Thread: Is time universal? NO (and its proof)

  1. #541
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    I think the idea of simultaneity is flawed even before SRT. How precise is the human ability to tell differences in time? If 2 events happened .000000000000000001 seconds apart wouldn't they just look simultaneous? If there is a potentially infinite number of "locations" in time an event could occur at, what is the probability of any 2 events occuring at exactly the same time? 0 unless they were caused by the same thing and everything involved in the processes inbetween were completely uniform. How often does that happen? Never...

    Anyways I think the idea of a universal time is still not out of the question. Like what if you went .9c in relation to something that was going .9c in relation that was going .9c etc etc and once you got going fast enough the rules changed because you finally found that the speed of light has an absolute vale it just appears to be going c in comparison to you from any inertial frame of reference that is not close enough to light itself because of some odd reason.

    So anotherwords, something like light really travels at a rate of 50c in relation to some "rest" reference which we simply have not experienced. As long as we stay between 0 and 50c we experience the whole Special relativity thing. But if we get up to 50c the rules change. In this situation how could we tell the difference unless we reached such a boundary? We couldn't... Our little physicists would just be happily dancing to their special relativity tune until one day where they would experience something where the rules had changed and have to start all over again.
    Last edited by kriminal99; 10-23-05 at 12:10 PM.

  2. #542
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    Quote Originally Posted by MacM
    My only objection here is your continued use of the term "Proves". ...
    good point. I agree. No one (other than mathematicians) really proves anything. I should have said "strongly confirms"

    BTW I am still waiting for Aer to tell in which assumption I made the error and for you to confirm I understand uniKEF change during the eclipse of moon event.

  3. #543
    Registered Senior Member MacM's Avatar
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    Quote Originally Posted by kriminal99
    I think the idea of simultaneity is flawed even before SRT. How precise is the human ability to tell differences in time? If 2 events happened .000000000000000001 seconds apart wouldn't they just look simultaneous? If there is a potentially infinite number of "locations" in time an event could occur at, what is the probability of any 2 events occuring at exactly the same time? 0 unless they were caused by the same thing and everything involved in the processes inbetween were completely uniform. How often does that happen? Never...

    Anyways I think the idea of a universal time is still not out of the question. Like what if you went .9c in relation to something that was going .9c in relation that was going .9c etc etc and once you got going fast enough the rules changed because you finally found that the speed of light has an absolute vale it just appears to be going c in comparison to you from any inertial frame of reference that is not close enough to light itself because of some odd reason.
    At a technical level I fully agree but I think the issue is discussed more from a gendankin view point. That is unachievable absolute simultaneity is not possible pragmatically but the issue deals more with the macro affect and not the technical micro affects.

  4. #544
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    Quote Originally Posted by MacM
    ....Aer has correctly{exception taken til he tells which assuption is wrong} stated you have a tendancy to make an assumption and based on that assumption then claim your assumption is proven. They are not.
    You also only tell that you have answered instead of givining the answer to either Aer's or my question about how the absorption depends upon density or the number of atoms the flux passes etc.

    Yes I ask to embarrass you as I have for months since you never give any simple answer such as "When the density of a star increases by 8 and the total mass of a star remains constant (I.e. radius is reduce by 2) the flux absorption per atom increases by "factor X" - this is necessary as the total flux intersected by the star is decreased by factor of four.

    This is the 14th time I have asked with no intelligent reply - I bet there will be no reply to the 20th time I ask also.

    Very strange behavior for one who really wants other to take his theory seriously. Why not tell? Instead of avoid the issue? ?????
    Last edited by Billy T; 10-26-05 at 09:56 AM.

  5. #545
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    Quote Originally Posted by Billy T
    You also only tell that you have answered instead of givining the answer to either Aer's or my question about how the absorption depends upon density or the number of atoms the flux passes etc.

    Yes I ask to embarrass you as I have for months since you never give any simple answer such as "When the density of a star increases by 8 and the total mass of a star remains constant (I.e. radius is reduce by 2) the flux absorption per atom increases by "factor X" - this is necessary as the total flux intersected by the star is decreased by factor of four.

