintain the Lorentz invariance: Lorentz invariance only applies within the static block model, and that static block universe model is deficient as it cannot account rationally for the actual growth of the block.
indentWhat we see then with Einstein's model is a problem of event-meshing failure: fast moving objects take shortcuts into the future and try to interact with other things which have taken longer paths through time to get there, and they are supposed to meet up and interact with each other even though some of them will get there too early for this to be possible. (You will see this more clearly when you play with the interactive diagram further down this page.) The big problem is that the only kind of time that's officially allowed in Einstein's model is the "time" dimension, so if we are to respect this sole kind of time that the theory allows for, we are forced to have clocks tick at the same rate on all paths: the rocket's clocks must tick once for every tick of the clocks on Earth, and that gets the rocket back to the point of the reunion with the Earth a full two years too soon. The events simply don't mesh together correctly, so that version of the model is immediately in severe difficulty. The only solutions to this problem are either to allow clocks moving on different paths to tick at different rates relative to each other (but that means allowing tick-to-tick ratios other than 1:1 for different paths through Spacetime) or to tolerate event-meshing failure during the construction phase, though that leads to events at any single Spacetime location changing there over Newtonian time. If we use ratios other than 1:1, we are also forced to bring in a Newtonian time to work in combination with the "time" dimension that's already in the model so as to allow some clocks to tick more slowly than others, but that's not something that Einstein's followers are at all keen to allow into the model as it breaks his rules. However, they have come up with a stunningly elegant solution to resolve this difficulty: they simply smuggle in this Newtonian time to allow tick-to-tick ratios other than 1:1, but they then deny that they have done so and claim they aren't using any kind of time other than the "time" dimension that's allowed in the model. With this added Newtonian time (which they claim they aren't using even though they depend on it), events can now mesh together properly with the rocket being united with the Earth after two years of the "time" dimension's time for the rocket, after four years of the "time" dimension's time for the Earth, and after a bit more than four years of Newtonian time for them both (and it's a bit more because the Earth is moving too: its clocks must run a bit slower as a result).
indentSo, they bring in an external time and secretly add it to the model as a vital part of its mechanism while denying that they are doing so, and then they point to the static block universe and chant "Lorentz invariance" like a mantra in order to show that the model works without the added Newtonian time. You will find experts who will claim to their dying day that it is possible to vary the ratios without bringing in this external time, but if you ask them to talk through all the events of a universe as it plays out some action (such as a rocket leaving the Earth and then returning home to it), you will see that they are clearly using their own time (which is external to the model) to enable these different ratios to be brought in, because they are not mapping it 1:1 to the time in the model on all paths. By bringing in this external time, they are also either bringing with it an absolute frame of reference or they're destroying the Lorentz invariance (as the interactive diagram a short way below demonstrates), but again they refuse to accept that they are doing so. Their education has trained them to believe that Lorentz invariance eliminates all the contradictions and that the theory works fine: the proof that it is fine is that everything works beautifully in the static block universe model without needing a Newtonian time, and if anyone points to the problem of how to create the block universe in the first place, that's fine too because they can construct it under a Newtonian time (which they pretend isn't there) and then confirm that it isn't there by pointing back at the static block universe model and chanting "Lorentz invariance", completely ignoring the construction phase again. In short, they are highly contrary people who are determined to have their cake and eat it. It is quite shocking that such irrational people can hold such sway in science and that they are allowed to drown out anyone who tries to point out the glaring error in their model, but then it must be hard for them to back down even if they can see that they are wrong because they have bought so deeply into what is undoubtedly the most embarrassing mistake in the history of science.

To help you fully appreciate the fundamental error that Einstein and his followers have made, it is worth taking a walk through the events of the rocket's journey under three different models for time, and we'll do this with the aid of an interactive diagram (below the next paragraph). The picture above this paragraph represents the same thought experiment with a standard Spacetime diagram. The time dimension is shown vertically while a single space dimension is shown horizontally. Early events are represented low on the diagram while later ones are shown progressively higher up. Note that all the action takes place on a single line through space, so only one space dimension needs to be shown. The events shown in the diagram involve two planets passing each other at a relative speed of 0.866 the speed of light, but one of them is shown as being stationary in the space dimension while moving up vertically through the time dimension (it follows the straight path through points X and Z-a). The other planet follows the straight, sloping path through points X and Z-b, and it is moving through the space dimension as well as through the time dimension. The other two lines on the diagram show the paths of two rockets, as will be explained in a moment. The planets pass each other at point X. In the picture underneath this paragraph you will find an alternative representation of exactly the same events: it treats the second planet as stationary, showing things from it's frame of reference instead. When the two planets go past each other, they nearly touch. The people on each planet (who will naturally regard their own planet as stationary) measure the other planet's speed as 86.6% of the speed of light as it races past them. A rocket is launched from each planet at the moment when the two planets pass each other (at location X), and each rocket accelerates in an instant to fly alongside the other planet (the one from which they were not launched). After a year by their clocks, the rockets turn round and head for home as fast relative to their home planet as the speed they went away from it during the first half of their trip (which will be measured as 99% the speed of light by people on the planet they're leaving).

You should now compare the two diagrams above with the interactive diagram below (which is actually a simulation). If you run it, you'll see that the red rocket leaves the blue planet at point X and travels with the green planet for a year until it reaches a Spacetime location called Y-b, then it returns home to the blue planet, meeting up with it at a location in Spacetime called Z-a. On arrival it finds that four years have gone by on the blue planet while only two years have gone by in the red rocket. While all that's going on, the orange rocket has left the green planet and travelled with the blue planet for a year until they reach a Spacetime location called Y-a, then it returns home to the green planet and meets up with it at a Spacetime location called Z-b. On arrival, it finds that four years have gone by on the green planet while only two years have gone by in the orange rocket, so the story is very much the same for both rockets and for both planets. Note that I have used 250 of my time units for a year to simplify the JavaScript program that runs the interactive diagram, so if you want to convert back to years at any point you should divide the time counter by 250. There are three modes to the diagram, each showing different ways in which this part of this block of Spacetime might have been generated during the construction phase (Spacetime diagrams normally only show the complete block with all events already played out in full, but to understand relativity properly it is essential to think about how the block was constructed). Note that all three modes would plot out the exact same Spacetime diagrams as the ones above if they were designed to draw Spacetime diagrams, so the Spacetime diagrams above are fully compatible with the interactive diagram in all three of its modes.









