The Relative Effect

In part, the previous discussions outlining the issue of reference frames and the Doppler effect illustrated that the perception of any system in motion may depend on the relative perspective of the observer.  The idea of relativity, in terms of both special and general, has already been discussed in terms of the ‘unification’ of spacetime; where the essence of special relativity was first encapsulated in a quote by Hermann Minkowski back in 1908:

Henceforth space by itself, and time by itself,
are doomed to fade away into mere shadows,
and only a kind of union of the two will preserve an independent reality.”

Later, the central idea of general relativity was encapsulated by John Archibald Wheeler in an even more succinct quote:

“Spacetime tells matter how to move;
matter tells spacetime how to curve.”

Of course, in the current context, we are starting to give more consideration to issues associated with a wave model of matter. For example, it might said that sound waves propagate with velocity [c] through the medium of air, which experimentation might reasonably establish as the primary, if not absolute, reference frame for the velocity of the source and receiver of sound waves. However, if it were not possible to establish the medium of air as a reference frame; how might we establish the velocity between source and receiver in this conceptual case. Well, based on the relativistic premise, either the inertial source or receiver can assume itself to be stationary, which then leads to the conclusion that the other frame must have a relative velocity [v].

OK, but how would this relative velocity [v] be  determined?

While we might start with wave relationship [c=f0λ0], the imposed ambiguity of  the relative velocity [v] with respect to the ‘absolute’ reference frame of the air medium is problematic. For example, if the receiver were travelling towards the emitter with velocity [v], we might realise that the detection rate of sequential wave peaks would increase, i.e. leading to a higher measured frequency [fM], while the measured wavelength [λM] would shorten by a corresponding amount. We might quantify this effect as follows:

[1]     

In the form of [1], the [±] sign would simply reflect whether the velocity [v] was towards or away from the reference frame in question, i.e. source or receiver. However, while the turning point of [±v] would allow the measurement to be established for a relative velocity [v=0], it could not guarantee that either the source or receiver was stationary with respect to the air medium, which within this conceptual example cannot be detected. As such, neither the source or receiver frame can necessarily determine the absolute frequency [f] or wavelength [λ]. However, based on [1], the wave propagation velocity [c] would still be calculated to be invariant in all reference frame, as implied by ‘relativistic’ theory. As this is quite a fundamental point, we might try to illustrate the different relative perspectives:

The background (grey) grid is representative of the propagation medium, which in the case of sound waves is air. In the case of air, the observer [C] can physically exist and [vpm1] and [vpm2] determined by direct measurement. However, this is not the case within a matter wave model, where observers [A] and [B] can only establish their relative velocity [v] to each other and the wave propagation velocity [c] via the relationship [c=fλ] within their reference frame; because the measurement of frequency [fM] and wavelength [λM] is a function of the relative velocity [v], as shown in [1], although we might now generalize [1] as follows:

[2]     

In the form of [2], frequency [f0] and wavelength [λ0] do not necessarily represent the absolute values as seen by observer [C], only the values determine by [A] and [B] when their relative velocity [v] is zero, which does not preclude [vpm] being non-zero. With reference to Yuri Ivanov’s concept of compressed standing waves, it might be argued that any wave model, inclusive of matter, must also encompass all the equipment used to measure frequency and wavelength in any given reference frame, e.g. [A] or [B].  If so, the measurement of time and distance might ultimately have to be quantified in terms of the measured frequency [fM] and wavelength [λM], both of which appear to be relative concepts.

But does this mean that the physical universe is entirely subjective, i.e. relative?

While everybody and everything must exist within its own local wave reference frame, if the medium of wave propagation is physical, it might still be argued that an absolute frame exists, i.e. where the measurement of the waves is defined by [c=f0λ0].

Does this really change the relative perspective?

Let us consider the normal example, e.g. two spaceships [A] and [B] are travelling close to the speed of light [c], but pass each other in opposite directions. Now relativity might suggest that both reference frames, as defined by these spaceships, would measure the tick of the clock in the other system running slower. If so, does this mean that the occupants of both spaceships are aging slower than the other at the ‘same’  time? However, if we accept the possibility of an absolute reference frame with respect to the medium of space, the concept of universal time might be retained, such that the issue of time dilation, as required by the Lorentz transforms, is now determined as a function of the relative velocity [vpm] with respect to the absolute frame, i.e. the media of space, not each other.

So how might time be affected in a relative reference frame?

This question is considered in a two-stage discussion, which starts with the idea of a Wave Clock to outline some basic principles and then extends the discussion to the Light Clock, which tries to cover some of the wider implications of both the Doppler effect and relativity.