Education and Crank Claims: Special Relativity

Discussion in 'Physics & Math' started by rpenner, Oct 5, 2011.

  1. AlphaNumeric Fully ionized Registered Senior Member

    In a similar vein, while I was explaining everything to Magneto I write up a perhaps more compact and straight forward demonstration of how his version is nothing but a rotated version of Rpenners, ie 2 directions remain unchanged still, here. I think having it all in a single post with no unrelated stuff thrown in makes it a bit easier, plus since I knew where I was going with it it's laid out a bit better. For example, there's a much simpler argument why there are always N-1 directions left unchanged by a boost in N dimensional space (so N+1 dimensional space-time), so I provided it.
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  3. DonQuixote Registered Senior Member

    OnlyMe said:

    Yes, I have heard this before, too.
    Funny thing is that B can never return to A without messing with the uniform movement (sorry, I always forget the right names - inertial movement?)

    But a thought strikes me: What is the reason B can't just look out the window of the train and view the string of sync'ed clocks that A very conveniently has placed on the ground along the rails? After all, Einstein says that A can sync the clocks in *his* frame. Why can't B just look at one of them, instead of mucking around with sending light signals back and forth and viewing things at a distance? He would just look at A's clocks, notice any discrepancy between A's clocks and his own, and then send the result back to A by any means he finds suitable (homing pigeon?).
    (Edit: Of course, he wouldn't have to if he had thought of placing his own clocks in the windows of his very long train for A to see.)

    This was actually going to be my next, alternative interpretation of "as vieved/seen/judged from" - a direct comparison, without vieving at a distance.

    But then you say this is not possible?

    But then again I received this reply from Magneto 1: [POST]283484[/POST]

    which seems reasonable to me - that the phrase "as viewed/seen/judged from X" means "as meassured by coordinate system X".

    That seems to be in line with E's use in the little book.
    Last edited: Oct 9, 2011
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  5. DonQuixote Registered Senior Member

    The relativity of simultaneity

    Again, thanks or the link, I read a little bit whenever I have the time.

    I have been mulling over relativity of simultaneity, you know the bit where he talks about lightening strikes that happens simultaneously in the stationary frame.

    I cannot for the life of me see that anything that happens in the experiment happens outside of the stationary frame! That includes the deduction that the moving observer sees the light from the lightening strikes as not reaching him simultaneously. All of it is as meassured from (or deduced in terms of) the stationary frame.

    How, then, can it be concluded that "What is simultaneous in the stationary frame is not necessarily simultaneous in the moving frame"?

    (I would not object to this: "What is simultaneous in the stationary frame is not necessarily simultaneous in the moving frame - as viewed from the stationary frame", but that is not what is concluded, I believe?)

    Moreover, it is obvious from the perspective of the stationary frame that whether the moving observer will receive the light signals simultaneously or not (as viewed from the stationary frame) is not dependent on the moving observer's velocity, but his position in the stationary frame. He would receive the signals simultanelusly if he happened to be at the midpoint of the train station as defined by the stationary system at the same time as the stationary system received it (obviously). He would still have the same velocity, however.

    Obviously, I must be missing something here, because this makes no sense to me.

    Edit: The method for meassuring simultaneity is weird also. Why doesn't he just meassure it with the already sync'ed clocks at the place where the lightning occurs? I think he even mentions somewhere in the beginning that this is how one should meassure with clocks.
    Last edited: Oct 9, 2011
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  7. AlphaNumeric Fully ionized Registered Senior Member

    It doesn't make any sense really to talk about the moving frame's point of view as viewed by the stationary frame. Person A can compute what Person B sees, that's what all the calculations are for, but A sees what A sees and B sees what B sees.

    A sees two events as simultaneous and B doesn't. A can realise B won't, if A knows about relativity.
  8. DonQuixote Registered Senior Member

    But A doesn't know about relativity in the sense of what E is deducing from these experiments. E is using this experiment for that deduction. A doesn't even have to know the postulates of relativity. The only thing we have to ensure is that he doesn't observe anything that violates the postulates. On the background of what he then observes, we will see if E's deductions from the potulates are justified.

    Is this an urnreasonble way of thinking?
  9. Janus58 Valued Senior Member

    You mean something like this:

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    Where the expanding white circles represent the light flashes.

    The embankment observer is halfway between the origins of the flashes both when they are emitted and when they arrive, thus he concludes that the flashes originated at the same time.

