New Equations Go Beyond Einstein’s Theory of General Relativity

Quantum Transfiguration of Kruskal Black Holes

Artist depiction of loop quantum gravity effects in a black hole. The bottom half of the image depicts the black hole which, according to general relativity, traps everything including light. Loop quantum gravity, a theory that extends Einstein’s general relativity using quantum mechanics, overcomes this tremendous pull and liberates everything shown in the top half of image, thus solving the fundamental problem of black hole singularity. Photo Credit: A. Corichi and J. P. Ruiz.

When stars collapse, they can create black holes, which are everywhere throughout the universe and therefore important to be studied. Black holes are mysterious objects with an outer edge called an event horizon, which traps everything including light. Einstein’s theory of general relativity predicted that once an object falls inside an event horizon, it ends up at the center of the black hole called a singularity where it is completely crushed. At this point of singularity, gravitational attraction is infinite and all known laws of physics break down including Einstein’s theory. Theoretical physicists have been questioning if singularities really exist through complex mathematical equations over the past several decades with little success until now. LSU Department of Physics & Astronomy Associate Professor Parampreet Singh and collaborators LSU Postdoctoral Researcher Javier Olmedo and Abhay Ashtekar, the Eberly Professor of Physics at Penn State developed new mathematical equations that go beyond Einstein’s theory of general relativity overcoming its key limitation—the central singularity of black holes. This research was published recently in Physical Review Letters and Physical Review D and was highlighted by the editors of the American Physical Society.

Theoretical physicists developed a theory called loop quantum gravity in the 1990s that marries the laws of microscopic physics, or quantum mechanics, with gravity, which explains the dynamics of space and time. Ashtekar, Olmedos and Singh’s new equations describe black holes in loop quantum gravity and showed that black hole singularity does not exist.

“In Einstein’s theory, space-time is a fabric that can be divided as small as we want. This is essentially the cause of the singularity where the gravitational field becomes infinite. In loop quantum gravity, the fabric of space-time has a tile-like structure, which cannot be divided beyond the smallest tile. My colleagues and I have shown that this is the case inside black holes and therefore there is no singularity,” Singh said.

Instead of singularity, loop quantum gravity predicts a funnel to another branch of the space-time.

“These tile-like units of geometry—called ‘quantum excitations’— which resolve the singularity problem are orders of magnitude smaller than we can detect with today’s technology, but we have precise mathematical equations that predict their behavior,” said Ashtekar, who is one of the founding fathers of loop quantum gravity.

“At LSU, we have been developing state-of-the-art computational techniques to extract physical consequences of these physical equations using supercomputers, bringing us closer to reliably test quantum gravity,” Singh said.

Einstein’s theory fails not only at the center of the black holes but also to explain how the universe was created from the Big Bang singularity. Therefore, a decade ago, Ashtekar, Singh and collaborators began to extend physics beyond the Big Bang and make new predictions using loop quantum gravity. Using the mathematical equations and computational techniques of loop quantum gravity, they showed that the Big Bang is replaced by the “Big Bounce.” But, the problem of overcoming black hole singularity is exceptionally complex.

“The fate of black holes in a quantum theory of gravity is, in my view, the most important problem in theoretical physics,” said Jorge Pullin, the Horace Hearne professor of theoretical physics at LSU, who was not part of this study.

The research was supported by the U.S. National Science Foundation, the Urania Stott Fund of the Pittsburgh Foundation, the Penn State Eberly College of Science and the Ministry of Economy and Competitiveness, or MINECO, in Spain.


128 Comments on "New Equations Go Beyond Einstein’s Theory of General Relativity"

  1. Abhash Kumar singh | December 21, 2018 at 10:55 pm | Reply

    If v>=10c,then we can pass the black hole.

  2. Science achieved many breakthroughs this year, first the Riemann hypothesis, then the artificial sun made by China and now about this quantum loop gravity. This truly proves that nothing is impossible…

  3. In my childhood I learned about heaven and hell which are outside our realm. Now I learn about “another branch of the space-time”. It seems that some physicists publish their visions similarly to biblical prophets. Star Trek movies had shown how people can travel faster than light. Did they show how to switch to a parallel Universe?

  4. Helpful article on singularity, space time and gravity. I especially like your adding a link to the original article.
    Following are some of my thoughts on the matter. According to current theory, small pieces of randomly moving matter in space attract each other with their individual minuscule gravitational fields and thereby eventually form increasing larger amounts of matter, eventually leading to stars and planets. The high concentrations of matter warp nearby space-time and create a gravity effect.

    The Einstein field equations EFE describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. A re-interpretation of the EFE could lead to the following alternative explanation of how matter collects to form planets and stars, and how spacetime is warped by matter. Rather than matter first collecting, and then distorting space-time and thereby creating gravity effect, I hypothesize  that discontinuous areas of SpaceTime could result in concentrated areas of gravity which then attract collections of matter. In a way, this is a reversal of the classic chicken (matter) or the egg (gravity) argument.

  5. @Donald Marks: Amazing idea! The answer to the chicken, egg question would be a link between Einstein general relativity and Standard Model

    P.S unless the existence of the question itself is already the link… 🙂

  6. @Donald Marks: [brainstorming idea] imagine that this primal energy points is pushed towards or away from each other through the ripples caused by those more dense areas of matter/energy which drives us into a conclusion what are those ripples made of? Highs Field 2.0 :). Interesting thought.

  7. Thank you for the article. This is all well beyond my ability to comment upon, but I find it absolutely fascinating nonetheless

  8. Ashiq Hussain Kumar | December 22, 2018 at 7:27 am | Reply

    Though I’ve not gained much knowledge yet(self studying for engeenering) but I could say that there exists no universal law …All laws that we say governing nature and not actually accepted everywhere ,every law is restricted upto its own world!!!This is my thought!!!I know I’m mad and so just what I think I just made this mad comment!!!

  9. Jay Impellizzeri | December 22, 2018 at 11:48 am | Reply

    Does anti-singularity combine with non-locality (re: I think Bell) to demonstrate a multitude, perhaps observably preceding the appearance of a space-time singularity?

