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.
We aren’t measuring light, we’re measuring time. A light clock is a good choice because it is simple, it is constant by supposition, and it gets straight to the issues of special relativity.
This issue does not come up. In the measurements I presented, the speed of light cancels out.
It’s more like trying to weigh a spring on a spring scale, which is perfectly reasonable.
But if you have some aversion to light clocks, substitute some other real clock that doesn’t assume absolute time.
And not many of these posts have been science (which was my point).
Well you should be.
Yeah, by being one of them.
That’s what I stated as the problem.
It is more like measuring springiness with a spring scale.
“Absolute time”??
A scale “assumes” absolute weight.
Yet if going between planets, you have to use your head to figure out what you are [b]actually seeing[/b].
And when you are using light to measure time and are going between time frames, guess what… You have to use your head to figure out what you are [b]actually seeing.[/b]
Actually weight is a function of mass and gravity. Mass is invariant but weight actually does vary based on gravity. Most scales measure weight and are thus equally valid on any planet the same object will have different weights in different gravities. Something that weighs 5 lb on the earth will weigh about 1 lb on the moon on the same scale and it would be correct. Something that measures mass is called a balance in physics to avoid this confusion, and something massing 5 lb on earth will still mass 5 lb on the moon. This is further confused by the imperial system using the same term for both mass and weight (lb) where the metric system uses different units (kg for mass and Newtons for weight).
More importantly where do you get this idea there is an actual happening that differs from what you observe, in other words an absolute thing, be it time, space, or weight? Do you have any evidence that it exists other than your assertion that it does? In any case if you are working with SRT, which you must if you want to create a paradox in SRT, you must give that up as the premise of SRT is that there is no absolute accept the observed speed of light in an inertial reference frame, and the uniformity of the laws of physics in all reference frames. As a consequence of this we can see anything observed in one reference frame, such as the passage of time on a clock, will be just as valid as the observed passage of time on another clock in another reference frame, but just as importantly and just as validly the observer in the first reference frame will observe the clock in the second to be slow, just as the observer in the second reference frame will observe the clock in the first as slow.
Since we assume nothing but the observed speed of light in an inertial reference frame, and the uniformity of the laws of physics in all reference frames we cannot say either the first or the second reference frame is more correct than the other. We are left with two choices, either both are correct and space and time are relative, or neither is correct which means all physical laws are incorrect in all reference frames, a logical contradiction of the assumption and thus impossible, or the speed of light is not measured the same in both reference frames, again a logical contradiction and therefore impossible.
Therefore time and space are relative to the observer’s frame of reference and there is no absolute time or space. And then we don’t need to figure what we “actually” observe because what we observe is correct in our reference frame. We only need to use logic if we want to figure out what someone in a different reference frame saw based on our observations, but again their observations are no more correct than ours. Even if you know we started in their reference frame and know what the setup there was and then left and made our observations from a different reference frame.
And I’m working on a mathematical explanation of what the two observers see with your button/clock scenario. I don’t think you will accept the answer when I give it to you but I am interested in seeing it work out, and maybe Carleas will find it interesting.
Who has been saying anything about absolutes other than you two?? I seriously have no need for a lecture on SRT, but glad to see that you have at least learned the basics.
And interesting that you should mention the invariance of mass. Just yesterday, I was formulating yet another paradox utilizing a free-fall-mass accelerometer and Carleas’s favorite light clock. That would make my third. I’m sure I could form very many. But from what I have seen, your group seems to have trouble with merely the Twin Clock Paradox.
As far as me accepting anything, logic is the key. Math works great ONLY if you don’t misunderstand what the terms actually represent in reality. That is why merely pointing to someone else’s equations doesn’t cut it - too much room for misinterpretation (the very cause of fantasy religions).
So you really DO have trouble reading… and presuming. I never said anything other than both time frames KNOW that the clocks were identically set and identically treated.
You will see when you present you analysis of the paradox (dubiously presuming that you don’t get too irrational about it).
James: A light clock is a bad choice for measuring light.
Carleas: We aren’t measuring light, we’re measuring time.
James: Well you should be [measuring light].
[/quotes]
Why should I be measuring light? I’m talking about a clock, which isn’t used to measure light, it’s used to measure time. One of the premises (also called a “supposition”, not a dirty word in math or logic) on which special relativity is based is the constancy of the speed of light in all frames of reference. Therefore, a light clock will always accurately keep time, but will different frames of reference will disagree about how much time it has recorded.
You need to be significantly more verbose about this. Do you disagree that the light clock accurately measures the passage of time? The only reason c cancels out is because the speed of the train was stipulated to be .5c. If you’re uncomfortable with it cancelling, we can just call it ~150000 km/s, and then c will stick around. Provide an argument for what the light clock is missing, e.g. use multiple sentences, perhaps a syllogism or two, maybe even an equals sign, preferably with numbers or numeric variables around it; something more than telling me its bad because a clock should be measuring light instead of time.
