Mac's Final Relativity Thread

Discussion in 'Pseudoscience Archive' started by MacM, Jun 30, 2009.

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  1. phyti Registered Senior Member

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    732
    billy, post 837'

    -Here you are comparing distances and time!.
    So who is in the fruit business?

    -It's still irrelevant how far the astronut travels.
    In this scenario with distance as 4 ly:
    A clock reads 0 at departure, 3 yr at arrival (for some
    mysterious reason), and 6 yr at return.
    E clock reads 0 at departure, 5 yr at arrival, and 10 yr at return.
    A receives 10 annual signals from earth during his 6 yr trip.
    It seems the earth clock is running faster than his own,
    or his clock is running slower than the earth clock.

    My argument is for true science, in terms of the known rules of
    physics, not pseudo-science, science fiction, Harry Potter
    physics, or mystical magical expositions that are designed to
    sell books!

    It doesn't matter how far the astronut clock travels, the
    longer it's away the greater the time difference. The universe
    does not contract because someone launches a space craft.
    There has never been a documented case of this happening in the
    history of NASA. The rules of physics do not allow it.
    It's only in the mind of the one making the trip, and like a
    hallucination, it is not shared by any one else, i.e. the rest
    of the universe. It's not a mental disorder but is an altered
    perception.
    The point of the example, like the twins problem is, the only
    way the the traveling clock can be behind when reunited is if
    it physically ran slower (given identical clocks). It only
    appears to run at earth rate because the astronut has altered
    perception. The astronut is a composition of atoms just as the
    clock is, thus experiences the same effects as the clock and
    all matter that is moving in that frame.


    Einstein developed the geometric-mathematical theory in pure
    abstract terms, without regard to physical explanations.
    Interpretation is left to the reader or other authors.
    I've read the material, done the math, and have proof of my
    statements. How about you?
     
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  3. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    Phyti, when you put it that way it makes sense.

    http://galileoandeinstein.physics.virginia.edu/lectures/mass_increase.html
    I have used that link a few times to remind myself that SR says that the invariant speed of light has consequences that become meaningful as objects are accelerated to the speed of light.

    No object with mass can ever be accelerated to the speed of light because it would take an infinite amount of energy to do so. If that is true, and I believe it is, then the consequences of accelerating an object are time dilation and increased mass associated with the relativistic conservation of momentum.

    If acceleration increases the relative mass of an object, which I also believe is true, then there is more mass in the space occupied by the accelerated object. Another way to say the same thing is that there is less space required for an accelerated object. Either way, if that is true and if you can say that an object of mass has its own energy density, then an accelerated object experiences increased energy density.

    If the speed of light is invariant and the mass of the object increases, the functioning of mass within the space occupied by the accelerated object slows down, accounting for relativistic time dilation due to increased mass.
     
    Last edited: Aug 16, 2009
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  5. prometheus viva voce! Registered Senior Member

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    First of all, you're going to say I'm getting at you because that's what I like doing - I'm not and you can check my posting history here and on physorg to see that I've pointed this out to a lot of people if you want to verify that.

    The equation relating energy and mass in SR is \(E^2 = |\vec{p}|^2 c^2 + m^2 c^4\). You derive this equation by taking the norm of the energy momentum four vector which implies that the term containing the mass is a Lorentz invariant, in other words, that mass does not vary with velocity.

    So why do pop science books and first lecture courses in SR tell you that mass does vary with velocity like \(m = \gamma m_0\)? It's because people have a very Newtonian intuition - Kinetic energy is \(\frac{1}{2} m v^2 \) etc. and all you have to do you go from the Newtonian to the relativistic is simply to stick \(m = \gamma m_0\) in your equations so \(\frac{1}{2} m v^2 \) becomes \(\frac{1}{2} \gamma m_0 v^2 \) etc.

    This works in practice, but the concept of relativistic mass that varies with velocity is not right, and anything that you get from assuming that mass varies with velocity will not be right either.
     
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  7. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    23,198
    Not true, misunderstood or deliberate lie.

    You are becoming more like MacM with each post by misquoting or lying.

