Paradox of the Stopped Clock

[James_S_Saint]

@Carleas

@James S Saint

Any problem with that?

Yes, the same problem that you seem to think you’ve addressed. You’re misinterpreting your own claim:

@James S Saint

He cannot conclude what he has no means to measure

Note that it’s “he cannot conclude,” not “he can conclude in the negative.” Just because we aren’t letting him measure, e.g., the time between the arrival of the images from the two clocks, does not mean that he is content to conclude that they are synchronous.

First, it was Einstein’s statement, not mine individually.

Secondly, we are not concerned with synchronicity. We are concerned with merely identical setting.

@Carleas

@James S Saint

No one said anything about them being synchronous to the train, but “set identical” to each other.

1. I didn’t say synchronous to the train, I said “synchronized in [the train’s] frame.”

That is what I meant (I couldn’t think of how to say it) - same response though - he can’t proclaim anything about it - yet.

@Carleas

1. Two clocks that are “set identical” are called “synchronous.”

Neither true nor claimed by me (nor relevant).

@Carleas

1. The clocks are not “set identical” in the train’s frame.

Now you are arguing with yourself;

@James S Saint

D) He witnesses that they both read identically.

How can he conclude that they are not set identically?

@Carleas

I don’t disagree with anything you’re saying, but I would argue that this shows that simultaneity is relative:

@Carleas

They flash at different times, but because they are not measuring time as it passes in the train’s frame of reference, they flash the same image.

That was stated and you agreed.

@Carleas

Any number of measurements made by an observer on the train would reveal that the clocks are not telling time appropriately in the train’s frame of reference.

Perhaps, but not relevant. We are only ensuring that both the train observer and the station observers know that they were set identically. You are the one who brought up synchronicity.

You agreed that they know this.

So back to the question of;
Equal Setting + Equal Treatment = Equal Result.

They both know that the setting was equal. They both know that the treatment was equal.

[Dienes]

@James S Saint

A) The train observer knows that light goes the same speed whether going forward or backward with his own motion.
B) He knows and can see the distance traveled by the photons was the same.

The train observer will not see the distances travel as the same, as the front clock will move towards the photon and the back clock will move away from it. Thus it will appear to the train observer that the clocks were illuminated at different times and merely happened to display the same thing when illuminated. Using SRT he can work out that the clocks flashed at the same time in their own reference frame, but that’s not what he observed and knowing that all reference frames are equally valid he has no reason to say the clocks are actually set identically in an absolute sense. Any attempt to say the clocks are set identically must include the frame of reference that observation is made in, and the statement will only be correct in that reference frame (or one moving at the same velocity as it). It is exactly as accurate to say the clocks were set unequally in a different reference frame, but again that statement is only valid in that reference frame.

Consider this:
A man sees a clock reading 1:00.
Some time passes.
He sees a second clock that reads 1:00.

Will he conclude that the clocks are set the same?

Does it have any meaning to say two clocks are set identically but at different times?

[James_S_Saint]

@Dienes

@James S Saint

A) The train observer knows that light goes the same speed whether going forward or backward with his own motion.
B) He knows and can see the distance traveled by the photons was the same.

The train observer will not see the distances travel as the same, as the front clock will move towards the photon and the back clock will move away from it.

Ahh… but now you are jumping ahead.

The train observer sees that the distances ARE equal, but he sees that the button is moving out of center from the photon’s origin. Thus he is faced with the exact same paradox, only earlier. Just as with the station’s clock, he sees the object moving out of center of the photons. But the DISTANCE from button to each timer he sees as steadily equal.

@Dienes

Thus it will appear to the train observer that the clocks were illuminated at different times and merely happened to display the same thing when illuminated.

Except that he knows that when together (back to back) they were set identical and identically treated afterward (your complaint of direction of separation is not applicable).

@Dienes

Using SRT he can work out that the clocks flashed at the same time in their own reference frame,

Only if he ignores what he already knew for sake of a theory that is under test. As Einstein said, “Until you can measure it, you cannot conclude else you deceive yourself” (paraphrased). He directly witnessed the setup. He cannot then use a presupposed theory to deny what he has already seen, else he is reverse engineering the evidence to suit the theory = bad Science (= religion).

@Dienes

he has no reason to say the clocks are actually set identically in an absolute sense.

