## torsdag 30 juli 2020

### Philosophy of Science

To say that something is complicated can be easy. To say that something is easy may be complicated.

What is easy can be understood. Science means understanding, and so the objective of science is to make things easy.

This connects to the observation (Arthus Clarke's 1st Law) that if someone (an elderly scientist) says that something is impossible (no solution possible), it is usually wrong, while if someone says that something is possible (there is a solution), then it is usually right.

## söndag 12 juli 2020

### Can a Coordinate Transformation Contain Physics?

The Special Theory of Relativity SR is identical to the Lorentz coordinate transformation. The General Theory of Relativity involves as an essential step transformations of space-time coordinates.

Many-Minds Relativity shows, in a careful mathematical analysis, that SR is empty as a theory about real physics. The argument is in brief that since SR is identical to the Lorentz transformation, and a coordinate transformation in itself does not contain any physics, SR is empty of physics.

Why does a coordinate transformation not contain any physics? Consider for example the coordinate transformation of a pure translation from an $x$-axis to an $x^\prime$-axis, as 1d Euclidean coordinate systems, of the form $x^\prime = x - v$, with $v$ a constant.  One property of such a transformation is that distances are conserved, or are invariant, under transformation: If $x^\prime = x - v$ and $y^\prime = y - v$, then $x^\prime - y^\prime = x - y$. So far no physics has been introduced and so the coordinate transformation cannot have any physical meaning. A natural way to give physical meaning is to say the coordinate $x$ represents the position of a physical body $X$ and $y$ the position of a body $Y$. The positions of $X$ and $Y$ can then alternatively be expressed in terms of $x^\prime$ and $y^\prime$.

Now, can we say that the transformation contains any physics of the position of the bodies? Can we say that since the transformation expresses that distances are conserved under the transformation, we can conclude a law physics expressing that translation of a rigid body does not change the shape of the body? Is this a law of physics, which may be false, or simply a law of logic or language and not physics which cannot be false? I guess, you we would agree with me that it is not a true law of physics. That a rigid body does not change shape is built in into the meaning of a rigid body, and has nothing to do with physics with the shape of a body determined by physical forces. It cannot be used to say that in a rigid body there are forces which maintain its shape. It would be like pulling a rabbit out of an empty hat.

Choice of coordinate systems in physics directly connects to the choice of units in physics. If you believe that the choice of units contains physics, that using a meter stick instead of yard stick changes the size of physical objects, then you are well prepared to accept the wonders of SR. If you understand that this is not the case, then you will (like me and many others) have a hard time with SR.

We can add a common time coordinate $t$ to the $x$ and $x^\prime$ systems into a Galilean space-time transformation of the form
• $x^\prime = x-vt$, $t^\prime =t$,
between a $(x,t)$-system and a $(x^\prime ,t^\prime)$, with the $x^\prime$-axis translating with respect to the $x$-axis with speed $v$, but still with the same lack of real physics.

The Lorentz transformation of SR is a similar linear coordinate transformation from a a space-time $(x,t)$-system to a space-time system $(x^\prime ,t^\prime )$-system of the form
• $x^\prime =\gamma (x-vt)$, $t^\prime = \gamma (t-vx)$, $\gamma =\frac{1}{\sqrt(1-v^2)}$,
• $x =\gamma (x^\prime+vt^\prime )$, $t = \gamma (t^\prime+vx^\prime )$.
where $\vert v\vert <1$, with now also the time variable beeing subject to transformation, and in particular the property that a $x = t$ is transformed into $x^\prime = t^\prime$ and back.

In order for the Lorentz coordinate transformation to contain physics, the coordinates must be given some physical meaning. Einstein did this by associating space-time coordinates $(x,t)$ to events (of some unspecified physical nature) or rather to observations of events (of some unspecified physical nature), like a body $X$ observed to be at position $x$ at time $t$. Einstein associated the system $(x^\prime ,t^\prime )$ to represent coordinates with the $x^\prime$ axis translating with speed $v$, like in the Galilean transformation, but now with also the time variable being subject to transformation.

