Is relativity self-contradictory??

Discussion in 'Physics & Math' started by Prosoothus, Aug 30, 2002.

  1. Prosoothus Registered Senior Member

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    I recently began having a debate with Tom2 on the "How does spacetime curvature become infinite?" thread. Since our debate is off-topic for that thread, I decided to continue the debate on this new thread.

    I was previously explaining to Tom2 that relativity contradicts itself. The formulas used for time dilation and length contraction are simply patches to a hole that was created by the absolute model. In other words, the patch is proof that there's a hole, and the hole is proof that the absolute model is correct, and that relativity is wrong.

    As proof of this, I am providing the mathematical explanation, given below, that length contraction and time dilation are used to attempt to make the principle of invariance of light correct (even though it isn't).

    To illustrate my point, let's take two mirrors with light bouncing between them. As the two mirrors begin to move forward (so that the motion of the mirrors is parallel with the bouncing light), it appears that the light slows down. Relativity attempts to compensate for this "slowing" by compensating the effect with length contraction and time dilation. Below, I will explain this "slowing down" effect using the absolute model (assuming that the invariance of light is wrong), therefore proving that relativity is wrong, since the absolute and relative models both can't be correct.

    First, assume you have two mirrors, and there is light bouncing back and forth between the mirrors. Now let's say that you start moving the mirrors forward, so that the motion of the mirrors is parallel with the motion of the light (the direction doesn't matter).

    According to the ABSOLUTE model, the time it takes for the light to reach the mirror that is moving away from it is longer:

    t1=d/(c-v)

    where d is the distance between the mirrors and v is the speed of the moving mirrors.

    But the time it takes for the light to reach the mirror that is moving towards it is shorter:

    t2=d/(c+v)

    The time it takes the light to reach a mirror and return would be:

    t3=t1+t2
    t3=(d/(c-v))+(d/(c+v))
    t3=(d(c-v)+d(c+v))/(c+v)(c-v)
    t3=(dc-dv+dc+dv)/(c^2-cv+cv-v^2)
    t3=2dc/(c^2-v^2)

    The average time of the one-way trip of the light would be:

    t=t3/2
    t=(2dc/(c^2-v^2))/2
    t=dc/(c^2-v^2)

    The average speed of the one-way trip of light would be:

    v=d/t
    v=d*(c^2-v^2)/dc
    V=(c^2-v^2)/c REMEMBER THIS RESULT!!!!!

    Now Einstein dictates that in this situation there is time dilation AND length contraction.

    The time dilation is

    T=T0/sqrt(1-(v^2/c^2)

    we want to find T0:

    T0=T*sqrt(1-(v^2/c^2))

    The length contraction is:

    L=L0*sqrt(1-(v^2/c^2))

    we want L0:

    L0=L/sqrt(1-(v^2/c^2))

    Since v=d/t then:

    v1=L0/TO
    v1=L/sqrt(1-(v^2/c^2))*1/T*sqrt(1-(v^2/c^2))

    Since we have that v obtained from the ABSOLUTE model above, let's remove L and T so that we only have the length contraction and time dilation factors:

    a=1/sqrt(1-(v^2/c^2))*1/sqrt(1-(v^2/c^2))
    a=1/(1-(v^2/c^2))

    since 1-(v^2/c^2)=(c^2-v^2)/c^2 then

    a=1/((c^2-v^2)/c^2)
    a=c^2/(c^2-v^2)

    Now let's see what we get when we multiply the velocity obtained from the absolute model with the effects of time dilation and length contraction:

    v=V*a
    v=((c^2-v^2)/c) * (c^2/(c^2-v^2))
    v=c

    In other words, time dilation and length contraction patch the results from the absolute model to make v=c. Therefore, Einstein's formulas for time dilation and length contraction are proof that the absolute model is right, and that relativity is wrong.

    Tom
     
    Last edited: Aug 31, 2002
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  3. Merlijn curious cat Registered Senior Member

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    eeeh no

    You contradict yourself. You must remember, it can only hold when the mirrors have a constant velocity!
    I think you should first learn more about the exact condictions; formulate a more precise experiment; Show why relativity cannot be right; and tell us what is the alternative.

    Honestly, I have seen none of the above!

    Your high school math is to the theory as swords to a balrog.
     
