Gravitational Time Dilation Explains Dark Matter




 by Jose Gregorio Baquero



In a similar way of how relativistic length contraction explain electromagnetism, relativistic effects explain the observations evidencing the existence unaccounted gravity attributed to Dark Matter around galaxies and galaxy clusters. When all forms of traveling energy quanta get closer to galaxies get delayed due to gravitational time dilations. Ultimately the accumulative effect is a substantial increase in energy density when seen from a frame of reference far from the center of galaxies in an Density Wave like mechanism. That increased energy density is imperceptible for an observer within the galaxy’s inner frames of reference.  The higher concentration of travelling energy around galaxies in effect has an equivalent relativistic mass that is creating extra gravitational distortion in spacetime. This extra gravity is at least a substantial part of the unaccounted gravity attributed to Dark Matter.


From the beginning of existence all forms of energy’s own movement created and still is creating new fabric of spacetime. Every unit of volume of space in the universe is being crossed from all possible spatial directions by traveling energy   quanta in the form of neutrinos, electromagnetic  waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of waves and particles yet to be discovered. The lines traced by each quantum of energy (world lines) can be seen as fibers that intersect themselves in a way that they weave spacetime fabric. The “fibers” of this Energy Felt get denser around galaxies and galaxy clusters. Any field studied by quantum mechanics is a manifestation of the Energy Felt in a particular range of frequencies of the energy spectrum.

Using a thought experiment this document proves that traveling energy quanta (neutrinos, electromagnetic  waves, gravitational waves, cosmic rays, stellar winds, emitted vacuum energy and all other kinds of energy and particles yet to be discovered) are getting relativistically accumulated around galaxies and galaxy clusters and must be considered as an important factor on the total gravity around cosmic structures.

Explaining “Observed” Dark Matter using General Relativity

Let’s imagine two identical laser pointers, Pa and Pb. Pa is going to be pointing in that way that its emitted photons (A) will pass parallel to Andromeda Galaxy galactic plane, at a minimum distance of one radius of Andromeda (Ra). Similarly Pb is pointing perfectly parallel to Pa in a way that its emitted photons (B) will pass at a minimum distance of 10 times Andromeda Radius (10Ra), for simplicity let’s omit gravitational lensing distortion. We set two light detectors, Da and Db at the other side of the galaxy in order to catch the photons emitted by Pa and Pb respectively.


General Relativity tells us that there is a different gravitational time dilation on the two different frames of reference; the frame of reference at Ra distance to the galactic plane and the frame of reference at 10Ra. For a rough calculation let’s use  Andromeda’s mass including Dark Matter and calculate time for the two frames of reference at the moment when each photon gets to its closest point to the galaxy’s center.


There is a gravitational time dilation ratio (Ta/Tb) of 100.002% at the instant when the photons are closest to the center of the galaxy.

If time dilation for photons emitted by Pa were to remain constant along the 220.000 light years across the galaxy the photons hitting Da would take 161 days more than the photons hitting Db as measured by a clock on Db , but this is not the case. The gravitational field varies through the photons voyage.figure-2For all photons traveling on a plane parallel to the galaxy disk at Ra distance the ratio (Ta/Tb) decreases when the photons are farther away from the center of the galaxy depending on the actual mass-energy distribution of the galaxy. This is better visualized  by a tridimensional distribution curved surface.figure-3Generalizing the time dilation ratio for two different radii (r, Ȓ) we can have:

Average Time of Relativistic Accumulation for a Static Frame of Reference at R

figure-4To calculate an average of time dilation ratio  as measured on a static frame of reference we will integrate spherical surfaces (onion layers) multiplied by time dilation ratio while the radius varies and our product will be divided by the volume for Ȓ. Our approximation will use mass including Dark Matter as if it were inside an hypothetical black hole our integral will be calculated starting at Schwarzschild radius  (rs)  all the way to a non orbital (static) radius (Ȓ ).

The average time of relativistic accumulation   for a sphere with r=Ȓ  as measured on a static frame of reference:equation-4This means that on average a traveling photon (boson or any relativistic particle) will stay at least 27 days longer inside the sphere with the radius of the galaxy  as measured on a static frame of reference at R

Average Time of Relativistic Accumulation for an Orbiting Frame of Reference

If we calculate the average of time dilation ratio  as measured from a orbiting star (frame of reference orbiting the galaxy) we will have to use the time dilation for a circular orbit for a given orbital radius (R ), a constant, as our denominator and for our numerator we will have the integral from the Schwarzschild radius  to orbital radius ( R) of all spherical surfaces (onion layers) multiplied by time dilation ratio (non rotational) while the radius varies. The result will be divided by the volume for R. This approximation also will use mass including Dark Matter as if it were inside an hypothetical  black hole.