. . . . .   X Y-a   . Z-a   . .   Y-b .   Z-b


    1       -200          

1:1 ratio for clock ticks on all paths - note that events fail to mesh correctly.

These interactive equivalents of the earlier Spacetime diagram show how events might unfold during the construction phase of a universe under three different models. Everything in a Spacetime diagram has to move up the diagram over time even if it is stationary in space, but objects which are moving rapidly through space will have to move upwards more rapidly than slower objects if they are taking shortcuts into the future. In mode 1 we have a 1:1 tick-to-tick ratio for clocks on all paths, and this allows you to see some objects taking shortcuts into the future by moving more quickly up the diagram than other objects. You can also see the event-meshing failures that result, e.g. rockets reaching reunion points with their planets before their planets have arrived there and thus having to attempt to interact with them even though they're not there! If you change the frame of reference, you can see though that at least the actual events which have taken place are not changed by this change of frame: you are merely seeing the same moment in the generation of the future from the past with a different slant. In short, mode 1 displays Lorentz invariance and does not produce contradictions, but the event-meshing failure is a major problem for it (which I will comment on further below because there is actually one way to make it work, but it is most certainly not Einstein's model and it requires a kind of time to be added which is clearly Newtonian in nature). If you then switch to mode 2, the first of the variable ratio modes, the shortcuts are avoided and all events will now mesh together correctly, but you can also see that the Lorentz invariance has been lost: if you stop the action at any point and then change the frame of reference in this mode (for example, when the time counter reaches 360 or 550), events are changed as a result of switching frame, some events being undone while other events which hadn't happened before have suddenly happened. That can't be allowed to happen if this is a single frozen moment in time during the growth of a block universe (or the generation of future from past in any part of a model of a universe), but it is the direct result of trying to treat all frames of reference as equally valid when in reality they cannot be, so this is just another way of seeing the contradictions in the accounts of events from different frames. [With most browsers, you can repeat the action of a button which you have just clicked by using the Return key instead, and holding it down will repeat the clicks at high speed: this is particularly useful for changing frame.] Mode 3, the second variable ratio mode, doesn't allow events to change when you switch frame, so it cures both of the problems, but the consequence is that it imposes an absolute frame of reference on the development of the universe in order to restore the Lorentz invariance: what you see now is time passing at fudamentally different relative rates for things travelling in different directions through Spacetime, but everything happens in a way which is always consistent with the absolute frame of reference (which I have tied to frame A in this case). By the way, someone has complained that in mode 1 it looks as if some objects are moving faster than the speed of light, but he had misunderstood the diagram: you can only measure the relative speed of objects through space by comparing their progress between two points on their paths at the same two altitudes on the diagram. If you don't understand the diagram, you're in no position to reject it. If you have any difficulty with understanding how to read the diagram, feel free to ask questions at the provocatively-named Facebook page Relativity is dead which was set up specifically for this purpose.

There is one way out of the problem for mode 1, but it's messy. It would be quite possible to tolerate event-meshing failures during the construction phase of the block because the mess would sort itself over time as slower objects (the ones taking the longest paths through the "time" dimension) catch up with the points of failure and start to change the future events to make them conform to Einstein's rules. The block would thereby settle down over time and end up creating a stable block in which there is no longer any event-meshing failure: Einstein's theories would then appear valid to the current inhabitants of the block, but the same inhabitants during the construction phase of the block where events don't mesh correctly would know all to well that his model is not telling the whole story. That leads to additional complications as it brings in an infinite number of different versions of each inhabitant passing through the block at different times (of the Newtonian variety) and experiencing different events at the same Spacetime locations. To get a clearer idea of the implications of this, see the little section about backwards time travel a short way below, but one thing worth stating here is that time was not required to start at the big bang (under any viable model): Einstein's "time" dimension might start at the big time, but every model that could actually work has Newtonian time in it, either instead of or in addition to the "time dimension", and that Newtonian time would have no difficulty stretching back before the big bang.

While we're looking at Spacetime diagrams, it's important to understand a couple of confusing terms which you will encounter repeatedly elsewhere. Co-ordinate time (the vertical distance up the Spacetime diagram) is not a real kind of time in Einstein's model (unless you accept that a Newtonian time has to be brought in to control tick-to-tick ratios as in mode 3, in which case one frame of reference has a co-ordinate time which matches up with absolute time while the rest will not). Co-ordinate time is with Einstein's model just an artifact of Spacetime diagrams, and the only real kind of time in the model is "proper time". Proper time ("proper" doesn't have it's normal English meaning here: it means "own" in this context, as in "objects following different paths have their own time") is the only kind of time that officially exists in the model, this being the time recorded by the clocks in rockets and on planets, and it quite genuinely is Lorentz invariant: any contradictions involving co-ordinate time which come out of rival accounts of the action when using different frames of reference are not contradictions in any real kind of time in the model, so they can be ignored. However, as you have already seen, these contradictions can't really be ignored once you have understood that the model only works properly if you also bring in a Newtonian time to make events mesh correctly and to stop them magically happening and unhappening as you change frame of reference: as soon as you bring that in, you bring the contradictions right back into play and you have to recognise that Lorentz invariance does not apply to this Newtonian time unless you also have an absolute frame of reference (which takes things even further away from Einstein's model).


