[David Cooper]

Please follow the maths in my previous replies, which shows how any difference between out and return speeds  always leads to a mean round-trip speed less than the maximum. Therefore any discrepancy, however caused, will be revealed by comparing the measured two-way speed in orthogonal directions. If there is no discrepancy, then the one-way speed must equal the two-way speed.  No physics, no relativity, just algebra.

Please get up to speed with the maths - whenever a round trip involves a speed difference between the two directions, that always leads to a lower speed for the round trip which is cancelled out by the slowing of apparent time in the clock whose movement is causing that difference in speed for the two directions. You are cheating by using absolute time for your clock, and you aren't allowed to do that because you don't have an absolute-time clock on your plane (or at your ground stations).

I've worked out how to turn the counter-intuitive aspect of the other thought experiment into something that makes full sense. The best way to do it's to start with a long tube stationary in space and put a clock at either end with a mirror on the end of the second hand. We're going to play tennis with a photon. The clock at one end turns clockwise and the other anticlockwise (if we're looking at them from half way along the tube). Both clocks are covered by a screen with a hole in it, one clock having the hole in the 12 position and the other having its hole in the 6 position. The clocks are kept in sync by radio signals sent from half way along the tube. Our photon runs along the tube from the 12 of one clock as the tube rotates. By the time it reaches the other clock, the 6 position of that clock is in the right place for the photon to go through the hole and bounce off the mirror. When it gets back to the other clock, the tube has rotated 180 degrees again and the 12 position with the hole is back in place in time to bat the photon back again.

What happens when we move the tube lengthways at relativistic speed? Communication delays lead to the leading clock running behind time, which is good, because it takes light longer to reach it. If we replace the radio signals with an axle connecting to the hands of the clocks, it will twist (without stress) due to communication delays and provide the exact same lag of the leading clock. The trailing clock will run ahead of its expected schedule too for the same reason. If we turn the whole thing round so that the trailing clock becomes the lead clock (and the lead becomes the trailing), then the lag reverses and the photon continues to hit the holes every time and at the exact times when the mirrors are behind them (although we'll lose our photon while turning the tube round, so we'll need to introduce a new one - the same thing happens if the tube is not racing along through space, so the observed behaviour is identical for someone co-moving with the apparatus).

The tube rotates more slowly when it's moving through space at extreme speeds, so this enables the photon to travel from one mirror to the other with next to no rotation of the tube in one direction. The same photon making the return trip will take a very long time to cover the distance, but the tube will rotate nearly 360 degrees at a very slow rate of rotation and will have the hole and mirror in the exact place at the right time to hit the photon when it arrives. That is why it is counter-intuitive - you initially think it will need to twist more one way than the other and you know that it will actually twist the same amount in both directions, so when you think about light taking an extremely short time to pass through the apparatus in one direction and the extremely long time it will take to pass through it the other way, it feels as if it should be possible to detect the one-way speed of light with this experiment, but no - the twist moves the holes closer together for light moving one way through the apparatus while moving them further apart for the other direction, and the amount of rotation of the tube required to complete correct alignment varies in exactly the way required to hide the movement of the apparatus through space from the co-moving observer. This experiment illustrates beautifully the ability of relativity to keep the preferred frame hidden from us. The naive analysis leads to error and false belief systems - this experiment is promoted as a way to detect the one-way speed of light, but only by those who haven't thought it through properly or who deliberately seek to mislead.

[Edited to change 180 degrees to "nearly 360".]

[alancalverd]

I haven't used "absolute time" for my clock. I have used the same clock to measure the time taken for  a radio wave to transit in three different directions from the same point. Since none of the "ground" stations is moving with respect to the "air" station, any absolute movement of the entire system through the aether will result in a discrepancy between the measured speeds.

And why muck about with a perfectly good experiment that doesn't require the complicated "synchronisation" of anything?

And what  on earth do you mean by "moving the tube lengthways at relativistic speed"? Moving it with respect to what?   It's already travelling at a relativistic speed away from  distant galaxies!

