You obviously do not understand the notion of proper distance. Proper distance is the distance measured by an observer at rest wrt the distance being measured. So, in the example above, \(D'=D \sqrt{1-(v/c)^2}\), is NOT a proper distance since the observer measuring it is in motion (with speed \(v\)) wrt the distance being measured. In the frame of the vehicle, the distance is shorter: \(D'=D \sqrt{1-(v/c)^2}\), as explained in the muon experiment. In the frame of the road, the distance is D.
Tach, there is nothing in your post that is different than what I said. You did avoid answering the question. Take the second situation, even as the observer in the vehicle measures the distance as you describe, when they have completed the journey from start to finish line, have they traveled the proper distance in the road's frame of reference?
I pointed out that you don't understand the notion of proper distance. I pointed out that you don't understand length/distance contraction. I pointed out that you don't understand the muon experiment. Not "even", there is no doubt about it (except in your mind). Once again, in the road frame the distance traveled is \(D\). In the vehicle frame, the distance traveled is \(D \sqrt{1-(v/c)^2}\). Why do you have so much trouble with this basic concept?
While I am sure that one can find fault with the letter of this post, try to see the intent. It has occurred to me that there may be another way to describe the difference between the length of an object and a distance between two points in space, as they relate to the issue at hand.., length contraction as a function of velocity. In the case of a distance defined by two points in space, there is an invariant proper distance associated with the at rest frame of reference of the two points. I believe everyone is aware that any observer in motion relative to the at rest frame of the proper distance will measure the distance between the two points, as less than the proper distance. This is well described by the formula Tach presented, \(D'=D \sqrt{1-(v/c)^2}\), where \(D\) is the proper distance and \(D'\) is the distance measure by an observer in motion relative to the rest frame of the proper distance. In the case of the length of an object, there is a difference. The proper length of an object will have a similar relationship with the length as measured by an observer in motion relative to the object. There is a difference between the object and the distance though. The object itself can be in motion and experience length contraction in the direction of its velocity, though an observer at rest with respect to the object will notice no change, since his/her measuring rods will be length contracted in the same way as the object itself. To an oustide observer, whether they are in motion or at rest relative to the object's initial at rest frame, who measures the object, both when it is at rest and when it is in motion, the two measurements will not be the same. While to an observer moving with the object the object's length will remain constant. Where \(L\) is the proper length of an object at rest, an observer in motion relative to the object will measure it length as \(L'\), \(L'=L \sqrt{1-(v/c)^2}\) When that same object is in motion it's length will be length contracted such that the observer in motion relative to the object's initial rest frame, will measure the object's length as, \(L"=L' \sqrt{1-(v/c)^2}\). In the case of an object which does experience length contraction proportional with its velocity, to an outside observer its proper length changes with its velocity. Since distances do not have a velocity, the proper distance is constant. Where thought experiments like the twin paradox and practical experience can confirm time dilation, since clocks retain the effects of having run at differencing rates relative to their velocity, the length of an object does not retain such information. The issue I have been attempting to make is that while the proper length of an object as defined by an observer moving with the object, (in the object's rest frame) does not change for that observer, it does change for any external observer. And once again this is not the case for distances in space where the at rest frame of reference definning the proper distance, is never in motion. Not in flat space(time)
No, there isn't. You have made it quite clear that you don't understand frames of reference , nor do you understand how length contraction applies in relativistic physics.
You do not know any of this to be true. The only real issue is that you don't understand what I am saying. So here you contend that the observer in the moving vehicle does not measure the road as length contracted? Tach, the vehicle is in contact with the road at all points and times. It remains an object moving in the road's frame of reference.
Tach, you appear to be a lost cause. It is not even clear you read anything. You cherry pick and comment, as argument without any substance. Just repeating, "you're wrong, you don't understand", is no proof of anything, other than your own limited vocabulary and understanding. It certainly does not rise to the level of discussion.