  10. “Reality is an illusion, however make your illusion worthwhile.”~Wayne Hicks

  11. Ikeyi Oghenekparobo | December 22, 2018 at 2:39 pm | Reply

    Great article!
    It seems there will never be a fully established universal theory or law after all; a new discovery will always be made, one that will disprove and extend a previously held one (no matter how reverential we may uphold the latter, or how great the postulator may be-Enstein, Newton,etc.) Einstein’s General Relativity predicts the existence of a singularity at the centre of a black hole, now this Loop Quantum Gravity theory disproves that; Newtonian Mechanics assumes a universal time frame, and Einstein’s theory says there’s no such a thing as that.
    One theory says something and a new, more robust one comes along that paints quite a different, more general picture.
    This is the nature of Physics, and Science in general. Knowledge grows, and previously held theories crumble in wake of new ones. The search for an ultimate theory of the universe will forever be elusive!

  12. Israel Ospina Londoño | December 22, 2018 at 6:26 pm | Reply

    Interesante artículo. Sobre todo muy importante ya que si se comprueba, sería el inicio o tal vez la continuación de la caída de elementos fundamentales de la Teoría de la Relatividad de Albert Einstein (si no fué un plagio a los físicos Poincaré, Lorentz, Heiysenberg y otros).
    Hace mucho tiempo estaba buscando un sitio como este.

  13. Samuel Lewis Reich | December 22, 2018 at 6:53 pm | Reply

    If one takes into account the axial Doppler shift, there is additional dimensions for time perceived by and observer of a moving object (proper time). Because there is the angle of observation in the axial Doppler shift (angle between a line from the observer to the observed and the motion). Multi-dimension time kills General relativity. For a discussion of this go to this link:

  14. If there’s no singularity then the density wont be infinite and subsequently the energy emitted by it wont be infinite too.. so by Einstein’s theory their gravitational pull would be less than that actually predicted wont it?

  15. Albert Einstein was wrong about the speed of light for which that was just his perception through a vacuum. Therefore, the speed of light is infinite in my opinion.

  16. General Theory of, not Theory of General. The theory is general, not the relativity.

  17. Math is nothing more than a linguistic metaphor, a map for describing our experiences. We must remember that the map is not the territory. Math is a linear system, and there are no strait lines in reality, just circles and spirals. Can math accurately describe these? NO!
    PI=3.141592654… :it can not be written down!
    PHI=1.618…. :it can not be written down!
    We can use math to a precision that works for describing OUR EXPERIENCES. That does not mean it is the translation of reality.
    IF people could finally find the “Universal Equation” that completely describes the universe, bringing together all the equations that they have to describe all the phenomenon in the Universe (an unrealistic expectation of “God” by my guess) they will find that the Buddha described it years ago in another language, and the Vedas before that. In math it is:
    (1=0=∞) (one=zero=infinity: we each are are nothing yet everything)
    When theoretical physicists factor in the findings of Cognitive Science they will begin to understand that.
    Or at least that is what came to me while meditating.

    • Kunjbihari sagar | December 23, 2018 at 7:12 pm | Reply

      Send me more details of it

      • I read George Lakoff ([was/is?] professor of Linguistics at the University of California, Berkley): “Women, Fire, and Dangerous Things: What Categories Reveal about the Mind”; but, with Mark Johnson, “Metaphors We Live By” may better express the Cognitive Science foundation of what I am trying to convey.
        There are only a handful of “base metaphors” on which all other metaphors are based, and all language is based on metaphors. These “base” metaphors are something like “in/out,” “up/down,” etc…
        Their theory is NOT that “Math can not be a universal language based on a reality that our bodies have evolved to comprehend,” (as I remember the Gnostic teachings to be that Math is God’s language that we are held to learn, if my history holds) but rather that “we understand Math in terms of our basic Embodied Mind’s perceptions, and therefore our comprehension of systems that don’t adhere to those perceptions (quantum physics) falls apart”.
        What does it mean for light to be a wave of energy and a particle at the same time? That is the translation of the Mathematical language through our natural linguistic metaphorical system into our perceptual comprehension. That only means WE CAN NOT ACTUALLY COMPREHEND THE MATH in terms of our Embodied Mind.
        The limits to this Embodied Mind may very well be unknowable to us. Therefore we come up with equations that seem to work, but when they are all added together, they simplify to 1=0=∞
        Or something like that, if I understand their proposition.

      • In other words:
        There MAY be some aspect of the Universe that we *can*not* comprehend because it will not fit into the categories of our perceptions; therefore we can not create a mathematical equation (linguistical expression) for it, and therefore our sum-of-equations becomes 1=0=∞. However, even that statement is misleading, because “aspect” is a metaphor based on the “parts” metaphor based on the “thing” metaphor which is rooted in our handful (pun intended) of Base Metaphors of the Embodied Mind; since we can understand “things” and “parts” therefore “aspects”, we could then ultimately understand what is is I am saying we can not.
        So we are stuck in a linguistical conundrum, and Math is very rooted in those same Base Metaphors of the Embodied Mind.
        Many call that “aspect” the “spiritual dimension”; but that uses words and therefore metaphors that we can understand.
        Taoist say that the Tao that can be spoken of is no the Tao.
        Somewheres in the Christian Bible it says God has no “name” other than “God” because naming “God” limits “him” to a metaphor, which is comprehend-able to us.
        Other “religions” say “God” has so many, many names (or in Hindu there are many Gods which are all part of the greater One), again because limiting “him” to a single metaphor is misleading us in to thinking we can ultimately comprehend “him”.

      • Finally, I ask, and subtly suggest in these comments, does the Embodied Mind and its natural ability to comprehend Math yield Meditational Experiences of Oneness with the Universe combined with the understanding that ultimately we are nothing in the face of everything, yet we are that everything? 1=0=∞

  18. The speed of light is not infinite, if it was your eyes couldn’t see colors, each color is a fixed speed that your retina and brain understand.Einstein is still right.

  19. Just as Eisteins theory took us beyond Newtons understanding. New theories like this will take us beyond Einsteins. It’s an exciting time with the competing theories about time, space and other dimensions.

  20. @Lynx: I gotchu, bro

  21. My bs meter has hit the speed of infinity my attention tubes have melted and above all else the price of eggs in China has remained the same as yesterday.

  22. @Lynx – yup!

  23. Einstein’e relativity is a wrong theory. There is nothing called spacetime in nature, not to mention the existence of black holes as singularities of spacetime. All the theories based on relativistic spacetime model are wrong. The fatal mistake of Einstein’s relativity is that it uses Lorentz Transformation to redefine time and space and the newly defined time is no longer the physical time we measure with physical clocks. We know the physical time shown on any physical clock is T = tf/k where t is the theoretical time, f is the frequency of the clock and k is a reference frame independent calibration constant. In Newton’s mechanics, f is a reference frame independent constant too. Therefore, we can set k = f to make the clock show the theoretical time i.e. the absolute Galilean time: T = tf/k = tf/f = t.

