Is special relativity incomplete?

[stevendaryl]

This seems to be weird to me. Do you mean that when Bob and Alice meet together at the same place and the same time, Bob will see 5 years older than Alice and Alice will see 5 years older than Bob? It is so much confusing me.

If Alice and Bob continue away from each other at constant velocity, then they can never meet. In order for them to meet, one or the other (or both) must change direction or speed of their motion. To figure out which one is older when they get back together, you must look at how they move to get back together.

The picture below shows an analogy to the "paradox" of mutual time dilation that occurs in good old 2-dimensional Euclidean geometry. Alice and Bob are traveling in their cars, and they come to a fork in the road, represented by the lower left vertex of the triangle. Bob decides to take the road that goes to the northeast, while Alice decides to travel straight east. Assume that their two roads make a 45 degree angle. When they get back together, who will have traveled the farthest?

Here's Alice's reasoning:

There are markers on each road that tells how far we've traveled (in miles). When I get to road marker #5 on my road, I look straight to my left, and I see that it corresponds to marker #7 of Bob's road. Similarly, when I get to road marker #10 on my road, I look straight to my left, and see road marker #14 of Bob's road. Bob's markers are increasing faster than mine, so when we get back together, Bob will have traveled farther. (In the picture, the red lines indicate Alice's view of which of her markers correspond to which markers of Bob.)​

Here's Bob's reasoning:

When I get to marker #5, I look straight to my right, and see that it corresponds to marker #7 of Alice's road. Similarly, when I get to marker #10, it corresponds to Alice's marker #14. So Alice's markers are increasing faster than mine. So when we get back together, Alice will have traveled farther (In the picture, the blue--or maybe they're purple--lines show Bob's view of which of his markers correspond to which of Alice's)​

So who is right? Well, Alice is. When they get back together, at the lower right vertex of the triangle, Bob will have traveled farther. Does that mean that there is an absolute answer to the question of which road markers are increasing faster? No. The difference between Alice and Bob is that Bob makes a right-angle turn half-way along his trip. When he turns, he completely changes his view of which of Alice's markers correspond to which of Bob's. Immediately before Bob's turn, at the top of the triangle, if he looks to his right, he will see Alice's marker #20. Immediately after he turns, when he looks to the right, he will see Alice's marker #0. So when he makes the turn, the correspondence between his marker and the corresponding marker for Alice changes. Because of this, Bob's accounting of how long each of their trips is will be wrong.

A similar thing happens in the twin paradox. For the two twins to get back together, Bob must change his velocity (assume it's Bob). During this change, his notion of which of his birthdays correspond to which of Alice's birthdays must change abruptly. Because of this change, Bob's accounting of their relative ages will be wrong when they get back together.

 

[MikeLizzi]

Hi All,
Here is a URL to an exercise I did for myself a while ago. It addresses cases where skeptics don't want to consider a back and forth sceneario like the traditional twins. I hope it can contribute some clarity, not add more confusion.

http://www.relativitysimulation.com/Documents/LookingForContradictionsWhenMovingClocksRunSlow.htm

 

[flexible_time]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion. Someone may have some critiques about technical issues such as how to separate twin at a far distance but that is not the main point I would like to know. Maybe such technical issues could be the real cause for my confusion.

 

[A.T.]

... I assumed in my original post that there is neither acceleration nor change in the direction... they are separated from each other at a distance r and are approaching each other in a uniform motion...

If they are twins and are now separated and approaching each other, there must have been some change in the direction since the separation.

 

[jbriggs444]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion.

It does change anything essential if the subjects are initially separated and are approaching or if they are initially together and are receding. If they are approaching, you have the problem agreeing on a simultaneity convention for starting the respective clocks. If they are receding you have the problem agreeing on a simultaneity convention for reading the respective clocks.

If they are together twice then, as has already been discussed, at least one must have accelerated in the interim.

 

[Vitro]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion. Someone may have some critiques about technical issues such as how to separate twin at a far distance but that is not the main point I would like to know. Maybe such technical issues could be the real cause for my confusion.