    My point was exactly the opposite. I said time dilation was like speed, an instantaneous thing (an apple). Then I said accumulation was like distance traveled, something requiring a start and stop accumulation events (oranges). I assumed that you knew one should NOT compare apples to oranges. I.e. one should NOT compare or mix time dilation to time accumulated just as one should NOT compare speed to distance. My post was so clear on this that you must simply be lying in your post. Thus, I will treat you as I treat MacM, only respond to correct your lying about what I have posted. No longer try to help you correctly understand SR as it obvious you have no desire to.

    I did not read rest of your post - hope there are no more lies about what I said.

    The fundamental cause of the error most “anti-SR” people make is to assume their common sense is correct.

    For example, in the twin paradox, where both start and stop accumulation of clock times are indeed simultaneous as they take place in the same frame, common sense tells that the period of travel / accumulation of the traveling clock / brother MUST be the same as the never moved / accelerated/ clock or brother.

    This however, is not the case in reality. The traveler’s journey in a different frame, was NOT as long in time duration* as the stay at home clock or brother. - A very non-intuitive, common sense violating, but true, fact that follows mathematically from the two postulates of SR: (1) Speed of light is same in all frames. (2) Physics is same in all inertial frames.
    ------------
    * "Duration" is the interval between the start and stop accumulation of clock ticks or seconds. These start and stop events were simultaneous as in the same frame, side-by-side. None the less, the travel was in a different frame and the traveler's duration was less than the stay at home brother or clock. There are many examples of "common sense" being violated. For example, the two slit interference pattern persists on the photographic film even with long time exposure and very very low intensity light (So low that never is more than one photon existing.) I.e. each phonon passes thru BOTH slits - a clear violation of common sense, but an experimental fact.

    SUMMARY: When applied to events never experienced in the formation basis of one's common sense, there is no reason to assume common sense is valid. – In fact, many experimental PROOFS that it is often false / INVALID exist. The "twin Paradox" is another, unless one want to dispute the two above mentioned foundations of SR or say mathematical derivations from them are false.
     
    Last edited by a moderator: Aug 16, 2009
  8. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Messages:
    6,677
    So our difference is that I agree with the view that acceleration increases the relative mass of an object and your position is that it doesn’t.

    Rather than work out this difference on Mac’s thread I will start another thread if you are willing to discuss this difference. I am certain that you have a handle on the math and I have never faulted you on that. But you have never responded when I ask you about the correspondence between reality and math, i.e. do you think that there can be a precise correspondence between the two, and if not, to what degree does it matter to relativistic conservation of momentum.

    I’ll want to discuss some ideas that stem from the Theory of Special Relativity and relate SR to our individual views of reality. That assumes that we each have views of reality and that they differ. I would like to see how they differ and how, if at all, that difference affects our individual perspectives on relativistic mass increase due to acceleration and the conservation of momentum.
     
    Last edited: Aug 16, 2009
  9. MacM Registered Senior Member

    Messages:
    10,104
    When are you going to learn you can't bullshi_ your way around this stuff.

    You fail to read or understand the issue. Of course the end result is the same in all frames.

    The issue is the fuse burn physics are not the same. In one frame the fuses burn at the same rate in another they have different time dilations and do not burn at the same rate duevto their orientations.

    News Flash - Bullshit. I've never said any such thing. I was responding to your assertion about the "Laws of Relativity". Relativity is based on Postulates and as I have appropriately pointed out:

    a postulate is to "Assume without proof to be true, real or necessary".

    So how in the hell do you equate that to a law of physics? You can't.

    What indeed. I have accused you several times of flip-flopping, lying, etc which you deny.

    Here you say (after having been given notice you screwed up) that your analysis was perfectly correct and that I previously agreed it had no errors and tht I am being inconsistant.

    That is a flat lie. I responded that I accepted your solution without approval of your mathematics because it showed the affect I meant to demonstrate.

    I have since had to point out that you used w=(v+u)/(1+vu/c^2) when you should have used (v-u)/(1-vu/c^2).

    You have deliberately failed to acknowlwege your error and lie about my position. Now acknowledge your error or admit you are displaying the characteristics of being a "Crank".