    However, prior to the moment when he sees the flashes, the train observer is not halfway between the origins and will be closer to one than his is to the other. How long it takes the flash to reach him, by his watch depends depends on how far he was from the origin when the flash left. One way to look at it is that since he measures the speed of light as a constant with respect to himself, he must see the light expand outward as a circle from a point that maintains a fixed distance from himself. Since he cannot be a equal distance from the origins when each flash starts, each flash must travel a different distance to reach him. If they traveled different distances at the same speed and arrived at the same time, they had to have left at different times. So what happens according to the train observer is this:

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    One flash occurs, then the other, and the flashes reaches both observers at the same time.
  10. DonQuixote Registered Senior Member

    I must admit I coudn't quite follow all of that, I am not used to thinking about this as expanding circles. I believe your first graphic is representative of what is going on - as meassured by the stationary system (I am quite aware that this is only a naming convention). As far as I can tell, the moving observer has mo means of even determining whether or not the phenomena he is observing the effect of are equidistant from him, or what distance they're at, and he can make no deductions from the simultaneity or not of the effects (when the light reaches him).
  11. DonQuixote Registered Senior Member

    When one makes a graphic of these things, It appears to me that one is only putting it all in one reference frame, that of the graphic. I'm not sure that it is really instructive for discussions of relativity.

    Might be wrong, though. Has happened before.
  12. Janus58 Valued Senior Member

    Yes he can. One thing that both observers must agree upon(besides the fact that they both see the flashes simultaneously) is the points on the embankment from which the flashes originated. These are marked by the red dots. If you want, you can think of them as strobe lights mounted to the track. The train observer must agree with the embankment observer that the flashes originated from the strobes.

    He sees the flashes at the same time that he is halfway between the strobes ( again, this not something that the two observers can disagree about.)

    Since it took some non-zero time for the flashes to reach him and he is moving relative to the strobes, he could not have been halfway between them when either of the strobes fired; he had to be closer to one than he was to the other.

    The postulates of SR require that the speed of light be invariant. Thus, as measured in his frame, the light flashes coming from each strobe must travel at the same speed relative to the observer.

    If he is an unequal distance from the strobes when they fire, and the flashes coming from each travel at the same speed, the only way he could see the flashes at the same time is if the strobes fired at different times.

    The other way to look at it is that once he sees the flashes, he can "back-track" the flashes and determine when they and the red dots (strobes) were the same distance from him. If he does this he will come to a different answer for each flash/strobe pair, leading to the conclusion that the strobes did not fire at the same time.
  13. Janus58 Valued Senior Member

    No. The first graphic is from the rest frame of the embankment. (this is why the tracks do not move and the train travels from left to right)

    The second graphic is from the rest frame of the train. (Here, the train does not move and the embankment moves right to left.)

    That's the point of doing the two graphics, to show how events occur according to each.
  14. DonQuixote Registered Senior Member

    Are you saying that when (simultaneously as) the position of the moving observer is at the same point as the stationary observer, there are also (simultaneously) (according to the train) two points on the train that corresponds to the strobes, and according to the reference frame of the train, these are equidistant from the moving observer?

    Because that was what I couldn't find in the description of the experiment (E's text). I could find no agreement about anything. I will try to read even closer.
  15. Janus58 Valued Senior Member

    It's in the second paragraph:
  16. James R Just this guy, you know? Staff Member


    You may as well drop the pretense that you'd have any hope of getting an academic position in a physics department at any university. There are people here who have actually taught in such departments - AlphaNumeric being one, of course.

    Repeated unsolicited references to your book will be considered advertisements here. This is not a legal matter, but one of site policy.

    Don't let the door hit you on your way out!
  17. DonQuixote Registered Senior Member

    I know where to find it, thank you. OnlyMe pointed me to it earlier.

    But I didn't catch your answer. I asked if you ment that:

    "When (simultaneously as) the position of the moving observer is at the same point as the stationary observer, there are also (simultaneously) (according to the train) two points on the train that corresponds to the strobes, and according to the reference frame of the train, these are equidistant from the moving observer?"
  18. DonQuixote Registered Senior Member

    Yes, you are right, I was wrong. Everything in the second graphic seemed to move to me, but it was late here. Sorry for the noise.
  19. Pete It's not rocket surgery Registered Senior Member

    And that puts you among the smartest people on Sciforums.
    Last edited: Oct 10, 2011
  20. DonQuixote Registered Senior Member

    Hehe, thanks, but I think, and indeed hope you are wrong. After all, I come here for help and guidance. It's just that I don't have a lot of prestige invested in being able to comprehend a moving graphic in the middle of the night.

