1) Deep learning has achieved breakthroughs in machine learning but is limited in its ability to generalize and its lack of explainability. It is also purely a "black box" approach.
2) Both specialized and general intelligence exist in humans, but the source of human intelligence is still not fully understood. General intelligence allows humans to learn new skills but humans do not understand the mechanisms behind their own intelligence.
3) The author proposes a new framework for artificial intelligence based on optimizing knowledge representations from an information theory perspective. This framework aims to explain the source of learning abilities like generalization and improve machine learning capabilities.
5. Reconciling Einstein’s Relativity
with Quantum Physics
From quantum wave propagation to curved spacetime and invariance of the laws of physics
Re-establish Einstein’s general relativity on the solid foundation of quantum physics
Xiaofei Huang, Ph.D., Foster City, CA 94404, HuangZeng@yahoo.com
破解爱恩斯坦广义相对论，统一物理学基础
A simple mechanism for gravity and relativity
• Why gravity can be treated as curved space and time?
• Why a point mass moves along a geodesic line?
• How the laws of physics appear to be the same in all inertial
frames with and without gravity?
Relativity=Equality for All Inertial Frames with and without Gravity
6. Einstein’s relativity belongs to classical physics
In Einstein’s relativity, a photon moves as point-like object with a definite position and velocity at any given
time. Based on that picture, Einstein’s light clock and light ruler are designed to explain time dilation and
length contraction. With the same point of view, the classical motion equation for light, 𝒄 𝟐
𝒕 𝟐
− 𝒙 𝟐
= 𝟎, has
been used to derive the Lorentz transformation, a key transformation in relativity. Also, his geodesic
equation describes the motion of a point-like object in a gravitational field. In his theory, the spacetime
metric 𝒈 𝝁𝝂 is used to define the gravitational potential.
However, all of those are approximation at the classical limit, just like F=ma. They are valid at the
macroscopic scale, but not the microscopic scale. In the quantum world, no photon or any other particle
moves like a point object with a definite position at any given time instance. Instead, it moves like a wave
without a definite position at any given time governed by quantum laws.
Therefore, Einstein’s light clock and ruler would never work in reality. They only exist in our imaginations.
They should not be used to derive time dilation and length contraction. The classical motion equation for
light is also invalid in reality. It should not be used to derive the Lorentz transformation. Those calculations
are purely classical. They are merely pretty, purely hypothetical, mathematical exercises.
Most importantly, the spacetime metric 𝒈 𝝁𝝂 𝒅𝒙 𝝁
𝒅𝒙 𝝂
is invalid at the microscopic scale due to the
Heisenberg’s uncertainty principle. It should not be served as a fundamental concept in relativity. Instead,
we need to find the real fundamentals of relativity and true mechanism such that the laws of physics remain
the same for everyone in the universe.
7. Reconciling Relativity with Quantum Mechanics
Special relativity has been established around 1905 and general relativity is around 1915.
Both of them are more than a decade ahead of the establishment of quantum theory. All
the concepts used in relativity are classical ones. For example, objects have definite position
and velocity at any time instance. Each object has a definite trajectory in spacetime.
However, those pictures are inaccurate, often times misleading in the quantum world. You
can not simply treat an atomic system as a solar system because each electron of the atom
doesn’t have a definite orbit. Rather, it has a cloud of probability.
It is desirable to reconcile relativity with quantum theory. It will shown here that relativity
can be established based on quantum wave propagation rather than the spacetime
geometry. The latter is just a classical limit of the former. It also offers a mechanism for the
first time to explain how the laws of physics remain the same for all observers.
Einstein and many others have done brilliant work at establishing classical relativity theory
more than 100 years ago. It is time for us now to extend it beyond its classical limitations.
8. A Key Insight
It has been found in quantum mechanics that, for any free particle, either a boson or a
fermion, its motion is governed by the Klein-Gordon equation as
−
𝟏
𝒄 𝟐
𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐
+ 𝝏 𝒚
𝟐
+ 𝝏 𝒛
𝟐
𝝍 𝒙, 𝒚, 𝒛, 𝒕 =
𝒎 𝟐
𝒄 𝟐
ℏ 𝟐
𝝍 𝒙, 𝒚, 𝒛, 𝒕
Where 𝜓 is the wave function describing the state of the particle, m is its mass, c is the
speed of light, and ℏ is the reduced Planck constant.