    But in special relativity, frequency is a reference frame dependent variable and can’t be eliminated by setting k = f, thus, T can never be relativistic time t: T = tf/k != t. Therefore, relativistic time is never the clock time i.e. the physical time. On the other hand, when a clock is observed in another inertial reference frame, t’ = γt and f’ = f/γ and T’ = t’f’/k = γt(f/γ)/k = ft/k = T, which means that clock time won’t change with the change of the inertial reference frame, Lorentz invariant and absolute. That is, a clock still measures the absolute time in special relativity. As relativistic time is not the physical time we measure with physical clocks, special relativity is wrong.

    The fact that physical time (i.e. clock time) is absolute has been clearly demonstrated by the clocks on the GPS satellites which are synchronized not only relative to the ground clocks but also relative to each other, directly denies the claim of special relativity that clocks can never be synchronized relative to more than one inertial reference frame no matter how you correct them.

  24. Daurrie Kesslyn | January 18, 2019 at 11:36 am | Reply

    Besides the instruction as cause for everything imminent in existence, a function of polarity as (residual) provisional augmentations of space, light was created with space at its boundaries. The structures and compositions of matter upon their creation are derived from the atomic and subatomic plenums, expressed as sine derivation with (timed-tined-polarity, two time grids – one next to one) polarity’s (spin to tine time) all collective arrangements of these tiny constituents (polarity’s sines to twine-time) for motions of all mechanical macroscopic facts. (particle-wave)

    CP Violation

    (Spatial spin speed or universal quantum field proxies, all approximate, proximate differential variable(s) restrained by (splitting) gravitation into the other forces thus combining energy/mass to quanta/time, vice versa, [these immeasurable atomic, subatomic collective arrangements, field forms of the immaterial, some subatomic parts are also immaterial as an anti-particle’s integuments] like the unconscious as conflux to human consciousness… in an electric-magnetic dual!)

    This Truth May Scare You! (2018-2019)
    Anonymous Official

  25. hiroji kurihara | January 20, 2019 at 6:58 pm | Reply

    Equivalence principle

    On a plain, imagine two gravity sources and fine circular waves (gravity). On every point, vector of two gravity acts as a resultant force and there is a point where the resultant force disappears. Next, gravity source is one. Huge elevator cabin is in free fall. Fortunately, this elevator is empty. So, resultant force of gravity and inertial force that acts on every point of the structure does not disappear.

    Sorry, I cannot receive E-mail. I do not have PC.

  26. hiroji kurihara | January 26, 2019 at 7:43 pm | Reply

    Equivalence Principle

    Let’s start from accelerated motion. Many substances (solids, fluids, etc) are moving in various accelerated motion. According to this motion, inertial force occurs. Imagine water of a current. Involvement between inertial force and gravity will be on resultant force only.《P.S.》Acceleration is not relative and inertial force is not fictitious. The two are corresponding qualitatively and quantitatively.

    Sorry, I cannot receive E-mail. I do not have PC.

  27. hiroji kurihara | February 9, 2019 at 6:56 pm | Reply

    Equivalence principle

    Free fall of an elevator will be (one of the) problems of resultant force (composition of forces). All will be explicable as a problem of resultant force.

    There are two pictures. In each picture, vector of two forces (f = f’) acting on a point are drawn. Direction of vectors is opposite (right and left). In one picture, forces are gravity and gravity. In the other picture, gravity and inertial force. Two pictures will not be the same (an infinite small area will be also).

    Sorry, I cannot receive E-mail. I do not have PC.

  28. Science will never be able to find out and understand many phenomena in the universe because it does not know the basis of the universe. First of all, no one knows what is matter, how and from what forms and how gravity and magnetism originate and who causes them. Besides this, science did not understand the sequence of formation and processes of the origin and disappearance of celestial bodies. Black holes are not the result of a star explosion. They are created under the influence of gravity, when in a given system, it accumulates so much mass that it represents a critical mass and critical gravity, when the matter returns to the form of the substance from which it was formed, and that substance is Aether that fills the infinite universe. Einstein’s Fatamagoras have been entangled in science, and to this day, many theories are unsurpassed and have no foothold in natural laws.

  29. Hiroji Kurihara | March 17, 2019 at 7:19 pm | Reply

    Gravitational acceleration

    Who started to say gravitational acceleration ? Is it a technical term really ? It seems to be an adjective.

    Is there a difference between an acceleration caused by an ordinal force ? If there is not a difference, a thing called gravitational acceleration will not exist.

    • Hiroji Kurihara | April 1, 2019 at 7:31 pm | Reply

      Turn your eyes to accelerated motion and inertial force. It does not matter what gravity is.

  30. Hiroji kurihara | May 2, 2019 at 8:03 pm | Reply

    Allow me to show new URL of my web site (service of geocities japan ends on Mar 2019).

  31. Hiroji kurihara | May 24, 2019 at 7:35 pm | Reply

    Equivalence principle

    Every inertial force is measurable. Every gravitational force is measurable also. Principally. In an elevator in free fall, there is no exception.

  32. Hiroji kurihara | May 29, 2019 at 4:52 pm | Reply

    An elevator in free fall

    Are the two indistinguishable? Vector of the two are opposite.

  33. hiroji Kurihara | May 30, 2019 at 6:05 pm | Reply

    Equivalence principle

    In space, there are two gravitational sources (point source). In the middle of the two, a small area is selected. This area will be a state of weightlessness (not zero gravity). Like an elevator in free fall.

  34. Gerges Francis Tawdrous | June 2, 2019 at 10:21 am | Reply

    Best Regards
    Why This Equation Is Incomplete One?
    The matter is created in motion (my hypothesis)
    That means without motion the matter will be perished –
    The motion here means the matter outer motion – as the moon motion around Earth- and I don’t mean the atoms motion inside the matter-
    The Matter is created with the space because the space is the necessary component for the matter motion-
    That means
    The matter and space are created from the same origin to be complementary to each other
    That’s why the previous Equation is incomplete one
    ETotal = EMass + ESpace
    ETotal = mc2 + ESpace
    This is The complete Equation
    Please read my paper
    Special Theory Of Relativity (Questions For Discussion)
    Gerges Francis Tawdrous +201022532292

  35. Hiroji kurihara | September 23, 2019 at 6:31 pm | Reply

    Free fall

    There is inumerable vectors of inertial forces and gravity everywhere. On an elevator cabin, why they are making a big fuss ?