For mathematical model and testing with rotation curves:!AtzwZU8adFtMhYpzKbtPUKY6LnFYCg!AtzwZU8adFtMhYpU_xcjcfnKlyKlow

This means that on average a traveling photon (boson or any relativistic particle) will stay about 1.76 seconds longer inside the sphere with the radius of the galaxy  as measured on a orbiting frame of reference at R

Energy Felt Density Needed to Account for Dark Matter

Let’s imagine the Volume of Accumulation (U)  by multiplying the surface of the sphere with radius (R ) times the distance a photon travels in the time of accumulation. The before mentioned Volume will need to have an Energy equivalent mass equal to the “observed” Dark Matter mass calculated for that particular orbital radius (R ) using the orbital velocity (V). Therefore the Energy Felt Density ( ) will be calculated by dividing the energy equivalent for Dark Matter Mass by the Volume of Accumulation.

Energy Felt Density calculated for a static frame of reference:

For mathematical model and testing with rotation curves:!AtzwZU8adFtMhYpzKbtPUKY6LnFYCg!AtzwZU8adFtMhYpU_xcjcfnKlyKlow

Gravitational Lensing and Rotation Curve Discrepancies

When an observer on Earth calculates Dark Matter mass by  measuring the bending of light caused by Gravitational Lensing there is a discrepancy with the calculated Dark Matter mass calculated from rotation velocities. While the rotation velocities calculation uses the orbiting probe at radius R (stars, dwarf galaxies, etc) frame of reference time dilation; the calculation from gravitational lensing uses the observer’s orbing frame of reference time dilation. This is needed since the observer becomes a part of the system (e.g. moving observer-rainbow system).

Discussion and Conclusion

The Dark Matter phenomenon explained as the Relativistic Accumulation of Mass-Energy allows us to mathematically calculate an approximation to Energy Felt density for a first time. No other phenomenon had given us the most remote chance to observe a quantifiable manifestation of this energy. Current Vacuum Energy Density (10^-9 joules/cubic meter ), calculated from universe expansion observations, differs greatly with predictions from quantum electrodynamics (QED) and stochastic electrodynamics (SED) where it is required a value 120 orders of magnitude larger (10^113 joules/cubic meter). Our calculated Energy Felt Density values indicate that there is a much higher energy density across the universe and that the observed values correspond only to the resultant of positive and negative (e.g. potential, gravitational) energy density interactions.

Cosmologists agree on being an inflationary period in the early universe where similar energy (in nature but not in magnitude) to that of observed Vacuum Energy rapidly inflated the universe exponentially in a very short period of time. It is currently believed that most of the inflaton field energy got transformed into other types of radiation and matter particles which density were diluted by further expansion of the universe. It is not completely ruled out that the remnant of that energy is still been created across the universe in ways that are very difficult to measure experimentally although Casimir Effect experiments have demonstrated the existence of such energy. Some cosmologists believe that a small oscillation on the current Vacuum Energy value could be responsible for the creation of Dark Matter.

As an analogy, we could think of the universe as the proverbial inflating balloon whose surface represents our spatial dimensions. Our balloon now is a special one; it is made out of latex fibers that when stretched won’t break. Rather, the fiber will separate slightly allowing  the air to escape through the miniscule holes. With an initial colossal  air pressure the balloon started inflating at an exponentially accelerated rate while all the air was contained (when energy density was so high that that energy acted, effectively,  onto itself). During the inflation period there was very little cooling in the universe since all new space created had new intrinsic energy created with it. There was matter formation; that is there was creation of elementary particles but they rapidly decayed back to energy because of the high temperature and continuous energy bombardment. There is the point when the balloon latex fibers got stretched and very little air started to escape. The universe started to cool down at a greater rate allowing for a big part of the remnant energy to transform into elementary particles like neutrinos and electrons. Cooling allowed quarks to form and after it photons were able to travel through space. The balloon rapidly slowed its inflation since not only  the air pressure diminished but at the same time the remnant pressure was less effective at inflating it. This analogy illustrates how nowadays the universe can have a higher vacuum energy density than that calculated from current universe expansion rates.

