As I have said again and again they are in different positions in space and that has an effect on their position in time as well if you observe them from a different reference frame.
But it takes longer than just the distance between them accounts for thus there is more than just the distance causing the delay thus they must have flashed at different times.
And as I have pointed out again and again, they were set within the same time frame when the train wasn’t even moving.
There was only one time frame when they were set
They were not touched from that point on.
So again, how are they treated differently?
How do you know how much delay the distance is going to account for? I’m certain that you haven’t done the math because if you do the math, your argument gets even worse, much worse.
He can’t ignore that they haven’t been touched just so he can accept that your theory is right. Why not ignore the theory and accept that they haven’t been touched? Why does his knowledge of your theory take precedent over his knowledge of them not being touched? Why would one theory have favor over another much simpler theory (not being touched)?
The fact they are in different spatial positions, no matter when they were placed there, means they will be in different temporal positions, no matter when they are observed.
I’m not arguing they have been touched. I am saying that according to SRT they will be observed to have been lit up at different times.
As far as why we should go with SRT, first you are trying to create a paradox in SRT so you have to actually do what SRT says or your paradox is in Jamesativity. Second when you actually do an experiment like this and not just a thought experiment you find that your physical observations will match the predictions of SRT better than any other theory yet proposed.
Which has what to do with what?
The station time frame sets and sees that they read identically, separated or not.
From that point on, they are treated identically.
“Temporal positions” isn’t relevant.
No one is arguing that point. I stated that myself.
The question is, what image of time will been seen by the train from each?
And how can he explain any difference when he knows they were not touched other than to say that his perception of them is in error (which only makes sense).
No experiment can defy the Equivalency Equation else the experiment is wrong (or all of Science is wrong).
You don’t have an actual experiment for this to argue with any more than I do. Thus you are merely claiming a theory without substance. I have shown logical order that must be true regardless of any experiment.
But since you have decided to continue with this non-sense, let me show you a little of the mathematics Paradox…
They are only identical in the station’s reference frame. If you go into a different reference frame they will display different times. No matter when the observation is made, during the separation or some time after its complete. The fact they are in different positions is different treatment in the framework of SRT. Since they have had different treatment in SRT the Equivalency Equation does not apply.
A question for you is how is there any way to consider them to have had equal treatment and not end up in the same position? And don’t just say position is irrelevant because in SRT position is very important, as is clearly shown by the Lorentz Equations that you were unable to find a flaw in.
The observer on the train will see the same image from each clock but at different times. Because he sees the same displayed time from the first clock, followed by a delay, followed by the same displayed time on the second clock he concludes the clocks are out of sync. Because he knows that no reference frame is more correct than any other he has no reason to say his observations are incorrect. If his perception of them on the train is in error his observations of them off the train are also in error. If the observations off the train are in error we can say nothing at all about anything ever. Or we can say that all reference frames are just as valid as each other.
SRT does not defy the Equivalency Equation. Separating the clocks is treating them differently, thus the Equivalency Equation does not apply. Again it does not matter if the observer on the train sees the clocks being separated or just sees the result (that they are in different places) you cannot apply the Equivalency Equation because the treatment was different. And again if you want to make a paradox in SRT you must actually apply what SRT says or your paradox is in Jamesativity and says nothing about SRT.
As I said before: There is no paradox if you actually follow what SRT says. The observer on the train will see both clocks light up when they display 4:00, but will see them light up at different times. An observer at the station will see both light up when they display 4:00 and will see them light up at the same time. Both reference frames yield the same end result (the clocks stopped at 4:00), but they disagree on the order of events. No paradox.
As there is no way to determine that one frame is the absolute frame of reference you must conclude that both are right or both are wrong. If both are right it leads to logically sound but counter intuitive results. If both are wrong then all observations everywhere in all circumstances are wrong. If all observations are wrong then observations that support the Equivalency Equation are wrong and by your own logic this cannot be. Therefore we can only conclude that all frames of reference are equally valid and the order of events is dependent on the observers frame of reference.
