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Parallel Projection of 3-space unto a plane at c.

  1. Aug 14, 2011 #1
    EDIT: I am looking for a correction in my understanding of relativity. A model of the universe as it appears to a photon will be presented in a LOGICALLY RIGOROUS MANNER based on my understanding of physics by examining the limiting effect as one approaches the speed of light. Since my understanding of physics may be (and is most likely) wrong, I expect that the model that is constructed to be wrong and inconsistent with the laws of physics. Quoting from below, "It's better to be wrong with rigorous logic based on false axioms than to be right with faulty logic based on correct axioms." It it my belief that errors are the "primary engine of human learning." I am highly proficient in multivariable calculus, linear algebra and several other mathematical fields and am considering to double major in physics based on my recent interests in physics over the past year. So I ask of you to tell me where I go wrong when building this model.

    In regards to length contraction:

    An observer moving at the speed of light would see the universe as a 2D plane perpendicular to his direction of travel, where all 3D objects would be orthogonally projected onto that 2D plane, this is because as one approaches the speed of light, space in the direction of his travel shrinks to zero.

    In regards to time contraction:

    Also, if we call the point in time in which a photon is emitted A, and the point in time in which it is absorbed B, then we can say that the photon experiences all events during time A and time B in zero time, this is because as one approaches the speed of light, events occur at faster rates, until the time between events becomes equal to zero, which causes the paradox "Did event A cause B or did B cause A?" (this paradox is resolved later on).

    This is the same as saying that instead of the observer's PRESENT being the 3-D surface of his lightcone, his present is actually the 4-D interpolation of his lightcone at Time A and Time B (using a 3-D representation of space-time, with two space dimensions representing the hypersurface and the third dimension representing time, it would be the 3-D interpolation of the surfaces of the past line cone at A and at B, which forms a solid cone subtracted by the solid lightcone of Time A).

    If we put both of these together:
    Knowing that a past light cone extends to the Big Bang (whose hypersurface is a point (or all points contained by infinite positive curvature) and a future light cone extend potentially to the end of the universe, the observer's light cone, when interpolated will allow the observer to witness all events in each interpolated light cone from the start of the Big Bang until the end of the universe in zero time.

    This means we lost a dimension, we lost the dimension of time. Time was orthogonally projected into 2-space* by moving at the speed of light, which is why all events occur simultaneously to the observer, and if time is measured by the passing of events and all events have passed, then time stops because there are no more events to pass.

    *However, we must also remember that the observer has also lost a spatial dimension due to length contraction. Therefore time and length (the dimension parallel to the worldine of the observer**) are both orthogonally projected into 2-space.

    Thus a photon experiences a timeless 2D universe where the worldline of each particle is a 2-D line upon the 2-D surface of its existence, where point particles would become line particles. This 2D universe would have a particle horizon whose radius would be equal to the radius at the base of lightcone B (the end of the photon's existence, which is either when it is absorbed or the universe ends).

    If we consider the possibility that the universe has no end and the photon is never absorbed, then it is possible that the radius of this solid lightcircle is infinite. Thus the "present time-frame" of the photon would be the entire 2D hypersurface of its universe. The photon would in fact experience a universal simultaneity in zero time and time would not progress any further (because time cannot progress if there are no more events to pass time). Since time does not elapse, the apparent contradiction of a photon moving at c in respect to itself while at rest is irrelevant because particles with velocity do not move when there is no passage of time and thus their velocity is indeterminable. OBJECTS MOVE THROUGH SPACE, NOT THROUGH TIME.

    Also since a photon would experience all events in zero time, there would be no more photons since they all would have been absorbed, compressed to a singularity at the big crunch (or in the case of an open universe, entered a horizon, such as an event horizon or went over the particle horizon, and such the photon would never be able to come in contact with any other photon, which is the same as heat death).

    We should however determine what causality means in a timeless universe. At speeds very close to light, the idea of causality means that event A caused event B. However all equations in relativity, classical mechanics and quantum mechanics are time reversible. So an observer can also say event B caused event A. However the term "event" describes the 4D interpolation of the light cones between the start and end of an event, therefore event A never caused event B, because they are both the same event that starts at time t1 and ends at time t2. So the idea of a 4d dimensionally interpolated surface is actually familiar to us. What matters is how fast we perceive this interpolation. In the case of a photon, this interpolation is perceived in zero time. So if causality is the progression of interpolation, then causality is not violated since the interpolation IS COMPLETED zero time and therefore the 2D projection of every particle's worldline onto the flat 2D universe would still allow an observer to determine the order of events, except they would be unable to determine the ARROW of time (whether event A caused B, or B caused A, which really doesn't matter since all the equations are time reversible).