Also, it is currently accepted by the scientific community  that neutrinos, specially primordial neutrinos, make out at least 10% of Dark Matter (Hot Dark Matter). This estimate is not taking into account the mechanism described on this paper. A bigger contribution has been ruled out because neutrinos are traveling at relativistic speeds; that is higher speed than any escape velocity (at any possible orbit). The phenomenon here described- Relativistically Accumulated Mass-Energy- can easily explain a significant accumulation of Hot Dark Matter not previously accounted by any calculation previously performed.

A star orbiting at Ȓ distance from the center of the galaxy will “feel” the combined effect of the gravity generated by the baryonic mass and the relativistically accumulated mass-energy inside that sphere. All the mass (baryonic and relativistically accumulated mass-energy) located outside that sphere is also “felt” but its gravitational net effect cancels out. This is similar to calculations for an object falling through a hole towards the center of a planet where its acceleration only depends on the mass of a sphere with a radius equal to the object distance to the center of that planet. Furthermore, we do not have observations of the gravitational effects of Dark Matter taken outside of the Milky Way and time in our frame of reference is dilated differently to time at a point far away from the Milky Way. Our observations therefore should show differences with those of an observer outside our galaxy.

In the space between galaxies energy density gets higher than that of the surrounding space because of both galaxies’ gravity compounded effect. These structures connect galaxies and galaxy clusters together forming the Cosmic Web. Dark Matter concentration ratio is different for different galaxies and galaxy clusters, not only because differences in mass distribution but also because galaxies have different masses. In addition, younger galaxies do have less Dark Matter in proportion to regular matter  since the mass-energy relativistic accumulation has a compounding effect over time: The higher the energy density ratio; the more mass-energy relativistic accumulation, the more mass-energy relativistic accumulation; the more gravity, the more gravity; the more mass-energy relativistic accumulation. Even though in the early universe energy density was higher, that density was more uniformly distributed. That means that the further away we look to younger galaxies, the less Dark Matter we should find. What causes the mass-energy relativistic accumulation is the difference in energy density close to the galaxies in comparison with that of the galaxies’ surrounding space.

Traveling Energy particles and waves that come from outside the galaxy are not rotating with the galaxy. They will pass by if unobstructed. The time dilation on the frames of reference when close to the galaxy is greater specially if compared with orbiting frames of reference at a greater distance . Similarly to how relativity (length contraction) explains electromagnetism, relativistic particle and waves density is higher in the frames of reference closer to the galaxy than those far from the galaxy. In a way, there is a reservoir of traveling energy around galaxies that is constantly renewed with new energy.

It is this paper conclusion that there is no need for particularly special particles forming Dark Matter substance or even parallel universes’ escaped  gravity to account for the extra gravity existing around cosmic structures.  In a way, Dark Matter is just traveling energy. The purpose of this paper is to demonstrate the mechanism for mass-energy relativistic accumulation around galaxies and calculation for actual Dark Matter accumulated by this phenomenon will need to be performed using more precise models. Einstein was right and his findings continue to enlighten our understanding of the universe.



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58 thoughts on “Gravitational Time Dilation Explains Dark Matter

  1. Hi Gregorio 🙂
    While I did come to this idea in a different way I have great appreciation for the work you have put it. Have you modeled it on a computer yet? I would really like to see a visualization of your math. Perhaps someone can assist you. I have a tab up in my browser, yesterday they released the first image of black hole, and I am here posting to your blog because I have a very strong hunch a picture of your model, from even an animation (while organics are not out of the question), would be even more impressive, if indeed your math is correct. Thank you and Godspeed.

    Liked by 1 person

  2. Would your relativistic theory expand to include Casimir cavities? do the longer wavelength virtual particles also still exist inside the cavity imperceptible to a local nano observer? current theory says they are included but a relativistic interpretation of Casimir effect might explain some things better.


  3. This is very interesting. I was suspecting such an effect, and I found your blog/paper ! Have you published this as a paper ? I would like to read scientific community’s opinions on this.


  4. Hi i was about to write an article along this lines of approach towards dark matter. It is similar but entirely different. I would like to coauthor with you a different article. Would you be interested?


    1. I do not quite understand your statement:

      “If time dilation for photons emitted by Pa were to remain constant along the 220.000 light years across the galaxy the photons hitting Da would take 161 days more than the photons hitting Db as measured by a clock on Db , but this is not the case. ”

      The time taken for the photon is the same for both sensor is exactly the same, assuming that the distance are identical. Light travels at exactly the same speed.

      On the contrary in GR, the space nearer to a gravitation well contracts just as how in SR , length contraction take place with time dilation. Thus the photon would take longer near to the gravity well, but due to a relativistic need to travel more space but not due to time dilation as you pointed out. In fact, in SR Einstein assumed the speed of light is constant from any pt of reference and derived that space and time is not Lorentz invariant.