The Klein-Gordon equation can be generalized in a straightforward way to (remaining in
Cartesian coordinates)
𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 𝝍 𝒙, 𝒚, 𝒛, 𝒕 =
𝒎 𝟐
𝒄 𝟐
ℏ 𝟐
𝝍 𝒙, 𝒚, 𝒛, 𝒕
It has been found by the author that the above motion equation falls back to Einstein’s
geodesic equation in general relativity at the classical limit. That is, at the limit, when each
particle has a finite position and velocity at any given time, each free particle follows a path
in spacetime that has the longest proper time s, where 𝒔 = ∫ 𝒅𝒔 and 𝒅𝒔 = −𝒈 𝝁𝝂 𝒅𝒙 𝝁 𝒅𝒙 𝝂.
9. Important Conclusions from the Insight
The generalized Klein-Gordon equation is more general than Einstein’s geodesic
equation.
The universal wave propagation operator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 is more fundamental than the
spacetime metric 𝒈 𝝁𝝂 𝒅𝒙 𝝁 𝒅𝒙 𝝂 at understanding relativity.
The spacetime metric 𝒈 𝝁𝝂 𝒅𝒙 𝝁 𝒅𝒙 𝝂 is only an emergent behavior of the universal
wave propagation operator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 at the classical limit when each object has a
definite position and velocity at any given time.
The universal wave propagation parameters 𝒈 𝝁𝝂(𝜇, 𝜈 = 0,1,2,3) determines the
geometry of spacetime with the spacetime metric as 𝒈 𝝁𝝂. 𝒈 𝝁𝝂 is the inverse of 𝒈 𝝁𝝂
.
𝒈 𝝁𝝂 is a covariant tensor and 𝒈 𝝁𝝂
is a contravariant tensor.
Gravitational potential is defined by the wave propagation parameters 𝒈 𝝁𝝂
, instead
of the spacetime metric 𝒈 𝝁𝝂 as suggested by Einstein.
10. Essence of Relativity
It is hypothesized by the author that at the most fundamental level of nature, everything in the
universe is made of particle waves and field waves. All of those waves, either free or in
interactions with others, are governed by the same universal wave propagation operator
𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 using Cartesian coordinates in Newton’s absolute space and time.
At any spacetime point, the universal wave propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 remains in the
quadratic form under any linear transformation in spacetime (covariance). It can always be
normalized by a linear transformation in spacetime to the standard form:
−
𝟏
𝒄 𝟐
𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐
+ 𝝏 𝒚
𝟐
+ 𝝏 𝒛
𝟐
using a linear transformation in spacetime coordinates. It keeps the same form under the
Lorentz transformation. This is the true essence of general relativity. Different spacetime
transformations lead to different perceived space and time, specific to each observer. It
explains why the laws of physics appear to be the same to all observers regardless of their
(uniform) motions and gravity. This is a true mechanical explanation for relativity.
Based on the above observation, we have the general principle of relativity as
The laws of physics appear to be the same in all inertial frames with or without
gravity.
11. Essence of Relativity (II)
The true essence of relativity is not the symmetry of space and time, but the normalizability of
the universal wave propagation operator from its general from 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 to its standard form
−
𝟏
𝒄 𝟐 𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐 + 𝝏 𝒚
𝟐 + 𝝏 𝒛
𝟐. This property is more fundamental than the symmetry of spacetime.
At the classical limit, 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 defines a spacetime geometry with the metric 𝒈 𝝁𝝂. Its standard
form −
𝟏
𝒄 𝟐 𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐 + 𝝏 𝒚
𝟐 + 𝝏 𝒛
𝟐 has the Lorentz symmetry in terms of spacetime transformation. In
history, before the discovery of quantum theory, it is natural for scientists to discover this
symmetry first as the essence of relativity. However, this is only valid at the sense of classical
physics. At the subatomic scale, this is not true anymore. Instead, we should say that −
𝟏
𝒄 𝟐 𝝏 𝒕
𝟐
+
𝝏 𝒙
𝟐 + 𝝏 𝒚
𝟐 + 𝝏 𝒛
𝟐 possesses the Lorentz symmetry in terms of spacetime transformation.
All state variables should be geometrical-like entities such as vectors and gradients so that they
are transformed accordingly under the transformation of space and time coordinates. They are
called, in fancy mathematical terms, covariant variables or contravariant variables. All equations
that are based on geometrical entities and 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 are linear covariant. In particular, when
𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 is reduced to 𝜼 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 (𝜼 𝝁𝝂
Minkowski metric), those equations are Lorentz invariant,
which must also be Lorentz covariant.