    And yes I am familiar with the Second Law of Thermodynamics and the arrow of time. There is no arrow of time in a timeless universe, so saying A implied B or B implied A is perfectly fine in a timeless universe (usage of the word "imply" instead of "caused" preserves the logic of the statement). The commutative law of addition that f + g = g + f implies that 3+6 = 6+3 is true, it does not "cause" it to become true over time. So a timeless universe has causality replaced with mathematical implication.

    **It is my understanding that an observer sees himself in the middle of the universe, whether the universe is open, flat or closed and thus his worldline appears as a straight line through time to himself, even if his worldline appears curved to an observer elsewhere. Therefore in regards to projecting 4-space onto 2-space, we are projecting it onto the 2D plane perpendicular to his worldline.
     
    Last edited: Aug 15, 2011
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  3. Aug 14, 2011 #2

    ghwellsjr

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    Last edited by a moderator: Apr 26, 2017
  4. Aug 14, 2011 #3
    That's like saying I can't determine the value of an indeterminate point by using the squeeze theorem.

    http://en.wikipedia.org/wiki/Squeeze_theorem

    Use an observer traveling at 99.99% the speed of light and try to determine what his rest frame looks like. Now try 99.999% and 99.9999% etc. We can see that this limits to 2D space.

    The only real problem pointed out in that FAQ is that the photon must be moving relative to itself while at rest. However, things can't move where there's no time elapsing. Time doesn't elapse for this observer, time doesn't exist, therefore photons do not APPEAR move because they are moving over zero elapsed time, which results in no motion regardless of the velocity of the particle.

    In fact everything I wrote above seems perfectly logical, although hard to envision or make human sense of since we believe in this fictitious entity of time.

    EDIT: Now that I reread that FAQ, the author of that FAQ solves the first problem with his claim leading into the second problem, which is essentially what I said, there is no time. He then proceeds to say "In the rest frame of a photon..." an idea which he claimed to be absurd. Also he fails to mention that the two dimensions of space perpendicular to the observer's direction of travel do not experience length contraction and thus saying "all coordinates in the past present and future" are zero, when in fact they can be any two dimensional vector, not to mention that "past, present and future" have no meaning to a timeless universe, another contradiction in his reasoning. The third problem concerns Poincare transformations and arithmetic anomalies such as division by zero and zero divided by zero. Anyone with decent knowledge of basic calculus knows we can use limits to circumvent this problem.

    So of course it makes no sense to him, his reasoning contradicts itself.

    Also there are very few articles on the subject and not a single article on the impossibility/absurdity of the subject in a logical manner. I apologize, but the FAQ response was illogical, whether or not his conclusion is right.

    http://www.quantumtheorys.com/Distance-Time/Photon%20Kinematics.html [Broken]

    This link seems to go along my thinking.

    Also my thoughts about this came from this article published about photon rest mass from the physics department the University of Michigan.

    http://prl.aps.org/abstract/PRL/v26/i2/p115_1
     
    Last edited by a moderator: May 5, 2017
  5. Aug 15, 2011 #4

    ghwellsjr

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    Are you interested in learning anything at all about relativity?
     
  6. Aug 15, 2011 #5
    Yes, but I would like it pointed out where my above example is wrong. Show me I am wrong, I highly doubt with my limited understanding of relativity that I am right, but I need a concrete example, not a reference to the FAQ which uses an illogical statement to resolve the problem. The primary engine of human learning is by making mistakes.

    EDIT 2: Also you're the same person who gave my the FAQ link and I showed (above post) that the link makes illogical arguments. Therefore I cannot take you seriously since you believe in illogical answers. Also the author of that link has no credentials and neither do you (and neither do I, but at least I have rigorous logic BASED on my understanding of physics, although that understanding may be and is most likely wrong, and thus I need my understanding corrected, not my logic).

    It's better to be wrong with rigorous logic based on false axioms then to be right based on faulty logic based on correct axioms.

    Obviously I have sufficient knowledge of linear algebra and calculus to understand that length and time contraction result in orthogonal projections so my idea of "determining the limit" as the observer approaches c has merit in addressing this problem.

