Apparent Violations of Principle of Relativity?

[BruceAW]

TL;DR

I consider the concept of ' 'Proper motion', in response to apparent violations of the principle of relativity.
Relativistic mass. Parallel currents., violate inertial frames of reference. Cavendish balance, can measure relativistic mass..
I am aware of Lorentz transformations

I have for a long time been pondering the concept of 'Absolute velocity'. Or, 'Proper motion'.
The velocity of an object, with respect to the center of mass of the universe, and the cosmic microwave background radiation.
Ways, it seems to make more sense, than merely relative velocities, with no preferred frame of reference.

The principle of relativity ,Which can be paraphrased as.
'Any inertial frame of reference (at zero or constant velocity), is as valid as any other, for observing and understanding motions and forces.'
Or. If two observers have a constant relative velocity. Then either may be considered 'at rest', and the other to have the whole of the relative velocity.

The first time I questioned 'relativity' was in relation to relativistic mass (Mrl)
(I will assume 'we' know relativistic mass is gravitational)
Relativistic mass, Mrl = M/sqrt[1-(v^2 /c^2)
{Relativistic mass, Mrl . rest mass, M. Velocity v. light speed,c.}
If we imagine that an observer,moving at velocity V (With respect to what??)
Has a Cavendish balance, that can measure the gravitational attraction between two sample test masses, the effect of various velocities, on their relativistic mass, Mrl, could be measured.
If they could be accelerated, in various ways until the minimum value of relativistic mass, was measured. they could be considered to be 'at rest', in that situation. And, their rest mass, M, could be determined.
To measure the magnitude of their velocity, they then only measure relativistic mass,Mrl, and calculate V, with the equation for Mr as a function of M and v, (above)
{v = c* sqrt[1 - M^2/Mrl^2 ], I velieve. But the point is, a value for v ccould be calculated from measurements of rest mass M , and relativistic mass M.}

This implies to me, a 'prefered frame of reference', where the measure of the gravitational force between the test masses is least.
And a 'proper motion', calculated from comparison of the rest mass and relativistic mass.

Also, there is the case of two charges moving 'side by side'. each other, at equal velocities V in the x direction. Maintaining equal x coordinates. A short distance from each other in the y direction.
I have read that this conundrum, is sorted out by application of Lorents transformations.
But, please hear me out..
Two electrons, with a relative velocity V, with respect to, and moving away from, observer A , along the x axis.
Observer A, sees the electrons converging, due to the attractive magnetic force, of 'parallel currents'.
Observer B, moving with the electrons, Must also, see them converge!
But, observer B, sees the electrons 'at rest', in the x direction. And, expects, them to move away from each other, due to elevtrostatic repulsion.
Observer B, must conclude that the electrons are moving at a significant velocity V. Which he could calculate from the motion of the electrons. With respect to the 'prefered frame of reference', in which we can calculate the magnetic forces of parallel currents.)
He might have to use Lorentz transformations to calculate the correct velocity.
But, No Lorentz transformation, involving the 'Gamma function' (1 / sqrt[1-(v^2/c^2)], will change the sign of a measurement of an attractive force, to some relativistic repulsive force.
{ {I think}}

Another example of a violation to 'relativity', might be, 'Critical Ionization Velocity'.
https://en.wikipedia.org/wiki/Critical_ionization_velocity
Hydrogen ionizes, at 0.5 m/s. With Respect to what?
Could this be due to repulsive magnetic forces of the anti-parallel currents?

 

[Ibix]

I will assume 'we' know relativistic mass is gravitational

You assume wrongly. The source of gravity in relativity is the stress-energy tensor.

a Cavendish balance, that can measure the gravitational attraction between two sample test masses

This will measure the rest mass of the sample masses, since it is at rest with respect to them, so the only relevant part of the stress-energy tensor is the rest energy density of the samples.

But, please hear me out.

Why? You already stated the obvious result - the charges repel. The Lorentz transforms applied to the Faraday tensor will let you work out the details in the frame where the charges are moving if you want.

Another example of a violation to 'relativity', might be, 'Critical Ionization Velocity'.

That depends on the velocity difference between two media. That is not a violation of relativity.

You keep asking: velocity relative to what. In each case you have mentioned except the last, it is relative to an arbitrarily chosen standard of rest. Usually, you and your lab, although not always.

 

[Nugatory]

(I will assume 'we' know relativistic mass is gravitational)

But we already know that relativistic mass is unrelated to gravitational mass

Observer A, sees the electrons converging, due to the attractive magnetic force, of 'parallel currents'.
Observer B, moving with the electrons, Must also, see them converge!
But, observer B, sees the electrons 'at rest', in the x direction. And, expects, them to move away from each other, due to elevtrostatic repulsion.

You have to correctly transform both the electrical and magnetic fields according to Maxwell's equations. When you do the apparent paradox disappears.

This thread is closed. We can host a discussion of some of the complicated and easily misunderstood corner cases of special relativity, and we can help you understand the parts of the the theory that appear contradictory at first glance , but that's not this thread.