    Last edited: Aug 30, 2002
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  5. Crisp Gone 4ever Registered Senior Member

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    Hi Tom,

    "In other words, time dilation and length contraction patch the results from the absolute model to make v=c. Therefore, Einstein's formulas for time dilation and length contraction are proof that the absolute model is right, and that relativity is wrong."

    Where does it prove that ? You have simply established a relation where you would let the speed of light vary (dependent on the direction of motion) and what relativity would predict. Your absolute model is what a Newtonian theory would predict. However, and this is exactly what relativity is all about: by assuming the extra condition "the speed of light is invariant for all observers" in addition to all Newtonian postulates, you get a model/description/theory that works better for extreme situations (high speeds, high energies).

    What you have done is calculated a Newtonian result and compared it to a relativistic result: it is obvious that there are differences, but the extra assumptions in relativity are there to create the minor corrections required on Newtonian results. In this case, it is a multiplier factor (which is not unexpected since time dilation and length contraction formules involve a multiplication factor gamma). However, if you let v become much smaller than c (v << c) then your multiplier reduces to "a = 1", i.e. the relativistic and Newtonian result are the same (note: Newtonian mechanics are a limiting case, low speeds i.e. v << c, of relativity).

    To conclude: your calculation is easily explained from both a Newtonian (which is your point of view) and a relativistic position.

    And above all, the calculation does not tell us why we should prefer your absolute Newtonian world above the relativistic world (that seems to look a lot more like the real world).

    Bye!

    Crisp
     
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  7. Prosoothus Registered Senior Member

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    Crisp,

    There is NO similarity between the Newtonian theory and relativity. They are opposites:

    Newtonian theory (absolute model):

    1) There is an absolute frame of reference.
    2) The omnidirectional speed of light is only c in the absolute frame of reference.

    Relativity:

    1) There is no absolute frame of reference.
    2) The omnidirectional speed of light is c in all frames of reference.

    One model contradicts the other, so you can't derive one model from the other. Let me remind you again, I derived the formulas from the absolute model (assuming that the principle of invariance of light is wrong). If time dilation and length contraction patch the results from the absolute model so nicely, how can you argue that the absolute model is wrong. And if the absolute model is right, then relativity must be wrong. Or do you believe that they can both be correct??

    As far as I see it, there are only two choices:

    1) The principle of invariance of light is wrong

    or

    2) The principle of invariance of light is correct

    Which one is it??

    It appears that Einstein knew that 1 was right, so he used length contraction and time dilation to convert 1 into 2 in order to preserve his theory.

    Truthfully, if length contraction and time dilation didn't perfectly patch the results from the absolute model, I would assume that relativity might be correct. But as you can see, this is not the case.

    The fact is that time dilation and length contraction patch a hole. And the hole can ONLY be derived from one thing: THE ABSOLUTE MODEL. And the absolute model ASSUMES that the principle of invariance of light is WRONG.

    If you believe that the hole can be derived from anything else besides the absolute model (and the assumption that the principle of invariance of light is wrong), please show me your formulas. And don't use the formulas for length contraction or time dilation to obtain the result, since we both know that it wouldn't qualify as proof.

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    Tom
     
    Last edited: Aug 31, 2002
  8. Prosoothus Registered Senior Member

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    Merlijn,

    I proved that relativity is wrong with my post. As I pointed out to Crisp, time dilation and length contraction PERFECTLY patch the results from the absolute model.

    Let me remind you, I used the assumption that the principle of invariance of light is wrong in order to obtain the results for the absolute model. The ironic part is that relativity patches the results obtained from the absolute model. If the absolute model was wrong, there would be NOTHING to patch.

    The alternative to what??? The fact that moving atomic clocks measure that time slows down???

    If you look at the construction of atomic clocks, you will find that the caesium atoms in the clocks are stimulated and seperated using electromagnetic radiation. If the absolute model is correct, and the principle of invariance of light is wrong, then the speed of the electromagnetic radiation, relative to the clock, is influenced by the motion of the clock. The resulting change in the speed of the electromagnetic radiation in the clock, will influence the clock to give a false reading. As you can see, there is no need to use time dilation or length contraction to explain the "perceived" slowing down of time by the atomic clock.

    One more thing : The math I used was intentionally simple so that everyone could understand. Even you.

