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The General Principle of Relativity

  1. Jun 26, 2008 #1
    The General "Principle" of Relativity

    In the most general sense, mechanics describe the interactions of space, time, energy and mass.
    Whether quantum or classical, all mechanics are subject to the principle of relativity with respect to
    any quantitative values defined for the ontological identities above.
    As a fundamental principle of all mechanics, the principle of relativity makes us aware of the necessity
    to qualify any statement about the physical nature of an event as a statement of relativistic measure.
    Even though it is implicitly or explicitly associated with all mechanics, the principle of relativity has for the most part
    been relegated to those consideration in physics in which motion plays a significant role in determining the mechanics of an event.
    This is apparent in the fact that quantum field theory is a background dependent theory unable to fully incorporate
    the general principle of relativity. As Einstein pointed out, the heuristic significance of the general principle of relativity
    is such that it is unbelievable that physics has proceeded for almost a century without it. To ask what would physics be
    without gravity is the question most commonly understood by this comment, and yet, that is not the question at all.
    What would physics be without gravity is not as significant or nonsensical a question in the study of particle physics
    where the effects of gravity is negligible. The question is 'what would physics be without the general "principle" of relativity'.

    It is the principle that has been ignored and only the general "theory" that has been considered as pertinent to the problem of unification.
    To appreciate the difference and the significance one must consider the "principle" of relativity as having a greater role in
    physics than defining a geometrical framework for the kinematics of systems in motion.
    That space, time and mass are quantitatively relative measures has become a working convention in physics.
    That space, time and mass are qualitatively relative ontologies has been implied since Einstein's first publication of E=mc^2.
    (which was actually and in my opinion more insightfully, m=E/c^2)
    I am curious to know if anyone has read any publications that consider a qualitative distinction of ontology a relativistic measure?
     
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  3. Jun 26, 2008 #2

    ZapperZ

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    Re: The General "Principle" of Relativity

    Let me ask you this before addressing what you just said here, so that we are clear on one very important FACT.

    If I ask you to put a value on something called the "degree of certainty", with a higher number representing something that has more certainty, which do you think will have a higher number based on what we currently know, QFT or GR?

    Zz.
     
  4. Jun 26, 2008 #3

    Fra

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    fuzzy reflection

    I am far from sure I understood your question but my fuzzy association is that you suggest that ontologies can be seen as measures. So by defining a measure on a set of possible ontologies, we are effectively defining another ontology? Depending on what you have in mind that's partly plausible to me in the sense that if we associate measures with questions, then all we can consider as ontological constructs are what questions to ask :)

    I think the last word is far from said regarding the state of logic in the foundations and formalisms of physics.

    /Fredrik
     
  5. Jun 26, 2008 #4
    Re: The General "Principle" of Relativity

    At the risk of being misinterpreted, the most direct answer to your question would be: the General Principle of relativity will play a more significant and fundamental role in modeling unification than QFT.
    The overwhelming evidence supporting both leads me to think there is no reasonable option but to accept both are correct but incomplete. They are each conjugate expressions of a more fundamental principle. I think this more fundamental principle is in fact, the principle of relativity, when extended to include the relative, qualitative nature of dimension.
     
  6. Jun 26, 2008 #5
    Re: fuzzy reflection

    True, but I think there is a less philosophical approach. In the same sense that we acknowledge the time dilation of a frame in motion, we can ask - where did the time go, what conservation or symmetry accounts for the translatory nature of dimension? If time dilates, length contracts and mass increases...it is not a large leap to the idea that the principle of relativity expresses a law of conservation and/or symmetry of dimension. Where does the loss of time and length go? I think the answer is obvious, the proof is giving me trouble.
     
  7. Jun 26, 2008 #6

    Fra

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    Re: fuzzy reflection

    I mainly reflected on your post, I still don't think I understood your quest.

    "where the loss of time goes" is something I don't think I understand.

    I tend to make philosophical expressions but I think the spirit of intent can be strongly formalised as a kind of "theory of measures", and I'm not talking about "measure theory" of mathematics I'm more talking about a physical theory of evolving measures, where measures are constructed and evolving as per an again evolving logic.

    If we are comparing two observers, we are comparing two different measures. So the first observer at best may ask how his measures relates to a presumed measured measure in the environment.

    But I don't understand the question "where the time goes"? As I understood your questions it was pretty philosophical too? or? (I assume you are talking about possible QG theories?)

    /Fredrik
     
  8. Jun 26, 2008 #7
    Re: fuzzy reflection

    My question is somewhat philosophical as can be said of any idea not refined to theory.
    What I mean by "where does the time go" might make more sense in the following context.
    Any closed system of a physical nature must uphold the laws of conservation.
    From the simple premise that all physical systems are comprised of the fundamental dimensions of physics, (space, time and mass) it follows that any quantitative expression of a change in one, requires a quantitative change in one or both of the others to uphold the laws of conservation.
    That these changes are relative measures of frames in motion does not exclude such changes from upholding the laws of conservation.
    If the time of a frame in motion slows and the length of a frame in motion contracts, the reduction of these two dimensions requires the third - the mass of a frame in motion - must increase to uphold the laws of conservation.
    This is a naively simple concept, but it points to a very fundamental dynamic of space, time and mass that is approached in GR but not fully exploited in any of the literature I have found.
     
