What caused us to have relative time

[Dale]

In short, E had no justification for his relative simultan. as far as I can see. Do you see any?

Of course he had justification. The two postulates. Not only do they justify it, they require it.

 

[ghwellsjr]

Well, the 1st post. does not pertain to simultaneity at all, it merely says that all inertial observers must find the same general laws. And the 2nd post. says that such observers must all get c for light's speed from Point A to Point B in their respective frames, but I fail to see this happening experimentally or even how it could happen.

The 2nd postulate does not say that observers must all get c for light's speed between two points, it defines it.

OTOH, any pair of clocks in any inertial frame could possibly become absolutely synch'd by sheer accident (or by monkeys pushing buttons), and yet this would not in any way violate any physical law, so said clocks won't self-destuct or destroy the universe. They are not forbidden.

What is your definition of "absolutely synch'd"? Are you going to continue to keep it a secret? How can we respond if you won't give us your view?

If you read Einstein, you will see that he merely recommended *discarding* absolutely synch'd clocks, but never said that they cannot actually exist.

I don't recall Einstein ever saying that. Could you please provide an online link and either specify the exact location in the material where he said those words and/or provide an exact quote?

 

[spaced-out]

Of course he had justification. The two postulates. Not only do they justify it, they require it.

Mr. Dale, can you tell me how the postulates justify using light rays from two events to determine their temporal order? Thanks!

 

[spaced-out]

The 2nd postulate does not say that observers must all get c for light's speed between two points, it defines it.

Exactly how?

What is your definition of "absolutely synch'd"? Are you going to continue to keep it a secret? How can we respond if you won't give us your view?

My def is the same as E's:
"[In classical physics] [t]he simultaneity of two definite events with reference to one inertial system involves the simultaneity of these events in reference to all [other] inertial systems. This is what is meant when we say that the time of classical physics is absolute." [Einstein's book _Relativity_, p. 149]

I don't recall Einstein ever saying that. Could you please provide an online link and either specify the exact location in the material where he said those words and/or provide an exact quote?

"Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears."

http://www.bartleby.com/173/9.html

 

[Nugatory]

Mr. Dale, can you tell me how the postulates justify using light rays from two events to determine their temporal order? Thanks!

If you accept the postulate of the constant speed of light, then you can determine the temporal order from the distance and the light travel time: If a light signal is emitted from a point 5 light-seconds away from me and it reaches me at time N, I can infer that the emission event occurred at time N-5. This let's us make statements like "Emission event A happened at a point 10 light-seconds away and the light reached me at time 12; Emission event B happened at a point 4 light seconds away from me and the light reached me at time 7; Therefore B happened one second after A". That's temporal ordering, based on the postulate of the constancy of the speed of light.

[Edit - this is also the justification for using the light arrival times as the basis of the "which happened first" analysis in the train experiment on relativity of simultaneity. The train experiment is simplified a bit by placing the observers in the middle so that the distances between both events and the observer is equal, but you can go back and do the numerical calculations in terms of the separation distance, and you'll get the same outcomes]

 

[Nugatory]

And the 2nd post. says that such observers must all get c for light's speed from Point A to Point B in their respective frames, but I fail to see this happening experimentally or even how it could happen.

There are several arguments in favor of this constant speed of light postulate.

One is the argument from the laws of electricity and magnetism that I gave back in post #20. Constructing a sensible physics around the prediction of a constant velocity equal to c was the big unsolved problem of physics during the second half of the 19th century, and the reason why the title of the 1905 paper was "On the electrodynamics of moving bodies".

The second is the experimental evidence, starting from the Michelson Morley experiments: Try this section of the FAQ on experimental confirmation of special relativity.

The third is that when we carry these postulates to their logical conclusion, we find experimental testable predictions that have been tested, have been confirmed to the limits of experimental accuracy, and that cannot be explained by any other currently known theory. For that, you can refer to other sections of that FAQ.

 

[Integral]

We need to eventually stop asking "why" and just take some postulates, that I can agree. Sadly, the postulate about light speed constancy is (to me at least) very far from being logical, natural or easy to accept. Maybe it "just is" the way how universe works and there is nothing more fundamental behind that, but I hope that some day there is a new theory, based on logical and obviously true sounding postulates, that also includes and explains the results of relativity.

