I need someone who knows the math

Discussion in 'Physics & Math' started by BigBangIsGod, Mar 4, 2016.

  1. paddoboy Valued Senior Member

    Messages:
    27,543
    More unsupported allegations against anyone that dares to show you up for what you are?
    Obviously you ignore the facts as they stand with regards to rpenner and yourself and Dan....[1] He [rpenner] is right principley and [2] He is right Mathematically and [3] as most accepted by mainstream due to sensibility, logicity, and as aligning with the evidence available.
    That frustrates and irks you.

    You and Dan on the other hand have been shown to be grossly wrong in both interpretation, mathematical content and failing the scientific methodology.
    That also obviously frustrates and irks you as well as Dan.

    You have said a few times that science/cosmology advances and gains with robust discussions and debate, even the discussing of unsupported hypothetical alternatives.
    In essence while that is correct, it totally unravels and becomes codswallop, when one side of the discussions/debate is hindered by the ludicrous claims that one is never wrong, or one is omnipotent, or one is unable to or afraid to reveal any lack of relative qualifications due to that revealing the agenda that is the driving force behind much of the silly alternative codswallop that is being put under the guise of science.
    Your exposure in that regard, and on various issues over the last few months and in which I have humbly played a part, also frustrates and irks you.

    At last it appears that this failing on this forum, may now be being reviewed.
    Let's hope a decision is forthcoming sooner rather than later.
     
    Last edited: Mar 12, 2016
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Previously, I wrote that claims about atoms being in constant motion were irrelevant to discussion of the geometry of space-time.
    That's 1) because the phenomenology of the Higgs particle is irrelevant to the geometry of space-time as the physical theory of the Higgs mechanism is written as a Lagrangian density which assumes the geometry of space-time to be four-dimensional and Lorentzian and thus the geometry of space-time is more fundamental than the physics built on top of it. 2) Likewise for quantum mechanics and electromagenetism. Finally, 3) aside from the theoretical underpinnings of physical theory to be based on the assumption that space-time is Lorentzian, the discovery of the Higgs particle did nothing to imply there was anything newly wrong with that assumption. Thus your objection is a non-sequitur and you have failed in your burden of proof to support your claim.

    That's the Bohr model, not the quantum mechanical description of an atom as the ground state of a spectrum of bound configurations.
    You can't have a state of motion with respect to something that doesn't give rise to a preferred standard of rest. The pervasive Higgs field, like the quantum vacuum of a field with 0 expectation value, is exactly one of those things that doesn't have a state of motion.
    Examples of motion are hardly counterexamples to the claim that space-time has a Lorentzian geometry.
    Already done in quantum mechanics and quantum electrodynamics.
    How can there be motion if space is not as real as time? Your claim makes no sense in a way that belies your claim that you have the support of evidence.


    Localized means an event has a maximum bound on what its proper spatial extent is and a maximum bound on what its proper temporal extent is. Thus when those bounds are negligible, the event is "point-like." An example is a car crash which is localized to a few meters and a handful of seconds. A more pointlike example is a bullet hitting a target. A still more point-like example is the pair-production of an electron-positron pair from a gamma ray. Just as I can give the position of a store by relations to other nearby landmarks or by its GPS coordinates, all of these events have a well-defined when and where which has a meaning independent of you use of coordinate systems.

    The concept is found in Euclidean plane construction. Two lines intersect in the plane at a single point. That point is localized as the unique intersection of two lines. Indeed, if you have a disjoint ordered pair of continuous families of non-intersecting curves in the plane, each indexed by a real number, then a point in the plane is found in only one curve of each set. And this pair of lines can be indexed by an ordered pair of real numbers. These would be examples of general coordinates for a point in a plane. Thus geometry is more fundamental than localization of points which is more fundamental than coordinates systems.

    Personally, the existence or measurement of real things cannot be "relative" to anything. That's why coordinate separation, lengths of moving rods, coordinate time and simultaneity of distant events are not real for me, while proper time and covariant predictions of the laws of physics are real for me.


    It is more correct to say it is a view about physics which originates in physical theories dating back to 1905-1916, but remains equally valid today. Nothing happened in the last 30 years to change the status of the geometry of space-time as the background perquisite to talking about particle physics.