12. Relativity=Equality
The normalizable universal wave propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 described before
brings equality to all inertial frames with or without gravity such that a hydrogen
atom or a water molecule appears to be the same in structure and properties in
each frame, regardless of its motion and local gravity. The protein molecules
inside anyone’s bodies must be invariant to the motion of their planet and the
motion of themselves. They must also be invariant to the gravitational pulling
imposed on them by their planet. Otherwise, human beings can not travel into
space and land on the moon. Life is impossible on any planet.
Einstein’s general relativity failed to bring equality to all inertial frames at the
presence of gravity. With his theory, different gravitational fields and different
motion speeds of different frames will lead different structures and properties for
the same atom or molecule. It could mean disaster for living beings dwelling on
different planets or different elevations on the same planet. This could be the
most fundamental flaw of Einstein’s theory.
13. Linear Covariance vs General Covariance
Linear covariance is the invariance in form of the laws of physics under all possible linear transformations of
coordinates. Inertial frames corresponds to linear transformation. Accelerating and rotating frames
correspond to curvilinear transformations.
In terms of linear covariance, any covariant tensor is still a tensor obviously. Therefore, 𝒈 𝝁𝝂
is a rank-2
contravariant tensor. The regular derivative of any tensor is also a tensor since it is transformed just like a
tensor. However, this is not true in terms of general covariance.
In particular, 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 is covariant in terms of linear covariance. To make it clear, note that 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 remains
the same in form under any linear transformation of spacetime. If the operator has this form in absolute
space and time, then it remains the same in form in any inertial frames. However, it is not covariant in terms
of general covariance. It is not invariant in form in curvilinear coordinate transformation, covariant
derivatives should be used instead here.
Linear covariance brings equality to all inertial frames with or without gravity. This is critical important to
have the sameness property for all atoms and molecules. However, Einstein’s general covariance fails to
achieve this fundamental equality.
Einstein generalized Lorentz covariance for special relativity to general covariance for general relativity.
However, Einstein could possibly generalize the principle of relativity in the wrong direction. To be
more specific, the principle of relativity should be generalized to all inertial frames with gravity from
ones without gravity, instead to all Gaussian coordinate systems using tensor expression.
14. Generalizing to Fancy Curvilinear Coordinates
Using a curvilinear coordinate system, the universal wave propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂
should be rewritten as 𝒈 𝝁𝝂
𝛁𝝁 𝛁𝝂, where 𝛁 𝝁 is the covariant derivative. Based on its definition,
𝒈 𝝁𝝂 𝛁𝝁 𝛁𝝂 can be rewritten as
𝒈 𝝁𝝂
(𝝏 𝝁 𝝏 𝝂 − 𝚪𝝁𝝂
𝝈
𝝏 𝝈)
where 𝚪𝝁𝝂
𝝈
is the Christoffel symbol defined as
𝚪𝝁𝝂
𝝈 =
𝟏
𝟐 𝝆=𝟎
𝟑
𝒈 𝝆𝝈 𝝏 𝝂 𝒈 𝝁𝝆 + 𝝏 𝝁 𝒈 𝝂𝝆 − 𝝏 𝝆 𝒈 𝝁𝝂
Here, 𝒈 𝝁𝝂 is the inverse of 𝒈 𝝁𝝂
. There are 40 Christoffel symbols for 4 dimensional
spacetime. Each one has the above complex form.
Using curvilinear coordinates is a fancy mathematical generalization. It doesn’t offer much
extra insight into physical reality. Often times, it makes the computation in relativity
extremely tedious, burying physical concepts into an ocean of mathematical symbols,
notations, and indices. Furthermore, it is unlikely that nature implements the super complex
operator 𝒈 𝝁𝝂
𝛁 𝝁 𝛁𝝂 instead of the simply operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂. Unfortunately, Einstein took this
hard, tedious, and problematic way to study relativity in a strenuous heroic effect and we
still inherit most of it up to now.
15. Invariance of the Laws of Physics
If nature implements 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂, then the laws of physics remain the same in form in tensor
expression in all inertial frames (linear covariance), but not in accelerating and rotating frames
simply because the operator losses its quadratic form (not general covariant). At the origin of
any inertial frame, 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 can be normalized to the standard form 𝜼 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 where 𝜼 𝝁𝝂 is the
Minkowski metric. The operator has the same form at the origin.