    Actually, reading it again, I was less wrong about what I said than about what I meant. But then what I meant was based on a faulty understanding of what the graphic represented. It still holds that the graphics only hold for one frame of reference each, and it could hardly be otherwise, I think. I just thought a third reference frame was introduced, that of the graphic, but I was wrong about that.

    I really hope my admission of being wrong about that does not result in nobody responding to the other things I have said here. I still would like Janus58 to answer if my rephrasing of what he said about what must be agreed upon between the different frames of reference in the simultaneity experiment is something he would agree to. One of the ways we can make sure we understand each other is to rephrase and check if the meaning is preserved.

    Just a few days ago, I thought that there indeed had to be such an agreement between the two frames, and that Einstein had said so. I was actively looking for it when I read the relevant passages of "Relativity" (or what OnlyMe calls "the little book"). Much to my suprise, I could not find it. On the contrary, it seemed to me as if Einstein is very careful not to say this. If Janus58 agrees with my description and still insists it is in there, I will look closer. But for the moment, I maintain my posistion. (I will of course look closely at the book anyway.)

    I have also posed quite a few simple questions recently that no one seems to find it worth to reply to. I am not sure why. Maybe tey're too simple.

    In one of the first replies to my questions in this thread, someone said: Einstein doesn't need to state the obvious, so maybe that's the reason. But there's not much that is obvious about these relativity-things, as can be seen by the confusion created by the subject. Actually, most people in this forum appear to be quite bright to me, even if not everybody can be right. The quality of the debate-climate, on the other hand, does not impress me much, although everyone has been civil to me. But I think stating the obvious anyway, is a good policy. Since what is obvious to you, may not be to someone else.

    So except the graphics thing, I am not retracting any of my questions. I hope that admitting one mistake should not result in complete silence on the other matters. If that is what usually happens, I can see why no one admits to being wrong, ever.

    Nice to see you, Pete. I remember you were very patient in the simultaneity-thread.
    Last edited: Oct 10, 2011
  21. Janus58 Valued Senior Member

    The answer is "yes", with a qualifier. The points on the train that correspond with the strobes at that moment according to the train will not be the same points of the train that correspond with the strobes according to the embankment observer.

    The reason for this is length contraction. Imagine that the strobes are 2 km apart as measured by the embankment observer (each is 1 km from him.), and the train is moving at 0.5c

    Now the train, which is moving with respect to him, will be length contracted. So if each car is 10m long in it own frame, it will be only 8.66 m long according to the embankment. This means that just about 231 cars will fit between the strobes in this frame. If we number the cars, when car 115 passes the embankment observer, car 1 will be at one strobe and car 231 will be at the other.

    Now consider things from the frame of the train. Our observer is sitting in car 115, and according to him the railway is zooming past at 0.5c. Each of his cars is 10 m long so car 1 is 1155. m from him and car 231 is 1155 m from him. The embankment is length contracted, so the distance between the two strobe (2 km in their own frame), is only 1.732 meters apart in the trains frame. This means that only a little over 173 cars will fit between the strobes. It also means that when car 115 and the embankment observer are next to each other, one strobe is next to car 28 and the other is next to car 201.

    The following image shows what is happening at the moment the two observers (m and M) pass according to both frames. The embankment frame is the top one. Here I have marked the points on the embankment as A, B and M and the points on the train as a,b and m.

    In the embankment frame we see that M aligns with m, A aligns with a and B aligns with b all at the same instant as the train moves from left to right.

    In the lower image, we see things according to the frame of train. Here, when M and m align neither A and a align nor B and b align.
    If we consider that the embankment is moving right to left. B and b must have aligned at some time before this moment and A and a will align at some time after this moment.

    Please Register or Log in to view the hidden image!

  22. rpenner Fully Wired Registered Senior Member

    I'm back. Google+ and other things have been eating up a lot of my time.

    Hopefully, I haven't done too much violence to your posts in this attempt to summarize the threads of conversion in this forum.

