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Constructive criticism please.

  1. Apr 6, 2008 #1
    I would like to thank Janus and selfAdjoint for their very helpful criticism. It was their arguments against my ideas four years ago that set me clear on the difference between ideas and potentially valuable work.
    I was convinced, as I have seen so many others since, that my ideas would be so clear to others that they would cheer me on. My first reaction to criticism was to defend my ideas at all costs. It soon became apparent that any well intended, constructive criticism from anyone is in fact the most valuable cheering-on one can hope to find. It just takes time to get past one's ego to see criticism as a necessary and beneficial test of any new idea.
    So, in a 180 deg. turn of perspective and after four years of critical examination of my own, I would like to ask those of you interested in helping me, to criticize as you see fit, the premise of my work below. I now feel very selfish in asking for what I previously feared.

    A frame of reference holds no meaning with respect to the equations of mechanics unless it meets the following minimum criteria.
    A system of coordinates of spatially rigid measures extended on three perpendicular axis of common origin, to which is assigned the property rest. Thus all measures of mechanics will hold to the equations of mechanics because both are quantified with respect to the property rest attributed to the frame's coordinates.
    Or as Einstein said, "The laws of electrodynamics and optics will be valid for any frame of reference in which the equations of mechanics hold good".[1]
    Einstein removed the property of "absolute" rest from the laws of physics and replaced it with the property of any system of coordinates which hold the equations of mechanics good.
    Because rest and motion are conjugate properties, the equations of mechanics are not quantitatively true statements(upheld) unless one or the other (rest or motion) has been quantitatively defined.
    If the definition of a frame of reference as the property rest is not provided, removing the property of "absolute" rest renders the equations of mechanics universally arbitrary statements and arbitrary is not at all the same as relative. It is the relative nature of the property rest as attributed to a frame that upholds the equations and allows them to be translated from one frame to another. It is the constancy of light that determines the formula of this translation.
    "That the speed of light is constant regardless the motion of the source is very interesting, that it is constant regardless the motion of the observer is remarkable".[2] For it must then be constant regardless the source and observer when they are the same frame. This property of light, that it moves away from an observer at the same speed even when that observer is moving at near light speed, is why Einstein considered the constancy of the speed of light "plays the part, physically, of an infinitely great velocity".[3]
    It is important to realize the ontological significance of this constancy. No matter how clever we may be in designing or discovering the equations that translate the kinematics of this physically real phenomena, we must understand what they mean. At present we do not. In more general terms we must consider the state of physics with respect to this lack of knowledge. In other words, is not enough to sustain the equations of mechanics with respect to the constancy of the speed of light through translatory equations of kinematics. The equations must express dynamics that give rise to the constancy of the speed of light.
    Put in everyday language we might say, - do not tell me the speed of light is constant "because" time dilates and length contracts, but tell my why time dilates and length contracts without telling me "because" the speed of light is constant.


    [1] "On the Electrodynamics of Moving Bodies" A. Einstein (Annalen der Physik. 17:891, 1905) Eng, translation.
    [2] (I am still sourcing this reference. My best guess to date is John Stachel in a lecture at the Perimeter Institute, 2005.)
    [3] "On the Electrodynamics of Moving Bodies" A. Einstein (Annalen der Physik. 17:891, 1905) Eng, translation.

    I have, as I suspect many on this forum, thought long and hard about this question. It is in my opinion, a question that must be answered before any significant progress will be seen again in theoretical physics.
     
  2. jcsd
  3. Apr 6, 2008 #2
    I don’t see where you have clearly stated what “this question” is.

    But I take as your premise for it or your work to be that the logic of Gamma Factoring both justifies “c” and dilation/contraction is a circular logic with an incomplete explanation. Meaning that that if the cause is left unknown and not understood there remains variables in how we take observations that could cause use to draw invalid conclusions.
    So I guess “your work” must start from considering the possibilities that we have some fundamentally incorrect conclusion that affects how we observe and interpret reality.