Take it step by step, first you need to separate the twins to distance r. So you take a pair of twins who are the same age when side by side and you separate them to distance r, and let's assume they are mutually at rest now. How do you know or can you tell if they are still the same age now? The details of how you separated them matter.

Now, let's say you confirmed they are still the same age, you set them to approach at uniform speed. How did you get them to that relative speed, which one did you accelerate, or if both how much each? That also matters. If you ignore the details or just assume things that are not so you'll likely run into contradictions.

 

[Dale]

rating.", then the paradox is unavoidable. I could not find a way to resolve this paradox yet and am still searching for. Would be appreciable if you correct me

One reason that we use math in science is for clarity. In this case what the math says is:
$d\tau_B/dt_A<1$
And
$d\tau_A/dt_B<1$

There is clearly no inherent contradiction between these two mathematical statements.

Translating them into English the first one says "B's clock runs slow in A's frame" and the second one says "A's clock runs slow in B's frame". There is still no contradiction, although the clarity is lost.

 

[Herman Trivilino]

It is the prediction based on SR, but seems to be inconsistent with the result.

The experimental results are consistent with the theoretical predictions. More so than for just about any other theory that's ever been created. The reason, I think, is because the theoretical predictions seem so inconsistent with our everyday experiences.

But now, 111 years after the creation of the theory, it has become a part of the everyday life of engineers, technicians, and scientists. It is confirmed by measurements taken every minute of every day across the globe.

I can see it as an analogy with the famous so called "Unstoppable Force paradox". Bear with me to explain more for those who are not familiar with it.

There is no such thing as an irresistible force or an immovable object.

SR says, borrowing your view point, that in view of A, A must see B's clock running at a slower rate and in view of B, B must see A's clock running at a slower rate. Here I think what SR says about A and B is similar to what the Chinese sales man who is trying to sell spear and shield. I am really curious about the answer when we ask "what would happen if A meet B?".

If A and B both undergo inertial motion relative to each other they can meet once and only once. They will never have the opportunity to meet a second time to compare their clocks. So it is very much like your analogy in the sense that in both cases an impossible situation is being proposed. I wouldn't make anything more of the analogy than that.

 

[stevendaryl]

One reason that we use math in science is for clarity. In this case what the math says is:
$d\tau_B/dt_A<1$
And
$d\tau_A/dt_B<1$

There is clearly no inherent contradiction between these two mathematical statements.

Yes. The problem is that people often ignore (or don't understand) the difference between \tau_A and t_A.

 

[tomdodd4598]

This is just a clarification to fix some confusions. I assumed in my original post that there is neither acceleration nor change in the direction in the thought experiment and they are separated from each other at a distance r and are approaching each other in a uniform motion. Someone may have some critiques about technical issues such as how to separate twin at a far distance but that is not the main point I would like to know. Maybe such technical issues could be the real cause for my confusion.

Enough people have explained the standard twin paradox solution, and I will attempt to help you with your specific problem of A and B starting separated by a distance d, approaching each other at some speed v, and meeting at a time d/v later. First we have to think about how the initial conditions are achieved - there are two possibilities:
1: A and B started together and were separated by the distance d, or
2: A and B had never previously been together, and just so happen to be on their collision course.
Scenario 1: This is the twin paradox, the solution to which has already been explained multiple times in this thread.
Scenario 2: There is almost no meaning to the measurement when they meet - both A and B will get the same 'result'. A might be younger, B might be younger or they will have the same age if the system was symmetric. Their definitions of simultaneity and 'now' are totally different.
The problem with your thought experiment is that there's no sense of relative age to begin with. In order to determine which has experienced less time, there needs to have been an initial comparison, in which case you would have scenario 1.

 

[Charles Carter]

What you describe in your original post pertains to vectors in a Gallilean system, i.e. no Lorentz factor for time dilation.
If I sit at a table with a glass on my left and a pitcher on my right, which is in front and which behind? An inertial reference frame, explicit or implicit, is necessary to describe any vector. And a vector can be described in any number of inertial frames.

