[David Cooper]

Hi Kris,

The math is quite simple; the problem is that you are using bits and pieces from one theory and another bits from the reality which the same theory is explicitly excluding. The length contraction was a postulate in SR (never confirmed experimentally; some people still argue that it is not physical phenomenon) which is applicable to a moving body relative to another body which is "at rest". It is not possible to determine which body is in motion and which one is at rest.

The idea of length contraction came about as a result of the Michelson Morley experiment and was needed in order to account for the unexpected null result. All theories have to account for the result of that experiment. I have never seen any viable explanation of it other than physical length contraction, and although SR allows it to be a kind of illusion (because the object is not physically changed, but merely presented with a different orientation within a 4D geometry), it is no illusion within a 3D frame of reference where it is measured as contracted - you must be allowed to fit more objects into a given amount of space when they're contracted. The physical need for length contraction is also understood - we can measure the amount of relativistic mass added to particles in particle accelerators and see how at higher speeds the energy put in progressively adds more to the relativistic mass and less to the speed of the particle, thereby ensuring that it can never reach the speed of light. When you take relativistic mass into account, you'll find that orbits must length-contract as the system (e.g. planets going round a star) moves faster through space. The same length contraction must also occur within small objects - if a rod rotates about its centre such that one end is periodically moving faster through space than the other, the end that moves faster through space will lag behind where you might expect it to be, leading to the rod bending, but that bend will be undetectable to anyone co-moving with the rod - they will continue to measure it as straight at all times. This lagging of the forward movement automatically requires length-contraction as the material bunches up, but there is no compression force on it because the communication distances for forces between the particles of the rod are lengthened by the higher speed of movement. If you want to deny length-contraction, read through this thread https://www.thenakedscientists.com/forum/index.php?topic=70299.0 and join the conversation there - I will be happy to show you that without length-contraction you would need to have light move at superluminal speed to account for the null result of MMX - some photons would need to move faster than others which are going in the same direction, and some of them would even run into direct contradiction by requiring the same photon to overtake itself.

And there is no possibility of discovering if the whole system is in motion, so the only possibility to determine length contraction is to make arbitrary one frame at rest relative to another which is constant motion.

Why do you think you need to be able to discover whether the whole system's in motion? Obviously it would be nice to know that, but it is not necessary to find out in order to determine that a system will appear to behave the same way to any observers co-moving with it regardless of what speed it is moving at through space (and to determine that no observer moving at any other speed will be able to tell either).

Your idea that both the rod and the lasers may travel at some constant speed (0.86c) should not be detectable by any theoretical or practical means. However the fact the rod traveling in one direction is shortened and lengthened in opposite direction can be detected by measuring by one clock the time it takes for both edges of the rod to pass the laser .

The fact that the rod might be uncontracted or contracted, or that it might be contracted more when moving in one direction and contracted less when moving in the other direction, does not lead to it being possible to measure these contractions unless you can already identify an absolute frame of reference to use as the base for your measurements. You don't have that to use as a base though, so you can only make conditional measurements, and the conditional measurements that you make will be the same no matter what speed the system is actually moving at through space.
 

Let's say the rod is traveling in the direction of the system (which is moving with 0.86c). First front edge is passing A, then trailing edge. Because the rod is lengthened, it should take a bit more time in comparison to the rod of original length. Now we transport the rod in opposite direction. The rod is shortened, so the time it takes for both ends to pass point A will be a bit shorter. Carefully measuring the time difference (while monitoring rigorously the speed of the rod) we could calculate the absolute speed of the system.

If the rod has less contraction on it than the clocks, the leading end will start clock B before the trailing end starts clock A. If the rod has more contraction on it than the clocks, the trailing end will start clock A before the leading end starts clock B. In both cases, the trailing clock is started first, giving it extra time to tick up a high score before light from the other clock can reach it. The clocks will count up the same number of ticks as if the system was stationary and you will generate a null result from the experiment just like the MMX.

This is definitely invalidated by the theory which introduced length contraction in first place.

Your only hope of your experiment not producing a null result is if the MMX doesn't produce a null result.

[Kris Kuitkowski]

If the rod has less contraction on it than the clocks, the leading end will start clock B before the trailing end starts clock A. If the rod has more contraction on it than the clocks, the trailing end will start clock A before the leading end starts clock B. In both cases, the trailing clock is started first, giving it extra time to tick up a high score before light from the other clock can reach it. The clocks will count up the same number of ticks as if the system was stationary and you will generate a null result from the experiment just like the MMX.

That is not what I have said. Please read again. Or look at this example:

Let's have a pipe 1m diameter at 45 degrees to your 0.68c moving frame. The ball of 1m diameter is just moving through it . Any increase in physical dimension of the ball would stop the movement of the ball. If the ball is moving at 10(sqrt2)m/s, there will be 10m/s speed component parallel (or antiparallel) to your 0.68c frame. Following your reasoning the movement of the ball will be possible in only one direction through the pipe (with the component 10m/s antiparallel to the speed of your 0.68c frame)

[David Cooper]

That is not what I have said. Please read again.

