# Special Relativity in a Parallel Universe

JesseM
Perspicacious said:
JesseM,

It's all answered in section 2 (The Definition of Time), which is less than a page and a half in length. I don't believe that the graph and Greek symbols can be easily copied and pasted here.
OK, section 2 talks about two rulers with clocks mounted along them moving past each other at constant velocity. This is exactly the model that Einstein used to define the physical meaning of a given observer's coordinate system, except that he also defined a synchronization scheme involving light-signals for the clocks on each ruler. You may want to look at my thread An illustration of relativity with rulers and clocks where I showed exactly what relativity predicts about what different clocks on each ruler would read at the time they meet, complete with diagrams.

But what I don't see in section 2 is a clear definition of how an observer sitting on one ruler would define the "rate" that a clock on another ruler is ticking. In terms of the diagram in section 2, suppose that when clock A which sits on the 0 meter mark of the top ruler $$\Gamma '$$ is next to clock B on the 0 meter mark of the bottom ruler $$\Gamma$$, both clocks read "0 seconds"; then when clock A is next to clock C on the 3 meter mark of ruler $$\Gamma$$, clock A reads "1 second" while clock C reads "2 seconds". Does this mean that from the perspective of ruler $$\Gamma$$, clock A is ticking at half the rate of its own clocks, and that it's moving at 3/2 marks per second? If not, how do you define the rate of ticking and speed of clock A from the perspective of ruler $$\Gamma$$, in terms of measurements made by that ruler/clock system?

The equation for Shubertian clock time at point x of ruler $$\Gamma$$ is T = -x'/u + xi(x). The equation for Shubertian clock time at point x' of ruler $$\Gamma'$$ is T' = x/u + zeta(x'). Clock rates in both systems are equal because spacing on the rulers are equal and time is assumed to be homogeneous. That's an important concept. "Time possesses an indistinguishable sameness everywhere, point by point, across all inertial frames of reference." It's an undeniable fact that observers in both systems will agree on the exact number of spacings per second that they measure. That's a clock. It is the mighty axiom of homogeneity that asserts that the definition of clock time is identical and uniform in these systems, not lopsided and reciprocal as illustrated by the train analogy in section 1.

The caption under the Special & General Relativity forum of https://www.physicsforums.com says, "Space and time are relative concepts rather than absolute concepts." Shubert believes that's just a lot of senseless, overhyped malarkey. His revolutionary new paradigm states that it's possible and much more reasonable to rephrase relativity with absolute concepts and maintain all the factual, empirical aspects of the theory. He wants professional mathematicians and physicists to stand up and repudiate all the popular, infantile drivel in physics.

I've said on the moderated newsgroup sci.physics.research that moving clocks tick at the same rate of stationary clocks and no one there expressed any difficulty with this childishly simple perspective.

sci.physics.research/msg/2c401d21602c6e7c

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JesseM
Perspicacious said:
The equation for Shubertian clock time at point x of ruler $$\Gamma$$ is T = -x'/u + xi(x). The equation for Shubertian clock time at point x' of ruler $$\Gamma'$$ is T' = x/u + zeta(x'). Clock rates in both systems are equal because spacing on the rulers are equal and time is assumed to be homogeneous.
That doesn't help me, because you haven't told me how you even define the notion of "clock rates" in terms of actual measurements of the readings on clocks as they pass each other. Could you address the specific example I posted earlier?
In terms of the diagram in section 2, suppose that when clock A which sits on the 0 meter mark of the top ruler $$\Gamma '$$ is next to clock B on the 0 meter mark of the bottom ruler $$\Gamma$$, both clocks read "0 seconds"; then when clock A is next to clock C on the 3 meter mark of ruler $$\Gamma$$, clock A reads "1 second" while clock C reads "2 seconds". Does this mean that from the perspective of ruler $$\Gamma$$, clock A is ticking at half the rate of its own clocks, and that it's moving at 3/2 marks per second? If not, how do you define the rate of ticking and speed of clock A from the perspective of ruler $$\Gamma$$, in terms of measurements made by that ruler/clock system?
Also, do you agree that if the clocks on each ruler are synchronized according to Einstein's procedure (which is necessary in order for both ruler/clock systems to measure the same speed of light), then in the example I gave on the An illustration of relativity with rulers and clocks, the diagrams I include give the correct predictions for how clock-readings on one ruler would match up with clock-readings on the other? If not, then Shubert's theory isn't just an alternative way of thinking about relativity, it's actually making different physical predictions than relativity.
Perspicacious said:
That means that "time possesses an indistinguishable sameness everywhere, point by point, across all inertial frames of reference." It's an undeniable fact that observers in both systems will agree on the exact number of spacings per second that they measure. That's a clock.
Wait, so you don't even care what the readings on the clocks attached to the other ruler are, you only care about how many spacings per second pass you? That doesn't seem to match what's in the paper, and in that case you aren't measuring the rate that the clocks on the other ruler tick at all.
Perspicacious said:
I've said on the moderated newsgroup sci.physics.research that moving clocks tick at the same rate of stationary clocks and no one there expressed any difficulty with this childishly simple perspective.