    As I just went over in this thread, toy models treating only limited aspects of special relativity do not generalize to the content of special relativity. There is a time dilation factor associated with relative velocity, but not with instantaneous relative velocity when the standard against which that velocity is measured is not inertial because the relativity of simultaneity for space-like separated events means "now" in the current state of motion is not parallel to the "now" of a different state of motion.

    And this is the second time in this thread you have brought up that F=ma is not valid in special relativity. You haven't managed to read what I said about it last time.

    There is nothing wrong with those relations in special relativity. The catch is coordinate acceleration is not the same thing as proper acceleration.

    Some interesting things can be done on a phonograph.
    Baseless and sterile claims that diminish your claim to be an authority.
    You now seem to finally agree with me that space-time has a geometry only to make more unsupported claims and abuse of language.

    Yes. I cautioned against putting too much stock in toy depictions of special relativity such as saying that time dilation factors from instantaneous relative velocity is sufficient to generalize to all clock problems and used Dingle's breakdown as a example. Then in Post #103 that exact page was already looked at.

    That is hardly a correct summary.

    They don't present pet ideas as if they had strong empirical support at the rate of the physics outsiders. They very well be self-righteous enforcers of pop science viewpoints, but they've got some of the right ideas down pat.

    I completely dislike how they escalate to name-calling when extinction of sterile claims proves a stronger method against anti-science. That way when debunked claims or arguments are repeated, or telling questions avoided one knows the opponent has run out of stock arguments and is too dim to perceive it. I don't know what anyone's education is, but it should be obvious you can't win an argument against a narcissist — they already have their knowledge of victory welded tight against the light of reality — so I seek to argue for the sake of the hypothetical third party rational ready. I like to argue for the ages and write for the back seats.

    But to do so, one has to actually parse the content of the post, unwholesome as the sterility or lack of basis for the claims might be.
     
    Last edited: Mar 12, 2016
    danshawen likes this.
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. The God Valued Senior Member

    Messages:
    3,546
    Good observation, I hope Mods also see and spend a couple of minutes how a thread gets derailed and take some corrective pre-emptive steps...may be your observations will make these posters rethink on their popscience stand and also the tactic of starting abuses..
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. The God Valued Senior Member

    Messages:
    3,546
    No; logic, sensibility and evidence never irk me.....what irks me is the misrepresentation of mainstream and supporting the mainstream without understanding the same in totality. You may be speaking the truth on certain facts, but if your argument is that it comes from mainstream guys and it must be right, then you are just a noise, part of a senseless mob.

    If you agree with this, then let the discussion continue, and if you feel or others who are well conversant with the subject feel that the poster has lost the argument and just sticking for the sake of his false pride, then drop the matter, instead of abuses or calling names...

    Do you realise Why I make such comments when I am arguing with you or with Physbang or Brucep or Origin ? I never made such statements when I interacted with Schmelzer or Q-reeus or now rpenner.....Because mostly you guys posts are contentless, you want to bulldoze or resort to abuses. So I have to use such stuff, that irks you and in the process you further drop yourselves.

    I am sorry, this may not please you, but there is nothing which you have done to counter my stand...in most of the cases you have not even understood the point as raised by me, leave aside exposing that.
     
    Last edited: Mar 12, 2016
  8. The God Valued Senior Member

    Messages:
    3,546
    Whenever the time dilation paradox is discussed, lot of heated argument starts. My stand on GR/BH is not positive but I have never raised questions on SR, barring few issues especially on Time Dilation Paradox. Detailed discussion apart I wish to give an analogy as follows, this can be used by those who wish to counter this paradox issue in lay discussions...

    ---Say the two guys of equal height around 6' are standing some substantial distance apart, then each sees the other guy shorter, you can say that this is virtual height. Similarly when two guys are travelling in two different spacecrafts with relative motion between them, then each guy sees that others clock is slowing down, you can say this as virtual time lapse...
     
    Last edited: Mar 12, 2016
  9. danshawen Valued Senior Member

    Messages:
    3,951
    Anything which has inertial mass, not to mention giving mass to other fundamental particles inside and outside of atomic structure, manifestly has a state of motion. It has a state of motion that not only presses into fundamental particles of atomic structure from all sides/directions, but also imparts additional inertia to the entire structure in a given instantaneous direction proportional to interactions associated with every and any other forces which act on the entire structure.

