The observer on the train sees light travelling at the same speed because he and his clocks are in essence made of it. He calibrates his clock using the local motion of light, then he uses his clock to measure the speed of light. See below. It’s actually going slower “within his frame”, but he can’t see that it is.
This is all right except that it’s all wrong. The changes of SR are not ones of perspective, they are ones of the fundamental location of where events occur. SR tells us where things will be if we use the best possible ideal measurement. If I send a rocket to hit the surface of a star and I only assume that it looks flattened, I will miss it. If one learns how to apply SR correctly, we can predict exactly what ever reference frame will identify as the dimensions of an object as long as we have the knowledge of the dimensions in one frame. We know, before we accelerate, what dimensions a star will have in any given frame of reference in which we might make ourself at rest in. We know, before we accelerate, that we are currently flattened relative to that frame of reference. We know that if we use that frame of reference to identify the physics of our current scenario and we only assume that we merely look flattened that we will make predictions that are incorrect.
With a disc-shaped object seen from the side, we can make adjustments to our estimation of the size and shape of the object that will make our predictions more correct. We cannot do this with the transformations of SR–they are already assuming that we have ideal measurement.
We know that. The issue is that he must see his spinner turning at the speed of light if it is a light spinner. And even if it isn’t, he sees no position change in the forward motion of the spinner with respect to himself, thus he sees no dilation of any kind, thus the spinner does not change its spin as far as he is concerned.
Transverse motion is the same for the train and the station. The station doesn’t see any change in the position between the 2 rotations of the 2 spinners, especially obvious if they are light spinners. The only dilation is occurring in the direction of the train toward the station.
James, how does making it a ‘spinner’ versus a photon bouncing back and forth between two mirrors change the effect of motion on the distance traveled?
We agree that for a stationary observer looking at a clock in her own frame, the light must travel at speed c a distance 2L, while for an observer in motion relative to the clock, the light must travel a distance 2D, at the same speed c. The measured time that the trip takes is different, because time equals distance divided by speed. Since D>L, t’ measured by the moving observer is greater than t measured by the stationary observer.
Similarly, a stationary observer with respect to a spinner whose edge moves at c measures a point on the edge to move 1/4 of the way around the circumference in time t. But for an observer in motion relative to the clock, the time t’ that it takes for the edge to move the same quarter rotation is greater, because the length of the path along a helix of radius r is greater than the circumference of a circle of the same radius, and the speed is c in both frames.
Same speed and different distances necessitate different times. Is this the “relativity of count”?
Farsight, I see what you’re saying, but I think it’s still a matter of language. We could equally accurately say that, even though we are stationary relative to the star, the star is really flattened for a moving frame of reference. It’s already flattened that way, and it’s not flattened for us, and both are right. Without giving one frame of reference priority over any other, it seems impossible to say that the stationary frame is more accurate than any other.
So in our experiment with two observers coming at the star from different directions, it doesn’t seem that we have to conclude that we can’t both be right. Rather, we are both right, in every way that it could possibly have any effect.
Your Wiki argument has nothing to do with spinners at all as far as I can tell. And thus it makes a poor foundation to attempt an argument. Look at the diagram I showed you and realize that the train viewer sees nothing but a spinner turning. He does not see the path you are referring to and thus what he does see, must obey SR all by itself.
It’s more than language, Carleas. That moving frame of reference isn’t something real, it’s just an artefact of measurement. And “both are right” doesn’t work. Think about you and I each lying prone, we’re 2m long, but we’re passing each other at a relativistic speed, so we look 1m long to each other. We can’t both scoop each other with our 1m butterfly nets. We aren’t both right.
James: you’re not seeing this spinner thing. Set gravity to one side, and think of light moving at some fixed speed relative to the absolute universe. Now think of pair production where we make an electron (and a positron) from light, and think of its magnetic dipole moment and the Einstein-de Haas effect. Or think of annihilation where we can combine a proton+antiproton or an electron+positron to get light. Yes, there are issues with Einstein clock synchronisation, but there’s hard scientific evidence that says matter is “spinners of light”. And that’s why special relativity works.
Emm… I know that particles are “spinners of light”, but I don’t see what the rest of what you said relates to the issue.
The train viewer is not aware of any helical paths going on. Regardless of how fast his relative frame might be moving to something else, all he sees is something spinning. That something can be spinning at the speed of light as he would measure light, it doesn’t really matter.