  36. Difference of motion

    Differene of inertial motion and accelerated motion will be difference of motion relative to aether frame. And accelerated motion and inertial force are the front and back of a fact. Inertial force is not a fictitious force.

  37. Hiroji kurihara | September 24, 2019 at 1:11 pm | Reply

    Horizontal Doppler effect

    On a plane, pararell lines are drawn. On each line, light sources (frequency is the same ) are moving in the opposite direction. Imagine light sources form japanese letter エ. Phenomenon horizontal Doppler effect will not be.

  38. Hiroji kurihara | September 26, 2019 at 4:22 pm | Reply

    New equivalence principle ?

    A passenger car is accelerating (at a, to the right). A body is hung from the roof by a string. Can the string distinguish mg caused by acceleration and by gravity ? No, it is a joke. But a picture of an elevator seems to be a joke also.

  39. Hiroji kurihara | September 28, 2019 at 5:06 pm | Reply

    Accelerated motion
    Accelerated motion will be the motion relative to aether frame. Vector causes the same vector of inertial force. Gravity has no connection.

    From every inertial frame, accelerated motion is possible to know qualitatively and quantitatively.

  40. Hiroji kurihara | October 2, 2019 at 9:22 pm | Reply

    A site on anti relativity
    A web site written by member volunteers of Japan science council is now being published (in Japanese). URL is

  41. Hiroji kurihara | October 13, 2019 at 11:16 pm | Reply

    Equivalence principle
    Two forces the same vector in strength are acting on a particle from the opposite. The two are inertial force, tension and gravity. Different combinations are three. Forget the equivalence principle.

  42. Hiroji kurihara | October 16, 2019 at 3:57 pm | Reply

    Equivalence principle
    From the roof of an elevator cabin, a body is hung by a string. The elevator begins acceleration upward. Can the string distinguish between gravity and inertial force ?

  43. Hiroji kurihara | October 26, 2019 at 10:54 am | Reply

    Equivalence principle
    An elevator in free fall is explained fully by Newton. There is no room for Einstein.

  44. Hiroji kurihara | October 30, 2019 at 1:33 pm | Reply

    Gravitational mass and inertial mass
    A point mass is falling in free fall. According to the law of action and reaction, gravity and inertial force are equal. And g and a, as acceleration are equal also (direction is opposite). So, two mass are equal (mass is mass !?).

  45. Hiroji kurihara | October 30, 2019 at 6:54 pm | Reply

    Acceleration and non acceleration
    On a plane (no friction), there is a body. Difference between the two above will be evident. It is enough to keep an eye on inertial force.

  46. Hiroji kurihara | October 31, 2019 at 2:03 pm | Reply

    Inertial force
    Inertial force is depending on m. So, it is not fictitious.

  47. Hiroji kurihara | October 31, 2019 at 2:34 pm | Reply

    Acceleration and non acceleration
    On a plane, there is a body. Different between the two above will be evident. It is enough to keep an eye on inertial force.

  48. Hiroji kurihara | November 1, 2019 at 7:03 pm | Reply

    True identity of acceleration must be shown by inertial force or geometrical expression of motion starting from an inertial frame. Though it is a great formula ; F = ma, acceleration will not be connected directly to external force.

  49. Hiroji kurihara | November 12, 2019 at 8:08 pm | Reply

    Inertial force

    On a slope (no friction), a body is sliding down. Action is gravity mg. Then, how about the reaction ? It is resolved to two vectors. Inertial force is not fictitious.

  50. Hiroji kurihara | November 13, 2019 at 2:39 pm | Reply

    Equivalence principle is nonsense (I say again)

    An elevator in free fall is explained fully by Newton. No different explanation is possible. And it is the same even if limited to the infinite small area.

  51. Hiroji kurihara | November 16, 2019 at 3:59 pm | Reply

    Inertial force is not fictitious

    On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.

    There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.

  52. Hiroji kurihara | November 18, 2019 at 10:11 pm | Reply


    From nothing, a seems not to emerge. By acceleration of body relative to aether, am will emerge. Qualitatively and quantitatively.

  53. Hiroji kurihara | November 21, 2019 at 4:17 pm | Reply

    Acceleration (I say again)

    On a plane, a straight line is drawn. On this line, two bodies are receding. One is at a standstill, the other is accelerated uniformly. On the one, inertial force is emerging but not on the other. All is shown by a and ma.

    But what distinguishes acceleration and nonacceleration ? In above picture, uniform isotropic aether will be hidden. This picture is not picture of geometry.

  54. Hiroji kurihara | November 23, 2019 at 3:22 pm | Reply

    Space is rest frame

    Into space, let us draw plural vectors of acceleration a. Space will be rest frame.

  55. Hiroji kurihara | December 16, 2019 at 3:22 pm | Reply

    Elf fires

    Are there still berievers of relativity? Elf fires. It is not a thing of this world.

  56. Hiroji kurihara | January 5, 2020 at 8:45 pm | Reply

    Equivalence principle (I say again)

    Vector of inertial force is shown by an arrow. Vector of gravity cannot be shown by an arrow generally. The two are different generally as pHysics facts.

  57. Hiroji kurihara | January 11, 2020 at 8:25 pm | Reply

    Accelerated frame and non-accelerated frame

    There are plural accelerated frames and plural non-accelerated frames. The two will not be relative.

  58. Hiroji kurihara | February 14, 2020 at 2:40 pm | Reply


    Speed of light relative to mediums (water or air) is constant. Speed of light relative to aether (physical substance) is constant also. Aberrations show this.

  59. Hiroji kurihara | March 6, 2020 at 9:04 pm | Reply

    About inertial force (I say again)

    On a plane, there are two passenger cars. One is accelerating and the other is at a standstill. Difference of the motion of the two is not relative but absolute.

    On a plane, a passenger car is accelerating. On the floor (no friction), a body is put. This body is not accelerated (to everyone). In physics of 20th century, nonsenses overflow.