      1. “the contribution from the change in path, being of second order in M, is negligible” from
        Only when photons are traveling close to black holes or neutron stars the contribution due to extra path in 3D are accounted, otherwise the delay due to extra path is negligible.
        In a galaxy a tiny percentage of possible paths pass close to black holes. For the purpose of calculating average delay it was not taken into account for that reason.


      2. Thank you for the speedy reply. The path extension is as significant as the time dilation compared to an observer in flat Mìnkowski space time. There is no time delay for photon in any frame of refrence. Space time will have to curve to preserve causality among all events.


      3. I think the article extra path contribution on average is very small, if something it would increase the effects in a tiny portion. I could not find a simple way to calculate that contribution anyways. As is, the model reproduces perfectly the rotation curves in all tested galaxies without free parameters. It explains gravitational lensing discrepancies, it predicts the minimal extra gravity effects close to galaxy centers. It also predicts rotation speeds to rise again at the outskirts of spiral galaxies. It presents an explanation to big scale observed phenomena like bullet cluster and cosmic web formation.
        It also suggests how the baryonic oscillations in the Cosmic Microwave Background could have been formed with a similar mechanism.
        What is important is that the delay is real and given the right traveling energy density the proposed mechanism actually reproduces the rotation curves observations perfectly, an impossibility for any other existing model.


  5. Thank you, Gregorio. Although the maths is way above my head, this explanation for the gravity assigned to “Dark Matter” is more palatable to me than the ghostly theory in the Standard Model.


    1. Thank you for you support.
      Although, what I claim is that it is not necessary to extend the standard model of physics to explain the extra gravity attributed to “Dark Matter”. The main reason for that is that none (not even the recently claimed success of the Self Interacting Dark Matter models) can reproduce perfectly the rotation curves as this model does. Matter particles simply can’t reproduce the behavior of galaxies in inner orbits.


  6. One problem here: your assumed mass for andromeda looks to be the *virial mass* of Andromeda (in astrophysics these numbers are always in solar masses – for M31 Mvir is ~2 x 10^12 solar masses, which looks to me to be pretty close to your mass in kg). But that value is for the mass *within the virial radius*, which for M31 is ~300 kpc, *not* the ~30 kpc you’re assuming here (which I think you got from the M31 wikipedia article’s “220,000 light years” – note that that is *not* any particularly physically meaningful value – it’s just a rough “how big it looks” number). So your effect would appear to be 1000x too *strong*, as the volume the effect would operate in would need to be some 10x larger…? If the effective mass was that large, M31 could not exist as it is observed to, as the required rotation speeds and mass profile would dramatically alter the spiral structure (and would also be inconsistent with the observed speeds of the satellite galaxies of M31).


    1. Because of your observations, I went back and recalculated vacuum energy density using 250km/s orbital velocity (instead of 301km/s taken from Wikipedia article). The model is giving me now 2*10^7 joules/m^3. This made me think that the mechanism is not that sensible to mass as it is to size (radius^3).


    2. Thank you for your feedback. On the actual model, I calculated mass at the edge of the visible disk from a given rotation speed at that radius, This model can be improved if the mass inside the Gaussian surfaces varies in function of the variable radius for its integration. The whole point of the exercise is to demonstrate how this mechanism can increase the curvature of spacetime. If vacuum energy values are as predicted from Casimir Effect Experiments-Theory then a more refined model could actually measure that energy density value. Thank you again for your input.


  7. Hi,
    My wife told me you had suggested I contact you after reading your article on 37 THOUGHTS ON “GRAVITATIONAL TIME DILATION EXPLAINS DARK MATTER. As one reader commented: His math was a little rusty…), so is mine! However, I think I understood most of the math and understood your hypothesis. The Article was not difficult to read and I was pleased to find someone like you who was willing to take a risk and Hypothesize a possible solution to the mysteries of dark matter and energy.

    Liked by 1 person

    1. Thank you for your comment. Some physicists have criticized the idea to be too simple; I responded that as simple as it should be. It seems that there is an expectation for a complicated explanation or at least weird extensions to the standard model of particle physics to get this mysteries solved. Did you read both posts?


  8. My understanding leaves me believing this is not an explanation of what dark matter is, but rather this is a thought experiment that justifies its presence?

    Has it been explored the idea that dark matter or dark energy are the result of the junctions between gravity waves from different sources and that the amplification of the waves as they compliment each other somehow strengthens the weak force of gravity? In a way this could be compared to how sound waves are amplified when the wave peaks meet instead of cancel each other out.

