
#127
Mar512, 02:12 PM

P: 1,098

Thanks for the reply Dalespam.
Maybe if I pose my question differently it will become more apparent where my confusion is. In what scenario would two observers have the same measure of length / time, but not agree on simultinaity? To your point in the last comment, when I think of relative motion, I immediatly consider their measure of length / time to not be equal "parts/units" comparatively. If RoS includes relative motion, how can length / time measure the same (comparatively) for each observer? Lastly, sure you know now that I don't know math, can this demonstration of RoS without LC / TD be concluded with thought? 



#128
Mar512, 06:43 PM

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P: 16,466





#129
Mar512, 06:57 PM

P: 1,098

Ah okay and phew!




#130
Mar612, 06:42 AM

P: 3,178

RoS in the sense that we can't determine absolute simultaneity relates to the PoR, and the basic features that enable the PoR despite constant c are TD and LC. Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation). 



#131
Mar612, 08:52 AM

P: 1,098

Ah okay, I didn't (nor have I ever) seen that mentioned. There is always something new in SR from my perspective, this one is particularly suprising given what I do know of SR concepts.
I can't make the distinction you mention with "Note that Einstein's constant c (independent of the motion of the source) should not be confused with invariance of c (relativity principle for light propagation)." Is there a simply way to make that distinction more clear (for me)? Maybe I should just consider scenarios of each, maybe that's where my confusion is. If so wow, good eye Harrylin! I only have the one understanding of RoS, where two events seperated spatialy could be measured as occuring simultaniously depending on relative motion. 



#132
Mar712, 09:20 AM

P: 3,178

1. Just look up "invariant" on Wikipedia: http://en.wikipedia.org/wiki/Invariant Note that (at least today!) the word "constant" doesn't appear on that page. In the context of SR, people mean with "invariant" that a frame transformation doesn't change it. Then look up "physical constants" on Wikipedia: http://en.wikipedia.org/wiki/Physical_constant Note that (at least today!) the word "frame" doesn't appear on that page. According to SR, such physical constants are not affected by a frame transformation; and that may be the reason that the distinction is often blurred. However, in classical physics it was assumed that the speed of light is a constant that is independent of the motion of the source ("the speed of light is a constant c"). Maxwell assumed that the speed of light could only be exactly c relative to a light medium  just like the speed c of sound in air. Consequently, in classical optics it was though that the speed of light is a constant but not invariant. Similarly, Einstein's second postulate of SR refers to a single inertial frame. The speed of light is assumed to be a constant c: the same in all directions, and independent of the motion of the source. That postulate seemed incompatible with the relativity principle according to which all physical constants should be invariant (the speed of sound is variant, so how can the speed of light be invariant?). Is that clearer? 



#133
Mar912, 12:33 AM

P: 359

I have not trouble with the idea that the postulates of relativity allow us to reason what should be the case, if the postulates are assumed to be true; and what effects must occur, in order for the assumptions to hold true; but insofar as they relate to the physical world, then I think we have to be able to discuss cause and effect at some point; reasoning alone, as far as I am aware, doesn't cause physical effects (of the sort we are talking about). It might be worth drawing the distinction, again, between an invariant measurement of c [itex]\text{(mC)}[/itex] and an invariant actual c [itex]\text{(aC)}[/itex]; where [itex]\text{mC}[/itex] does not necessarily imply [itex]\text{aC}[/itex] ; as per the example where two reference frames measure the speed of light to be c, but because the instruments used are of different lengths, the actual speed represented by the measurements is different. You mentioned that I had neglected RoS, and so had drawn the wrong conclusion; however, RoS is a consequence of the actual speed of light (c) remaining invariant, not necessarily of an invariant measurement of ca 300/000 km/s. [itex](\text{PoR} \cap \text{mC})[/itex] does not necessarily imply [itex](\text{LC} \cap \text{TD} \cap \text{RoS})[/itex] but [itex](\text{PoR} \cap \text{mC})\leftrightarrow (\text{LC} \cap \text{TD})[/itex] If we consider, that we can only ever, really, speak about the measurement of c, and not the actual speed", then: [itex](\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{aC})[/itex] Which leaves us with the formulation: [itex](\text{PoR} \cap \text{mC} \cap \text{RoS})\leftrightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})[/itex] which appears to be circular. 



#134
Mar912, 07:33 AM

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P: 16,466





#135
Mar912, 07:55 AM

P: 3,178

Harald 



#136
Mar1112, 07:41 PM

P: 359

As for the temporal separation, that would probably be a more philosophical discussion on the nature of "cause" and "effect". 



#137
Mar1112, 07:56 PM

P: 359

I think that saying that no absolute simultaneity can be measured is somewhat of a category mistake, because absolute simultaneity is not a physical object. However, a consequence of RoS, I believe, is that for each individual observer, their "past" state continues to exist in some reference frame, and their "future" state also "exists" in some reference frame; this requires each observer to make unverifiable assumptions about the existence of "past" and "future"; absolute simultaneity, however, doesn't require such assumptions, it simply requires us to accept the empirical evidence that an ever changing present moment is all that exists  this is because, I'm pretty sure, no observation of "past" or "future" can be made by an observer. 



#138
Mar1212, 07:16 AM

P: 3,178

Perhaps you mean that an observer who is using a certain reference system can attribute certain distant events that he/she has not yet seen, to the past or future while using another reference system, the contrary would be attributed to those events. 



#139
Mar1212, 07:37 AM

P: 255

The best way to understand SR is geometrically. Take a sheet of paper and draw a simple spacetime diagram: put two dots on the sheet horizontally aligned to represent two events which are simultaneous in the frame of the drawing and spatially separated. Now get some transparent film, draw graph lines on it and place it over the paper so one grid line passes though the two events. Rotate the film a few degrees to represent a different frame and the events can no longer lie on the same gridline, they are not simultaneous in the new frame. What special relativity says is that there is no intrinsically preferred frame in reality, any choices of frame is equally valid.
Note that this is jut an analogy, to get an accurate picture you have to rotate the vertical and horizontal lines in opposite directions (e.g clockwise and anticlockwise). Length contraction and time dilation are just names for the effect of changing coordinate separations resulting from frame rotation. 



#140
Mar1212, 07:46 AM

P: 3,178





#141
Mar1212, 05:21 PM

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P: 16,466

If you assume the Lorentz transform then all you can say is [itex]\text{LT} \rightarrow (\text{LC} \cap \text{TD} \cap \text{RoS})[/itex] and you cannot make any claims about whether or not any of them are implied by any of the others. I am certainly happy to do that, but it basically ends the entire discussion after my original point that you had neglected RoS. 



#142
Mar1312, 01:17 AM

P: 359

For example, let's say that you measure the speed of light to be ca. 300,000 km/s, using your instruments; then I measure the speed of light to be ca. 300,000 km/s using my instruments, but my metre stick is contracted such that "my meter" is shorter than "your metre", and "my second" (measured by my slower clock) is longer than "your second", then it means that the actual speeds represented by those measurements are different. In reality, the light in my reference frame took a little longer than a second to travel a distance shorter than 300,000 km/s  although our units of measurement are the same, the actual speeds represented by those measurements are different. To accept this as true, however, would require that observer to assume that, not only the past events continue to exist, but also their "past self"; the same can be said of "future" events and "future self"; each and every observer would have to make this assumption, despite the fact that this would be contrary to the empirical evidence (with regard to "past" and "future"). 



#143
Mar1312, 01:20 AM

P: 359





#144
Mar1312, 01:21 AM

P: 359




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