    This is the 14th time I have asked with no intelligent reply - I bet there will be no reply to the 20th time I ask also.

    Very strange behavior for one who really wants other to take his theory seriously. Why not tell? Instead of avoid the issue? ?????
    Pardon my bluntness but fuck you. Enough is enough. You have been told many tiomes what you request is not requred. UG can be ascertained from the integration in comparison to the conventional value G. UG is all you need to know not the distribution between U and ~ which comprise UG.

    So blow it out your ass.

  6. #546
    Valued Senior Member Neddy Bate's Avatar
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    In our train/embankment experiment (with equi-distant, frame-synchronized clocks), I am not sure that we have factored out the Doppler effect. We made all clocks synchronized in their own frame, but recall that this does not make them synchronized in the opposite frame. It seems to me (I could easily be wrong) that approaching clocks are unsychronized "positively" and departing clocks are unsychronized "negatively". This is strikingly analogous to the Doppler effect.

    Quote Originally Posted by Pete
    </em>If this condition is dictated for our train, it means than the braking is simultaneous in the "averaged" frame... the frame in which the train's initial motion and the embankment's motion are equal and opposite. The braking is not simultaneous in either the train's frame or the embankment frame.
    While I was away, I had thoughts similar to the above. The embankment would not be immune to acceleration because the super-brake action would have the train working to accelerate the embankment. Only by assigning the embankment a mass that is much larger than the train's can this be factored out. I didn't want to have to consider mass in this thought experiment, if I could avoid it. However, it seems that acceleration would create pseudo-gravity with or without mass, as in g=9.8m/s^2 which is true on Earth's surface regardless of any mass present.

    Neglecting mass, even a massless embankment can be considered to accelerate during 'braking' against a massless train's (negative) acceleration. Neither one can be considered to be anchored to anything massless in the universe. So, it seems that they would come to rest in the "averaged" frame unless a large difference in mass is propsed to keep the majority of the acceleration in one frame.

    ON a different note, I have practically given up on the problem of the train being prevented from deforming (losing its length-contraction in frame E, while all of the super-brakes acting along its entire length). The best I could come up with was that the super-brakes are length-contracted and unsynchronized in the train frame, so that the braking is applied progressively. This rules out the proposition of an instantaneous acceleration from v>0 to v=0 in zero time (at least in one frame). I assume SR would say that say that between the time the first part of the brake squeezed, and the last part of the brake squeezed, (in frame T), the distance of train "squeezed" would be the full, uncontracted length of the brakepad system in frame E.

  7. #547
    Please use Sugar Cane Alcohol Billy T's Avatar
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    Quote Originally Posted by Neddy Bate
    In our train/embankment experiment (with equi-distant, frame-synchronized clocks), I am not sure that we have factored out the Doppler effect. We made all clocks synchronized in their own frame, but recall that this does not make them synchronized in the opposite frame. It seems to me (I could easily be wrong) that approaching clocks are unsychronized "positively" and departing clocks are unsychronized "negatively". This is strikingly analogous to the Doppler effect. ...
    I have not read rest of post yet but let me tell why I think you are wrong.

    Consider four clocks "synchronized in their own frame" arranged as follows:

    a............b
    .......A..........B with A & B moving to the right ------> (as the "lower case clocks" see it.)

    A is moving away from a and towards b but a & b are keeping the same time. How is it true that whatever time is showing on A it is "positive" wrt to b but "negative" wrt to a?

    Turn it around: b is moving towards A and away from B - Again same question?