  60. Hiroji kurihara | March 11, 2020 at 1:10 am | Reply

    Sagnac effect

    Let’s try to explain Sagnac effect by the emission theory. There is a picture of light pathes (a light source and two mirrors form equilateral triangle). On this triangle, there are three emission points,(different inertial frames). It will be a cause of this effect.

  61. Hiroji kurihara | March 23, 2020 at 2:01 am | Reply

    Equivalence principle

    Difference between acceleration and nonacceleration seems to be more basic. If so, equivalence principle is invalid.

  62. Hiroji kurihara | April 12, 2020 at 5:26 pm | Reply

    On acceleration, there is a web site as follows.

    “Orders of magnitude (acceleration) – Wikipedia”

  63. Hiroji kurihara | April 16, 2020 at 6:36 pm | Reply

    Acceleration and nonacceleration

    A passenger car is accelerating (uniformly). A body is hung from the roof, a body is placed on the floor (no friction) and a station building. Physics seems not to distinguish the three.

  64. Hiroji kurihara | May 2, 2020 at 8:40 pm | Reply

    Perihelion shift of Mercury

    Mercury revolving is decided in two (hemisphere A facing the sun and the other B). Inertial force is A<B and gravity is A>B (center of gravity is not on the orbit).

  65. Hiroji kurihara | May 3, 2020 at 6:25 pm | Reply

    Perihelion shift of Mercury

    Yesterday’s post must be the most natural explanation of perihelion shift of Mercury. Because the value of pergee movement of the moon is remarkable (around 8.85 years). On the other hand, value of asteroids will not be found. Common explanation is not acceptable.

  66. Hiroji kurihara | May 5, 2020 at 6:20 pm | Reply

    Perihelion shift of Mercury

    Perihelion shift moves forward constantly. It cannot be explained by gravity of other planets.

    On asteroids, no perihelion shift will be observed. Some size is needed.

    Cause of perigee movement of the moon is written to be the sun. But it will be the same phenomenon to perihelion shift of planets. Not acceptable.

  67. Hiroji kurihara | May 7, 2020 at 4:39 pm | Reply

    Perihelion shift of Mercury

    The value of perihelion shift of planets is constant. It will not be three body problem or many body problem. And it will be the same to binary star.

  68. Hiroji kurihara | May 11, 2020 at 5:25 pm | Reply

    Time dilation

    Two passenger cars are passing each other. At the front of side wall of each car, the same light source (frequency is the same also) is settled and light ray is emitted backward at 45 degrees. Each ray is reflected by mirror sticked on the side wall wholely and is coming back. Time dilation is impossible.

  69. Hiroji kurihara | May 29, 2020 at 5:37 pm | Reply

    Gravity lense

    Gravity lenses are said to be a positive evidence of GR. However if gravity of gravitational source can be estimated, which is real GR or Newton’s theory will be clarified.

  70. Hiroji kurihara | June 3, 2020 at 2:39 pm | Reply

    Perihelion shift of Mercury

    “It can be safely said that gravity of other planets has no effect on the perihelion shift of Mercury”. It’s in a website.

    Imagine that with long radius of orbit of Mercury, the space of the solar system is divided into left and right. The probability that other planets exist on the two is equal. There will be no shift of perihelion in one direction at constant speed (common view is wrong).

    But main cause of perihelion shift of Jupiter and Saturn will be mutual effect of gravity. Each perihelion is shifted every moment.

  71. Hiroji kurihara | June 6, 2020 at 5:26 pm | Reply

    Perihelion shift of Mercury

    There is a model of Mercury. A long lod penetrates a true sphere and at the both ends of the lod, weights are set. This model is rotating horizontally and is moving on the orbit of Mercury (two planes fall on). Main forces acting on the weights are gravity of the sun and inertial force (centrifugal force). And each force acting on the outside weight and inside weight is different.

    Inertial force pulls the orbit to the outside. But actual orbit of Mercury is pulled to the inside. Gravity of the sun acting on the two weights is inversely proportional to the square of the distance (not come out even. not plus minus zero). In Mercury, the action of gravity will be superior.

  72. Hiroji kurihara | June 10, 2020 at 2:52 pm | Reply

    Perihelion shift of Mercury

    A model of Mercury is shown previously. Now, there are plural models. Length of lods and mass of weight each is different. These are revoleved around separately on the real orbit of Mercury. Maybe, all will be explained by Newton’s theory (including 575 arcsec).

  73. Hiroji kurihara | June 10, 2020 at 7:13 pm | Reply

    Perihelion shift of Mercury

    Value 5.75 arcsec/year seems to be an observed value. In a website, contribution of other planets to this value is shown. These are added simply !! And value 5.75 arcsec (and contributions) seems to be constant every year !! On these problems, further explanation seems not to be done.

    I say again, other planets will not be main cause of this value 5.75 arcsec.

  74. Hiroji kurihara | June 15, 2020 at 3:09 pm | Reply

    Perihelion shift of Mercury

    This is the top of tall tower. Two rods of equal mass and different length are arranged vertically (heigth of center of gravity is the same). Now, two rods start to fall at the same time. The fall of center of gravity will not be the same. Because the strength of gravity is inversely proportional to the square of the distance. This will be the main cause for perihelion shift of Mercury.

  75. Hiroji kurihara | June 23, 2020 at 9:44 pm | Reply

    Perihelion shift of Mercury

    Let’s reconsider the main cause of perihelion shift again. On Mercury or Venus, main cause will be the size of sphere. On Earth or Mars, effect of satellite is added. On asteroids each, effects of size is negligible. On Jupiter or Saturn each, the powerful and unstable effect of the other will act. On Uranus or Neptune each, slight and unstable effect of the other all planets will act. Anyway, common view on Mercury is wrong.

  76. Hiroji kurihara | June 23, 2020 at 10:03 pm | Reply

    Perihelion shift of Mercury

    Mercury has an own size as a sphere. Therefore, the sun’s gravity will have a different effect on Mercury than it does on the center of gravity. Actual orbit will be different from that the center of gravity must follow. On Mercury, it will be the main cause of the perihelion shift.

  77. Hiroji kurihara | June 25, 2020 at 6:20 pm | Reply

    Perihelion shift of Mercury

    In an binary system (formed by main star and companion star), periapis is shifted also. Motion of companion star (apsidal shift) will be depending considerably on its size. Common view (says main cause is pertubation of other planets) will be invalid.

    Main cause of perihelion shift of Mercury is said to be gravity of the other planets. But position of other planets move (also position of perihelion of Mercury moves). If so, values 5.75 secarc/year is unthinkable. Main cause lwill be in Mercury itself. And also it will be the same on values of perihelion shift of the other planets.

