Relativistic MASS FROM TIME Dilation

[Original research to make physics understandable to We The People.]

A reason for the stall of theoretical physics in the last 40 years? Physicists have not enough intuitive understanding of physics (in particular, of what is important in physics). The phenomenon affects both Relativity and Quantum Physics. Both Twentieth Century fields are more philosophically subtle than vulgar physicists think. One needs more context than the usual credo has it.

Here is my intuitive proof of the famous relativistic mass formula. It explains intuitively an observation made late in the Nineteenth Century (19C): when particles are accelerated, they augment in mass, rather than speed. Relativistic Mass Basic

Buridan contemplated “impetus”, which we now call “momentum” = MV. When A Force Is Applied Indefinitely, V, The Speed, Stalls, While M Keeps On Augmenting.

I reveal that: The basic reason for the augmentation of “relativistic mass” is that FORCE GETS DILUTED BY LOCAL TIME… DILUTION. (This apparent play on words reflects exactly what’s going on!)

The fundamental fact of The Theory of Relativity is TIME DILATION. Time Dilation says that, when something moves fast, time there runs slows. Time Dilation is shocking to those who do not understand where it comes from (I will treat it in another essay). Time Dilation in a moving frame is not an axiom in physics, because it can be easily demonstrated theoretically, or experimentally. It comes from the constancy of the speed of light (locally, in any frame of reference).

Relativity compares physics in the frame at rest R, with physics in the moving frame, M. (So Relativity is relative, but not as relative that some physicists, in particular Einstein, have made it sound. See my future “Time Dilation”.) Say v is the speed of M relative to R (as usual, c denotes the speed of light).

Time in the moving M slows down relative to time in the resting R:

Time of M = (Time of R) [Square Root (1- vv/cc)]. This is Time Dilation.

Basics Theorems Of Relativity. Time Dilation (the middle one) Implies The Other Two. Time Dilation Is Itself A Theorem

Basics Theorems Of Relativity. Time Dilation (the middle one) Implies The Other Two. Time Dilation Is Itself A Theorem

The Local Time Equation (Middle) Implies Both the Local Length Contraction Equation, and the “Relativistic Mass: Equation

What is a force? Anything which changes momentum. Say the force F consists into a flow of particles (a bit like quanta, in a way). Let’s call it the STRAFING. The particles have all equal mass, and the same momentum, they arrive at equal intervals, and they travel perpendicularly to the trajectory of the mass m.

If m was standing still, at rest in R (the “rest reference frame”), F would progressively accelerate m (BURIDAN law). Now suppose m is moving at rest in M, that is at v, relative to R. Now in M, time runs slow. This means that m gets hit a lot more by the STRAFING.

Because visualize this: the STRAFFING (= the application of the force F) is launched inside R, the “rest frame”. But it is received in M. So the frequency of hits in M is lower by [Square Root (1- vv/cc)]. That means the force on m, in M, is lower by that amount. In other words, m in M, viewed from R, behaves exactly as if its inertial mass was not m, but m/[Square Root (1 – vv/cc)] .   Here is my little theory in a drawing (the text below will explain the details):

Force Can Be Viewed As Transfer Of Momentum ("Impetus") By Quanta. Clearly Then It Is Received Slowly Because Time Dilation

Force Can Be Viewed As Transfer Of Momentum (“Impetus”) By Quanta. Clearly Then It Is Received Slowly Because Time Dilation

The application of force in the moving frame Is DILUTED by Time Dilation. So Inertial Mass appears larger by as much as Local time is dilated.

In the drawing above, I depicted the force as applied transversally. But it could be applied from any direction: the transmission of momentum impulses would still be diluted by slow local time. Also the assumption that momentum would be quantified is no different from, say the Riemann Integral in mathematical analysis: from F = d(mv)/dt, the Buridan equation (a generalization of Newton’s Second Law), one can view the integral of the action of F as the sum of these little impulses (understanding fully may require a familiarity with integral calculus).

Questions are welcome, and let’s recap: time runs slow in the moving frame, so force applies slow. Thus mass appears huge. In the end, time dilation blocks completely the application of force F, so the particle never reaches the speed of light. The explanation is transparent, from first principles.

It could be presented in a cartoon for primary school children, and be understood, the way all fundamental physics should be.

Patrice Ayme’  

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20 Responses to “Relativistic MASS FROM TIME Dilation”

  1. pshakkottai Says:

    Hi Patrice:The moving frame is accelerating. Does this make any difference? Obviously not, so it must apply. I am impressed.


