Some Questions of the Special Relativity

PART 2.

Back to part 1: Three types of velocities. Rapidity parameter y and rapidity r.

Forward to part 3: Different forms of space-time transformations. Quantum velocities in Special Relativity.

Interval

In classical mechanics the length of a rod is determined by the expression r=sqr(x²+y²+z²), which is valid in any system and is invariant value. The values x, y, z are projections of the rod on the axes, and these values are not invariant values, - they can change under transition from one system to another system. In the relativistic physics we loose the r invariant, but find the new invariant, - the interval

s=sqr(x²+y²+z²-c²t²).

The choice of signs (signature) is not yet generally accepted. According to our choice of signature the interval will be some positive number when the r is bigger than ct. In this case the interval is space-like. In another case the interval is some imaginary number; the square of interval is negative; the interval is time-like.

Four-dimensional velocities.

Four-dimensional radius vector of a point:

R = (x, y, z, ict) = (r, ict),

Where r is the three-dimensional radius vector of a point. For clearness the three-dimensional vectors we will write in a solid; four-dimensional - solid underline. The units of components of R are meters. If we divide R by c, we'll receive the 4-vector r, with components measured in seconds,

r = (x/c, y/c, z/c, it) = (r/c, it).

Four-dimensional velocity is usually written in the following form:

U = dR/dt = (gv, icg),

Or in the form, normalized to unit vector:

u = dr/(dt) = (gv/c, ig).

The both formulae look simpler if we change gv by b. Moreover, if there exist two types of three-dimensional velocities, then there must exist two types of four-dimensional velocities. It is logically more correctly to name the values U and u as proper 4-velocity, because they were received by differentiating on proper time. Let's also change the designations U and u by B and b:

B = dR/dt = (b, icg),
b = dr/dt = (b/c, ig).

Then it is logically correct to suppose that coordinate 4-velocity can be received at differentiating on coordinate time:

V = dR/dt = (v, ic),
v = dr/dt = (v/?, i).

By squaring the 4-velocities we'll receive the following scalars:

B² = b² + (icg)² = - c²,
b² = (b/c)² + (ig)² = - 1,
V² == v² + (ic)² = - (c/g)²,
v² = (v/c)² + i² = - 1/g².

We can see that the squares of proper 4-velocities are invariants, but the squares of coordinate 4-velocities are not invariants.

If we multiply the vector of proper 4-velocity by invariant mass m, we'll receive the new 4-vector, - the energy-momentum, or 4-momentum:

P = mB = (mb, micg) = (p, iE/c).

The same expression we'll receive by multiplying the coordinate 4-velocity by relativistic mass:

P = Vm_r = Vm₀g = (m₀gv, im₀cg) = (p, iE/c),

Where m_r - relativistic mass, m₀ - rest mass.

By squaring the 4-momentum and using the known formula E²=p²c²+m²c⁴, we'll receive the new invariant:

(p² + i²E²/c²) = -E₀²/c².

Which under multiplying by -c² gives the square of rest energy E₀², and by dividing by -c² it gives the square of rest mass m₀², or invariant mass m². The choice between m₀² and m² depends on the used math formalism, does mass depend of velocity, or it is an invariant. Both formalisms are still alive now.

Three-dimensional momentum looks better if we use the proper velocity:

p = mb = mgv.

If we write the momentum through the relativistic mass, the expression looks better, if we use the coordinate velocity:

p = m_rb/g = m_rv.

Nevertheless, here we can see the deep symmetry between velocities.

If we take the derivative dP/dt, then we'll have the force 4-vector:

F = dP/dt = (f, img³(vdv/dt)/c) = (f, i(vf)/c) = (f, iN/c),

Where, f - three-dimensional force vector; N - is the force power.

If we take the similar derivative but on the proper time dP/dt, then

F = dP/dt = (fg, img⁴(vdv/dt)/c) = (fg, ig(vf)/c),

Which gives F² = f², if v and f are parallel to each other.

Types of acceleration

Thus, we know that the motion of the material body can be described by two types of velocities v and b, and by the rapidity, measured in m/s, which is also interesting.

But what acceleration is the proper acceleration? Which acceleration must be constant at the uniform accelerated motion, in order the astronaut would not die from overloading, and not become weightless after some time of flight?