    For example: Newton expected Absolute Space and Absolute Time. But based on relativity we conclude neither space nor time is absolute thus allowing for “space-time” and General Relativity interpretations. However, if you develop an explanation for dilation/contraction that accounts for a distorted viewing of what is in fact Newtonian Absolute Space & Time, it would explain incorrect conclusions such as misperceiving the meaning of “c”.

    If I have your premise correct do you have fundamental conclusion in physics you wish to consider might be wrong e.g. no Absolute Space and Absolute Time. Or is your question simply what if a constant “c” is incorrect.
     
  4. Apr 6, 2008 #3

    Ich

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    Why do you think so? Relativity is about geometry. What dynamics would I have to conjure, for example, that the sum of two sides of a triangle is longer than the third side? Do you accept this statement without anyone providing a dynamical explanation? If so, why do you think that it is necessary that relativity gives one for the predicted (and observed) efects?
     
  5. Apr 6, 2008 #4

    rbj

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    so does any inertial frame of reference meet that first criteria? or does it have to be a particular frame of reference that Nature has assigned the property rest?
     
  6. Apr 6, 2008 #5
    You're right RandallB, I did not state a question that can be directly addressed.
    I should have asked if anyone finds fault in the reasoning that leads up to the statement, why is the speed of light a constant and what is it about the nature of the universe that it is the specific speed it is?
    I was too concerned with pre-empting the circular, kinematical logic that might be offered as an answer, I forgot to make it clear what the question was.

    You have got the general idea of the premise. I do not think the principle of relativity has been fully comprehended nor consolidated in the laws of physics. However I have no serious dispute with either theory (SR, GR) in as far as they go to describe the relativistic framework of the laws. I think they are incomplete in so much as they take time to be nothing more than the kinematics by which it is measured.
    I hoped to present my ideas one step at a time in order to use the feedback and criticism as constructive aids to making the most succinct and logical presentation.


    Ich, I don't expect any theory to state more than it needs to justify its predictions. I was not talking about the equations of relativity, I was talking about the equations of mechanics in general. I could have said the mathematical logic that leads us to accept as true, the kinematics of a theory, should at some time, not necessarily in the same theory, lead us to accept as true, the dynamics of a theory. Einstein's special relativity is a brilliant piece of work. But even he had no illusions that it explained "why" light was a constant.
    Your analogy is good, but geometry does not need dynamics, kinematics do. The geometry that describes the kinematics of motion does not need dynamics, but the kinematics the geometry describes does.

    rbj, I did not qualify a frame as necessarily inertial, but by definition, any inertial frame would meet this criteria. Nature does not assign the property rest except from the perspective that all properties are assigned by Nature, but that is not the distinction being made here with respect to upholding the equations of mechanics in a frame of reference.
     
  7. Apr 6, 2008 #6
    For what it is worth:

    By only questioning the postulates of a theory you will never grow a better understanding of it.

    You effectively stop at the door and keep handing pamphlets to others who want to step through the door or who already stepped through it before. But you never step through the door yourself.
     
  8. Apr 6, 2008 #7

    rbj

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    so you're assigning a coordinate frame the property "rest" when it is accelerated?

    this is gettting curiouser and curiouser.
     
  9. Apr 6, 2008 #8
    Yes, I understand this issue. The whole of physics is this way and Quantum Mechanics is no exception either. It's related to our predisposition toward a mechanistic description. For good reason physics does not concern itself with describing parts, rather it describes symmetries in our observations. We simply cannot be sure that infinities, spacial dimensions, Godel's theorem, and/or measurability will ever allow such a theory, even in principle. Symmetries do not lose any predictive value with or without a mechanistic interpretation. We didn't give up our mechanistic assumption willingly, it was forced on us by some very strange behavior in nature. The accusations of indoctrination is unfounded. If you can deliver the goods mechanistically then do so. What is less than honest is to simply claim a priori X must be so, or that some limited interpretation of a small piece of physics proves it.

