pzkpfw Posted September 9, 2014 Posted September 9, 2014 Well, here's my attempt: Even with relativity, some things are absolute. One of those is relative motion. While both observers can consider themselves as at rest, and the other as moving, there is no frame where both are at rest. Another is that events occurring at a single location (which equates to "an observer") will be agreed on by all (to be simultaneous or not). For example, two cars drive into a stop sign at the same time. There is no observer (whether standing "still" by the pole or "flying by" at Mach 3) who will think one car hit the sign first - there'd be no pole remaining for the other car to hit, and all observers will agree if both cars hit the pole. So if the flashes were simultaneous in the embankment frame and the equidistant embankment observer sees them at the same time, will the train observer see them at the same time? No. Because he is moving, according to the embankment observer, and light travels at a finite speed, one flash must reach the train observer before the other. And the train observer won't disagree; the flashes can't reach him at the same time in one frame, and at different times in another frame. And if the flashes were simultaneous in the train frame and the equidistant train observer sees them at the same time, will the embankment observer see them at the same time? No. Because she is moving, according to the train observer, and light travels at a finite speed, one flash must reach the embankment observer before the other. And the embankment observer won't disagree; the flashes can't reach her at the same time in one frame, and at different times in another frame. Because there is relative motion, the flashes can't reach one observer at the same time, and the other observer at the same time. But each observer (both at rest and equidistant, according to them) needs to see those flashes at the same time to consider them simultaneous. The flashes can be simultaneous in either (or neither) relatively-moving observers frame, but can't be simultaneous in both frames.
phildukephd Posted September 10, 2014 Posted September 10, 2014 (edited) Science is based on experimental confirmation. Dr. Einstein did thought experiments but received the Nobel Prize for experimental confirmation that validated his predictions regarding the apparent change in position of stars whose light passed close to, the Sun during a total wclipse. Since then many attempts have been made to refute his work, but they only confirm it. The ability to predict, to control, and to produce new phenomena, are the criteria on which a scientific belief lives or dies. It may be I am missing something here, but don't the Michaelson- Morley experimental results show Einstein's theory re different frameworks is correct? What other explanation is there for their repeated and confirmed finding using the velocity of light that the Earth is not rotating/moving with respect to the Sun? And of course there are many more tests made via modern technology that confirm Einstein's thnking. I believe in the value of thought experiments, but their experimental confirmation is very desirable. and eventually absolutely necessary. I suggest that a hypothesis that cannot be tested remains of little value until it is tested. Regards, Phillip Duke PhD Edited September 10, 2014 by phildukephd
imatfaal Posted September 10, 2014 Posted September 10, 2014 Science is based on experimental confirmation. Dr. Einstein did thought experiments but received the Nobel Prize for experimental confirmation that validated his predictions regarding the apparent change in position of stars whose light passed close to, the Sun during a total wclipse. .. Oops - Einstein received his Nobel for services to theoretical physics especially the Photoelectric Effect. A third group of studies, for which in particular Einstein has received the Nobel Prize, falls within the domain of the quantum theory founded by Planck in 1900. http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/press.html Since then many attempts have been made to refute his work, but they only confirm it. Does not the work of Hawking and Penrose show that GR becomes internally inconsistent within the event horizon of a black hole - ie predict a physical singularity in the centre; this is a minor point but most think that GR has limits of applicability beyond which quantum field theory will hold sway. You have stated elsewhere that a limit of application "invalidates" newtonian mechanics - so for consistency...
studiot Posted September 10, 2014 Posted September 10, 2014 Philip Duke, you have recieved a number of negative votes for failing to discuss in a proper and scientific manner. (not from me I might add) I am going to say +1 here because, even if incorrect, your response corresponds to the spirit of this forum.
imatfaal Posted September 10, 2014 Posted September 10, 2014 It may be I am missing something here, but don't the Michaelson- Morley experimental results show Einstein's theory re different frameworks is correct? The MM showed a null result when a positive result would have been expected if we were moving through a luminiferous ether. Bradley's observation of Stellar Aberration showed that we were not stationary to it either. MM was considerably before the annus mirabilis
studiot Posted September 10, 2014 Posted September 10, 2014 The Special Theory of Relativity is resting on three assumptions: One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Relativity discussion often arouses (excess) passion, and that seems the case here. Although your posts are long enough to be sermons, you appear to be seeking a rational discussion. First and foremost is the question what is relativity. Well relativity causes us to re-examine both space and time (and therefore all quantities derived from these such as velocity) so we cannot use them in our definition as that leads to circular arguments. That means that none of your three assumptions above are available. The guiding principle is a sort of conservation principle (but not a conservation law as in the conservation of energy) which can be phrased that we want (assume) that the laws of physics are such that they work out the same in all reference systems. Contrary to popular story much of this work was done (well) before Einstein. In fact so far previous to Einstein that Newton and Galileo before him held to this principle, but only knew of the laws of mechanics. We have named the earliest and simplest form of (mechanical) relativity after Galileo. Einstein extended this to other areas of physical laws such as electromagnetism. this did not invalidate Galilean relativity, merely restricted its domain of applicability. Today we use the following basic definition "It is impossible to distinguish between inertial frames by using any physical law)" The modern approach is to test exisitng and proposed physical laws against this principle. When this is done, and I'm sorry but this is where the maths comes in, we end up with the more famous formulae.