  9. Jun 26, 2008 #8

    ZapperZ

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    Re: The General "Principle" of Relativity

    You really didn't answer my question, did you?

    Zz.
     
  10. Jun 26, 2008 #9

    Mentz114

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    Re: The General "Principle" of Relativity

    Chrisc,
    It will never make sense. Time is what is measured by clocks. It is not matter or energy, or something that can be conserved. If the rate of a clock changes - no time has been gained or lost. Asking where it 'has gone' is not meaningful.

    M
     
  11. Jun 26, 2008 #10
    Re: The General "Principle" of Relativity

    I thought I did, but if you want a more decisive answer, I would place a degree of certainty on GR that far exceeds any existing QFT.
     
  12. Jun 26, 2008 #11
    Re: The General "Principle" of Relativity

    "Time is what is measured by clocks". Think about what you've just said.
    Mass is what is measured by accelerometers, Length is what is measured by rulers.
    If I return to Earth after a year long journey at near light speed, I will find you have long since died and turned to dust.
    In this sense, asking where the ticks on my clock have gone should have the most physically real and "meaningful" significance to you.
    I was conserved, you were not.
     
  13. Jun 26, 2008 #12

    ZapperZ

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    Re: The General "Principle" of Relativity

    .. and what made you say that? Do you use GR in your modern electronics? You certainly do with QFT. Field theoretic methods are extensively used in solid state/condensed matter physics, which is the branch of physics dealing with the magnetism, semiconductors, superconductors, etc. In other words, you are currently using materials in which our understanding have came out via QFT.

    When was the last time you used GR other than when you used a GPS?

    Zz.
     
  14. Jun 26, 2008 #13

    Mentz114

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    Re: The General "Principle" of Relativity

    Chrisc,

    Same to you. What is your definition of time ?

    Apart from the mass bit this is true. I presume you mean 'acceleration' is measured by accelerometers.
    No it wouldn't. Don't presume you can read my mind. Especially as I'm dead at the time you are talking about.
    You're trying to make a mystery out of the different ageing/proper times of different frames. It is strange, but I don't see how you can get a 'law of conservation of time' from it.

    M
     
  15. Jun 27, 2008 #14
    Re: The General "Principle" of Relativity

    I'm sorry, I took the intent of your question was to discover my opinion on the certainty of the future of QFT and/or GR in the pursuit of unification. I take it your question was meant to weigh the the sum of all applied science and technology derived from QFT against that of GR.

    I have no doubt that all the knowledge and evidence accumulated in the pursuit of QFT will prove to be
    of great value and utility. However, with respect to unification, I think the incorporation of QFT into the Standard Model will prove to be little more than another temporary fix for a theory that is in desperate need of a new foundation.
    As far as quantizing space-time, it is a natural path to unification given the philosophical divergence of QT and GR.
    But it is only one of the two more obvious paths where either continuous is made discrete or discrete is made continuous. There is a third less obvious path where discrete and continuous unite. Discrete being a finite cessation of a continuous process. (I'll stop here so as not to raise objections by the moderators)

    My question was regarding the possibility of extending the general principle of relativity as a more fundamental approach to unification than the quantization of space-time. Simply because the former requires a deeper understanding of space, time and mass, whereas the latter holds all three in the same circular logic that has failed for over eighty years. This is not to say the Standard Model has failed. It is arguably the most significant creation of the human mind and will continue to be fruitful for many years to come. But when one stands back from the enticing beauty of its parts, one sees a very ugly, patchwork of a theory that sooner or later will have to be torn apart and rewoven into a more consistent, principled model.
     
  16. Jun 27, 2008 #15
    Re: The General "Principle" of Relativity

    Time is one of three fundamental dimensions of physics, as is space, as is mass. It is not the kinematical evidence by which it is marked.

    Well, as a person with an interest in physics you should.
    I did not presume to read your mind, I said "should" not "would".

    On the contrary I'm trying to make it perfectly clear that it is not a mystery.
    Strange is what we call things we don't understand.
    Is Lorentz invariance not an expression of conservation?
    The continuous symmetry of space, time and mass as evidenced by the translatory measures between frames in motion is an expression of a law of conservation of dimension.
     
  17. Jun 27, 2008 #16

    Fra

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    Re: The General "Principle" of Relativity

    This was my impression.

    What is your opinon on this
    "Are We Cruising a Hypothesis Space?", C. C. RODRIGUEZ
    -- http://arxiv.org/abs/physics/9808009

    He tries to generalise the logic of Einsteins equations as a general inference on information spaces. I reflected on that in https://www.physicsforums.com/showthread.php?t=241825.

    Einsteins equation is a relation between matter and geometry. He generalisation is that there is an equivalent relation between information and geometry of information space.