[David Cooper]

I haven't used "absolute time" for my clock. I have used the same clock to measure the time taken for  a radio wave to transit in three different directions from the same point. Since none of the "ground" stations is moving with respect to the "air" station, any absolute movement of the entire system through the aether will result in a discrepancy between the measured speeds.

Any movement of the system through the fabric of space will slow your clocks and completely cancel out the effect that you wrongly believe your clocks would pick up.

And why muck about with a perfectly good experiment that doesn't require the complicated "synchronisation" of anything?

You claim the experiment can pick up the one-way speed of light, but I've explained why it can't by showing it to be directly equivalent to a pair of clocks, and we know very well how clocks behave in that kind of scenario - they do not allow you to detect the one-way speed of light because they run at different rates as you move them around and in a synchronised pair the lead one will lag behind the trailing one to the exact right extent to hide the system's movement through the fabric of space. Your analysis of the experiment is therefore incompetent.

And what  on earth do you mean by "moving the tube lengthways at relativistic speed"? Moving it with respect to what?   It's already travelling at a relativistic speed away from  distant galaxies!

Moving it relative to the fabric of space. The distant galaxies are moving away due to expansion of the fabric - the preferred frame shifts for different locations because of that expansion.

[guest4091]

n the around the world light path, the frame is the earth N-S pole. The initial position of the emitter-detector moves eastward at v. Light moves at c east and west.
Since the rotation speed is so small compared to c, a graphic proof is not possible, but we can use the coordinate transforms to prove
measured light speed is c for E and W, and all inertial frames.
With g=gamma:

x'=g(x-vt)
t'=g(t-xv/cc)

Substituting a=v/c, t=x=1/(1-a), c=1,

x'=g[1/(1-a)-a/(1-a)]=g
t'=g[1/(1-a)-a/(1-a)]=g

c'=x'/t'=1

The example in the graphic used a=.3, but all speeds yield the same result.
https://app.box.com/s/o84dfa03hu6e266toil3ccccvv3iffs5

[alancalverd]

You claim the experiment can pick up the one-way speed of light, but I've explained why it can't by showing it to be directly equivalent to a pair of clocks,

I cannot see how one clock is equivalent to a pair of clocks, or why (a+b)(a-b) is not equal to a²-b² in your universe.

[David Cooper]

Speed up the rotation. You can have a ring of fibre-optic cable rotate at close to c and make the light in it do multiple circuits too (because it'll do many laps in one direction for every lap in the other relative to the start-finish line). You can then attach tags to the cable in as many places as you like and assert that the speed of the light in the cable passes each of those tags at the same speed relative to it in both directions, but you can't make that work for a single frame of reference.

[David Cooper]

You claim the experiment can pick up the one-way speed of light, but I've explained why it can't by showing it to be directly equivalent to a pair of clocks,

I cannot see how one clock is equivalent to a pair of clocks,

You have a pair of discs with holes in them separated by 1km on either end of a long rotating axle. The rotation of the axle is a kind of clock, and because the two ends of it get out of phase with each other, each disc will behaves like an independent clock, and indeed the axle itself becomes an infinite series of independent clocks as it twists.

...or why (a+b)(a-b) is not equal to a²-b² in your universe.

If you move a light clock through space, it ticks more slowly, but if you measure its tick rate against another clock that's co-moving with it, you won't notice that it's ticking more slowly as that other clock will be slowed equally. It's only if you have a magic absolute-time clock that you'll be able to show up the slowing of the moving light clock. The result is that no matter how fast you move a system through the fabric of space, you'll never be able to detect that movement by looking at the clocks that are part of that system unless they records absolute time, but we don't have access to any clocks that can do that.

[David Cooper]

For Kris,

I've had a bit of time to look at Kris's proposed experiment properly and can see why it feels as if the experiment should work (meaning detect the one-way speed of light) as well as why it doesn't actually work.