Someone down the tracks merely sees a spinner coming at him along its axis. The rotation of the spinner is transverse to the travel toward him, so the y and z components of the Lorentz remain zero. The only motion that is subject to Lorentz contractions is the x axis motion. Thus the spinner coming toward him looks just like his own spinner. Both of those frames could be zipping off through space and merely closing on each other. That wouldn’t change anything they perceived.
Adding energy and momentum to a different axis (the train’s motion) cannot alter the first axis’ momentum (the rotation), else conservation of momentum could not exist. Whatever is happening in one plane cannot have effect on any transverse axis. In effect, that would constitute “spooky action at a distance”.
The light spinner is the easy thing to visualize. No one can view a light spinner as doing anything but spinning at the same speed of light. If the spinner was mounted inline rather than transverse, the shape of the spinner would be affected and thus the distances would come into play, but that isn’t the case for the transverse spinner. There are no contractions or dilations of any kind.
The only reason any issue comes up is the fact that the train thinks it has traveled down the track faster than the station thinks it has. They could both see the spinners in parallel motion and spinning identically, especially if they were light spinners because every light spinner of the same size must be seen as spinning at the same speed. That is the fundamental concern of SR, the consistency of the measure of the speed of light.
There really isn’t any 2 ways about it. The train’s dilated time causes the train to count fewer spins. End of story.
That is all totally irrelevant as far as I can tell. YOU know that the light is traveling in a helical arc, or else you are yourself instead. The viewers have no perception of such an arc at all, but they MUST see the light spinner spinning at the speed of light. And in fact, perhaps the train’s spinner isn’t the one moving at all, but rather it is the station. The very fundamental issue of Relativity is that it doesn’t matter who is moving, they must observe the same speed of light and they cannot even know if they are traveling or not.
Actually all of this talk of helicals doesn’t matter at all, because the train sees its spinner spinning at the speed of light and the station sees its own spinner spinning at the speed of light. Who’s is “really” spinning faster, if at all, is irrelevant. The train thinks the journey took 9 seconds and the station thinks it took 10. They have no choice but to count a different number of spins in a different amount of time.
— THAT is the Relativity of Count.
This is a basic mistake made by beginners in relativity class. One cannot simply declare that an object is a certain length (in this case, that two objects are both 2m long). One must declare the length of an object in a certain frame of reference. Once one does this, using SR it becomes a logical necessity that the two people passing each other are different lengths in different reference frames.
Let me rephrase the question, if I may, because I don’t seem to be making myself clear. There’s a train with a spinner. The rotation of the spinner is in y and z (that’s what I understand you to mean by “transverse”). The train is traveling in the x direction past an observer (the station).
What I’m saying is that the observer path of the edge of the spinner is longer for the observer at the station than it is for the observer on the train. The reason that this is true is that the x component of that distance is greater for the observer at the station than for the observer on the train. The observer on the train, who sees the spinner as stationary, sees no movement in x of the edge of the spinner. The observer at the station, on the other hand, sees the spinner as moving in the x direction, so that the x component of the motion of a point on the edge of the spinner is not zero.
If you look at the wikipedia example, the motion of the photon is y. Even though motion of travel of the light clock is along x, the path of the photon is affected by that motion: because the distance traveled has an x component, and the x component is different for the stationary and co-moving observer, the the distance traveled by the photon is different, and so the time measured by the light clock is different.
The exact same effect is at play here. The observer on the train sees no x component to the distance traveled by the edge of the spinner. The observer on the station sees an x component, so the distance traveled by the edge of the spinner is different.
Suppose the observer on the train is standing beside the spinner (a separation of z), so that when she looks at the spinner, she sees the edge moving up and down (back and forth in y). The edge of the spinner traces a straight line. An observer on the station instead sees a sine wave: the motion up and down is extended over a distance x as the train and spinner travel past. The distance between the maximum and minimum y is the same for both observers. The path traveled in one rotation as observed by the observer on the train is then 2∆y. But for the observer on the station, it has an additional x component. It moves 2∆y in the y direction, and some distance x in the x direction. It moves farther, but because the edge moves at c for both observers, it takes longer for the observer on the station.
Also known as time dilation? What is the implication of this that is supposedly so damning? It’s acknowledged that clocks will “count” different amounts of time.
No, not “past”. The train is merely approaching the station head on.
But realize that the station isn’t really observing the train’s spinner. The station is using its own spinner.
But then if you take that to the extreme of 0.5c, the train counts 100 during the same journey that the station counts 200. That is a hell of a difference. The train won’t get that count until he is an equal distance past the station.
Distance is the “measure of relative position”.
Velocity/Motion is the “measure of change in relative position”.
Time is the “measure of relative velocity/motion”.
Time dilation is the “measure of change in relative velocity/motion”.