  78. Hiroji kurihara | June 29, 2020 at 4:46 pm | Reply

    All of propagation of light (I say again)

    Bradley found annual aberration on gamma star : Eltanin. In books, picture of ellipse is shown. However, this ellipse must be warped because of secular aberration (not only Eltanin). With this warp, the motion of solar system relative to aether must be clarified.

    Light emitted from a source in outer space will follow the emission theory. But for a few seconds only. The corner cube settled on the surface of the moon proves this.

    The motion of an observer relative to light waves is the same as the motion of an observer relative to sound waves. Light waves are light waves. An observer is an observer. And everything follows Galilean transformation.

    The speed of light in medium is c/n. The MM experiment ( done in air) is nonsense.

  79. Hiroji kurihara | July 7, 2020 at 4:57 pm | Reply

    Perihelion shift of Mercury (the truth)

    In Mercury (in terms of Mercury’s size), the non-uniformity of the Sun’s gravity may be the main cause of perihelion shift. In artificial satellites, the effects of non-uniformity of the Earth’s gravity (the position of the center of mass and the center of gravity are different) are also mentioned.

  80. Hiroji kurihara | July 9, 2020 at 5:44 pm | Reply

    Perihelion shift of Mercury (rewritten)

    Mercury is moving on the revolution orbit. The sun’s gravity is equal to the centrifugal force. Because the two are action and reaction. Following are some explanations. Centrifugal force follows Mercury’s mass. But in addition, gravity is affected by the size of Mercury (and acting position of gravity is different). These are caused by the non-uniformity of gravity (in the space occupied by Mercury). And after perihelion passage, orbit will be pulled inward (from its original orbit).

    High tide level twice a day is the same. Gravity and centrifugal force caused by the moon will be action and reaction. Centrifugal force is not fictitious.

  81. Hiroji kurihara | July 16, 2020 at 1:48 am | Reply

    Moon and earth (an essay)

    In an illustration, the moon and the earth are drawn side by side. Because of the lunar attractive force, seawater is bulged in the left and right edges of the round earth. The bulge is symmetrical. Two resultant forces pull two bulges (to the opposite direction : outward). Two resultant forces each are composed of the lunar attractive force and the centrifugal force caused by earth’s orbital motion (moves around the common center of gravity with the moon). Two resultant forces will be equal strength. This will explain that the level of high tides twice a day are generally the same.

    Also, the lunar attractive force acting on the earth’s center of gravity (not the center of mass) and the centrifugal force resulting from its orbital motion (mentioned above) will be action-reaction and will be equal.

    P.S. Is action-reaction in the sky exactly equal ?

  82. Hiroji kurihara | July 17, 2020 at 10:35 pm | Reply

    Moon and Earth (rewritten)

    Suppose the moon and the earth is two-body problem. And imagine, the earth is revolving (not rotating) around the common center of gravity with the moon. The orbit is a perfect circle. If lunar attractive force acting on the center of gravity of the earth is action, the centrifugal force of the earth is a reaction. And the strength of the two will be equal. This will be also true for the earth as a whole.

    In an illustration, the earth is drawn next to moon. Imagine two points on the surface of the earth closest to the moon and farthest from the moon. The difference between lunar attractive force and the centrifugal force of the earth at above two points will be almost equal and therefore the resultant force will also be almost equal. This will explain that the level of high tides twice a day are almost equal.

    Note: Is the law of action and reaction valid for celestial bodies on elliptical orbits ?

  83. Hiroji kurihara | July 24, 2020 at 9:26 pm | Reply

    Moon and earth (rewritten again)

    Allow me to rewrite again.

    Moon and earth are supposed to be two-body problem. Also it is supposed that the common center of gravity of moon and earth is situated outside the earth. And the orbit of earth is a perfect circle, and earth is a perfect sphere. In the illustration, the surface of earth closest to moon is A and the surface farthest from moon is B. At the two points A and B, the strength of resultant forces of moon’s gravity and centrifugal force (of earth) will be the same (act to opposite directions). Otherwise, earth cannot stay on orbit of perfect circle. This will explain that the level of high tide twice a day are the same.

  84. Hiroji kurihara | August 1, 2020 at 7:01 pm | Reply

    Moon and earth (an essay)

    As moon passes overhead, high tide (one of two high tides a day) will come after a short delay. But why ? Why is seawater with a low specific gravity bulged ? Newton imagined that moon will continue falling. Earth will continue falling also. And seawater will cotinue falling too. So, it doesn’t matter how specific gravity is.

  85. Hiroji kurihara | August 7, 2020 at 7:25 pm | Reply

    Pelihelion shift of Mercury (an essay)

    Some wide binaries are separated by one light years. And many wide binaries are at most (as much as) by 1000 au. These motion will be treated as mass points (a point). On the other hand, many close binaries are detected. What are physicists who repeat nonsense on perihelion shift of Mercury ?

  86. Hiroji kurihara | August 8, 2020 at 5:02 pm | Reply

    Moon and earth (an essay)

    Moon and earth are supposed to be two-body problem. In the illustration, the surface of earth closest to moon is A and the surface farthest from moon is B. At the two points A and B, the strength of resultant forces of moon’s gravity and centrifugal force (of earth) will be the same (act to opposite directions). It will be proved by the sameness of high tides.

    Also it will be proved by stability of orbits of each body.

  87. Hiroji kurihara | August 14, 2020 at 2:02 am | Reply

    Moon and earth (an essay)

    Moon and earth are supposed to be two-body problem. Also supposed that common center of gravity of the two is outside of earth : the orbit of earth is perfect circle : and earth is a perfefct sphere. The strength of moon’s attractive force acting on earth and centrifugal force due to revolution of earth are equal in total (as action reaction : as centrifugal force and centrepital force).

    The points on the surface of earth closest to moon is A and the surface farthest from moon is B. It will mean that the forces acting on the two points AB must be offset. It will explaine that level of high tides twice a day is the same.

  88. Hiroji kurihara | August 15, 2020 at 5:06 pm | Reply

    Perihelion shift of Mercury (again)

    The main forces acting on Mercury are attractive force of sun and centrifugal force only. Hemisphere of Mercury facing sun is supposed to be A and the other hemisphere is B. The attractive force of the sun acting on the two will be A>B, and the centrifugal force will be B>A. From the look of the perihelion shift, the attractive force acting on Mercury as a whole will be slightly stronger.