christopherkirkreves Posted September 10, 2014 Author Posted September 10, 2014 Thank you for the responses. --- pzkpfw wrote: “Another is that events occurring at a single location (which equates to "an observer") will be agreed on by all (to be simultaneous or not). For example, two cars drive into a stop sign at the same time. There is no observer (whether standing "still" by the pole or "flying by" at Mach 3) who will think one car hit the sign first - there'd be no pole remaining for the other car to hit, and all observers will agree if both cars hit the pole.” I believe you are talking about the general area of non-synchronized clocks between inertial frames of reference. So, for example, in Comstock’s thought experiment both the man in the car and the man in the road will agree that the two flashes of light reach the clocks in the car at the front and the rear of the car at the same time. And, in fact, if these clocks had light sensitive switches where they mechanical hands were frozen at a particular reading when the flashes of light reach them, they would have to show the same time otherwise there would be a paradox and this theory would either, one, show that we live in a paradoxical world, or, two, then be shown to be false. I believe you are saying the same thing with the cars and pole example you use. No? The non-synchronization of clocks comes much later in this theoretical structure. In fact, I don’t believe it is addressed in Einstein’s book, but it is definitely today part of the theory. If I’m right it arouse as a consequence of the Space-time diagrams. However, it definitely comes after the Lorentz transformations and the establishment of length contraction and time dilation. What I am talking about is the thought experiment that comes before these transformations and the establishment that “events which are simultaneous in one inertial frame of reference are not simultaneous in another” as true (as far as thought experiments go) so that this counterintuitive assumption of the Lorentz transformations is not simply suspect. “So if the flashes were simultaneous in the embankment frame and the equidistant embankment observer sees them at the same time, will the train observer see them at the same time? No. Because he is moving, according to the embankment observer, and light travels at a finite speed, one flash must reach the train observer before the other. And the train observer won't disagree; the flashes can't reach him at the same time in one frame, and at different times in another frame.” If this is right, then this becomes a test of absolute rest; if we can in fact say that it is the man on the train who is moving (“Because he is moving …”). Or, if this is right, then the two flashes of light moving through the vacuum of space (as Einstein stipulates in his thought experiment) are somehow more connected to the inertial frame of reference than to the inertial frame of reference of the train. This could be perhaps argued is the case because the flashes of light originated from two points in the inertial frame of reference of the embankment. But this would be a totally new theory in physics are relativity. Right now, the understanding is that the motion of the emanating source of light is independent of the velocity of that light (and this applies to the man in the train). “The flashes can be simultaneous in either (or neither) relatively-moving observers frame, but can't be simultaneous in both frames.” This may or may not be true. I understand your argument. (There is the possibility that light travels towards all things, but that is a much, much more complicated and a much, much later and not appropriate here argument.) However, even if you are right, this does not shore up Einstein’s two lightning bolt strikes thought experiment. You are making a different argument. (And, again, you may be right and so maybe instead of replacing Einstein’s argument with Comstock’s we can replace it with yours.) Einstein does not say that maybe the guy on the embankment sees both of the flashes at the same time while the guy on the train sees one flash of light before the other or maybe the guy on the train sees both flashes of light at the same time while the guy on the embankment sees one flash before the other, we just don’t know (sort of in line with the same kind of thinking in the “twin paradox”). He does not say this. He says: “Hence the observer [the man on the train] will see the beam of light emitted from B earlier than he will see that emitted from A.” (p. 30) So, while I respect your reasoning, I don’t think it leads to shoring up Einstein’s two lightning bolt strikes thought experiment. Both the man on the embankment and the man on the train are in equal positions to see the two flashes of light at the same time, but Einstein says that it is the man on the train (and not the man on the embankment) who does and will see one flash of light before the other. And if I’ve missed and/or overlooked any of your important points, please let me know. Thank you. ----- phildukephd wrote: “It may be I am missing something here, but don't the Michaelson- Morley experimental results show Einstein's theory re different frameworks is correct?” Michelson-Morley does not involve different frames of reference. The observers and the beams of light were all in the same inertial frame of reference at all times. “And of course there are many more tests made via modern technology that confirm Einstein's thnking.” Yes. I hope I don’t come across as disputing this. Yes, there are lots of various empirical physical tests confirming both the Special and the General Theories of Relativity. “I believe in the value of thought experiments, but their experimental confirmation is very desirable. and eventually absolutely necessary. I suggest that a hypothesis that cannot be tested remains of little value until it is tested.” I have also posted in this thread a proposed empirical physical test of the initial assumptions that “the velocity of light is invariable for all observers;” which, if my limited research is correct, has not yet been directly tested. Please let me know if I’ve missed anything. Thank you. -------- studio said: “Although your posts are long enough to be sermons, you appear to be seeking a rational discussion.” I was criticized for not addressing all of the points being made against me. I did not think they were relevant to showing (or even addressing) that Einstein was wrong … specifically … when he concluded based on the two lightning bolts strikes thought experiment that “events which are simultaneous relative to the embankment are not simultaneous relative to the train.” And now that I am taking the time to address each criticism/critique … well now … “That means that none of your three assumptions above are