Deriving Newton's gravity law from Heisenberg's uncertainty principle

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Currently the biggest open problem in physics is that there is a conflict between Einstein's General theory of relativity and quantum physics. These two theories just do not talk to each other.

The problem arises when we look at space-time at small scales. According to General Relativity (GR), space-time is totally smooth. But, Quantum Mechanics ensures that space can never be smooth at small scales. Physicists hate this.

The whole goal of physics to to be provide a description of the world. But now they have two contradictory descriptions of the world.

Many physicists are working on this problem as we speak. Recently, we discovered an awesome scientific paper from a researcher named M. E. McCulloch. Dr McCulloch is a lecturer in Geomatics at Plymouth University, UK. In his paper, Dr McCulloch has shown that Newton’s gravity law can be derived from Heisenberg's uncertainty principle. Now, this is pretty amazing.

The paper is just 2 pages long and any high school student can understand this. Lets see how it works.

We can understand this intuitively as well. According to the uncertainity principle, if uncertainity in position decreases, the uncertainity in momentum increases. Now, if the radius of orbit decreases, the uncertainity in position decreases. Therefore, momentum (or force) must increase. By summing up the uncertainities over all the plank masses, we arrive at the law of gravity. The derivation also obtains correct value for the gravitational constant G.

Of course, Newton's theory of gravity has been superceded by Einstein's GTR. However, Newton's formula works for small, slow moving objects.

Dr. McCulloch is now working on resolving the discrepancy between GTR and quantum theory. Do check out his other papers on his website.

[aniruddhdeshpande]

This is clearly wrong. Delta x is not the radius. It is the uncertainty of position. Delta p is not the momentum its the uncertainty in momentum. Clearly a wrong derivation.

[KipIngram]

The paper isn't sound, in my opinion. Particularly I see "deltas" of quantities conflated with total quantities, and things like that. It's also somewhat circular - the constant G is used in obtaining the Planck mass, and then lo and behold, we get the right equation at the end. It's really just one logic error after another.

[alexanderpoltorak]

Unfortunately, this paper does not hold water. The author makes one error upon another. He is clearly lacking in understanding of the basics of quantum mechanics.

However, the idea of deriving Newton's law of gravity from the Uncertainty Principle is not new. It is easy to do in a naive form of quantum field theory, which assumes that physical forces such as gravity and electromagnetism (along with strong and weak forces) are mediated by virtual particles. We know that according to the Heisenberg Uncertainty Principle, the product of uncertainties in measuring energy and measuring time has to be equal or greater than the Planck constant h. Hence, we can temporarily violate the energy conservation law by borrowing some energy from a particle of matter (electron or any fermion) so long as we pay it back in time within the constrains of the Heisenberg inequality. In other words, the more energy we borrow, the sooner we have to "pay it back, " because the greater is delta E, the smaller has to be delta t. This allows for spontaneous creation of virtual field-particles -- mesons. For example, an electron is surrounded by a cloud of virtual photons which pop out of nowhere (by borrowing free energy from the electron in accordance with the Heisenberg Uncertainty Principle) and, after a flitting moment, being absorbed back by the electron. We note that, based on the Uncertainty Principle, weaker virtual photons (those that have less energy), live longer and, therefore, can travel further. If another electron happens to be in a vicinity of the virtual photon, it will absorb it thereby exchanging energy and momentum with the original electron and causing them to repel. Noting that virtual photons travel with the speed of light c, we obtain that the the energy of virtual photons (i.e., the potential of the electrostatic field represented by the cloud of virtual photons) falls off proportionate to the distance from the electron, or that force repelling two electrons from each other falls off proportionate to the reverse square of the distance -- the famous inverse-square law that, in the case of electrostatic field is called Coulomb's law, and, in case of gravitational field, is called the Newton's Law of gravity. Gravity, in the quantum field theory, is thought of being mediated by virtual gravitons, which immediately leads to the inverse-square law -- Newton's Law of gravity -- based on the Heisenberg Uncertainty Principle.