sci.physics.research/msg/2c401d21602c6e7c
Uh, the post you link to was the last one on the thread, no one even responded to it. On the other two threads I linked to from sci.physics research where you or Eugene Shubert (you are the same person, right?) discussed the ideas in the paper, pretty much everyone took issue with them.

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Physics is the mathematical study of all conceivable universes. A universe is a mathematical model that describes spacetime, matter, energy and their interactions. Think of each model universe as filling one page in the atlas of all possible universes. "Philosophy is written in this grand book, the universe, ... But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics." - Galileo Galilei.

Two universes are said to be isomorphic if every observable fact about one universe is also true in the other. In two seemingly distinct mathematical models, the equations describing each universe might be vastly dissimilar, but if the math leads to identical predictions, then the two universes are essentially the same (isomorphic).

Consider this example. In one universe, a celebrated physicist constructs what he calls a theory of relativity. The theory is based on empirical observations yet a few skeptics don't see the need for his implausible sounding rhetoric. The theory says trains get smaller and smaller as they move away from train stations. Observers at train stations do in fact see distant train tracks getting narrower and narrower to accommodate the shrinking of distant trains. But everything is relative. Passengers on moving trains can think of themselves as stationary. They see receding train stations getting smaller and smaller and the train tracks to them getting narrower also. Approaching train stations get bigger and bigger. Consistent mathematics can support this and all observations will confirm each and every one of the predictions. Not surprisingly, there is a parallel universe where different definitions are used and a different philosophy is believed. In that parallel universe, it is agreed that the lengths of objects can only be defined by co-moving measuring rods. There, it is axiomatic that only local, co-moving measurements of length express the actual truth about an objective reality.

In Einstein's model of the theory of relativity, moving clocks run slow and moving objects shrink in the direction of motion. Lucky for you, I'm not going to have you learn an outdated and tortured way of reasoning. I will not be repeating Einstein's rhetoric about shrinking trains. It suffices to construct a universe where common sense remains intact and also embodies all the true and factual results of historic relativity theory.

By explicit construction of moving clocks in our new universe, it will be obvious that moving clocks tick at the same rate as stationary clocks. There is also a real desynchrony effect. If you don't believe in modern physics, I advise that you try to follow the reasoning of this paper line by line. That's the way our universe really works.

The Lorentz transformation has always been perceived as a rule for translating the perspective of one observer's sense of space and time to the perspective of other observers in relative motion. Forget about your faith in Hendrick A. Lorentz and Albert Einstein. It's time to learn a conceptually simpler interpretation.

http://www.everythingimportant.org/relativity/

So what you are saying is that you don't understand anything that I've said?

The title of Shubert's paper identifies the subject: "A Derivation of the Lorentz Transformation from Newton’s First Law of Motion and the Homogeneity of Time".

JesseM
There is already another thread on your theory/interpretation in the 'Theory Development' forum (as I said there, the interpretation isn't really meaningful unless you are able to define explicitly how we're supposed to define the rate that a clock is ticking, in terms of measurements made on our own clocks and rulers). As it says in the sticky IMPORTANT! Read before posting at the top of this forum:
This forum is meant as a place to discuss the Theory of Relativity and is for the benefit of those who wish to learn about or expand their understanding of said theory. It is not meant as a soapbox for those who wish to argue Relativity's validity, or advertise their own personal theories. All future posts of this nature shall either be deleted or moved by the discretion of the Mentors.

So what you are saying is that you don't understand anything that I've said?