To start with, let's look at a range of speeds of movement for the rod past the clocks. I've done my calculations based on the clocks being one metre apart instead of ten metres, and the rod too is one metre long. I'm also going to move the rod much faster than Kris would want to do so, but I'm doing this solely to make the numbers easier to work with and easier to understand - the pattern they reveal tells you all you need to know about what would happen with slower speeds. So, the speeds I'm using are 0.1c, 0.01c, 0.001c and 0.0001c, the slowest of these being apx 30km/s. In the four lines below, we have those speeds followed by the length of the 1m rod when length-contracted by moving at each speed, then the approximate amount of shortening of the rod in mm:-

0.1c, 0.9949874371m, 5mm
0.01c,  0.9999499987m, 0.05mm
0.001c, 0.9999995m, 0.0005mm (= 0.5 microns)
0.0001c, 0.999999995m, 0.000005mm (= 0.005 microns)

You can see form this that the length contraction figures are settling into a pattern of going down ten times more quickly than the speed, so by the time you get to speeds like one mm/s, there's almost no delay at all between the ends of the rods passing first and second clocks.

What happens though if we move the whole system at 0.866c through space? We need to convert the speeds for the rod carefully because it isn't a simple matter of adding each one to 0.866c - you do have to add them to 0.866, but you then have to adjust the result by dividing it by 1 plus 0.866 times the speed being added. So, the four new speeds for the rod passing the clocks are listed at the start of the four lines below. As before, they are followed by their contracted lengths in metres, then the amount of shortening of the rod in mm:-

0.8890328965c, 0.4578433236m, 42.5667637mm
0.868503939c, 0.495682265m, 4.317734962mm
0.8662751875c, 0.4995671122m, 0.4328878101mm
0.8660504016c, 0.4999567m, 0.04330002031mm (= 43.3 microns)

[Be aware that the contracted clock separation at 0.866c is to 0.5m, so you can see the lengths tending towards that.] The actual relative speeds of the rod to the clocks (as measured by someone stationary while the clocks move relative to him at 0.866c) are as follows:-

0.02300749272c
0.002478535216c
0.0002497837156c
0.00002499781557c

Let's name our two frames of reference to make it easier to refer to them when switching between them. The original frame is frame R (rest) and the other frame is frame M (moving). The numbers given in all the blocks of numbers above are of measurements made from frame R. For someone moving along with the clocks in the later four examples (someone who is at rest in frame M), the rod appears to be moving at 0.1c, 0.01c, 0.001c and 0.0001c in those same four cases, so these are frame M numbers. Notice that the actual relative speeds (the frame R ones for the moving system) are tending towards being a quarter of the perceived speeds (the frame M ones), and the reason for that is simple: length contraction means that the rod will move forward half as far though space in frame R to appear to have moved any given distance in frame M, but the functionality of the moving system has also been slowed to half speed, so the relative movement is doubly reduced, and that's why it's reduced to a quarter.

What we now need to do is calculate how long it will take for the leading end of the rod to reach clock B after the trailing end has reached clock A, so you'll see the numbers for that below. The first four lines are for the system stationary in frame R, while the second four lines are for the system moving at 0.866c in frame R. The speeds are in mm per nanosecond, and in each line they are followed by the gap to be closed (in mm), and then the time required to close them (in nanoseconds):-

30mm/ns, 5mm, 1/6ns
3mm/ns, 0.05mm, 1/60ns
0.3mm/ns, 0.0005mm, 1/600ns
0.03mm/ns, 0.000005mm, 1/6000ns

6.9mm/ns, 42.5667637mm, 6.109663242ns
0.74356mm/ns, 4.317734962mm, 5.806841361ns
0.074935mm/ns, 0.4328878101mm, 5.776844066ns
0.007499mm/ns, 0.04330002031mm, 5.774105922ns

So, you can see in the case of the first four (where the clocks are stationary in frame R), the times taken to close the gap tend towards zero, but in the other four cases (where the clocks are moving at 0.866c in frame R), they are tending to a different value somewhere around 5.77ns. What significance does this number have?