[samarthsai]

I think that the uncertainty in position and momentum is their standard deviation and this cannot be linked to the radius between the bodies. Please correct me if I am wrong.
Regards

[charan]

Uncertainty can't be applied to large scale objects where gravity acts on them ...
Gravity is a large scale phenomena and uncertainty is at atomic level.
You have to go to string theory or Grand Unification theory which are under Development only
So upto now GTR and Quantum Physics are

[danishsamir]

It's actually The Uncertainty Principle not Uncertainaty principle

[vpsbanna]

Such a great forming eqn and derive is so amazing The relation of heisen principal and grqvity both are Amazing

[quantumbubbles]

Thank you. This is all so well explained, making it easy to understand.
I've got just one tiny question: does this work only for a plank made of wood, or can it be any material?

[fahmi]

You can also see the paper entitled ' On the Relativistic Heisenberg Uncertainty with respect to the mass-action equivalence', written by Fima Ardianto Putra in journal of Result in Physics, Elsevier, vol;12, March. There is interesting point of view regarding the the new definition of mass that elaborate Einstein mass-energy equivalence. The author is extending it to the concept of explicit symmetry breaking and gravitation in the next paper.

[ArpanD]

The philosophy is suggestive of what you say. But mathematically we will not be able to put deltaX = radius, for deltaX approximately equals wavelength and radius of the particles is not always equal to wavelength. Moreover Fr^2/c should be hMm/m^2p^2 instead of HMm/m^2p. Anyway nice video. I like the philosophical idea.

[brianmcmullen]

Amazing stuff. Thanks for bringing more light to this theory!

[duncankilburn]

I tried this logic against Coulomb's analagous inverse-square law and found the electric charge constant would need to be 11.7x larger than it is to fit the experimental value for epsilon-zero.

This concept is interesting but p=E/c only works for particles with no rest mass so unconvinced by the 3rd step.

[volodymyrbezverkhniy]

Heisenberg's uncertainty principle: Δх * Δр ≥ ħ/2

The Heisenberg's uncertainty principle is correct, moreover, it is fundamental. If the uncertainty principle is incorrect, then all quantum mechanics is incorrect. Heisenberg's justified the ncertainty principle in order to save quantum mechanics. He understood that if it is possible to measure with every accuracy both the coordinate and momentum of a microparticle, then quantum mechanics will collapse, and therefore further justification was already a technical issue. It is the uncertainty principle that prohibits microparticles in quantum mechanics from having a trajectory. If the coordinates of the electron are measured at definite time intervals Δt, then their results do not lie on some smooth curve. On the contrary, the more accurately the measurements are made, the more "jumpy", chaotic the results will be. A smooth trajectory can only be obtained if the measurement accuracy is small, for example, the trajectory of an electron in a Wilson chamber (the width of the trajectory is enormous compared to the microworld, so the accuracy is small).

Heisenberg's formulated the uncertainty principle thus:

if you are studying a body and you are able to determine the x-component of a pulse with an uncertainty Δp, then you can not simultaneously determine the coordinate x of the body with an accuracy greater than Δx = h / Δp.

Here is a more general formulation of the principle of uncertainty: it is impossible to arrange in any way an instrument that determines which of the two mutually exclusive events has occurred, without the interference pattern being destroyed.

It should be immediately said that the Heisenberg uncertainty principle inevitably follows from the particle-wave nature of microparticles (there is a corpuscular-wave dualism is the principle of uncertainty, there is no corpuscle-wave dualism - there is no uncertainty principle, and in principle quantum mechanics, too). Therefore, there is an exact quantitative analogy between the Heisenberg uncertainty relation and the properties of waves.

Consider a time-varying signal, for example, a sound wave. It is pointless to talk about the frequency spectrum of the signal at any point in time. To accurately determine the frequency, it is necessary to observe the signal for some time, thus losing the accuracy of time determination. In other words, sound can not simultaneously have the exact value of its fixation time, as it has a very short pulse, and the exact frequency value, as it is for a continuous (and, in principle, infinitely long) pure tone (pure sine wave). The time position and frequency of the wave are mathematically completely analogous to the coordinate and (quantum-mechanical) momentum of the particle.

