Doppler Mass Shift (DMS)
Doppler Mass Shift (DMS)
The term Doppler Mass Shift ("DMS") refers to the apparent change in mass due to an object's relative motion. Unlike the concept of relativistic mass, DMS takes into account the relative direction of motion of the object wrt the observer, and not just the relative speed.
Concept of Doppler Mass Shift
We may choose to measure the inertial mass of a body by applying a know force and watching how the body responds – for a given force, a low-mass body will react by altering its state of motion more rapidly than a body with greater inertial mass, and greater inertia. We would normally imagine performing this exercise with a body that is initially stationary, or has a low relative velocity to the measuring equipment, because otherwise Doppler effects will complicate how the force is applied and how the the response measured, giving a "false reading" of the object's mass depending on how it is moving.
Alternatively, we might take the readings for a fast-moving body, but compensate for motion effects in out calculations.
According to the purist, uninterpreted "observerspace" reasoning, there is no such thing as a "false reading" – if our hardware designed to measure mass reports an apparent change in mass due to velocity, then, in terms of directly-observed, uninterpreted reality, this is in fact what happens. Observerspace logic insists that – to the greatest extent possible – reality should not just be consistent, it should be seen to be consistent.(notes)
If a body recedes at v m/s, then the body will see us to be receding, and the signals that we aim at the body will be Doppler-redshifted and consequently apply a reduced force, causing less of an acceleration in the body than we'd otherwise expect. Not only is the object "genuinely" responding more weakly to the applied force, out view of it is also Doppler-redshifted, meaning that we see the object's signal-stream to be time-stretched, making the reduced change in velocity per second appear even slower. The receding body's mass appears increased.
Conversely, if a body approaches at v m/s, any accelerating radiation that we aim at it will hit with more energy than we put in due to the Doppler blueshift, and will cause more of a change in velocity in the body. Since we see the signals from the approaching body with a Doppler time-compression, the stronger change in motion is seen to happen even more quickly. The approaching body's mass appears decreased.
We could also try to measure variations in the body's apparent inertial mass by watching the rate of known reactions in the body, or in a system of bodies with an overall velocity wrt us, which coudl eb used as a "clock". If we do this, since the apparent clockrate of a receding body is slower and the apparent rate of an approaching body is higher, we end up assigning different rates of apparent timeflow and therefore relating the decrease in detected clockrate to an apparent increase in inertial mass when the body recedes, and the increase in clockrate registering on our detectors to an apparent decrease in the body's inertia.
The existence of a transverse DMS effect depends on the propagation model or Doppler equations being used, but with both Newtonian mechanics and special relativity, the DMS concept gives a predicted increase in apparent inertial mass whose strength goes to infinity as the relative transverse velocity approaches v=c (in the early days of special relativity, the SR version of this apparent mass-increase was referred to as "relativistic mass").
While it is trivially easy to argue that these one-way effects are illusory and unphysical, the Observerspace Principle requires the associated "apparent" physics to match. The Principle of Equivalence says that if the inertial mass of a body is changed, its gravitational mass should also change, so if we watch a moving gravitational source (such as a planet), it should seem to exert a stronger pull on our equipment when the planet is receding rather than approaching, and if we gently release a test object towards the planet, the object's impact velocity should be greater if the planet recedes than if it approaches. These outcomes are both physically correct.
If we photograph the same moving body from different angles, the different rates of apparent timeflow at different viewing angles can be interpreted as showing the existence of a polarised gravitational field around the body, which would then (if it was real) need to be associated with polarised lensing effects, and apparent increases and decreases in the dimensions of a body immersed in the field when compared to background reference-rulers. In fact, both of these effects are (visually) real – a counterpart of the polarised lensing effect shows up in standard physics as the conventional velocity-based aberration of lightrays, and the apparent contraction and expansion of rulers appears in the literature (post-1959) as the Terrell-Penrose Doppler length-change effect. While all these visual effects could be dismissed as unreal, or better explained using simpler arguments, the fact remains that the "misguided" observerspace view appears to have a logical internal consistency, and also to be consistent with the phenomenology of raw experimental data.
If we wanted to use the Doppler Mass Shift concept to go beyond existing physics, we could point out that since the same DMS arguments apply to both "gravitational" and "non-gravitational" bodies, that simply-moving masses ought to show effect associated with polarised field distortions, specifically the dragging of nearby light. We've known since ~1850 that this is also a physically correct result (Fizeau experiment) ... however, where DMS arguments go beyond standard theory is that by introducing the idea of velocity-dependent curvature, they require inertial physics to be modellable as a problem in curved rather than flat spacetime. This seems to suggest a different from of relativistic model that operates according to Cliffordian rather than Minkowskian principles.
This seems to be the reason why this concept is not currently part of textbook physics - although the arguments are simple and the immediate consequences correct, the idea then leads to the invalidation of special relativity's flat-spacetime derivations, and the replacement of C20th GR with a more advanced acoustic metric-compatible version.
- "Observerspace" logic does break down in some extreme or larger-scale situations, but it provides a good "rule of thumb" for deriving how "reasonably local" physics ought to behave.