Light goes 1m in 3.3333333...ns, but the system is contracted to half its rest length, so we only need to cover half a metre. Light passes the rod more quickly in one direction than the other though. Why does this matter? Well, we want to compare our timings with the synchronisation of the clocks based on sending out a signal from the midpoint between them and how long  the delay is between that signal reaching clock A and reaching clock B. That signal only has to cover a gap of quarter of a metre, though the clocks are moving at 0.866c, so it will take longer to close that gap in one direction than the other. Are you thinking what I'm thinking yet? Might that delay be somewhere in the region of our 5.77ns?

We need to work out how long the synchronisation signal takes to travel from half way between the clocks to clock B (which is moving away from the light or radio signal) and then subtract the time that it takes to travel from half way between the clocks to clock A (which is moving towards the light or radio signal) as this will let us put a figure on how much the clocks are out of sync due to their high speed of movement through space. It takes 6.220084679ns for light to travel from half way between the clocks to clock B [and we get that number by multiplying a quarter of 3.333333333... by 1/(1-sin(60))], and it takes 0.4465819874ns for it to travel from half way between the clocks to clock A [which we get by multiplying a quarter of 3.3333333333... by 1/(1+sin(60))], so the clocks are out of sync. by 5.773502692ns.

So, the reason the experiment sounded as if it should work was that the stationary system has a moving rod with length-contraction acting on it which tends towards zero contraction as the speed of the rod is reduced, leading to simultaneous starting of the two clocks, but when the system is moving, the length-contraction of the rod follows a different pattern (even though it doesn't appear that way to a co-moving observer). Look at the figures for the stationary system with the shortening going from 5mm to a hundredth of that, then a ten thousandth, then a millionth. Then look at the figures for the moving system where it starts at 42mm (already a much greater gap, and this despite the clock separation distance being halved), then going to a tenth of 43, then a hundredth, and then a thousandth - the gap is reducing at a much gentler rate which keeps pace with the change in speed of the rod such that any slower speed you use will simply have the gap reduce in proportion, thereby needing the same length of time for the movement of the rod to close it and start the second clock. To a frame M observer, the clocks at rest in frame M will appear to be started just as simultaneously as the clocks at rest in frame R appear to a frame R observer. This means that if you build your experiment, it is guaranteed to produce a null result.

[Kris Kuitkowski]

Hi Kris,

If we run the experiment with the clocks stationary and the rod moving, the clocks will count how long it takes for light to reach them from the other clock after the rod starts them running. If we view this from a different frame of reference, we must see the clocks count up the same number of ticks. All frames of reference are believed to act exactly as if they are the one that represents an absolute frame, so no matter how fast the experiment runs through space, the clocks should count up the same values every time you run the experiment and make it impossible to measure the speed of the apparatus through space. Everything happening in the experiment must conform to the normal rules, so it cannot possibly work. And yet somehow, it still sounds as if it should work. There's something really weird going on that needs to be understood. Why does the thought experiment's argument sound so convincing? That's what I'm trying to explore, and I'll keep working on it until I can explain it.

Hi David,

Using this experiment, we do not even need synchronized clocks. Instead we can reflect the light from A' and B' to the photo sensor somewhere  in front and using digital oscilloscope measure the difference in arrival time of the two signals.
 I think it can be done with 2 lasers, 2 mirrors and one 10ghz digital oscilloscope

[David Cooper]

Hi Kris,

I know that we don't need synchronised clocks, but when you move the rod, it does length-contract a little and leads to a tiny delay in starting clock B after clock A has started running. If the whole system is moving (i.e. the clocks as well as the rod) then the length contraction on the rod will be greater relative to the length-contraction on whatever it is that maintains the separation distance between the clocks, and that means there's a greater delay before clock B is started - a delay which guarantees that the clocks will always produce the same numbers when you run your experiment regardless of how fast the system is moving through space. The faster the system moves, the greater the delay there will be before clock B is started, but if you're co-moving with the clocks, you will not detect any increase in that delay at all because you will have a very different view of which events are simultaneous, and that happens because of the way your clocks are synchronised in that frame and the delays in getting signals from one place to another. The calculations show that the experiment will produce a null result, and that doesn't make it an attractive experiment to put a lot of time and money into.