If nature implements 𝒈 𝝁𝝂
𝜵 𝝁 𝜵 𝝂, then the laws of physics remain the same in form in tensor
expression in all frames (general covariance). In this case, it can be normalized to the standard
form 𝜼 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 in the Gaussian normal coordinates (having specific acceleration, rotation, and
distortion of spacetime), and gravity and relative motion can be canceled out at the same time.
At the origin of any inertial frame, 𝒈 𝝁𝝂
𝜵 𝝁 𝜵 𝝂can be normalized to 𝜼 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 − 𝜼 𝝁𝝂
𝜞 𝝁𝝂
𝝈
𝝏 𝝈. In this
case, the extra term 𝜼 𝝁𝝂 𝜞 𝝁𝝂
𝝈 𝝏 𝝈 is dependent on the motion speed of the frame and the
gravitational potential 𝒈 𝝁𝝂
. The operator failed to keep the same form in this case. This could
be a fatal design flaw because the sameness property for atoms and molecule will be lost
for different inertial frames.
Readers should not be fooled by the mathematical shorthand notation 𝒈 𝝁𝝂
𝜵 𝝁 𝜵 𝝂. In terms of
computational complexity, 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 has only 10 items added up, but 𝒈 𝝁𝝂
𝜵 𝝁 𝜵 𝝂 is super complex
with 490 items added up. Furthermore, 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 is a simple wave propagation operator with 10
parameters 𝒈 𝝁𝝂 while 𝒈 𝝁𝝂 𝜵 𝝁 𝜵 𝝂 needs to compute the inverse of 𝒈 𝝁𝝂, plus their derivatives, and
plus the multiplication of those derivatives with 𝒈 𝝁𝝂
themselves. Does nature choose such a
super complex, flawed design? Or it choose the simple, elegant design for the equality of all
inertial frames so that life is possible.
16. Quantum Particle Motion In General
In general, when both an electromagnetic field and a gravitational field is presented, it
is hypothesized by the author that the motion equation for a quantum particle is
𝒈 𝝁𝝂 𝒊ℏ𝝏 𝝁 −
𝒆
𝒄
𝑨 𝝁 𝒊ℏ𝝏 𝝂 −
𝒆
𝒄
𝑨 𝝂 𝝍 = 𝒎𝒄𝝍
where (𝑨 𝟎, 𝑨 𝟏, 𝑨 𝟐, 𝑨 𝟑) is the electromagnetic 4-potential, and e is the electric charge.
In this general case, the wave function 𝜓 must have four components.
When there is no gravity, the above equation falls back to the important Dirac
equation in quantum theory:
𝒊ℏ𝝏 𝟎 −
𝒆
𝒄
𝑨 𝟎
𝟐
−
𝝁=𝟏
𝟑
𝒊ℏ𝝏 𝝁 −
𝒆
𝒄
𝑨 𝝁
𝟐
𝝍 = 𝒎𝒄𝝍
17. Quantum Gravitational Field Equation
In terms of the universal wave propagation operator 𝑔 𝜇𝜈
𝜕𝜇 𝜕 𝜈, the electromagnetic field
equation can be written as
𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 𝑨(𝒙, 𝒚, 𝒛, 𝒕) = 𝝁 𝟎 𝑱(𝒙, 𝒚, 𝒛, 𝒕)
where 𝑨(𝒙, 𝒚, 𝒛, 𝒕) is a 4-component vector field called the electromagnetic potential field, 𝝁 𝟎
is the vacuum permeability, and J(𝒙, 𝒚, 𝒛, 𝒕) is a 4-component vector field defining the electric
current field. The equation is linear covariant.
