Possibly all three. Definitely 2) and 3). In the case of 3), the net force decreases, but that's because a resisting force increases. As regards 1), it might be the case, but if it is, it's hard to quantify mathematically. The so-called relativistic mass doesn't actually imply any increase in the rest mass. But the rest mass might possibly be increasing nevertheless.

All this just shows how confused people were. There's no reason or excuse in remaining confused. Electrodynamics is uniquely defined by the properties that the equations of motion of fields and particles are invariant under global Lorentz transformations, gauge transformations and don't contain derivatives of order higher than two. These properties are necessary and sufficient.

And they imply in particular that the mass of any object is invariant, that the energy depends on the reference frame in a psrticular way but what matters is a particular combination of energy and momentum and that the force, likewise depends on the reference frame. And that only quantities that are invariant under Lorentz transformations and gauge transformations make any sense-since only those don't depend on the reference frame-all other quantities are useful for constructing the invariants. Not all questions make sense.

1) the inertial mass, m, of the particle increases when v/c increases in Lorentz factor – that is “relativistic mass” m=γm0, m0 is “rest mass”;

2) the energy of the particle increases when v/c increases – the scalar energy E=mc2 always, independently on v/c;

3) the force that the particle feels decreases when v/c increases – that looks as rather vague proposition, any force is f=dP/dt, where dP/dt is determined by external something, in this case an accelerator’s technique, and directly doesn’t depend on v/c.

Besides that

“…And they imply in particular that the mass of any object is invariant...”

- really is also – though is a standard tenet in mainstream physics a rather vague - claim. Really particles always move in 4D space with metrics(cτ,X,Y,Z) of the utmost universal “kinematical” Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, [5]4D spacetime with metrics (cτ,X,Y,Z,ct) only with 4D speeds of light, c [“bold” means 4D vector] always having 4D momentums P=mc, and energies E=Pc; including having rest mass particles, if are at rest in 3DXYZ space, move with the speed of light only along cτ-axis, at that P=P0=m0c.

If such particle is impacted by 3D space momentum, p, and so has 3D speed V and momentum p=mV, since the 4D space is fundamentally Cartesian, the particle momentum’s cτ-component remains be P0=mVcτ=m0c, i.e. this component at 3D space interactions – what is mostly in Matter - is constant, while real particle’s “rest mass” in co-moving with the particle frame is m;

- from what it follows that rest mass is “invariant”, i.e. observer in co-moving frame measures rest mass = m0. This clarification isn’t too essential at “kinematical” 3D particles interactions, say, at experiments on accelerators, however that can be essential at considerations of coupled by some fundamental Nature forces systems of particles, bodies, etc.

More see the Shevchenko-Tokarevsky’s informational physical model

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics

Cheers

Sergey Shevchenko , The energy-momentum four-vector is a very interesting concept. But don't forget that relativistic mass is merely a definition, based on the product of the rest mass and the asymptotic factor. What we don't know is whether or not the actual rest mass itself increases with speed. That would add in a new complexity which might be very difficult to model mathematically.

I don't know the answer.

1) relies on 'relativistic mass' which is no longer generally accepted (by me).

2) is what happens.

3) The force on a a particle depends on external interaction, not the particle's velocity.

No one (me) believes Weber's electrodynamics.

Did Wien write before Minkowski?

Mass is a measurement of energy and not only matter as in Newtonian mechanics. In Einstein's special theory of special relativity,as an object moves faster, its observed mass(relativistic mass)increases. This increase is negligible at everyday or Galilean speeds. But as an object approaches the speed of light, its observed mass becomes infinitely large. As a result, an infinite amount of energy is required to make an object move at the speed of light. For this reason, it is impossible for any matter to travel faster than light speed.

In this interesting YouTube video,Top Physicist and Columbia-University Professor Brian Greene explains the importance of relativistic mass and its relation to the speed of light.

https://youtu.be/ezU-zfjm7ew

Frederick David Tombe ,

Frederick David Tombe,

“…The energy-momentum four-vector is a very interesting concept. But don't forget that relativistic mass is merely a definition, based on the product of the rest mass and the asymptotic factor….”

