That is the critical point, my argument hinges on the partitioning of energy into 'spark' and 'passive' components.
The spark energy ($W = F \cdot d$) is the small, measurable energy we input locally in the platform frame.
The passive energy is the vast, undetectable (in the platform frame)...
You are absolutely applying the standard relativistic methodology correctly, and I understand your point about the transformation of forces and distances.
However, the core purpose of this thought experiment is to test the foundational Principle of Relativity itself. The principle asserts that...
Here is the detailed math:
In all standard experiments (e.g., collisions, springs between objects at rest), applying equal work ($W = F \cdot d$) results in equal impulses ($J = F \cdot \Delta t$) and perfectly symmetric outcomes within the inertial frame.
This experiment is designed to create...
We are making all measurement in the inertial frame (the space craft or moving platform), if interaction duration differ, then this will be signature of rest frames, but the time of the projectile itself is different, the radiation activity for example will differ, since each projectile is...
Yes, precisely. The key hypothesis is that the interaction duration is a measure of absolute time. If we could measure different durations for this process, it would be a direct signature of a rest frame, as it would indicate the process's timing is governed by a frame other than the local one.
The measurement of forces and distance will be in the inertial frame, the force meter will be installed inside the magnetic linear accelerator on every electromagnet, so from the inertial frame we are applying same force over same distance on moving bodies in opposite directions, hence from rest...
You are right that $W = F \cdot d$ and $J = F \cdot \Delta t$ are standard physics. The unique claim isn't the formulas themselves, but the predicted experimental outcome.
In all standard experiments (collisions, springs between objects at rest), applying equal work ($F \cdot d$) results in...
If the inertial frame is moving at 100 m/s in rest frame, each projectile mass equal 1 kg, initial launch caused 10 m/s relative velocities inside the inertial frame. Magnetic accelerator applies 500 N over 0.1 m. Then the difference in projectile's velocities will be 0.1 m/s. The interaction...
The long linear accelerator is applying positive acceleration on body with initial velocity not at rest, starting from rest and interacting for short distance will not produce measurable anisotropy, they will be symmetric because the interaction distance is very short (like in explosion) which...
You are correct that in a closed cycle (e.g., accelerating and then decelerating a particle in an accelerator), the effects cancel out, preserving symmetry. This is why no anisotropy is observed in standard accelerator operations.
The proposed anisotropy is path-dependent, not...
This experiment is unique because it applies force over a fixed distance, not time. The impulse $J = F \Delta t$ depends on the interaction time $\Delta t$.
From the rest frame perspective, $\Delta t \approx d / v_{abs}$. Therefore, a projectile with a higher absolute velocity ($v_{abs} = V+u$)...
Thank you for this crucial point. You are absolutely correct that from the platform's inertial frame, the analysis must be self-contained, and in that frame, the setup is symmetric, leading to the expectation that $\Delta t_1 = \Delta t_2$.
The purpose of the long linear accelerator version is...
I totally agree with you: in other frames the interaction durations will look different, while in the lab frame everything is symmetric. However, proponents of a universal rest frame would argue that those differing interaction times must also show up inside the inertial frame, because an...
This idea is novel because it relies on interactions with bodies moving in different inertial frames, where we apply positive acceleration to each one in the direction of its motion. In the usual scenarios, explosions studied in textbooks, all the bodies start out in the same inertial frame...
Basically, we are applying the same force over the same distance and therefore doing the same work on both projectiles. But here’s the catch: from the rest-frame perspective, the projectile velocities will be and . That seems to imply different interaction durations with the same force, which...