A Modification in the Interpretation of Relativistic Red Shifts - mir

A significant factor in relativistic Red Shifts has not yet been accounted for. The known phenomenon of Time Dilation has a consequence (at relativistic velocities) of a significant Red Shift, as great as 30% of that due to the Relativistic Doppler effect. Two separate consequences of Time Dilation have effect, with the result that observed distant objects are likely to be radiating dozens of times as much energy as previously thought, while also being only two-thirds as far away from us. These consequences greatly modify many important conclusions in astrophysics, including the overall size of the Universe.

Time Dilation Red Shift

Mathematical Proof

Dilation Effect on Apparent Temperatures

Conclusion

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In their rest-frame, hydrogen atoms oscillate at their unique natural frequencies. An effect of this is the creation of the well-known spectral line series of Hydrogen, such as the Balmer series. The frequency and wavelength of this emitted light is constant, and identifies the glowing gas unambiguously as Hydrogen, for viewers in the relativistic rest-frame of the source, that is, for viewers who have no relative velocity to the glowing Hydrogen source.

Doppler Shift

However, if a viewer is in a frame-of-reference which moves (at a constant velocity) relative to the source, then the well-known Doppler effect applies. This is effectively a modification of perceived frequencies due to the reception of more wave fronts per second when moving toward the source, or receiving fewer wave fronts per second when moving away from the source. If a light source is moving toward us, we perceive its spectrum lines as appearing Blue-shifted. If it recedes from us, we see the spectrum lines as shifted toward the red. After the standard Doppler equation is adjusted for relativistic velocity effects, this has generally been given as the primary explanation of the Red Shift observed in distant receding galaxies, quasars, and other objects.

(There are several other relativistic effects that create a Red Shift, but their effects are extremely minimal for all known celestial objects and circumstances, so they will not be further discussed here.)

When relativistic velocities are involved, it is suggested that there is another significant contributing factor within the observed Red Shift.

A New Time Dilation Red Shift

Special relativity has another consequence which applies to this relativistic situation, that of Time Dilation (or Time Dilatation). The sensation of the rate of the passage of time is affected by the relative velocity of the source along the line-of-sight in the viewer's reference frame.

The unique atomic frequencies, which create the spectral lines, are identified in their rest-frame. Consider a scientist, moving along with a distant object that is rapidly receding from us. If he takes a spectrum of the glowing Hydrogen there, he would get the exact same spectrum we get with our rest-frame Hydrogen in our laboratory, with the lines exactly at the known wavelengths.

Time Dilation says that all processes that occur in that rapidly receding environment would appear to occur more slowly when observed from our rest frame as observers on Earth. In the case of the glowing Hydrogen, the individual atoms of Hydrogen would appear to move more slowly. This would have two separate effects, when viewed from Earth. The time interval between oscillation cycle maxima would appear to be longer when viewed from Earth, which would manifest itself as a Red Shift. The apparent velocity of the individual Hydrogen atoms would be lower, which would manifest itself as an apparent temperature lower than was actually the case.

The first of these is a Red Shift, whether the source is moving toward OR away from the observer. This fact, that this oscillation interval appears longer to observers on Earth due to Time Dilation, when we observe such atoms oscillating in a distant, relativistically traveling source, causes us to see a lower frequency; that is, a redward-shifted spectrum, for BOTH objects receding from us AND for objects approaching us.

(This is a different manifestation of the same effect as in the Twins Paradox, where a very powerful telescope on Earth, watching a relativistically traveling spaceship going to (or coming from) a distant star, would see seemingly slowed down movements of the occupants of the spaceship, even though those occupants would NOT be aware of any change. Molecules vibrating on the spaceship would also seem (to Earth observers) to have slowed down, so they would appear to Earth observers to be radiating energy at a lower frequency or redder color than would otherwise be the case; i.e. a Red Shift.)

This effect is NOT just another way of describing the Relativistic Doppler effect. Where the Doppler effect shifts receding sources toward the red and approaching sources toward the blue, the Time Dilation effect ALWAYS shifts the spectrum toward the red irrespective of direction. The effect being presented here is a unique and previously apparently undescribed phenomenon.

