Special Relativity in a Parallel Universe

[Perspicacious]

good question

In SR, why do some say that it is meaningless to compare clocks that are not in the same location?

The meaninglessness is based on the fact that remote clock comparisons can be dreamed up in many distinct ways. You mentioned one, the outcome of which is that approaching clocks are speeding up and receding clocks are slowing down. Yes, that's justifiable. There is also another distinct definition, which is in perfect agreement with experiment, where moving clocks tick at the same rate as stationary clocks.

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

 

[JesseM]

There is also another distinct definition, which is in perfect agreement with experiment, where moving clocks tick at the same rate as stationary clocks.

Do you mean that this formulation says that if I am an inertial observer, then in my coordinate system, a moving clock will tick at the same rate as a stationary one? That would seem to be in obvious contradiction with the experimental predictions of relativity, because if a clock makes a round trip away from me and back, relativity predicts the clock will have lost time relative to mine.

 

[Aer]

Do you mean that this formulation says that if I am an inertial observer, then in my coordinate system, a moving clock will tick at the same rate as a stationary one? That would seem to be in obvious contradiction with the experimental predictions of relativity, because if a clock makes a round trip away from me and back, relativity predicts the clock will have lost time relative to mine.

I do not know which formula you are referring to, but I would suspect that what was implied is that 1 second in my frame according to me is equivilent to 1 second in a frame moving relative to me according to itself, but each frame sees the other frames second as less than his own.

 

[Perspicacious]

Do you mean that this formulation says that if I am an inertial observer, then in my coordinate system, a moving clock will tick at the same rate as a stationary one?

Precisely, but only if no external forces are applied to the moving clock. If the clock were to accelerate out of its own inertial frame of reference, then all bets are off.

That would seem to be in obvious contradiction with the experimental predictions of relativity, because if a clock makes a round trip away from me and back, relativity predicts the clock will have lost time relative to mine.

The paper that I cited computes the effect of a round trip on moving clocks and obtains the undisputed, experimentally verifiable result.

 

[JesseM]

Precisely, but only if no external forces are applied to the moving clock. If the clock were to accelerate out of its own inertial frame of reference, then all bets are off.

So what about the case where a ship moves away from Earth at constant velocity, accelerates briefly, and then returns to Earth at constant velocity? Would the coordinate system in that paper say that the ship-clock was ticking at the same rate as the earth-clock during both inertial legs of the journey, and only running at a different rate during the accelerating phase?

 

[Perspicacious]

Would the coordinate system in that paper say that the ship-clock was ticking at the same rate as the earth-clock during both inertial legs of the journey, and only running at a different rate during the accelerating phase?

The time in the accelerating phase is considered negligible. The rates at which all inertial clocks tick are obviously equal, if you understand the paper. I haven't seen any rebuttal to the stated definition of clock time yet. It's kind of miraculous why the clocks become desynchronized on a final comparison but I don't see a mistake in the math.

 

[JesseM]

The time in the accelerating phase is considered negligible. The rates at which all inertial clocks tick are obviously equal, if you understand the paper. I haven't seen any rebuttal to the stated definition of clock time yet. It's kind of miraculous why the clocks become desynchronized on a final comparison but I don't see a mistake in the math.

Wait, are you saying that throughout the entire journey the two clocks are synchronized, but somehow at the instant they meet they're not in sync? That doesn't sound possible--have you actually done the math for this example?

 

[Perspicacious]

Wait, are you saying that throughout the entire journey the two clocks are synchronized, but somehow at the instant they meet they're not in sync?

No. I'm only saying that don't see any mistakes in the paper.

 

[Aer]

No. I'm only saying that don't see any mistakes in the paper.

Consider yourself jumping from a train going 100mph to another train going -100mph. In order for your acceleration to be instanteous, you must be smacked against the wall immediately upon jumping into the train and feel the crunch of being forced in the opposite direction. How do you think you'd hold up? Would you be able to withstand such a trip? Now consider a particle doing the exact same thing but at .9c and -.9c. Would the particle survive? Does time for a non-existing particle have any meaning to you?

 

[Perspicacious]

Aer,

I see no reason why particles can't accelerate from .9c to -.9c in particle collisions. The math in the paper assumes point particles and also assumes, only for ease of computation, that the acceleration of a point particle is either instantaneous or only takes a negligible amount of time.

If every atom of an astronaut were to accelerate uniformly to .5c in 1 sec., why would the astronaut feel the acceleration? We feel acceleration in a rocket when the thrusters are fired because our molecules are being forced into the seat cushions. If every point of an unstressed extended object were to accelerate uniformly so that the distances between points are always constant in every instantaneous co-moving inertial frame of reference, then no force would be felt at all.