Conclusion

Einstein's theory, as it is normally taught, is clearly wrong, but it can be salvaged to a large degree in one of two ways: one by accepting that it needs to have a Newtonian time added to it (and also that this brings with it an absolute frame of reference), or alternatively it has to tolerate event-meshing failure during the construction phase (i.e. a mess that doesn't fit with what we actually see in the universe, but which can again work if you add Newtonian time to allow the block to change over Newtonian time: in an earlier era of Newtonian time, the visible events in our universe may have displayed astronomical numbers of event-meshing failures which earlier versions of ourselves would have been well aware of but which no longer show up). With either of these corrections in place, it could still be a better theory than LET if it did a better job of accounting for gravity, but it only makes gravity look simple by warping everything else to make it look as if gravity isn't a force. You will find when you study General Relativity that clocks are slowed by gravity, and Einstein's interpretation of this slowing is that things take shortcuts into the future when sitting in a gravitational field, just as fast moving objects take shortcuts, and I've written a bit about this further down this page, but my immediate priority has been to arm you with the essential knowledge and understanding which will protect you from the people who seek to shut down your ability to think rationally. I want you to be able to tell when you are being fed misinformation about relativity by the "experts" who dominate the physics world and who police physics forums where they ruthlessly shout down anyone who objects to their misinformation or who points to the faults with Einstein's theory. These "experts" also fill the Internet with education sites which push the same misinformation about relativity, leading most people to believe that LET has been disproved and that Einstein's theory is the only game in town, but in reality, LET is still a fully viable theory. It is actually Einstein's theory which is in difficulty because of the unnecessary complexity in the mechanisms required to run things along its time dimension at different speeds under the control of a separate Newtonian time, and this is particularly awkward with photons which travel all distances in zero time of the time dimension while covering zero distance of its space dimensions (distance is compressed for fast-moving objects). [The "experts" will try to tell you that this is not the case, but logically it must be so because a photon cannot travel any path between two points in more time than the fastest possible object with mass. The reason they insist that this is not the case is that they can't handle the implications.] What really matters about Einstein's theory though is not any of his silly claims, but the idea of a four-dimensional Spacetime. This is important because Einstein's mechanism for gravity depends upon the introduction of the "time dimension" which allows gravity not to be a force: within the Spacetime model, planets can orbit stars simply by following straight lines through a curved Spacetime rather than being pulled round their orbits by a force of gravity. Whether it is right or wrong, and regardless of how contrived it may be, it is unquestionably a fascinating alternative way of looking at the universe. A working model of this though can only be built if Newtonian time is added to it: there is no other way of fixing the faults. The excuse for rejecting LET in favour of SR/GR has always been that SR/GR is supposedly simpler as it doesn't need an absolute frame of reference and absolute, Newtonian time, but this claim is ludicrous given how much extra baggage actually has to be added to the model to make it "work". The whole thing is almost certainly just a contrived mathematical abstraction which adds an inordinate amount of unnecessary complexity for no functional benefit. Anyone who still thinks Einstein's model is valid after reading all the above needs to read the section following this one and then click on the link to test their beliefs to destruction: it will spell out to them exactly where the holes in their reasoning lie.

You can read more about Einstein's Relativity all over the place, and it's now safe for you to do so because you will be able to tell when people are trying to mess with your mind. If you want to read more about LET there is little choice because it has been systematically neglected by the establishment, so the best place to look is Conspiracy of Light (which has an unfortunate name, but it will provide you with good information).


Take the relativity exam.

This page has just set before you a logical proof that Einstein's model is substantially wrong, but many people (including some professional physicists) fail to recognise it as a logical proof because their existing beliefs override their ability to reason correctly: they've been taught the basics badly, leading them to imagine that it's okay to mix incompatible versions of the model into one faulty mess which they think works because they can point to different versions of the model and say that each part works in at least one version. It doesn't register with them that their model can only be viable if all parts of it work within a single version of the model. For example, it's no good pointing at mode 1 to explain one thing which doesn't work in mode 2 and then pointing at mode 2 to explain another thing which mode 1 can't handle, because those two modes are incompatible, but that's exactly what they do. If they were able to reason correctly, they would pick one mode and stick to that single mode throughout, and if their model can't handle something that they claim it can account for, they would then be duty bound to accept that it's wrong. But they refuse to do this and fail to keep incompatible models in separate compartments in their heads. I keep finding this problem in other fields too where people mix incompatible models while imagining they're doing good science, and it's a terrible waste of time trying to take them through the argument when they resort to playing every avoidance trick in the book as soon as they realise that they're being taken into into territory that would put them at odds either with the establishment or with their own treasured beliefs. Fortunately though, there is a solution to this: software can walk them through a proof without someone like me having to spend hours dragging them through it all, so I have now created an interactive exam for them and they must either pass, fail or run away from it (which also counts as a fail). If they don't run away, it is impossible for them to fail this exam without taking a path through the program that shows them to be wrong on a very clear, simple point on a par with believing 2+2=5, and it will be demonstrated to them so clearly each time that they should not be able to settle on any of the wrong answers unless their IQ is measured in the negative. This program forces them to accept or reject each point clearly, and it won't let them get away with going round and round in circles either: it forces them to stop playing avoidance games and to get out of the loop to pass or fail.

To take the test, right click on this link to open it in a new tab. (You should open it in a new tab so that you can access the interactive diagram above at the same time.)


An example of the same problem in General Relativity

I'll now move on to a thought experiment which explores the same issue with General Relativity, but this one is a bit simpler in that we don't have to consider different frames of reference.