    Wrt Relativity all we can say is that all our measurements show C to be constant, and yes I've been through the one way speed thing so much it about makes me barf. Depending on the parameters you choose you can use a varying speed of C in a mathematically consistent way. Pretty much similar to a disagreement between observers on a distance. Yet you must normalize the predictions for what an observer actually measures, i.e., a constant C. Einstein simply threw out everything except what we actually measure, leaving only the symmetries. The fact that some Lorentzian interpretation can in principle work can't touch the success of the symmetries. To those wanting to know why: it all appears like perfectly circular reasoning. It is the fact that it matches observations that defines its legitimacy, not the reasoning itself. The reasoning must be consistent but only nature rules on validity. It will remain unaffected in its predictive power regardless of any interpretation correct or otherwise that we attach to it.

    That being said, personally I do hold out hope for a mechanism or ethereal type theory. It obviously can't take the form of any type that has previously been articulated. Absolute frames, particle motion/pressures, etc. as often described are empirically absurd. I have reviewed many attempts and to date they all empirically break down somewhere. Space-time dilation is one of the easiest effects to qualitatively mimic in an ether type theory. Yet contrary to the claims of many it proves nothing. Even a successful version, that as yet don't exist, that merely mimicked what we already know is of no value whatsoever.

    Yes I understand the difficulties people have with working with just the symmetries. So I don't take it lightly when I'm criticizing the mental contortions people go through to demonstrate their interpretations. I went through it myself. Though the same arguments get tiresome. The logic as taught by the mentors here is empirically valid, mathematically consistent, and derived from sound physical arguements. If you have some interpretation that differs significantly from those aspects then nature has already ruled badly on your case.
     
  10. Apr 7, 2008 #9
    MeJennifer, I like your analogy. It is very true and often the case, but I have gone through the door. I have not stopped at the door and I certainly do not want to dissuade anyone else from going through. I would suggest I'm taking an exit pole, for what I found in the room behind that door was fascinating but incomplete. The very reason I am at your analogous door is because you must see and understand the contents of that room before entering the next.

    rbj, I will get to accelerating frames shortly, it is not as contrary as you might think, but it is certainly curioser.


    my_wan, I understand the frustration in giving way to predictive power over reason but I do not think we must give up that power to find reason. I don't think I ever accused anyone of indoctrination and I will deliver the goods. Einstein didn't "throw out everything except what we can measure" he held very tightly to principle, but I understand your point. He did not deny the evidence in favour of a more psychologically pleasing approach.
    There are certain principles in physics that cannot be denied without resorting to mysticism. Symmetry, as you mention, is certainly one of them as is its cousin, conservation. But the discovery of symmetries in and of themselves is not enough as Emmy Noether pointed out. It is the realization of their deeper, ontological implications and significance that is the real power of symmetries. If you've been through the difficulties of working with "just" symmetries, you understand they express and reveal relationships so deeply hidden that at times we have not seen them when looking right at them. I think you will appreciate more than most, the symmetry that reveals itself the model I will present.
    I would suggest that Nature never behaves "very strange" except when our ideas of how Nature should behave are wrong. Nature is discovered not contrived. I understand your position and I agree with the principle of fruitful pursuit, but I think we have begun to loose sight of the goal. In our pursuit to understand Nature we have become obsessed with the process.
     