Let's say the rod is traveling in the direction of the system (which is moving with 0.86c). First front edge is passing A, then trailing edge. Because the rod is lengthened, it should take a bit more time in comparison to the rod of original length. Now we transport the rod in opposite direction. The rod is shortened, so the time it takes for both ends to pass point A will be a bit shorter. Carefully measuring the time difference (while monitoring rigorously the speed of the rod) we could calculate the absolute speed of the system. This is definitely invalidated by the theory which introduced length contraction in first place.

Sorry - I thought you'd got muddled when you referred to the two ends of the rod passing clock A, so I didn't realise you were exploring a new aspect of this. Remember that with the three rod system moving at 0.99c, the true speeds of travel of a moving rod in opposite directions relative to the middle rod (which is moving at 0.99c) were not 0.05c each way relative to the clocks, but 0.0009480705 and 0.001046817, so when the rod is less contracted (by moving less quickly through space) it is moving faster relative to the middle rod, while when more contracted (by faster movement through space) it is moving more slowly relative to the middle rod, and that means the timings that you measure for it passing one point on the middle rod will be identical to a local clock on the middle rod.

Or look at this example:

Let's have a pipe 1m diameter at 45 degrees to your 0.68c moving frame. The ball of 1m diameter is just moving through it . Any increase in physical dimension of the ball would stop the movement of the ball. If the ball is moving at 10(sqrt2)m/s, there will be 10m/s speed component parallel (or antiparallel) to your 0.68c frame. Following your reasoning the movement of the ball will be possible in only one direction through the pipe (with the component 10m/s antiparallel to the speed of your 0.68c frame)

I'm not sure I can make full sense of your description (does antiparallel mean perpendicular?), but what I can do is show you a program (which runs using JavaScript on a webpage) that should help you understand this kind of scenario, and you can then program in your own objects if you want to test your own numbers. Use a proper computer rather than a tablet or phone because it works best if you control it using a keyboard. Open http://www.magicschoolbook.com/science/ref-frame-camera.htm in another tab, then program in the following series of objects (copy these numbers onto a piece of paper first to make this easier, and be careful not to make any mistakes as you can't correct them afterwards - take your time and tick them on the piece of paper as you go so that you don't lose your place, and don't click the "reset" button unless you want to delete the objects to start again):-

0, 0, 180, 220, 220, 180, -180, -220, -220, -180, 0, 0, 0
0, 0, 80, 120, 120, 80, -80, -120, -120, -80, 0, 0, 0

That gives you eight white dots to indicate the pipe at 45 degrees. Now you need to add three square "balls" (you can imagine each square to contain a ball, and the way the square distorts should enable you to visualise how the ball distorts, or alternatively you can simply regard them as cubes of ice sliding through a square-section tube). You would be wise to highlight and copy the value 0.6123724357 first so that you can paste it into the dialogue box the four times when you need it (but be aware that the second two times you also need to make it negative):-

0, 0, 40, 0, 0, 40, -40. 0, 0, -40, 0, 0, 1
0, 0, 30, -10, 10, -30, -30, 10, -10, 30, 0.6123724357, 0.6123724357, 2
0, 0, 30, -10, 10, -30, -30, 10, -10, 30, -0.6123724357, -0.6123724357, 4

You now have three squares, one stationary and two moving at 0.866c in opposite directions (which is the speed that the vectors -0.6124... combine to give you). The moving squares are shown contracted to half their rest length. When you click the "start/stop" button on the screen (or press the "S" key on the keyboard), you'll see the two length-contracted squares move in opposite directions along the pipe. (You can click the "direction" button or press the "D" key to run them backwards if you want to get them back into the pipe once they've left it.)

What you should do next though is change the frame of reference you're viewing them from, and some frames are already tied to the number keys for you, so if you press "3", for example, you'll get to a frame that's moving at 0.866c on the Y axis direction, although the display remains centred on the pipe at all times to stop it moving down and off the bottom of the screen. If you click on "Set Frame velocity" you can choose a frame of reference of your own by typing in the required vectors for its speed, so using 0.6123724357 for both vectors will show you the green "ball" as it would appear to someone co-moving with it, thereby removing all the contraction from it, while anything that isn't co-moving with that "ball" will show the amount of length-contraction that it should be seen to have from that frame.

The pipe isn't moving, of course, but with relativity, when you observe it from a different frame it will look and behave exactly as if it is moving. To check that this is the case, you can move the "balls" back to where they started, select a frame such as X = 0, Y = -0.866 and then note down the numbers displayed below the action (just above the main text on the page) for each of the five objects (the first two of which are the pipe). You can use these values to type in the objects from scratch such that the pipe will move at 0.866c upwards through the absolute frame. When you then switch to displaying the frame X = 0, Y = 0.866 you'll see it look identical to what you originally programmed in with the system stationary in the absolute frame, showing you the symmetry of the behaviour of different frames, all of them looking just like that absolute frame if you make the system stationary in it and then switch away from that frame to see how it warps, and all the warping will look just the same as it did before. There are never any differences that could enable any observer co-moving with any object to measure different values for the system moving at different speeds through space. Importantly, this program was written specifically for Lorentz Ether Theory using an absolute frame - all the maths that runs it is designed to make all the moves within that absolute frame before converting to how things would appear from other frames of reference, and it's using radically different maths from any program of this kind that someone in the SR camp might write, but what it displays on the screen at the end of the process is identical.