available.” All theories rest on assumptions. All of Physics rests on the assumption that “the physical world exists.” Rene Descartes and David Hume have shown us that this cannot be “know.” And therefore when dealing with Physics we must “assume” this. And that’s fine. Assumptions are everywhere. If we got hung up on only dealing with things not based on assumptions we’d end up saying nothing more than Descartes did in “I think, therefore I am,” and then now saying nothing more than Hume did in “Thought exits.” Of course the Special Theory of Relativity rests on the assumption “There is no absolute rest.” None of what Einstein said would make sense if we thought “well maybe there is absolute rest.” Of course the Special Theory of Relativity rests on the assumption “The velocity of light is independent of the motion of the emanating source.” None of what Einstein said would make we thought “maybe the velocity of light depends of the velocity of the emanating source.” Of course the Special Theory of Relativity rests on the assumption “The velocity of light is invariant for all observers.” None of what Einstein said would make sense if we thought “well maybe the velocity of light depends on the motion of the observer.” And while he does not just come straight out and list these three assumptions in a row, they all can be contextually found in the first ten chapters of his book. (And, I’m sorry, but I’m too tired from this “sermon” to flip around the pages and pull out quotes. But they are all there.) “The guiding principle is a sort of conservation principle (but not a conservation law as in the conservation of energy) which can be phrased that we want (assume) that the laws of physics are such that they work out the same in all reference systems” As xyzt pointed out earlier, I have made mistakes by summarizing (glossing over) things. In addition to the three assumptions I listed I could have included others (such as “The Special Theory of Relativity rests on the assumption that the physical world exists” and “The Special Theory of Relativity rests on the assumptions that not only does the physical world exits but it is knowable” and so on.) And I could have included the “assumption” that “the laws of physics are the same for all inertial frames of reference.” And, now that I think about it, I was wrong. I didn’t include this assumption because I didn’t think it was relevant to the point I was making (that the two flashes of light thought experiment does not work). But, now I think I should have included it. I’m sorry about that. In my first post in this thread I should have written: The Special Theory of Relativity is resting on four assumptions (relevant to this discussion): One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Four. The law of physics hold true (are the same) in all inertial frames of reference. However, I do not agree with you that the three assumptions that I listed are not assumptions of this theory. This theory would make no sense without them. And while I do not agree that the three assumptions that I listed need to be thrown out and replaced with the one assumption you listed, I do agree with you that I was wrong for not listing this assumption. Thank you. And please let me know if I’ve missed anything. --- Thank you. - Christopher (PS: Sorry for the typos that are inevitably all over the place in here.)
studiot Posted September 10, 2014 Posted September 10, 2014 (edited) Two. The velocity of light is independent of the motion of the emanating source. What a pity you did not address the short piece I wrote since I was hoping you actually wanted a discussion. The above quote that you have now repeated several times has nothing whatsoever to do with relativity of any sort. It is a simple piece of classical mathematics to prove that the velocity of any wave is independent of the motion of the emanating source. This applies to sound waves, electromagnetic waves, waves on a violin string or whatever. So yes it is true but it is not a fundamental assumption of relativity. I did actually supply the one and only 'assumption' you need for Einstein's relativity. Edited September 10, 2014 by studiot
pzkpfw Posted September 11, 2014 Posted September 11, 2014 (edited) I believe you are talking about the general area of non-synchronized clocks ... No? It's simply: all observers will agree whether events at a single location are simultaneous or not. This goes (in the train/embankment thing) to each observer agreeing whether the other observer sees the flashes at the same time. Specifically: If two flashes happen to hit the train observer at the same time, the embankment observer will agree they hit the train observer at the same time. If two flashes happen to hit the embankment observer at the same time, the train observer will agree they hit the embankment observer at the same time. This seems important to your understaning of R.O.S. If this is right, then this becomes a test of absolute rest; if we can in fact say that it is the man on the train who is moving (“Because he is moving …”). ... No. In this particular setup, both observers consider themselves as equidistant to the flashes, and both of course can consider themselevs as at rest. If one of them (either of them!) happens to see the two flashes at the same time they can consider those flashes to be simultaneous. There is no absolute rest here, any observer (whom any other observer might consider to be "moving") can experience events that are simultaneous. However, even if you are right, this does not shore up Einstein’s two lightning bolt strikes thought experiment. You are making a different argument. ... No. I'm trying to help you understand the one under discussion. ... Einstein does not say that maybe the guy on the embankment sees both of the flashes at the same time while the guy on the train sees one flash of light before the other or maybe the guy on the train sees both flashes of light at the same time while the guy on the embankment sees one flash before the other, we just don’t know (sort of in line with the same kind of thinking in the “twin paradox”). He does not say this. He says: “Hence the observer [the man on the train] will see the beam of light emitted from B earlier than he will see that emitted from A.” (p. 30). ... because the scenario discussed there is one where the strikes happen to be simultaneous in the embankment frame. So, while I respect your reasoning, I don’t think it leads to shoring up Einstein’s two lightning bolt strikes thought experiment. Both the man on the embankment and the man on the train are in equal positions to see the two flashes of light at the same time, but Einstein says that it is the man on the train (and not the man on the embankment) who does and will see one flash of light before the other. See: http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I#Section_9_-_The_Relativity_of_Simultaneity We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). While the thought experiment is talked-through with strikes that happen to be simultaneous in the embankment frame, the result is clearly meant to apply to any frame. Think it through from the point of view of the train observer, who may consider himself as at rest. If the strikes happen to be seen at the same time by him, then they are simultaneous in his frame, and so won't be simultaneous in the embankment frame. Edited September 11, 2014 by pzkpfw