    You did not. Your veloicty addition applies to the fuse burning in the aditive direction to the craft's velocity and the TNT was specifically oriented with the fuse ;oint in the direction of motion.

    Such that the flame velocity viewed from the resting frame is something LESS than the velocity of the craft, not more.

    Your refusal to acknowledge this is most telling. You are either ignorant or unwilling to ever admit error. Personally I don't think you are ignorant but I really do not expect you to ever admit error.

    But in any case others I'm surec can see the truth here. The fuse burns from the from of the craft back towards the TNT which is in the opposit direction of the crafts motion and hence you should have used (v-u) format not (v+u). So stuff it lair.

    .
    This is hardly a physics reply. Now address the issue which is that in one frame fuses burn at equal rates and in the other they do not because in one frame the fuse burn time is based on time dilation at 0.6c and the other fuse due to velocity additon has a burn rate based time dilation at a velocity <0.6c due to veloicty addition. . That is physics (According to SR unfortuntely)

    New Flash. James R denies there are such thaings as clocks and that they can be synchronized to demonstratesd different tick rates of the clocks. He therefore rejects all special relativity.

    Agreed and since I didn't mention it why are you?????:bugeye:

    DUH? That is not a response it is a dodge. If not explain to us just how your traveling observer detects that distance has contracted. Go ahead we are waiting.

    It is a known distance between points "A" & "B" as measured while at rest. The measurement while in motion remains the same because even IF distance contracts so does the meter sticks the traveling observer uses to measure distance and he still sees the same number of mile markers pass by. His measurements of those miles still comes out to 5,280 feet per mile.


    WOW. James R is now desperate. He denies velocity time dilation as part of special relativty all together.


    Haven't you folks been lead to believe, even by James R that relative velocity causes time dilation? I hought so too.:shrug:
     
  10. MacM Registered Senior Member

    Messages:
    10,104
    Pardon my french folks but "Screw you James R". I think your above post demonstrates that it is you and not I that are on the outside looking in here. You now deny that velocity addition affects the respective burn times of the fuses and you now deny velocity time dilation has anything to do with special relativity.????????????????????

    You have apparently had a nervous breakdown because you are promoting outright BS.
     
  11. MacM Registered Senior Member

    Messages:
    10,104
    Excellent post. I especially liked this one "Harry Potter
    physics,

    Yes within a limited application relativity is good a predicting results but it is mere math and not physics because modern science ignorese the aspects of relativity that are not supported by emperical data, logic or possible physics..
     
  12. MacM Registered Senior Member

    Messages:
    10,104
    How dare you draw this baseless link to my name asshole.
     
  13. prometheus viva voce! Registered Senior Member

    Messages:
    2,045
    Not quite. Acceleration is a different kettle of fish because you have external forces acting. Acceleration can cause particle creation in a similar way to Hawking radiation from a black hole by a mechanism called the Unruh effect.

    My point is that, if you have some particle with a mass m it's mass will always be the same in inertial motion, ie at rest or at some constant speed.

    Go for it. If it's going to be a discussion of SR then physics and maths would be the appropriate forum. If there's going to be a lot of speculations then put it in pseudo.
     
  14. phyti Registered Senior Member

    Messages:
    732
    Billy T;

    I don't lie about people, so don't take everything personally.
    I'll disagree with you because you don't provide a physics reason for those slow clocks!
    Anyway, this one's for you.