  11. Apr 7, 2008 #10
    There are a few more principles that need to be clearly communicated before returning to the consequences of the definition of a frame of reference given above.
    Part II
    There is a perceived symmetry in the laws of mechanics that is often a source of confusion. It is the symmetry of the laws of mechanics through time-reversal, often confused with the symmetry of the equations through time-reversal.
    The symmetry of the equations is easily understood as a conservation of quantitative values via a "negative" time signature. The laws these equations express are not all so easily conserved or quantified through time-reversal.
    The following thought experiment helps clarify this point.
    Consider a simple collision of two bodies as follows:
    A mass(M) in constant linear motion(v) collides with a larger mass (2M) at rest. The first mass (M) comes to rest and the second (2M) is set in constant linear motion at 1/2v.
    The conservation of momentum Mv = 2M(1/2v) holds a symmetry across time-reversal when time is expressed in terms of the velocity, 2M(1/2d/-t) = M(d/-t). But when we look at what this expresses in the laws of conservation of momentum we find: a larger mass (2M) moving with constant linear motion 1/2v, comes to rest upon colliding with a smaller mass (M) and sets the smaller mass(M) in constant linear motion v, a velocity greater than that of the larger mass before collision. This requires all the momentum of the larger mass (2M) is translated to the kinetic energy (greater velocity) of the smaller mass (M). It is a contradiction of the second law of thermodynamics. It has never been seen in Nature.
    But of course we have never observed the reversal of time either, so it would appear we are saying the same thing here. The second law is an observational law. It states the increase in entropy with the progression of time. We have never seen it contradicted because we have never seen a reversal of time. As the laws of mechanics have been derived and confirmed through observation, it is not unusual, in fact it is perfectly reasonable that they express the kinematics and dynamics of only time forward events.
    The laws then are not time-reverse symmetric without a complete reversal of dynamics in general. In other words, we would not see a reversal of time, or a contradiction of the second law, as if such an event is upheld by the laws, we would not see anything. The photons traveling to our eyes in forward time sight, would travel away from our eyes to their source. This is a simplified example of complete dynamic reversal but it makes the point that we cannot expect the laws of mechanics, derived from the observations of forward-time events, to be time-reverse symmetric without fully understanding what time-reversal means.
    To understand time-reversal with respect to dynamics we must first be very clear on what time is. A period of time is a measure of the motion of a system. The system may be mechanical, electrodynamics or any other event we agree is of consistent frequency - a clock. The motion of a system is a measure of the displacement of space. We could discuss at length the philosophical implications of such a circular logic, but it will, as history has proven, be of little value in narrowing our definition of time. As physics is concerned with measurement through observation, we will leave the definition of time as - the displacement of space.
    If we measure the rate of time to differ from one place to another, we can say nothing more than the rate of displacement of space (the meter of our clock) is different at one place than the other. If we measure the rate of time to change in the same place, we can say nothing more than the rate of displacement of space changes in the same place. As the displacement of space, time is and therefore time-reversal is, a physically real dynamic. By themselves, the dimensions time and space are unintelligible. Together they represent a continuum of measurable, quantifiable nature. That we cannot separate one from the other is no longer a epistemological dilemma. That we still separate space-time from mass is.
     
  12. Apr 7, 2008 #11

    Mentz114

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    Chrisc,

    I look forward to an explanation of this extraordinary statement. Presumably you'll ascribe some intrinsic properties to space.
     
  13. Apr 7, 2008 #12
    I have invested quiet a bit of time in mechanistic theories. I am not adverse to them in principle and even maintain some hope. However, to characterize forfeiting mechanistic theories as giving up on "reason" is more than I can concur. I even consider it a false dichotomy.

    You refer to the articulation of ontology as the real power. To me this smells of a one true ontology myth. Two mutually exclusive ontologies can fully and correctly describe the same system. It's not unlike a one true political party. To characterize it as "the real power" begs the question: Historically, how could it be said that ontology has driven our understanding of science. In fact it was the other way around, science is what drove the ontological implications. It seems the real power is the influence it has on you. I will not object to this, or your efforts, but it would be helpful for you to recognize it for what it is. I could make lists of good realistic reasons why such a theory may never be possible, even if nature is ultimately purely mechanistic.

    I'm looking forward to it. I will not even complain about ascribing physical properties to space. If I wreck your model don't be deterred in your efforts. Don't try and deny and ignore the issues either. That alone will speak very well of you. Good luck.

    Next Post:
    Think again. Elastic collisions don't work this way. (M) will recoil in a collision with mass (2M).
    http://en.wikipedia.org/wiki/Elastic_collision

    The problems with the above description, as quoted, is a bit too severe for me to consider getting into thermodynamics or definitions of time on that premise.