He need not conclude absoluteness. He merely needs to not deny what he already has witnessed.

@Dienes

Consider this:
A man sees a clock reading 1:00.
Some time passes.
He sees a second clock that reads 1:00.

Will he conclude that the clocks are set the same?

Not relevant to the example.

He SAW them set identically. He SAW them being treated identically. He SAW equal readings (results) which he knows could only have come from the photons striking the timers.
Equal Setting + Equal Treatment = Equal Result.

That is a theory that he cannot deny regardless of anything he sees or otherwise believes (else he cannot ever accept any theory from Science at all).

[Carleas]

@James S Saint

B) He knows and can see the distance traveled by the photons was the same.

@Dienes

The train observer will not see the distances travel as the same, as the front clock will move towards the photon and the back clock will move away from it.

@James S Saint

Ahh… but now you are jumping ahead.

How is this jumping ahead? It’s a direct contradiction of one of the premises.

@James S Saint

The train observer sees that the distances ARE equal

Dienes is right on this one; I missed this too. If I throw a football to you while you’re running away from me, the distance the football travels before it hits you isn’t the distance from me to you when I throw it, it’s the distance when you catch it. Similarly, if the clocks are moving (which they are in the train’s frame), then they will move towards and away from the photons, respectively, so the photons will travel different distances.

@James S Saint

He SAW them set identically.

This seems to beg the question: The train observer needs to begin with the premise that the clocks are set identically. Nothing he observes within the context of the scenario tell him that that is the case.

@James S Saint

He SAW them being treated identically.

If they were “treated identically,” how did they end up at different positions?

@Dienes

Consider this:
A man sees a clock reading 1:00.
Some time passes.
He sees a second clock that reads 1:00.

Will he conclude that the clocks are set the same?

Does it have any meaning to say two clocks are set identically but at different times?

James, you need to respond to this. If your paradox is about things being “set identically,” and that is some special term that doesn’t mean “reading the same time at the same time,” you need to offer some usable definition.

[James_S_Saint]

Carleas, forever the politician.

No, he isn’t right. And as I have been mistaken before, I gave you too much credit for seeing why he isn’t.

Your argument has been from the very beginning that it is impossible for the timers to be set identical. You have tried to use Relativity of Simultaneity to prove your case. Because you said it is “impossible”, all I have to do is come up with a single example of how it is possible for both train observer and station observer to know that they are set identically.

Originally, I merely stated that the person setting them, set them at the same time, end of story. But you claimed such is impossible because they will not be the same time from the train’s perspective (or the station depending on when/where they are set).

1. You know that when 2 clocks are in the same location, as in back to back, they will appear to both frames as the same time.
2. It is at that point when they are set identically
3. The timers are then moved slowly apart for the distance of the railcar, thus treated identically.

Already the Equivalency Equation demands that they are equal. But it doesn’t demand that they will be seen as equal, because the elements involved in sight have not been treated equally. In fact, it implies that they must appear unequal, merely because sight is dependent on closeness and the closeness to an observer was not treated equally.

4. A button is pressed that both parties can see is centered between the 2 timers.
5. When the photons from the button reach the timers, they do indeed display that they are still identical to both parties.

Any speculation whatsoever concerning any theories are immediately trumped by the Equivalency Equation and the witnessing of those events.

Both parties know that they were equally set. Both parties know that they were equally treated. Both parties know that the closeness has changed and thus they must not appear equally running (simultaneity). Thus both parties know to ignore the timing from sight as it involves unequally treated closeness, but attend to the image from the timers and the witnessing of the treatment.

No theory of Science can contend with the Equivalency Equation.

I have provided one example of how they can be known as and seen as equally set by both parties.
Thus the setup is NOT impossible.

Every paradox has a real solution. You will never find a paradox that I personally cannot logically resolve. You have merely been focused on and distracted by a tempting notion.

End of this Red Herring distraction from the REAL solution.

[Dienes]

@James S Saint

Ahh… but now you are jumping ahead.

The train observer sees that the distances ARE equal, but he sees that the button is moving out of center from the photon’s origin. Thus he is faced with the exact same paradox, only earlier. Just as with the station’s clock, he sees the object moving out of center of the photons. But the DISTANCE from button to each timer he sees as steadily equal.