    A Lagrangian that doesn't model this is incomplete, and any model of spacetime that does not include it is incomplete. Static geometry isn't going to cut it precisely because every part of the correct model is dynamic. Four dimensions are unsupportable. An infinite number of rotations coupled with both linear and rotational energy propagation modes accomplish the same function AND relativity without introducing unnecessary and undesirable mathematical complexity based on nothing but a mathematician's inclination to use things quadratic to describe everything and anything that seems unclear. Relativity was very clear before Minkowski mucked it with light cones and 4D rotations and the like. My guess is, how dull student Albert figured that sooner or later, his own math would trip him up. It did, but somehow, no one else ever noticed. Funny, but it's time to apply the kaboshes to his inconsistent nonsense. It rendered relativity incompatible with QM. The rotational mode of propagation is faster than the linear speed of light, but you won't find that idea in any of Minkowski's quadratic Pythagorean complex nonsense.

    So, major inconsistencies here. When you actually get to see a Higgs boson for a zeptosecond or two, it has already interacted via the Higgs mechanism by means of interacting with quantum spins in a manner that no boson other than one of spin zero can. No matter which orientation or direction the fundamental particle is propagating , the Higgs field interacts with it and the excitation produces a boson that can add or remove linear and/or rotational inertia, the only type of interaction that assures that the energy remains bound in all inertial and rotational relativistic reference frames.

    Any other view I can think of would be inconsistent with the nature of reality we observe. The interaction accounts for the shapes of large concentrations of baryonic inertial mass; radial symmetry is everywhere from things the size of electrons to entire galaxies. Inertial mass without gravitational mass would be an absurdity in this universe. If it is not in your model, then something is wrong with your model.
     
    Last edited: Mar 12, 2016
  10. danshawen Valued Senior Member

    Messages:
    3,951
    For the rotational mode of propagation I'm talking about, because quantum spin is faster than the linear speed of light, it is similar in terms of real physical propagation to what is otherwise observed as Cherenkov radiation, except that it is lossless and the energy is entirely confined to the physical aggregate bound energy of the particle.

    Tell me the model doesn't work. You are looking at it, and are also composed of it.

    If I don't write these ideas down somewhere, they will be lost for sure.

    Entanglement spin flips are already known to be faster than light in a vacuum.
     
  11. paddoboy Valued Senior Member

    Messages:
    27,543
    While being man enough to accept rpenner's criticism, perhaps you overlooked the criticism directed at you?
    I mean in recent times you are the one that has been suspended and also two threads moved to the fringes.
    I certainly though disagree with rpenner and his remark about defending science as self righteous enforcers: Science does not need defending as it stands on its own two feet due to the scientific method and peer review in general.
    I just find it highly arrogant, presumptuous and pretentious, that pretenders and would be's if they could be's, have the audacity to claim that mainstream science is wrong, when they are unqualified, uncredentialed and are burdened with an agenda.

    I find the reverse argument as far more logical and sensible.
    That is how does any unqualified would be if he could be pretender, have the audacity to claim mainstream cosmology is wrong, when they themselves are not totally conversant with the incumbent model.

    Please Register or Log in to view the hidden image!

    Sorry old friend, I saw what you did there.

    Please Register or Log in to view the hidden image!

    That's not nice, or honest.
    What I said......
    You have said a few times that science/cosmology advances and gains with robust discussions and debate, even the discussing of unsupported hypothetical alternatives.
    In essence while that is correct, it totally unravels and becomes codswallop, when one side of the discussions/debate is hindered by the ludicrous claims that one is never wrong, or one is omnipotent, or one is unable to or afraid to reveal any lack of relative qualifications due to that revealing the agenda that is the driving force behind much of the silly alternative codswallop that is being put under the guise of science.