robinpike Posted September 11, 2014 Posted September 11, 2014 (edited) Hi Christopher - I am sympathetic to your questions. The two lightning strike thought experiment appears to be able to be reduced down to understanding this simple scenario... A 'moving' observer, say going to the right, passes a 'standing still' observer and at the point of passing, a flash of light is created ahead of them from the right that moves towards them both. Obviously, the 'moving' observer is going to see the flash of light first. However, with the light approaching each observer at the same closing 'speed of light', and each observer at that point being the same distance from the light, how is this possible? The explanation would seem to require a mention of how length as well as time is perceived? However, the videos that have been included in these posts on the two lightning flash thought experiment do not seem to require length contraction in their explanation. So perhaps it would help if someone, for the above simply stated scenario (rather than the two lightning flash thought experiment), could describe what the complete explanation is, one from the 'moving' observer's point of view, and one from the 'standing still' observer's point of view. I would like to understand those explanations first and then I may have some more questions. Thanks. Edited September 11, 2014 by robinpike
studiot Posted September 11, 2014 Posted September 11, 2014 (edited) RobinPike The explanation would seem to require a mention of how length as well as time is perceived? Simultaneity is defined by time difference being zero. In particular the time difference between two events in space-time with coordinates (x1,t1) and (x2,t2) in some coordinate system is found by subtracting the time coordinates only [math]\Delta t = {t_2} - {t_1}[/math] If [math]\Delta t = 0[/math] That is t1 = t2 The two events are said to be simultaneous. Robin, the important thing to notice here is that this time difference is independent of the space coordinate, x. Since our coordinate system is completely general this statement applies to any coordinate system. So far we have only one coordinate system and all this has all been from the point of view of an observer in that system. So let us introduce a second coordinate system with coordinates (X,T), moving with velocity V relative to the first coordinate system. In this second system the same two points now have coordinates (X1, T1) and (X2, T2) and our second observer is moving with the second system at velocity V relative to the first. In this second system the coordinates of the same two points are given by the Lorenz transformation of the coordinates in the first system. In particular the time values in the second system are [math]T_1 = \frac{{\frac{{\left( {{t_1} - V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]{T_2} = \frac{{\frac{{\left( {{t_2} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] Note that in general the time values in the second coordinate system depend upon both the space and time values in the first system. If we now do the same time subtraction in the second system [math]\Delta T = {T_2} - {T_1}[/math] we find that [math]\Delta T = \frac{{\frac{{\left( {{t_2} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }} - \frac{{\frac{{\left( {{t_1} - V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]\Delta T = \frac{{\frac{{\left( {{t_2} - V{x_2} - {t_1} + V{x_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] [math]\Delta T = \frac{{\frac{{\left( {V{x_1} - V{x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }} - \frac{{\frac{{\left( {{t_2} - {t_1}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] I am sorry for the arithmetic but it is only what is taught in junior high school maths. Anyway since we have stated that the events are simultaneous in the first system t1 = t2 So the right hand part of that huge expression becoms zero leaving [math]\Delta T = \frac{{\frac{{V\left( {{x_1} - {x_2}} \right)}}{{{c^2}}}}}{{\sqrt {\frac{{\left( {1 - {V^2}} \right)}}{{{c^2}}}} }}[/math] But we are asking the question Under what conditions is this simultaneous in the second system? ie when is [math]\Delta T = 0[/math] ? and the equation tells us that for this to happen x1 = x2 That is they are in the same place in the first coordinate system. So two simultaneous events that are measured as in the same place in the first coordinate system will be seen as simultaneous in any coordinate system, since our second one was completely general. However this equation tells us yet more. It suggests that there may be events seen as simultaneous in the second system that are not seen as simultaneous in the first. The condition for this is for the relative velocity times the space difference to equal the non zero time difference in the first. [math]\frac{{\left( {V{x_1} - V{x_2}} \right)}}{{{c^2}}} = \frac{{\left( {{t_2} - {t_1}} \right)}}{{{c^2}}}[/math] [math]V\left( {{x_1} - {x_2}} \right) = \left( {{t_2} - {t_1}} \right)[/math] To examine this let us perform the same process on the space difference in the second system, using the Lorenz space transformation in this instance to find the difference in position of the two points in the second system is [math]\Delta X = {X_2} - {X_1}[/math] [math]\Delta X = \frac{{\left( {{x_2} - {x_1}} \right) - V\left( {{t_2} - {t_1}} \right)}}{{\sqrt {1 - \frac{{{V^2}}}{{{c^2}}}} }}[/math] But since they are simultaneous in all systems, (t2 - t1) = 0 Thus [math]\Delta X = LorenzTransformation({x_2} - {x_1}) = LT(\Delta x)[/math] Since x1 was a general point this implies that for every point in the first coordinate system there is a second point, x2, where events seen as simultaneous in one system will also be seen as simultaneous in the other. Edited September 11, 2014 by studiot