 

[flexible_time]

Thanks for everyone, thanks for many kind feedbacks.

Although many gave me some kind learning, I still doubt that SR is complete. Even further I believe in the absoluteness of time and space. Yes, you can laugh at me here but give me another chance to try my reasoning if you don't mind.

Let's begin with what Ibix wrote because I think it is pretty good point to begin with.

Ibix wrote in post #5, "There is no answer to the question "is something moving or not" unless it is accelerating."

I think what the upper argument means is that there is no absolute time and position of for every objects in the world and everyone will agree with the upper argument.

But I know one exception for the upper, it is the LIGHT. For light, I will say I know the answer for it and the answer is that light is always moving, not resting in the vacuum and light does not accelerate in the empty space. I think that light should be included in the "something". We also know that the speed of light in empty space is always constant c to every observers and I think that it shows the existence of absoluteness of time and space clearly, at least for one physical object, photon.

I can read that, from wiki, "The theory of relativity does not allow the existence of absolute time because of the nonexistence of absolute simultaneity.". IMHO, the word "simultaneity" can be defined by considering the notion of time and space together and so does for velocity. So if the nonexistence of absolute simultaneity is true, then the nonexistence of absolute speed must be true. Can you think of a case that the former is true and the latter is false? I can't.

I learned that the speed for any object can be measured and decidable only by comparing two inertial reference frames but only one exception is the photon because it is decidable without comparing with anything, simply it's the absolute speed. I cannot think of how the absolute measurement will be possible only by using relative values without the absolute values.

So I would like read more from you if I argue that the speed of light is the absolute value without regard to any external observer and it proves that the existence of the absolute time and space.

 

[Ibix]

Ibix wrote in post #5, "There is no answer to the question "is something moving or not" unless it is accelerating."

I think what the upper argument means is that there is no absolute time and position of for every objects in the world and everyone will agree with the upper argument.

But I know one exception for the upper, it is the LIGHT.

We weren't talking about light when I said that, I think. You are correct that light is always moving in every frame of reference.

This in no way shows the absolutenes of time and space. If one posits an absolute notion of simultaneity, one recovers Galilean relativity in which nothing is expected to have a finite invariant speed. The invariant speed in Galilean relativity is infinity. For example, see http://arxiv.org/abs/physics/0302045 which derives both Galilean and Einsteinian relativity from the principle of relativity.

 

[Dale]

But I know one exception for the upper, it is the LIGHT. For light, I will say I know the answer for it and the answer is that light is always moving, not resting in the vacuum and light does not accelerate in the empty space. I think that light should be included in the "something". We also know that the speed of light in empty space is always constant c to every observers and

Yes, that is correct. This is the second postulate of relativity.

I think that it shows the existence of absoluteness of time and space clearly, at least for one physical object, photon

No, it doesn't. How could a postulate of relativity contradict relativity? This was shown by Einstein in 1905.

https://www.fourmilab.ch/etexts/einstein/specrel

Can you think of a case that the former is true and the latter is false? I can't

I can. The Lorentz transform, as shown by Einstein in 1905.

 

[Vitro]

@flexible_time, the fact that the speed of light is the same in all inertial frames is the very thing that lead to Special Relativity, to relativity of simultaneity, time dilation and length contraction. A constant and finite speed of light in all inertial frames is in direct contradiction with an absolute simultaneity and here's why:

Imagine a long straight rod with a pulsing light right in the middle. In the rest frame of the rod and assuming constant speed of light a pulse from the light will reach the ends of the rod at the same time, which gives us two simultaneous events. Agree so far?

Now, in another reference frame moving wrt the previous one the ends of the rod are moving, one is running away from the light pulse while the other is heading towards it. So, assuming the same speed of light in this frame too, how can you get the events of the pulse reaching the two ends be simultaneous? Please note that when we say the speed of light is constant we mean wrt the frame where you measure it, not wrt the light source.