[Kris Kuitkowski]

Hi David,
1.The experiment could be done with lasers moving at half speed (-v/2) towards the rod which will move with the speed v/2.
Any length contraction of the rod should be the same as contraction of the lasers mounting.
2. the experiment can be run using different speeds of the rod and separation of the signals can be compared. If the separation of the signals indeed increases with the speed, the length contraction should be taken into account. If not, we can ignore it.
3. We do not (and we can't) measure the length of the rod in some absolute rest frame. If we are moving at 0.866c through the space, we can't really know it, so our measurement is valid in our inertial frame (for example, the if we measure 1m,in our inertial frame 0.66c, in some inertial frame at absolute rest it would be 2m) Any length contraction should be also calculated in regard to our inertial frame.

[David Cooper]

Hi Kris,

1.The experiment could be done with lasers moving at half speed (-v/2) towards the rod which will move with the speed v/2.
Any length contraction of the rod should be the same as contraction of the lasers mounting.

I'm assuming these lasers are attached to the clocks and are used for sending light pulses from one clock to the other. We really have two rods, one with a clock at each end while the other is just a rod. Both rods are the same length as each other when they're stationary relative to each other. If by luck they are both stationary in space before we do the experiment, we can move one in one direction and the other in the opposite direction at the same speed, with the result that both will contract to the same extent. However, if they were both moving through space at high speed when they were stationary relative to each other, when we move them past each other to do the experiment, one of them will contract a bit more while the other will lengthen a bit (because they were both contracted already). We won't know which rod is extending and which is contracting, but whichever way round it is, we will get a null result. If the rod with the clocks is the one that contracts while the other rod extends (or uncontracts a bit), clock B will start running before clock A, but the light signal from clock B will take much longer to reach clock A and the light from clock A will get to clock B more quickly such that both clocks always stop with the same two times recorded on them.

You can test this for yourself by crunching the numbers in the way that I did in post #67. Pick speeds for the two rods and work out the length-contraction on them, first on the basis that the system is at rest, then on the basis that it's moving at high speed to the right, and then on the basis that it's moving at high speed to the left. Then work out how long light will take to reach one clock from the other. If you can't produce numbers that show that the experiment could produce anything other than a null result, I don't think anyone sane will want to put any time or money into building it, so you're going to have to do some maths to test your idea and look to see if you can find any circumstance in which a different result could somehow emerge from it. I looked at a stationary system and a system moving at 0.866c, but I didn't test -0.866c, so that might be a good place for you to start. When doing the calculations, make sure you don't type in approximate values when you reuse results of one part of a calculation in the next - store them in memory and use them again from there as you'll need to maintain their high precision. It helps if your calculator has multiple memories available on it.

[Kris Kuitkowski]

Hi David,
I was thinking about your analysis in #67.
I think your calculations are right but your reasoning is incorrect. If you were to measure length contraction of the moving rod in the inertial frame of the lasers, you have to do the calculation in relation to this frame. Regardless how fast the whole setup would be travelling through the space, you can only make your measurements from the point of view of your inertial frame. Even if you travelling at .999c you perceive the rod travelling at say 3m/s and length contraction will be d(sqrt(1-(3m/s)^2)/c^2) ;  your calculations would be only valid if you were to make the measurement from within the rest frame if you believe you were moving at 0.86c  (or the frame which is moving with the speed of 0.86c relative to you).This would require you to establish an absolute rest frame, which according to current knowledge, is impossible.

[guest4091]

Hi David,
I was thinking about your analysis in #67.
I think your calculations are right but your reasoning is incorrect. If you were to measure length contraction of the moving rod in the inertial frame of the lasers, you have to do the calculation in relation to this frame. Regardless how fast the whole setup would be travelling through the space, you can only make your measurements from the point of view of your inertial frame. Even if you travelling at .999c you perceive the rod travelling at say 3m/s and length contraction will be d(sqrt(1-(3m/s)^2)/c^2) ;  your calculations would be only valid if you were to make the measurement from within the rest frame if you believe you were moving at 0.86c  (or the frame which is moving with the speed of 0.86c relative to you).This would require you to establish an absolute rest frame, which according to current knowledge, is impossible.