xyzt Posted September 11, 2014 Posted September 11, 2014 (edited) xyzt said: 1. “False, GR subsumes SR, it does not "rest on SR"” “Subsumes” or “rests” I don’t care. The point is that you don’t get to the theory of General Relativity without the theory of Special Relativity. One of the foundations of General Relativity is the thought experiment showing that acceleration and gravitation are equivalent (and later modified so say just so on a “local” level). And this is separate and independent of Special Relativity. But the General Theory of Relativity also rests on the idea that because in a spinning disk the outer edges move faster than the inner portions to another body at rest to the spinning disk and so, given the conclusions of the Special Theory of Relativity, the clocks at the edge of this disk will run more slowly than clocks at the center of the disk and (quoting from page 90): “Thus o our circular dis, or, to make the case more general, in every gravitational field, a clock will go more quickly or les quickly, according to the position in which the clock is situated (at rest).” You need the Special Theory of Relativity to get to the General Theory of Relativity, and, before all that, you need first show that “events which are simultaneous in one inertial frame of reference are not simultaneous in another inertial frame of reference” so be able to make the counterintuitive claim that “all inertial frames of reference have their own particular time” without simply asserting something counterintuitive as true. 2. “False. SR rests on a set of axioms. Relativity of simultaneity is a CONSEQUENCE of those axioms.” Yes. I agree. I misspoke. I was summarizing. I am sorry. However, what this simply means is that after accepting the axioms of the Special Theory of Relativity the first part of that theory reasoned out (the two flashes of light thought experiment leading to the conclusion “events which are simultaneous in one inertial frame of reference are not simultaneous in another inertial frame of reference”) is incorrect. And, so, it is not what the Special Theory of Relativity is actually resting on that needs to be replaced with Comstock’s thought experiment, but rather the first part of the Special Theory of Relativity, that then the rest of the Lorentz Transformations and the rest of the Special Theory of relativity is resting on, that needs to be replaced. I misspoke. I will try to be more precise in the futurre. 3. “False. You simply misunderstand the thought experiment. In addition, thought experiments cannot be used to disprove (falsify) a theory, only real experiments can do that. As an aside, RoS is not testable. There is some debate about this issue in the philosophical (not physical circles) but the bottom line is that it isn't testable.” So, you made a whole bunch of false statements and you come back with "I mis-spoke". Please show me why the man on the embankment will see the two flashes of light simultaneously while the man on the train will see one before the other. Please show why I misunderstand this thought experiment. And, again, I’m not talking about the actual physical world. I am talking about whether or not this thought experiment works as a thought experiment in “showing” what it purports to show: that events which are simultaneous with respect to the embankment are not simultaneous with respect to the train. I already did. Here it is again. The Lorentz transforms tie the time [math]t'[/math] of the observer on the platform to the time [math]t[/math] of the observer on the train: [math]t'=\gamma(t-vx/c^2)[/math] where v is the relative speed train-platform. Form the above, the temporal separation between two events ransforms as : [math]dt'=\gamma(dt-vdx/c^2)[/math] The events (the light flashes) have a [math]dt=0[/math] temporal separation in the frame of the train. They also have a spatial separation [/math]dx=L[/math], where L is the length of the train car, so, in the frame of the patform: [math]dt'=\gamma(0-vL/c^2)=-\gamma vL/c^2[/math] So, [math]dt' \ne 0[/math] The condition for this is for the relative velocity times the space difference to equal the non zero time difference in the first. [math]\frac{{\left( {V{x_1} - V{x_2}} \right)}}{{{c^2}}} = \frac{{\left( {{t_2} - {t_1}} \right)}}{{{c^2}}}[/math] [math]V\left( {{x_1} - {x_2}} \right) = \left( {{t_2} - {t_1}} \right)[/math] This is wrong, the units are incorrect. What you wanted to write is: [math]\frac{V x_1-V x_2 }{c^2} =t_2 - t_1[/math] If you want "absolute simultaneity", this can only happen when [math]x_1=x_2[/math], i.e. the events must be also co-located. One can never have "absolute simultaneity" for spatially separated events. Edited September 11, 2014 by xyzt
studiot Posted September 11, 2014 Posted September 11, 2014 This is wrong, the units are incorrect. What you wanted to write is: Thank you for drawing this to my attention. I see immediately where it went wrong right at the outset. I spend far too much time and effort getting the LaTex to present at all and end up without the expression coming out as I orignally had it on paper. Edit is not available to me and I am not going o write it all out again. I don't think I will bother in future.
robinpike Posted September 12, 2014 Posted September 12, 2014 Studiot, thanks for the maths (and no worry about the typo's). So for my simple scenario, we can use the maths for the 'moving' observer, and we can use the maths for the 'standing still' observer, but am I right in thinking that the maths cannot be used for the flash of light (or at least if used it it is meaningless)? If that is the case, what is the maths that can be used for the flash of light?
studiot Posted September 12, 2014 Posted September 12, 2014 (edited) Good morning Robin and thank you for your kind thoughts. I see that you are still online so I am posting this quickly, but will take the time to post a more measured response later today. Briefly to address your scenariao. I extracted your point about relativity of length because it was a good one. Essentially we can say that the source of the flash and the stationary observer (S) are in the same frame. So S measures a distance d to the source and the flash takes a time t to reach him, such that d/t =c. The strategy is to show that although the moving observer (M) sees a different distance to the source and a different time of flight of the flash, M still measures their ratio as c. Note also that S and M will see the light at different frequencies due to the doppler effect. Edited September 12, 2014 by studiot
robinpike Posted September 12, 2014 Posted September 12, 2014 Studiot, yes, that is how I understand the scenario. The two observers see different distances and different times (and the frequency of the light is different) from their position in space and the source of the flash of light. I was just wondering if it is valid to consider what the light 'sees' - i.e. in the 'distance' and 'time' from its source to when it meets / passes an observer in space? I suspect we are unable to answer, and so suspicious that we are misunderstanding something about space, time and light. Anyway I am interested in people's thoughts on answering such a question.