This is not jumping ahead at all. Both observers will see the distance from the emitters to the button as equal, but just as the button is moving away from the train observer the front emitter is moving towards him. Thus the distance the photon must travel to reach the front emitter is shorter than the distance the rear photon will travel. So the train observer sees the front emitter light up first.

Only if he ignores what he already knew for sake of a theory that is under test. As Einstein said, “Until you can measure it, you cannot conclude else you deceive yourself” (paraphrased). He directly witnessed the setup. He cannot then use a presupposed theory to deny what he has already seen, else he is reverse engineering the evidence to suit the theory = bad Science (= religion).

We are not trying to prove SRT here, you are trying to prove that there is a paradox within SRT. Thus you must assume SRT to be correct as your first step, otherwise your paradox is outside SRT and is not a paradox. If you do not assume SRT is true then your ‘paradox’ is not a paradox in SRT but in Jamesativity.

He need not conclude absoluteness. He merely needs to not deny what he already has witnessed.

But what has he witnessed? Two clocks an equal distance from him showing the same display after at two different times not proportionate to the distance separating the two sources. How can he conclude that they are identical? Which leads directly to:

@Dienes

Consider this:
A man sees a clock reading 1:00.
Some time passes.
He sees a second clock that reads 1:00.

Will he conclude that the clocks are set the same?

[Dienes]

@James S Saint

1. You know that when 2 clocks are in the same location, as in back to back, they will appear to both frames as the same time.
2. It is at that point when they are set identically
3. The timers are then moved slowly apart for the distance of the railcar, thus treated identically.

Moving them in opposite directions is not equal treatment. If it was they would have to end up in the same place. If we stand back to back and I walk 1 mile north and you walk 1 mile south do we end up in the same place? Your argument is that the magnitude of the speed and distance traveled is all that maters, no theory of physics and no observations of reality agree with that.

So we see clearly that even if we set them identically while they are together separating them must be unequal treatment. In SRT, which you assumed true in your first step so as your ‘paradox’ would disprove SRT, separating things spatially in the direction of motion of a reference frame also separates them temporally in that reference frame. Thus in both reference frames they are not treated equally so your equivalence equation is not relevant.

[James_S_Saint]

@Dienes

This is not jumping ahead at all. Both observers will see the distance from the emitters to the button as equal, but just as the button is moving away from the train observer the front emitter is moving towards him. Thus the distance the photon must travel to reach the front emitter is shorter than the distance the rear photon will travel. So the train observer sees the front emitter light up first.

Yes, he will, but he will see that it reads identically to the other. He has already run into a paradox. They must be equal, yet they seemingly, by ISRT, can’t be equal because of the extra time it took for the photons to reach the identically set timers.

@Dienes

We are not trying to prove SRT here, you are trying to prove that there is a paradox within SRT.

No, I am using the Equivalency Equation to prove the setup. YOU are presuming ISRT overrides the EE. It doesn’t and can’t. I don’t need ISRT to substantiate the setup as the EE is a higher principle. If you contend with ISRT, you simply disprove your ISRT, at best.

@Dienes

Thus you must assume SRT to be correct as your first step, otherwise your paradox is outside SRT and is not a paradox.

It becomes a paradox at the point of the station, IF you had accepted the equal setup in the original scenario. But because you now claim argument with the setup, you now have the paradox at the setup. Your IRST must now prove itself to be either in agreement with EE, or to be false.

@Dienes

Will he conclude that the clocks are set the same?

How can he rationally argue that they are not?
He has seen their faces. He has seen that they were equally set. He has seen that they were equally treated. He has seen that one is now closer to him and he must give extra time for any measurement of time from it. But he hasn’t measured any time from them, only their setting. Any other assumption he makes contradicts the EE.

[James_S_Saint]

@Dienes

Moving them in opposite directions is not equal treatment. If it was they would have to end up in the same place.

That was covered. The Equivalency Equation deals with elements relevant to the issue at hand.

The degree/magnitude of colinear motion is the only element relevant to time dilation and thus synchronicity. The degree/magnitude of motion was equal for the timers.

The direction of motion, doesn’t affect time dilation, but merely the closeness of each. The closeness is relevant to the appearance of synchronicity and time delay of any flash reaching the observer.

The appearance of synchronicity is NOT any part of the setup.

