I can prove that it must have weight, or else energy conservation law is broken.
Relativistic mass is easily exchangeable with rest mass, and there is realy no definition to tell which mass is rest and which is relativistic.

Also light have only relativistic weight, but it still is affected by gravity.
here is example of prpetual motion device based on negletion of that fact.
http://www.richardclegg.org/htdocs/perpetual/mtl.html

Similar device can be made if you neglect relativistic mass weight.
Box with 2 flywheels whose energy periodicaly is converted to matter and antimater and back ro relativistic mass, (matter and antimater realy have rest mass and weight nobody will argue with that) remember that box is closed and have no energy or mass input or output.
We put that box on spring, and it will bounce up and down.

If someone knows, please tell any experimental evidense that relativistic mass have or do not have weight, without experimet there is no sure way to say how it is realy, but alowing it to have weight makes everything much simpler.
of course you can use various space-time curvature stuff, but it has no real meaning even if mathematicaly can substitute reality. Afterall mathematicaly you can always substitute force with acceleration, if mass is constant, so lets assume that gravity is force (N/kg), not acceleration.

When a matter moves very fast (relativistic velocity) it has an additional energy E=mvv/2. The rest mass has energy E=mcc. According to that all this energies may be attractive.
It is not so simply. Thare are many theories.
In the Heim Theory and LQG the space is a special discrete stoff and the energy (photons, baryons, bosons, neutrinos, rezonans) are just an oscillation of this stoff. The gravitation is the inward oscillation and kinetic energy is the oscillation of the whole particle.
The faster velocity means higher frequency of the particle vibration. The higher frequency means more mass (frequency of the electron and proton) but very high oscillation breaks the structures (ionization of the atom).
There are some theories that a matter in relativistic velocity is repulsive for the environment. The kinetic energy propagated through the space will be stronger then the attractive
gravity.http://www.physorg.com/news10789.html
Very close to the speed of light this kinetic energy may be transformed into particle-antiparticle moving in oposite direction.
That way , it seems not possible to create an overdense singularity. This concentration of the energy causes just an outburst of the gamma radiation.
All energies are attractive gravitationally but kinetic energy drives oscillations and rotations and is repulsive at least.
Kinetic and gravitational energy in a Black Hole:
http://www.nature.com/news/2005/0503...0328-8_pf.html.
http://www.blackholes.int.pl

At least I am not the only one who thinks that all energies are attractive.

About this repulsion stuff I am not sure, but it looks that you logicaly need more than light speed to reverse gravity, if you accept that it propagates at speed of light. Anyway if they do some experiments it will be tested.

Time slows when an object approaches the speed of light so faster velocity means slower frequency of the particle vibration.

The time dilation is for an outer distant observer. That way it is not possible to reach a speed of light by a massive object. In the particle with a rest mass the information has to go and reach all the components of the particle. Such a particle become almost flat in the dorection of the movement. According to that an electron has a space structure like a system of the wave.
We observe Cosmic Rays - protons mostly with GeV energy and very fast vibration with a speed close to light. This energy passing the other proton with this relativistic velocity to it causes a creation of the particle-antiparticle moving just in opposite direction.
The energy can't stay at rest (Schroendiger Zitterbewegung) it oscillate together with a space. A sum of the energy gives higher frequency. The higher frequency is more attracive gravity but more repulsive kinetic energy too. This kinetic energy destroys even the stronger EM attractive force.

An object falling into a black hole reaches the speed of light as it crosses the event horizon. The event horizon is a calculated point. It is not a solid surface so there is nothing to stop a falling object from reaching the speed of light.

The acceleration of an object causes the object’s time to slow so increasing forward speed slows the internal vibrations of the object.

The problem of the Event Horizon of a Black Hole is not solved yet.
We suppose the Black Hole exists.
We suppose that an object fallig into BH become as fast as the light.
We know that particle with a rest mass can't move with speed of light.
For a distant observer the object at the Event Horizon slows down - less velocity, less energy.

We observe the accretion disk around the BH - there are very fast moving particles. If it is very close to Event Horizon they move as fast as the light almost. This particles emit the X-rays.

