About the Lengths of World Lines and of Time Units When Comparing Groups of Inertial Frames by Frank Ullmann

Dear Frank,

Thank you for trying to accommodate Minkowski's geometry to Cartesian coordination system (CCS) that is consistently impossible. That is one of the reasons I propose a different coordination system (NCS) which has not most of CCS' disadvantages. According to this, time dilation is geometrically explicable and inertia frames - although there is no such a frame in Nature - are equivalent.

Best wishes, Ioannis

Dear Ioannis,

Thank you for your comment. I am not quite sure, but I think you might misinterpret my conclusions. Provided that I did not made a mistake then I have shown that a necessary condition for it to be possible that space and time form a four-dimensional structure (called space-time) endowed with geometrical properties is not satisfied. This would mean that space-time actually do not have properties that could be called geometrical.

Kind regards, Frank

Frank

"Now, it is important to note that we have not shown that special relativity is wrong. In fact, we have merely shown - as indicated above - that the geometric interpretation of the equations of special relativity is not possible."

Excellent. I'm in full agreement, and point out Cartesian co-ordinates exist in vector space, which is geometry, where motion is an invalid concept. I've gone on to derive an interesting alternative where each frame is a geometry in itself, with boundary conditions representing LT's as Doppler diffraction zones.

"But predictions arising from special relativity do not depend on the geometric interpretation of special relativity. Therefore, what we have shown does not change what can be predicted on the basis of special relativity."

Precisely. The model I derive from this better explains the SR postulates logically, and all via a quantum mechanism. I hope you'll read my essay and comment. (but be warned, it is densely layered!).

Best wishes

Peter

Hi Peter,

Thank you for your friendly remarks.

Kind regards, Frank

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Dear Frank,

I just finished reading your essay (for the first time, at least!) Here are a few questions and thoughts:

1. Just to be sure, on page 1, by "length," do you always mean "spacetime interval with respect to the Minkowski metric?"

2. Similarly, when you write,"all world lines of this set lead from event A to event B and (secondly) the number of time units determined by counting time units along one random of these world lines is different from the number of the time units determined by counting time units along any other of these world lines," do you mean counting proper time units along each world line (I think this is what you mean), or time units in some arbitrary fixed frame?

3. You write, "the ratio of the length of each randomly chosen pair of world lines of this set is equal to the ratio of the numbers of time units counted along these very world lines." Right! The proper time along such a world line is equal to minus the spacetime interval.

4. When you say, "we must be allowed to assume that time units counted along these different world lines are actually all of equal length," the immediate question is "in what frame of reference?" If you started with two identical clocks y and z ticking at the same rate in a particular frame X, then boosted each into different frames Y and Z, the rate of y measured in Y would be the same as the rate of z measured in Z, but the rates of y and z in a third frame, for instance, X, would be different.

5. Right... the "spacelike components" of light paths with common initial and terminal events, measured in any chosen frame, will be equal.

6. Equation 2 worries me, essentially because of the "twin paradox." The "spacelike components" of the light paths are equal as measured in any chosen frame, but not necessary as measured along the worldlines. For instance, suppose A and B are pure timelike-separated in a given frame (e.g. A is my desk at 5 PM and B is my desk at 8 PM). The light path for a light clock that remains in this frame will be 3c long measured in this frame, but the light path for a light clock that travels outward near the speed of light and then returns will be shorter as measured on the "travelling" worldline. In the ratios L_i/n_i and L_j/n_j, it seems that L_i and L_j have to be measured in a single frame, but n_i and n_j are measured along worldlines. I don't know if I'm making any sense here...

Let me think about it a bit more... I am trying to finish reading all the essays people have asked to read before tomorrow, and I am experiencing a bit of information overload. Also, SR is supposed to become "easy" if you think about it long enough, but this never seems to happen, at least not with me! Anyway, let me know what you think! Take care,

Ben Dribus

P.S. I put in a rating for you because I don't know if I'll get back to it before tomorrow... it might be nicer if we could ignore this whole aspect as authors, but I've found that people like to know. I suppose since so many people automatically down-rate to gain an advantage, every honest rating is a help. Anyway, take care,

Ben