We also need to clearly understand that the Heisenberg's uncertainty principle practically prohibits predicting behavior (in the classical sense, since Newton was able to predict the position of the planets), for example, an electron in the future. This means that if the electron is in a state described by the most complete way possible in quantum mechanics, then its behavior at the following moments is fundamentally ambiguous. Therefore, quantum mechanics can not make strict predictions (in the classical sense). The task of quantum mechanics consists only in determining the probability of obtaining a particular result in the measurement, and this is fundamental. That is why the uncertainty principle has such a fundamental meaning (there is no uncertainty principle - there is no quantum mechanics). But this does not mean that we do not know any "laws or variables that are hidden from us", etc. No. It's just the reality. This is analogous to how a particle can exhibit corpuscular and wave properties - just this is reality and nothing more. And even if we know the "hidden parameters" (compare, understand why the wave properties and corpuscular ones are manifested), this reality will not change, and the uncertainty principle will also work, but we will understand it more fully.

It must be added that not all physical quantities in quantum mechanics are measurable simultaneously, that is, they can have simultaneously definite values. If physical quantities can simultaneously have definite values, then in quantum mechanics they say that their operators commute. The sets of such physical quantities (complete sets) that have simultaneously defined values are remarkable in that no other physical quantity (not being their function) can have a definite value in this state. The fully described states (for example, the description of the electron state) in quantum mechanics arise as a result of the simultaneous measurement of a complete set of physical quantities. By results of such measurement it is possible to determine the probability of the results of subsequent measurements, regardless of what happened with the electron before the first measurement.

If physical quantities can not simultaneously have definite values, then their operators do not commute. The Heisenberg uncertainty principle establishes the limit of the accuracy of the simultaneous determination of a pair of physical quantities that are not described by commuting operators (for example, coordinates and momentum, current and voltage, electric and magnetic fields).

Let's add a little history. A. Einstein assumed that there are hidden variables in quantum mechanics that underlie the observed probabilities. He did not like the principle of uncertainty, and his discussions with N. Bohr and W. Heisenberg greatly influenced quantum mechanics and science as a whole.

In the Copenhagen interpretation of quantum mechanics (N. Bohr and followers), the uncertainty principle is adopted at the elementary level, and it is in this interpretation that it is believed that this can not be predicted at all by any method. And it was this interpretation that Einstein questioned when he wrote to Max Born: "God does not play dice." To which Niels Bohr, answered: "Einstein, do not tell to God what to do." Einstein was convinced that this interpretation was erroneous. His reasoning was based on the fact that all the already known probability distributions were the result of deterministic events. The distribution of the tossed coin or rolling bone can be described by the probability distribution (50% eagle, 50% tails). But this does not mean that their physical movements are unpredictable. Conventional mechanics can calculate exactly how each coin will land, if the forces acting on it are known, and the eagles / tails will still be randomly distributed (with random initial forces). But it is unlikely that this experience can be extended to quantum mechanics.

The position of Bohr and Einstein must be viewed as views from different angles of view on one phenomenon (problem), and in the end it may turn out that they are right together. This can be demonstrated by lottery. Despite the fact that theoretically the results of the lottery can be predicted uniquely by the laws of classical mechanics, knowing all the initial conditions (it is necessary only to determine all the forces and perturbations, and to make the necessary calculations), in practice the lottery results are always probabilistic, and only in theory they can be predicted (try win the jackpot :). Even in this simplest case, we will be "inaccessible" to all the initial data for calculations. It is logical to assume that the quantum system will be incomparably more complicated than the lottery, and therefore, if we master the "true" laws of the quantum world, the probabilistic picture will remain, since the microworld is such in essence. Moreover, if you think about it, then our world is also probabilistic. It is deterministic only in theory, and practically, in everyday life, we can only predict, for example, tomorrow (or a second, or a year, or 10 years) with a certain probability (who can guarantee the event of tomorrow with 100% probability?). And what is interesting is that only after having lived it (by making a measurement), we can say what probability was realized. Quantum mechanics in action :).


Benzene on the basis of the three-electron bond:
REVIEW. Benzene on the basis of the three-electron bond (full version, 93 p.).

1. Structure of the benzene molecule on the basis of the three-electron bond.

2. Experimental confirmation of the existence of the three-electron bond and theoretical basis ot its existence.

3. A short analysis of chemical bonds.

4. Supplement to the theoretical justification of existence of the three-electron bond.

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[chandan]

Sorry momentum is not energy by c. It can be done when rest mass is zero but Planck masses are having rest mass . You are forgetting rest mass energy

[GoldenHay]

I think gravity is a combination of quantum uncertainty and the fundamental forces. There is probably a higher chance of particles popping into existence, or strings vibrating stronger (whatever you prefer) in the direction of other masses, which throws off the equilibrium of atoms, making them tumble/move towards the other atoms, because of the fundamental forces trying to restore the equilibrium inside the atoms, by dragging the outer particles along. Or in other words, a quantum perpetuum mobile. Can i haz No Bell prize nao?