The title of Shubert's paper identifies the subject: "A Derivation of the Lorentz Transformation from Newton’s First Law of Motion and the Homogeneity of Time".

Perspicacious said:
Two universes are said to be isomorphic if every observable fact about one universe is also true in the other. In two seemingly distinct mathematical models, the equations describing each universe might be vastly dissimilar, but if the math leads to identical predictions, then the two universes are essentially the same (isomorphic).
The subject is explicitly stated to be about an isomorphic copy of Einstein's theory.

JesseM
Perspicacious said:
The subject is explicitly stated to be about an isomorphic copy of Einstein's theory.
Isn't it supposed to be an alternate "interpretation", one which makes claims that differ from the obvious interpretation of what the Lorentz transform predicts, like the claim that all clocks tick at the same rate? If the author is not able to explicitly define what he means by the statement "all clocks tick at the same rate" in terms of a general method of comparing the rates of different clocks, then this is not a meaningful alternative interpretation.

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JesseM
Perspicacious said:
So what you are saying is that you don't understand anything that I've said?

The title of Shubert's paper identifies the subject: "A Derivation of the Lorentz Transformation from Newton’s First Law of Motion and the Homogeneity of Time".
Yet it makes claims which clearly differ from what's predicted by the Lorentz transformation, like the bit about clocks in relative motion ticking at the same rate. If you can't define what it means to compare the "rate" of two clocks, like in the specific example I asked about above, then this is meaningless as an alternate interpretation.

JesseM said:
Isn't it supposed to be an alternate "interpretation",
Yes, as in the preference for heliocentric orbits above geocentric epicycles. There is no disagreement about what is observed; therefore Shubert doesn't have a new theory. It is merely that his perspective is a conceptually simpler interpretation.

It's a well-researched and undisputed fact that standard instruction in special relativity (with its customary phraseology) is misleading and confusing. [1]. Shubert's revolutionary new paradigm states that it's possible and much more reasonable to rephrase relativity with absolute concepts and maintain all the factual, empirical aspects of the theory.

JesseM said:
one which makes claims that differ from the obvious interpretation of what the Lorentz transform predicts,
The popular view of special relativity has observable predictions and unobservable predictions. Shubert only disagrees with what is unobservable.

JesseM said:
like the claim that all clocks tick at the same rate?
As opposed to the assertion that moving clocks run slow. Exactly.

JesseM said:
If the author is not able to explicitly define what he means by the statement "all clocks tick at the same rate" in terms of a general method of comparing the rates of different clocks,
There is no cosmic everywhere present "now." Instantaneousness does not exist. There is no way to measure what Shubert says is unobservable. Shubert is presupposing a philosophical perspective and gives a clear visual representation of it in his Shubertian clock model of spacetime.

JesseM said:
then this is not a meaningful alternative interpretation.
Shubert's theory agrees with experiment, ignores unobservables and doesn't use senseless ambiguities to explain the nature of spacetime. His is a calm mathematical approach.

95% of Shubert's paper focuses on a new and very clear definition of time, using this definition to derive the Lorentz transformation in two different ways, and using this clarification to compute the time desynchrony effect in special relativity with incredible ease.

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JesseM
Perspicacious said:
As opposed to the assertion that moving clocks run slow. Exactly.
But relativity gives a procedure for defining the term "speed of a clock" that makes the statement that "moving clocks run slow" meaningful. If at time t=0 seconds in my coordinate system a moving clock reads "0 seconds", and at time t=2 seconds in my coordinate system a moving clock reads "1 second", then in relativity (and in Newtonian physics and every other theory), that would mean the clock is running at half the normal rate in my coordinate system. And these coordinates have physical meaning--when I say that the moving clock reads 1 second at time t=2 seconds in my coordinate system, I mean that at the moment the moving clock read 1 second, it was passing right next to one of the clocks on my ruler which read 2 seconds.

