Relativistic Mass

Discussion in 'Physics & Math' started by Little Bang, Jul 1, 2015.

  1. RajeshTrivedi Valued Senior Member

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    Oh ! My My !

    You know string and twistors ? String is burnt but Twistors are still intact...interesting stuff.

    ...Sometimes the forced capitulation brings in desired change than the voluntary catharsis....Enjoy !!
     
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  3. danshawen Valued Senior Member

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    Either you understand Einstein's expression for relativistic mass increase due to relativistic motion or you don't. There is ample reason to assert its validity that have litte to do with cosmology. The LHC sees the effect (inertial mass increase) every day it operates. How it is that some people claim there is something wrong with the principle of equivalence or that somehow it is disjoint with cosmology, no one has yet adequately explained.

    Energy may become bound in matter in a number of ways. Relative motion happens to be one of them. It has to be. Only if you believe somehow this effect is somehow not "real' do you get things with inertial mass traveling faster than light in a vacuum, which is nonsense, and takes it into the realm of mathematical fantasy. Exactly the way LB has pointed out, using calculus for gravitational dynamics in regions of space in which dt is different everywhere, is just erroneous.

    Mathematics without the inconvenience of bindings to physical reality yield results that are as useless as they are delusional.
     
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  5. Q-reeus Banned Valued Senior Member

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    danshawen - the obliqueness of your above makes it difficult for me to decipher, other than the feeling their is a general disagreement with #156. If you think that critique somehow contradicts anything I have previously posted here, or misrepresents your viewpoints in #149, #150, or is otherwise incorrect, please detail precisely where and how.
     
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  7. danshawen Valued Senior Member

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    A reasonable request! I still remember, it was once difficult to get those here from anyone but rpenner.

    I will put the idea into a more rigorous analysis and post it as a new math thread. You may recall, it was Newton who developed calculus (the notation was however reworked by many others since then). The underlying assumption of the calculus is still that time dilation = o everywhere.

    This will cause unresolvable math errors for any calculus that involves DISTANCE, TIME, VELOCITY, LINEAR OR ROTATIONAL ACCELERATIION, or any combination of the aforementioned, including and especially when used to analyze the gravitational or relativistic interactions that are the topic of this thread.

    You can't use things like the chain rule, the product rule, the quotient rule, nor any analogous integration methods if dt is actually not constant everywhere. And it isn't.

    Is that clear? Einstein's geometry was never the same as Euclid's, Newton's or Galileo's. I don't care who taught you that it was.

    Burn your math PhDs. They are worthless for any physics purpose other than kindling, or perhaps for analysis of static mechanical systems or velocities on the order of slugs.
     
    Last edited: Jul 5, 2015
  8. OnlyMe Valued Senior Member

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    Dan, from your first sentence above, it is not clear just what you believe Einstein's thoughts about relativistic mass were. Think about the quote below, extracted from Lev Okun's paper.

    Letter from Albert Einstein to Lincoln Barnett, 19 June 1948. Einstein wrote in German; the letter was typed and sent in English. The highlighted passage in this excerpt says: "It is not good to introduce the concept of the mass M = m/(1-v^2/c^2)^(1/2) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." (Reprinted by permission of the Hebrew University of Jerusalem, Israel.)
    Historically it seems the the relationship between inertia and mass was fairly straight forward. While I would not say that it has changed, I don't believe it is as simplistic as the historical concepts and assumptions, it is based on.

    It would seem that since our current understanding of gravity, attributes the field to both mass and energy, that if the equivalence principle is accurate (which I believe it is), the apparent increasing inertia of relativistic particles in the LHC is due not to an increasing mass, but an increasing combination of mass and energy?
     
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  9. paddoboy Valued Senior Member

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    27,543
    Capitulation?? Not really...It's called being man enough to admit to errors, which leaves you out in the cold.
    And of course as I have told you before and you are avoiding accepting that fact, your peers on this forum will judge you as they already have......and of course all of us.