  8. #548
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    Quote Originally Posted by MacM
    Pardon my bluntness but fuck you. Enough is enough. You have been told many tiomes what you request is not requred....So blow it out your ass.
    To Aer (see end note) & MacM: Here is why I need to know more than MacM has told about the explicit dependency of uniKEF force upon density &rho;:
    The ideal gas law (PV=nRT or P = &rho;*T in some system of units.) is a reasonable model of internal pressure of a star just starting to run out of fuel in the core, and just beginning the collapse to form a neutron star while:
    (1) There is still space between the ions and electrons; and,
    (2) The temperature is still low enough so that very few electrons have relativistic velocities. If a significant number do become realistic, then pressure dramatically increases. The pressure vs. (1/r) where r is the stellar radius curve looks something like:
    …………………..*
    …………………..*
    ………………….*
    …………………*
    ……………….*<--- (Here a significant number of electrons are becoming relativistic.)
    ……………*
    ………..*
    …..*
    *
    Sorry I lack the capacity to insert real drawings. See Chandasicar (a phonetic spelling of his name), if you want the details exactly.

    Point is there is a dramatic change in the slope of the star pressure, Ps, vs. inverse stellar radius, (1/r), curve for a shrinking, constant-mass star as some of the electrons are forced to combine with protons to make neutrons of the neutron star. Let agree to stay in the classical region -I.e. discussion stops when relativity starts to become significant, and far from any black holes, GR etc.

    Now lets consider what the uniKEF pressure is doing as the star shrinks:

    The "uniKEF pressure,” Pu, is simply the uniKEF gravitational force on surface atoms (directed to the center of the isolated star, of course) divided by the surface area. I do not know the form, but will express the absorption probability, AP, of flux in the constant mass (or proportional to each atomic scale piece of stellar mass) as AP(&rho; or r) and included in this the possibility that AP does not even depend upon &rho; explicitly {I.e. AP(&rho; ) = 1 is not excluded. I am not asserting that absorption does depend upon density of a constant mass object, just allowing that it might, to help MacM out of trouble.}

    Clearly, as MacM states, if the flux does not even pass thru an object, it can exert no pressure on that object. Thus Fs, the total surface force due to imbalance between the flux passing thru the star and the flux directly incident upon the star from space is proportional to the cross sectional area, A, of the star or Fs = K*r^2, where K is some constant and “r”: is the current radius of the shrinking star.

    This is a result of MacM’s required integration over the CoS, all 4 pi steradians of that isolated star’s CoS “cone,” if you like. The surface area of the star, As =4*A, is proportional to r^2 also. Thus, the ‘uniKEF pressure,” Pu, available for compressing the star is independent of r!
    Proof:
    Pu = Fs/(4*A) = (K*r^2) / As = (K*r^2) /(4*&pi;*r^2) = k, some other constant.

    Obviously a constant uniKEF pressure can not compress a star whose internal pressure is going rapidly up at an every increasing rate! That is why I stated that some AP(&rho; ) is required and included it to help MacM out. No amount of verbiage, hand waving, name calling, speaking of CoS, etc. can wipe out this fact.

    MacM has wisely and stead fastly refused to tell what is the functional form of AP(&rho; ). It must be different for each case considered! (A very flexible “theory” is uniKEF !!!) For example, MacM sets AP(&rho; ) = 1 when he wants to claim the inverse square law. No simple expression can reproduce the relatively abrupt (almost discontinuous) curve above shown. When I point this out, no wonder MacM loses control and resorts to name calling.

    Aer, if you are still attacking my “proofs” please tell me specifically where is the error in this argument. I suspect you know Chandarsicar well. How is uniKEF going to make his required break in the pressure vs. radius curve as neutrons start to form?

    I fully expect MacM, after a few well chosen vulgarities, will ask “Who wants to read or can follow that crap?” but I know you can Aer, and I would like to know where I am in error if you think so.
    Last edited by Billy T; 10-27-05 at 12:51 PM.

  9. #549
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    Quote Originally Posted by Billy T
    </em>I have not read rest of post yet but let me tell why I think you are wrong.

    Consider four clocks "synchronized in their own frame" arranged as follows:

    a............b
    .......A..........B with A & B moving to the right ------> (as the "lower case clocks" see it.)

    A is moving away from a and towards b but a & b are keeping the same time. How is it true that whatever time is showing on A it is "positive" wrt to b but "negative" wrt to a?

    Turn it around: b is moving towards A and away from B - Again same question?
    I decided to try to imagine a way to synchronize all clocks in both frames.