Imagine two space ships hovering over a black hole with one of them much closer to it than the other. The higher gravity near the black hole causes clocks in the lower ship to appear to tick at half the rate of clocks in the higher ship, but it's important to remember that the model only has one kind of time in it, so there is no possibility of the lower ship's clocks running slow - instead, their ship is moving on a course through Spacetime which takes it into the future in less time than the other ship. (If it doesn't do this but runs with its clocks slowed instead, then there must be an external time introduced to govern this, but that is completely banned by the model, so there can be no such option.)

Let's now imagine a game of tennis being played between these ships. A ball is repeatedly hit from one ship to the other and back again. For a valid theory to account for the generation of the universe, it has to create things and events in order of causation (and this applies to any part of the universe from the starting point of any series of events that we want to consider - things must happen strictly in order of causation). The ship that's higher up starts the game and the lower ship hits the ball back. (This may not by physically practical, but we could use a pulse of light instead of a ball - it makes no important difference.) The ball makes the round trip setting out from the higher ship on a tick of that ship's clock and returns two ticks later. The equivalent clock on the other ship is not synchronised with the one on the higher ship, but it so happens that the ball always arrives there on a tick, although it arrives there on every tick instead of every second one. For reasons of linguistic simplity, we'll call the length of time between two ticks a second. (It would need to be longer than an actual second for tennis balls if the hits aren't to be so energetic as to destroy them, but it could probably be a real second if we're using a pulse of light instead of a ball.)

What are the implications of this? As we generate the future of this scenario from the Spacetime location where this tennis match began (or perhaps from the point where the two ships separated in order to take up their positions for the match), no clock is ever allowed to run slow - the lower ship is moving twice as quickly into the future as the higher ship once it has taken up its position by the black hole. The higher ship sends the ball to the lower ship and the lower one sends it back. The lower ship moves more quickly into the future and sends the ball back again a second later, and again a second after that. The higher ship only hits the ball once every two seconds, so we can see that either the lower ship is hitting the ball back before the ball's been hit to it, or its clock is running slow, but the latter is banned by the model. This is another case of event-meshing failure if we're in a genuine creation phase for the universe (where the future was not already set in place) - the ship moving faster into the future can only hit the ball if the future of the ball is already set in place for it to be hit, and that means we are necessarily dealing with an eternal block universe which is not in the act of being generated, and that's no use at all - physics needs to account for the generation of that block, and it cannot do so by rules which only work within the block once it has already been created in its entirety. Einstein's theories only apply after the generation of the block is complete and cannot handle the actual generation phase without a calalogue of event-meshing failures. If we are actually in a genuine generation phase, there are points where what is happening now at a point in Spacetime must be at the leading edge of the generation of that Spacetime block, and no part of the future of the things passing through that point can have been set in place. For one player to move ahead of the other into the future by any means (whether rapid relative movement or by sitting deeper in a gravity well) and then to interact with the other is completely impossible during the generation phase - if they are to meet up correctly and avoid event-meshing failures, clocks that are deeper in gravitational wells must be running slow and must be under the governance of an external time.

Before the tennis match began, the two ships were initially sitting side by side. At some point, we can stop the tennis match and bring the space ships back together again, and after that we can repeat the whole process and send one of them (the same one as before) back down to the black hole to play another tennis match, and we can repeat this as many times as we like. The ship which spends more time near the black hole is supposedly taking a faster route into the future, but we repeatedly bring it back up to meet the other ship, and every time we do this they are together sharing a location in Spacetime. Again we can see that there must be event-meshing failures with this during the generation phase unless the clock of the lower ship is actively running slow under the governance of an external time while it is deep in the gravity well. Every simulation of the generation of a universe that has ever been done and every simulation of the generation of a universe that will ever be done has and will be done by using an external time to govern the unfolding of events if it is to avoid event-meshing failures, but you will find that the physicists deny this and assert that no external time has been introduced, but none of them has ever encountered a program which doesn't cheat by bringing in an external time to govern events. It's obiously necessary for the computer to run with its own clock while it does a simulation, but that time needs to be linked 1:1 with the ticks of all clocks being simulated in the model if it is to be used as the time of the clocks in the model, and that leads automatically to event-meshing failure during a simulation of genuine generation of a universe (or any scenario within a universe). The only way to make events mesh is to use different ratios for the ticks of the computer's clock and the ticks of the simulated clocks, and that is where the computer's clock becomes an external time that governs the relative rates of the simulated clocks - it is an external time which is being added into the functionality of the model to make it work even though it is banned from the model.

I've just had a conversation with a cosmologist who told me that he does exactly this kind of simulation without involving an external time. I asked to see his program code and offered to point out to him where he was introducing the external time, so he sent me links to some "simulations". It turned out that they were merely papers going through the maths of a couple of scenarios - they were not simulations at all, although they could certainly be simulated in the reader's brain, and indeed they would need to be for the reader to understand them fully, but it is inside the reader's brain that the external time is being brought in to govern the unfolding of events, and the reader is not necessarily going to have the wit to realise that he (the reader) is cheating. You cannot hide the cheating in a computer program though (unless you do so by obfuscation and make sure that it will take too much effort to understand how the program works), and that is why I asked to see the code. I very much doubt it will ever be forthcoming, but if he surprises me by providing it and it's documented sufficiently well that it's practical for others to follow it, I will show him exactly where and how the program cheats. (See the section after next for an update on this.)

I issue the same challenge to anyone else out there who thinks they can simulate through software the generation of a simple scenario like the ones in my two examples without using any external time to govern the unfolding of events in a manner that breaks the rules of the model. The only kind of time they are allowed to use is the one that's supposed to be in the model (they are allowed to use an external time for that), and I can tell you for free that it is an impossible task to generate either of those scenarios without cheating. It is ridiculous that this fault was not spotted a hundred years ago by a physicist or mathematician, but it's even more ridiculous that they can't recognise the error now when it's set before them in terms that any reasonably bright person should be able to follow even if they have no background in physics or mathematics. But this is the world in microcosm - people follow reputation rather than reason, so they fix themselves into wrong positions and reject anything that's put before them that shows up their error. That is just how most people are, and it's why the world is always stuck in such a mess.