    BTW.....You have not answered the obvious question about what happened to your second paper that was going to resurrect your first demolished paper.
    The answer to that is also obvious right rajesh?

    Please Register or Log in to view the hidden image!

     
  10. danshawen Valued Senior Member

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    3,951
    I agree with Einstein's assessment of relativistic mass, OnlyMe.

    Changing inertial reference frames in the relativistic universe means applying force / acceleration in a given direction. Such forces may add as non-Euclidean vectors but may never result in a relativistic velocity that is greater than c relative to any other inertial reference frame.

    Pushing something with a force in a given direction is, in some respects, similar to adding thermal energy to matter by means of infrared photons getting absorbed by electrons and increasing its temperature, except that in the case of adding additional translational kinetic energy, the object simply moves faster (or slower, if you push it in a direction opposite any previous pushes) with respect to its previous state of motion.

    If the force was instead applied to something carrying a source of photons like a laser, a Doppler shift would be observed that indicated that the energy of the source had been increased (on the approach) or decreased (as it moved away), but in either case, the energy added to the source is as real as any other kind of bound energy in the material that is moving. Matter is simply bound energy.

    If you buy General Relativity's principle of equivalence, you cannot escape the conclusion that an increase in inertial (relativistic) mass is equivalent to an increase in gravitational mass, and this is always the case to a very high degree of experimental accuracy.

    Lev Okun's paper is here:
    http://www.itep.ru/theor/persons/lab180/okun/em_3.pdf

    Your link seemed to be broken.

    Lev says:
    "… the gravitation l attraction between two relativistic bodies is determined by their energy—momentum tensors, not just by their energies.", with which I would also agree. In fact, Lev has already settled the arguments here, as far as I am concerned.
     
    Last edited: Jul 5, 2015
  11. Fednis48 Registered Senior Member

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    725
    Yay! People are actually explicitly changing their minds and coming to agreement! Science ftw.
    Rajesh, you're kind of missing the point here. Of course, as the two objects get closer to each other, both their kinetic energies and the strength of gravity between them will increase. But what I'm saying is different: that at a given distance, the strength of gravity depends on the objects' kinetic energies as well as their masses. That's a purely relativistic effect that Newton would not predict.
    Again, you make a great case for how elegant the underlying math is, but say nothing about the dynamics themselves. Saying that "their individual paths change according to the dynamics of the local spacetime curvature" is generically true, whereas I'm just looking for back-of-the-envelope insight into this specific situation. Since you say both mass and energy affect the spacetime curvature in the same way, would you agree that the objects will move towards each other more strongly if they are moving faster relative to each other?
    That escalated quickly...
     
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  12. danshawen Valued Senior Member

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    3,951
    There is no other way I can see to resolve the issue, Fednis48. This error seems to involve a good deal of math associated with physics (an understatement), but the conclusion is inescapable.

    If you can think of any other way out of this dilemma, I'd be very happy to learn about it. I probably have as much or more time / money invested in learning math associated with physics as anyone else here.

    I'm only glad I didn't spend much more time or effort learning calculus than I did. It had better change, and I don't see a means for any math that can be manipulated by a human being without it quickly becoming intractable. This idea needs to be a brand new thread.
     
  13. brucep Valued Senior Member

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    4,098
    Not to sure what you're getting at? This is the simple equations of motion
    dr_shell/dt_shell_= (2M/r)^1/2 for the falling objects local proper coordinates.
    And
    dr/dt_bkkpr = (1-2M/r)(2M/r)^1/2 for the falling object observed from remote coordinates

    As the object approaches the black hole dr_shell/dt_shell > 1 [c=1] and when the path is observed from remote coordinates dr/dt_bkkpr > 0.