Does Shubert have any well-defined procedure for defining the speed of a clock? For example, ignoring the issue of moving clocks for the moment, if I had two clocks side-by-side at rest with respect to one another, and one clock had been artificially sped up so that it ticked 2 seconds for every 1 second ticked by the other clock (for example, when one clock reads '5 seconds' the other reads '10 seconds'), would Shubert say that the sped-up clock was ticking twice as fast as the normal clock? If so, how would he justify this in terms of a general definition of what it means to talk about the "speed of a clock", if he doesn't use a definition like the one used in all the rest of physics?
Perspicacious said:
There is no cosmic everywhere present "now."
There is none in relativity either. Notice that my definition of the speed of a clock above depends only on local readings of pairs of clocks. If I have a row of clocks on a ruler at rest with respect to me, and a moving clock reads "0 seconds" at the same time it passes one of my clocks which reads "0 seconds", then later the moving clock reads "1 second" at the same time it passes a different one of my clocks which reads "2 seconds", then that means I say the moving clock is ticking at half the rate of my clocks.
Perspicacious said:
Shubert is presupposing a philosophical perspective and gives a clear visual representation of it in his Shubertian clock model of spacetime.
If Shubert cannot clearly define what he means when he talks about the "speed of a clock" in terms of actual physical measurements, then the statement that all clocks tick at the same speed is empty verbiage with no real meaning.

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JesseM said:
Does Shubert have any well-defined procedure for defining the speed of a clock? ... If Shubert cannot clearly define what he means when he talks about the "speed of a clock" ...

JesseM
Perspicacious said:
Like I said before, it would probably take hours to read through all the algebra, and all the discussions online about it suggested the paper's arguments don't make much sense, so I'm not going to bother if you won't do me the courtesy of answering my fairly simple questions about how Shubert defines "clock rates" in terms of actual physical measurements. You could at least give me the page number where this specific issue is addressed, if Shubert addresses it at all; when you suggested I read section 2, I did, but there was nothing there that answered this question.

So what you are saying is that you read Shubert's definition of time (section 2) and yet have no understanding of a Shubertian clock?

JesseM
Perspicacious said:
So what you are saying is that you read Shubert's definition of time (section 2) and yet have no understanding of a Shubertian clock?
OK, I looked it over again. I had initially assumed that each observer standing on a marking on a ruler would have his own (normal) clock, but now I see that the paper simply has observers on each marking, and each one just measures time by the regular series of markings on the other ruler moving past them. So when you say "all clocks tick at the same rate", all you mean is that all observers will see markings on the other ruler passing them at the same rate? This is true if you have only two rulers, but what if there's a ruler moving frictionlessly along my own both above and below me, and the two rulers are moving at different velocities relative to my own? Do both sets of markings qualify as two different "Shubertian clocks" for an observer on the middle ruler, and if so won't these two Shubertian clocks be ticking at different rates? Also, would you agree that the rate that markings pass me on a ruler is not a linear function of that ruler's velocity relative to me--that doubling the velocity does not double the rate that markings pass--due to the Lorentz contraction between markings as the velocity increases?

The Shubertian clock

JesseM said:
OK, I looked it over again. I had initially assumed that each observer standing on a marking on a ruler would have his own (normal) clock,
They do. All point observers wear wristwatches but the Shubertian clock is as large as the universe and is composed of moving number lines. It defines time everywhere.

It is shocking to some but each point in the universe has an idealized clock. The tick rate of that universal, everywhere present clock is 1 second per second.

JesseM said:
but now I see that the paper simply has observers on each marking, and each one just measures time by the regular series of markings on the other ruler moving past them.
Precisely.

JesseM said:
So when you say "all clocks tick at the same rate", all you mean is that all observers will see markings on the other ruler passing them at the same rate? This is true if you have only two rulers,
The statement is clearly true for any two moving lines out of an infinite bundle of moving lines.

JesseM said:
but what if there's a ruler moving frictionlessly along my own both above and below me, and the two rulers are moving at different velocities relative to my own?
That question is analyzed completely and answered thoroughly in section 5.

JesseM said:
Do both sets of markings qualify as two different "Shubertian clocks" for an observer on the middle ruler, and if so won't these two Shubertian clocks be ticking at different rates?
The beauty of section 5 is that the Shubertian clock is constructed, and in effect the Lorentz transformation is derived, by requiring that all the multiple possibilities give a consistent answer.

JesseM said:
Also, would you agree that the rate that markings pass me on a ruler is not a linear function of that ruler's velocity relative to me--that doubling the velocity does not double the rate that markings pass--due to the Lorentz contraction between markings as the velocity increases?
The paper begins by defining "proper velocity" in section 2, which indeed displays the linear property.