A few comments on backwards time travel

With Spacetime models, it may be possible for some things to peel off out of the block universe and loop back to re-enter it further back in "time", but this again reveals faults with the thinking of most physicists. If there is no Newtonian time and the only kind of time in the model is the "time" dimension, then an object which loops back in time and interacts with other things there will appear to cause some of their subsequent behaviour and will ultimately affect its own behaviour, with some of that causation feeding into it taking its loop back in time - we are seeing circular causality where X causes Y and Y then causes X. That cannot be genuine causation, and indeed it isn't, for there is no causation in that model at all - it is a static block which was never generated and merely exists eternally with all the apparent causation written through it by magic alone. Such a model would even appear to allow a dog to come back in time from the future and enter the block, then jump out of the block to come back in again and loop round and round with its own past becoming its own future: it's a magic dog that was never created, never ages, and which must forget anything it learns so that it can learn it again on the next lap. You might say that that is too bizarre and can be banned while still arguing that a dog could make one loop back in time before travelling alongside the original dog until the original leaves it to loop back into the past while the already-looped dog keeps going, but the circular causality is still in there and is exactly like the former dog example: that loop of causation is as magical as the eternally looping dog. I remind you again though that the travel is an illusion in this model (Einstein's model) as there is no movement whatsoever and nothing ever goes or loops anywhere - it is a universe that cannot ever have been created in cause-and-effect order and therefore the whole of it can only exist by magic (even without considering fanciful embellishments like looping dogs).

If we allow time to run though (to enable the actual movement of objects though the block and thus allow it to be generated rationally rather than by magic), we have brought in a Newtonian time, and considering backwards time travel helps to show this up even more clearly. We can now imagine a more functional block universe running in a model as close as possible to Einstein's as possible (without losing the functionality that we've just had to bring in to make it work). We can now send an object on a loop back in time and it can re-enter the block further back in the "past". As it interacts with other objects in the past though, it will have to change "history" by causing things to happen which hadn't originally done so, and that means the content of the block at that location will need to realign with the new events that are taking place there. This will cause a cascade of new event-meshing failures for a time and the resulting mess will propogate forwards in "time" through the block from there, gradually settling down to a new stable "history". The changes may then lead to the object that caused all these changes to be unable to take the loop back in time, so that will soon lead to it failing to re-enter the block lower down, thereby eliminating all the new changes down there that led to the big reorganisation, so the block will now have to revert to its orignal form with all those changes gradually undoing themselves again. This will involve a further cascade of event-meshing failure as the content of the block adjusts again, gradually settling down back into its original pattern, at which point we set the scenes for the object that went back in time earlier and then stopped doing so to start doing so again... We thus end up with an eternal oscillation between these two temporarily stable states for that part of the "history" of the block. All of these changes in the content of the block are necessarily taking place under Newtonian time. So, backwards time travel is impossible in Spacetime unless you add Newtonian time to it, and even then it creates a mess. Without that Newtonian time though, all you can have is the static block that was never generated and which, if you want to add backwards time travel into it, also has apparent circular causality added to its fake causality.


Twitter discussion with cosmologist

Twitter isn't an ideal place to hold a discussion, but here's the key action from my conversation with the cosmologist mentioned above (starting beyond the part where he made more wayward comments due to his skepticism that he was looking at anything worthwhile - these poor people encounter a lot of nutters and are totally unprepared for meeting with anyone attacking relativity who can actually reason properly and who has researched things in depth):-

Ask a top programmer to create an SR/GR simulation without bringing in an external time. It's impossible.

As someone who does relativistic simulation, you are incorrect. (The first phrase refers to himself.)

Show me your code and I'll show you where you've smuggled in an external time.

Here are a couple of my papers. Tell me where: ... (Links to two PDF files followed.)

If you think it's a program, what hardware are you running it on? If your brain is the hardware, how are you timing events?

Those papers used ode45 in Matlab running under OS X or Linux desktops and laptops.

I need to see what you're putting into ode45 and what you're getting out.

I need to see if the cheating's happening in the software or if it's outside of the software in the way you're using it.

Here you go. Here's the uniformly accelerating observer in flat space-time in matlab - the works.

ps- changing to other indertial frame just means changing the initial conditions on the 4-velocity components. All lovely relativity.

So you're talking about a graph plotter and not a simulation. My interactive diagram is a simulation. Your graph isn't.

The equations were integrated numerical - how is this not a simulation?

A simulation shows a graph being produced over time, so you can see how the events progress. Showing that progress is vital.

If you run simulation of rocket journey out and back with stay-at-home for comparison, it shows coordination of events.

Graph misses out all that & doesn't show up event-meshing failures or different relative time rates for different players.

If I turn my simulation into a graph plotter, after simulation I have graph which has lost all record of event coordination.

All three modes of my simulation would produce identical graph - all the key event coordination data is lost.

Not. The integration is the simulation, the plotting just shows the result. I could animate it, but it doesn't need it.

(Note: I'm not sure which of the above tweets the "Not" is responding to - this isn't a directly linear conversation and the linkage is not properly preserved by Twitter, or at least is not presented in such a way that you can see it. However, I think the "Not" is a response to "Showing that progress is vital". "The integration is the simulation" - this takes no account of the order in which different points are plotted out and how this is coordinated point by point between different players moving relative to each other, so he isn't doing a simulation at all. He appears to have very little understanding of what a simulation is.)

That is what it is showing, the position as a function of time by solving the relativistic equations. The line is a collection of...

...individual points, as a function of the proper time. When you say simulation, you mean movie. Not synonymous.