    I do realise that for anyone to claim that he is never wrong, or is omnipotent is inanely stupid, and when that is coupled with the fact that the same person also has claimed that GP-B was a fraudulent exercise, and that aLIGO most certainly reflects and agenda as the reason for such nonsensical claims.
    Also your self claim that you do like clowning around with such remarks is evident that you have just been demolished on a point/s of contention, and need to sidestep the issue before admitting you were/are wrong.
    When you put unsupported unqualified statements as based in fact, it is you actually trying to bulldoze your own point of view, driven by some agenda.
    As I tell you often, if you had anything of substance that was not agenda driven, you would not be here.
    ps: I'm also looking forward to attending Stockholm in November to see handsa receive his Nobel [tic mode on of course]
    It does not displease or please me at all.....You are entitled to make/claim whatever you like: Your expectations that it be taken seriously is what is in question, as rpenner noted and which you seem to have either glossed over and/or missed.
     
  12. danshawen Valued Senior Member

    Messages:
    3,951
    After weeks of general outrage the first time I suggested that perhaps Minkowski really had no basis for his formulation of relativity sinultanaeity or Minkowski rotation, I did research the man, his relationship to his students Einstein and Hilbert, and additional background research materials which explained his motivation, purpose and method for implementing his portions of relativity theory canon.

    I found what would be expected of a nineteenth century mathematician-cum-physicist. Whatever he got right was due to his less favored student Albert. E=mc^2 was not Minkowski's prediction nor Hilbert's. It was Einstein's all the way.

    In the beginning of a century in which we have discovered the Higgs boson and are beginning to come to grips with the c^2 speed of entanglement, Minkowski's versions of simultanaeity and 4D rotation have no place in the mathematics and physics that more closely reflect reality. E=mc^2 and an invariant +/- c. endure. Invariant 4D intervals, time based on linear energy propagation and Minkowski rotation don't.
     
    Last edited: Mar 13, 2016
  13. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Clearly erroneous in a way that marks you as an outsider to physics, math, history and usefulness. Minkowski space-time pervades all particle physics work and forms the basis for formulating general relativity.

    And it's not \(E=mc^2\)
    It's \((E/c)^2 = (mc)^2 + (\vec{p})^2, \; (E/c) \vec{v} = c \vec{p}\) in the more general case of a free particle in special relativity.

    Similarly \((c \Delta t)^2 = (c \Delta \tau)^2 + ( \Delta \vec{x} )^2, \; ( c \Delta t ) \vec{v} = c ( \Delta \vec{x} )\) for any inertial segment of a world-line.

    Thus if a massive particle has \((E/c, \vec{p}) = (2.0759332 \, \textrm{MeV}/c, 2.0120583 \, \textrm{MeV} / c \, \hat{x})\), that transforms the same way under special relativity as a coordinate separation along its world-line \(( c \Delta t, \Delta \vec{x}) = ( 2.0759332 \textrm{m}, 2.0120583 \textrm{m}\, \hat{x})\), and we know it's velocity \( v = \frac{63_{-0.000004}^{+0.000002}}{65} c\) and rest energy \(E_0 = 510999_{-0.4}^{+0.4} \, \textrm{eV}\).
     
  14. danshawen Valued Senior Member

    Messages:
    3,951
    This relation I am intimately familiar with, and have already referenced. The rest energy is invariant in the rest frame.

    When rest mass increases because an external force acts on a projectile to increase its energy /momentum with respect to the rest frame, that energy is stored in the bound rotational energy of each particle of each atom the projectile contains. And time dilates, the same as if the projectile were made of unbound energy and instead of mass increasing, the frequency increased instead. The effects do not tally the same because "at rest" with a top speed of just under c is not exactly or mathematically the same effect as "propagating at exactly c and unable to go any slower."

    "transforms the same way under special relativity as if light travel time (separation) increased." See? No "light cones", conic sections, or quadratic / Pythagorean / complex math needed at all, to explain or to obfuscate anything important.

    I grudgingly acknowledge this as a good approximation only because the relative velocities for most gravitational interactions are slow.

    His predictions will break down for orbiting a black hole because that feature is the domain of Special Relativity and static geometric approximations to relativistic effects is not as good. This has led to predictions from many that time stops for light and even for matter at the event horizon, independent of whether anything with mass can actually reach light speed or not (it cannot). Only to the same extent that it would stop for a photon propagating in a straight line, or for the rotational energy of an ordinary fundamental particle, or that tidal forces may render mass back into its rest energy. The Higgs has mass. The Higgs mechanism doesn't work to impart inertia at light speed for that reason. No big deal, as predictions go; the Higgs mechanism is the foundation of Special Relativity, and a better explanation of General Relativity as well.
     