    * About the thread
    Post 2 - DonQuixote Math scares me.
    Post 19 - billvon Thanks for thread and Post 1
    Post 26 - Trooper Even if math scares you, you can learn from the post. Presents a 1 hour Yale lecture on the topic for additional background.
    Post 27 - Emil "The mathematics is correct." (And?)
    Post 30 - wiminex (I lack the context to summarize this post.)
    Post 31 - CptBork How did Lorentz derive the Lorentz transforms? It might be something to post about later.
    Post 45 - wiminex (I lack the context to summarize this post.)
    Post 79 - chinglu Naked trolling.
    Post 81 - chinglu Naked trolling.
    Post 82 - Magneto_1 Naked Trolling. Empty "agree[ment]" with mathematics beyond the reach of the poster.
    Post 147 - Emil Unsupported and unconnected allegation that he is missed.
    Post 166 - James R (Moderator action suspended chinglu for 168 hours for "trolling.")
    Post 198 - CptBork I soon hope to provide a derivation of the Lorentz transform from the postulates of special relativity.

    Math, obviously, scares a lot of people because it is exact and fairly unforgiving. But it can also be a powerful ally. I hope to see your efforts, CptBork.

    * New moderators:
    Post 32 - Dywyddyr Motor Daddy and kin cause too much noise, we need more moderation.
    Post 187 - AlphaNumeric New Moderator! (prometheus is also a moderator)
    Post 189 - Magneto_1 I'm leaving.
    Post 191 - origin Congratulations, AlphaNumeric.

    Congratulations, prometheus and AlphaNumeric. You deserve better than this, but I can think of few who would be better at it.

    * History of independence of the speed of light
    Post 2 - DonQuixote Where does Einstein's first SR paper claim light's speed is independent of both motion of source and motion of observer?
    Post 3 - prometheus Observers can also be sources.
    Post 4 - DonQuixote Huh?
    Post 6 - Tach Motion is relative and no observer is preferred, so constant light speed is constant light speed, equally independent of source and observer.
    Post 9 - DonQuixote I'm willing to accept that was Einstein's intention to communicate.
    Post 10 - Tach Good.
    Post 11 - DonQuixote Did the Michelson-Morley experiment of 1887 test the independence of of the speed of light with respect to source or with respect to observer?
    Post 12 - rpenner The principle of relativity is that only relative velocities matter to physics. Therefore independence of the speed of light with respect to source is indistinguishable with Therefore independence of the speed of light with respect to observer.
    Post 14 - Tach Unsupported Claim: The Michelson-Morley experiment of 1887 didn't test the independence of the speed of light. (Except it did compare the round-trip speed of light of the two arms of the experiment and at various times was performed with laboratory lights, sunlight and starlight.)
    Post 15 - OnlyMe Einstein may have relied on Michelson-Morley or may have referred to H. Fizeau (who did work before Einstein was born.)
    Post 17 - DonQuixote Continued confusion about the why of Einstein's 1905 second postulate.
    Post 21 - OnlyMeLight and sound are not necessarily analogous phenomena. Complete independence of the speed of light is necessary to develop the mathematics of special relativity.
    Post 22 - DonQuixoteConfusion between instantaneous movement of the source and extended movement of the source and the nature of speed.
    Post 23 - TachThe second postulate (independence of the speed of light) is required to develop the mathematics of special relativity (the Lorentz transformation), which Einstein achieves in the 1905 paper.
    Post 24 - DonQuixoteTo read the paper, I will have to master the math. (And some electromagnetic theory would not hurt!)
    Post 25 - OnlyMe Description of H. Fizeau's 1859 paper. Additional discussion of measurement of speed.
    Post 28 - DonQuixote I'm satisfied.

    Here we see Tach at his most helpful. Good job, all.

    * That crazy first line of post 5
    Post 5 - Motor Daddy Miscellaneous concern trolling unrelated to the search for knowledge.
    Post 8 - prometheus Claim of unrelated distraction in reference to Post 4.

    Post 5 was neither self-contained nor limited to a single topic, so it will appear in other threads.