You are getting it backwards, I pointed out that you don't understand and do not want to accept the fact that the moving vehicle DOES measure the length of the road as being contracted. This was pointed out to you several times, yet, you still don't understand this basic fact. Your persistence in posting stuff to the contrary demonstrates your inability to understand basic relativity. What does it have to do with your inability to accept the relativistic treatment of the problem?
Here is a quote from one of my earlier posts. You apparently did not read it. Seems I said that the observer does measure the distance as length contracted. I just added that the act does not change the proper distance.
As Tach has said, you do seem to lack some basic understanding or frames of reference. "...an observational frame of reference is characterized only by its state of motion." -http://en.wikipedia.org/wiki/Frame_of_reference#Observational_frames_of_reference Only if the vehicle is at rest relative to the road is it in the road's frame. It is not moving in the road's frame, it is moving relative to the road's frame. This is the definition of a different frame; one that is not co-moving.
So you have a comprehension problem! I went back and edited the offending sentence to read, "If proper distances..."
The vehicle is not an observer. And the act of observing the distance from a moving frame does not change the proper distance. The vehicle can be in contact with the road and as such moving in its rest frame, while the observer in motion, observes the distance as length contracted. In the end the vehicle traveled the whole proper distance. And on arriving at the destination the driver/observer looks at the odometer and sees it reads the proper distance and that his/her measurement while moving was length contracted and did not represent the proper distance traveled.
Put an observer in the vehicle. You still don't get it , do you? In what frame? In what frame? Until you learn frames of reference, you will never get this and you will continue to deny the contraction of distances and you will keep denying the validity of the muon experiment as you keep doing it.
Why isn't the vehicle an admissible observation frame? Both the Earthbound and spacefaring observers are valid observer frames. Why aren't you being consistent with this example? You don't get that observations in SR are completely reciprocal. IOW, yes, the vehicle is moving in the road's frame, as observed by someone standing alongside the road, buy the road is moving within the vehicle's frame, as observed by someone in the vehicle. There is no distinguishing anything but relative motion. The proper length of the road is observed by the roadside observer, while the proper length of the vehicle is seen by the vehicle observer.
...and the length of the road is measured as being contracted wrt its proper length by the vehicle observer while the length of the vehicle is measured as being contracted wrt its proper length by the roadside observer. If we join forces we may get OnlyMe to learn some basic relativity in the next few months.
Tach, provide me one credible accessible reference, that describes length contraction in terms of distance.
I choose that example because in the case of a road and a vehicle, you have an odometer that replaces the function of clocks, when discussing time dilation. It provides the opportunity to distinguish between the reciprocal frame dependent observation and the odometer recorded distance traveled, which matches the proper distance marked on the road. There are other issues that could be discussed, but the issue seems hung up on over critical dissection of the words, rather than the intent. Edit: The vehicle is an acceptable frame for any observation. But it includes the odometer that registers the distance it travels. Either the length contracted measurement from the moving vehicle is an artifact of its velocity or the odometer does not accurately record distance.
So, the hyperphysics website isn't "credible"? Is it because it contradicts your beliefs? Google this. There are plenty of university sites that you can learn from.
I think the odometer is going to make things more confusing. An odometer works by essentially counting how many times one of the tires goes around, adding one circumference of the tire for every rotation. Before you could use such a thing in a relativity thought experiment, you would have to define whether the circumference of the tire remains the same size regardless of the vehicles speed, or if it becomes length contracted like the road. An easier way to do it is to have two cars driving the same speed, a certain distance apart. Both cars have synchronized clocks. At an agreed-upon time, the two cars simultaneously shoot a pellet into the road. In the reference frame of the road, the distance between the two pellet holes is \(L\). However, in the reference frame of the cars, the distance between the two pellet holes is \(L'\) where: \(L'=L \sqrt{1-(v/c)^2}\) I don't know why you are trying to make a distinction between length-contraction of distances and objects. There is no difference. If the road were not there, the distances between the pellets would still be as described above.