    • Patrice Ayme Says:

      Actually the moving frame is moving at a steady pace, so-called “uniform motion”: I am giving an intuitive explanation of “increasing mass” in so-called “SPECIAL” Relativity. (Poincare’ invented the notion and terminology of “Relativity”… Einstein invented (?) the difference between “Special” and “General” Relativity; the former is uniform, the latter, accelerated.)

      I did things upside down, as I should have written an essay of Time Dilation first. I think I have new, and more intuitive things to say there too. (I had an exchange with Ian Miller, who has a PhD in physical chemistry on this, and it got me to think… It’s funny because I have talked with research THEORETICAL physicists in top universities, literally, for years, and none of us got these simpler, and therefore deeper, ideas…)

      Actually, I discovered that the “general” relativity angle made time dilation more intuitive… That’s really doing things upside down, no wonder nobody thought about it before…

      Thanks for being impressed. The whole idea is to imprint people easily on Relativity…


    • Gmax Says:

      I think that’ s related to the twin paradox. If one starts with all at rest, the ‘moving frame’ gets to move because it has been accelerated. But then it moves at a steady pace


  2. brodix Says:


    A slightly separate point, but as I see it, the rest frame constitutes an equilibrium of the vacuum/space, to which motion, force and time are relative. This rest frame/equilibrium is where clocks run fastest, distance is greatest. This is obscured by time being treated as equal to space, rather than an effect and measure of the activity occurring in space. The measure of time/duration is simply the present state, as these actions occur, not external to the present. What is measured is frequency.

    Now mass is action in that rest frame and would seem to constitute a balance of forces, which if the energy of these opposing forces(longer frequency/ slower time) were reduced, less action, the mass would eventually be reduced to nothing. One way to do this would be for the frame to expand; As light.
    Mass is compressed light. E=mc2.

    So at light speed there is no mass, until it expands out so far, there is no more energy and it coalesces back as quanta, starting the cycle over again.

    Radiation is what expands between galaxies, as mass is what falls into them. So our measure of space contracts into galaxies and expands between them, in an overall cycle.

    Gravity is the vacuum created as this proto-mass coalesces, the waves contracting again, pulling it all back together.

    Fluctuation of the fluctuation.

    No need for the massive forces of inflation, dark matter, or dark energy to fill gaps in current theory.


  3. ianmillerblog Says:

    Funnily enough, Patrice, I was going to put a post on time dilation on my blog on Monday. I shall refer to your post. I like the general point you are making, but I have a question, just having read this and not giving it sufficient thought – if it is due to impulse, why is it v^2/c^2? [I may have tho think a bit more on this, but why not get you to do my thinking for me 🙂 ]

    My post will be back to my cat paradox. However, it is win accord with your thoughts because if you are right, you could change time dilation by taking the force generator up to near light speed.


    • Patrice Ayme Says:

      Dear Ian: I don’t understand your question. The key is that F, the force, is measured, in the REST frame. However the force F is applied in the MOVING frame, (because it is applied) to the moving mass. My point is that, if one visualize F as a succession of QUANTA (why not? That’s the point of the Einstein 1905 paper on the PHOTOELECTRIC effect), it is clear the application is slow, because time is slow in the moving frame.


      • ianmillerblog Says:

        Dear Patrice, Have I been too cryptic? Or writing before thought? I have given a bit more thought to this, so I shall leave it for a later post, when I shall post the link to yours.

        The question is, if you are travelling at near c with respect to Earth, what is the limit on the acceleration you can give to something in YOUR frame of reference? Your flow of whatever is conveying momenta starts in the second frame of reference at v = 0 (And no – I don’t believe that either, but I am becoming more convinced there is a background frame of reference, and Einstein was wrong in assuming that. Unfortunately, there is no way of getting observational evidence.)


        • Patrice Ayme Says:

          I also believe that Einstein made a subtle mistake which Poincare’ (true founder of Relativity) was careful not to make. About “Rest Frame”.


        • brodix Says:


          It may not be able to be inferred, but it is certainly implied by the fact that the frame with the fastest clock is closest to this universal rest frame and while there might always be a frame with a clock just a little faster, the diminishing rate of this increase points to the vacuum as having an absolute rest frame.

          I think physics makes a mistake in trying to dismiss space as simply an effect of measurement, because if we eliminate all physical attributes from space, then it still has the non-physical qualities of infinity and equilibrium, having nothing to limit, disturb, or bend it.

