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]]>5. Your blog occasionally mentions the big bang. I suggest you should indicate what is known by expert (but rarely spoken…) that, the big bang must have occurred in the galactic vicinity of Earth as a necessary condition to verify Hubble’s law, thus implying again Earth at the center of the universe.

Let me expound how cosmologists think about the Big Bang.

1. In the first 10 to power -32 seconds the part of the universe that we can see now expanded to the size of a grapefruit.

2. The total universe was bounded, but probably larger than that grapefruit. Topologically is was a three-sphere (the surface of a threedimensional ball is a two-sphere). In other words, each ‘straight line’ came back to itself.

That is somewhat hard to visualize. Think of the surface of earth *mapped* by showing two hemispheres as circular disks. Similarly you can ‘map’ a three-sphere by having two solid balls, and a rule how you get from one ball to the other ball. No point on the surface of the earth is “the center”, likewise there is no point in this early universe that is the center. All points corresponding to parts that can be seen now were closer than 10 cm from each other.

3. Somehere in that grapefruit was a speck quite a bit smaller than 0.1 mm (the thickness of a hair), that corresponded with our present galaxy. Not entirely, because all but 0.01% of the energy eventually became radiation and spread out over the now visible universe, after almost all matter and antimatter had annihilated each other. All the photons from that time are now the Cosmic Background Radiation.

4. This “grapefruit” kept expanding together with the whole three-sphere (i.e. the radius of curvature became larger and larger) and presently the radius is about 43 billion light years. The light from the farthest parts has been 13.7 billion years under way. While that light was speeding towards us, the matter that had emitted the light moved farther away, that is, space between it and us stretched. This stretching of the space caused the wavelength of the light to stretch too.

5. In case you wonder how mathematicians talk about curvature of a twodimensional surface, Here is how: walk in a closed curve, preferably consisting of longer or shorter ‘straight line’. Keep a pointer in your hand that all the time points in the same direction, i.e. makes the same angle with your direction of motion. When you reach a point where you change direction, turn a corner or so, you keep the direction. If you have returned to your starting point, your pointer points in different direction. It is rotated. The change in direction is proportional to the area you have enclosed with your curve. Divide that angle into that area, and take the square root. That’s the radius. In more than two dimensions, it’s a bit more complicated, but the idea is the same.

6. It is not true that the experts know that the Big Bang happened in the vicinity of Earth, except in the trivial sense that shortly after the Big Bang everything was in each other’s vicinity. The experts know it wasn’t an explosion like the parts of a bomb expanding into the empty surrounding space.

4. I introduced the diagram at the top of your blog, again, to honor the memory of Einstein and the other distinguished scientist. as you can see in Section I.4 of the cosmological debate. You and other bloggers complain that, in the analysis of this diagram, I pass from the universe without acceleration of the expansion to that with said acceleration, resulting in confusion. You and your contributors are correct because I wanted first study the diagram with the cosmological view of the early 1900, and then with more recent views. I admit that the distinction here considered did not turn out to be that happy. In any case, allow me to comment on that distinction here. So, let us analyze the diagram with the Doppler interpretation of Hubble’s law, z = v/c, which is evidently “linear in the velocity,” thus implying galaxies at the double distance from Earth must have double velocity, thus resulting in a relative velocity between said galaxies. This diagram can be equivalently represented by the version

Here follows a diagram that is erroneous. At the right, for 2 to the power *v*, with subindex 1 read 2*v*_{1}. and similarly below.