I provided you with some simple math and numbers so you won’t have to deal as much with common sense.
If a light clock is going to yield a different answer than an idealized clock, then you shouldn’t be using it. And if it is going to yield the same answer, then why use it?
Guys, this is about a train approaching 2 stop-clocks and a button. It can’t get much simpler. What’s the hold up?
Because the idealized clock assumes the outcome of the disagreement. If you assume that time is measured the same in all frames by an idealized clock, you assume that there is no time dilation and no relativity of simultaneity. If you assume that an idealized clock measures time differently in different frames, you assume time dilation and relativity of simultaneity. If you use a real clock (like the light clock), you can prove time dilation and relativity of simultaneity, showing that what you’re using isn’t an idealized clock, but an fantasy clock.
For one thing, we disagree about how clocks read time, and you’ve yet to suggest a clock that doesn’t assume your conclusion.
Not true at all. All of Einstein’s work used idealized clocks similar to typical mechanical clocks, merely more perfect and rigid body objects.
I have to accept that you have merely discovered that you can’t resolve it and now want to change the clock type so as to hide your error with another hidden assumption. You were permitted to put any time dilation calculation you wanted into it. If you have to change to a special clock to resolve it, you are testifying to the reality of the problem.
So there we have it.
Now the only question is whether Dienes can resolve anything.
Don’t get cocky, James. Crucial premises of your argument include that instantaneous velocity is always 0 and x really means ∆x, so if we’re going to talk about ad hoc positions to be treated as surrender, we should start with those.
The light clock is not my invention; Einstein wrote in his personal papers that, given the constancy of the speed of light, “a light signal, which is reflected back and forth between the ends of a rigid rod, constitutes an ideal clock.” Far from being a concession that you’ve created a unique problem for special relativity, I’ve used it to show that time is dilated, that therefore simultaneity is relative, and that therefore your suggested paradox is nothing that vanilla special relativity can’t handle.
“Ad hoc”??? What the hell are you smoking?
And I’ll explain what those things that (again) you misquoted from someone else (me) yet misunderstand after you two have resolved this one.
I don’t know why you are going on about this. You and I used time dilation together through probably 300 posts. The original write up used it;
Why are you all hung up over something that isn’t in contention?
The light clock proves time dilation, it makes the math rigorous. It lets us replace “tf” with L* sqrt(5) / 2c - L. You’ve said yourself that details matter. If you’re willing to accept that the light clock establishes time dilation, I’m willing to move on, but we’ve spent a lot of time avoiding the math that this paradox involves.
Yes, you have avoided it.
I gave you license to put any time dilation you wanted into it (as long as you apply it to BOTH stop-clocks).
Get on with it.
In the interests of getting on with it, I’m going to redo the equations using speed v instead of .5c and with the mirrors a distance L instead of a distance L/2 apart. You’ll see the point by the end of this post.
This time, we’ll look specifically at the differences in elapsed time measured by the station and the train. Call the elapsed time per tic as observed by the station, ∆t, and the elapsed time per tic as observed by the train ∆t’.
From the point of view of the station, the light in the clock travels L at speed c, so each tic happens every 2L/c. ∆t = 2L/c
From the point of view of the train, the photon between the plates is moving at an angle. Again we use the Pythagorean theorem A^2 + B^2 = C^2, but this time with A is L, B is vL/c (since the clock is traveling at v). So,
C = sqrt( L^2 + (v∆t’/2)^2 )
and we know that ∆t’ = 2 C/c [1]
Since we know that ∆t= 2L/c
We can substitute it in to find the ratio of ∆t’ to ∆t
∆t’ = ∆t / sqrt (1 - v^2/c^2) ∆t’/∆t = 1 / sqrt (1 - v^2/c^2)
This is the Lorentz factor, and deriving it is necessary to derive the Lorentz equations. Any questions so far?
[size=85][1] Sorry for the confusing labels; capital C is the length of the hypotenuse of the triangle, i.e. the distance that the train observer sees the light in the clock travel from one mirror to the other, little c is the speed of light).
[2] This multiplies the right side of the previous equations by c/c. The c in the numerator is the same as 1/c in the denominator, which is the same as sqrt(1/(c^2)).[/size]
We have known and accepted the equation for time dilation for months. You could have just said; tf = 1 / sqrt (1 - v^2/c^2)
Using that is fine with me, but if that is what you want to use, just use it carefully… and properly.
Or you could just plug in any random number. In the long run, it won’t matter. Time dilation isn’t the issue.
But you might want to note that v is the velocity between the frames. You don’t know if it is positive or negative.