    I am a building science analyst so this is well outside my educational realm, but I am deeply absorbed in the topic.

    Liked by 1 person

    1. This is an explanation of the gravitational effects attributed to the misnamed “Dark Matter”. The only direct measurements of vacuum energy so far have been given by the Casimir Effect at very small scales ( less than a micrometer). For bigger scales the effect is negligible but the energy is there regardless. We know very little at this time.

      Liked by 2 people

      1. It just seems logical for myself that existence is layered and builds higher and bigger until seen by humans and instruments. Probably on top of a negative or ghost particles on up to positives and large chemical masses. But I enjoy your material Greg. We may never get complete answers about our eternal recycling machine.


  9. Do you agree with the claim, that DM (travelling energy particles) is oscillating around massive objects without friction, its movement can be simplified by undamped harmonic oscillator (I found that on stackexchange – though this simplification was mocked by some other users)? Do u think that dark matter particles are constantly moving across the universe from one gravitational center to another? So they can exchange in gravitational net? Thank you for computing Gravitational Felt Density in different reference frames.


  10. “Dark Matter” is the result of Dark Energy, cP.

    V=25e 1.25u I/3m=(e/m)u.25I/3

    The I is the current of moving suns and the inflow of electrons, e! This is a Galactic Motors!


  11. here me out on this, as it’s coming from a comic website but check out the work the author does. It appears quite similar. Perhaps these guys could work together. He goes into discussing the idea of something he calls “Social Understanding reflex” Which is not what you’d think. It covers the topic of multiple forces interacting with each other from a person perspective to a galactic scale. Would you say this is relative work?


  12. Enjoyed reading about the many sub-Particulate world. +plus- or ghost matter. The fabric of dimension layers equalize through wormholes. Much like a pressure relief valve and unseen. Infinite recycle of matter, gases ect ect. Anyway i’ll stop’ Take care. P. Coleman~


  13. Looks beautiful.
    > take 161 days more
    Did you calculate the same, say, for the center of Galaxy (so w/o dark matter included) in _|_ direction of laser lights?
    Sorry, if it’s a stupid question, I left astrophysics many years ago and feel lazy to ponder the subject and check it on my own now.


    1. If I am right.
      Dark Matter should be called Dark Equivalent Mass.
      All forms of travelling energy (mainly vacuum energy) gets delayed around cosmic structures (Shapiro Delay). The net effect of the delay is extra spacetime curvature due to higher energy density differentials.

      Dark Energy is a little more difficult.
      Spacetime itself aka existence is made out of energy. Its quanta emits (Dark Energy) and absorbs(Gravity) energy. On my second blog I study one possibility for the nature of Dark Energy and Gravity phenomena.
      Thank you for your interest.

      Liked by 1 person

      1. What about the dark energy is around the cosmos …..and dark matters are the outlines and take place in every blank vacuum to push dark energy on its limit??
        And what if the dark energy maintain the blackholes high gravitational power and through this ,the singularity creates another “big bang “!!! And the cyclic process still goes on???


      2. I cannot comment on that. I can only go as far as the current proven scientific facts an mathematical logic takes me in order to formulate an hypothesis. If you can adjunct evidence that support your ideas then please write them down. I will be glad to read it,


  14. Really excellent but my math is way too rusty i really hope it turns out that you are right becasue the current theories all amount to a bunch of “we got nothing so hopefully this sort of explains why we have nothing” without ever giving us “something” else that explains it all with less NOT more vague hadnwaving.

    Liked by 1 person

  15. Thanks for following sciencesprings. I appreciate it very much. You can see the difference between what you do and what I do. You are obviously a very talented scientist and writer. I am not any kind of scientist. I pick up existing material I find in social media and take it out to about 800 non-specialists who do not otherwise see any science because the mainstream press presents almost nothing to the public.

    Liked by 2 people

  16. Gregory great blog. Congratulations.

    Even though I haven’t get into the dark matter discussion and study, I found your blog very interesting due to the mystery of dark matter and its complexity that only a few will daring to place in a paper.


    Liked by 2 people

    1. I did not find any paper, video, or any piece of information that explained the phenomenon I describe on the paper. And yes, if I am wrong I respectfully ask for the science community forgiveness for my audacity at trying.

      Liked by 1 person

      1. Well, Bravo for daring……only the dreamers will get to the place they dream of.

        “Daring ideas are like chessmen moved forward. They may be beaten, but they may start a winning game.”
        ― Johann Wolfgang von Goethe

        Liked by 2 people

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