Einstein then created SR by drawing conclusions about physics from the Lorentz transformation, like the fact that $x=t$ is the same as $x^\prime =t^\prime$ interpreted by Einstein to mean that a light signal always propagates with speed 1 in any (inertial) coordinate system. Einstein then proceeded to derive properties of space contraction and time dilation from the Lorentz transformation and boldly claimed that he thereby had discovered new truely astonishing real physics (apparently from mysterious forces twisting space and time).

Many early critics said that this was empty physics, for the reasons exposed above, but somehow Einstein managed to twist the brains of the physical community into believing that he had revealed deep new truths about real physics. This came to serve as footstep into modern physics, as weird empty physics based on transformations of coordinates brought to full bloom in the General Theory of Relativity in curved space-time.

Galileo of course understood that his coordinate transformation does not contain any real physics. Why do modern physicists insist that the Lorentz transformation contains real physics?  Lorentz did not believe so, but he was quickly side-stepped by not being modern enough.

Modern physics is in deep crisis. Why? Is it time now for post-modern physics?

The crisis is expressed in the obsession of modern physicists to focus efforts on a Theory of Everything a ToE, with the aim of explaining the basic four forces (electromagnetic, weak and strong nuclear and gravitation) as different manifestations of one basic force/interaction. No progress towards an answer has been made and the mystery of the origin of the four forces is as mysterious today as ever.

## måndag 6 juli 2020

### DigiMat: Physical Gravitational Collapse

We continue our DigiMat study of star formation by gravitational collapse into a high density hot spot.

In a fluid at rest without self gravitation a hot spot cannot develop without external forcing by transfer of energy from a cold surrounding. This is because without forcing, heat energy can only transfer from hot to cold, by the 2nd law of thermodynamics.

We now ask if in a fluid with self gravitation a hot spot can develop by surrounding cooling. We use DigiMat to give an answer: We thus simulate the motion of a fluid with self gravitation starting with the fluid at rest with constant  density, temperature and internal energy, assuming periodic boundary conditions for fluid variables. We set the gravitational potential to zero at the boundary and thus create a gravitational force directed to the center of the domain. Here is the result at a certain time:

What do we see? We see (crosscut of) central accumulation of mass/density (blue) combined with central heating and far-away cooling given by temperature (green), with black line the initial distribution. We thus effectively see a transfer of heat energy from cold to hot. This transfer is accomplished by gravitation, which from an initial state with zero fluid velocity attracts the fluid towards the center thereby increasing kinetic energy there, which then is transfered into heat energy as pressure finally retards the flow (and reverses the flow into expansion).

We thus find that the presence of a gravitational field can be viewed as a form of external forcing making possible transfer of heat energy from cold to warm. Gravitational collapse thus appears possible thermodynamically.

Gravitational collapse with transfer of heat energy from a cold exterior to a hot interior fits with the observation of interstellar dust at low temperture, about 20 K. The price of shining stars is chilly space between stars, by conservation of total energy.

## söndag 5 juli 2020

### DigiMat: Unphysical Gravitational Collapse

DigiMat offers a rich playground to explore the World. In DigiMat Model Workshop (70-74) you find a cosmological model in the form of fluid/thermodynamics with self gravitation. As an example consider the following simulation of the phenomenon of gravitational collapse:

What do we see? We see unphysical gravitational collapse with
1. gravitational potential peaking in the middle (light-blue)
2. high density middle (blue)
3. negative temperature middle (green)
with the unphysical nature signified by negative temperature. How do we know that the simulation is unphysical? This is because the negative temperature comes with negative Total Internal Energy E(t) (= -0.483 at a certain time t) with
• $E(t) = \int \rho (x,t)T(t,x)\,dx$,
• where $\rho$ is density and $T$ temperature.
Now, total internal energy E cannot be negative, neither density nor temperature can be negative. This connects to the basic energy balance of a self gravitating fluid/thermodynamic system which takes the form
• $TE(t) = E(t) + K(t)$ with
• $TE(t) =$ Total Energy at time $t$
• $K(t) =\frac{1}{2}\int\rho (x,t) |v(x,t)|^2dx$ Kinetic Energy, with $v(x,t)$ fluid velocity.
Notable is that Total Energy has no contribution from gravitation.