    Last edited: Mar 14, 2016
  15. danshawen Valued Senior Member

    Messages:
    3,951
    The actual foundational thought experiment that underlies all of relativity has never, to the best of my knowledge, been published anywhere. Here it is:

    There is only a single fundamental particle, an electron, in the universe. Forget about paired matter, antimatter, and also paired positive and negative electric charges for the moment. They are all sufficiently far removed to be unobservable forever.

    You are able to observe the rest mass of this electron you are observing. Suddenly, a strong external force is applied. It could be an electromagnetic, gravitational or other field or even a high energy photon that is encountered. So the electron you are observing begins to move relative to the inertialess field in which it propagates relative to whatever has just moved it.

    Model conservation of energy in this sparse universe of a single particle of bound energy. Do not neglect any relativity that is related to rest mass vs. mass that is moving with respect to something that has applied the force.

    All of Hamiltonian and Lagrangian dynamics will not be a sufficient answer. You must explain inertia and conservation of energy in fundamental detail; where it is before and after the force is applied, and you must respect special relativity for all interactions at any velocity of absolute value less than c.
     
    Last edited: Mar 14, 2016
  16. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    That is not a thought experiment. A thought experiment takes a given physical theory and works out the outcome under that physical theory under certain given conditions. You didn't put any visible thought into so-called experiment.

    Here in this thread, we are using special relativity, and we have:
    \(E_1^2 - (c \vec{p}_1)^2 = (m_e c^2)^2 = E_2^2 - (c \vec{p}_2)^2 \\ \frac{c^2}{E_1} \vec{p}_1 = \vec{v}_1 \neq \vec{v}_2 = \frac{c^2}{E_2} \vec{p}_2 \\ \vec{x}(t) = \left\{ \begin{array}{lll}\vec{x}_0 + (t - t_0) \vec{v}_1 & ; \quad \quad & t \lt t_0 \\ \vec{x}_0 + (t - t_0) \vec{v}_2 & ; \quad \quad & t \geq t_0 \end{array} \right. \)
    For arbitrary choices of \(\vec{x}_0, t_0, \vec{p}_1, \vec{p}_2\) we have \(E_1 = \sqrt{ (c \vec{p}_1)^2 + (m_e c^2)^2 } \geq m_e c^2, E_2 = \sqrt{ (c \vec{p}_2)^2 + (m_e c^2)^2 } \geq m_e c^2, \left| \frac{\vec{v}_1}{c} \right| = \left| \frac{\vec{p}_1}{\sqrt{ (\vec{p}_1)^2 + (m_e c)^2 }} \right| \leq 1, \left| \frac{\vec{v}_2}{c} \right| = \left| \frac{\vec{p}_2}{\sqrt{ (\vec{p}_2)^2 + (m_e c)^2 }} \right| \leq 1\)

    So we have an example of momentum non-conservation, because we necessarily neglect treatment of the undescribed outside force. Thus this is simpler than the case of elastic relativistic collision because we have less to work with.
    In the event that we are working in coordinates where \(\vec{p}_1 = 0\) then we are working in coordinates where there is energy non-conservation also.
    But we may always choose a Lorentz transform and choose to work in a set of inertial coordinates where \(\vec{p}'_1 = -\vec{p}'_2\) like elastic collision off an immovable wall.
    Also since the choice of \(\vec{x}_0, t_0\)are nowhere coupled to the choice of \(\vec{p}_1, \vec{p}_2\), we may elect to set them to zero for convince without changing the physics.

    Despite your buzzwords, you have not contributed physics discussion to your so-called thought experiment. You should be permanently banned from extolling your ideas about "bound energy" from the science-facing parts of the forum and they should be deleted, not responded to.
     
    Last edited: Mar 14, 2016
    origin and Ophiolite like this.
  17. danshawen Valued Senior Member

    Messages:
    3,951
    This approach is fine, but not the problem I was trying to describe. You have simply ignored the effect of the external force and given back the same formulae from your previous post.