Scientist explain that this very fast energetic particles interact with CMBR photons and due to Comptons scattering this gravitational energy is transformed into kinetic and thermal energy.

According to LQG and Heim theory gains the relativistic particle the energy from the interaction with the space structure.
Faster particle - higher frequency - more virtual paticles.

The speed of light is possible for a simple wave only.
The wave structures as particle with a rest mass can't reach the speed of light.

I admit that I don't understand what you're trying to say in the OP, but wrt this part ...

to what extent is the mass of the particle(s) being accelerated, in colliders*, factored in to the design of those colliders?

IIRC, the beam lines are aligned with a precision of microns (or smaller), and the collision points determined to what, a nanometre or so? If you do the math, I think you'd find that in something like RHIC the treatment of the mass of the accelerated particles, in terms of correcting the beam to account for those particles 'falling', is large enough to require explicit inclusion in the design.

*of the cyclotron, or circulating ring type; likely to be less important for lineacs.

You're confusing the issue by mixing mass and weight. Weight is the force a stationary object will exert in a given gravitational field. Since it is not practical to weigh a moving object--particulary one moving very fast--"inertia" is used instead of "weight." In particle accelerators, the change in inertia is very real, and must be taken into account in order for them to work. That is the experimental proof.

Why can't an object falling into a black hole move at the speed of light?

We speak about a movement in two different reference frames.
In one reference frame it is not possible to reach a speed of light by a particle with a rest mass. We observe high energetic particles accelerated in cyclotrons, in Earth atmosphere (Cosmic Rays), There are close to speed of light but never so fast.
In Black Hole is the space comoving with the Black Hole itself. It is a frame dragging. If the particle is moving very fast in the Black Hole frame it may move faster then "c" but relatively to us in a different reference frame.
It is similar like jets moving faster then "c" ejected from Quasar.

Nereid is correct here, although she has mixed up cyclotrons and the synchrotrons that followed them. The latter are the basis of modern storage rings such as those at SLAC, FNAL, CERN, KEK, BNL, or any other high energy physics lab. Acutally, one of the reasons cyclotrons are limited in the energy they can generate (aside from the increase in magnet size) are the relativistic effects that that type of accelerator cannot handle. As the particle's energy increases, it's relativistic or effective mass also increases. This mean that you need a stronger magnetic field to keep it in the same orbit at higher energies than you would predict if the particle's effective mass remained unchanged with energy. This effect messed up cyclotrons. In those machines magnetic field remained constant, but the orbital radius changed with increasing energy. Relativistic effects messed up the balance between orbital time and energy that cyclotrons depended on. The synchro-cyclotron was a stop-gap, that eventually led to the modern synchrotron. Here the orbit is constant, but the magnetic field that steers the beam is adjusted as energy increases to maintain that orbit. Here's a link that also explains the difference between cyclotrons and synchrotrons and the need to take relativistic effects into account in their design. For those who prefer wikipedia, here's their entry on cyclotrons. It includes descriptions of the relativistic limits as well. It also has links to articles on synchro-cyclotrons, synchrotrons, and linacs (which I haven't mentioned before).

__________________
"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

Thank you Eta C for explanation and links for experiments on cyclotrons.
I have found a link about a gravity of the relativistic mass - http://www.ph.rhul.ac.uk/course_mate...20dynamics.pdf
They (departament of physics of London University) prove that relativistic mass has its gravity.

What do you mean when you say relativistic mass has gravity? I don’t see how the information in the paper applies to gravity. You appear to be confusing relativistic mass with an actual increase in mass. Relativistic mass is an observer dependent space-time dilation and not an actual increase in mass.

Does a massive object moving at relativistic speed have more inertia than one would expect from Newtonian calculations?---Yes.
Does this increase in inertia appear to a distant observer as being identical to an increase in mass?---Yes.
Does a box with one or more spinning flywheels weigh more than a box with flywheels at rest?---No.
Is the mass of the universe greater because some of the galaxies are moving at close to the speed of light?---No.
Do objects falling into a black hole add more than their rest masses to the mass of a black hole?---No.