[pavanj]

This is wrong. Because in the equation where you multiplied M/mp X m/mp X h, you got, hmM/m^2p.but you will have to get (mp)^2 or m^2p^2

[unknownnepali]

i m not a professor but great lover and stillstudent of physics.i became surprised about the derivation.there is some conncection between gr and qm.

[souravmridha]

GTR is the explanation of how gravity works....and Newtown's formula can be also derived from from Einstein GTR by approximation.here whatever you show that doesn't tell how gravity works !!so Einstein field equation is more general than one more question the example which you showed the case of massive mass we can't consider plank's mass...it is just for small mass ..so this derivation change nothing it still work for subatomic particle not for massive mass...but Einstein field equation valid for any kind of mass that is more general.

[johnnyiannello]

Title: The fifth force implies no existance of blackholes?

We know by now that Newton's formula of gravitational potential on gravity, w=G*m(r)/r, (with singularity for star radius=r=0, m(r) is the mass of the star),
is modified by the presence of the "Fifth force" (or said anti-gravity effect) given from the formula of Fischbach E. 1986
(see even Rujula A.D. 1986, Cowsik R. 1990, Thomas J. 1989, formula without singularity).
The Fischbach's formula of the gravitational potential corrected is:
w=G*m(r)*(1-a*exp(-r/L))/r
where G is the universal gravitational constant, corrected by a=0.01:0.001, which is the intensity of the fifth force, called ipercharge,
that depends on the relative amount of neutrons upon number of protons, in range L=100:1000 meters, of mass m of the star on radius r.
The question of the title if the fifth force implies no existance of blackholes, is because there is no presence of singularity
in the gravitational potential corrected by Fischbach E.:
(theoreme of De Hospital for limits).

We know that in General Relativity the Einstein's Field Equations derived from the Newtons formula, (see Weinberg S. 1972 chapter 7.1.3 and 7.1.12),
have the presence of singularity for the radius of the star going to zero: r-->0, where the metric tensor A(r)=g(rr)=1/(1-2*G*m(r)/r),
(see Weinberg in chapter 11.1.11) gives the presence of blackholes with the Schwarzschild radius (1=2*G*m(R)/R).
But if we use the corrected gravitational potential of Fischbach E. 1986 without singularity, modifying the Einstein's Field Equations;
probably the new Einstein's Field Equations shall become without the presence of singularity; it is amazing;
giving a curvature that is bounded, with radius metric tensor A(r)=g(rr)<"curvature limit".
Infact, the metric tensor in radius r is for the Schwarzschild solution (see Weinberg 8.1.7 and 8.2.11);
and you can easily verify that it hasn't any singularity, (so g(rr) doesn't approach infinite value for any radius r, neither with Schwarzschild radius).
So blackholes do not exist for the presence of the fifth force?
But another question is the neutron stars with the fifth force: how are they phenomenologically? Do they exist? And how?

The new Einstein's Field Equations depending on the formula of Fischbach 1986, looks as:
R(ij) - 1/2 * g(ij) * R = {g(mn) * A(mn) + T(mn) * B(mn)} * T(ij) where the indices of tensors are i, j, m, n=1, 2, 3, 4;

where T(ij) is the energy momentum tensor, and R(ij) is the Ricci tensor, and g(ij) is the metric tensor. A(mn) and B(mn) are to be found.

Bibliography:
Cowsik R. et al. 1990: Phy.Rev. Lett.64:337
Fischbach E. et al. 1986: Phy.Rev.Lett.57:3
Rujula A.D. 1986: Phy.Lett.180:213.
Thomas J. 1989: Phy.Rev.Lett.63:1963
Weinberg S. 1972 "Gravitation and Cosmology" Wiley.

Good Research. Bye.

[yourfather]

I request you to make a video and disscuss the whole equation in detail
Please I really need help from a person like u .. who can really explain it better
Thank u for your consideration !..