    The synchronization process (in one frame) involves sending a light signal from one clock to the next, informing it of the correct time. Upon receiving the signal, the clock sets itself to the correct time plus the time it took for the signal to reach it. Then it sends a similar signal to the next clock in line, and so on.

    When I tried to do this across frames, the oncoming clocks were being synchronized "too soon" and the receding clocks were being synchronized "too late" for lack of a better expression. I concluded that the 'false synchronization' resulted in clocks that were faster on the approaching side and slower on the receding side. I can see now that I have made some errors.

    From frame E, the synch-signals being used in frame T either take more time (if sent toward the front of the train) or less time (if sent toward the rear of the train). Yet they are synchronized in frame T. I realize now that this is analogous to a horizontal light-clock. The ticking is 'uneven' because of the two ticks closer together (front-back) seperated by the longer duration pause in between (back-front). But of course the time dilation & length contraction formulae are meant to work with horizontal light clocks regardless of this.

    Can Pete's table be used to help make sense of the younger/older twin scenario? Say two twins start in frame E, and one jumps onto the train at clock TA, travels for awhile in frame T, and then jumps off again at clock EJ. There are two different "simultanaety shifts" during the two accelerations of the travelling twin, but it is supposed to be the duration of the time spent in frame T that determines the magnatude of the age difference. Does the travelling twin only age as much as clock TA was ticking in frame E even though they were actually in frame T?
    Last edited by Neddy Bate; 01-12-06 at 09:49 PM.

  10. #550
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    Quote Originally Posted by Neddy Bate
    Can Pete's table be used to help make sense of the younger/older twin scenario? Say two twins start in frame E, and one jumps onto the train at clock TA, travels for awhile in frame F, and then jumps off again at clock EJ. There are two different "simultanaety shifts" during the two accelerations of the travelling twin, but it is supposed to be the duration of the time spent in frame T that determines the magnatude of the age difference. Does the travelling twin only age as much as clock TA was ticking in frame E even though they were actually in frame T?
    You appear to be using a system simular to what I have preposed and that is a precalculated compensation for delay and dilation between clocks.

    Keep in mind you forward light and reverse light on the moving train can also be so compensated.

  11. #551
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    Quote Originally Posted by Neddy Bate
    ...I can see now that I have made some errors.
    If my illustration was particially responsible, I am pleased you learned from it.
    I think you sync method is OK, but prefer one that avoids all calculations and theories. I.e. brief (or long one with sharp onset, or quick color change, etc.) radiated from the midpoint between clock pairs (more trouble to actually do, pair by pair, but we are just thinking. "So what" if it is harder to do.)

    All this methode assumes is that "c down the tract" = "c up the tracks" & that your (contracted ?) tape measure returns to same length after transport to the other "half section." Your methode requires both these assumptions also plus "theoretical compenstions" for time of flight.

    Quote Originally Posted by Neddy Bate
    From frame E, the synch-signals being used in frame F ...{T you mean, don't you? OPther than this no problems with this paragraph.}

    Can Pete's table be used to help make sense of the younger/older twin scenario?
    Yes, via your following text.
    Quote Originally Posted by Neddy Bate
    Say two twins start in frame E, and one jumps onto the train at clock TA, travels for awhile in frame F {=T}, and then jumps off again at clock EJ. There are two different "simultanaety shifts" during the two accelerations of the travelling twin, but it is supposed to be the duration of the time spent in frame T that determines the magnatude of the age difference. Does the travelling twin only age as much as clock TA was ticking in frame E even though they were actually in frame T?
    Not quite accurately stated but OK. We neglect the time required to change frames because it can be arbitarly small % of total, by staying on the train longer, but with a finite acceleration, frame change does take time. (I think that this time approaches 0 as the acceleration aproaches infinity, but I don't like to break anyones bones etc, so I prefer to make the clocks TA & EJ millions of light years apart at t= 0 instead etc. (As they pass TA and EA are set to t = 0 and others in their frame off set from what they were showing by same amount.) Then the number of heart beats while accelerating can be neglected compared to the total.
    Now your question:No, he has aged less than the "time lapsed on clock EA" = ("get off value" of EJ") - (EA when jumping on train)

    BTW, I like you "one-way-travel" twin paradox scenario. I would, however, modify it slighly to make the accererated twin "good at tumbling" and have him make a few tumbles on the "flat car" in front of the train's engine and then on the ground when he gets off to avoid infinite accelerations.
    Last edited by Billy T; 10-28-05 at 10:18 AM.