 

[Herman Trivilino]

So I would like read more from you if I argue that the speed of light is the absolute value without regard to any external observer and it proves that the existence of the absolute time and space.

Proof is the wrong word to use here. The absolute nature of the speed of light, and the equivalence of inertial reference frames, implies that time and space are not absolute. That implication is not a proof, but rather a conclusion drawn from the assumptions. In other words, if the assumptions are false then so are the conclusions. It's the experimental verification that's occurred in the last 111 years that gives us confidence in the validity of the conclusion.

These experimental results have been confirmed to such an overwhelming extent that there is no room left for doubt. From GPS satellites to proton therapy to countless processes in between, relativity is confirmed in numerous ways every minute of every day in places all around the world.

 

[yogi]

This is a general comment, not directed to any particular post. The premise that all inertial frames are equivalent is at the heart of SR, but it has never been experimentally verified, and indeed may not be verifiable. Experiments are made with reference to the Earth - a clock accelerated to a high velocity with respect to the Earth will tick at a slower rate during the remainder of the voyage, whether it be a round trip or a one way trip. This is a case of real time dilation - whether the clocks are brought together and compared or the traveling clock is compared to the Earth's clock by a third clock located at the destination of the one way trip - there is no ambiguity as to which clock runs slow. The traveling clock will always be found to have logged less time than the Earth clock whether the two are brought together or the traveling clock is compared to a clock which has been placed at the destination (e.g., a planet in the same inertial frame as the Earth - not moving with rest thereto). This is the essence of Einstein's thought experiment described in Part IV of his 1905 paper. The same result can be achieved in the lab - instead of sending the moving clock to another planet, it is placed in a centrifuge - a clock in a centrifuge having peripheral velocity v runs at the same rate as a clock traveling in a straight line with velocity v.

But two clocks in oppositely rotating centrifuges (e.g., one rotating clockwise at rw, the other counter clockwise at rw) would each be calculated to run slower than the other from the perspective of the other, using SR because of the relative velocity difference. The situation, however, is symmetrical - in the case of two identical centrifuges running in opposite directions, both clocks run at the same rate - the mensuration process involved in determining the other clock to be running slower, is illusory - there is no real time dilation when there is no physical difference between the inertial systems of the two clocks, even though there is a velocity difference. Same with oppositely orbiting satellites at the same height. In this sense, the OP's question must be answered in the affirmative. The two types experiments must be distinguished - the case for real time dilation requires a more complete definition of the experiment. In real time dilation the two inertial systems must be physically distinguishable - for example in GR, the slow clock is the Clock in the gravitational potential of a mass (this is a negative energy condition that depends upon the escape velocity). In SR, the slow clock is the one with higher positive kinetic energy. Acceleration per se, has no effect upon clock rate, but in SR, the clock which has been accelerated usually winds up being in a higher energy state.

 

[jbriggs444]

in the case of two identical centrifuges running in opposite directions

there is no physical difference between the inertial systems of the two clocks

That is a rather bizarre notion of "inertial".

 

[yogi]

That is true - thank you for pointing that out. A centrifuge may not meet the conventional definition of an inertial system - just as a satellite in circular orbit experiences constant centripetal acceleration, it is non the less a perfectly good inertial frame - as pointed out by Penrose. In that case of course, the satellite is in free fall. In the sense that centripetal acceleration produces no change in kinetic energy there will be no "real" change in the clock rate - again - these different situations call for better descriptions of what is meant by an inertial system for the purpose of distinguishing between "real" time dilations and "apparent" time dilations.

 

[Dale]

The premise that all inertial frames are equivalent is at the heart of SR, but it has never been experimentally verified, and indeed may not be verifiable.

This is not correct at all. There is a huge body of literature and experimental evidence surrounding tests of Lorentz invariance. Many proposed theories predict small Lorentz violations so this is an active topic with many new developments.

The standard model extension is probably the best place to begin. https://en.m.wikipedia.org/wiki/Standard-Model_Extension

It is simply not the case that this is experimentally unverifiable or unverified.