To address this you do not look to Einstein and relativity. Instead look to Maxwell. He predicted the constancy of the speed of light in the 1860's. Physicists spend the next 40yrs trying to show him wrong. They couldn't. That is why Einstein was able to postulate it in 1905.

 

[Dale]

Mr. Dale, can you tell me how the postulates justify using light rays from two events to determine their temporal order? Thanks!

If you know the speed of a signal and the distance it traveled to reach you then you know when it was emitted. The second postulate asserts that you know the speed of a light signal.

 

[ghwellsjr]

Well, the 1st post. does not pertain to simultaneity at all, it merely says that all inertial observers must find the same general laws. And the 2nd post. says that such observers must all get c for light's speed from Point A to Point B in their respective frames, but I fail to see this happening experimentally or even how it could happen.

The 2nd postulate does not say that observers must all get c for light's speed between two points, it defines it.

Exactly how?

If you had read the article that I referenced in post #26, you'd already know the answer to your question. Here's the process:

1) Measure the distance between the two points with your ruler.

2) Place a mirror at the second point so that a flash of light emitted from the first point will reflect back to the first point.

3) Observe the time on a clock located at the first point when a flash of light is emitted from the first point and aimed at the mirror located at the second point.

4) Observe the time on the clock when the reflection of the flash off the mirror at the second point reaches back to the first point where the clock is located.

5) Double the distance measured in step 1 and divide it by the difference between the two observed clock times from steps 3 and 4. This is the measured value of c.

6) Divide the measured value of c from step 5 into the distance measured in step 1 to get the propagation time for light to go from the first point to the second point in order to fulfill the defined propagation speed of c.

7) Replace the mirror at the second point with a second clock.

8) Observe the time on the clock located at the first point when a flash of light is emitted from the first point and aimed at the second point.

9) Observe the time on the clock located at the second point when the flash of light reaches it.

10) Subtract the observed time on the first clock from the observed time on the second clock and compare the difference to the propagation time determined in step 6.

11) If the comparison is not zero, adjust the time on the second clock to get it closer to zero and repeat steps 8, 9 and 10 until the comparison is zero.

Is that exact enough for you?

OTOH, any pair of clocks in any inertial frame could possibly become absolutely synch'd by sheer accident (or by monkeys pushing buttons), and yet this would not in any way violate any physical law, so said clocks won't self-destuct or destroy the universe. They are not forbidden.

What is your definition of "absolutely synch'd"? Are you going to continue to keep it a secret? How can we respond if you won't give us your view?

My def is the same as E's:
"[In classical physics] [t]he simultaneity of two definite events with reference to one inertial system involves the simultaneity of these events in reference to all [other] inertial systems. This is what is meant when we say that the time of classical physics is absolute." [Einstein's book _Relativity_, p. 149]

Here's a link to your quote (it's about three quarters of the way down in the section entitled "The Field"):

http://www.relativitybook.com/resources/Einstein_space.html

And the very next sentence is:

According to the special theory of relativity it is otherwise.

And why is it otherwise? Because classical physics doesn't comport with reality. In post #26, I asked you for your definition of time that would comport with reality and you say it's the same as what classical physics defined. Your comment that "any pair of clocks in any inertial frame could possibly become absolutely synch'd by sheer accident" is not true as Einstein points out in this article. Don't you read the whole thing or do you like taking quotes out of context? Don't you understand that in classical physics, all clocks in all inertial frames can be absolutely synch'ed, no matter what their state of motion or acceleration?

But now that we know that classical physics does not comport with reality precisely because that concept is not true. At best you could define or assert the existence of a single inertial frame in which all stationary clocks are absolutely synch'd but those clocks would not be synch'd in another inertial frame moving with respect to the original one. Do you disagree with this statement?

So if your definition of "absolutely synch'd" is the same as Einstein's, then you must realize that his definition is for the purpose of showing that it is not adequate.

Do you want to try again?

If you read Einstein, you will see that he merely recommended *discarding* absolutely synch'd clocks, but never said that they cannot actually exist.

I don't recall Einstein ever saying that. Could you please provide an online link and either specify the exact location in the material where he said those words and/or provide an exact quote?

"Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears."

http://www.bartleby.com/173/9.html

This quote simply affirms the previous quote--that absolutely synch'd clocks are independent of motion in classical physics. But now we know this is not true. You cannot have all clocks absolutely synch'd. Do you disagree with this statement?

 

[spaced-out]

If you know the speed of a signal and the distance it traveled to reach you then you know when it was emitted. The second postulate asserts that you know the speed of a light signal.

But the one-way speed of light is based on E's def of simultan., which, in turn, is based on assuming that we can use light rays from events to determine their order.

 

[spaced-out]

At best you could define or assert the existence of a single inertial frame in which all stationary clocks are absolutely synch'd but those clocks would not be synch'd in another inertial frame moving with respect to the original one. Do you disagree with this statement?

(FYI: Your clock synch method unjustifiably assumes equal 1-way light speeds)
(FYI: The only reason E gave for discarding truly synch'd clocks was that they were "incompatible with the most natural def. of sim., but this def. assumes that it is OK to use light rays from events to determine their order, whilst totally ignoring different frame movement as the rays approach.)
(FYI: The overall purpose for the creation of SR was to work around the existing conflict btn the PR and the simple light law (the fact that light's speed in space is c constantly due mainly to light's source independency), but this conflict is bogus because the PR never denied absolute motion detect. since it alllows the law w = c - v for all observers.)

As for your above, just as with E synch., each frame's clocks could be independently truly synch'd (given a method for this), and they would remain that way unless a frame accelerated of course, but inert frames don't do this, so we are OK. It does not matter that one frame's clocks would not be synch'd with anothers because all that matters is that any given frame can use their truly synch'd clocks to measure its abs. spd. (as per the above simple equation that was given by E himself). After this, each frame can adjust for clock slowing and ruler contraction because the equations for this are known. And each frame can correctly meas. event order and temporal separation.

There was absolutely no reason whatsoever to abandon truly synch'd clocks (other than the current lack of a method for getting them that way, but this can change overnight).

 

[ghwellsjr]

At best you could define or assert the existence of a single inertial frame in which all stationary clocks are absolutely synch'd but those clocks would not be synch'd in another inertial frame moving with respect to the original one. Do you disagree with this statement?

(FYI: Your clock synch method unjustifiably assumes equal 1-way light speeds)

FYI: It's not my clock synch method, it's commonly attributed to Einstein. Einstein's postulate that all 1-way light speeds are equal does not need any justification other than that it comports with reality. Do you deny that it comports with reality?

(FYI: The only reason E gave for discarding truly synch'd clocks was that they were "incompatible with the most natural def. of sim., but this def. assumes that it is OK to use light rays from events to determine their order, whilst totally ignoring different frame movement as the rays approach.)

If you're going to talk about "truly synch'd clocks", you're going to have to define what you mean. And I don't know what you mean by "totally ignoring different frame movement as the rays approach".

(FYI: The overall purpose for the creation of SR was to work around the existing conflict btn the PR and the simple light law (the fact that light's speed in space is c constantly due mainly to light's source independency), but this conflict is bogus because the PR never denied absolute motion detect. since it alllows the law w = c - v for all observers.)

You're right, the conflict was bogus but not for the reason you state. There simply was no conflict, it was only apparent, as Einstein pointed out in his 1905 paper.

As for your above, just as with E synch., each frame's clocks could be independently truly synch'd (given a method for this), and they would remain that way unless a frame accelerated of course, but inert frames don't do this, so we are OK. It does not matter that one frame's clocks would not be synch'd with anothers because all that matters is that any given frame can use their truly synch'd clocks to measure its abs. spd. (as per the above simple equation that was given by E himself). After this, each frame can adjust for clock slowing and ruler contraction because the equations for this are known. And each frame can correctly meas. event order and temporal separation.

There was absolutely no reason whatsoever to abandon truly synch'd clocks (other than the current lack of a method for getting them that way, but this can change overnight).

Ok, let it change overnight. Let's hear your method. That's what I've been asking for from the very beginning. I expect an answer in 24 hours (based on GPS time). And make sure it comports with reality.

 

[Dale]

But the one-way speed of light is based on E's def of simultan., which, in turn, is based on assuming that we can use light rays from events to determine their order.