xyzt Posted September 12, 2014 Posted September 12, 2014 If that is the case, what is the maths that can be used for the flash of light? None, this has been explained to you in another thread.
studiot Posted September 12, 2014 Posted September 12, 2014 (edited) I was just wondering if it is valid to consider what the light 'sees' - i.e. in the 'distance' and 'time' from its source to when it meets / passes an observer in space? Every observer is considered at rest in his own frame of reference. So that is what the light 'sees'. Edit xyzt, I would be grateful if you already have a thread with the requested maths, for you to add a link to your post. Edited September 12, 2014 by studiot
xyzt Posted September 12, 2014 Posted September 12, 2014 Every observer is considered at rest in his own frame of reference. So that is what the light 'sees'. Edit xyzt, I would be grateful if you already have a thread with the requested maths, for you to add a link to your post. See here. One cannot attach a frame of reference to photons, SR forbids it and robinpike knows that already.
studiot Posted September 12, 2014 Posted September 12, 2014 See here. One cannot attach a frame of reference to photons, SR forbids it and robinpike knows that already. Thank you for the reference to that long and rather rambling thread. I did note that there was a general failure to distinguish between inertial frames of reference and general frames of reference, with continual discussion at cross purposes as a result. Even I did just that in your quote. I also noted that at the outset swansont's comment, which I agree with. swansont post#2 The frame of a photon is not an inertial frame. I do not think arguments about frames of reference add to this thread which is about the foundations of SR. The OP here posted populist listings of these, but in a science forum it is worth delving deeper and distinguishing between fundamental principles and consequenses.
christopherkirkreves Posted September 12, 2014 Author Posted September 12, 2014 To studiot: “So yes it is true but it is not a fundamental assumption of relativity.” Okay. I get it. I was wrong. I’m sorry. I misspoke. 1. The statement “There is no absolute rest” is less of an “assumption” and more of a “logical deduction.” 2. The statement “The velocity of light is independent of the motion of the emanating source” should be classified, as you point out, as more of something like a “principle” than an “assumption.” 3. However, the statement “The velocity of light is invariant for all observers” is still, as far as I know, an “assumption” because, as far as I know, this has yet to be empirically demonstrated. (Michelson-Morley does not demonstrate this.) And so, in the first section of my first post in this thread it should instead read: The Special Theory of Relativity is resting on four logical deductions, principles, and assumptions (relevant to this discussion): One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Four. The law of physics hold true (are the same) in all inertial frames of reference. However, logical deductions, principles, and assumptions could all be called “axioms.” (As xytz tried to correct me on earlier, but I guess I didn’t listen.) And so, in the first section of my first post in this thread it should instead read: The Special Theory of Relativity is resting on four axioms (relevant to this discussion): One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Four. The law of physics hold true (are the same) in all inertial frames of reference. And, since I’m really only talking about part of the Special Theory and not the whole thing, instead, it really should read: The “Two Lightning Bolt Strikes Thought Experiment” is resting on four axioms (relevant to this discussion): One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Four. The law of physics hold true (are the same) in all inertial frames of reference. Thank you for helping me make my language more precise. Now, has the first section of my original post been vetted enough in that it is now sufficiently precise enough to move onto the next section and discuss whether the “Two Lightning Bolt Strikes Thought Experiment” works as a thought experiment? Thank you. ---- To pzkpfw: If I understand your argument correctly, then you are saying: One: In the “Two Lightning Bolt Strikes Thought Experiment” it is set up so that it may either be the man on the train or the man on the embankment that sees the two flashes of light simultaneously, However, Two: Logic dictates that since the two men are in two different places relative to the sources of those lights when they perceive them, then if one man sees them simultaneously then the other man must see one before the other, And, Three: Einstein stipulates that the two flashes of light are simultaneous for the man on the embankment, And so, Four: The man on the embankment will see the two flashes of light simultaneously while the man on the train will see the one flash of light before the other. Am I close to understanding you? If this is your argument, it is correct on its face. However, this is not the argument Einstein is making. Einstein is not saying that either the man on the embankment or the man on the train may see the two flashes of light simultaneously. And its just that we stipulate that the man on the embankment sees the two flashes of light at the same time. And then, based on the logical argument that both men can’t see the two flashes at the same time and given our stipulation, we then therefore arrive at the conclusion that the man on the train sees one flash of light before the other. Einstein clearly believes that his thought experiment, as it is, leads to the conclusion that the man on the embankment will see the two flashes of light simultaneously while the man on the train will see one before the other and this thought experiment does this without saying something to the effect of “and the only reason why we know the man on the train sees the one flash of light before the other is because logic dictates that both men cannot see the two flashes of light simultaneously and we stipulated that the man on the embankment sees the two flashes of light simultaneously.” He believes based on his set up alone, he demonstrates that the two flashes of light will be perceived by the man on the embankment simultaneously and the man on the train will see the one flash of light before the other, and not based on us stipulating one or the other man [the man on the train or the man on the embankment] as the one who sees the two flashes of light simultaneously. (And, of course, I agree with you that if one man or the other may see the two flashes of light simultaneously while the other man then cannot see them simultaneously then this is not a test of absolute rest.) Thank you. ------------ To robinpike: “Obviously, the 'moving' observer is going to see the flash of light first.” Are you saying that it is the man on the train who is actually in motion and the man on the embankment who is actually at rest? Or, are you saying that it could either be the man on the embankment or the man on the train who is in motion and whichever one is in motion is going to see one flash before the other? I think this thought experiment leads to the idea that since neither man is in motion, from his own perspective, that both men will see the two flashes of light simultaneously. pzkpfw is more along the line of one of the two men will see the two flashes of light simultaneously, we just don’t which one until we stipulate which one, and then logic dictates that the other