"Ouch! The concept of `relativistic mass' is subject to misunderstanding. That's why we don't use it. First, it applies the name mass--belonging to the magnitude of a four-vector--to a very different concept, the time component of a four-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself." Spacetime Physics by Taylor and Wheeler.
http://math.ucr.edu/home/baez/physic...ity/SR/mass.ht

This problem become very important and it should be explained.
In old string theory and traditional physics are there the particles moving in an empty space. Every interaction needs a particle. That way moving particle has more kinetic energy and the gravity is produced by a rest mass only.

In Heim theory, Loop Quantum Gravity and String M-theory the particles are built of the vibrating space itself. That way is the intrinsic structure of the particle changed in its movement through the space.
The gravity is an inward warping of the space an there are not additional mediating particles.
The particles with the rest mass and photons are each of them build of the space alone. The difference is that photons move with a wave wth a speed of light. A free photon warps the space but it moves with this distirtion itself. That way it is not a space distortion behind or next to photon and it can not create a gravitational field because it moves as the every information with a speed of light.
The moving particle has its rest mass and kinetic energy. The kinetic energy means just additional oscillation of the rest mass and we can not distinguish them. It is just a faster inward oscillation of the space.

A box with one or more spinning flywheels weigh more than a box with flywheels at rest.
The galaxies are driven by a Dark Energy supplied from outside of our Observable Universe and the total mass is greater. The flat geometry (critical density) needs increase of the mass in an expanding Universe.
The photons falling down into the Bleck Hole increases its mass. If there is a point singularity inside BH there is no rest mass at all. The rotating Black Hole rotates with its space-time together and pulls everything according to its rest mass and rotating kinetic energy.

http://www.crystallizationcon.com/Photon-Graviton.htm
http://www.allanstime.com/UnifiedFie...ry/gravity.htm

Could it be that at the event horizon whatever matter is entering the blackhole is converted to pure energy and thereby attains the speed of light? When I think of blackholes I consider them to be merely balls of chaotic energy self-contained by the gravity of the energy. Conversion to energy at the event horizon would be consistent with the fact that matter "screams" x-rays as it is entering the blackhole which in my mind signals that a transformation is occurring.

The difference between a blackhole and the cosmic kernel is the fact that the cosmic kernel had "organized" energy which all pointed outwardly and also the cosmic kernel had the added "propulsion" of the anti-gravity effect of spacetime stretching.

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My invisible elf ??? Why he is made of dark matter and lives off of dark energy !!!
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You may be right about matter becoming pure energy at the event horizon. Even if there isn't an actual conversion of matter to energy, I think it would be hard to draw a line between the two.

If the cosmic kernel had/has enough mass to be a closed universe, then we may still be on the inside. The only difference between the cosmic kernel and a black hole may be a matter of which side of the event horizon we are on. The inside or the outside.

Under general relativity, the value that couples to gravitation is the stress-energy tensor, not just mass. What that means is that energy of any sort will have a gravitational effect. So, for example, in Bob Angstrom's example above, a box of spinning flywheels has more energy than the same box with the flywheels at rest. It will actually weigh slightly more. It's just that, in most cases, the difference is so tiny that it wouldn't be measurable.

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Conserve energy. Commute with the Hamiltonian.

I agree.

The extremaly concentrated energy will draggs the space and it will be a closed independent system but energy of any sort will have a gravitational effect.

A Galaxy Clusters in Hubble Deep Space escape with a speed close to light. It does not mean this galaxies are moving in the space so fast. Our Observable Universe get more Dark Energy and according to relations Mass/Radius decreases its average density like in Gravastar. The Galaxy Clusters are escaping with their space together.

What , if the antimatter falls down into a Black Hole ?
Does its gravity increase or decrease ?
There will be more gamma photons of the annihilation (relativistic mass).

Increase. Even antimatter has a positive mass and thus a postive stress-energy, which gets added to the black hole's stress-energy.