  12. #552
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    Quote Originally Posted by Billy T
    If my illustration was particially responsible, I am pleased you learned from it.
    I think you sync method is OK, but prefer one that avoids all calculations and theories. I.e. brief (or long one with sharp onset, or quick color change, etc.) radiated from the midpoint between clock pairs (more trouble to actually do, pair by pair, but we are just thinking. "So what" if it is harder to do.)

    All this methode assumes is that "c down the tract" = "c up the tracks" & that your (contracted ?) tape measure returns to same length after transport to the other "half section." Your methode requires both these assumptions also plus "theoretical compenstions" for time of flight.
    If one assumes that the speed of light is less than instantaneous, then calculations must be performed with c and distance in order to derive a time offset. This is the case for any synchronization. The simplest method of syncronization would involve a light pulse in the middle of the train, sensors at each clock, and a calculation to derive the time offset.

    Re: one way twin paradox

    Unless the twin doing the jumping is a point, the twin will experience the same problem as our train. That is to say, that any two portions of the jumping twin will not record the same elasped time during the acceleration process. If you would like to claim that the jumping twin experienced less elasped time, then first demostrate that the all clocks on the train experience less elapsed time.

  13. #553
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    Quote Originally Posted by Raphael
    ...Re: one way twin paradox
    Unless the twin doing the jumping is a point, the twin will experience the same problem as our train. ...
    I think you are right, but I like point twins as they tumble better also to keep the acceleration finite.

  14. #554
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    Quote Originally Posted by Raphael
    ...The simplest method of syncronization would involve a light pulse in the middle of the train, ....
    Well, we have come full circle - that was assumed in the first post when I created this thread. Is this support for GR's curved space? No, only for curved time.

  15. #555
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    If we take BillyT's original train/bomb example and combine it with with Pete's table (in which v=.866c), then we should be able to identify exactly where the two explosions go off.

    We can specify the locations of the two bombs at any pair of seperated train clocks (TA, TB, ...TJ). The location of emission of the triggering light signal would have to be midway between these two clocks (bombs) in frame T, by definition.

    Since the speed of light is c in the embankment frame, we should expect the rear bomb to go off first, and then the front bomb later. (The distance the triggering signal travels in frame E is longer toward the front bomb and shorter toward the rear bomb).

    Considering the length of the moving train is contracted by 50% in the embankment frame, the series of explosions is twice as fast as it would be if there was not length contraction. However, since the front half of the train is no different than the rear half, this does not seem to affect the proportional difference between the time required to travel forward compared with rearward.

    Effective speed of signal toward rear bomb (in frame E):
    Vr = (c + v)/2 = (1.866c)/2

    Effective speed of signal toward front bomb (in frame E):
    Vf = (c - v)/2 = (0.134c)/2

    (1.866c/2) : (0.134c/2) = (1.866c) : (0.134c) = (14:1) approx.

    So now I would expect to find a pair of readings on Pete's table where the train times are equal (synchronized in frame T), but the embankment times are approximately 14:1 as the ratio of elapsed time forward to rearward. I would also expect this pair of readings to be equi-distant from the emission point in the train frame.