Let's write comprehensible expressions for different types of acceleration.

dv/dt=d²r/dt².
Let's note in advance, that dv/dt = 1·dv/dt = g⁰dv/dt.

dv/dt=d(dr/dt)/dt = gd²r/dt².
dv/dt = g¹dv/dt.

db/dt = d(dr/dt)/dt = g³v(vdv/dt)/c² + gdv/dt.
If v || dv/dt, then db/dt = g³dv/dt.
If v is perpendicular to dv/dt, then db/dt = gdv/dt.

db/dt = d(dr/dt)/dt = g⁴v(vdv/dt)/c² + g²dv/dt.
If v || dv/dt, then db/dt = g⁴dv/dt.
If v is perpendicular to dv/dt, then db/dt = g²dv/dt.

dr/dt = (c·arth(v/c))' = g²dv/dt.
dr/dt = g³dv/dt,

Comparing the upper expressions, we can conclude that dr/dt = db/dt, at least if v || dv/dt.

It is well known from the relativistic mechanics that the second Newton low, written in the form f=ma, is nor correct. It's correct form is

f = m (g³v(va)/c² + ga),

Which is the basis for engineering computations for relativistic accelerators. If we compare this low with the acceleration db/dt:

db/dt = g³v(vdv/dt)/c² + gdv/dt,

We'll see, that they differ only by the factor m. Consequently

f = m·db/dt.

By the way, the mass again has the status of the measure of inertia. The Newton law is the relativistic law again, but it must be written through acceleration db/dt.

Four-accelerations.

It' simple to receive the following expressions:

dV/dt = (dv/dt, 0),
dV/dt = (gdv/dt, 0),
dB/dt = (db/dt, i(bdb/dt) / gc),
dB/dt = (gdb/dt, i(bdb/dt) / c),
dv/dt = (dv/(cdt), 0)
dv/dt = (gdv/(cdt), 0),
db/dt = (db/(cdt), i(bdb/dt) / gc²),
db/dt = (gdb/(cdt), i(bdb/dt) / c²).

If we multiply B = (b, icg), or b=(b/c,ig) by any of dB/dt, dB/dt, db/dt, db/dt, we'll have zero, i.e., vectors B and b are orthogonal to vectors dB/dt, dB/dt, db/dt, db/dt, and are parallel to each other in their own group.

(b·db/dt) = 0, (b·db/dt) = 0, and so on for any combinations of b and B.

But 4-vectors of v-velocities and v-accelerations are not orthogonal.

Relativistic rocket.

The relativistic rocket is the rocket in which the acceleration filling by the astronaut does not change with time. It is easy to show (look my Russian-language page) that proper uniformly accelerated rectilinear motion is described by the constant acceleration

db/dt = dr/dt = const.

The rocket must be made of two tanks, one is of matter, and another is of antimatter. In the combustion chamber the constantly decreasing portion of fuel are burning in every equal dt. The decreasing of portion of fuel is the result of rocket mass decreasing. Thus we can write

dp(M/M₀) = const (relatively time t).

Such process of fuel burning reminds us the law of radioactive decay. Computation shows that, if the start mass of a rocket is 1000 kg, if the proper acceleration of a rocket is 10 m/s², then all fuel will be used in the proper time of about 69 years.

From the other hand, if the Universe is closed and if it's curvature radius is equal to 2·10²⁵m, then the proper time needed for the Universe-round trip is 44 years, and coordinate time for this trip will be near to the "age" of the Universe, i.e. 13,3 billion years. If our Universe is the space-time crystal, and if the rocket will be launched, for example, in 2010, then we can see it today, approaching, from the opposite point of the sky. But what if we change our mind to launch the rocket? That will be defect of a crystal, and our rocket will not get to the future equivalent point, but we'll meet the rocket launched 13,3 billion years ago, with astronauts, who are about 40-years older, than their equivalent copies, remaining on the Earth.

If in the real Universe the proper acceleration is not db/dt=dr/dt, but dr/dt, for example, then the Universe-round trip will take the shorter time interval, but here we can not manage without the additional hypotheses.

Back to part 1: Three types of velocities. Rapidity parameter y and rapidity r.

Forward to part 3: Different forms of space-time transformations. Quantum velocities in Special Relativity.

Program of moving electron.

To index of Space Genetics.

Ivan Gorelik.

My Curriculum Vitae.

