I wasn't paying attention. Are they talking about something similar to the bar and ring paradox? :shrug Spoiler Bar and ring paradox The above paradox is complicated: It involves non-inertial frames of reference since at one moment the man is walking horizontally, and a moment later he is falling downward. It involves a physical deformation of the man (or segmented rod), since the rod is bent in one frame of reference and straight in another. These aspects of the problem introduce complications involving the stiffness of the bar which tends to obscure the real nature of the "paradox". A very similar but simpler problem involving only inertial frames is the "bar and ring" paradox (Ferraro 2007) in which a bar which is slightly larger in length than the diameter of a ring is moving upward and to the right with its long axis horizontal, while the ring is stationary and the plane of the ring is also horizontal. If the motion of the bar is such that the center of the bar coincides with the center of the ring at some point in time, then the bar will be Lorentz-contracted due to the forward component of its motion, and it will pass through the ring. The paradox occurs when the problem is considered in the rest frame of the bar. The ring is now moving downward and to the left, and will be Lorentz-contracted along its horizontal length, while the bar will not be contracted at all. How can the bar pass through the ring? The resolution of the paradox again lies in the relativity of simultaneity (Ferraro 2007). The length of a physical object is defined as the distance between two simultaneous events occurring at each end of the body, and since simultaneity is relative, so is this length. This variability in length is just the Lorentz contraction. Similarly, a physical angle is defined as the angle formed by three simultaneous events, and this angle will also be a relative quantity. In the above paradox, although the rod and the plane of the ring are parallel in the rest frame of the ring, they are not parallel in the rest frame of the rod. The uncontracted rod passes through the Lorentz-contracted ring because the plane of the ring is rotated relative to the rod by an amount sufficient to let the rod pass through. In mathematical terms, a Lorentz transformation can be separated into the product of a spatial rotation and a "proper" Lorentz transformation which involves no spatial rotation. The mathematical resolution of the bar and ring paradox is based on the fact that the product of two proper Lorentz transformations may produce a Lorentz transformation which is not proper, but rather includes a spatial rotation component.
Not really. Pete came up with this topic to address Tach's incessant haranguing and harping in an earlier thread.
This thread was supposed to stand alone as a separate discussion, to show that there is no general rule that says parallelism is frame invariant. Since the original post, no one has argued that the thought experiment indicates an internal inconsistency in relativity. The argument is about why it doesn't, ie about how the conflict is resolved. I think a key distinction is in what particular measurements are frame dependent, and what measurements represent frame invariant physical properties or relationships.
Mathematics is unphysical. We need to be careful about what we mean when we use the word "physical", except we aren't. "If you can measure something, then it's physical" will probably have to do. Oh yeah, I can remember reading something about Lorentz contraction being "unphysical" in the case of a (flattened) sphere, because of the way an observer in motion views a spherical object, there is no apparent contraction, even though the transform says the sphere is flattened in the direction of motion.
No such thing as an 'apparent contraction'. That's why I make it a point to use the term measurement or theoretical prediction rather than 'nonsense unphysical terms' like apparent. Mathematics can describe some physical stuff. But the discussion is about physics with mathematics as a useful language to convey the physics.
Relativity theory sets the rules. I've explained how it works. Most folks need to find out for themselves.
Check this out: http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html If there is no such thing as apparent contraction, what about apparent motion? Is that "physical"? If you say "observed" instead of "apparent", does it make any difference? Yes, No?
The term unphysical isn't a 'buzzword'. I explained how I used the term. You have a problem with that?
I try not to use vague words like apparent. I didn't say nobody ever uses it. Or that there exists no situation where it might be useful in conveying an idea without mathematics. Measurements are real not apparent. Theoretical predictions are real not apparent, Some are invariant and some are frame dependent. Length contraction, time dilation, gravitational time dilation, gravitational stretching, ... are real. Please don't misconstrue these comments as a disagreement with anything Roger Penrose wants to say. At least I mean the measurements are real.
Apparent isn't a vague word in my lexicon, and I think you will find many astronomers use it to mean something quite precise. Aren't you just replacing apparent (which I say is equivalent to observed), with real , and in what sense does that not mean you now have to define what you think real means? That is, are you implying that real isn't a vague word?
Good, I was hoping you would say that, because when I measure the speed of light in my box, it takes .65 seconds for light to travel the length of .5 light seconds! I know that to be real!
Measurements are physical not unphysical, is better. Information is the result of physical measurement, even more better. Ergo, information is physical. P.S. MotorDad, it's real in your diagram, but you don't do any physical measurements, so you're abusing the normal meaning of "measure the speed of".
Because you thought I was saying that I actually have a 1 cubic light second box, possibly in my garage? (rolls eyes)
That's why I use the term measurements since there shouldn't be any discussion about whether empirical measurement is something that is real or apparent. I'm not implying anything other than what I said. What's the purpose in equating apparent with observation. Generally when an observation is made measurements are associated with the observation. Physics should be semantics free. That's my opinion.
So when I observe the sun orbiting the earth daily, and measure that effect, that is how it really is?
brucep, you seem to be communicating a lot without clarifying what your stance is on the OP's subject. Do you believe as Tach does that because the rod hits the floor on both ends simultaneously in one frame but appears not to hit the floor on both ends simultaneously in another frame that the setup is unphysical?
No, I don't. Just chill man. Please Register or Log in to view the hidden image! I was just speaking in general, and replying to arf, not specifically directed at you.