    In the weak field, very large r, both measurements are essentially the same. As the two objects converge they speed up.
    A good example is to analyze the orbital paths of the binary Taylor and Hulse pulsars. For changes in pulsar velocity along the orbital path due to perturbation and the change in average orbital velocity due to the deterioration of the pulsar orbits as they emit gravitational waves. And finally what's dynamic. Gravitational radiation propagates the g field at the speed of light. The g field is the first derivative of the spacetime curvature component of the metric 2M/r. So Newton says action at a distance and Einstein says gravitational waves. Action at a distance requires the interaction to be instantaneous over distance while gravitational waves interact with the local spacetime curvature at c. Hope that is what you're looking for. Maybe one more thing. All objects emit gravitational radiation. I don't know if this would wash for a complete analysis but I like to draw a correlation between the infinitesimal gravitational waves and the infinitesimal local spacetime curvature. They're both very weak and difficult to empirically measure.
     
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  14. brucep Valued Senior Member

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    4,098
    What you said is pretty much true for Newton's model of gravity. Newton would predict that the energy per unit mass in the center of momentum frame is 0. That suggests that the only component that's involved in the gravitational action at a distance is the rest mass, center of momentum mass. This is interesting. If we choose to model the near Earth spacetime using Schwarzschild coordinates, spherically symmetric and non rotating, the earths center of momentum frame [rest frame] has rest energy per unit mass = 1 according to Einstein and energy per unit mass = 0 for Newton. Both cases should predict the earths gravitational interaction is associated with the center of momentum mass. With the relativistic theory predicting E/M_center of momentum=1 and the non relativistic theory predicting the energy per unit mass is 0. So let's ask what happens when we model the near Earth spacetime with Kerr coordinates. For this analysis we'd have to sum the earths rotation parameter, angular momentum, to the earth Schwarzschild mass to correctly answer the questions the Kerr metric is asking about the near earth spacetime. In this case the angular momentum is an infinitesimal compared to the earths mass. Other than 'for example' choosing Kerr coordinates for the near earth spacetime analysis is empirically irrelevant. For this thread everybody has cross mixed coordinate systems [theoretical models].
     
    Last edited: Jul 6, 2015
  15. paddoboy Valued Senior Member

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    27,543
    Thanks bruce.
     
  16. RajeshTrivedi Valued Senior Member

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    If this refers to any change on my side, then not at all....


    You raised the issue of increase in KE with under Newtonian in one of your posts, as follws..


    Then things got a bit changed, where you took away the Newtonian part explicitly, but still persisted with mixed terminology...geodesic, stress energy and acceleration in post...

    I had explicitly responded to both your points in separate posts as below..

     
  17. RajeshTrivedi Valued Senior Member

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    Post # 171

    Post # around 10
     
  18. paddoboy Valued Senior Member

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    bruce along with two others has you on ignore rajesh for your dishonesty and arrogance.
    So your contrived little message will not have any effect.
    But again I'll take this opportunity to ask you a couple of questions you are ignoring. You know that they are visible to the rest of the forum, right rajesh?

    Anyhow....
    Why should anyone accept your version of cosmology as a non expert without any Phd or anything remotely similar? Why should they believe you on your overall approach to cosmology, when you have continually refuted many professional experts?
    Why do you totally deny that everyone else on this forum are your peers?
    Why are you unable to accept that?
    And of course again, the paper you promised that was going to resurrect your other demolished paper and was to be released at the beginning of June...Has it been rejected?
    It's no shame to admit it you know.......just takes courage, and being a man.
     
  19. Q-reeus Banned Valued Senior Member

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    This is a corrective to #153, which presumably Fednis48 was happy with. Had neglected a few minor contributions, which in one case were precisely self-cancelling. That was the contributions of the lower 3 diagonal terms in the SET (stress energy tensor) - the principal stresses, in the case of a gas in a container. Positive gas pressure is exactly cancelled by negative container tensions, hence it remains true only microscale KE of gas molecules appreciably contributes to increased mass (plus a normally very minor contribution from collisional PE).