Extremely urgent note, 2009.

Attention! Magnetic trap of Devil!

There is a very big probability that magnetic trap will kill us all, if we will not stop powerful colliders.

Magnetic trap is an object, unifying hypothetical objects, connected primarily by magnetic forces: neutron drop / liquid; neutron hole; magnetic hole ...

It is probable that the microscopic magnetic trap can be created at the collider. Magnetic trap will grow capturing the normal substance. As a result, magnetic trap can destroy the Earth.

Magnetic hole is a magnetic analog of the black hole. The black hole is bounded by gravitational forces, and the magnetic hole is bounded by magnetic forces, which are many-many times stronger than gravity forces.

Magnetic hole is a magnetic dipole, in the form of a circle, where there is the critical magnetic field. The lines of magnetic induction are directed perpendicular to the plane of the circle. Nucleons are microscopic magnets, and they can be easily captured by the critical field of the hole. As a result the hole is growing.

The approximate computation shows that the minimal possible magnetic hole, which can capture a nucleon, has a mass slightly more than one thousand masses of nucleons. The Tevatron collider is now working near this region (1 TeV). The Large Hadron Collider (LHC) will be able to create the particles with the rest mass, which are seven times more that the minimal possible mass of magnetic hole.

According to publications, LHC will create microscopic black holes. Most theorists suggest that these black holes will disappear, because of the Hawking evaporation. However, we know that there are several theories of gravity. Some theories did not even admit the existence of black holes. In addition, there are several theories of black holes. Therefore, confidence in the classical theory of black holes and in a process of evaporation of black holes is very poor.

For several years, some scientists argue and demand to ban the construction of powerful colliders. Among the known dangerous objects that may lead to global catastrophe are the following: microscopic black holes, strangelets, magnetic monopoles, vacuum bubbles. I learned about these disputes and concerns only in early September 2008. And then I immediately noticed that the objects, bounded by magnetic forces, were almost not analyzed.

In early September, I assumed that the probability of a global catastrophe is less than 0.000001. However, after three months of analysis of the objects, bounded by magnetic forces, and after the analysis of space observations, my assessment of the global disaster has surpassed dozens of percents.

Some theorists suggest that the Higgs bosons will be registered at the LHC. And, if these particles will not been found, the theorists would be very surprised; - this would prove that the Standard Model is wrong. Higgs boson had received a new name, "the God particle". We know that the most of particles have their corresponding antiparticles. So, if there is a particle of God, then there is a particle of Devil. Two colliding particles can give two more massive particles, - the particle and its antiparticle, for example, an electron and positron. By adding the colliding energy, we can get the God particle and its anti-particle, the magnetic trap of Devil. Particles and antiparticles have diametrically opposed properties. Indeed, the Higgs boson causes the ordinary matter to have a mass. But the magnetic hole captures the substance and transforms its rest mass-energy into another form of matter, - the magnetic field of the Devil's trap. Say me now, are we have the right to touch the particle of God?

Microscopic magnetic holes created at the collider, will move to the center of the Earth, absorbing the matter in their path. Eventually they will merge together into a single and much stronger magnetic hole. The thin shell of the Earth, together with us, will be ejected into cosmic space, but the rest of the Earth will turn into an electric current loop of several meters radius. For comparison, the radius of a black hole of the same mass is 9 millimeters. Half of Earth’s mass will be transformed into magnetic field of neutron hole, and another half will be transformed into radiation and kinetic energy of the released shell.

Magnetic hole will not decay if it was born in such cold place, as the collider, where the temperature is close to 0 K. If the magnetic hole is born in a collision of space particle with atmospheric particle, it has a speed, which is close to the speed of light. As a result, such magnetic hole will evaporate almost immediately as a result of energetic collisions with atmospheric particles. Such evaporating magnetic hole will form a cosmic-ray particle shower. Such showers are observable.

Huge magnetic holes are also observable is cosmos.

In the remnants of supernova SN 1987A we can see a system of rings, which remind us the magnetic hole. It is possible that this magnetic hole is decaying now.

It seems as if these rings embrace a hyperboloid. And now look at the electron, moving along two hyperboles in coordinates x, ict, in my electron model program. Each electron crosses the entire Universe in a period of time, which is equal to the classical period of the electron. This paradoxical conclusion is the consequence of the Special Relativity Theory. The ring structure of SN 1987A and our electron model have common visible properties. The Earth and the Sun can be turned into the same ring structure.