But two clocks in oppositely rotating centrifuges (e.g., one rotating clockwise at rw, the other counter clockwise at rw) would each be calculated to run slower than the other from the perspective of the other, using SR because of the relative velocity difference.

This is not correct. The formulas for non inertial frames differs from inertial frames, and if you actually work out the math then you will see that it doesn't work out the way you claim.

 

[Herman Trivilino]

The premise that all inertial frames are equivalent is at the heart of SR, but it has never been experimentally verified, and indeed may not be verifiable.

That depends on what you mean by "verifiable". You will always be able to claim that any physical assertion is not verifiable because it's always possible that a counterexample will be found, disproving the assertion. That is a philosophical objection to the validity of scientific knowledge. But the fact is that scientists, engineers, and technicians have used the assertion to make advancements. The list of advancements is long, and includes things like proton therapy and the GPS.

The traveling clock will always be found to have logged less time than the Earth clock whether the two are brought together or the traveling clock is compared to a clock which has been placed at the destination (e.g., a planet in the same inertial frame as the Earth - not moving with rest thereto).

And the Earth clock will be found to have logged less time than the traveling clock. This is a fact that GPS engineers must take into account every minute of every day. If they didn't the GPS clocks would be so far out of sync that the system would no longer be able to reliably provide your location.

The Earth clock and destination clock, synchronized in their rest frame, will be out of sync with each other as observed by the traveler.

You are stuck in your thoughts, thinking that there is something special about Earth's frame of reference. One would think that after studying the history of science one would realize that being fooled in this way is something that keeps happening. Over and over again.

 

[yogi]

Einstein claimed in Part IV of his 1905 paper ..."if at points A and B ...stationary clocks viewed in the stationary system, are synchronous ; and if the clock A is moved with velocity v along a line AB to B, then on its arrival at B, the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)t(v^2/c^2)...t being the time occupied in the journey from A to B. It is at once apparent that this result still holds good if the clock moves from A to B along any polygonal line and also when the points A and B coincide. If we assume the result proved for a polygonal line is also true of a continuously curved line, we arrive at this result: If one of two synchronous clocks at point A is moved in a closed curve with constant velocity until it returns to A, the journey last t seconds, then by the clock which has remained at rest, the traveled clock on its arrival at A will be (1/2)tv^2/c^2 seconds slow.

Einstein's example considers curved constant velocity motion as a valid inertial frame. The experiments do not warrant the postulate that all inertial frames are equivalent - nor does the example require that the moving clock travel a straight path. A satellite in orbit is a perfectly valid inertial frame - the experiments are consistent therewith. There is no need to consider the Earth frame as special - it is convenient and as such it is almost always taken as the proper frame for conducting time dilation experiments. By whatever means the clocks are compared ... the results are not reciprocal - If the A clock lags behind B clock upon arrival at B, no amount of mathematical gymnastics can produce a different result - real time differences are a physical phenomena

Sadly, Einstein himself seems to have lost confidence in his first expose'. His later 1918 paper was a poor attempt to rationalize the traveling twin problem in terms of an artificial G field artificially introduced during turn around - what is more disturbing, several well respected Noble winners (including Feynman, Born and a few others) were influenced to endorse the proposition that GR is needed in order to solve the Twin problem. A curved path involves acceleration - but acceleration does not undermine the bases for the time difference, i.e., GR is not required or even appropriate.

In answer to post 51, GPS, satellite clocks are preset to compensate for the difference between gravitational potential and the kinetic energy associated with their orbital velocity. Thereafter, the clocks are updated periodically to correct for small drifts. (GPS clocks run faster because of their altitude and slower because of their velocity). The object of the corrections is to maintain sync for high accuracy positioning, While a GPS clock is a valid inertial frame, the object of the presetting and updating is to improve accuracy. The inertial frame of the satellite clock is different than the non rotating Earth centered frame, so corrections are required for the very reasons I have previously stressed, namely, all inertial frames are not equivalent.

 

[Dale]

Einstein's example considers curved constant velocity motion as a valid inertial frame.