    I think this tells me where your model is going though. I'm curious how far you were able to take it.
     
  14. Apr 8, 2008 #13
    my_wan, I'm sorry for the way my response sounded, I did not intend to imply you, or anyone has given up on reason. I meant there is no good reason to give up, or not concern ourselves with ontology. That the predictive power of symmetries of observation does not lose any predictive power without mechanistic interpretation, is not justification for ignoring ontology. As the branch of philosophy dealing with the physical, physics without ontology is mathematics.

    It is the "realization" of deeper meaning, ontological implications and significance of symmetries that I referred to as the "real power". As opposed to the recognition of symmetries themselves.

    Your argument on the priority of science before ontology makes me think you are taking my reference to ontology as a field of study. When I speak of ontology in physics I am referring to entities, conceptually sound or physically real, which are and likely always will be philosophically arguable, to which the symmetries and all other mathematical modeling are associated. The continuous symmetry of a sphere through spatial rotation, is still, a sphere. If we allow ourselves to distill ontology to nothing more than the mathematical models that define them, once again physics becomes mathematics.

    "Ascribing physical properties to space" as you say, is and has been critical to the formulation of any relativistic modeling since Leibniz. I will not be ascribing physical properties to space. I will subscribe to the notion space is physical in the sense that in the separation of bodies there exists something more than the separation of those bodies as it is not, even as an extension of those bodies, the bodies themselves.

    If you wreck my model, it will be difficult, but most appreciated. There is nothing worse than a mind wasted.

    If you are concerned about the distinction between rigid and elastic at the molecular level having significant theoretical impact on a relativistic model, you might as well stop reading now. I will not be offering the detailed account of molecular kinematics. My reference to the second law is in the most fundamental theoretical sense which holds up to and including macro bodies of composite nature. I will however show the model to play a major role in the observations and interpretations of all of physics. It is an extension of the principle of relativity that offers a broader, more unified framework for the laws.
     
  15. Apr 8, 2008 #14
    No offense taken. When posting on a forum I am speaking to a wider audience than just the direct recipient and my words were meant to be taken generally. With regard to you it was merely a caution from what I perceived, not an actual characterization of what I knew to be so.

    Yes I take ontological issues quiet seriously. Much more so than most. Yet often ontological assumptions can be a Pied Piper. In my own experience many of the implications I thought were required under certain ontological assumptions were in fact entirely independent assumptions.

    Yes I concur. Yet many of the things we often assume to be "real" in fact only have meaning under a certain choice of definitions. Suppose a force law theory of GR was developed that had all the predictive power and generality of GR but was otherwise exactly equivalent. QM has many equivalent ways of formulating it, some more intuitive than others. This would in no way invalidates the curved spaces of GR or the ontological implications associated with it. Whole classes of ontological assumptions are definitions and definitions alone.

    Consider a raw mechanistic ontology. What does this imply? It implies parts that bump into each other. Absolutely nothing more. Any notion of space or time imposed from the outside (our imagination) is purely imaginary. We are predisposed to certain types of definitions but they are nothing more than relationships we choose from perspective, not real in the ontologically real sense. Yet the symmetries will be innate to any possible consistent set of definitions. Symmetries go even farther in that their power is the same with or without referring to parts that bump into each other, or even the existence of these parts. Yes symmetries are king. Finding a way to define parts would be very cool, maybe even helpful to figure out how to define certain classes of symmetries and bounds properly.

    I have intensely considered ontology as a field of study. To a much greater degree than the notion of realism itself. Physics is not and has never been nothing but mathematics. If it was only mathematics I wouldn't be here. However, if I say this coin flips either heads or tails, never feet or anything else, I have defined a symmetry, a mathematical statement. When Newton said, "An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by a force", he made a mathematical statement. When you boil physics down to just the statements needed to derive predictions, not the skills, knowledge, or math needed to make those predictions, there is amazingly very few. Mathematicians often joke about the way physicist use math. Physics is math, even when described without it or in terms of real parts. Math is not physics.