(Note: my simulation is not a movie, but you can produce hundreds of different movies from it by changing mode and frame, and astronomical numbers of different movies if you change frame in the middle of making a movie. The simulation keeps track of where things are in Spacetime as events evolve, and the display shows them from one perspective at a time. In the second mode it has to recalculate the positions every time you switch frame, and the universe would have to do the same if it is to have a non-magical mechanism for coordinating events. His "simulation" is on the other side of being a movie - it produces a still image of the final result, showing an eternal block without showing how it was generated, and if you look into how the program draws these graphs, it will plot the path of one object, then plot the path of another, etc., not caring about the coordination of the extension of these paths as they grow up the diagram.)

It would show you the proper time measured would be different for each observer. This is done by undergraduates in research projects.

"different relative rate" - you mean time passes differently for different observers. Welcome to relativity.

Events are just locations (t,x,y,z) - they don't "fail to mesh". The proper time, tau, is different, events are not.

(Note: he still doesn't understand that we're interested in how the block universe is generated and not in the illusion that is written into the block after that generation phase is complete. There has to be a generation phase to build the block because if there isn't, the whole thing exists as it does by magic alone, and all the apparent causality written through it is a mere fiction as nothing there has ever had the chance to cause anything. If he produces a graph showing a rocket leaving the Earth at high speed and then returning, he would look at the graph and see the two lines meeting up at the right Spacetime location at the top and would say, "Job done!" He doesn't care whether they both arrive there at the same time or not, because he has failed to notice that real time is missing from his model, and he therefore ignores it. If he sticks to the rules of the model, he has a rocket taking a shortcut into the future and reaching the Spacetime location where the reunion takes place before the Earth can reach that location, but the graph shows them meeting at the correct place, so he sees no problem with the Earth somehow managing to get there in time even though it can't. Alternatively, if he runs time at a slower rate for the rocket, which involves breaking the rules of the model, he can make them arrive at the reunion point at the same time, but he is then using an external time to coordinate this, and he has to do the calculations on the basis of a frame which serves as an absolute frame, while other frames for the calculations would produce different accounts of events which contradict it. How can he be made to understand all this?)

You're still missing the point, relying on magic to coordinate the events with contradictions simply ignored.

My simulation runs under three models of time and shows how universe can/can't be generated rationally in them.

You have no coordination mechanism (other than by cheating).

In GR example, ships repeatedly reunited at construction front of universe and sharing Spacetime location: just like movie.

(Note: Twitter is obviously very limiting, making it hard to provide full explanations, so you have to rely on the other person being able to fill in the gaps, but this doesn't always happen. What he should be able to work out at this point is that if we have a series of events where a rocket repeatedly moves away from a planet at high speed and returns each time,or if it repeatedly goes off to sit by a black hole for a time and returns each time, we have a series of events where the two things, the rocket and the planet, share the same Spacetime location and do so simultaneously. Each reunion of these two players happens before the next reunion and after the one before - there is a sequence of events here, and the two players are at the construction front of the universe at each of these times during the construction phase of the universe. We aren't so interested in the way they hang around afterwards at those locations in an eternal block, but only care about what happens where the block is being generated. If we name all these reunion points in alphabetical order, we can see that A happens before B, and B before C, etc., and when they reach any of these points, all the events before that have happened while the ones after it have not - when they arrive at D, that is the cutting edge of the growth of the block and there is no existence yet of their reunion at E. They both arrive later at E exactly as the construction front reaches E, and the construction front has run along the paths of both these players. We can validly run their progress as a movie if we wish, and we can do so for both their paths, because any path can be run as a movie. Whenever the rocket leaves the planet, it leaves from a point such as D where we know that the event is simultaneous for both players. When the rocket reaches E, both players reach that point simultaneously. We have three movies to stitch together, and we know that the rocket's first leg's movie starts at the same time as the Earth's movie, and that the rocket's second leg's movie ends at the same time as the Earth's movie. We can't pin down where the rocket turned round, but to fit the movies together we know that we have to run the rocket's movies with time running slowed down on average. There are an infinite number of different possible ways of coordinating this (and they all contradict each other), but at least one of them must be right - there must be a combined movie which matches up with the way in which the construction fronts actually coordinated their progress in constructing the block. Each path must have a construction front running along it, and to deny that is to fail to understand the entire issue.)

Time must be running slow for the one that goes near black hole - it is not taking a shortcut into the future.

That slowing requires coordination with an external time. Without it you have event-meshing failure.

There is no "construction front of universe". Alas, I think we are done as I don't think you understand relativity. Cheers.

(And so at this point we see that he still doesn't understand that he cannot generate a universe in rational cause-and-effect order without a construction front. He is banning the generation of the block by any means other than magic. But this is what they all do: I have yet to find any physics expert who can get past this point. Of course, it's quite possible that he objects to the very idea of a block universe and rejects the idea of a construction front on that basis, but, if that's the case, he's making two errors: SR/GR demands that there is a block universe in order for it to have any possibility of functioning correctly in any phase of its existence, while what I'm describing in relation to the construction phase applies equally to an adapted SR/GR which doesn't rely on a block universe because it has already broken the rules of the model by bringing in an external time to coordinate the action on all paths. The problem is that almost everyone in physics has built their understanding upon an incomplete and faulty foundation because they have never been taken through the basics of relativity properly to be shown where it breaks - they are instead programmed to shut down their thinking to the point where they become incapable of seeing the glaring faults, and by the time they've learned enough to regard themselves as experts they then think it's beneath them to look back down at the foundations to check whether they've really built their expertise on top of something solid. The result is that they all gaily charge on with a fundamental error in their thinking, imagining that an invalidated theory is valid while at the same time ridiculing a rival theory which has not been invalidated. That is what this page aims to address, because, for the last hundred years, our universities have been churning out physicists who are selected on their ability to conform to required beliefs based on an error while completely disregarding reason, and any who put reason first are simply driven right out of the field.)