  89. Hiroji kurihara | August 28, 2020 at 3:41 pm | Reply

    Perihelion shift of Mercury (an essay)

    A celestial body called Vulcan is revolving on orbit of Mercury. It has the same mass and revolution cycle as Mercury. And diameter is twohold (the both stars are uniform in density). Since the sun’s gravitational field is non-uniform, the sun’s gravity acting on both stars will be slightly larger in Vulcan and smaller in Mercury. The value of perihelion shift also likely will be similar. In short, the size of the celestial body (close to the gravitational source like Mercury) will be the main reason for the perihelion shift.

    Imagine a cone with evenly spaced concentric circles on its surface. The non-uniformity of gravity will be exponential non-uniformity.

  90. Hiroji kurihara | August 30, 2020 at 12:48 pm | Reply

    Perihelion shift of Mercury (an essay)

    On planets, it is said that centrifugal force caused by orbital motion is balanced with attractive force of sun (and the action and reaction are equal). On Mercury, it will stand up also. But exactly ? Solar wind or some other solar- derived substances seem to go down slightly speed of orbital motion of Mercury (one of perturbation ?). If so, centrifugal force will be reduced accordingly. On the other hand, attractive force of sun will not be affected at all. This may be the main reason for the perihelion movement of Mercury.

  91. Hiroji kurihara | September 13, 2020 at 4:34 pm | Reply

    Propagation of gravity

    The propagation of gravity will be done in an instant. For this, here are two reasons. One reason is that two-body problem, many-body problem are true for celestial bodies. The other reason is that the whole solar system is in an uniform linear motion and planets are in elliptical revolution on their revolution planes.

  92. Isn’t it amazing what a spinning Top does on top of a levitating frisby

  93. Unless you know how to shrink the kids, spinning Tops make Smurfs get high

  94. Oh mary Mary quite contrary how does your garden grow…..overnight

  95. But then I can recharge wirelessly with a delighted If I choose to

  96. Hiroji kurihara | October 10, 2020 at 7:46 pm | Reply

    Centrifugal force : reconsidering

    Two mass points a and b (with large difference of mass) are in motion of two-body problem (a large, b small). One picture is in outer space, and the knot of a,b is gravity (b is in a circular motion). The other picture is on a plane (no friction), and the knot is tension of a string (the mass of the string is zero). In the two pictures, the centrifugal force of b is a vector that is on the extension line of a,b. The reaction is gravity in one picture and tension of the string in the other picture. Where and how is the centripetal force?

    Tension of the string between a and b is constant. Gravity is not constant.

  97. Hiroji kurihara | October 15, 2020 at 5:11 pm | Reply

    Inertial force is not fictitious

    Three passenger cars are moving in different accelerated motions. These are shown with the formula, F = ma, 2F = m2a, 3F = m3a. Inertial force will not be fictitious (even for those in the passenger car).

  98. Hiroji kurihara | October 26, 2020 at 3:40 pm | Reply

    About free fall

    Is there a unified explanation for free fall and similar form of fallings ? Is there a unified explanation for the local inertial frame and the adjacent spots ? Probably not.

  99. Hiroji kurihara | October 27, 2020 at 4:51 pm | Reply

    Local inertial frame

    An elevator is falling in free fall. On a horizontal plane, multiple observers are moving in uniform linear motions. For these observers, the elevator draws parabola and is in an accelerated frame. This is, the accelerated frame and the non-accelerated frame all are white and black. This means that there is no inertial frame in the accelerated frame. Even it be local.

  100. Hiroji kurihara | October 28, 2020 at 11:37 pm | Reply

    About inertial force

    In the action-reaction law, inertial force is always a reaction. Attention, action is a force and reaction is also a force. The accepted view that inertial force is fictitious force and has no reaction is unacceptable.

  101. Hiroji kurihara | October 30, 2020 at 5:31 pm | Reply

    About inertial force

    A body is placed on a plane (no friction). The body has two strings (zero mass), the left string is tied to a wall and the right string is pulled by the force ma to the right.

    Then the left string is removed. The body begins accelerating by force ma to the right. There is no change in the tension of the right string. According to the action-reaction law, inertial forces cannot be fictitious.

  102. Hiroji kurihara | November 1, 2020 at 2:03 pm | Reply

    Rotary motion (in vacuum)

    A disk is rotating (relative to the celestial sphere). At any mass point on the disk apart from the center, centripetal force is acting as action and centrifugal force is acting as reaction. Both are not fictitious force.

    Two disks A and B the same are rotating. The rotary speed of A is twice the rotary speed of B. The physical effect (of dynamics) of rotation does not extend beyond the disks.

  103. Hiroji kurihara | November 4, 2020 at 2:53 pm | Reply

    Action-reaction law (reposting)

    The original text of Newton’s third law starts with action and reaction (F=-F). But many texts in books and websites start with two bodies (objects). Why? To prevent people from realizing that the inertial force is not fictitious force, but true force.

  104. Hiroji kurihara | November 4, 2020 at 10:39 pm | Reply

    Local inertial frame

    On a plane (no friction), two elevators are separating horizontally. One is in accelerated motion, the other is in non-accelerated motion. With an accelerometer, it is possible to determine which one is accelerating. And there is no local inertial frame in an accelerating elevator.

  105. Hiroji kurihara | November 6, 2020 at 1:04 pm | Reply

    Local inertial frame

    An elevator is falling in free fall. Imagine many mass points regularly arranged in space inside the elevator. The direction and magnitude of vectors of the inertial force acting on the mass points are all the same. There will be no local inertial frame.

    Inertial force and gravity are acting on each mass point in the falling elevator. Is the action-reaction law valid for these two forces ? However, it is not problem of relativity.

  106. Hiroji kurihara | November 8, 2020 at 9:57 pm | Reply

    About emission theory

    The speed of light inside glass is c / n. And it is said that in the space between molecules in glass, light moves at c. If so, the speed of light going out of the glass (to vacuum) will also be c. The emission theory will be correct.

  107. Hiroji kurihara | November 11, 2020 at 11:39 pm | Reply

    Emission theory (restating)

    Light is emitted from two point sources. The two are moving in relative motion. Frequency is assumed to be the same. The speed of lights is the same for each of the two light source frame (wavelength is the same also). In short, the propagation of light will follow the motion of the light source. The natural explanation will be the emission theory. It is a hypothesis that emission theory is valid only for a few seconds.