That is why you change the velocity, v’, rather than the distance, x’.
If by using his spinner, he can see that he is approaching the station at a certain number of counts per second, he has a v’ (the train’s perception of velocity).
v’ = dx * td/dt’
v’ * t’ = dx * td {time dilation factor}
He knows that his time is going to be dilated from that of the station, so he must get a time reading from the station or a velocity reading from the station in order to know how much his own time is dilated and his velocity is expanded.
The alternative is to use an absolute frame by comparing spin in all directions. From that, he can calculate his “true velocity” and then know how fast the station is moving relative to absolute by comparing his perception of the station’s velocity along with his dilation of time. That would give him v from v’ and t from t’.
As long as he is restricted to using only one dimension, every point along any line is identical and thus any origin is arbitrary and he cannot know who is moving more. It is only by using an alternate dimension, he can discover his real situation.
And btw, from RM I know that distance doesn’t dilate because what causes distance is the number of points between one affect and another.
There are an infinite number of points between any 2 affects. And even though 2 * inf and inf are infinite, they are not equally infinite. Thus merely by moving, you cannot alter the number of points between 2 other affects from infinite to 2 * infinite. You would have to move them relative to each other, not yourself.
James, are you saying that the station measures the train’s spinner as stationary? The only way that it wouldn’t measure an x component of the distance moved by a point on the edge of the spinner is if the measured change in x was zero. But that’s absurd. There are a number of ways that the station could measure the motion of the train along x, and once it has, it is only be deluding itself that it can ignore the x component of the points motion.
I’m pretty sure they are. They are both ‘countable’ infinities. All finite sums of infinities are equal.
If we assume that space (or spacetime) is a continuum, then the cardinality of the set of points between any two given points is uncountable. However, the union of two uncountable sets of the same cardinality has the same cardinality. Therefore in some sense, “inf = 2*inf”.
Huh? I am saying that the station would see the train’s spinner moving in parallel to its own. When the train sped up, the spinner has no impetus to slow down rotation from the station’s perspective. that would be creating momentum in the y-axis.
I don’t know what you are thinking. The pictorial displays what I am talking about. The x-axis is the train’s motion. Of course the station would see the train’s spinner moving with the train along the x-axis, but the y and z axes do not change between the train and the station nor the spinners. They are only rotating in the y and z axes.
Look at the case for a real number line. If you count the points along the line, it will count to infinity. But now if you had 2 lines side by side, and you were counting both, your count will always be twice as much as the first time, even out near infinitely. So at no point will 2 * inf ever equal inf.
The limit as n reaches infinity is that 2*n is twice as great as n.
The y and z axes don’t need to change. The distance around the helix has a component of x. If x=0, the path is shorter than if x=v. Because the station knows the spinner to be moving, it must factor in that motion when calculating the distance traveled by a point on the edge of the spinner. The illustration you provided illustrates the difference in arc length.
I got this wrong when I said they were “countable”, but PhysBang corrected me (obliged, Phys). The infinity of points between any two points is uncountable, and is equal to the infinity of points between any other pair of points, no matter how far apart they are. From wiki:
So?? 
Wiki is probably talking about Cantor there. Cantor had issues. The Cardinality concerns are a different type of error that the old Europeans couldn’t figure out (or refused). The Greeks had it right.
You figure out any infinite series sum by watching it as it approaches infinity to see where it is headed. You know that if you count the whole numbers (to make them “countable”) along one line and also count along two lines, as n approaches infinity, the two line count will be steadily twice the one line count. That is how all “real” mathematics works throughout all calculus and infinite series issues. But I am not going to go through that on this thread. I’ll deal with Cantor some other time.
Why again are we worshiping a bunch of old Europeans?
So the distance traveled by a point on the edge of the spinner is the arc length. Since the arc length differs for the two observers, but the speed is the same (it’s c for both observers), the time it takes the point to travel that distance differs for the two observers.
While I agree with PhysBang that these infinities aren’t countable, I think the idea is the same: There’s an isomorphism that maps each entity in a single number line onto each entity in two number lines, so the two infinite sets contain the same number of entities.
That’s fine, it’s a complex issue. But if you don’t go through it, you can’t use it as an assumption in the argument that “distance doesn’t dilate because what causes distance is the number of points between one affect and another.” I dispute that distance dilation requires that there be a different number of points between two events in different frames, and I will not accept it as a premise in an argument.
Don’t be facetious, Physbang. We measure each other as 2m long when at rest with respect to one another.
But that’s a different situation than when two things are in motion relative to one another. Either you accept SR or you do not.