    The following is referencing the drawing 'space-measure.gif'.
    We measure the forward distance, sending a light signal from A (event 1) to a point at a distance x from the origin, where it's reflected (event 2) back to A (event 3). A is coincident with events 1 and 3, but measures event 2 indirectly using his clock. He assumes he is at rest, therefore divides his indicated time (3') by 2 and multiplies by c, resulting in event 2'. A vertical line from 2' to the x axis shows his calculated distance is greater than the physical distance d between A and event 2. Let the point be the far end of a rod of length d.
    Let g = gamma and t = the time for light to travel both ways (2d) along a rod at rest. Mathematically, for a moving rod, the radial axis (y or z) requires gt and the x axis requires ggt. For A gt becomes t, and ggt becomes gt, adjusting for time dilation.
    The x time still includes compensation for motion of the frame, but a true rest frame would not require this. A can conclude the rod stretched or the speed of light in the x direction is less than c.
    SR theory is built on ideal symmetry and a constant light speed, therefore an x coordinate transformation is required (1/gamma) to reduce A's calculated length to d.
    Notice SR transforms the calculated length, not the actual length. This is necessary since U measures the rod as d. It is this difference between A's calculated distance and U's measured distance that is interpreted as length contraction.
    In summary, the observer who chooses to consider his moving frame at rest, will reassign the time of the forward remote event as earlier on his clock and later for backward events. This explains his skewed spatial axis of simultaneity. In the process of constructing a pseudo rest frame, time dilation only removes some of the extra time due to light compensating for the motion of the moving frame. SR provides the transformation that completes the work.
    If A chooses to accept his motion, then knowing SR he adjusts his time with the inverse g function, length contraction is not needed, and A agrees with the description by U.
     
  15. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

    Messages:
    6,677
    Having a civil discussion with you would be fine but you already picked up on the point that I was intending to make. There is a difference between velocity and change in velocity as you point out in your response.

    Now if you maintain that acceleration does not affect the relativistic mass of an object then maybe we still have a topic to discuss.

    From the rest frame, the mass of the accelerating object increases relative to its mass at rest. If that is what you are saying then we agree, God forbid.
     
  16. Billy T Use Sugar Cane Alcohol car Fuel Valued Senior Member

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    23,198
    That is because there is no physical change in either frame - SR's strange, counter-intuitive effects, are caused by describing things / events etc. in ANOTHER frame with OUR frame's units (meter stick and seconds).

    In the twin paradox I explained that the duration of the traveler' trip was less that the non-traveler's wait period for him to return, even though both started their accumulators and stopped them simultaneous together in ONE frame. Yes, this goes against your common sense - so what? - Common sense is often wrong when applied to conditions never experienced when your common sense was being developed. - See footnote of prior post about the low-intensity double-slit inference pattern requiring that each photon go thru BOTH slits. Etc.

    It is much like the short armed King of France describing the length of rope the English King sent him as 115 yards when he is only being charged for 100 yards, back in the era when a yard was the distance from the kings nose to his finger tip of outstretched arm. There was no physical change in the length of the rope either - No "physical reason to provide" - The rope was just DESCRIBED in a new frame's units.
    --------------
    --------------
    On your linked drawing:

    "We measure the forward distance, sending a light signal from A (event 1) to a point at a distance x from the origin, where it's reflected (event 2) back to A (event 3)."

    I think I am to assume that A is at the origin for event 1 and traveling along the line with A near the end of it so will. I am not understanding what you mean by “forward distances,” especially as you also speak of “backwards distances.” Distance is a scaler, never negative, much like speed.


    "A is coincident with events 1 and 3, but measures event 2 indirectly using his clock."

    I think you mean events 1 & 3 are co-located* with A when they occur (not at other times) but what about event 2 is being measured? Does event 2 have a duration that can be measured by A's clock?
    If yes, when is the duration start? When did it stop?
    If, no what is measured? Where it was? When it was(by whose clock?)? How far way from A’s position when 2 occurred? (and here we need to be careful to distinguish if that is A’s position when light from event 2 reaches A or some other time earlier when time (whose time?) had A simultaneously at that location when event 2 occurred, even though A is not (and can not be) aware of event 2 yet.

    I’ll stop here as what you are stating is not well enough defined for me to continue. (Many similar problems in the remaining of your post, but thanks for taking the effort to make the drawing.)

    When just trying to guess what your point is from the drawing, I need first to understand why one axis is labeled U-t and the other U-s. You seem to have two clocks or observers called A & U. Are they both together at the origin initially (I assumed in my first comments that A is at the origin initially, but have not much information on where U is at t=0.)
    -------------
    *Your "coincident" could mean either at the same location or at the same time (or both). I do not want to get into a dictionary discussion with you but "co-located" and "simultaneously" are better terms to use if you do not intentionally want to be vague.
     
