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CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: About the Lengths of World Lines and of Time Units When Comparing Groups of Inertial Frames by Frank Ullmann [refresh]
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Author Frank Ullmann wrote on Aug. 10, 2012 @ 12:47 GMT
Essay Abstract

We explore whether our interpretation of special relativity - according to which we consider space and time as space-time equipped with geometric properties - leads to conclusions that go beyond those drawn directly from the equations of special relativity. To do so, we develop a method that allows us to determine the ratio of the lengths of any two polygonal time-like world lines both connecting the same two events. It turns out that all such world lines have the same length, regardless of the number of time units counted along each of them, whereas at the same time the mean lengths of the time units are different if their numbers are different. Therefore, if different numbers of time units are counted, this cannot have a geometric cause.

Author Bio

I have studied theoretical physics at the Goethe Universität in Frankfurt. There are two questions that keep me up at night: what makes gravity so special and what is time?

Download Essay PDF File

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Ioannis Hadjidakis wrote on Aug. 13, 2012 @ 08:53 GMT
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

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Frank Ullmann replied on Aug. 15, 2012 @ 15:42 GMT
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

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Peter Jackson wrote on Aug. 20, 2012 @ 17:15 GMT

"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


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Frank Ullmann replied on Aug. 28, 2012 @ 13:20 GMT
Hi Peter,

Thank you for your friendly remarks.

Kind regards, Frank

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:12 GMT
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
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
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

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Member Benjamin F. Dribus wrote on Oct. 4, 2012 @ 22:36 GMT
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...

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Author Frank Ullmann replied on Oct. 24, 2012 @ 17:56 GMT
Dear Ben,

I am sorry for being late in my reply but I got knocked out by the flu for a week. You have posted same good questions (particularly by 4 and 6).

Here are my answers:

(see attachment)

Kind regards,


attachments: replies_Frank_Ulmann_FQXI.pdf

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Member Benjamin F. Dribus wrote on Oct. 4, 2012 @ 22:46 GMT
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,


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