[Dienes]

@James S Saint

@Dienes

This is not jumping ahead at all. Both observers will see the distance from the emitters to the button as equal, but just as the button is moving away from the train observer the front emitter is moving towards him. Thus the distance the photon must travel to reach the front emitter is shorter than the distance the rear photon will travel. So the train observer sees the front emitter light up first.

Yes, he will, but he will see that it reads identically to the other. He has already run into a paradox. They must be equal, yet they seemingly, by ISRT, can’t be equal because of the extra time it took for the photons to reach the identically set timers.

Why must they be equal? All he has seen is that they display the same image at different times not proportional to their spacial distance from him and thus not equal to just the delay in the photons reaching him. The only logical solution I can see to that is that they are set differently in the train’s reference frame. If you want to simply assert they are equal you have assumed that SRT is false and thus any conclusion based on that cannot be used to disprove SRT.

@James S Saint

That was covered. The Equivalency Equation deals with elements relevant to the issue at hand.

The degree/magnitude of colinear motion is the only element relevant to time dilation and thus synchronicity. The degree/magnitude of motion was equal for the timers.

The direction of motion, doesn’t affect time dilation, but merely the closeness of each. The closeness is relevant to the appearance of synchronicity and time delay of any flash reaching the observer.

Um, in SRT the direction of spacial distance does impact the time displacement of an object. Thus two objects moving in opposite directions will not be equal in SRT. This is quite obvious if you look at the Lorentz Equations.

Given x as a spacial coordinate of an object and t as the temporal coordinate in inertial reference frame R, the Lorentz Equation to find the temporal coordinate t’ in a different inertial reference frame, R’, moving with velocity v relative to R is t’ = (1/sqrt(1-(v^2/c^2))(t-xv/c^2).

As this varies based on the t, v, and x we can clearly see that moving two objects in different directions will yield different x values and thus different t’ values. Thus moving them in different directions is different treatment and the equivalency equation does not apply.

[James_S_Saint]

@Dienes

Why must they be equal?

Because;

He has seen their faces.
He has seen that they were equally set.
He has seen that they were equally treated.
He has seen that one is now closer to him and he must give extra time for any measurement of time from it.
But he hasn’t measured any time from them, only their setting.
Any other assumption he makes contradicts the EE.

@Dienes

Um, in SRT the direction of spacial distance does impact the time displacement of an object.

Oh now you want to claim “time displacement” issues.

Wake up… He isn’t measuring ANY TIME at all. He doesn’t need it.

[Dienes]

@James S Saint

Because;

He has seen their faces.
He has seen that they were equally set.
He has seen that they were equally treated.
He has seen that one is now closer to him and he must give extra time for any measurement of time from it.
But he hasn’t measured any time from them, only their setting.
Any other assumption he makes contradicts the EE.

Well first they aren’t treated equally as I have shown. Second the time between when the first image arrives and the second image arriving is not proportional to just the distance between the clocks and the observer. So even adjusting for one being closer he still observes a delay between the images and should logically conclude they are set differently.

Oh now you want to claim “time displacement” issues.

Wake up… He isn’t measuring ANY TIME at all. He doesn’t need it.

He isn’t measuring time, but the clocks are otherwise they wouldn’t be clocks. For your ‘paradox’ to work the clocks must be in sync, but in SRT moving the clocks in opposite directions spatially moves them in opposite directions temporally as well in the train’s reference frame. When the clocks are moved temporally they are no longer in sync as they will no longer agree on their time. This is the same issue I have been arguing from the start.

In SRT its impossible to have two objects in an inertial reference frame separated by a distance in the direction of travel of another reference frame will appear to be at different temporal positions in the second reference frame as well. Thus if they agree on the time (are in sync) in the first reference frame they cannot agree on the time (be in sync) in the second reference frame. If you simply assert that both clocks agree on the time (are in sync) in both reference frames you are no longer working with SRT but Jamesativity so any conclusions you reach have no bearing on SRT but on Jamesativity.

[James_S_Saint]

@Dienes

Well first they aren’t treated equally as I have shown.

You have shown nothing. Merely repeating yourself.

@Dienes

Second the time between when the first image arrives and the second image arriving is not proportional to just the distance between the clocks and the observer. So even adjusting for one being closer he still observes a delay between the images and should logically conclude they are set differently.

He has no need to adjust for anything. He already has seen their faces and knows how they were treated.

@Dienes

He isn’t measuring time, but the clocks are otherwise they wouldn’t be clocks.