If the conversation isn't over, I'll add more of it here later. I've got files of other conversations with physics experts of the kind who run the top physics forums which display extreme lunacy, but that freak show can wait - at the moment we're dealing with a genuine cosmologist who gives us a rather more sane representation of where physics is today.

Well, he's definitely gone: he knows the advanced stuff, but he's failed on the basics. That's no surprise though, because none of these people have the courage to step away from the herd and to be ridiculed by them for failing to comply with the religious beliefs demanded of them by the clergy.

Well, I suppose it's time for the freak show then. We should start with this spectaclar p.m. conversation which had 17 people looking in on it by the end (without my invitation, so it quite clearly ceased to be a private conversation and can thus be made available here quite legitimately: they set the precedent for that themselves). This gang of "experts" argue that mode 2 is Einstein's model and that it doesn't have an external time smuggled into it to make it work (and that it doesn't generate contradictions either), but they are clearly hopelessly out of their depth and too dim to realise it. Here's a link to Dropbox where you can collect the three browser files and the three folders that go with them: conversation at physicsforums. The folders have to be unzipped, but all you need do is open them and copy the folder hiding within each to the same place as you downloaded the three browser files so that when the files are opened they will display everything properly with none of the content missing, and you will definitely want to see them in their full glory. The first page to read is the one called Misinformation3, and it has that name because earlier versions of page 1 also exist but contain fewer posts. Pages 2 and 3 are more clearly labelled as they contain the word "page", and again I have several versions of page 2 with fewer posts in them. I nearly slipped up with the third page as I only made one copy, captured moments before I was banned from the forum. And yes, that's how it works: they ban anyone who wins an argument against the Church of Einstein, and they won't allow anyone to discuss this page or the ideas it puts across because they know they have absolutely no way of countering the argument. They have lost, but instead of admitting it, they just try to suppress this and hope no one will ever find out. Go to physicsforums and try it out for yourself: ask them how they handle the problems with Einstein's model that I've discussed here and see how quickly they delete and ban you, but don't use your existing account (if you have one) as you won't want to lose it: use a false name and a disposable email address to set up a new account specially for the purpose (and you can use a different browser too if you're permanently signed in through your existing account: the cookies are only tied to a single browser). It is extraordinary that the leading physics forum has banned the discussion of some key parts of physics, but we are up against a mafia which does not play ball. Other forums are less fascist, but most will just set a few of their house trolls loose on any thread where you try to discuss this stuff while the better minds keep well out of the way because they know they have no answers to the argument: it certainly won't be referred on up to any professional physicists connected with the forum.

So, here's the situation we're in now: Einstein's model has been roundly disproved, but it appears to be impossible to inform the world because there is a wall of idiots ten miles deep standing in the way whose sole task is to defend all the current beliefs linked to venerated deities. If you have understood everything on this page, you will have see clearly that the only Spacetime models that are potenitally viable all have Newtonian time in them, so Einstein's attempt to eliminate Newtonian time has failed dismally. You will also realise that having two kinds of time in a model is far from elegant (i.e. it's contrived in the extreme), and that LET is much simpler explanation which is many times more likely to be a representation of the real universe.


Another horrid problem for SR/GR

Any attempt to coordinate events in such a way as to avoid event-meshing failure is going to run into extreme difficulty in another way, and this applies to both mode 2 and mode 3 in the interactive diagram. In LET, if little errors creep into the paths which objects take as they wander through space, they simply drift off their projected paths. however, if you have a time dimension, as in SR and GR, while similar errors which make objects wander about a fraction in the space dimensions will cause no real problem, any error at all with the time dimension will automatically lead to event-meshing failure if the coordination allows an object to get ahead of another in time. The coordination has to be absolutely perfect at all times to avoid this, all controlled by a mechanism that maintains this total coordination across the whole of space, even where it's expanding. That is one heck of a big ask. LET doesn't suffer from this problem because if time is out of phase in different locations for any reason, it doesn't matter a jot as things will always mesh together correctly regardless. This means that even if you bring in an external time and absolute frame to try to make a Spacetime structure viable (and duplicate the entirety of it for all possible frames so that each can function as if it is an absolute frame while contradicting all the others), it will still break on this. So, the only thing the believers have any right to cling to is the model in which event-meshing failure is tolerated during the construction phase and the "future" eventually changes as the block settles down to create the illusion that it "runs" under Einstein's rules, but a proper understanding of that model reveals that its time dimension is not time at all, while real time is Newtonian.


Thought Experiments

I'm going to finish by looking at a few thought experiments which come out of failed attempts to detect movement through the fabric of space.