    Quote Originally Posted by Pete
    <table border=1 cellpadding=4 align=center><tr><td></td><td>EA</td><td>EB</td><td>EC</td><td>ED</td><td>EE</td><td>EF</td><td>EG</td><td>EH</td><td>EI</td><td>EJ</td></tr><tr><td>TA</td><td>20,400</td><td>22,401</td><td>24,402</td><td>26,403</td><td>28,404</td><td>30,405</td><td>32,406</td><td>34,407</td><td>36,408</td><td>38,409</td></tr><tr><td>TB</td><td>21,402</td><td>23,403</td><td>25,404</td><td>27,405</td><td>29,406</td><td>31,407</td><td>33,408</td><td>35,409</td><td>37,410</td><td>39,411</td></tr><tr><td>TC</td><td>22,404</td><td>24,405</td><td>26,406</td><td>28,407</td><td>30,408</td><td>32,409</td><td>34,410</td><td>36,411</td><td>38,412</td><td>40,413</td></tr><tr><td>TD</td><td>23,406</td><td>25,407</td><td>27,408</td><td>29,409</td><td>31,410</td><td>33,411</td><td>35,412</td><td>37,413</td><td>39,414</td><td>41,415</td></tr><tr><td>TE</td><td>24,408</td><td>26,409</td><td>28,410</td><td>30,411</td><td>32,412</td><td>34,413</td><td>36,414</td><td>38,415</td><td>40,416</td><td>42,417</td></tr><tr><td>TF</td><td>25,410</td><td>27,411</td><td>29,412</td><td>31,413</td><td>33,414</td><td>35,415</td><td>37,416</td><td>39,417</td><td>41,418</td><td>43,419</td></tr><tr><td>TG</td><td>26,412</td><td>28,413</td><td>30,414</td><td>32,415</td><td>34,416</td><td>36,417</td><td>38,418</td><td>40,419</td><td>42,420</td><td>44,421</td></tr><tr><td>TH</td><td>27,414</td><td>29,415</td><td>31,416</td><td>33,417</td><td>35,418</td><td>37,419</td><td>39,420</td><td>41,421</td><td>43,422</td><td>45,423</td></tr><tr><td>TI</td><td>28,416</td><td>30,417</td><td>32,418</td><td>34,419</td><td>36,420</td><td>38,421</td><td>40,422</td><td>42,423</td><td>44,424</td><td>46,425</td></tr><tr><td>TJ</td><td>29,418</td><td>31,419</td><td>33,420</td><td>35,421</td><td>37,422</td><td>39,423</td><td>41,424</td><td>43,425</td><td>45,426</td><td>47,427</td></tr></table>
    Assume the emission point is EB,TE (26,409) and the rearward explosion goes off at EA,TH (27,414). The forward explosions must be at clock TB at time 414 which is off the table. We can extrapolate this to be the meeting of clocks TB,EM (45,414). The increment 27 - 26 = 1 therefore the expected increment from 26 should be 26 + 14 = 40 from the (14 : 1 ratio).

    Does anyone know why I am getting 45 instead of 40? I know there is a more straightforward way to do this calculation, but where is the flaw in the reasoning presented here?

  16. #556
    Hi Neddy,
    the distance between the clocks is 520m (519.3, exactly), so if a light-speed signal is emitted at EB,TE, it will reach EA exactly 1.732 &mu;s later in the embankment frame. Note that the EA,TH event occurs only 1 &mu;s later in that frame.

    In your previous post, you've effectively assumed a signal travelling 520m/&mu;s in the embankment frame, which is (1) faster than light, and (2) different in the train frame.

  17. #557
    Valued Senior Member Neddy Bate's Avatar
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    Quote Originally Posted by Pete
    </em>Hi Neddy,
    the distance between the clocks is 520m (519.3, exactly), so if a light-speed signal is emitted at EB,TE, it will reach EA exactly 1.732 &mu;s later in the embankment frame. Note that the EA,TH event occurs only 1 &mu;s later in that frame.

    In your previous post, you've effectively assumed a signal travelling 520m/&mu;s in the embankment frame, which is (1) faster than light, and (2) different in the train frame.
    Hi Pete,

    Thank you for your patience. Your table has really helped me to visualize what is supposed to be happeneing in SR, but I admit that I am still unclear on many of the details.

    (1) I am not sure why the actual distance in meters has to be established. At v=.866c, regardless of the units for distance between clocks or the units for time, the table will be of the same format. It will always demonstrate &gamma;=0.5 regardless of the units. Please note that I was looking for a proportion of 14:1 and not any particular value.