Magnetic collapse is much more rapid than the gravity collapse. At the process of magnetic collapse the nucleon turns such, that its magnetic dipole moment becomes parallel to the magnetic dipole moment of a trap. Gravity collapse needs displacing of a matter inside the Schwarzschild radius. The time interval of neutrino registration at neutrino observatories had proved the reality of magnetic collapse of dying stars.

Particle's collision energies and bombs:

Several eV - chemical bomb;
Several MeV - nuclear bomb;
Several TeV - hyper bomb.

Chemical bomb is accompanied by the change of chemical structure of matter.
Nuclear bomb is accompanied by the change of nuclear structure of matter.
Hyper bomb is accompanied by the transformation of solid matter into a field.

Scientific crime.

Only crazy people can try to create the particles with the rest mass, more than 1000 nucleon masses. It is very possible that in the region from 1000 to 7000 aum, hundreds types of particles and resonances can be created. It is clear, that the most of them will decay. But some of them will grow, capturing the ordinary matter.

Academician Migdal wrote 30 years ago about pion condensation in the strong fields. As a result he had come to conclusion that neutron stars can have any masses. My approximate computation also shows that the minimal possible neutron star can have a mass, about one thousand of nucleon masses. Such embryo of neutron star can by made in collider.

Not long ago the new strange unexpected particle was discovered at the Tevatron collider. It decays at several muons, up to eight units. Somebody had already named it the Halloween particle. I named it the muon hole. What will be made the next? The magnetic trap of Devil? It will not decay, but it will transform us into its magnetic field.

Majority of contemporary physicists imagine quark-gluon plasma as a suck with peas. That is a very dangerous imagination. Particles are not points with labels, where their quantum properties were written. Particles are not the material essences, independent of space-time; they are just space-time elements, strings. 

Dear reader, the situation is extremely serious. The physics now is in the deep crisis. Theorists, in order to save their religious Big Bang theory, invented “the dark energy" as a new either. They want now to test their wretched theories at the powerful Large Hadron Collider.

Those persons, with high ranks and high scientific degrees, who cry about the safety of LHC, had already made a crime now. The LHC was launched despite the fact that there were court trials. The Earth could be exploded the 21 of September 2008, but the accident, which had happened two days earlier, had saved us. Scientists-criminals must be punished. But they continue to lie about the safety of the LHC, and are preparing the global terrorist crime now.

Dear reader! Big Bang adherents can lead the Earth to the utter destruction. Particle collisions with the energy more then 1 TeV must be prohibited by the international law. The science must be cleared from the Big Bang delusion. Big-bangers want to touch the particle of God, but thus, they lead us into the magnetic trap of Devil. People, will you silently endure the massacre?

Some documents and links.

In November 2008, I arrived to Moscow in order to file a lawsuit against the Russian Academy of Sciences and against the most active propagandists/promoters of the LHC launch. Unfortunately, for lack of funds, I still (February 2009) can not to do it.

In late November at the "meeting of four" there was decided to hear my report "What will LHC give us, the particle of God, or magnetic trap of Devil?" at a workshop in one of the leading institutions of Moscow. But later, I received a "retreat" from this institution

In December, I sent the Letter to the President of Russia. In January, I received an answer in which it was stated that my letter was forwarded to the Russian Academy of Sciences.

In December, I sent the Letters to the Prosecutors Office of the Russian Federation. Soon after, I received the answer stating that my letter "was sent for review in the prescribed manner".

In the end of January I returned to Feodosia (Ukraine) and continued to inform about the risks of the global catastrophe. You can read some letters, which were send to the Google groups, - just click my Google-profile.

Reproduction of biospheres and civilizations. Who are you, dear reader: "a cell of good reason", "a curiosity cell", or "thoughtless muscular cell"?

Magnetic trap of Devil. Recent calculations show that it is not excluded that microscopic magnetic traps were already created, and they are growing now somewhere inside the Earth.

Arguments, proving that "The LHC will lead to global catastrophe"; "Magnetic holes exist"; "We will not be able to prevent the LHC launch and the following global catastrophe". Religious and mystic arguments.

Read the frequently updated page
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for more news, links and developments of this topic.

The end of Extremely urgent note, 2009.