To give this little scenario some numbers to play with, lets say;
The train observer can see the clocks and is going to do all of his calculations merely from what he sees with no other assumptions…
As per ISRT, he ignores the time that it takes for the light to get to him. What he sees is Reality.
The clocks are set to be identical in the station’s frame of reference.
The train is going 0.5 times the speed of light.
The clocks are 6 light-micro-seconds (lus) apart (after length dilation concerns)
When the back clock, B, reads 10us (by the train observer), the train is 6 lus from that clock.
Since the clocks are separated by 6 lus, the front clock, F, must read 4us at that same moment, thus we have;
[4F, 10B] as our initial sighting from the train.
And at that moment is when the button gets pushed;
[4F, 10B] Button pushed
He can see that due to the motion of the clocks toward him it will take 2us for the light to get to the F clock;
[6F, 12B] is when the front clock should trigger and flash
And he can see that due to the motion of the clocks, it will take 4us for the light to get to the B clock;
[8F, 14B] is when the back clock should trigger and flash
Then he waits for the images. 5us later;
[6F, 12B] He sees the image of 6 from F
[8F, 14B] He sees the image of 14 from B
[6F – 14B] with 2us between their sightings
=====================================
But also assuming ISRT;
When the train is 6 lms away and the button is pushed, the station will read;
[16F - 16B]
6 us later the clocks must stop (reversing length dilation);
[22F - 22B]
=====================================
That is what we would expect from Relativity of Simultaneity
But the clocks can only stop at one setting, so did they stop at;
[22F - 22B] or at;
[6F - 14B]
Or perhaps at a different time than either?
THAT is the PARADOX and using ISRT from the get-go.
…and yes, your ISRT DOES assert a violation of the Equivalency Equation.
Hahaha
You cannot ignore both time and length dilation and claim to be working with SRT. Also the time it takes an image to reach him from a clock is not constant, it depends on where he is so it will not be a constant 2us. Your ‘math’ is riddled with errors and thus the conclusion is invalid.
If you repeat it and apply what SRT actually says you will see that both observers will see the clocks light up when they read the same thing, but will not agree on the order of events.
How does SRT violate the Equivalency Equation? No two things that start in the same place and are treated equally (not equally in magnitude but opposite in direction) will be viewed differently.
Are you blind or just inept??
How about YOU repeat it and show your calculations if you want to disagree with something.
I have explained that one too many times already. You are getting ridiculous.
No you never showed that it violated the equivalence equation, you simply asserted that opposite directions were equal. By that logic 1 = -1.
Okay, things have been on an even keel so far. Please don’t let this turn into character assassination. Or it will turn into a LT.
This is the current state of the debate having been narrowed down to the issue of the mere setup of the original scenario with this as a proposed example to demonstrate the same paradox in a simpler form;
If anyone has a LOGIC based response, have at it.
Isn’t the button supposed to be pushed when the train is aligned with it? Wouldn’t that put the train 3 lus from both buttons? I guess we can use this setup is you insist.
No you must account for time dilation of the clocks which is given by gamma(t- vx/c^2) if you are using the standard coordinate system. To find this its probably a good idea to explicitly state your coordinate systems. You can say the back clock reads 10us after time dilation by demanding that in the setup, but if you want to remain in SRT you will have to figure what the front clock says.
Using your setup where the train starts 6 lus from the back clock and thus 12 lus from the front clock and a velocity of .5c and an elapsed time of 2 and 4 us the light does not take 2us to reach him from each emitter. He would be 5 lus from the back clock when it emits and 10 lus from the front clock when it emits. Giving travel times to reach the observer of 2.5us and 5us respectively.
So compute the time dilation of the front clock to find out what it actually reads at the initial condition and then recompute your answer using the correct time it takes the light to reach him and we can move on to the next step. It will help to reduce confusion if you explicitly state your coordinate systems.