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Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

I do not mix them. In short question is this: if we take box with spining flywheels inside and box with stopped flywheels which will have more weight. I supopose everybody agree that soining flywheel have more mass. same with acelerated particles, if we have fast particle and slow particle, fast must have more weight. if only rest mass is affected by gravity and all mass is affected by inertia, ir will be wrong, this way slow particle will fall faster than slow particle.
also that beats equivivalency between acceleration and gravity pustulate. if relativistic mass do not have weight.

And the relativistic mass has a weight.
The very fast object may become a Black Hole. It is very difficult for a small object because we can not hold the photons at the object (it explodes before it become a BH).
A very fast star may become BH.
The far away Galaxy Cluster is not BH because it do not move relatively to its space. It moves within its dragging space-time.

http://math.ucr.edu/home/baez/physic...lack_fast.html - it is wrong.

And your proof of this? No, I don't want word salad. Show us with the math where a moving particle will turn into a black hole.

Well, I don't think so, it agrees with the GR math. Please show us where the GR math is wrong, otherwise, what you posted about is just something you asserted, without any kind of support.

__________________
Some try to tell me, thoughts they cannot defend,... - Moody Blues.

Neptune- The original Dark Matter.

The author feels that this technique of deliberately lying will actually make it easier for you to learn the ideas. - Donald Knuth

We know that energy supplied into a Black Hole increases its gravity.
More energy (photons) - more relativistic mass - more gravity.
Relativistic mass increases gravity.

A small Black Hole does not exists - it explodes before it become BH.
A moving fast star does not explode. If this star approaches close to supermassive BH it may gain velocity near the speed of light.
We know that relativistic particles have relativistic mass. The star with a relativistic velocity has a relativistic mass too. That way this star may become a Black Hole. It is an observational fact that binary Black Holes exchange their energy via the gravitational field, not EM.

GR math is good. A star gains a relativistic mass when it moves relatively to its surrounding space. It is not depend on a reference frame. We observe the particles moving faster then speed of light in a different reference frames. Does it gains a super relativistic mass ? no. Because it moves within its space-time. The relativistic mass is created in a movement relatively to its space, in its reference frame.

We produce a matter-antimatter by collision of relativistic particles. New created particles have their gravity. Is this gravity created in the moment of the pair creation or it was in the relativistic particle before already ?

We do not need any math here.
Does the relativistic mass have a weight or not ?

Tensor's request is a good one - "Show us with the math where a moving particle will turn into a black hole." It is also a direct, pertinent question wrt the claims that you, czeslaw, are making.

This is not a request that asks whether we need math or not; it is a direct, pertinent request that you - or any other proponent of this idea - show us, using math, equations, numbers and stuff, that a moving particle will, indeed, turn into a black hole.

If you cannot (or are unwilling to) provide the relevant math to back up your claims, then please say so.

Only relative to a non-moving mass.

Quote:
Originally Posted by czeslaw
http://math.ucr.edu/home/baez/physic...lack_fast.html - it is wrong.

czeslaw, just read all of this link, including the FAQ's. It explains the common misconceptions and it is right.

Speed has nothing to do with black hole creation!

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RussT
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Everything is, as it should be, otherwise, it wouldn't be!

I wrote that particle can not turn in a black hole. It gains a relativistic mass - we know it experimentally - but it is not enough to reach the conditions for Black Hole.
The star can gain a relativistic energy and relativistic mass creating a Black Hole. It is what we observe during collision of the neutron stars.
The relativistic mass is not an imaginary mass it is additional oscillation of the space-time and it creates an additionally gravitational field. This gravitational field is exchanged between stars in binary systems (we observe it). Some scientists call it gravitational wave. The star moving close to other star exchange its gravitational energy and that way its orbit is shifted.
It is like Mercury orbit around Sun.
I do not believe that the clasic Black Hole exists. It might be a Gravastar only.
Recent observations of the collisions of the neutron stars shows the mysterious effects.
It is difficult to make the math. Nobody knows how behave a star close to other Black Hole.
Mercury's orbit change because the time delation in gravitational field of Sun.
It is because stronger gravitational field close to Sun. There is higher oscillation of the space-time close to Sun. It is not an imaginary or relatively effect. It is because the movement in a defined space.
Gravity increases not relatively to an observer but relatively to the space of the moving object.