He only sees the flash of their face. He cannot measure time that way.

In fact, the timers could be set in his presence the day before while he was in their frame.
He need not see the timers at all from the train to know that they are set identically.

[James_S_Saint]

Tell you what…

Since we have narrowed the whole issue to merely the setup, let’s make the entire paradox about that one concern;

1. Instead of timers, we use stop-clocks that stop when struck by the light and flash their reading.
2. The clocks are set back to back and then slowly separated as witnessed by all parties in that same frame.
3. A button is place half way between the stop-clocks (formerly timers)
4. The stop-clocks are locked and forbidden to be touched.
5. One observer gets onto the train and as the train nears the stop-clocks, the button is pushed.
6. The train observer sees the same image from both stop-clocks and they stop.
7. When the train observer gets off the train, he checks and sees that both timers stopped at the same reading.

But according to your ISRT, he could not have seen the same image. Yet he did and verified it.

[Dienes]

@James S Saint

@Dienes

Well first they aren’t treated equally as I have shown.

You have shown nothing. Merely repeating yourself.

No I have shown through the Lorentz Equations that spacial displacement in opposite directions is also temporal displacement in opposite directions. You simply keep asserting that I am wrong without giving any evidence that I am.

@Dienes

Second the time between when the first image arrives and the second image arriving is not proportional to just the distance between the clocks and the observer. So even adjusting for one being closer he still observes a delay between the images and should logically conclude they are set differently.

He has no need to adjust for anything. He already has seen their faces and knows how they were treated.

If he’s not adjusting for anything and knows they are clocks then when he sees them have the same image at different times he will conclude they are not in sync and thus not set identically.

@Dienes

He isn’t measuring time, but the clocks are otherwise they wouldn’t be clocks.

He only sees the flash of their face. He cannot measure time that way.

In fact, the timers could be set in his presence the day before while he was in their frame.
He need not see the timers at all from the train to know that they are set identically.

Even if they were set in sync with the observer there he will still observe them to be out of sync when he passes on the train because in the train’s reference frame the clocks are not in the same place spatially and are therefore in different temporal locations as well. No amount of prior knowledge will change the observations. The same image will arrive at different times that is not proportional to the distance separating the emitters from the observer. Same image at different times from two clocks must imply the clocks are not equal.

[James_S_Saint]

@Dienes

No I have shown through the Lorentz Equations that spacial displacement in opposite directions is also temporal displacement in opposite directions. You simply keep asserting that I am wrong without giving any evidence that I am.

No. I explained why your response was not appropriate. But you ignore my answer so as to merely repeat yourself.

Now address the paradox of the setup itself as described above.

I warned you that if you challenge the Equivalency Equation, you would have to at best, merely prove your ISRT to be false. So let’s have it.

@James S Saint

Since we have narrowed the whole issue to merely the setup, let’s make the entire paradox about that one concern;

1. Instead of timers, we use stop-clocks that stop when struck by the light and flash their reading.
2. The clocks are set back to back and then slowly separated as witnessed by all parties in that same frame.
3. A button is place half way between the stop-clocks (formerly timers)
4. The stop-clocks are locked and forbidden to be touched.
5. One observer gets onto the train and as the train nears the stop-clocks, the button is pushed.
6. The train observer sees the same image from both stop-clocks and they stop.
7. When the train observer gets off the train, he checks and sees that both timers stopped at the same reading.

But according to your ISRT, he could not have seen the same image. Yet he did and verified it.

[Dienes]

@James S Saint

Tell you what…

Since we have narrowed the whole issue to merely the setup, let’s make the entire paradox about that one concern;

1. Instead of timers, we use stop-clocks that stop when struck by the light and flash their reading.
2. The clocks are set back to back and then slowly separated as witnessed by all parties in that same frame.
3. A button is place half way between the stop-clocks (formerly timers)
4. The stop-clocks are locked and forbidden to be touched.
5. One observer gets onto the train and as the train nears the stop-clocks, the button is pushed.
6. The train observer sees the same image from both stop-clocks and they stop.
7. When the train observer gets off the train, he checks and sees that both timers stopped at the same reading.

But according to your ISRT, he could not have seen the same image. Yet he did and verified it.

There is still no paradox. The observer on the train will see the clocks being out of sync but also stopped at different times. The clock that’s running ahead will stop first, then some time will pass and then the second clock will stop while displaying the same thing the first clock did.