That isn't a big problem.

If you have a system of formal logic with some set of axioms, A, and some set of theorems, T, then it is almost always possible to pick some subset of T, A', such that from A' you can derive A. In other words, it is almost always possible to switch which statements you consider to be assumed postulates and which you consider derived consequences.

The usual approach to SR considers the speed of light to be a postulate, and the relativity of simultaneity follows from that. You certainly can construct equivalent alternate axiomatizations of relativity where the speed of light is a derived consequence of the simultaneity convention. They are logically equivalent, so all you have to do is to pick either one you prefer and use it.

 

[spaced-out]

FYI: It's not my clock synch method, it's commonly attributed to Einstein. Einstein's postulate that all 1-way light speeds are equal does not need any justification other than that it comports with reality. Do you deny that it comports with reality?

As I said, it has not happened experimentally, and I fail to see how it can happen. Indeed, I fail to see it happening even on paper. Can you show it on paper using a couple of clocks (that are mutually at rest, as in E's def.)?

If you're going to talk about "truly synch'd clocks", you're going to have to define what you mean. And I don't know what you mean by "totally ignoring different frame movement as the rays approach".

"If an observer sitting in the position M’ in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A."
http://www.bartleby.com/173/9.html

The only reason that the two observers see the light rays differently is their different motions as they view the rays. But E simply ignores this fact and declares that time is relative. In reality, the events happened in only one way, either truly sim. or not, so time is not relative merely because E decided to ignore diff observer motions during the experiment and making them equivalent and "both right."

You're right, the conflict was bogus but not for the reason you state. There simply was no conflict, it was only apparent, as Einstein pointed out in his 1905 paper.

Let me ask you this: OK, what was the apparent conflict?

Ok, let it change overnight. Let's hear your method. That's what I've been asking for from the very beginning. I expect an answer in 24 hours (based on GPS time). And make sure it comports with reality.

To say that there is no reason for discarding truly synch'd clocks does not demand a method for producing them. Also, to say that there is no physical reason why such clocks cannot exist does not call for a showing of how. BTW, if you were put to the test, how would you obtain absolute synch? Could you simply propel two mechanical objects equally toward the clocks from midway btn them?

 

[Sugdub]

If you had to give a physical reason for relative time, what would it be? ...

As already explained by some key contributors to this thread, your question cannot be answered if it is to be understood as “why is the world such that ...”. In the following, taking due account of the sound definition of “time” by ghwellsjr in # 6, I'll assume that the correct wording for your question is “how does the SR theory justify that clocks in relative motion in respect to each other do not tick at the same speed?” Please correct me if my interpretation of your question is wrong.

My answer to the newly formulated question is that the SR theory cannot provide such a justification, this answer being based on pure logical considerations.
If the clocks do not tick at the same speed, it means that one ticks faster than the other: the output of the theory is an order relationship. But logically speaking, an order in the conclusion of a rationale development can only be derived from some order relationship in the inputs to this development. Worded in a slightly different way, an asymmetry in the conclusion can only derive from an asymmetry in the inputs to the reasoning.
Well, let's now look at the inputs: two postulates which formulation aims at specifying equivalence relationships (physics laws are equally valid in all inertial reference frames, and the speed of light is the same in all such frames), plus one symmetrical problem-setting hypothesis stating that two identical clocks are in relative motion in respect to each other.
Three options: either one of the inputs hides an asymmetry / order relationship, or one input is missing, or else the expected conclusion cannot be arrived at from a pure logical standpoint.
I'll discard the first option on the ground that the principle of relativity of motion forbids that one of the clocks could be said moving objectively faster than the other. I'll discard the second option because I fail to see which input is missing. Hence my conclusion.

Let's be very clear: I'm not challenging experimental facts whatever they might show. I'm not rejecting the SR theory, far from it. But I can't see how it could justify that clocks in relative motion in respect to each other would run at a different speed. But may be this is not what the SR theory actually claims … may be somebody will make a very clear statement that will shed some light on this apparent deadlock.

Thanks

 

[Nugatory]

As I said, it has not happened experimentally, and I fail to see how it can happen. Indeed, I fail to see it happening even on paper. Can u show it on paper using a couple of clocks (that are mutually at rest, as in E's def.)?