A signal from the midpoint of A-B when aligned to the midpoint of A'-B', synchs each pair of clocks dirrently depending on speed. The only time the axis of simultaneiy for each align is when they have the same speed, i.e. at rest relative to the other, a trivial problem.
If you have ever tried to square a circle, you should see the futility.

[David Cooper]

Hi David,
I was thinking about your analysis in #67.
I think your calculations are right but your reasoning is incorrect. If you were to measure length contraction of the moving rod in the inertial frame of the lasers, you have to do the calculation in relation to this frame.

Which means that if you assume the lasers and clocks are stationary, you will measure the rod to be length-contracted to such a small extent that the clocks would start practically simultaneously and will record the same time as each other by the time the light from the other clock reaches them, although clock A may record a tiny amount of extra time than clock B if the clocks are sufficiently accurate for the tiny amount of length-contraction acting on the rod to show up. However, if the clocks and lasers are actually moving at 0.866c, there will be a lot more length-contraction acting on the rod relative to the length-contraction acting on the clock separation and a big delay between the clock A starting to count up from zero and clock B starting to do the same. Crucially though, it won't look like that at all to an observer co-moving with the clocks because his measurements of the rod will not reveal to him the true length, and he will see both clocks start counting simultaneously, making it appear to him as if the system is stationary.

This would require you to establish an absolute rest frame, which according to current knowledge, is impossible.

You don't need to identify an absolute rest frame because all frames behave as if they are that absolute rest frame to anyone doing experiments based on that frame. If you happen to be moving at 0.866c and observe a system which is stationary in the absolute rest frame, it would look to you as if it was moving at 0.866c and you would measure the same length-contraction on system and amplified length-contraction on the rod as someone stationary in the absolute frame who measures the behaviour of an identical set of apparatus moving at 0.866c. That's what relativity does - it hides all the differences from us and does so in such a systematic way that all attempts to find an asymmetry have ended in failure. I've been caught out by it several times, on each occasion thinking I'd identified something that would enable an experiment to show up a difference in the behaviour of different frames in some way, but each time it evaporated away as I found I'd made incorrect assumptions about some key part of it. The maths of relativity is astonishing, and so far it has had an answer to every challenge anyone has thrown at it - it simply refuses to let us measure the one-way speed of light.

[Kris Kuitkowski]

Which means that if you assume the lasers and clocks are stationary, you will measure the rod to be length-contracted to such a small extent that the clocks would start practically simultaneously and will record the same time as each other by the time the light from the other clock reaches them, although clock A may record a tiny amount of extra time than clock B if the clocks are sufficiently accurate for the tiny amount of length-contraction acting on the rod to show up. However, if the clocks and lasers are actually moving at 0.866c, there will be a lot more length-contraction acting on the rod relative to the length-contraction acting on the clock separation and a big delay between the clock A starting to count up from zero and clock B starting to do the same. Crucially though, it won't look like that at all to an observer co-moving with the clocks because his measurements of the rod will not reveal to him the true length, and he will see both clocks start counting simultaneously, making it appear to him as if the system is stationary.

So how you can calculate any length contraction? Let's say 2 spaceships passing each other at relative speed of 0.1c. How would you know they are not moving at 0.99c in relation to some distant galaxy?

[David Cooper]

So how you can calculate any length contraction? Let's say 2 spaceships passing each other at relative speed of 0.1c. How would you know they are not moving at 0.99c in relation to some distant galaxy?

You need to calculate the length contraction for them more than once using a range of different frames as the absolute frame for the base of the calculations, but it will only take a few different frames to show you that no frame can possibly give you a different end result when observers co-moving with the rockets make their measurements.

If your spaceships are passing each other at 0.1c and both are moving at the same speed relative to an absolute frame, you would use the speed 0.05c for both ships (perhaps calling one -0.05c) and calculate that they are both contracted to 0.9987492178 of their rest length.