The square room in a rocket

Imagine a square room in a rocket with a lamp in the middle. If the rocket isn't moving, all four (or all six) of its walls will be equally well lit (although they'll be dimmer in the corners as the light will have spread out more by the time it reaches into them). But what happens if you move the rocket along at high speed? It ought to take a lot longer for the light from the lamp to reach the front wall of the room which is rushing away from where the light was emitted, and that means it should be spreading out far more before it hits the wall, making that wall many times dimmer. Also, the back wall is rushing towards the lamp, so the light will obviously hit it before it's had the chance to spread out as much as it would do in a stationary rocket, thereby making that wall much brighter. Well, that's what you'd think would happen, but in reality the walls of the room will always remain equally well lit regardless of the speed of travel, thereby preventing you from using a light meter to work out your speed of travel.
indentTo explain why this happens, it's helpful to imagine a gun pointing at 90 degrees out of the window of a moving car. The target is set up on the roof of another car which is driving in the same direction as the first and level with it, perhaps several lanes away across a wide, straight motorway. When the bullet travels through the barrel of the gun, the gun is moving with the car, so that sideways movement is transferred to the bullet to enable it to hit the target even though the target may have moved several metres further along the road before the bullet reaches it - the bullet clearly does not travel at 90 degrees to the road from where it left the gun, but it moves forwards at the same time, keeping pace with the cars, only losing a little ground due to drag. If you did this experiment on the moon with no air to get in the way, the accuracy of shooting the target on a moving car from a moving car (with both moving at the same speed and in the same direction) would be exactly the same as shooting the target on a stationary car from a stationary car (assuming a perfectly smooth road, perfectly straight driving, no vibration, etc.). Let's now transfer this knowledge to light. When light is emitted from the moving laser in the Michelson Morley experiment above, almost exactly the same thing happens - the light actually leaves the laser at 60 degrees to the vertical instead of moving vertically up the screen (assuming that the laser is moving at 86.6% the speed of light - other speeds will result in all manner of different angles). If you look at the line of dots marking out the paths that the light follows, you'll see why this is the case - the green dot and the first of the blue ones clearly show the path the light actually took through the moving laser. There is a difference between light and bullets though, and that is that the movement of the car adds speed to the bullet, but light doesn't pick up any extra speed from the movement of the laser - it is only the direction it travels in that is changed by the laser's movement.
indentSo, what does that tell us about how the moving room is illuminated? Well, it reveals that a moving lamp will throw more of its light forwards than backwards, because the light which the lamp thinks it's sending out sideways at 90 degrees to its direction of travel is actually going to be sent out forwards, in this case at 30 degrees to the lamp's direction of travel. This concentration forwards of the light and reduction in the amount of light sent backwards helps to explain how the walls of the room remain equally well lit at any speed, though it only works out properly if the room is also contracted in length: if the rocket is moving at 86.6% the speed of light, the room will contract to half its normal length. This act of contraction will change the directions in which light is emitted such that it still ends up illuminating the room correctly.

Optical effects

One of my failed attempts to find a flaw with relativity gives a particularly interesting picture of how relativity works. Imagine a disc lying on the floor with four points on it round the edge labelled as North, East, South and West. There is a straight line drawn across the disc from North to South, and another straight line crossing it at right angles connecting West to East. At each of the four named points there is a post sticking up in the air perpendicular to the disc. At the center of the disc where the two lines cross, there is an air-filled glass bubble. I have just described a model of a peculiar space ship, but now I want you to imagine that you are in the real version of this ship, travelling through space at 86.6% the speed of light, the North edge of the disc leading the way. At this very high speed, the disc has been compressed to half its normal length, though this is not noticeable to you as you sit inside the glass bubble. The North and South posts are only half as far away from you as the East and West posts, but they all look to you as if they are just as far away as each other. The light from the North post will reach you quickest because you are travelling straight towards it at close to the speed that the light is moving towards you. The light from the East and West posts will take much longer to reach you, and the light from the South post will take longest of all. The result of this means that the North post should look bigger and closer than the East and West posts, and the South post should look tiny and distant: you are effectively looking at the South post from eight to nine times as far away as its actual physical distance. And yet all the posts look the same size as each other! How can this be? Well, the focal length of your eyes (or of any camera you might use) is also affected by the speed of travel: when you look towards the North post, your eyes behave like wide-angle lenses, but when you look at the South post they turn into telephoto lenses. This happens because the distance from lens to retina (or lens to film-plane) is affected by your speed of travel in exactly the same way as the distance from the post to your eye: if you are looking forwards, the light will effectively only have to travel just over half the distance from the lens to your retina before it actually hits your retina (your retina moves towards it and meets it just short of half way); whereas if you are looking backwards, the light will have to travel eight to nine times the distance between lens and retina before it can complete the journey from lens to retina (as the retina keeps moving away from it and it takes a long time for it to catch up).
indentWhat happens then if we switch on a light at the South post pointing towards the glass bubble and a second light of equal brightness at the North post pointing towards the glass bubble from the other direction? The light from the North post doesn't spread out much before it meets the glass bubble, but the light from the South post spreads out a great deal before it catches up with the glass bubble. The result of this is that the North light ought to look much brighter than the South light and it should be possible to work out the the actual speed of the space ship through the fabric of space by comparing the brightness of the two lights. And yet it turns out that this is not the case either (as we can guess from our earlier thought experiment with the square room in a rocket). A moving light will actually put out more of its photons in the direction it is travelling in than the number of photons it emits in the other direction, probably because an orbiting electron in an atom takes longer to travel forwards past the nucleus of its atom than backwards, and assuming that electrons emit light in the direction in which they are travelling at the time, they are therefore more likely to launch a photon forwards. You might then think it would be possible to trick nature by using a mirror to bounce the stronger light backwards or the weaker light forwards, but this won't work either: a flat mirror which is moving can act as if it is curved because the wave front of the light is curved. If we're looking at the situation where light is chasing a moving mirror, the first part of the wave front will hit the mirror first, and then the rest of the wave front will hit progressively later, but the mirror will be moving progressively further away throughout this time, so it looks to the light as if the mirror is convex: this spreads out the reflected light and makes it weaken rapidly as it radiates backwards. If light hits a mirror which is moving towards it, the opposite will happen: the flat mirror will behave as if it is concave and will reflect the light back in the opposite direction in such a way that it radiates out less rapidly. A flat, moving mirror will only behave as if it is flat if the light hitting it has an absolutely straight wave front, such as light coming from infinity or a laser.

Rotation

It's also worth thinking about how length-contraction occurs in a rotating object like a disk. If a disk rotates quickly, the outer parts of it should length contract, and that will make them try to press inwards to compress the inner parts of the disk. In reality though, the disk would fly apart before this compression became significant. If the disk is moving really fast through space and is also rotating quickly, we would also have an uneven distribution of material on the disk as the material in the half going forwards faster would be length-contracted more than the material in the other half which may not be moving fast through space at all. Such a disk would actually fly to bits before such an effect would show up, but it must still happen. In the case of a rotating planet, this length contraction will mean that more material can be fitted into the circumference of the planet than would fit if the planet was not spinning.






























































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