As I said, it has not happened experimentally, and I fail to see how it can happen. Indeed, I fail to see it happening even on paper

The speed of light being the same for all observers has been confirmed by experiment many times. Indeed, some of these experiments were done before Einstein discovered SR in 1905, and one of the motivations for his postulate of the one-way speed of light was the total failure of these experiments to find any differences in light speed.

But I may be misunderstanding what you're trying to say here? You haven't replied to my post #36 in this thread, so I'm not sure.

 

[PAllen]

If the clocks do not tick at the same speed, it means that one ticks faster than the other: the output of the theory is an order relationship.

This is where you go wrong by not realizing the perfectly symmetrical claim made by SR and observed in experiment:

Each observer finds the other clock going slow. There is no observer independent order relationship. There is no asymmetry at all in what SR claims for a symmetric set up.

 

[PeterDonis]

But may be this is not what the SR theory actually claims

You're right; it isn't. What SR actually claims is that there is no invariant way to compare the "tick rates" of clocks in relative motion. The reason for that is the relativity of simultaneity: clocks in relative motion have different notions of which events happen "at the same time". Comparing the "tick rates" of clocks requires agreement between the clocks on which events happen at the same time, and clocks in relative motion don't meet that requirement.

 

[PeterDonis]

Each observer finds the other clock going slow.

More precisely: each observer finds that the other clock registers less elapsed time than his own between events, when he uses *his* standard of simultaneity. But the two observers use different standards of simultaneity.

 

[Dale]

Worded in a slightly different way, an asymmetry in the conclusion can only derive from an asymmetry in the inputs to the reasoning.

There is no asymmetry in the conclusion. If A and B are two clocks moving inertially wrt each other then A runs slow in B's frame and B runs slow in A's frame. The situations are completely symmetric. Any clock runs slow in any inertial frame where it is moving.

the output of the theory is an order relationship.

No, the output of the theory is a pair of order relationships. A is slower than B in B's frame and B is slower than A in A's frame. Because it is a pair of relationships the relationships are symmetric even though there is an ordering.

 

[Dale]

E simply ignores this fact and declares that time is relative.

No, as I have told you several times already, he derives it from the two postulates.

 

[Ibix]

Isn't the relativity of simultaneity basically the x dependence of the Lorentz transform of time? If there were no x dependence then all observers would agree on the order of events.

Unfortunately, you can't remove the x dependence by letting c be non-constant. You can only do it by making both v and c proportional to x - in other words, rejecting the whole bourgeois notion of "velocity" as a useful concept. I think you can do that by a sufficiently crazy choice of curved coordinate systems but it wreaks havoc on every other aspect of physics, to the point that one needs some heavy duty maths just to work out how long a ruler is. Or, indeed, to define what length is in such a system.

Your only other option is to say that the Lorentz transforms are flat out wrong. Be careful! It'll get you banned, and you are also rejecting the theoretical basis for expecting nuclear reactors to work. Among other things.

Either option seems to me to be an awfully high price to pay for sweeping relativity of simultaneity under the carpet.

 

[pervect]

There is a lot of papers that mention that the choice of simultaneity is a convention - and while this is true, there is some fine print to this freedom.

The "fine print" is that if you want to apply Newton's laws in the low velocity limit, you can't just use whatever convention you like - your choice of conventions is restricted. You can't randomly choose a notion of simultaneity and expect Newton's laws to work.

In fact, it turns out that you're pretty much restricted to using Einstein's simulateity convention, if you require isotropy and linearity - though I haven't seen any paper that formally discusses this issue.

My quick informal argument for why this is true is below:

Newton's laws are isotropic, so any notion of simultaneity that is not isotropic won't be compatible with Newton's laws.

Similarly, applying a non-linear tranformation to space will "break" Newton's laws, so it is important that the transformation be linear.

 

[Sugdub]

I fully concur that:

...Each observer finds the other clock going slow. ...