As suggested before, gravitational waves should also be governed by the same universal wave
propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 as any other field waves. Therefore, we can postulate a
gravitational wave equation in the same form as the electromagnetic field equation as follows:
𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 𝑨 𝑮(𝒙, 𝒚, 𝒛, 𝒕) = 𝟒𝝅𝑮𝑱 𝑮(𝒙, 𝒚, 𝒛, 𝒕)
where 𝑨 𝑮(𝒙, 𝒚, 𝒛, 𝒕) is a 4-component vector field defining the gravitational potential field, 𝑮 is
the Newton’s constant, and 𝑱 𝑮(𝒙, 𝒚, 𝒛, 𝒕) is a 4-component vector field defining the matter
current field. Here, 𝒈 𝝁𝝂
is a function of 𝑨 𝑮 as 𝒈 𝝁𝝂
(𝑨 𝑮). That is, the gravitational potential 𝐴 𝐺
determines the wave propagation parameters 𝒈 𝝁𝝂
. When the potential equals zero, 𝒈 𝝁𝝂
falls
back to the standard Minkowski metric 𝜼 𝝁𝝂
. The function 𝒈 𝝁𝝂
(𝑨 𝑮) should be fined by
experimental data, such as the PPN parameter 𝛾.
The field equation is Lorentz covariant. Einstein’s field equation is a super-complex,
general covariant approximation to it.
18. A Simple Quantum Experiment to Disprove
Einstein’s General Relativity
If we believe in the equality of all inertial frames at the presence of gravity, the double-slit
experiment can be used to disprove Einstein’s general relativity experimentally. It can be
used to find out the wave propagation operator is linear covariant as 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 or general
covariant as 𝒈 𝝁𝝂
𝛁 𝝁 𝛁𝝂 proposed by Einstein. General covariance is the very foundation of
Einstein’s general relativity. If the experiment’s result agree with 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂, then Einstein’s
general relativity is disproved completely at the most fundamental level.
To conduct the experiment, we can shoot up an electron upwards to pass through a
double-slit put horizontally on its path. Behind the double-slit, we put a screen tilted with
different angles against horizon. Under its own gravity, the interference pattern of the
electron generated by the wave propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂 will squeeze the electron
wave vertically, but not so for 𝒈 𝝁𝝂
𝛁 𝝁 𝛁𝝂 when we simulate it using an accelerating frame
equivalent to the gravity. Simply put, this experiment will show that gravity is not
equivalent to acceleration at the subatomic scale. This is a simple experiment to reveal the
most fundamental truth of nature.
19. Is this the Time for a New Relativity Theory?
Einstein’s general relativity is not compatible with quantum theory. The new
quantum gravity theory presented here doesn’t have this troubling issue.
Moreover, the new theory doesn’t have many other troubling issues of general
relativity like black hole problem, flatness problem, cosmology constant
problem, singularity problem, vacuum energy problem, and quantum
normalization problem. It is a call now to re-establish the theory on the
foundation of quantum physics.
Notes de l'éditeur
This video offers a simple mechanical explanation for the first time for gravity and relativity based on quantum wave propagation. It re-establishes Einstein’s general relativity on the solid footing of quantum physics. The new theory explains why gravity can be treated as curved space and time, why a point mass moves along a geodesic line, and how the laws of physics appear to be the same in all inertial frames with and without gravity. It also points out that Einstein’s general relativity failed to bring equality to inertial frames in terms of laws of physics at the presence of gravity. This fundamental flaw will also be fixed in the new theory.
Covariance under the linear transformation of coordinates
Under any linear transformation, the partial derivative of any tensor is still a tensor!!!
Without generalizing to acceleration (curvilinear coordinates), using strictly linear transformations, 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 is covariant.
The spacetime metric 𝑔 𝜇𝜈 𝑑 𝑥 𝜇 𝑑 𝑥 𝜈 is covariant under curvilinear transformation. Since classical physics is solely based on this spacetime metric, the classical physics is covariant under curvilinear transformation such as acceleration. However, quantum physics which is based on 𝑔 𝜇𝜈 𝜕 𝜇 𝜕 𝜈 is not covariant under curvilinear transformation. That is, at the most fundamental level of nature, the laws of nature is only covariant under linear transformation of coordinates, not curvilinear ones. That is, we can’t generalize laws of physics to accelerating frames. Einstein is half right (classical physics) and half wrong (quantum physics).
In Newton’s true space and time, 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 = 𝒈 𝝁𝝂 𝛁 𝝁 𝛁 𝝂 or equivalently 𝒈 𝝁𝝂 𝚪 𝝁𝝂 𝝈 =0, is a constraint on 𝒈 𝝁𝝂 for the propagator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 to have the covariance property. In particular, if 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 = 𝒈 𝝁𝝂 𝛁 𝝁 𝛁 𝝂 in one coordinate system, then it is still satisfied after any linear transformation of spacetime. If nature implements this constraint, then all the laws of physics are covariant.