    I'll provisionally go with that.

    Don't worry, it's not a waste. Anything worthwhile is worth many failures. I've wrecked more of my ideas than I can count.

    Hmm, I don't want to read too much into that as I seemed to have done in the previous post. I must confess that the generality with which thermodynamics crosses boundaries in physics is not a surprise to me.

    Unless you post to Independent Research it's unlikely to be very acceptable here. The rules here are well defined with very sound reasoning for them. You can post your ideas there, PM me with links or info, or I can suggest public forums where we can express ideas without concern for mainstream legitimacy. Forgive me if I'm not optimistic about being surprised. It's just a learned expectation. However, you have paid a good share of effort to be here today. Perhaps something can be learned here, and I can always hope to be surprised. There exist a range of empirical issues that must be addressed in any type of mechanistic theory, even incomplete ones. Good luck Chrisc.
     
  16. Apr 8, 2008 #15
    Chrisc;
    See if this answers any of your questions.
     
  17. Apr 8, 2008 #16
    Just a quick note to whomever wrote the paper on velocity at that page... More than one vertex are vertices.
     
  18. Apr 8, 2008 #17

    JesseM

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    I haven't read all your posts, but I think you're missing something basic here. "The speed of light is constant" is not really a truth about physical reality at all--it is just an assumption made for the purposes of having a definition of what it means for inertial clocks with the same rest frame but at different locations to be "synchronized". Einstein assumed that each inertial observer would assign coordinates to events using a rigid grid of rulers at rest relative to himself, with synchronized clocks attached to each marking on the ruler; then if the observer spots a distant event in his telescope, he can just look at the marking on his ruler that it was next to as it happened in order to assign spatial coordinates to the event, and look at the reading on the clock attached to that marking at the moment the event happened to assign a time-coordinate to the event. In this way he can assign coordinates to events using only local measurements, without having to worry about the optical effects that create a delay between when the event happened and when he actually sees it.

    The problem is defining what it means for clocks attached to different markings to be "synchronized". Einstein said, let's define two clocks to be synchronized using light signals; if you set off a flash at the midpoint between two clocks, then we'll define them as synchronized if they each read the same time at the moment the light from the flash reaches them. This is just a convention about how each observer should define the word "synchronized", it needn't be seen as a physical claim about whether the clocks "really are" synchronized in any objective sense.

    But Einstein's actual physical hypothesis was this: if every inertial observer constructs their coordinate system according to this procedure, then the laws of physics will have the property that they obey the same equations in each observer's coordinate system. This is true if the laws of physics have a symmetry called "Lorentz-invariance"; we can easily imagine a universe in which the laws were such that this hypothesis would be false, so this is a genuinely physical hypothesis rather than just a matter of conventions.

    So then Einstein took the two assumptions--that each inertial coordinate system observes the same laws of physics (which means that if a ruler moving at speed v in one coordinate system is shrunk by [tex]\sqrt{1 - v^2/c^2}[/tex], this must be true in every other coordinate system too), and that each coordinate system must define simultaneity using the convention that light should have the same speed in all directions, and showed that together they could be used to derive length contraction and time dilation. As I said, the second part about light moving the same speed in both directions is just a convention which shouldn't be seen as a physical claim at all, but the first part about the laws of physics obeying the same equations in all the coordinate systems constructed in this way is a physical hypothesis which can be tested experimentally. So far, all the equations of the fundamental laws found so far do respect Lorentz-invariance.
     
  19. Apr 9, 2008 #18
    For more reading on what JesseM said concerning the speed of light is not really a truth about physical reality but a definition. It is however a physically consistent definition.

    Comments on "Note on varying speed of light theories"
    http://arxiv.org/abs/0705.4507
     
  20. Apr 9, 2008 #19
    JesseM, Thank you. Your explanation was very well stated. I do understand the relative nature of measurement with respect to the constancy of the speed of light.
    The constancy of light however "is" a physical constant by virtue of the fact that the laws of physics are Lorentz invariant. I know that there is a tendency to hold an absolute frame of reference when reasoning this through, but I assure I am not.

    my_wan, thank you for the link, I will read this tonight.
     