    In the case of a spinning flywheel, there is in addition to rotational KE, elastic energy owing to the centrifugally induced stresses - mainly hoop but also some radial component, in any case tensile. These are formally just part of the upper-left rest-energy term. In such a situation there is no positive stress cancellation of the tensile stresses, which thus contribute negatively to the overall gravitating mass. To a far lesser extent than the rest mass, but to a far greater extent than the positive contribution of elastic energy.
    I will just add here that there are some problematic issues with the GR notion of stress as source term(s), some of which I covered quite some time back but won't repeat the matter here.
     
  20. brucep Valued Senior Member

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    4,098
    Yeah it's kinda fun to read your message and try to imagine what Rajesh said. LOL^2. Sometimes I crack myself up.
     
  21. Q-reeus Banned Valued Senior Member

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    As you lacked a straight answer, here's mine. On several occasions I have mentioned the field pancakes at relativistic velocities. Several members continue under the mistaken notion all that matters is the relativistic mass/energy. If that were so then a simple 'yes' answer would suffice, but it's not that simple. Firstly, one needs to settle on the appropriate scale of the scenario - is it dominated by GR metric considerations, or just SR kinematics? My guess is the latter is what interests you - the case of a 'test mass' (i.e. small enough not to significantly perturb the spacetime curvature owing to the larger body) speeding radially towards a larger mass such as earth. Or two test masses speeding toward each other viewed from some given inertial frame, in a notionally flat background metric.

    Let's begin with the simplest possible scenario. Two test masses A and B both of proper mass m and stationary in some inertial frame S. Then the Newtonian force of one on the other has magnitude F = m.m.G/r^2, with r the separation distance. Now move to a frame S' moving at constant speed v wrt S and collinear with the separation vector r between A and B. In S' the separation distance is now reduced by the factor 1/γ = √(1-β^2), β = v/c. Also the relativistic energies are increased by factor γ. There is no gravitomagnetic interaction in this case - just gravitoelectric. Naively then one might conclude an increased force F' = γm.γm.G/(r/γ)^2 = (γ^4)F. However according to SR, F' = F, regardless of the source of F in S. We have neglected that the fields have pancaked in S'! In order to restore F' = F, longitudinal field of each mass is reduced by factor 1/γ^2 wrt in S.

    Suppose we next choose to evaluate in a scenario with the rest frame being that of mass A, with mass B moving at some constant velocity v wrt A. Given an instantaneous 'present' separation distance r as measured in A's frame, the Newtonian gravitational force of B on A is less than if v = 0, by a net factor 1/γ^2, in accordance with foregoing. On the other hand, the force of A on B is greater by the factor γ. Which does not contradict the finding F' = F given above!

    As seen from B's frame, the Newtonian force of A on B is increased by the factor γ^2/γ^2 = 1, i.e. the same as for v =0. While the force of B on A goes up as γ^3 wrt frame S. There is no real paradox - in the latter instance the instantaneous separation distance - defined in A's frame, in B's frame has shrunk to r/γ. Which frame one chooses to work from has consequences!

    For the other case (test mass + massive body) a somewhat more general situation of arbitrary relative velocities but restricted to the rest reference frame of a massive body, Okun's article gives a nice formula (16). If you want sophisticated tensor expressions, one could look at e.g.
    http://physics.stackexchange.com/qu...rce-between-two-masses-including-relativistic
     
    Last edited: Jul 6, 2015
  22. Q-reeus Banned Valued Senior Member

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    Erratum: In 2nd last para in #178, "While the force of B on A goes up as γ^3 wrt frame S.", should read "While the force of B on A goes up as γ^3 wrt the case v = 0."
     
  23. Fednis48 Registered Senior Member

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    725
    Thanks, Q-reeus; that's exactly what I was looking for. The "field pancakes" are not something I'd heard of before, but they make sense.
     
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