    What I am really looking for in that thread is a first principle construction of the indexspace and a manifold (rather than starting with it), including it's measures.

    /Fredrik
     
  18. Jun 27, 2008 #17

    Mentz114

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    Re: The General "Principle" of Relativity

    Chrisc,
    In my opinion 'Time is a dimension' is a bit circular, but I'm more interested in your question
    which I do understand. Strictly, a conserved quantity is derived from Noether's theorem, with each of the generators of every continuous compact symmetry group of the Lagrangian giving rise to a conserved quantity and current. So, to get a conservation law you need a Lagrangian that has symmetries. It is a dynamic statement.

    The invariance of the proper interval under Lorentz transformation is kinematic and does not give rise to a conserved 'charge' or current ( I'm not 100% sure of this, I must add).

    What Lorentz invariance gives us is something that all inertial observers can agree on, so it's a conservation of sanity law.

    It's an interesting question, maybe someone else has views ?

    M
     
  19. Jun 27, 2008 #18

    DrGreg

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    Re: The General "Principle" of Relativity

    In your example, you have travelled nearly a light-year, I have travelled nowhere, yet we are both at the same place. Where has all the distance gone?

    You might think that's a different sort of question to "where has all the time gone", but it terms of relativity they are actually very similar questions.

    (And as Mentz114 pointed out, accelerometers measure acceleration, not mass. The clue is in the name.)

    ____

    There is a difference between "conservation" and "invariance".

    A quantity is conserved if a single observer calculates the same value for two events before and after an incident. Examples are energy and momentum, in "closed" systems.

    A quantity is invariant if two different observers calculate the same value for a single quantity. Examples are proper time along a trajectory (worldline), proper acceleration, proper mass (a.k.a. rest mass), and the proper interval ds.
     
  20. Jun 27, 2008 #19

    Fra

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    Re: The General "Principle" of Relativity

    I consider the entire discussion to be a little fuzzy since it's conditional on the notion of space and time in the first place, but loosely speaking information geometric reflections may gives rise to local lorentz-like symmetries, as a result of that parametrisations are relational (ie that the clock is part of the system), and choosing a clock simply means a choice of parameterisation. But any choice of parameterisation are constrained by a sort of local symmetry in a differential sense.

    "The Information Geometry of Space and Time"
    -- http://arxiv.org/PS_cache/gr-qc/pdf/0508/0508108v2.pdf

    "We see here a “foliation” invariance, a rudimentary form of local Lorentz invariance".

    However the explicit construction of full spacetime is yet incomplete. But in this context I consider all symmetries to be emergent in the sense of an expectation based on incomplete information. If the geometric properties and the manifold themselves are attributes of our knowledge, expectations remain effective conserved quantitites until challanged. A logically plausible response pattern is to follow your expectations until challanged. Then consider what happens when all systems in the environment implements the same logic.

    /Fredrik
     
  21. Jun 28, 2008 #20
    Re: The General "Principle" of Relativity

    Fra, this is interesting if it is going where I think it is.
    I will read the paper and get back to you. Probably with more questions than answers.

    Mentz114, I'm stating a very general principle and you're stating a very specific case of that principle.
    You are taking my general statement of a law of conservation of "dimension"
    and changing it to a specific case of energy.
    As Fra pointed out, I am suggesting Noether's theorem , can be considered in
    a much more general sense.
    Her theorem may apply to how we associate dimension and dynamics.
    In the general case:
    For every quantifiable system of dynamics there exists a qualifiable system of dimension.
    As the total energy of a system is conserved through a translational symmetry,
    likewise the total dimension of a system is conserved through a translational symmetry.
    Just as the energy conservation may result from the transformation of kinetic to
    gravitational potential, the dimensional conservation may result from the transformation
    of space-time to mass.

    DrGreg, I don't think that's fundamentally different. You have stated a similar question with respect to the
    dimension Length (space). To answer your question "Where has all the distance gone?"
    I would suggest it is quite literally transformed dimension of differing configuration for
    each twin but. The total energy of the closed systems that are twin one and two is
    conserved. It is just much more difficult to pin down the kinematical equations for
    the dead twins constituent particles as they are now spread out, so to speak.
    You are restricting your conception of conservation and invariance to specific expressions
    of a system.
    The equations of mechanics are upheld in all inertial frames even though they
    express quantitative discrepancies between frames with respect to specific dimensions.
    They are upheld because they do not demand specific or unique quantitative values
    but express relational quantities of the dimensions.
    They are upheld because the quantitative discrepancy in any one dimension
    is compensated for in the other dimensions sustaining the validity of the relations
    expressed by the equations.

    Fra, I agree, symmetries are emergent in the sense you've described.
    We conserve the properties and indeed the dimensions themselves in the conservation of our present understanding of symmetries.
    Once new symmetries are realized the conservation is of a more unified nature
    i.e. the conservation of space and time are expressed in the continuum space-time. The conservation
    of space, time and mass will be expressed in the continuum of space-time-mass.
    The axis of the symmetries that will conserve dimension across ontological transformations is the key.
     
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