The observers knowledge of how it was setup doesn’t change his observations that the clocks are out of sync when he is on the train. This is perfectly logical as his knowledge of the setup is from a different reference frame than his observations on the train. They must be out of sync because the images arrived at different times that just their spatial separation cannot account for. After you account for the spatial separation it reduces to the observer seeing the first image, some time passing, then the observer seeing the same image from the second clock. Therefore he concludes that in the train’s reference frame the clocks were out of sync.

This does not contradict what he saw when everything was setup because the train’s reference frame is not more correct than any other reference frame. But it also means that the clocks are not identical in an absolute sense either. the clocks’ agreement and thus synchronicity is dependent on what reference frame they are measured in.

And again you are changing the question when you start to get backed into a corner.

[James_S_Saint]

@Dienes

The observers knowledge of how it was setup doesn’t change his observations that the clocks are out of sync when he is on the train.

He doesn’t see the clock faces until they flash.
I take it that you forgot that the entire 7 day experiment was done at night, so they could see the flashes.

@Dienes

The clock that’s running ahead will stop first, then some time will pass and then the second clock will stop while displaying the same thing the first clock did.

But he knows that neither is “running ahead”. They are identical clocks and in the same time frame.

@Dienes

There is still no paradox. The observer on the train will see the clocks being out of sync but also stopped at different times.

How is that not a paradox?
He knows that they were set equally.
He knows that they have stayed in the same environment the entire time.
He knows that they only stop when hit by the light.

Equal Setting + Equal Treatment = Equal Result

Yet one is closer to him and according to your ISRT, must read differently.

[Dienes]

But he knows that neither is “running ahead”. They are identical clocks and in the same time frame.

They are set the same in one reference frame. In another they are not set the same. As I said in my last post:

The observers knowledge of how it was setup doesn’t change his observations that the clocks are out of sync when he is on the train. This is perfectly logical as his knowledge of the setup is from a different reference frame than his observations on the train. They must be out of sync because the images arrived at different times that just their spatial separation cannot account for. After you account for the spatial separation it reduces to the observer seeing the first image, some time passing, then the observer seeing the same image from the second clock. Therefore he concludes that in the train’s reference frame the clocks were out of sync.

This does not contradict what he saw when everything was setup because the train’s reference frame is not more correct than any other reference frame. But it also means that the clocks are not identical in an absolute sense either. the clocks’ agreement and thus synchronicity is dependent on what reference frame they are measured in.

@Dienes

There is still no paradox. The observer on the train will see the clocks being out of sync but also stopped at different times.

How is that not a paradox?
He knows that they were set equally.
He knows that they have stayed in the same environment the entire time.
He knows that they only stop when hit by the light.

Equal Setting + Equal Treatment = Equal Result

Yet one is closer to him and according to your ISRT, must read differently.

You are clearly having some problems with simple logic at this point. They are set equally in one reference frame, not in all reference frames. The clocks have not changed reference frames but the observer has. He no longer observes them as equal as I showed above. He also knows the clocks will stop when the light hits them, but because he observes the clocks as moving the light will reach them at different times. Thus the clocks will stop at different times in the train’s reference frame. But because the clocks are not in sync in the train’s reference frame (because they showed the same display at two different times above) stopping at different times in the train’s reference frame does not mean stopping when two different times are displayed.

No matter how often you repeat Equal Setting + Equal Treatment = Equal Result will not make it applicable. The timers cannot be set the same in different reference frames if they are not in the same place, and if they are moved to different places that’s not equal treatment in SRT so they will not remain equal.

[James_S_Saint]

@Dienes

But he knows that neither is “running ahead”. They are identical clocks and in the same time frame.

They are set the same in one reference frame. In another they are not set the same.

The other frame doesn’t even exist when they are set.

@Dienes

You are clearly having some problems with simple logic at this point.

Are you talking to yourself now? Or are you simply not reading what you don’t want to read?

@James S Saint

@Dienes

The observers knowledge of how it was setup doesn’t change his observations that the clocks are out of sync when he is on the train.

[size=150]He doesn’t see the clock faces until they flash.[/size]

@Dienes

No matter how often you repeat Equal Setting + Equal Treatment = Equal Result will not make it applicable.

That equation is ALWAYS applicable.