Figure 2: *A diagram on the geometric inconsistency of the expansion of the universe due to the lack of invariant for all observers of relative velocities between galaxies.*

In this alternative, Earth is on the left, the galaxies G1 and G2 at double distance from Earth are aligned along the horizontal axis, thus having a relative velocity which is completely absent for the infinitely possible observers O1, O2, etc. along the perpendicular to the horizontal axis at mid distance from G1 and G2. This is the case because galaxies G1 and G2 are at the same distance for the indicated infinity of observers, thus confirming the geometric inconsistency of the expansion of the universe and its historical rejection by Einstein and other distinguished scientists. The comment in your blog:

In the ‘proof’ Santilli forgets that G moves as well. Actually Euclid, 2300 years ago, could have explained to him why he is wrong.is correct in saying that galaxy G moves, thus correctly implying that the diagram should be considered at one given time. However, the motion is linear in the velocity for all galaxies, thus implying that, at a later time, the diagram remains exactly the same, the sole difference being the increased distances, thus establishing the inconsistency of the expansion of the universe at any desired time.

The diagram is erroneous because O1 through O4 are apparently thought to be stationary. If they represent galaxies with observers in them, hence also moving radially away, then the same reasoning applies as with G in the previous comments.

If one is willing to put observers in the picture that are stationary with respect to Earth, why not put a single one at G2?

The latter part of Santilli’s comment is unclear. What does “the motion is linear in the velocities” mean? The relative velocities (as vectors) are linearly dependent on the relative position vectors, but I see no way how one can read the quoted phrase to mean just that. After a certain time *t* all distances have increased with a factor 1 + *t*/*T*, where *T* can be thought of as the time since the Big Bang (ignoring the effects of slowing down or speeding up due to gravitation or the value of a cosmological constant); *T* is just the inverse of the Hubble parameter *H*.

If all distances have increased or decreased with the same factor, then the picture of the positions looks the same. Not only the distances EG1 and EG2 have grown with that factor, but also the distances from E to the various Os and also the lengths of all line segments pictured, such as G1 to O2 or O4 to G2, etc. etc. There is no inconsistency. Maybe a study of my explanation of September 10, 2018 would help.

I will not go into the discussion of accelerations. It is unclear which accelerations Santilli is thinking of. The fact that the expansion of the universe is speeding up is a discovery of 1998, that resulted in a Nobel prize in 2011. The above discussion (and also the discussion at beginning of my blog) is only about the simple geometry of Santilli’s diagrams.

The next point illustrates that Santilli seems not know that the Big Bang wasn’t an explosion. I do this in a next reaction.

]]>The full text is now (September 22) “Post 161” on http://www.galileoprincipia.org/Lawsuit-against-Frank-Israel-and-Pepijin-van-Erp.php

This post erroneously describes me as “Head of the Dutch Sceptic Society”. The Foundation Skepsis doesn’t have a head at all. It has a chairman, Frank Israel, and I am secretary.

I reproduce some parts of the argument of Post 161.

2. The historical reason moving Einstein and other scientists to reject the expansion of the universe is that that Hubble’s law “z = Kd.c” (Ref. [3] of the cosmology debate) establishes experimentally that the cosmological redshift “z” is the same for the same distance “d” in all possible “radial” direction from Earth, thus implying a return to the Middle Ages with Earth at the center of the universe. When I was in High School in Italy, I remember vividly Italian newspapers reporting this view by Enrico Fermi along the above lines. Again, you have the right to disagree, but the quotation in your blog of this historical fact is recommendable.

I refer to https://phys.org/news/2014-02-einstein-conversion-static-universe.html

for a short survey of the way Einstein’s views evolved. At first Einstein put a ‘cosmological term’ in his theory of general relativity, to make the universe static. He had of course no experimental fact suggesting that the universe was static. He also didn’t realize that the equilibrium was unstable, similar to an egg balancing on one its ends.

Lemaître heard of Hubble’s results and proposed the expanding universe. He called the initial state the ‘atome primitif’. Einstein thought that Lemaître was wrong, but in 1931 admitted that Lemaître was right. From then on he called his introduction of the cosmological term his greatest blunder. Lemaître, on the contrary, kept the term and gave it an interpretation.

This is all well known, and I never heard the story that Einstein didn’t believe in the expanding universe. If so, what was he doing when he developed with Willem de Sitter the Einstein-de Sitter model of the universe?