    I have visited many old threads in the PF forums about this subject, and the question has ALWAYS been asked someone with little mathematical knowledge with extremely contradicting claims or questions about something due to an "easy-to-see" misinterpretation of relativity. Thus I am not surprised that this question usually gets bad publicity on the forums and is put on the FAQ page. The FAQ page definitely thwarts different people from asking this question again and again by tricking them with an answer which is also illogical in order to make them go away.

    Here's is how someone defined the photon reference frame.

    "In the limit of accelerating in the direction of a photon the photon will lose all energy. In other words the reference of the photon is where it's proper energy is zero (since it's proper mass is zero)."

    The word "limit" is used here as well. We are trying to come up with a model of this observer's reference frame by examining what happens as we approach the limit.

    Someone mentions in the same thread that the 4-momentum results in 0/0 which is undefined and thus this subject is pointless. However that's not correct, because 0/0 is indeterminable. The case of 0/0 is almost always solved with a limit or the squeeze theorem.

    In fact it seems like every time someone puts forward an argument to declare the problem is pointless, it turns out their response lacks logical merit.

    So what am I looking for? A logical demonstration that the above is wrong.

    EDIT: This is by ZapperZ a PF mentor with a PhD in physics.

    "I believe that what robphy just did it EXTREMELY valuable. This is because there are many people here who are using these terms without understanding that there are precise definitions and properties as defined in physics. And since we ARE here discussing physics, when you use such terms in ridiculous ways, and the rest of us starts to scratch our heads, do NOT simply assume that we are being "pedantic".

    Look at the term you are using. If you do not have a clue on the underlying mathematical descriptions of it, chances are, you don't know what it is. So leave open the possibility that MAYBE, you used it in an inconsistent fashion, or maybe even in ways that it wasn't meant to be used.

    Zz."

    Every term I am using is well understood and well defined. Therefore I am going to assume that you are being pedantic.

    EDIT 3:
    I absolutely AGREE with this statement and it is consistent with the above model of the universe for a photon.
     
    Last edited: Aug 15, 2011
  7. Aug 15, 2011 #6

    ghwellsjr

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    It doesn't matter whether you are right or wrong.This is not the forum for you to be building your own model of the universe.

    From the Sticky https://www.physicsforums.com/showthread.php?t=17355":

    This forum is meant as a place to discuss the Theory of Relativity and is for the benefit of those who wish to learn about or expand their understanding of said theory. It is not meant as a soapbox for those who wish to argue Relativity's validity, or advertise their own personal theories. All future posts of this nature shall either be deleted or moved by the discretion of the Mentors.
     
    Last edited by a moderator: Apr 26, 2017
  8. Aug 15, 2011 #7

    Dale

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    The squeeze theorem is irrelevant because you don't have an upper bound.

    You can certainly speak about physics in inertial reference frames in the limit as you approach c, but not at c. If your math skills are as good as you claim, you should be able to immediately grasp the distinction and the reason for the distinction.
     
  9. Aug 15, 2011 #8
    The squeeze theorem reference as a sarcastic remark about infinities and did not pertain directly to the discussion.

    If we were talking about the energy increase as we approach c, yes you would not be able to evaluate the problem at its limit since it would take infinite time or infinite energy to reach c.

    However, I can certainly discuss what happens with an increase in velocity, since I only only need a finite increase in velocity to reach c. This is the perspective that is being used. If the inverted Lorentz factor is assumed to be a quadratic surface (sqrt(1-v^2/c^2) then I can certainly evaluate the limit of this function when v^2 = c^2. This limit is in fact zero. I can also talk about approaching the limit of a defined point on a curve if I wish. What is the limit of (x^2/4) as x goes to 10? I can tell you that it approaches 25 from the left (regardless of what happens from the right), does that mean it can never be 25? Of course not, I can actually make the leap from 24.999 to 25 in this instance, I can evaluate the limit directly.

    So another person came forward with an illogical argument, good job.
     
    Last edited: Aug 15, 2011
  10. Aug 15, 2011 #9

    Dale

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    I don't know why you would say this, it is incorrect. There is no boost which gets you to c, only boosts which approach c. It is not even a matter of energy, it is just the math.
     
  11. Aug 15, 2011 #10
    Then this is the topic that I need to research and where my understanding of physics was wrong. I thank for for pointing this out so that I may better my understanding.

    Also, before I go on, based on some quick google searches, you are talking about the matrix transformation known as a Lorentz boost?
     
    Last edited: Aug 15, 2011
  12. Aug 15, 2011 #11

    D H

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    With that, thread locked. Do your research, and do keep in mind that this forum is not a place for personal theories.
     
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