man is the one in motion and so he will see the one flash of light before the other. If you think that one of these two men must be in motion, then I think you agree more with pzkpfw than me. “The explanation would seem to require a mention of how length as well as time is perceived?” In the first ten chapters of his book where he lays out and concludes what he does in the “Two Lightning Bolt Strikes” thought experiment, he defines what length and time are for the purposes of this thought experiment. They are what you would intuitively expect: measuring rods and clocks. It is only after he has proven (or after he believes he has proven) that “events which are simultaneously in one inertial frame of reference are not simultaneous in another inertial frame of reference and therefore every inertial frame of reference has its own particular time” and so justifying an assumption of the Lorentz transformations and so then finding the ramifications of the Lorentz transformations of “time is slower between inertial frames of reference, and from both perspectives” and “length in the direction of motion is shorter between inertial frames of reference, and from both perspectives” and so leading to all the weird length and time ideas that flow from the Theory of Relativity. But, at the point of the “Two Lightning Bolt Strikes” thought experiment, Einstein defines “length” and “time” and he does so in the common sense way you’d expect these concepts to be defined (pre Lorentz transformations). Thank you. ----------- To studiot: “In this second system the coordinates of the same two points are given by the Lorenz transformation of the coordinates in the first system.” I have no idea if your math is correct or not. Maybe someday I take the hard plunge and learn the math. However, in the context of the “Two Lightning Bolt Strikes” thought experiment we are pre math. Whether or not the man on the embankment will see the two flashes of light simultaneously, while the man on the train will see the one flash of light before the other, does not depend on numbers. And it certainly does not depend on the numbers found in the Lorentz transformations. The Lorentz transformations rest of establishment of “every inertial frame of reference has its own particular time” and this is established (or attempted to be established) through the “Two Lightning Bolt Strikes” thought experiment, and so to explain the results of the “Two Lightning Bolt Strikes” thought experiment via the mathematics of the Lorentz transformations would be to engage in circular logic. ------------ To xytz: “So, you made a whole bunch of false statements and you come back with "I mis-spoke".” If I’m standing on my floor I can say “My body is resting on the floor” and I can say “My body is resting on my feet.” The first statement makes perfect sense. The second statement also makes perfect sense to us because we intuitively understand that the words “my body” actually to mean “the rest of my body other than my feet” because my feet which are part of “my body” are not resting on themselves. And so while the second statement makes sense, in a technical sense it is also wrong. I said that the “Special Theory of Relativity is resting on the Two Lighting Bolt Strikes thought experiment.” In the same way that the statement “My body is resting on my feet” is technically wrong, then so am I here in this statement about Special Relativity. However, what I said is essentially or basically true in the same way that the statement “My body is resting on my feet” is essentially or basically true. I believe that me just coming out straight forward and saying that “I was wrong” and “I misspoke” and not trying to argue that “while my was technically wrong it was essentially or basically right” in the same way that saying “My body is resting on my feet” is technically wrong while essentially right was being gracious and was an attempt to avoid another tangential line of argument in this thread that I would then need to address. I understand that it is part of the Internet culture, and specifically the forum culture, to never admit to a mistake, and if you do then you are open to having that admission highlighted with the implication that if you admitted to a mistake in at one time then the rest of what you have said should be suspect. But, of course, I disagree. And so, in the last section of my first post in this thread it should be corrected to read: The General Theory of Relativity is resting [in part] on the Special Theory of Relativity and the [main body of the] Special Theory of Relativity is resting on its [initial] two lightning bolt strikes thought experiment and the two lightning bolt strikes thought experiment is false. The foundation of this theoretical structure must be revised. (see Comstock, D.F. (1910), “The Principle of Relativity”, Science 31 (803): 767–772) Thank you for helping me make my language more precise. And I don’t believe the diction between “subsumes” or “rest” matters. If you think so fine. I don’t. And if you do believe that such a distinction between these two terms and concepts does matter then please show me why. If I agree with you I will correct my language. And if I don’t agree with you I will tell you why and we can discuss. “I already did. Here it is again. The Lorentz transforms tie the time of the observer on the platform to the time of the observer on the train:” On page 30 of his book Einstein writes: “We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.” And he does so without any claim to have only arrived at this conclusion based on the mathematics of the Lorentz transformations. He believes he arrives at this conclusion based on the four implicit and explicit axioms found contextually as he spells out the “Two Lightning Bolt Strikes” thought experiment. And I argue (and others in the forum have told me that I’m wrong) that this thought experiment is the bases of the Lorentz transformations (in that it is then what makes the counterintuitive assumption of the Lorentz transformations that every inertial frame of reference has its own particular time then a reasonable assumption), and if I’m right, then to use the math of the Lorentz transformations to prove that the “Two Lighting Bolt Strikes” thought experiment works is then to engage in circular logic (in using something assuming the conclusion as then also the premise of the same thought experiment). Thank you. - Christopher
xyzt Posted September 12, 2014 Posted September 12, 2014 (edited) and if I’m right, then to use the math of the Lorentz transformations to prove that the “Two Lighting Bolt Strikes” thought experiment works is then to engage in circular logic You aren't right, you are badly and profoundly wrong. Doesn't seem to stop you from posting the same errors over and over. Edited September 12, 2014 by xyzt
studiot Posted September 12, 2014 Posted September 12, 2014 One. There is no absolute rest. Two. The velocity of light is independent of the motion of the emanating source. Three. The velocity of light is invariant for all observers. Four. The law of physics hold true (are the same) in all inertial frames of reference. Christopher, it is your thread and you are putting in an enormous amount of work. So I can only assume you are really interested in developing an understanding of SR. I have already commented on your four assumptions, axioms, call them what you will. In particular number two. Note I have not said any are wrong or right, just offered to discuss whether they are necessary or the best group of assumptions. Do you wish to listen as well as preach?