What Fermi thought about this I don’t know, and memories of Italian newspaper articles of long ago are not a good reference. Nobody in his right mind thinks that the Hubble discovery implies a geocentric world image. Indeed, if the Hubble law is correct (leaving aside whether the redshift is due to a physical speed or to the expansion of the intervening space), then each inhabitant of each of the one hundred billion or so visible galaxies would see exactly the same: radial expansion proportional to the distance , implying that all visible matter was at the same point in a distant past.

3. With the understanding that I could be wrong, you portray the view that the speed of galaxies is measured. Allow me to indicate that this is not the case. The “sole” quantity which is actually “measured” in contemporary cosmology is the cosmological redshift “z”. The conjecture that billions of trillions of galaxies move away from Earth (at times with superluminal speeds) is a “purely theoretical assumption” stemming from the “interpretation” of Hubble’s law with the Doppler axiom of special relativity, “z = v/c.” I recommend that you clarify this additional basic point in your blog to prevent predictable political nonscientific interpretations.

Let us be clear. Indeed we measure a redshift. For those not entirely familiar with this: one measures the position of a strong line in the spectrum of a galaxy. This yield the observed frequency g. In a laboratory on earth the real frequency f is determined. As g < f, the fraction f/g is more than 1 and we write f/g = 1+z. If z is small then v/c = z. The exact value, if one takes special relativity into account, and if the frequency shift is due to motion of the far away galaxy, we have v/c = w/(1+w), where w = z + z*z/2. If we are dealing with 'cosmological redshift' i.e. expanding space the formulas become different. Note that there not 'billions of trillions' of galaxies but about 100 billion as far as we can see. Maybe somewhat more, there might be galaxies that are so small that we can't see them. However, I have only dealt with Santilli's misconception that 'expansion = geocentric view'.

]]>Suppose we have a triangle ABC. You may think of A as the position of earth, and B and C as the position of two galaxies. The fact that B moves away radially from A means that the side AB is lengthened after 1 second to AB’. The fact that the speed of B is proportional to the distance of A to B means that in 1 second the length of AB’ equals the length of AB times 1 + h. Here the value of h is about 2.3 times 10 to the power -18 (= 1/T, where T is the number of seconds since the Big Bang).

It is immaterial in this context whether the increase of distance is due to an increase of the space or due to proper motion.

So AB : AB’ = 1 : 1+h. Similarly C moves in this 1 second radially to C’, and AC:AC’ = 1: 1+h.

Of course the angle at A of triangles ABC and AB’C’ is the same. So we have exactly the case side-angle-side of the theory about similar triangles, treated as Proposition 6 in Book VI of the Elements of Euclid. Hence ABC and AB’C’ are similar, more precisely, they are equiangular, and hence the sides are all proportional (case angle-angle-angle, Book VI, Proposition 4). In other words BC:B’C’ = 1 : 1+h, and BC is parallel to B’C’ which means that C is moving radially away from B as seen from B. This should be perfectly clear to anyone who has attended the math classes in junior high school.

Such a meticulous proof should be quite unnecessary. It is common knowledge that if you make the sides of rectangle larger by a certain factor, then the diagonals increase with the same factor. That’s basically the same as we just discussed if you think of the triangle formed by two sides of a rectangle and the diagonal. Anyone measuring distances on a map knows this: if the distances on a map are (for example) 100,000 times as small as the real distance in the north-south direction, and also 100,000 times as small in the east-west direction, then all real distances are 100,000 times the corresponding map distances and this number is called the scale of the map.

If someone is contradicting this basic geometry, not once, but many times in the course of ten years, we may well conjecture that his knowledge of basic maths leaves something to be desired.