I don’t know why you want the train aligned with the button. Such would merely confuse the issue. Unless that is why, I guess.
You cannot calculate a time dilation end result because you do not know any point where they were equal to your own and who accelerated from whom. But you CAN, if you wish, alter the amount of time being passed on the clocks AFTER the noted 10us so as to reflect a slowness compared to the train’s clock. The time dilation would be 0.5
But you have a problem of presumption. The observer does not know whether the train’s clock is slower or the station’s clocks.
I had to show a time stamp, so I chose to show what I personally know the station clocks would read from the station’s perspective. But the train observer doesn’t know that. Although, if he is clever, he could reverse deduce it. But note that he has no means to know if the clocks were ever set identically. And your end result will not change your dilemma.
Agreed.
The 2us and 4us are referring to the light from the button to the clocks, not to the train.
Hmm going back I was mistaken. I had thought you had kept the button press the same as in all the other scenarios, but you didn’t for some reason.
Actually by your setup we know that the clocks are known to be set the same and in sync in the station’s reference frame:
So we can and must account for the time dilation from the train’s perspective. If you don’t do this you aren’t working in SRT but in Jamesativity. Again this is given by gamma(t- vx/c^2) (but those values of t, x, and v are in the station’s reference frame not the trains). Its probably a good idea to explicitly state your coordinate systems as it will help you keep track of everything.
We do know which clock will run slower. The ones on the station will appear to run slower to an observer on the train and the ones on the train will appear to run slower to an observer on the station. But we have no clocks on the train so we can ignore that part. And the time dilation will not b .5 where did you come up with that?
Actually you used 2us twice, once for the light from the button to the clocks and once for the light from the clocks to the observer.
However in my haste to point out these obvious errors I missed a more subtle one. While it takes 2us for the light to go from the button to the clocks in the train’s reference frame the clocks are not in the train’s reference frame. They do not advance 2us, they advance less. You will have to also figure out what this is and then increment the clocks this much to find out what time they light up at. I will give you a hint and let you know they are not dilated 50%, that would be the dilation if the train were traveling at about 86.5% of the speed of light. Since you already made a mistake calculating this its probably a good idea to show your work.
For someone who supposedly already knows the answer and is only here to enlighten us plebs you sure are having a lot of trouble.
We should be using real clocks, as opposed to imaginary clocks. SRT shows that time passes at different speeds in different reference frames, and that’s going to be significant: the train will see the clocks ticking at a different speed, and that is related to how far the train will travel for every change of the face of the clock.
Let’s specify that we’re using light clocks. Suppose each clock is a pair of mirrors a distance L/2 apart, with a photon bouncing back and forth between them perpendicular to the direction of motion. Each time the photon completes the round trip, we can call it a tick, and counting the number of ticks will be how we measure time.
From the point of view of the station, the light in the clock travels L at speed c, so each tick happens every L/c. A train traveling .5c will travel .5L each time it ticks (.5c * L/c).
From the point of view of the train, the clocks themselves are traveling .5c, so the photon between the plates is moving at an angle. We find this by using the Pythagorean theorem a^2 + b^2 = c^2. a is L/2, b is L/4 (since the clock is traveling at .5c, the photon must move half as far horizontally as it travels vertically). So,
c = sqrt( (L/2)^2 + (L/4)^2 ) = sqrt( (L^2)/4 + (L^2)/16 ) = sqrt( (5/16 * L^2 ) = L* sqrt(5)/4
Since it travels twice that to complete a round trip, the total distance traveled is
L * sqrt(5) / 2 > L
The time this takes is
L* sqrt(5) / 2c
and the distance the clock moves in this time is
L* sqrt(5) / 4 > .5L
These clocks are more useful than clocks we’ve been implicitly assuming to read the same in both reference frames. The latter is a sort of “magic clock” that we take for granted, but which isn’t actually achievable; relativity requires us to rigorously examine what we mean by time, and a light clock is a good way to do this because the speed of light is taken to be perfectly constant. Using real clocks highlight the fact of length contraction. Please correct me if my math is wrong.