    Even fourth graders now view charts and graphs of the infamous "binding energy vs. number of nucleons", which I had to wait for until my second year of college physics to see for the first time.

    For some of us, it isn't enough to know that energy is bound if you don't understand the mechanism(s) by which it is bound.

    It isn't enough to know that energy is conserved if you don't understand why it is conserved.

    It isn't enough to understand that inertia is given by some mechanism if you don't even have a model of what exactly gives rise to time, time dilation or relativity itself, because inertia is not given by any force that does not receive inertia in exchange, and time is an essential component of this understanding.

    And I have also demonstrated in this thread that "someone who knows the math" does not necessarily know or understand these things.

    And thank you profusely again for demonstrating this so well, rpenner.
     
  18. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    I have ignored nothing. You wrote:
    Which I calculated in the limit of \(\Delta t \to 0\). A strong external force that appears out of nowhere and vanishes just the same.

    If what you meant was a strong constant force, then you need to define if you mean to hold \(m \frac{d^2\vec{x}}{dt^2}\), \(\frac{d \vec{p}}{dt}\), or \(\frac{d^2 x'}{d t'^2}\) constant.

    Case I:

    \( \vec{x}(t) = \left\{ \begin{array}{lll} \vec{x}_0 + (t - t_0) \vec{v}_1 & ; \quad \quad & t \lt t_0 \\ \vec{x}_0 + (t - t_0) \vec{v}_1 + \frac{1}{2} (t - t_0)^2 \vec{a} & ; \quad \quad & t_0 \leq t \lt t_0 + \frac{ - \vec{v}_1 \cdot \vec{a} + \sqrt{ ( \vec{v}_1 \cdot \vec{a} )^2 + \vec{a}^2 ( c^2 - \vec{v}_1^2) }}{ \vec{a}^2 } \end{array} \right. \)

    With \(t_0 = 0, \vec{x}_0 = 0, \vec{v}_1 = 0\) we have:

    \( \vec{x}(t) = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \frac{1}{2} t^2 \vec{a} & ; \quad \quad & 0 \leq t \lt \frac{ c } { | \vec{a} | } \end{array} \right. \)

    This equation has no hallmarks of being generally useful in special relativity.


    Case II:

    With \(t_0 = 0, \vec{x}_0 = 0, \vec{v}_1 = 0\) we have:

    \( \vec{p}(t) = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ t \vec{F} & ; \quad \quad & 0 \leq t \end{array} \right. \)

    Let \(\lambda = \left| \frac{ F }{ m_e c } \right|\).

    Thus
    \( E(t) = \sqrt{ ( m_e c^2 )^2 + ( c \vec{p}(t) )^2} = \left\{ \begin{array}{lll} m_e c^2 & ; \quad \quad & t \lt 0 \\ m_e c^2 \sqrt{ 1 + \lambda^2 t^2 } & ; \quad \quad & 0 \leq t \end{array} \right. \)

    And
    \( \vec{v}(t) = \frac{ \vec{p}(t) }{ \sqrt{ m_e^2 c^2 + \vec{p}^2(t)}} c = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \frac{ c t \lambda }{\sqrt{ 1 + \lambda^2 t^2 }} \hat{F} & ; \quad \quad & 0 \leq t \end{array} \right. \)


    Case III:

    Let \(\lambda = \left| \frac{ F }{ m_e c } \right|\) again.

    We want to solve (for reasons below)
    \(\left( 1 - \beta (t ) \right) ^{-\frac{3}{2}} \beta'(t) = \lambda , \beta(0) = 0\) with solution \(\beta = \frac{\lambda t}{\sqrt{ 1 + \lambda^2 t^2}} \)

    So
    \(\vec{a}(t) = c \beta' = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \frac{ \lambda c }{ \left( 1 + \lambda^2 t^2 \right)^{\frac{3}{2}} } \hat{F} = \left| \frac{ F}{ m_e } \right| \left( 1 + \left( \frac{ F t }{ m_e c } \right)^2 \right)^{- \frac{3}{2}} \hat{F} & ; \quad \quad & 0 \leq t \end{array} \right. \)

    So
    \( \vec{v}(t) = c \beta = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \frac{ \lambda c t }{ \sqrt{1 + \lambda^2 t^2} } \hat{F} = \left| \frac{ F t}{ m_e } \right| \frac{ 1 }{ \sqrt{1 + \left( \frac{ F t }{ m_e c } \right)^2 } } \hat{F} & ; \quad \quad & 0 \leq t \end{array} \right. \)

    But this is the SAME case as II.

