Astrophysical jet and length contraction

Astrophysical jets are flows of matter that moves at relativistic speed. They are opportunity to see length contraction in action. An astrophysical jet is analyzed to explain the length contraction effect.

Astrophysical jets are ejected from compact objects such as black holes. https://en.wikipedia.org/wiki/Astrophysical_jet#/media/File:M87_jet.jpg is a photograph of the jet ejected by the supermassive black hole at the center of the galaxy M87 which stretches over 5 000 light-years. Matter in this jet moves at almost the speed of light and undergoes relativistic effects.

Almost all predictions of Special Relativity are proven by experiment except one: length contraction. Indeed, it is impossible to accelerate chunk of matter to relativistic speed to directly measure length contraction on Earth. Fortunately, length contraction should occur in astrophysical jets where we could finally see this effect for real.

An astrophysical jet is a moving cloud of particles whose velocity varies from almost the speed of light in the ejection region to very slow thousand light-years away. We name the jets in these 2 regions fast jet and slow jet. The fast jet should be strongly length-contracted while the slow jet should not. Let us compare a moving cloud of particles with the air inside a ball. The air inside a moving ball moves with the ball and would seem denser than the air inside the same ball at rest because the flat moving ball has a contracted surface. In the same way, fast jet should seem denser than slow jet. Since the particles of an astrophysical jet emit photons, the fast jet should be brighter than the slow jet. As the slowdown of the jet is gradual, we expect that the brightness of a jet decreases gradually from the fast jet to the slow jet. However, we do not see such gradual decrease of brightness in the photograph. Why?

Please read the article at
PDF: Astrophysical jet and length contraction https://pengkuanonphysics.blogspot.com/2019/08/astrophysical-jet-and-length-contraction.html
or
Word: https://www.academia.edu/40066246/Astrophysical_jet_and_length_contraction

How to test length contraction by experiment?

Relativistic length contraction is theoretically predicted but not directly tested, which lead to incorrect interpretation of the theory illustrated by Bell’s spaceship paradox and Ehrenfest paradox. But these paradoxes can help us designing experiments to test length contraction.

Ideal direct experimental proof should contain the following steps:
1. Measure the tested object’s length at rest, the value l0.
2. Put this object in motion.
3. Measure the object’s speed, the value v.
4. Measure the object’s length in motion, the value l.
5. Check if these 3 values verify length contraction law.

For doing this experiment, the difference of length l0  l should be in measurable range. If the object is a chunk of matter, l0  l is not measurable. For example, matter objects with the highest speed we can make are satellites, whose speed is generally 7.8 km/s. If a satellite is made of a string of 100 km long, the value of l0  l would be 0.03 mm, which is absolutely not measurable from the ground. This is why contraction of length has never been measured.

Below I propose two experiments inspired from Bell’s spaceship paradox and Ehrenfest paradox.

Please read the article at
PDF: How to test length contraction by experiment? https://pengkuanonphysics.blogspot.com/2019/06/how-to-test-length-contraction-by.html
or
Word: https://www.academia.edu/39584663/How_to_test_length_contraction_by_experiment

Twin paradox when Earth is the moving frame

We analyze the mathematical mechanism that slows the time of the traveler in the twin paradox and explain what distinguishes the traveler’s frame from the Earth’s frame

Please read the article at
PDF: Twin paradox when Earth is the moving frame https://pengkuanonphysics.blogspot.com/2019/05/twin-paradox-when-earth-is-moving-frame.html
or
Word: https://www.academia.edu/39216040/Twin_paradox_when_Earth_is_the_moving_frame

Graphic of set counting and infinite number

When counting a set, we can plot a graphic that represents the members of the set on the plane (x, y) to observe visually the counting. Also, graphic of counting of infinite set helps us to understand infinite natural number.

PDF Graphic of set counting and infinite number https://pengkuanonmaths.blogspot.com/2018/11/graphic-of-set-counting-and-infinite.html

or Word https://www.academia.edu/37766761/Graphic_of_set_counting_and_infinite_number

 

Analysis of the proof of Cantor’s theorem

Cantor’s theorem states that the power set of ℕ is uncountable. This article carefully analyzes this proof to clarify its logical reasoning

Please read the article at

PDF Analysis of the proof of Cantor’s theorem http://pengkuanonmaths.blogspot.com/2018/09/analysis-of-proof-of-cantors-theorem.html
or Word https://www.academia.edu/37356452/Analysis_of_the_proof_of_Cantors_theorem

Longitudinal magnetic force and high field magnet

Theoretical explanation of longitudinal magnetic force and its practical application in high field magnet. Although longitudinal force is not explained in classical theory, its action has been demonstrated by several experiments long time ago. For example Nasilowski effect. But why is it not recognized in theory? The reason is that it shows no significant effect on practical devices, so no physicist is interested in exploring these experiments. But I have found a huge effect of longitudinal force in high field resistive magnets which could improve their performance.

Please read the article at
Longitudinal magnetic force and high field magnet
PDF http://pengkuanem.blogspot.com/2018/06/longitudinal-magnetic-force-and-high.html
or
Word https://www.academia.edu/36787024/Longitudinal_magnetic_force_and_high_field_magnet

Showing tangential magnetic force by experiment

Theoretical explanation of tangential magnetic force and the experiment of rotating coil. Tangential magnetic force is tangent to the current on which it acts. For the classical theory this force does not exist. However, my experiment « Continuous rotation of a circular coil experiment » showed that a force tangent to the current must be there. If tangential magnetic force exists, why was it not detected in almost 200 years?

Please read the article at
Showing tangential magnetic force by experiment
PDF http://pengkuanem.blogspot.com/2018/05/showing-tangential-magnetic-force-by.html
or
Word https://www.academia.edu/36652163/Showing_tangential_magnetic_force_by_experiment

Plasma under Coulomb magnetic force

Nuclear fusion reactors use strong magnetic field to confine plasma in reaction chambers. The magnetic field is so designed that plasma should follow field lines which do not encounter the chambers’ wall. But it seems that a mysterious force pushes plasma off its track. For explaining this force, Coulomb magnetic force law for plasma is derived.

Please read the article at
Plasma under Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/04/plasma-under-coulomb-magnetic-force.html
or
Word https://www.academia.edu/36379490/Plasma_under_Coulomb_magnetic_force

Coulomb magnetic force

The relativistic length contraction effect and changing distance effect produce 2 different magnetic forces. Together they form complete magnetic force.
I have derived 2 magnetic forces with Coulomb’s law and charges’ velocity. The first force dFlc is derived in «Length-contraction magnetic-force between arbitrary currents». The second force dFcd is derived in «Changing distance effect». dFlc and dFcd are added together to give the expression for complete magnetic force dFcm.

Please read the article at
Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/03/coulomb-magnetic-force.html
or
Word https://www.academia.edu/36278169/Coulomb_magnetic_force

PDF Changing distance effect http://pengkuanem.blogspot.com/2018/03/changing-distance-effect.html or
Word https://www.academia.edu/36272940/Changing_distance_effect