          Which as it then is not needing any physical cause, presents a formidable foundation for the rest of physics. The fluctuation arising from/disturbing this vacuum.

          Three dimensions are really just the xyz coordinate system and are a mapping device. They are no more foundational to space, than longitude, latitude and altitude are foundational to the surface of this planet.

          They define the volume, area and distance from a particular point of reference, the zero point of the coordinate system.

          As an ideal of location, the zero point is an oxymoron, as having zero dimensionality, it has no location. Much as a zero dimensional apple has no location, or the shutter speed of a camera set at zero has to picture.


  4. Gmax Says:

    I think I got it. The force applies slowly because the time is slow in the fast thing. But then why is that, and why the fast is not slow and the slow fast? See what I mean?


    • Patrice Ayme Says:

      Well, yes, the relativity of frames is not completely relative. I intent to write a time dilation essay, gluing together versions of comments I made to Ian Miller… My version of time dilation has ORIGINAL elements… Which make the situation easier to grasp, I claim


  5. Patrice Ayme Says:

    [Sent to Ianmiller blog, about the cat/twin paradox.]

    I deduced mass dilation from time dilation [original research!), so I feel rather fierce.

    And I agree there is a rest mass problem. Poincare’, the founder of Relativity, saw it, and Einstein, Poincare”s parrot, did not. Something about the brain limitations of parrots.

    This being said, I don’t see the problem here. First, cats are nice. So why don’t you put Horatio in your spaceship? it would provide you with company, and would make become batty more difficult (cats eat bats).

    Let’s put numbers on it. Say one accelerates at g, Earth gravity. After a day or so, the rocket ship will get so close to light speed that its gamma factor, 1/square root [1-vv/cc] would be around 100. That means a round trip to Eridani will take 21 years, Earth time, but only two months and a half, ship time. So Horatio will be just be fine.

    I will write two essays on the general subject. First, I agree there is a preferred rest frame (so did Einstein, decades later, if one reads between his lines!)
    Second, the acceleration is truly a General Relativity effect. So the Twin Paradox belongs to GR, not SR.
    Third, Quantum Physics proves Einstein wrong on time. And Bergson right (people can google the names).

    Ian Miller:


    • Ian Miller Says:

      on March 29, 2016 at 6:28 am said:

      I put Horatio in a different ship to ensure there was a third object viewed externally from two different frames of reference. The point I was trying to make is there is a preferred reference frame; of course you can calculate the right end point, BUT according to most text books, and as far as I am aware, Einstein, all frames of reference are suppose to be of equivalent status.

      Acceleration belongs to GR, but the coasting still belongs to SR. Time is additive. Mass is an interesting concept, and thoughts belong elsewhere.


      • Patrice Ayme Says:

        The point is that at 100 gamma the PROPER TIME back and forth to Eridani is only two and a half month. At the speed of light, it takes zero time (OK, it’s impossible to get there, agreed).
        The question of having an absolute rest frame at any point of space is a different matter entirely.


        • Ian Miller Says:

          on March 29, 2016 at 8:54 pm said:

          Agreed. As an aside, you will often see people talk about absolute rest masses. That only makes sense if there is an absolute rest frame of reference.


  6. What is the cause of the Lorentz contraction? | ianmillerblog Says:

    […] you also get a corresponding mass increase for a physical reason rather than a mathematical one ( ). If I have this right, the argument is that if time dilates, then collision of the object with […]


  7. Patrice Ayme Says:

    [Sent to Ianmiller blog, April 18, 2016.]

    Neither Poincare’, nor Einstein, thought greatly of “spacetime”, an invention of Einstein’s professor (who did not himself think highly of Einstein as a student: he called him a “lazy dog”).

    Poincare’ said that “spacetime” was a useless complication (but I think he mulled over a much deeper critique, which I will imminently proffer). Quantum Physics does not treat time and space on the same footing. At all. However, QFT makes time imaginary, and then treats it as if it were space (don’t ask…)


  8. “Proof” That Faster Than Light Communications Are Impossible Is False | Patrice Ayme's Thoughts Says:

    […] There are theories everywhere, and the more ingrained they are, the more suspiciously they should be looked at. From the basic equations of relativity it is clear that if one adds speeds less than the speed of light, one will get a speed less than the speed of light. It is also clear that adding impulse to a mass will make it more massive, while its speed will asymptotically approach that of light (and, as I explained, the reason is intuitive, from Time Dilation). […]


  9. Patrice Ayme Says:

    Genesis Poincare Relativity: from Seminaire Poincare!

    Click to access darrigol2.pdf


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