    Thus for cases II and III:
    \( \frac{d t'}{d t} = \gamma^{-1} (t)= \sqrt{ 1 - \frac{ \vec{v}^2(t) }{c^2}} = \left\{ \begin{array}{lll} 1 & ; \quad \quad & t \lt 0 \\ \frac{ 1 }{ \sqrt{1 + \lambda^2 t^2} } = \frac{ 1 }{ \sqrt{1 + \left( \frac{ F t }{ m_e c } \right)^2 } } & ; \quad \quad & 0 \leq t \end{array} \right. \)

    Thus
    \( t(t') = \left\{ \begin{array}{lll} t' & ; \quad \quad & t \lt 0 \\ \frac{\sinh ( \lambda t) }{\lambda} = \frac{ m_e c }{ | F | } \sinh \left| \frac{ F t' }{ m_e c } \right| & ; \quad \quad & 0 \leq t \end{array} \right. \)

    And
    \( \frac{\partial x'}{\partial x} = \gamma (t)= \frac{1}{ \sqrt{ 1 - \frac{ \vec{v}^2(t) }{c^2}} } = \left\{ \begin{array}{lll} 1 & ; \quad \quad & t \lt 0 \\ \sqrt{1 + \lambda^2 t^2} = \sqrt{1 + \left( \frac{ F t }{ m_e c } \right)^2 } & ; \quad \quad & 0 \leq t \end{array} \right. \)

    So
    \( \frac{d^2 x'}{d t'^2} = \frac{\partial x'}{partial x} \frac{d^2 x}{d t^2} \left( \frac{d t}{d \tau} \right)^2 = \gamma^3(t) \vec{a}(t) = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \lambda c \hat{F} = \frac{ \vec{F} }{ m_e } & ; \quad \quad & 0 \leq t \end{array} \right. \)
    as desired.

    Thus
    \( \vec{x}(t) = \left\{ \begin{array}{lll} 0 & ; \quad \quad & t \lt 0 \\ \frac{c}{\lambda} \left( \sqrt{1 + \lambda^2 t^2} - 1 \right) \hat{F} = \frac{m_e c^2}{\left| F \right| } \left( \sqrt{ 1 + \left( \frac{ F t }{ m_e c } \right)^2 } - 1 \right) \hat{F} & ; \quad \quad & 0 \leq t \end{array} \right. \)
     
    Last edited: Mar 15, 2016
    danshawen likes this.
  19. The God Valued Senior Member

    Messages:
    3,546
    This binding energy concept needs push, there is no way the concept of equivalence principle can be explained by keeping the binding energy hidden between bonds......there is deeper meaning to that. I strongly feel that equivalence principle is the key to New Cosmology. I am getting convinced (not fully yet) that Einstein GR Equations are good, but not the GR premises.
     
    danshawen likes this.
  20. The God Valued Senior Member

    Messages:
    3,546
    double posting
     
  21. danshawen Valued Senior Member

    Messages:
    3,951
    This is a treasure. If you hold something constant, particularly a velocity or an acceleration, it is only a constant WITH RESPECT TO SOMETHING ELSE, in this case, did you mean the <coordinate system of> electron, or the external force/photon? It has to be the former, right, because A PHOTON TRAVELING AT c DOES NOT HAVE A COORDINATE SYSTEM, SEE? Your inconsistencies are manifest.

    And since the photon is the boson associated with ALL forces that can ever be exerted on an electron (including gravity), then either you must accept that there must be THREE bosons associated with such interaction (photon, Higgs, the graviton), or else you must admit that the bosons in the Standard Model of particle physics seem to be multiplying with no apparent end in sight. This is an example of how inconsistencies creep into the math based on a flawed physical model. The math may be consistent, but the physics isn't.