    Last edited by a moderator: Aug 17, 2009
  17. phyti Registered Senior Member

    Messages:
    732
    quantum wave, post 842;

    -Thanks for a positive comment, they are rare here!

    Prior to 1900 time was considered absolute, i.e. the same for everyone.
    Special Relativity redefined time as relative to the viewer and
    depending on their motion. This is ultimately due to the speed of light
    being constant, finite, and independent of its source. Whatever effect
    you consider within SR, it probably relates to this.

    I recommend starting with the light clock because it shows the reason in
    terms of physics for time dilation. The principle is simple, if light travels
    farther it requires more time.
    Time dilation is thus a function of speed, and consider acceleration as a
    sequence of increasing speed increments.

    As for the mass thing:
    Imagine a 10m long platform accelerated uniformly by burning pollen packets.
    A bee that always flies at 10 m/sec relative to the air, delivers a packet
    from the back to the front of the platform and returns. The initial platform
    speed v = 0, the transit time t is 2 sec. As the platform speeds up, the
    (v,t) values are, (2, 2.1), (4, 2.4), (6, 3.1), (8, .56), (9, 10.5),and
    finally (10, ?), when no transfer can be made.

    To the external observer the acceleration rate is slowing.
    This is interpreted as inertial resistance, i.e. increase in mass,
    when it is actually time dilation.
    The bee represents the photon in this analogy, and does not imply a limiting
    speed of 10m/s, but models the time light compensates for the motion of the
    moving frame.

    As mentioned by prometheus, the intrinsic mass of the object is constant.
     
  18. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    MacM:

    That is incorrect. In each frame the fuses burn at the same rate in that frame. In the ground frame, one fuse is shorter than the other, whereas in the box frame the fuses are the same length.

    I previously spent some time explaining to you that ALL of the laws of physics are based on postulates. You missed the point again. No surprises there.

    I have directed you at least four times to read post #778, but clearly you haven't bothered.

    Now, go back and read the bloody thing, paying particular attention to the diagram I provided in that post.

    Then, you can apologise to me for your stupid mistake and admit that I have been correct all along. Note that post #778 has not been edited in any way since it was originally posted.

    I will await your admission that you made the mistake, not me. Are you big enough to admit that you have been wrong? I don't think you are. I don't think you're capable of admitting when you're wrong, probably because it happens so damn often.

    And again I am forced to teach you basic relativity. Length contracted distances are measured using the rulers in the frame doing the measuring. Duh! So, when the ground frame measures a fuse as being length contracted, it is being measured using ground-frame rulers, not rulers in the moving frame.

    Will you admit your mistake here? Of course you won't.

    Do you have a reading comprehension problem? Look at the words in inverted commas. I did not mention "velocity time dilation", whatever that is. I specifically mentioned your "velocity dilation" nonsense, in which relative velocity supposedly is different in different frames.

    Will you admit this mistake of yours? No, I'm sure you won't.
     
  19. MacM Registered Senior Member

    Messages:
    10,104
    Why do you ALWAYS pretend to be teaching. I know all this and have shown I know this by my posts.

    Did you not read what I wrote, do you have an english comprehension problem or are you just being your typical obstinate person trying to cast negative innuendo?

    The fact is and I repeat in very clear english:

    In the rocket frame the fuses both burn at the same rate. From the ground frame the orthogonal fuses burn rate is time dialted by t'=t(1-v^2/c^2)^0.5 based on a velocity of 0.6c.

    But the TNT aligned with the contraction the fuse is pointed in the direction of motion and the flame is moving in the opposite direction from the motion of the craft and hence the velocity additiion required to compute relavistic affect is in the format of w=(v-u)/(1-vu/c^2) AND NOT YOUR (v+u)/(1+vu/c^2)^0.5.

    But as I replied when you screwed that up. I accepted your post for it correctly pointed out the fact that from that frame the fuses no longer had equal burn rates but that I was NOT confirming on your math.