Le Repteux Posted September 12, 2014 Posted September 12, 2014 (edited) Hi everybody, I agree with Christopher, even if observations prove that the numbers from relativity formulas are right, the mind experiments on which the theory rests contain contradictions. To me, the main reason is because light was not originally useful for us to measure motion, but for particles of matter to measure their own motion and to use that information to move properly one before the other . More precisely, I think that bodies in inertial motion rely on the limited speed of light to keep moving at the same pace, and that they rely on its timing to resist a change in direction or in speed. (see here) In the mind experience above, it is not the time of arrival of the light flashes that would be important for the particles, it is their frequency. If the flashes are emitted from the train, for the observer on the train, the frequencies would be the same because the doppler effect at the source is canceled by the doppler effect at the observer, and for the man on the embankment, the frequencies would be different because of the doppler effect at the source. If the flashes are emitted from the embankment, for the observer in the train, the frequencies would be different because of the doppler effect at the observer, and for the observer on the embankment, they would be the same because there is no doppler effect. Observing the frequencies directly does not create contradictions, but observing a mind experience as if the light emitted from every thing we imagine struck our eyes at the same time does. The only way to experiment with light is when it hits our instruments, and a ray of light traveling before our eyes in a mind experiment does not hit our eyes. If it is so, you may say, why do we observe relativistic effects? Because, if particles use the information from other particles to move with respect to them the way I suggest they do, since their motion cannot exceed the speed of their information, the frequency and the direction of that motion is subjected to relativistic effects. Edited September 12, 2014 by Le Repteux 1
xyzt Posted September 12, 2014 Posted September 12, 2014 (edited) Hi everybody, I agree with Christopher, even if observations prove that the numbers from relativity formulas are right, the mind experiments on which the theory rests contain contradictions. Of course you agree. The fact that you two agree doesn't make either of yoy right, it makes both of you equally wrong. Relativity is a non-contradictory theory. Only cranks who misinterpret relativity claim that they have found "contradictions". To me, the main reason is because light was not originally useful for us to measure motion, but for particles of matter to measure their own motion and to use that information to move properly one before the other . More precisely, I think that bodies in inertial motion rely on the limited speed of light to keep moving at the same pace, and that they rely on its timing to resist a change in direction or in speed. (see here) Promoting your own fringe theories does not constitute a valid argument. In the mind experience above, it is not the time of arrival of the light flashes that would be important for the particles, it is their frequency. If the flashes are emitted from the train, for the observer on the train, the frequencies would be the same because the doppler effect at the source is canceled by the doppler effect at the observer, and for the man on the embankment, the frequencies would be different because of the doppler effect at the source. If the flashes are emitted from the embankment, for the observer in the train, the frequencies would be different because of the doppler effect at the observer, and for the observer on the embankment, they would be the same because there is no doppler effect. Interestingly enough: -there is no Doppler effect for the observer on the train -there is no Doppler effect for the observer on the platform The reason is that: -the observer on the train is co-moving with the light source , therefore, no Doppler -the observer on the platform is a little more complicated, there is a cancellation of the Doppler effects due to the waves being reflected, so the receding effect is cancelled by the opposite effect : Trailing mirror [math]f_{platform}=f_{src}\sqrt{\frac{1-\beta}{1+\beta}}\sqrt{\frac{1+\beta}{1-\beta}}=f_{src}[/math] Leading mirror is the opposite [math]f_{platform}=f_{src}\sqrt{\frac{1+\beta}{1-\beta}}\sqrt{\frac{1-\beta}{1+\beta}}=f_{src}[/math] Observing the frequencies directly does not create contradictions, but observing a mind experience as if the light emitted from every thing we imagine struck our eyes at the same time does. The only way to experiment with light is when it hits our instruments, and a ray of light traveling before our eyes in a mind experiment does not hit our eyes. Err, mainstream physics relies on experiment for validation. Neither of you seem to grasp the fact that "mind experiments" are worth naught in physics. Besides, as I have just shown, your "contradictions" in mind experiments are just your basic misunderstandings. If it is so, you may say, why do we observe relativistic effects? Because, if particles use the information from other particles to move with respect to them the way I suggest they do, since their motion cannot exceed the speed of their information, the frequency and the direction of that motion is subjected to relativistic effects. Seriously? Edited September 12, 2014 by xyzt
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