  108. Hiroji kurihara | November 13, 2020 at 6:15 pm | Reply

    Emission theory

    Emission theory will be valid on the light leaving light source (in vacuum). But it will be valid for a few seconds only. And it will explain all of the behavior of light. No special treatment is needed. Galilean transformation is everything. Space-time is absolute. Goodbye Lorentz transformation. Goodbye warped coordinates.

  109. Hiroji kurihara | November 14, 2020 at 4:55 pm | Reply

    Speed of light can vary (restating)

    For an observer, speed of sound waves and water surface waves can vary. It is the same for light waves propagating through aether. It is the same also for light waves that follow the emission theory. Goodby relativity.

  110. Hiroji kurihara | November 16, 2020 at 7:28 pm | Reply

    Acceleration and non-acceleration (inference)

    A passenger car is accelerating to the right. In rear of the car, there is a light source and in front, an observer. The number of waves existing in the passenger car during acceleration will be larger than before acceleration. The difference between acceleration and non-acceleration will not be relative but be absolute. PS : Inside of the passenger car is vacuum.

  111. Hiroji kurihara | April 3, 2021 at 6:28 pm | Reply

    Space and time will be absolute (a supposition)

    Perhaps, space and time each will be absolute. Each will not be affected by any phenomenon or situation (at all). If so, relativity is impossible.

  112. Hiroji kurihara | April 19, 2021 at 7:46 pm | Reply

    Constancy of speed of light will be impossible

    Plane waves of light come from the upper left (in outer space) and is incident on two glass cubes A and B. A is stationary and B is moving upward at a constant speed. Wavelength of light in cubes is A > B. Since speed of coming light relative to the cubes is different, the wavelength in the cubes is also different.

  113. Hiroji kurihara | April 19, 2021 at 7:49 pm | Reply

    Constancy of speed of light is impossible

    Plane waves of light come from the upper left (in outer space) and is incident on two glass cubes A and B. A is stationary and B is moving upward at a constant speed. Wavelength of light in cubes is A > B. Since speed of coming light relative to the cubes is different, the wavelength in the cubes is also different.

  114. Hiroji kurihara | April 24, 2021 at 6:01 pm | Reply

    Constancy of speed of light (Reexamination)

    Constancy of speed of light is not possible always. No, it will be possible limitedly in the following two events only. Btw, speed of light in mediums is not subject of this reexamination.

    1) A geometric point and a light source are in the same inertial frame. Distance between the two is supposed to be within a few light seconds.
    2) A geometric point is stationary in aether frame. Light propagated in aether comes to this point. Distance from the light source is supposed to be more than a few light seconds.

    Translated with (free version)

  115. Hiroji kurihara | May 31, 2021 at 2:09 pm | Reply

    It will be impossible

    Constancy of light speed will be impossible. It will be clear if the formula c = f λ is looked at.
    Equivalence principle will be impossible. It will be clear if the formula F = m a is looked at.

  116. Hiroji kurihara | July 9, 2021 at 6:05 pm | Reply

    Allow me to rewrite my post (24.April).

    Constancy of speed of light (Reexamination)

    Constancy of speed of light is not possible always. No, it will be
    possible limitedly in the following two events only. Btw, speed of
    light in mediums is not subject of this reexamination.

    1) A measurement point and a light source are stationary in the same
    inertial frame. Distance between the two is within a few light
    seconds. Speed of light is c.
    2) A measurement point is stationary in aether frame. Light
    propagated in aether is coming to this point. Distance from the
    light source is more than a few light sveconds. Speed of light will
    not be c.

    Translated with (free version)

  117. Hiroji kurihara | July 14, 2021 at 3:16 pm | Reply

    Supplement to my post (July 9)

    1) In space far from light source, propagation of light follows aether frame. See again various aberrations.
    2) In space close to light source, propagation of light follows the emission theory. See again various facts.
    3) In outer space, a mirror is moving at a uniform speed. Plane waves of light of a star are reflected by this mirror. 1) and 2) must be seen as facts.

  118. Hiroji kurihara | August 6, 2021 at 5:30 pm | Reply


    Existence of aether (uniform isotropic) is precondition for Newton’s first and second laws of motion. There can be no other explanation.

  119. Hiroji kurihara | August 19, 2021 at 6:43 pm | Reply

    Aberration (reexamination)

    Aberration is caused by various motions of Earth relative to stationary aether (uniform isotropic). Light that enters upper air of Earth (from aether) is bent in the direction of motion of Earth. As a phenomenon, aberration is completed in the upper air. The same as refraction.

    Therefore, illustration of raindrops and an umbrella is NG. Result of Airy’s experiment with a water-filled telescope is only natural. It is said that apparent displacement of stars is displaced in the direction of Earth’s motion, but in fact, it will be the opposite. You can check this by drawing light bending (in upper air) on a paper.

  120. Hiroji kurihara | September 3, 2021 at 9:09 pm | Reply

    Free fall (reexamination)

    Problem of free fall in an elevator will be problem of resultant force of inertial force and gravity (nothing else). In any local area, it will be so also.
    Note: Inertial forces acting on every local area of the cabin (supposition: mass of every local area is m) is the same ma.
    Note: External force (gravity) and inertial force acting on entire cabin are equal (Newton’s second law and third law of motion). How about in local area ? To image will not be difficult.

  121. Hiroji kurihara | September 5, 2021 at 8:44 pm | Reply

    Supplement to my post (sep 3 2021)

    Even in a resultant force, inertial force is inertial force, and gravity is gravity. Vector follows own law each and is inviolable.

    Cabin is made by a 3D printer. Material is uniform.

    On a plane (no fliction), elevator cabin is moving in a uniformly accelerated linear motion (to the right). Inertial force acting on every local area (mass is m) of the cabin is the same ma (vector is the same also).

  122. Hiroji kurihara | September 6, 2021 at 6:21 pm | Reply

    Free fall (an essay)

    An elevator cabin is falling in free fall. Cabin is made up of n mass points (with the same mass of m). Free fall is supposed to be a uniform acceleration.

    Inertial force acting on each mass point is the same ma. No exceptions. On the other hand, magnitude of gravity acting on each mass point is not the same slightly. Difference depends on the position of the mass point. P.S. For the entire cabin, magnitude of inertial force and gravity is equal.

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