    Tom
     
    Last edited: Aug 31, 2002
  9. Neutrino_Albatross Legion of Dynamic Discord Registered Senior Member

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    751
    So,

    how exactly is it possible to ignore all the experimental evidence that realativity myst be true just because you personally dislike it?

    Or mabey the evil scientists forged the results of the experiments so the world woulnd't find out their precious theory was wrong?
     
  10. James R Just this guy, you know? Staff Member

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    34,678
    Tom,

    It seems you've conveniently forgotten our past discussions on this topic.

    Oh well...
     
  11. James R Just this guy, you know? Staff Member

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    34,678
    Let's pick apart Tom's maths a little.
    What does this mean? Remember that Tom claims to be postulating an absolute reference frame. Now V is supposed to be the speed of light as determined by somebody watching the mirrors and the light bouncing between them, with the whole apparatus moving. Notice that V depends on v (the speed of the mirrors). But why should the speed of light be affected by the movement of the mirrors? After all, unless it is being reflected it is moving in empty space. Shouldn't its speed be the usual value (=c)? In fact, Tom assumes that is its speed in the very first step of his calculation, which includes the constant c.

    Tom appears to be assuming the speed of light is c in order to try to prove that its speed is in fact (c^2-v^2)/c.

    Something is very wrong here.

    How about an explanation, Tom?
     
  12. Crisp Gone 4ever Registered Senior Member

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    Hi Tom,

    "One model contradicts the other, so you can't derive one model from the other. Let me remind you again, I derived the formulas from the absolute model (assuming that the principle of invariance of light is wrong)."

    Exactly my point: by assuming that the speed of light works in an additive way (c+V as you used), you leave out the invariance of the speed of light and you are basically reducing relativity to Newtonian mechanics.

    Note that there is no mention of an absolute frame of reference in Newtonian mechanics (Newtonian mechanics is also a relative theory!!!).

    I perhaps was wrong dismissing your theory as "pure classical Newtonian mechanics", but it resembles it quite a lot

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    .

    "If time dilation and length contraction patch the results from the absolute model so nicely, how can you argue that the absolute model is wrong. And if the absolute model is right, then relativity must be wrong."

    As I tried to explain in my previous post, it is not suprising that time dilatation and length contraction "patch" your absolute results. That is a direct consequence of the invariance of the speed of light! This has been told to you before, but I'll repeat it once more: (-> means "leads to")

    invariance of the speed of light
    -> time dilatation and length contraction
    -> Lorentz transformations

    In the Lorentz transformations, there is a slight difference between the classical Newtonian transformations (called "Galilean transformations"). This difference is exactly a multiplicative factor GAMMA that occurs in the Lorentz transformations. Since (roughly speaking) the basic difference between Newtonian mechanics and Relativity is this GAMMA factor in the transformations, it is not suprising that your result (which is basically Newtonian mechanics with an absolute frame of reference) differs from the relativity result by a multiplicative factor, which you labeled "a" (the effects of time dilatation and length contraction).

    You see this as a "patch", I see it as a direct result of the GAMMA factor in the Lorentz transformations. And moreover, as I already said, just because it looks like a "patch" doesn't mean that we should prefer one calculation over the other. You need to provide more evidence for your absolute model before making such a claim.

    Bye!

    Crisp
     
  13. Prosoothus Registered Senior Member

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    1,973
    James R,

    The omnidirectional speed of light is only c in the absolute frame of reference.

    As the mirrors move, the speed of light does not change in the absolute frame of reference: it remains c. However, the light appears to speed up and slow down relative to the observer traveling with the mirrors. As the light is traveling towards the mirror that is moving away from the light, the light appears to be moving slower than c (c-v) to the observer traveling with the clock. However, when the light is traveling towards the mirror that is moving towards the light, the light appears to be traveling faster than c (c+v) to the same observer.

    When the observer measures the roundtrip speed of the light (to a mirror and back) the light appears to be traveling at the speed of (c^2-v^2)/c, while in reality, the one-way speed of the light remains c in the absolute frame of reference.

    Tom
     
  14. Prosoothus Registered Senior Member

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    Crisp,

    Let's break this down to simple math:

    v(relativity)=v(roundtrip from absolute model) * GAMMA

    where v(relativity)=c


    The fact is that :

    GAMMA=v(relativity)/v(roundtrip from absloute model)

    This means that the GAMMA factor is derived from the absolute model. It also means that the GAMMA factor is proof of the absolute model. As far as I know, there is no other way to derive the GAMMA factor than from the ABSOLUTE MODEL.