    (2) All that matters about frame T is that the distance between the 'explosion clocks' is properly bisected by the 'emission clock' and that the times on the 'explosion clocks' are synchronious. This is clearly the case with clocks TB<-- TE -->TH because TE is midway between TB and TH. Also, TB and TH both read 414 at time of explosion, so the events are synchronious in frame T, as proposed:
    Quote Originally Posted by Neddy Bate
    </em>Assume the emission point is EB,TE (26,409) and the rearward explosion goes off at EA,TH (27,414). The forward explosions must be at clock TB at time 414 which is off the table. We can extrapolate this to be the meeting of clocks TB,EM (45,414). The increment 27 - 26 = 1 therefore the expected increment from 26 should be 26 + 14 = 40 from the (14 : 1 ratio).

    Does anyone know why I am getting 45 instead of 40? I know there is a more straightforward way to do this calculation, but where is the flaw in the reasoning presented here?
    I was expecting 14:1 ratio on the embankment clocks (based on the classical calculation of light travelling toward moving clocks), but it turned out to be 19:1 ratio (based on the table showing &gamma;=0.5).

    Frankly I'm impressed that it even comes close, because previously I would have thought reciprocal time dilation to be physically impossible. Here it becomes possible, even though the calulations do not seem to be working out. Clearly I am still missing something, but I still think it's pretty neat. I will continue trying...

  18. #558
    Hi Neddy,
    The table is only correct if the distance between the clocks in their rest frame is equal to the distance light travels in 1.732 ticks.

    The precise units don't matter (I arbitrarily chose microseconds), but the above relationship is fixed by the table.

    Here's why:
    From the table, we know that the gamma factor is 2.
    From the gamma factor, SR allows us to calculate the relative velocity as a fraction of light speed:
    v = c/&radic;(1-gamma&sup2;) = 0.866c

    OK so far?

    Now, think about the table again. What else does it tell us about the relative velocity?
    In the embankment frame, clock TA passes one embankment clock every 2 ticks.
    So, the velocity of the train is clearly half a clock-spacing per tick.
    Since we already know the velocity, this fixes the relationship between ticks and clock-spacing, as described in the first sentence!

    You should check that result. I might I have the exact figure wrong.
    Is light speed 1.732 clock spaces per tick, or one clock space per 1.732 ticks???
    Last edited by Pete; 11-01-05 at 08:36 PM.

  19. #559
    Quote Originally Posted by Neddy Bate
    Frankly I'm impressed that it even comes close, because previously I would have thought reciprocal time dilation to be physically impossible. Here it becomes possible, even though the calulations do not seem to be working out. Clearly I am still missing something, but I still think it's pretty neat. I will continue trying...
    Try placing the rearward explosion in different places and work it through.

    For example, if the signal leaves EE,TA to trigger an explosion at ED,TE, what are the implications? What if the explosion were at EC,TJ? How about EA,TP?

    The last one is particularly interesting, because the interval from EE,TA to EA,TP is close to light-like (assuming my previous post is correct). This means it should give us an almost consistent result for the other explosion.

  20. #560
    Valued Senior Member Neddy Bate's Avatar
    Posts
    1,192
    Quote Originally Posted by Pete
    Try placing the rearward explosion in different places and work it through.

    For example, if the signal leaves EE,TA to trigger an explosion at ED,TE, what are the implications? What if the explosion were at EC,TJ? How about EA,TP?

    The last one is particularly interesting, because the interval from EE,TA to EA,TP is close to light-like (assuming my previous post is correct). This means it should give us an almost consistent result for the other explosion.
    You're right, and you beat me to the post. I was just working out a different calculation, and I got a 13:1 ratio when I used a different set of clocks. Obviously if I used the "correct" set (based on the true value of c) I would get 14:1.

    Well I am happy to have been wrong, because it helped me to internalize the correct approach. You should be a professor, Pete, if you are not already one! Thanks again.

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