    * On cranks
    Post 32 - Dywyddyr Motor Daddy and kin cause too much noise, we need more moderation.
    Post 33 - CptBork It's without substance, a temper tantrum, and should be moderated away.
    Post 34 - DonQuixote Could the thread have been better engineered to attract cranks?
    Post 36 - Emil More cranks will come.
    Post 39 - AlexG Cranks come from on the basis of the title itself, not predicated on the OP.
    Post 41 - OnlyMe I don't consider DonQuixote a crank. Motor Daddy is a boring and useless crank who should be moderated away for the good of the thread.
    Post 42 - OnlyMe The OP tried to restrict the form of the discussion to something more than naked crackpot assertions.
    Post 43 - Motor Daddy You are free to address my posts.
    Post 44 - AlphaNumeric This is hypocrisy.
    Post 48 - Emil Crankdom is relative. (Unsupported claim in a confused post.)
    Post 54 - origin Nothing is to be gained by engaging Motor Daddy, and by doing so the thread suffers.
    Post 58 - DonQuixote (in re 41), Thank you.
    Post 94 - AlexG Did rpenner engineer this thread to attract cranks?
    Post 96 - OnlyMe Perhaps. Is he assuming too much of the readers?
    Post 97 - CptBork If he kept it entirely at the layman level, he couldn't address most of this topic at all. Cranks are crazy to think less math makes their ideas more reliable.
    Post 99 - OnlyMe I just thought he could explain more.
    Post 159 - Tach The name of the thread guaranteed cranks would attack it.
    Post 160 - AlphaNumeric Crank methodology is remarkable similar for having so many different views. Is there a common environmental cause?
    Post 161 - Tach It's a genetic disorder.
    Post 167 - AlexG rpenner probably did engineer this thread to attract cranks for the good of the forum.
    Post 168 - OnlyMe I see both "education" and "crank claims" and rpenner has supplied some of the former and others are all to happy to supply the later.
    Post 169 - AlexG rpenner's low post volume is evidence for the view that the thread has been efficiently engineered to attract cranks.
    Post 177 - Tach AlexG is probably correct.

    I neither engineered nor hoped for the ensuing firestorm. Clearly a lot of posters need to stop making claims and start with education.

    * Fake math is no way to make an argument
    Post 82 - Magneto_1 Crank Claim: One can change just part of equations one doesn't understand and leave the resulting expressions equally valid.
    Post 113 - Magneto_1 Repeat.
    Post 117 - Magneto_1 Repeat.
    Post 145 - Magneto_1 Repeat.
    Post 162 - Magneto_1 Repeat.
    Post 170 - AlphaNumeric Your wording and math is dishonest.
    Post 172 - Magneto_1 Slightly different unreliable math.
    Post 173 - AlphaNumeric You have disgraced yourself.
    Post 174 - Magneto_1 More error-filled or unreliable equations.
    Post 182 - Magneto_1 More unreliable math.
    Post 185 - Magneto_1 Yet more unreliable math.

    Well, this would be an case study in math being unforgiving.

    * Can you do physics without math?
    Post 121 - Magneto_1 Crank Claim: Physics is not math.
    Post 128 - AlphaNumeric Physics is always expressed in the language of math, because math is the language of symmetry, and every symmetry is a statement of reliable simplification.
    Post 185 - Magneto_1 Repeat.

    Just what measure of self-introspection does one have to have in order to notice that pretending to do math weakens the claim that math is not needed to speak to the physics?

    * Elasticity?
    Post 82 - Magneto_1 Crank Claim: Length contraction in the direction of motion is the same phenomenon as elasticity.
    Post 95 - OnlyMe No, it is not the same phenomenon.

    I don't think we will ever find reason to deeply compare elasticity and Lorentz contraction, but elasticity is about deformation associated with restoring forces. If Lorentz contraction was associated with restoring forces then both 1) Newton's law of Inertia and 2) the principle of relativity should be experimentally refuted -- which they have not been.

    * Instantaneous velocity
    Post 69 - DonQuixote Crank Claim: It is unreasonable to define a velocity at a point.
    Post 76 - OnlyMe It's unreasonable to measure velocity at a point.

    Velocity is a geometrical description of a world-line in 4-dimensional space-time akin to slope. Average velocity is defined between two points on the world-line, but for smooth curves through space-time there is a well-defined limit of the average velocity as the two points move closer to each other. This limit, as the time between points goes to zero, is the instantaneous velocity and is part of the reason Newton needed to develop calculus.