  21. Apr 9, 2008 #20
    Part III
    (I must qualify my original post as I missed the word "constant" which is inserted below)
    A frame is a set of constant spatial coordinates extended on three perpendicular axis from a common origin. To distinguish a frame from a frame of reference requires attributing the coordinates of the latter with the property rest. When we then speak of an observer in a frame of reference, we intend the coordinates of the frame to hold the property rest such that with respect to the coordinates, the observer finds the equations of mechanics are upheld. On the strength of Newton's first law, it is reasoned that a frame of reference will uphold the equations of mechanics as tested by an observer within the frame, when that frame is measured at rest or in constant velocity with respect to a second frame of reference. Observers, one in each of two frames of reference in motion with respect to each other, will then find the equations of mechanics are upheld in both frames of reference, but only with respect to the property rest attributed to the coordinates of their own frame of reference. While it is reasonable to infer that each observer upon measuring the motion of the other's frame of reference to be of constant velocity with respect to their own, could quite justifiably translate the property of rest from their frame to the other thereby upholding the equations with respect to the coordinates of the other, such a translation can only be justified "after" measuring the state of motion of the other with respect to the property of rest attributed to their own frame.
    Keeping in mind this definition of a frame of reference, we can now consider what is meant by an accelerating frame of reference.
    An accelerating frame is a set of constant spatial coordinates extended on three perpendicular axis from a common origin which, with respect to an observer's frame of reference, are measured to be in a state of acceleration. For ease of consideration we will take this acceleration as constant. When we begin to reason an observer in such a frame testing the equations of mechanics, it becomes apparent they cannot attribute the coordinates of the frame with the property rest, a qualification which must exist to test the equations with respect to Newton's first law, unless we can, in accordance with Newton's second law, attribute a constant force acting equally on the observer and all test bodies within the frame, such that all accelerate equally with the coordinates of their frame. But as gravity is the only force known to persuade bodies of different mass to accelerate equally, we must conclude that outside of imagination, the only accelerating frame that can be qualified as a frame of reference is a frame in free fall.
    What we have done here is made the distinction that a frame is only a frame of reference when it is an inertial frame. This appears to be too strict a limitation, but it is the only possible means of qualifying a frame of reference in first principles while upholding the empirical status of Newton's first two laws of motion. In other words, what removes all other frames from this qualification is our inability to distinguish in first principles, acceleration from gravitation with respect to these same laws, which has become known as the equivalence of acceleration and gravitation.
    When Newton's laws are the only empirical knowledge we have to test the equations, we find no distinction between an accelerating frame and a frame resisting gravitation. But if we make use of Einstein's second postulate, "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body"[1] when testing the equations, we find we can distinguish between the two.
    We will use the well known "spaceship" thought experiment popularized by Feynman's lectures to demonstrate this distinction.
    The frequency of the light signals from the front of the ship, as detected and measured against the clock at the back of the ship, indicate the clock at the front of the ship is running faster. While the same experiment in an identical ship with identical clocks sitting on the earths surface will produce the same evidence,(a change in the rate of time of the two clocks), the difference between results of these two constructs and therefore the distinction that can be measured against any similar test is in the "constancy" of the change in the rate of a clock. An accelerating frame will, by virtue of the definition of acceleration and the constancy of the speed of light, continue to reduce the time between emission and detection at the front and back of the ship respectively. Gravitation will not. The change in the rate of the clocks in a gravitational field remains constant.
    The constancy of the frequency of light signals will in this manner serve to distinguish an accelerating frame from a frame resisting gravitation. The constancy of time with respect to the motion of a frame is the only distinction (non-trivial) that qualifies the equivalence of acceleration and gravitation, and will be shown to reveal a previously unknown (authors best knowledge) correlation between time and gravitation.
     
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