- “The energy-momentum four-vector” of moving in 3DXYZspace, say, a particle, is defined in the SR in 4D Minkowski space with [really] metrics (it,X,Y,Z), P4≡(iE/c, p), p is the particle’s momentum in the 3D space [in textbooks the imaginary unity above is absent, however really exists, and only is hidden by covariance/contravariance mathematical technique], E is the particle’s energy. What is rather strange, energy and momentum, though are linked, are different parameters of material objects.

In the SS&VT physical model it is rigorously proven that in Matter’s spacetime all dimensions fundamentally are, of course,[mathematically] real, and is rigorously shown that real utmost fundamental and universal spacetime has metrics (cτ,X,Y,Z), and is fundamentally Cartesian – first of all the cτ-dimension is fundamentally/materially/ physically is orthogonal to any 3D line. Correspondingly the real 4D momentum of a particle, P≡(m0c, p), where “rest mass”, m0, isn’t equal to zero if relates to the “T-particles”; a “S-particle” photon has 4D momentum, P≡(0,p); P2=(m0c)2+p2 , energy of any/every particles E=Pc.

Note also the important point: since from the SR postulates that there is no absolute Matter’s spacetime and that all inertial reference frames are absolutely equally equivalent and legitimate any number of senseless consequences follow [the simplest and evident one is the Dingle objection] completely rigorously it follows that Matter’s spacetime is absolute,

- and so some “absolute frames” that are at rest in absolute 3D space are possible. Though because of the action of really extremely mighty Galileo-Poincaré relativity principle the frames in most cases, including at everyday physical practice, are really equivalent, the absolute frame fundamentally differs from any other [moving is the space] frame in that in an absolute frame all material objects parameters have real values, while in other frames the values are unreal. So at consideration of physical situations in some cases it is more rational to do that in an absolute frame, and further to consider it in other frames.

Including so there can be situation when the relativity principle doesn’t act completely, and so it is possible to observe absolute motion and to measure the absolute velocity of Sun planet system, as that happens for a pair of free clocks; such – practically for sure really doable - experiment was proposed yet in 2013-2016, more see https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible

“Relativistic mass” by no means differs principally from “rest mass”, both are only “measures of inertia”, besides the point that the 4D momentum cτ-component remains be constant at any 3D space interactions being equal to m0c, and so m0 is invariant in inertial reference frames, despite that really the “rest mass” of moving particle in co-moving frame really is “relativistic mass”, So to

“….. What we don't know is whether or not the actual rest mass itself increases with speed. That would add in a new complexity which might be very difficult to model mathematically.

I don't know the answer. …”

- see above – and the yesterday SS post.

“…Mass is a measurement of energy and not only matter as in Newtonian mechanics..”

- in Newtonian mechanics “mass” isn’t some “matter” - as that in those time humans used this notion in everyday practice, but in the mechanics is completely scientific physical parameter of bodies “measure of inertia”;

- and by no means it is a measure of “energy”, inertia and energy are, though fundamentally linked and so co-existent always together, but fundamentally different parameters of “matter”.

More see the SS post above and papers that are linked in the post.

Cheers

What is "the SS&VT physical model"?

“…

“What is "the SS&VT physical model"?”

- the SS&VT informational physical model is expounded in 3 main papers: https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics,

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force

The model is completely consistent with all really reliable experimental data, and reliable mainstream physics theoretical results; a few specific experiments that test just the model – and corresponding points in mainstream physics, of course, are described in

https://www.researchgate.net/publication/215526868_The_informational_model_-_possible_tests, and

https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment - tests of Gravity model and observation of quantum nature of Gravity;

https://www.researchgate.net/publication/259463954_Measurement_of_the_absolute_speed_is_possible - observation of absolute motion and measurement of absolute velocity in the 3D space.

Cheers

L'énergie de la particule augmente puisque elle est proportionnelle au facteur de Lorentz gamma, par contre la masse diminue elle se transforme sous forme d'énergie