What we see in the simulation is accelerated fluid motion from a gravitational potential with central peak (light-blue) accompanied by an increase of kinetic energy balanced by a decrease of internal energy/decrease of temperature (green), while density is increasing (blue). But there is a limit to this process, because temperature/internal energy cannot become negative.

When the simulation passes this limit and temperture/internal energy becomes negative, the simulation turns unphysical and thus produces numerical artefacts, not physics.

Before collapse of the numerics, density and kinetic energy are increasing while temperature decreases. This means that the concentration of mass towards the center does not come with an increase of temperature, but instead with a decrease of temperature.

This shows that a common idea of "stars being ignited by gravitational collapse" (see Wikipedia quote below) is incorrect in the sense that the ignition does not come from increasing temperature. The ignition of stars thus can only be the result of a concentration of mass (triggering nuclear fusion balancing further concentration), and not any fire ball sucking energy from gravitation.

And the other way around, if a black hole is what results if star ignition/fusion does not take place, it must be a very cold place.

To see physical uncollapse run the code with larger gas constant $\gamma$ (e.g. 1 instead of 0.1)!

Summary: With Total Energy = Internal Energy + Kinetic Energy without contribution from gravitation, there is no physics of unlimited sucking of energy from gravitational collapse.  There is no physics of unlimited sucking of energy from internal energy (allowing negative internal energy).

More precisely, the energy balance takes the form
• $\frac{dE}{dt} = -W+P+D, •$\frac{dK}{dt} = W-P-D,
where $p=\gamma\rho T$ and $\phi$ gravitational potential (with minus sign),  and
• $W(t) = \int p(x,t)\nabla\cdot v(x,t)\,dx$,
• $P(t)=\int\phi\nabla\cdot (\rho (x,t)v(x,t))\,dx$, where $-\Delta\phi =\rho$ (and thus $\phi >0$),
• $D\ge 0$ turbulent dissipation,
which as a 1st law of energy balance gives $E+K$ constant with $D\ge 0$ as a 2nd law. See Computational Thermodynamics.

Now you are ready to experiment yourself with DigiMat, and seek deeper understanding of how stars are formed...by thermodynamics, gravitation and fusion.

Notice that fusion opens a new source of positive contribution to internal energy, which can be transformed into high temperature and high velocity. Without fusion this option is closed and the amount of internal energy is limited by given total energy.

We observe that energy without gravitation can be transferred from $E$ to $K$ (only) in expansion with $\int p\nabla\cdot v\, dx>0$ and vice versa from $K$ to $E$ (only) in contraction with  $\int p\nabla\cdot v\, dx<0$. Gravitation can transfer energy from $E$ to $K$ (only) in contraction with $\int\phi\nabla\cdot (\rho v)\,dx <0$ and the other way around.

Is it true that
• DigiMat unlocks the grand challenges in science, education and industry?

Compare with Wikipedia presenting the standard view:
• A star is born through the gradual gravitational collapse of a cloud of interstellar matter. The compression caused by the collapse raises the temperature until thermonuclear fusion occurs at the center of the star.
True?

## fredag 3 juli 2020

### DigiMat: BIG BANG

DigiMat is now being launched to a broad public. Here is an example of a DigiMat simulation of BIG BANG from Model Workshop of DigiMat BodyandSoul:

See expansion of BigBang initial data as central concentration of high density/temperature spreading out into low density/temperature space headed by a shock wave and followed by expansion with  scaling linearly with distance in accordance with Hubble's Law. DigiMat students master the coding of this example in early school years. Try yourself by clicking on the code link above.

Question: Is the shock wave beyond the observation horizon (since it is not observed)?