    Math is a fine tool for science, and its greatest asset is self-consistency, but all by itself, math is not science, AND it is eminently practical for math to be consistent at a certain level of science, and out-to-lunch at a slightly deeper one. Gödel's incompleteness theorems assure this is the case. Newton's classical mechanics vs. Einstein's Special Relativity is the best example I can think of. Possibly it was even the model for some of Gödel's research.

    And every physics student in my class felt that kind of pain when relativity was understood, and all of Newton's careful calculations fell out from under us like an enormous intellectual sinkhole had opened a chasm beneath us. Or all of the air was being slowly released from the rather large balloon of our egos for having passed all of the tests assessed on classical mechanics, only to discover it was only an approximation after all.

    Some of us, including yours truly, were a bit angry at the prospect of basically having to relearn physics again from scratch. But I do understand, and even if there were a better way to present it to physics students, I would not change even a nuance of the experience. If it doesn't humble your intellect, your ego, and your belief system, it is unlikely that anything ever will.

    I'm certain, no one would ever wish to face the prospect of experiencing something like that more than once in their lives, nevertheless…
     
    Last edited: Mar 15, 2016
  22. rpenner Fully Wired Valued Senior Member

    Messages:
    4,833
    Again and again, your bring up your troubled educational history as if you are some special privileged snowflake. You didn't have to "relearn physics" but simply badly misjudged how high "up" was. Statements to the effect that relativity and quantum physics were basically revolutionary in the early 1900's were hardly state secrets. What you are describing are simple introductory courses which progress in historical fashion with physics at a scale human can see and touch, physics which is approximately true in the limit of treating \(G\) or \(\frac{1}{c^2}\) or \(\hbar\) as negligible.

    You complain about physics where \(\frac{1}{c^2} \neq 0\) can't be ignored, but you didn't even master physics where \(G \neq 0\) can't be ignored. Orbital mechanics and planetary dynamics in a multi-body system are seriously challenging compared to the simple and non-original calculations I worked out above. Calculations which you opined might be novel in the first line of post #172.

    I was initially inclined to agree, but then I discovered you were distracted by irrelevancies.

    If the phrase "constant acceleration" is to have meaning in special relativity, case I rules out constant coordinate acceleration for inevitably one runs into the limiting velocity. Case II is the case of constant momentum transfer per coordinate time. Case III is the case of constant "proper acceleration". Multiple approaches were tried due to the lack of effort you put into post #172.

    I worked it out as holding \(\frac{d \vec{p}}{d t}\) constant in the inertial coordinates where the electron was initially at rest and for holding the acceleration to be the same constant in any comoving inertial frame that held the electron to be instantaneously at rest. Coordinates are imaginary things we use to describe motion in concrete terms, so it is a misnomer to speak of the electron's coordinate system. Therefore, I'm pretty sure that your choice to be vague in post #172 about the nature of the force badly impairs your current desire to talk about the coordinate system of any such force carrier.

    If you will notice, nowhere is the physics of the force carrier described because as I called out, this is an exercise in momentum non-conservation.

    No. Throughout I used an inertial coordinate system where the electron was originally at rest because that cleanly separated the physics of the acceleration that I wished to describe from the initial conditions. As in Case I, that choice greatly simplified both the equations of motion and the calculation of quantities.

    There was no photon in evidence throughout. If you wanted a model of Compton scattering, you are barking up the wrong tree.

    I'm not old enough to have invented physics. You are confusing me with God, Einstein or perhaps your much-maligned physics instructor.

    Despite your buzzwords, you have not contributed physics discussion to your so-called thought experiment. You should be permanently banned from extolling your ideas about "bound energy" from the science-facing parts of the forum and they should be deleted, not responded to.
     
  23. danshawen Valued Senior Member

    Messages:
    3,951
    You are the treasure. If it is a case of "momentum <or energy> non-conservation", then you have both answered my question and proven my point (that a better model is needed).

    Sorry it took a while to get that all out. I don't think I ever claimed that I was not a bit slow in the uptake. No question, I've learned more from you than anyone else here, and about half of my physics and math professors too, rpenner. I will try and repay you by never bringing up any of these ideas on any part of this forum or any other again. It was never my intention to aggravate you.

    I only wish I could do more to thank or compensate you. I cannot assure you that someone else might pick up where I left off, but as for myself, I am all in.
     

Share This Page