]]>Please don’t forget to state the title of the blog you are reacting to, ]]>

Je moest bewijzen, dat als t.o.v. een gegeven oorsprong de ruimte uniform expandeerde, de afstand tussen alle punten onderling met dezelfde factor groter werd. Ik kreeg dat bewijs niet op papier en had genoteerd: “mij een raadsel”.

In één regel vond ik het bewijs door de corrector erbij gezet, zoiets van: als vector a -> N.a en vector b -> N.b, zal de verschilvector a-b -> N.a – N.b , dus ook a-b -> N. (a-b). De corrector had er vriendelijk bij gezet: “It’s quite simple, my dear Watson”.

De hr. Santilli moet dus zijn Lineaire Algebra nog eens herlezen.

Met een ballon kun je het ook laten zien: blaas maar op: alle punten krijgen een gelijke vergrotingsfactor van de afstand. Zet de ballon gelijkmatig in de tijd uit, dan betreft het de snelheden. Als je de ballon versneld laat groter worden betreft het ook de versnellingen. Of dit nu op de afstanden, de snelheden of de versnellingen in zo’n expanderende ruimte betrekking heeft, maakt dus niet uit, want die hangen ieder onderling lineair samen in die ruimte met dezelfde uniforme factor of uniforme tijdsafgeleiden daarvan. ]]>

Another remark is that I do not justice to Santilli. He doesn’t speak about speeds but about accelerations. Here the problem is that Santilli says different things at different time. Here is a list of sources:

speech of 2011, published 2013 (look at p. 346)

http://www.santilli-foundation.org/docs/IRS-confirmations-212.pdf

likewise 2013

http://www.prweb.com/releases/2013/12/prweb11433287.htm

http://www.santilli-foundation.org/Conf-2013-No-Univ-Exp.php

http://www.santilli-foundation.org/Confirm-No-Exp.php

http://www.i-b-r.org/Prof-Santilli-Interview.html

In 2014 a movie, look at 37:40 and further and watch the speaker getting quite enthousiastic about his discovery:

ftp://www.world-lecture-series.org/Lie-Santilli-Isotheory-2014.mp4

in 2015:

https://web.archive.org/web/20160115090348/http://www.scientificethics.org/denunciation-christian-corda.htm

http://www.thunder-energies.com/docs/dark-matter-2015.pdf

http://www.prweb.com/releases/2015/04/prweb12637959.htm

In the last version all mention of accelerations are gone. In the earlier version the ‘accelerations’ seem to make no sense, or they seem to mean ‘different speeds’. Somehow the author seems to think that as G1 moves to the position of G2, its speed will double. But that is not what any astronomer claims.

The original Hubble law and corresponding calculation of the age of the universe assume that the speeds are constant over time, which leads to the conclusion that all (visible) galaxies were some time ago at the same point. Modern research has made it plausible that this is not precisely true. One might conjecture that the speeds slowly decrease because gravity keeps pulling the galaxies together, slowing the radial expansion. But the speed of expansion seems to be slowly increasing, judging from accurate measurements.

Back to Santilli. His statements in the quoted sources are so confused that they are nearly uninterpretable. With utmost charity one might conjecture that is meant that each point in space has an expansion rate of its own, and that when a galaxy moves farther away it will go quicker by an amount specified in the Hubble law. But this is totally at odds with the real Hubble law (which only talks about what we see now), and moreover, it has no role in the argument. And indeed in the last version the ‘accelerations’ are gone, so the argument becomes clear, hence more clearly wrong.

]]>Ik neem aan dat je gelijk hebt. Door zo inhoudelijk te reageren geef je misschien de tegenpartij munitie. “Zie je wel, ze zijn betrokken en dus aansprakelijk”. Ik zou daar voorzichtig mee zijn.

De literatuuropgave duidt op een zekere bezetenheid, en is m.i. een analyse waard. Voor de leek zeer indrukwekkend en onbegrijpelijk, maar afkomstig uit een beperkt aantal bronnen, enzovoort.

Sterkte,

Martin Vos ]]>