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AETHERIAN LENGTH CONTRACTION. If the aetherwind is 00 km/s, ie if the observer is in the absolute frame, then Mac, an aetherist, will agree with Einstein's 0.014 mm. Using the same factor.
AETHERWIND. But if the aetherwind is blowing at 500 km/s vertically upwards through the observer then Mac will say that the train will appear shorter by 0.140 mm, ie approx 10 times the Einsteinian number. This is because Mac draws a triangle 500 km/s high & 50 km/s long with a hypotenuse of 502.5 km/s, the 502.5 km/s being the aether wind blowing through the train. Mac uses the 502.5 for the v, giving a factor of 0.999 998 597. This gives a 1.40 mm contraction along the almost vertical angle of the 502.5 km/s. But the train is not on that angle, it is horizontal, so Mac calculates the horizontal component of the 1.40 mm by using the factor 50/502.5 which gives 0.140 mm.
EINSTEINIAN TIME DILATION. An atomic clock (which Mac knows ticks at 1,000,000 cps in the observer's stationary frame) goes past the observer at 50 km/s. Einstein would say that the clock appears to tick slower by 0.013 888 889 cps. Here the standard Lorentz time dilation factor of (1-vv/cc)^0.5 for 50 km/s is 0.999 999 986 111 111, ie the same as for length contraction.
AETHERIAN TICKING DILATION. If the aetherwind is 00 km/s, ie if the observer is in the absolute frame, then Mac will agree with Einstein's 0.013 888 889 cps. Using the same factor.
AETHERWIND. But if the aetherwind is blowing at 500 km/s vertically upwards through the observer then Mac will say that the clock will appear to tick slower by 0.013 888 927 cps.
That is almost identical to the Einsteinian 0.013 888 889 cps. The question arises, why is this so close to the Einsteinian number, when the earlier similar scenario for length contraction gave an Aetherian number 10 times the Einsteinian number?
The answer is that in the case of length contraction Mac could ignore the 500 km/s vertical aetherwind because the horizontal component was zero km/s. But Mac cant ignore it for ticking, because ticking is they say a scalar. In other words, ticking depends on the speed of the aetherwind, whereas length contraction depends on the velocity of the aetherwind. Therefore Mac knows that the 1,000,000 cps in the stationary frame (K) will have an actual value of 999,998,611 cps in the observer's frame (k), & an actual value of 999,998,597 cps in the clock's frame (k'). And Mac knows that the observer in frame (k) will believe/feel that his own identical atomic clock has an apparent ticking of 1,000,000 cps, because it too is affected by the 500 km/s wind.
CRAWLER'S LAW says that the apparent ticking of an atomic clock is identical in every inertial frame (even though the actual ticking will usually be different)(the actual will depend on the speed of the aetherwind)(but the apparent wont, it never varies).
Where were we? Ok, as it turns out, 0.999,998,611 divided by 0.999,998,597 is 0.999,999,986.111 072, very close to the Einsteinian 0.999 999 986 111 111. The end result is that the difference amounts to only 3.4 nano seconds in a day.
That’s the way it goes. Einstein's silly STR gives goodish numbers very easily & quickly in some scenarios. When i say goodish, in fact i believe that both theories are wrong. I reckon that the factor for length contraction & the factor for ticking dilation are both wrong. But that’s another story.
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In the previous example i used a 500 km/s vertical aetherwind. Today i look at a 500 km/s horizontal wind blowing S to N, & the 1 km train goes at 50 km/s along 8 different headings. So too the atomic clock.
If the aetherwind blows at 500 km/s south to north through Earth at 20 deg off Earth's axis then at any one instant it is blowing vertically up at some place on latitude 70 deg N & vertically down at some place on latitude 70 deg S. And always it is blowing horizontally S to N at two places, one on latitude 20 deg N & one on 20 deg S. So this aint a silly example.
As expected an Einsteinian predicts the same length contraction & time dilation as she predicted for yesterday's example, ie 0.014 cps & 0.014 mm. And as expected the Einsteinian theory gives the same TD & LC for each of the 8 headings. Here we ignore GTR & orbit etc complications.
But Mac sees that in each case the wind is S to N, & the train/clock go away at 50 km/s along 8 different angles. Therefore Mac has to calculate the vector addition of the 500 & the 50 in each case, to get the true value of the wind blowing throo the train & clock.
TICKING For ticking dilation the full combined true vector (km/s) is all that is needed (to insert into the equation for the dilation factor), the direction of the wind & the direction of travel of the clock don't make any difference to ticking. The atomic clock is rated at 1,000,000 cps.
LENGTH But in the case of length contraction Mac needs to find the component of each full vector along the line of the rails (simple geometry needing Sine). Anyhow in the end the results from excel are as follows. The train is 1,000,000 mm long.
