I beleive that delta's or change in a value all come from the light clock thought experiment. I hope to show that these values are not necessary or valid when they come from that derivation, even though I am not sure how to show the value in the proper font so please bear with me.
In the light clock derivations I see two problems that deal with this problem. For one, the change is time is supposed to represent the amount of time a clock measures as it ticks. But does it actually do this? They say that as the photon hits the bottom mirror and comes back up that is one secound, but there is no information involved about the height of the clock or how many times that the clock would ticked because of its height. For example, the simple inference of time dialation on the wiki page "time dialation"
In this example the L or length of the height of the triangle has been removed from the equation completely. So then it is saying that this solution should work for any triangle of any height, and the height of the triangle is no longer relavent.
So then it is easy to say that the change in time of one secound would be the same as one tick on a clock. But then what have we done here? We have set the change in time equal to the amount of time that has passed. So then when you put the amount of time that has passed into the equation for the change in time you get the wrong value. You get an answer that is greater for the object in motion, not less than the clock that was at rest. So then you have to take the inverse of that value since it was the change in time and not the actual time even though you inserted a value that was just the amount of time that had passed by to get a value that shows that time for a moving object runs slower. In classical physics a unit of time was the amount of times a clocked ticked not the change in time.
So then what would be the real solution that could be used for the actual time that had passed? It is simple, all you have to do is get rid of the delta's altogether and assign the time variables correctly. Just forget about the clock, and think in terms of the distance light has traveled over time.
The object in motion would measure a photon to travel in a straight line perpendicular to its direction of motion a distance (ct'). The dialated time only needs to be used here for A in the pythagorean therom. This is because he uses his clock that would in turn measure a shorter length of time that would allow him to measure the same speed of light if he assumed he was at rest.
Then the observer at rest would use his own clock to measure the distance the object traveled (vt). He would also measure the photon to travel at an angle a distance (ct) the hypotenus. Both of these measurements come from the observer at rest using his own clock that he assumes in not dialated in respect to time.
So then (ct')^2+(vt)^2=(ct)^2
c^2t'^2=c^2t^2-v^2t^2
c^2t'^2=c^2t^2(1-(v/c^2))
t'^2=t^2(1-(v/c)^2)
t'=t^2 sqrt(1 - (v/c)^2)
Does the last equation look familar? t' is the same as tau or the proper time. I have just derived a simple inference to the proper time or tau. I have done this by only assuming that time dialates so that both observers will measure the same speed for light as though it traveled a certain distance, not according to how many times a clock would be seen to tick.
Then the problem is then if tau is the proper time it does not give the same values for dialeted time as the equation on the wiki page described previously. They do not equal each other, so then one is wrong and the other is correct. But they are both taught in physics. Then if tau is correct and it is not the same as the change in time calculations then delta's would no longer be valid since it is derived without them. So then what implications or changes would have to be made to modern physics? This is the theory that started it all, and I have seen versions of the 1905 paper Einstein made use tau for time dialtion.
Has our inability to descibe mathmatically clocks in motion failed us? Then wouldn't any clock expereince some sort of "time dialation" even though it didn't use light as a pendelum? It could after all assume that it was at rest while in constant motion and any pendelum would act in the same manner as though it was at rest. But, with tau it only deals with the measured velocity of light to keep it the same. And the difference between the two equations is practically switching the variebles and taking the inverse of it.
In the light clock derivations I see two problems that deal with this problem. For one, the change is time is supposed to represent the amount of time a clock measures as it ticks. But does it actually do this? They say that as the photon hits the bottom mirror and comes back up that is one secound, but there is no information involved about the height of the clock or how many times that the clock would ticked because of its height. For example, the simple inference of time dialation on the wiki page "time dialation"
In this example the L or length of the height of the triangle has been removed from the equation completely. So then it is saying that this solution should work for any triangle of any height, and the height of the triangle is no longer relavent.
So then it is easy to say that the change in time of one secound would be the same as one tick on a clock. But then what have we done here? We have set the change in time equal to the amount of time that has passed. So then when you put the amount of time that has passed into the equation for the change in time you get the wrong value. You get an answer that is greater for the object in motion, not less than the clock that was at rest. So then you have to take the inverse of that value since it was the change in time and not the actual time even though you inserted a value that was just the amount of time that had passed by to get a value that shows that time for a moving object runs slower. In classical physics a unit of time was the amount of times a clocked ticked not the change in time.
So then what would be the real solution that could be used for the actual time that had passed? It is simple, all you have to do is get rid of the delta's altogether and assign the time variables correctly. Just forget about the clock, and think in terms of the distance light has traveled over time.
The object in motion would measure a photon to travel in a straight line perpendicular to its direction of motion a distance (ct'). The dialated time only needs to be used here for A in the pythagorean therom. This is because he uses his clock that would in turn measure a shorter length of time that would allow him to measure the same speed of light if he assumed he was at rest.
Then the observer at rest would use his own clock to measure the distance the object traveled (vt). He would also measure the photon to travel at an angle a distance (ct) the hypotenus. Both of these measurements come from the observer at rest using his own clock that he assumes in not dialated in respect to time.
So then (ct')^2+(vt)^2=(ct)^2
c^2t'^2=c^2t^2-v^2t^2
c^2t'^2=c^2t^2(1-(v/c^2))
t'^2=t^2(1-(v/c)^2)
t'=t^2 sqrt(1 - (v/c)^2)
Does the last equation look familar? t' is the same as tau or the proper time. I have just derived a simple inference to the proper time or tau. I have done this by only assuming that time dialates so that both observers will measure the same speed for light as though it traveled a certain distance, not according to how many times a clock would be seen to tick.
Then the problem is then if tau is the proper time it does not give the same values for dialeted time as the equation on the wiki page described previously. They do not equal each other, so then one is wrong and the other is correct. But they are both taught in physics. Then if tau is correct and it is not the same as the change in time calculations then delta's would no longer be valid since it is derived without them. So then what implications or changes would have to be made to modern physics? This is the theory that started it all, and I have seen versions of the 1905 paper Einstein made use tau for time dialtion.
Has our inability to descibe mathmatically clocks in motion failed us? Then wouldn't any clock expereince some sort of "time dialation" even though it didn't use light as a pendelum? It could after all assume that it was at rest while in constant motion and any pendelum would act in the same manner as though it was at rest. But, with tau it only deals with the measured velocity of light to keep it the same. And the difference between the two equations is practically switching the variebles and taking the inverse of it.