But this is not the point. I was – explicitly – assessing whether the SR theory can or cannot demonstrate that clocks in relative motion to each other actually run at a different path, i.e. whether there is more than a simple (and reciprocal) “appearance”. And I demonstrated that SR cannot reach that conclusion: whereas relatively moving clocks appear to be running slow (this is reciprocal because there is no asymmetry between observers' roles), SR cannot conclude that they actually are running slow (because this would mean an asymmetry in the actual behavior of the clocks).
Conclusion: According to SR, relatively moving clocks actually don't run slow, this is just an appearance. In other words, and to remain plugged to the initial debate, my time flow is not relative, and if others' time flows appear to be relative to their state of motion in respect to me, this is only an appearance.

 

[Nugatory]

Conclusion: According to SR, relatively moving clocks actually don't run slow, this is just an appearance. In other words, and to remain plugged to the initial debate, my time flow is not relative, and if others' time flows appear to be relative to their state of motion in respect to me, this is only an appearance.

I don't see how you reconcile "just an appearance" with the fact of the muon lifetime measurements (and innumerable other examples observed in particle accelerators).

A question: is what you're calling "my time flow" any different than the proper time measured along your world-line? If so, how?

 

[Dale]

I was – explicitly – assessing whether the SR theory can or cannot demonstrate that clocks in relative motion to each other actually run at a different path

Do you have a scientific definition of "actually". If not, then I think you are talking about some irrelevant (to this forum) philosophical question and not a relevant scientific question.

 

[Mentz114]

I was – explicitly – assessing whether the SR theory can or cannot demonstrate that clocks in relative motion to each other actually run at a different path, i.e. whether there is more than a simple (and reciprocal) “appearance”. And I demonstrated that SR cannot reach that conclusion: whereas relatively moving clocks appear to be running slow (this is reciprocal because there is no asymmetry between observers' roles), SR cannot conclude that they actually are running slow (because this would mean an asymmetry in the actual behavior of the clocks).

This is wrong. I repeat what has been said before here - SR says that a clock shows the proper time along a worldline and provides a way to calculate the elapsed time between events on the worldline. This results in the 'clock paradox' ( Einsteins term) which is not a paradox but actually ensures that causal paradoxes do not happen.

If you could only grasp this it would remove all your (big) misunderstandings.

 

[Sugdub]

Do you have a scientific definition of "actually". If not, then I think you are talking about some irrelevant (to this forum) philosophical question and not a relevant scientific question.

You are welcome. Concerning clocks “actually" running slow I precisely mean what physicists indicate in the context of the “twins” thought experiment: the “moving twin”, when coming back, will be younger than the other one, because his/her clock ran slower all along the trip.
My statement is that SR cannot, from a pure logical standpoint, justify that the “moving clock” ran slower: all inputs being fully symmetrical, the conclusion cannot be non-symmetrical.
Thanks.

 

[PAllen]

You are welcome. Concerning clocks “actually" running slow I precisely mean what physicists indicate in the context of the “twins” thought experiment: the “moving twin”, when coming back, will be younger than the other one, because his/her clock ran slower all along the trip.
My statement is that SR cannot, from a pure logical standpoint, justify that the “moving clock” ran slower: all inputs being fully symmetrical, the conclusion cannot be non-symmetrical.
Thanks.

How about this as a demonstration of symmetric, "actual" time dilation.Alice and Betty each have a sample of the same type of radio-isotope. They are approaching each other rapidly. Alice has laid out an array of geiger counters at rest relative to her, that Betty is passing. Betty has arranged an array of geiger counters at rest relative to her that Alice passing. After they pass each other and each collects information from the geiger counters, Alice finds Betty's isotope was decaying slow compared to hers. Betty finds Alice's isotope was decaying slow compared to hers. Note there is no question of visual effects or Doppler going one here - only the passing of momentarily co-located geiger counters.

 

[Nugatory]

My statement is that SR cannot, from a pure logical standpoint, justify that the “moving clock” ran slower: all inputs being fully symmetrical, the conclusion cannot be non-symmetrical.
Thanks.

All inputs are not symmetrical in the SR version of the twin paradox, which is why it is at least logically possible that conclusion be non-symmetric.

The asymmetry is physically apparent in the fact that the twins experience different acceleration.

It will also show up quite clearly if you just try working the problem in a frame in which the traveling twin is at rest during either the outbound or the inbound leg of the trip (Try it! Don't just take my word for it).