Not a prob.
That statement was not of this scenario. I did inform YOU that the station clocks were set in sync, but the train observer doesn’t know that. He can only go by what he sees (as per ISRT). If you wish to place time dilation into the scenario, go for it. But like I said, it won’t remove your dilemma.
Well, now you are talking “dienesivity”, but still do what you think works.
Yes, I did misstate that the observer only had to wait 2us for the first flash. I had originally had him only 3 lus from the B clock and didn’t catch everything, so my mistake. Change that to 5us or change the train back to 3 lus from the clock. The rest should be the same.
That is up to your time dilation choice. I left it at zero because it won’t change the dilemma and again, who is moving and who isn’t is a question for you to ignore, yet still answer will calculation.
You help yourself. I was going by memory (usually a bad idea in my case). Like said, it isn’t going to help you.
Well, if you actually addressed the real answer, there wouldn’t be a problem with all of this and I wouldn’t have to set up math problems for you to work out. I’m not your high school teacher.
And btw, when you pick at insignificant errors while ignoring the end result, you put yourself in that category. So far, I have made 1 insignificant error and you have made one significant error in accusation. I am ahead. 
No. A light clock is a bad choice for measuring light. When you presume of one, you presume of the other and thus measure nothing.
“How much do these 10 apples weigh?”
“10 times as much as this one apple.”
I’m pretty sure it was part of this scenario as it was step 2 in the post you outlined the train/button scenario in. It will big a big part in resolving your ‘paradox’. If you don’t wish to have time dilation in the train’s reference frame you are not in SRT and thus not creating a paradox of SRT. And you cannot say that we can’t apply it because we don’t know which frame is actually moving because that’s a meaningless statement in SRT. We know there is a relative motion between them. As far as the observer not knowing the clocks are in sync he doesn’t have to, his knowledge will not change his observations, but in trying to accurately show what SRT predicts he will observe you will have to apply the time dilation, if you don’t your solution is in jamesativity not SRT.
What? That’s exactly what SRT predicts. Go look it up anywhere or if you think all sources are equally incorrect for some reason its one of the simpler results of the premises of SRT to derive. In fact Carleas derived it in his post above. Its easier to illustrate why if you use light clocks, but any clock will show the same effect (that it ticks slower when observed from a reference frame with relative motion to the clock).
Um, it will pretty seriously change the outcome and again failing to do it means you are not working in SRT.
You aren’t my high school teacher but you are trying to convince me of something using math. Doing all the math wrong and refusing to correct it is not a good way to do it. Since you are the one trying to show the paradox I will wait for you to fix your errors and then we can go on to the rest of your solution.
Actually you made 2 mistakes that completely invalidate your argument (not dilating the initial condition of the front clock, and not accounting for time dilation in the times the clocks display when lit up), and the additional grievous error of claiming that your mistakes are not relevant and thus putting your argument outside SRT and thus disproving your ‘paradox’ right off. And one minor error in when the observer will see the lit up clocks.
And how am I in error for simply disagreeing with you in a point that has not yet been settled? By my count that puts you at 3.1 errors and me at 0, so I’m ahead. Of course you will just go back to your equivalency equation logic and say -1 = 1 and thus you are ahead because 0 is greater than 3.
Emm… are you having trouble reading?
I told you to put it in there as you wish. It is right there in what you quoted.
I’m not going to confuse you by getting into that issue. You do what you think works. We’ll take it from there.
Then by all means, stop stalling and get to it.
No. I am providing you with some math because you can’t handle logic.
I haven’t refused to correct anything. You are the one who claims that your ISRT fixes the paradox. So fix it.
.
And that is why you aren’t the score keeper. 