    If I'm wrong, and the GAMMA factor can be derived without the use of the absolute model, please explain.

    Tom
     
  15. James R Just this guy, you know? Staff Member

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    34,678
    Tom,

    I see. So, you're working in the reference frame of somebody travelling with the mirrors. Ok...
    Sorry. I'm lost again. What exactly are T0, T, L0 and L in these equations? And what is v1?
     
  16. Merlijn curious cat Registered Senior Member

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    1,014
    T0 and L0 are the 'dimensions' of time and length when the frame is at rest
    T and L are the dimensions when travelling near c
    and I believe v1 is meant to be the velocity of the mirrors.
    But I am not sure he means this.

    I think the most probelematic part of the derivation is:
     
  17. Prosoothus Registered Senior Member

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    1,973
    James R,

    Let me simplify it:

    Let's say sqrt(1-(v^2/c^2))=Gamma

    Then time dilation is:

    T=T0/Gamma

    And length contraction is:

    L=LO*Gamma

    We have L and T from the absolute model (V=L/T). Therefore, we need to find L0 an T0:

    T0=T*Gamma
    L0=L/Gamma

    We want to find the result of L0/T0:

    L0/T0=(L/Gamma)/(T*Gamma)
    L0/T0=(L/Gamma)*(1/(T*Gamma))
    L0/T0=(L/T) * (1/Gamma^2)

    We take L/T from the absolute model (V) which equals (c^2-v^2)/c:

    L0/T0 = ((c^2-v^2)/c) * (1/Gamma^2)

    Since (1/Gamma^2) = (c^2/(c^2-v^2)) :

    L0/T0= ((c^2-v^2)/c) * (c^2/(c^2-v^2))

    L0/T0=c


    Tom
     
  18. James R Just this guy, you know? Staff Member

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    34,678
    Tom,

    You don't need to repeat your previous derivation. Just tell me what you understand L, L0, T and T0 to be, in your own words.
     
  19. Crisp Gone 4ever Registered Senior Member

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    1,339
    Hi Tom,

    "If I'm wrong, and the GAMMA factor can be derived without the use of the absolute model, please explain."

    I believe this was demonstrated already in our previous discussions on relativity. The formulas for time dilatation and length contraction have the GAMMA factor in them, and those are derived in Special Relativity without assuming the existance of an absolute frame of reference.

    Bye!

    Crisp
     
  20. Prosoothus Registered Senior Member

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    James,

    L an T would be distance and time without the effects of time dilation and length contraction, while L0 and T0 would be distance and time after the effects of time dilation. Tha actual values of L, L0, T, T0 are insignificant in the equations. The values that matter are L/T and L0/T0:

    V1=L/T This I obtained from the absolute model.

    V2=L0/T0 This, according to relativity, is equal to c

    In other words, I obtained V1 from the absloute model and I had to multiply it by the length contraction and divide it by the time dilation to get the resulting speed that is dictated by relativity.

    Tom
     
  21. Prosoothus Registered Senior Member

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    Crisp,

    I'm sorry because I either didn't read the post you are referring to, or I forgot it (or didn't understand it

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    ).

    I'd appreciate if you, or James, can illustrate how the Gamma factor can be derived without using the absolute model.

    Tom
     
  22. James R Just this guy, you know? Staff Member

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    Tom,

    <i>L an T would be distance and time without the effects of time dilation and length contraction, while L0 and T0 would be distance and time after the effects of time dilation.</i>

    So, who measures L and T, and who measures L0 and T0? Are these different quantities actually observed by any observer, or are they a mathematical game, in your opinion?
     
  23. Prosoothus Registered Senior Member

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    1,973
    James,

    It all depends what the observer, who is measuring distance and time, assumes.

    If the observer assumes that the average speed of the roundtrip of light is equal to (c^2-v^2)/c, as derived from the absolute model, then the observer will always measure distance to be L and time to be T in any frame of reference. And the values for L and T would remain constant regardless of speed.

    However, if the observer assumes that the average speed of the roundtrip of light is always equal to c in all frames of reference(therefore, the one-way speed of light is equal to c in all frames of reference), as dictated by relativity, the observer will measure L0 as distance and T0 as time. L0 and T0 will change depending on speed.

    Tom
     

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