 

[JesseM]

Consider yourself jumping from a train going 100mph to another train going -100mph. In order for your acceleration to be instanteous, you must be smacked against the wall immediately upon jumping into the train and feel the crunch of being forced in the opposite direction. How do you think you'd hold up? Would you be able to withstand such a trip? Now consider a particle doing the exact same thing but at .9c and -.9c. Would the particle survive? Does time for a non-existing particle have any meaning to you?

Aer, it's standard in discussions of the twin paradox to assume a near-instantaneous acceleration, it's just a thought-experiment so the fact that this would crush you is not relevant.

 

[JesseM]

No. I'm only saying that don't see any mistakes in the paper.

But you said that the paper "computes the effect of a round trip on moving clocks and obtains the undisputed, experimentally verifiable result." So if it computes the results, does it say the clocks are synchronized throughout the trip or doesn't it? If a clock moves away from me at 0.8c for 1 year, then comes back towards me at 0.8c for another year, what would be the function tau(t) giving the reading tau of a clock onboard the ship at any time t in my coordinate system?

 

[Aer]

Aer,

I see no reason why particles can't accelerate from .9c to -.9c in particle collisions. The math in the paper assumes point particles and also assumes, only for ease of computation, that the acceleration of a point particle is either instantaneous or only takes a negligible amount of time.

I do not question this. However if the particle experiences this level of high speed "particle-particle collision" (The particle necessarily is colliding with particles in the wall) Would the particle still exist in it's defined "particle" form or would it be broken apart and give off gamma rays for instance. I am not claiming to know what would happen which is why I posed the question - my response was not an answer.

 

[Aer]

Aer, it's standard in discussions of the twin paradox to assume a near-instantaneous acceleration, it's just a thought-experiment so the fact that this would crush you is not relevant.

Read my response to Perspicacious above.

 

[Perspicacious]

If a clock moves away from me at 0.8c for 1 year, then comes back towards me at 0.8c for another year, what would be the function tau(t) giving the reading tau of a clock onboard the ship at any time t in my coordinate system?

The paper asserts that your question is an outdated and tortured way of reasoning and avoids that approach altogether. The comparison you request should not be made, which is the point of this thread. Shubert's methodologies are based on a new definition of time.

 

[JesseM]

Read my response to Perspicacious above.

It's still irrelevant to the thought-experiment, we're not dealing with realistic particles as imagined in quantum theory here, just idealized indestructible clocks of zero size. Anyway, by making the inbound and outbound legs of the trip arbitrarily long, you can make the period of acceleration arbitrarily small compared to the time of the entire trip, which is all that really matters--the acceleration could still be spread out over a day or something, but if the inbound and outbound legs lasted 100,000 years you can basically ignore the acceleration period when computing the difference in the twins' clocks when they reunite.

 

[JesseM]

The paper asserts that your question is an outdated and tortured way of reasoning and avoids that approach altogether. The comparison you request should not be made, which is the point of this thread. Shubert's methodologies are based on a new definition of time.

But earlier you said "There is also another distinct definition, which is in perfect agreement with experiment, where moving clocks tick at the same rate as stationary clocks." How can you say they "tick at the same rate" if you're not comparing the time on one clock with the time on the other clock "at the same moment" in some coordinate system?

Also, is it really necessary to link to the paper every time you refer to the paper in a response to me? Just curious, are you trying to advertise the paper because you are actually the author of the paper yourself?

 

[Perspicacious]

How can you say they "tick at the same rate" if you're not comparing the time on one clock with the time on the other clock "at the same moment" in some coordinate system?

If you would just read the paper you would find out. I'm not going to answer any more questions about a paper you refuse to read.

 

[Aer]

It's still irrelevant to the thought-experiment, we're not dealing with realistic particles as imagined in quantum theory here, just idealized indestructible clocks of zero size. Anyway, by making the inbound and outbound legs of the trip arbitrarily long, you can make the period of acceleration arbitrarily small compared to the time of the entire trip, which is all that really matters--the acceleration could still be spread out over a day or something, but if the inbound and outbound legs lasted 100,000 years you can basically ignore the acceleration period when computing the difference in the twins' clocks when they reunite.

Very well, you want to make the acceleration period infinitely small compared to the length of the trip - I have no problem with this. However, this doesn't resolve the issue that there still is an interval of time for the acceleration to occur or otherwise the dt in dv/dt would be undefined - In other words, dt cannot be thought of as 0 but it can be thought of as approaching 0. Now you may be wondering what my point is, which is as follows:
if the trip is 100,000 years long, then according to the tripper (good word, yes - I know), right before he starts his "instantaneous acceleration" to the frame of visitee his frame should be thought of as an inertial frame and according to him, 100,000 years have passed while time for the visitee was less than this. But, when the tripper decelerates to visitee, his clock will agree that visitee has experienced 100,000 years and that he has experienced less than this. (Please note that I am not a physicists, but that this view is exactly as was described to me by a professor of physics).