    You have subsequently tried to lie and say I agreed with your math and hence are flip-flopping. Go back and read my reply again. Why do you suppose I qualified my reply?

    Further you mention the lorentz contraction but that fact has no bearing on the burn rate. The total material to burn hasn't changed it is just more compacted IF contraction actually takes place.


    I missed nothing. You apparently continue to ignore the fact I posted regarding what a postulate is "to assume without proof to be true, real or necessary..

    Sorry assuming without proof to be true is hardly a standard I base my physics on.

    James R there is just no basis to keep going back to your posts. You keep repeating the same old rhetoric and making the same irrelevant points.

    Putting it in this context I accept your challenge. I'll post my rebuttal.

    Again pretending to teach. You have said nothing I haven't already said. Further more it has nothing to do with the burn rate issue.

    In the rocket frame the fuses both burn at the same rate. From the ground frame the orthogonal fuses burn rate is time dialted by t'=t(1-v^2/c^2)^0.5 based on a velocity of 0.6c.

    But the TNT aligned with the contraction the fuse is pointed in the direction of motion and the flame is moving in the opposite direction from the motion of the craft and hence the velocity additiion required to compute relavistic affect is in the format of w=(v-u)/(1-vu/c^2) AND NOT YOUR (v+u)/(1+vu/c^2)^0.5.

    But as I replied when you screwed that up. I accepted your post for it correctly pointed out the fact that from that frame the fuses no longer had equal burn rates but that I was NOT confirming on your math.

    You have subsequently tried to lie and say I agreed with your math and hence are flip-flopping. Go back and read my reply again. Why do you suppose I qualified my reply?

    Further you mention the lorentz contraction but that fact has no bearing on the burn rate. The total material to burn hasn't changed it is just more compacted IF contraction actually takes place.

    I would admit an error as I have in the past. But there is no error here on my part. The error is on your part thinking you can post this garbage and never be cornered to actually respond to the issue.

    My analysis of what a moving observer has from which to draw his conclusions is correct.

    Please post the physical basis for why the moving frame observer would not conclude that he was not traveling at a higher velocity. Post on what basis other than dogma and rhetoric he would ever conclude that he traveled only 48 miles between cities seperated by 60 miles.

    Go ahead give us ANY basic physics foundation for such conclusions SR asserts. Or are you just reciting SR dogma?

    //////////////////////////////////////// 778 //////////////////////////////////////

    Here is my rebuttal:

    You posted:

    That is incorrect just as I have tried to explain to you. For "B" to have greater time dilation , hence detonate later, the velocity addition would have to yield a flame speed 0.6c+x.

    The flame was specifically stipulated to be moving opposite of the crafts direction of motion since the fuse is pointed in the direction of motion such that the flame speed is collectively LESS or 0.6c-x and hence suffers less time dilation than "A".

    Now it is time for YOUR apology.
     
    Last edited: Aug 17, 2009
  20. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    You didn't look at the diagram in post #778, did you? Go and look at it. That's five times I've told you.
     
  21. MacM Registered Senior Member

    Messages:
    10,104
    OK lets nip this in the bud. Yourv 855:

    This statement implies the diagram has not been changed but that refers to the diagram "AFTER" you had already changed it. Really clever but you have been caught with your hands in the cookie jar this time.

    The arrow points in the same direction as I had stipulated the fuse would be pointed it was drawn the fuse on the forward side, but you redrew my diagram puttingthe fuse on the back side so I assume you are going to claim that the flame is in the direction of the arrow.

    But in my text I stipulate the fuse was pointed in the direction of motion. according to the arrow. It could not have been confusing.

    According to YOUR modification of my diagram then your math is correct but you have altered the scenario from mine and used my sketch and done it in an obscure manner making it appear to be a quote from me. So I will not tolerate your assertions. You screwed up by redrawing my sketch, posting it as my quote and then attaching it to your math.

    Further your assertions about me are false on this issue. In the box frame they detonate simultaneously and in the ground frame they do not and that was precisely what I claimed. So all your huff and puff about MacM and his understandings, etc is outright BS.

    You have confirmed my initial claim but attempt to make it appear you have been teaching. You have not.