When you take into account the fact that the chosen frame almost certainly isn't the absolute frame and decide to see what happens if that frame is actually moving at 0.99c through the real absolute frame (which will again be a guess as to which frame is the absolute frame), you then need to work out the speeds for the rockets by adding 0.05c to 0.99c (for the rocket moving faster through space) and then dividing the result by 1 + 0.05 x 0.99, so that rocket's actual speed through the new "absolute" frame will be 0.9909480705 (giving it a length of 0.134257506 times its rest length), while the other rocket's speed is found by subtracting 0.05 from 0.99 before dividing by 1 - 0.05 x 0.99, so that rocket's actual speed would be 0.9889531825 (giving it a length of 0.1482282117 times its rest length).

The rest length of anything moving at 0.99c is 0.1410673598 its rest length, so we can now look at the percentage changes in lengths, but to make it easier to describe this, I'll introduce a rod which has the same rest length as the two rockets, and the two rockets are passing it in opposite directions at what the rod measures as the same speed. In the original case where the system was stationary, the length contraction on both ships was to about 99.87% of the length of the rod. In the later case where the rod is moving at 0.99c and the rockets are passing it in opposite directions at what the rod again measures as the same speed, the rockets moving faster than the rod through space is contracted to about 95.17% of the length of the rod (which is itself severely contracted), while the rocket moving slower through space is contracted to about 105.1% of the length of the more-severely contracted rod. Those percentages are a lot further away from 100% than the 99.87% in the original case, but an observer co-moving with the rod wouldn't be able to measure that severity of extra contraction - he would measure both rockets as being 99.87% of the rod's length.

[Kris Kuitkowski]

Hi David,
Try to analyze the scenario at 0.86c when the rod is moving from opposite direction: according to your reasoning it will be expanded not contracted, by the same amount (very nearly)as contraction in the other direction. This would give you opportunity to measure your absolute frame as well as the contraction/expansion (which so far never been directly measured)
But to be absolutely sure there is no  tricks relativity is playing on you, you could devise an experiment with 2 rod moving in opposite directions. The difficulty would be to adjust the speeds and timings of the rods passing the lasers so the lasers would get through the slits on both rods simultaneously.(the light would either pass through both pair of slits or neither).  It could be challenging but not impossible.

[David Cooper]

Hi Kris,

In the case with the system moving at 0.866c, if the rod's moving a little faster than that and the clocks are moving a little slower, the rod will be shorter than the separation gap between the clocks, leading to clock A being started before clock B, whereas if the rod's moving a little slower than that and the clocks are moving a little faster, the rod will be longer than the separation gap between the clocks, leading to clock B being started before clock A. That delay will in both cases give a head start to whichever light signal has to move further through space to reach the other clock, and it will always be a big enough delay to ensure that the two clocks stop with the same times on them as if the system was stationary. You can check that by working out what the delay is and how long it will take the signals to go from each clock to the other - that's what I did at the end of post #67, so you need to learn how to do the same thing for any set of speeds that you want to work with for the parts of the apparatus. If you need help understanding how to apply the maths, I'll be happy to spell it out in more detail so that you can make sense of it, but you will have to crunch your own numbers from now on.

[Kris Kuitkowski]

In the case with the system moving at 0.866c, if the rod's moving a little faster than that and the clocks are moving a little slower, the rod will be shorter than the separation gap between the clocks, leading to clock A being started before clock B, whereas if the rod's moving a little slower than that and the clocks are moving a little faster, the rod will be longer than the separation gap between the clocks, leading to clock B being started before clock A. That delay will in both cases give a head start to whichever light signal has to move further through space to reach the other clock, and it will always be a big enough delay to ensure that the two clocks stop with the same times on them as if the system was stationary. You can check that by working out what the delay is and how long it will take the signals to go from each clock to the other - that's what I did at the end of post #67, so you need to learn how to do the same thing for any set of speeds that you want to work with for the parts of the apparatus. If you need help understanding how to apply the maths, I'll be happy to spell it out in more detail so that you can make sense of it, but you will have to crunch your own numbers from now on.

Hi David,
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. 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.
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 .
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.