Maybe he was wrong, but then how do you explain the reciprocity required by the derivation of the lorentz transformation in special relativity. If you do not know what I am talking about, then I will elaborate further in my thread on special relativity as this is off-topic to this thread.

 

[JesseM]

If you would just read the paper you would find out. I'm not going to answer any more questions about a paper you refuse to read.

Well, I'm not going to spend hours going through a lot of tedious math in a paper that is widely deemed to be the work of a crackpot if you aren't willing to try to show there is actually something meaningful there by summarizing what it could possibly mean to say two clocks "tick at the same rate" in the absence of a coordinate system.

 

[JesseM]

Very well, you want to make the acceleration period infinitely small compared to the length of the trip - I have no problem with this. However, this doesn't resolve the issue that there still is an interval of time for the acceleration to occur or otherwise the dt in dv/dt would be undefined - In other words, dt cannot be thought of as 0 but it can be thought of as approaching 0.

Yes, I never said it was actually zero, just that the ship "accelerates briefly" and that the acceleration is "near-instantaneous". As you say, we can just consider the limit as the acceleration period approaches zero.

Now you may be wondering what my point is, which is as follows:
if the trip is 100,000 years long, then according to the tripper (good word, yes - I know), right before he starts his "instantaneous acceleration" to the frame of visitee his frame should be thought of as an inertial frame and according to him, 100,000 years have passed while time for the visitee was less than this.

In the scenario I described, the acceleration occurred at the midpoint of the trip--he's moving away from the Earth fast, then turning around and returning so they can compare clocks at the same location (it doesn't make any difference whether he actually accelerates again when he reaches the Earth or if they just compare clocks at the moment he whizzes by arbitrarily close to the earth-twin). So he's not staying in a single inertial frame throughout those 100,000 years.

Are you imagining a scenario where he flies away from the earth, then at some point accelerates until his velocity is the same as the earth, but he's still at a great distance from the earth? In this case, yes, in his rest frame before he accelerates he'll have a definition of simultaneity that says the Earth has experienced less time than him, but then when he comes to rest relative to the earth, his new rest frame will have a different definition of simultaneity that says the Earth has experienced more time than him. Only by comparing clocks at the same location in space can you avoid having to deal with this issue of different frames defining simultaneity differently, and get an "objective" answer about who really experienced less time since the two departed.

 

[Perspicacious]

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.

 

[Aer]

Are you imagining a scenario where he flies away from the earth, then at some point accelerates until his velocity is the same as the earth, but he's still at a great distance from the earth? In this case, yes, in his rest frame before he accelerates he'll have a definition of simultaneity that says the Earth has experienced less time than him, but then when he comes to rest relative to the earth, his new rest frame will have a different definition of simultaneity that says the Earth has experienced more time than him. Only by comparing clocks at the same location in space can you avoid having to deal with this issue of different frames defining simultaneity differently, and get an "objective" answer about who really experienced less time since the two departed.

This contradicts what you told me in my thread on special relativity. I fully agree with the situtation you just described.

 

[JesseM]

This contradicts what you told me in my thread on special relativity. I fully agree with the situtation you just described.

Contradicts what? Did you catch my post about proper times right before you posted the thing about the lorentz transform and reciprocity?

 

[Aer]

Contradicts what? Did you catch my post about proper times right before you posted the thing about the lorentz transform and reciprocity?

Yes, I just noticed it - please take this conversion to the other thread.

 

[JesseM]

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?

 

[Perspicacious]

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

 

[JesseM]

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.

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.

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.

 

[Perspicacious]

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/

 

[Perspicacious]

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 https://www.physicsforums.com/showthread.php?t=80900 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.

 

[Perspicacious]

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]

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]

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.

 

[JesseM]

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.

 

[Perspicacious]

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.

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.

like the claim that all clocks tick at the same rate?

As opposed to the assertion that moving clocks run slow. Exactly.

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.

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.

 

[JesseM]

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?

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.

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.

 

[Perspicacious]

Endless ignorance ad nauseam

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" ...

Instead of imagining what Shubert's paper contains and writing endlessly about your guesses and suspicions, you should just read the paper yourself.

 

[JesseM]

Instead of imagining what Shubert's paper contains and writing endlessly about your guesses and suspicions, you should just read the paper yourself.

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.

 

[Perspicacious]

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]

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?

 

[Perspicacious]

The 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,

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.

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.

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.

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.

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.

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.