No, he most certainly does not. You are misreading the passage.

The only reference frame used in that section is the "stationary frame". B remains at rest in this frame so the "stationary frame" is B's frame not A's. No calculation of any kind is done in A's frame. There is no claim or statement of any kind regarding how things would be from A's perspective or in A's frame.

Please go back and re read the passage and re think your analysis.

The experiments do not warrant the postulate that all inertial frames are equivalent

This is false and was already addressed above. Many experiments do validate the postulate.

In addition to all of the recent SME experiments there are also a lot of older experiments, many of which are detailed in http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

A satellite in orbit is a perfectly valid inertial frame - the experiments are consistent therewith ... While a GPS clock is a valid inertial frame

Not really. In scenarios involving tidal gravity there are no global inertial frames, only locally inertial frames. They are only practically inertial over a small enough region of spacetime.

 

[flexible_time]

Firstly, I would like to express my undoubted respect to the greatness of SR. In fact, I have no doubt about many facts that every experimental result has been exactly matched with what SR predicted. But what puzzles me is that if it is true that one conclusion of SR is that there is no “absolute rest” and absolute moving”, then the Einstein’s theory of special relativity seems to be self-contradiction in that he concluded the nonexistence of absolute motion of any matter only after assuming the existence of absolute moving entity, light. In my opinion, it is much close to the fact that, using the notion of absolute space and time, he found a brilliant way to express the relativistic relation between inertial frames to such an overwhelming extent. So here I will try to show what would be problematic with his conclusion on the nonexistence of absolute motion.In Einstein’s 1905 paper, he wrote

“Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest.” It seems that this statement has the exact same meaning with "There is no answer to the question "is something moving or not" unless it is accelerating." because what really matters is the relativistic motion between inertial frame of references in the view point of relativity. So assuming SR view is correct, if two systems are both in uniform motion or “Galilean frames”, then I can conclude that two systems shows a perfect symmetry and are identical and “indiscernible” because they can declare each either rest or moving. Am I correct?If so far so good, then I question on the part of his paper quoted below.

“… when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.”From the previous conclusion, if two systems, the conductor and the magnet have both infinite length so that one can move forever while the other at rest, then two systems must be identical to produce the indistinguishable results only because they can be either at rest or moving equally. But as he already wrote, there is actually a “sharp distinction” between the two cases and this seems to violate the conclusion of SR. If the prediction fails to match with the experimental result, it means that the conclusion of SR is problematic. It also leads to that we need to find a better way to resolve the mismatch between the prediction and the result. I think one way would be accepting the existence of absolute motion in the exact same manner with what Einstein postulated in his SR. Also I have a raw idea on how to get the state of “absolute rest” for a matter but want to check whether my reasoning so far will make sense to you before writing such a personal idea.Please correct me if I am wrong.

 

[Ibix]

You are misunderstanding your second quotation. The bit before your bolding is the experimental result - what happens depends only on the relative motion of the magnet and the conductor. The bit you bolded and the rest is an illustration of the problems with Maxwell's equations in Newtonian physics (which is the combination he means by "the customary view"). Namely that they imply a detectable absolute rest frame, or at least a detectable ether, which does not match experiment. This was a well-known issue that had been a hot topic of research for decades at that point. Einstein solved it by introducing what became known as relativity theory, bringing our theoretical understanding in line with our experimental knowledge.

Actually, if you want to get rid of the idea of no absolute motion you are going to have to go back to Galileo at least and rebuild all of physics from there. Please be aware that doing so on this forum would almost certainly be interpreted as a violation of the rules and get you banned, as would discussing whatever your personal idea is. PF is not the place for such a discussion.

 

[flexible_time]

what happens depends only on the relative motion of the magnet and the conductor.