    I really hope others are paying attention here. There was no impetus for you to go in and move the fuse in my diagram then enclose it in your post as though it was a quote from my post. You tamperered with my diagram did you not before you put it in as a quote from my post? How do you justify changing others text and then posting it as a quote?


    MacM's initial diagram:

    *************************
    *..........................................*
    *./\fuse................................*
    *..!.......................................*
    *..!.......................................*
    *.T.......................................*----------------> Frame velocity
    *.N.......................................*
    *.T.......................................*
    *..........................................*
    *..........................................*
    *..T N T-----> fuse.................*
    *..........................................*
    **************************

    James R's post:

     
    Last edited: Aug 17, 2009
  22. noodler Banned Banned

    Messages:
    751
    Is this thread really about the relativity of understanding, and the rejection rate of established theories (relative to the understanding of them)?

    When I didn't understand relativity I tried to find out why it was "a problem", now I more or less do, and it's still a problem (not just for me or people who reject it either). It isn't a "static" result, or why is there all the research and attempts to reformulate GR?

    General implies "in all frames"; relativity is really about observation - observer A sees things differently than observer B because they're in different frames (have different velocities = are in relative motion). What's the big deal? Lorentz and Galileo are the big deal.

    When someone disagrees with a principle it's definitely their problem to show why it's "wrong" and why their version is correct. Or you're going to be saying it, but not doing much else - how significant is it that someone "can't agree" with Einstein these days? About as significant as someone who doesn't know how a car manages to move when you "press the accelerator".

    "It has an engine, and uses petrol", doesn't really do it....
     
    Last edited: Aug 17, 2009
  23. James R Just this guy, you know? Staff Member

    Messages:
    39,397
    Let's do this properly.

    Take two points in a box, A and B, connected by a fuse. In the rest frame of the box, let us assume that the fuse has length d'. The fuse is oriented parallel to the direction of motion of the box and burns from A towards B. The box moves relative to the ground with a Lorentz factor of \(\gamma\) and speed v in the SAME direction that the fuse burns.

    In the box frame, the fuse burns a distance d' in time t'. It's burn speed in this frame is u'=d'/t'.

    We now need to work out the burn speed of the fuse in the ground frame. To do that, we need to work out the distance it needs to cover and the time it takes to do so.

    Let event A be the event at which the fuse is lit. Its spacetime coordinates in the box frame are (x',t') = (0,0). Let event B be the event at which the fuse reaches point B. Its spacetime coordinates are (x',t') = (d',t').

    Now consider the ground frame. The spacetime coordinates of event A are taken to be (x,t) = (0,0). The spacetime coordinates of event B are calculated using the Lorentz transformations:

    \(x = \gamma(d' + vt')\)
    \(t = \gamma(t' + vd'/c^2)\)

    The fuse burn speed in the ground frame is u = x/t, or

    \(u = \frac{d' + vt'}{t' + vd'/c^2} = \frac{d'/t' + v}{1+(d'/t')(v/c^2)} =\frac{u' + v}{1 + u'v/c^2}\)

    Let's plug in some numbers. Put u'=0.4c for the burn speed in the box frame and v=0.6c for the speed of the box relative to the ground. The 0.4c is unrealistically fast, but all that matters for this example is that u' is slower than the speed of the box.

    In this case, we get u=0.806c. That is, in the ground frame the fuse burns at a faster rate than it does in the box frame (u'=0.4c). However, most of this speed is due to the motion of the box rather than the burning of the fuse itself.

    It is tempting to subtract off the speed of the box from u to get a more direct comparison, which would give u = 0.806c - 0.6c = 0.206c, from which we might conclude that the fuse burns slower in the ground frame than it does in the box frame. However, this calculation is not a correct one because we're dealing with relativistic speeds here that do not just subtract like this. In fact, if we properly "subtract off" the speed of the box in the ground frame, we're back to where we started, with the fuse burning at 0.4c (as was originally assumed). That is, ignoring the motion of the box the fuse burns at the same rate in both frames. But of course it does. It's the same fuse in both frames.
     
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