    * Special relativity isn't reality?
    Post 46 - Motor Daddy Crank Claim: While the math of the Lorentz transform does show that expanding light spheres map for one observer to expanding light spheres for a relatively moving observer, this does not reflect physical phenomena.
    Post 47 - billvon You are wrong, experiments show you are wrong, the math of the Lorentz experiments correctly summarize experimental results.
    Post 165 - Me-Ki-Gal (Reaction to post 47)

    Motor Daddy, I live in reality, I went to school with reality. Let me tell you, you don't know reality. Seriously now, if you could prove special relativity was not correct then you would have poked a hole in the postulates or in mathematics itself, so which is it? Ultimately, Motor Daddy has not fully embraced reality since H. Fizeau's 1859 experiments or Maxwell's 1865 statement of electrodynamics.

    * Conspiracy!
    Post 163 - Motor Daddy Crank Claim: A conspiracy of scientists suppresses the truth about the universe.
    Post 164 - arfa brane Your conspiracy is fictional.

    The truth will out -- that's the job of science. Scientists are lousy at suppressing truth. Conspiracies fail to keep secrets when too many people are involved and there are millions of scientists. Organizations of people (like fabled conspiracies) need motivation to keep organized -- what is the motive?

    * What is a scientific theory?
    Post 5 - Motor Daddy Crank Claim: Special Relativity is a crank theory. (Unsupported assertion.)
    Post 6 - Tach There is experimental confirmation of the postulates of Special Relativity.
    Post 9 - DonQuixote Although I am a skeptic, I am aware of the experimental records supporting Einstein.
    Post 10 - Tach Adding that many sensitive tests came after Einstein's 1905 paper.
    Post 11 - DonQuixote At least one experiment predated Einstein's 1905 paper.
    Post 40 - Motor Daddy Repetition.

    A scientific theory is a useful, precise, communicable and reliable description of a category of related phenomenon. Because it is precise and useful is can be compared with reality and potentially replaced with a more precise, more reliable or more applicable theory. This is the way science progresses.

    * What is an example of an ad hominem argument?
    Post 5 - Motor Daddy Crank Claim: Einstein was a crank. (Unsupported assertion.)
    Post 7 - Tach Claim of psychological projection.
    Post 40 - Motor Daddy Repetition.

    In a classic ad hominem fallacious argument, one makes a claim that the proponent is unsavory in some manner and then claim this renders his arguments suspect. This is of course invalid since even Hitler, wildly regarded as more unsavory than your run-of-the-mill crank, will argue that 1 + 1 = 2.

    * billvon's Manhattan student learning Euclidean distance
    Post 53 - billvon Analogy of the reliable mathematics of Euclidean distance contrasted with naive application of the Manhattan metric.
    Post 57 - Motor Daddy Demands proof that assuming the opposite of relativity leads to the proof of claims of relativity.
    Post 59 - billvon Your demand is unreasonable when you quoted, but did not indicate you read and certainly did not address, my analogy of a student not using the correct mathematics for distance. (in re post 53)
    Post 61 - Motor Daddy (A failure to grasp the analogy in post 59)
    Post 63 - billvon Ironic assertion of the analogous embrace of the Manhattan metric in attempt to goad Motor Daddy to actually make an argument for the adoption of the Euclidean metric.
    Post 67 - Motor Daddy The student should know 1) what the teacher asserts from the authority of acquired knowledge, 2) by experiment and observation of physical reality. For the student to do otherwise is illogical and clueless.
    Post 68 - billvon For those same reasons, you should not assert absolute space and time are the physics of our universe.
    Post 70 - Motor Daddy Rejection of the analogy.
    Post 72 - billvon The analogy holds.
    Post 74 - AlexG Naked assertion is Motor Daddy's stock-in-trade.
    Post 78 - James R Moderator proposal of action against Motor Daddy. Motor Daddy needs to attempt to connect with reality, not just the fantasy inside his head.
    Post 80 - rpenner Length contraction in the direction of movement makes sense if the Lorentz transform describes nature.
    Post 163 - Motor Daddy Light travels in absolute space and time. The world (and James R, in particular) seeks to suppress the truth.

    You can lead a horse to water, but you can't make him drink.
  23. DonQuixote Registered Senior Member

    I am a bit unsure about whether to accept your rephrasing of what I have said in general, but right now, I will only take exception to this:
    If you read it again, you will see that I clearly say:

    "a speed of something cannot be meassured at a point"

    I have made no statemens about defining speed at a point, as far as I can tell.

    Edit: I also don't think instantaneous velocity, whatever that is, had anything to do with my post.
    Last edited: Oct 11, 2011

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