.............ticking dilation cps................................. length contraction mm
heading....... Einstein...aether.....diff................ heading.....Einstein.... aether..... diff
...12:00........ -0.014.... 0.264..... 0.278.............. 12:00....... -0.014...... 0.264.... 0.278
10:30 1:30..... -0.014... 0.183..... 0.196........... 10:30 1:30.... -0.014 ...... 0.120..... 0.133
9:00 3:00...... -0.014... -0.014..... 0.000............ 9:00 3:00..... -0.014..... -0.140.... -0.126
7:30 4:30...... -0.014... -0.210.... -0.196............ 7:30 4:30..... -0.014..... -0.142.... -0.128
....6:00........ -0.014... -0.292.... -0.278............... 6:00........ -0.014...... -0.292... -0.278
As shown the Einsteinian time dilation is a goodish number when the clock is travelling at 3 o'c or 9 o'c, ie sideways to the wind, but when there is a bit of tailwind or headwind it is miles off. The exact number is -0.01388889 cps, & the exact Aetherian number is -0.01388893 cps.
As shown the Einsteinian length contraction is usually miles off, but as can be seen it looks like it will agree with the Aetherian LC somewhere tween 1:30 & 3:00, & tween 9:00 & 10:30.
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At Earth Ve = say 11.2 km/s. We insert Ve into the equation for the Lorentz time dilation factor (1-VV/cc)^0.5 & we get 0.999 993 048 838 221, which means that an atomic clock ticking at 1,000,000,000,000,000 cps when well away from Earth loses 695,116.18 cps after being transported to our laboratory on Earth. Had our laboratory been 1 m higher then the clock would have lost only 695,116.07 cps, a "gain" of 0.11 cps, which amounts to a gain of 0.0943 nano seconds per day.
EXCEL 15 DIGIT LIMIT. The above calculations are partly beyond the limit of what excel can handle (15 digits), so to get accurate excel numbers i had to multiply the Earth's mass by 10,000, & in the end divide the results by 10,000.
AETHERIAN TIME DILATION. Aether is annihilated in Earth (no proof) & aether flows in to replace the lost aether (no proof), the inflow being at the escape velocity Ve (no proof). If so then the aetherwind (Ve) blowing through the atomic clock is slower when the clock is 1 m higher, & if using the same equations (for Ve)(& for the Lorentz factor) as the Einsteinians then the results are the same too. In which case any clock tests "proving" GTR equally support aetherian relativity. But this analysis is faulty. Keep reading.
70 DEG N & S. However aetherian time dilation isn’t that simple, the Ve aetherwind inflow happens in conjunction with the background etc aetherwind which might be briefly say 500 km/s vertically upwards at some time of day along latitude 70 deg N, or briefly say 500 km/s vertically downwards at some time of day along latitude 70 deg S.
20 DEG N & S. Locations between latitude 20 deg N & 20 deg S will at one time of day have an aetherwind of say 500 km/s that is briefly 100% horizontal.
UPWARDS. Take the case of a vertical aetherwind blowing through the clock at 500 – 11.2 = 488.8 km/s, & this becomes 500 – 11.1999991 = 488.8000009 km/s when 1 m higher, & the clock is then slower, & the clock loses 4.175 ns/day (contrary to Einstein's gain of 0.0943 ns/day).
DOWNWARDS. Take the case of a vertical wind of 511.2 km/s, & this becomes 511.1999991 km/s when 1 m higher, & the clock is then faster, & the clock gains 4.372 ns/day, which is 46.4 times Einstein's gain of 0.0943 ns/day.
SIDEWAYS. Take the case of the aetherwind blowing horizontally through the laboratory at 500 km/s, with an additional component down of 11.2 km/s, or 11.1999991 km/s at 1 m higher elevation. The vector addition is 500.125 104 826 km/s, & is 500.125 104 806 km/s at 1 m, which gives a gain of 0.0956 ns/day (a little more than Einstein's gain of 0.0943 ns/day), & this sideways gain is identical in both hemispheres.
MIXTURE. The background aetherwind blows at approx 500 km/s on some vertical angle tween up & down, together with some horizontal sideways angle from the south or north including up to say 20 deg of sideways angle from the east or west.
AETHERWIND. The aetherwind includes (1) 42 km/s of inflow towards the Sun (measured at Earth's orbit), (2) 30 km/s due to Earth's orbit, (3) 0.4 km/s due to Earth's spin, (4) 11.2 km/s due to Earth's inflow, & (5) a steady background S to N wind of almost 500 km/s.
CLOCK GAIN OR LOSS. Therefore the aetherian clock gain (or in places loss) with elevation (1 m) will vary depending on location & time of day & day of year, & varying tween a loss of approx 4.175 ns/day & a gain of approx 4.372 ns/day.
EINSTEIN. But according to Einstein it is always a gain (never a loss), & at any one location this gain (approx 0.0943 ns/day) never varies with time or date, & is much the same at every location.
TESTS. A number of tests (in the northern hemisphere)(using atomic clocks on hills)(or in the laboratory) have supposedly confirmed Einstein's GTR that clocks tick faster when higher. However aether theory says that in most locations in the northern hemisphere clocks must tick slower when higher. Something smells fishy.
20 DEG NORTH & SOUTH. Locations between latitude 20 deg N & 20 deg S will at one time of day have an aetherwind that is briefly 100% horizontal, at which time the aetherian gain (0.0956 ns/day) will briefly be nearly equal to the Einsteinian gain (0.0943 ns/day). But i think that the few tests that have been carried out have all been outside that zone. So something smells fishy.
FISHY. I will have to have a think about possible reasons why ticking tests might support Einstein & contradict aether theory, ie reasons why the tests are wrong.
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