My argument is that there is no way we can determine or predict what will happen if we are allowed to use only relative motion of the magnet and the conductor. If the theory cannot predict the future using only its postulates predefined, it can be considered as "incomplete" to me because it will require more information to determine the future. Using the scheme with the infinite lengthy magnet and conductor, in my opinion, the relativistic view will be unable to determine who is moving or resting unambiguously. If the magnet in uniform motion can be declared to be resting initially and some time later declared to be moving by observer like me and changing my mind between the resting magnet and the moving magnet do actually produce a significant difference, then I am forced to think there is the existence of free will.

This was a well-known issue that had been a hot topic of research for decades at that point. Einstein solved it by introducing what became known as relativity theory, bringing our theoretical understanding in line with our experimental knowledge.

I don't have any knowledge on that now and not sure his solution can solve my puzzlement in the above.

 

[Ibix]

My argument is that there is no way we can determine or predict what will happen if we are allowed to use only relative motion of the magnet and the conductor.

Then your argument is wrong. We routinely use relativity together with electromagnetic theory to predict the function of things like the LHC which relies on electromagnets to control the motion of relativistic particles.

Using the scheme with the infinite lengthy magnet and conductor, in my opinion, the relativistic view will be unable to determine who is moving or resting unambiguously.

Of course not. No such determination can be made by experiment, so relativity theory cannot be used to determine it either. This is not a failure of the theory any more than its inability to determine the properties of unicorns.

If the magnet in uniform motion can be declared to be resting initially and some time later declared to be moving by observer like me and changing my mind between the resting magnet and the moving magnet do actually produce a significant difference

It doesn't produce any significant difference. That's the point. The major issue with electromagnetism prior to Einstein was that the theory did predict significant differences between one particular rest frame and all others, but no such frame could be found experimentally despite increasingly ingeneous efforts. Einstein was reminding his readers of that fact prior to fixing the theory by extending the concept of relativity from just applying to space to applying to space and time.

 

[flexible_time]

Thanks for pointing out my misunderstanding in reading Einstein's paper.

But what do you think about another my observations?

"the Einstein’s theory of special relativity seems to be self-contradiction in that he concluded the nonexistence of absolute motion of any matter only after assuming the existence of absolute moving entity, light."

I think the assumption and the conclusion must show a consistency in the sense that relativistic result must be derived from the relativistic property. The conclusion on the nonexistence of absolute time and space which is derived from the existence of absolute velocity of light which is absolutely moving in space seems to be similar with a son denying the connection with his mother.
One more thing I would like to point out is that it is impossible to see only the notion of absolute moving without the notion of absolute rest. I think the opposite notion of moving is resting. So if light is absolutely moving in space, then we need to accept that there exists the notion of "absolute rest" because the notion for moving and rest is like the head and tail of a coin as we always can see the relative resting and relative moving between two inertial frames. If you agree with light is moving absolutely in space, you must also accept the notion of absolute rest. What do you think that?

Added more.

What the second postulate of SR, the constant speed c of light in every inertial frame of reference, imply is that there is the absolute time because it fits well with the Newtons's definition for the absolute time.

Quoting Newton,

“Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external …”The constant speed of light means that light moves always and does change its position in time in every inertial frame of reference, in other words, time flows equably and the uniform time flow rate is defined as the unit distance r over the constant speed c of light independently of any perceiver or neighbors. This time flow rate in a true empty space is universal and does not change by anything so can be considered as "absolute".

 

[A.T.]

But what do you think about another my observations?

They are of no consequence for the correctness of quantitative predictions, thus are irrelevant to physics.

 

[russ_watters]

Thanks for pointing out my misunderstanding in reading Einstein's paper.

But what do you think about another my observations?

"the Einstein’s theory of special relativity seems to be self-contradiction in that he concluded the nonexistence of absolute motion of any matter only after assuming the existence of absolute moving entity, light."

I think the assumption and the conclusion must show a consistency in the sense that relativistic result must be derived from the relativistic property. The conclusion on the nonexistence of absolute time and space which is derived from the existence of absolute velocity of light which is absolutely moving in space seems to be similar with a son denying the connection with his mother.

You've stated this several times and it has been explained to you that (and how) it is wrong several times. I'm not sure what else can be said - it is up to you whether you want to believe the reality or not.