A relativistic APPROACHING source would therefore be Blue-shifted because of the Doppler effect and also Red-shifted because of Time Dilation. It turns out that the Doppler effect always has greater magnitude, so the net effect would be a Blue Shift, but significantly smaller than heretofore expected. A relativistically RECEDING source would be Red-shifted by BOTH effects. For that object, the observed Red Shift would be the sum of the two effects, and therefore greater than that from the Doppler effect alone.

This implies that velocities and distances that have been calculated exclusively based on relativistic Doppler effects are probably incorrect by a significant amount. For certain situations, the Time Dilation Red Shift can be fully 1/3 the magnitude of the Relativistic Doppler Red Shift. This would mean that an observed Red Shift might actually indicate a Doppler effect of only about 3/4 of current logic, where the other 1/4 was due to Time Dilation effects.

Calculations

The relativistic Doppler effect is given by:

where z is given as usual in octaves of wavelength shift.

For an object receding from us at v = 0.6c, this would give a Doppler Red Shift z = 1.0 (one octave)

For an object receding from us at v = 0.8c, this would give a Doppler Red Shift z = 2.0 (two octaves)

The Time Dilation effect (time slowing proportion) is given by:

For an object receding from us at v = 0.6c, this gives a Time Dilation factor of 0.8, which represents a Dilation Red Shift of z = 0.32

Therefore, an object receding from us at 0.6c would exhibit a Red Shift of z = 1.32 instead of z = 1.0.

For an object receding from us at v = 0.8c, this gives a Time Dilation factor of 0.6, which represents a Dilation Red Shift of z = 0.74

Therefore, an object receding from us at 0.8c would exhibit a Red Shift of z = 2.74 instead of z = 2.0.

[NOTE: If the Time Dilation factor is 0.5, then time appears to pass at exactly half its rest-frame rate, which would represent a 1.0 octave shift of the perceived frequency. The conversion is given by: z = -(log(TD_f))/(log(2)) ]

Observed z	(Old) Calculated Recessional Velocity /c Doppler Only	Revised Calculated Recessional Velocity /c Doppler +Dilation	Percent of total effect being Doppler

0.001	0.001	0.001	99.93%
0.01	0.010	0.010	99.3%
0.10	0.095	0.090	93%
0.50	0.385	0.334	83%
1.00	0.600	0.518	77%
2.00	0.800	0.719	74%
3.00	0.883	0.822	73%
4.00	0.923	0.879	73%
5.00	0.946	0.913	74%
7.00	0.969	0.951	76%

This result substantially modifies a number of conclusions which have been long accepted by the scientific community. The assumption that the general distances of very distant galaxies, per the Hubble Constant, is due exclusively to relativistic Doppler reasons, is apparently incorrect. The observed Red Shift is still primarily due to Doppler effects, but the total observed shift is sometimes about 30% larger than that which would be due to relativistic Doppler alone. Therefore, the actual velocity of recession should often be calculated based on about 75% of the observed Red Shifts, leaving out the part due to Time Dilation. (see the table above).

(Please refer to the table above)
For example, for a Red Shift of one octave (z = 1.0), the traditional relativistic Doppler calculations suggest a velocity of recession of 0.6c. With consideration of this new Dilation factor, the velocity of recession becomes about 0.518c. This is a significant change. The Dilation Red Shift contribution becomes even more prominent at higher total Red Shifts, with a maximum relative contribution at about z = 3.04. At z = 5.0, the normally calculated v = 0.946c becomes v = 0.913c.

This suggests that the actual distance of these galaxies and objects is considerably nearer than previously thought. With THIS consequence, the Universe is much smaller than previously thought, and therefore younger. Another major consequence of this is that the question of whether the Universe is open or closed is significantly altered. It may turn out that all the "missing mass" or "hidden matter" that has recently been postulated as necessary to describe the known Universe, may not be necessary. A smaller Universe (with the same mass) means the mutual gravitational effects of its component materials may be enough to explain all the empirical observations.

The ongoing discussions on the actual value of the Hubble constant, and its effects on the open-closed Universe topic are likely to be significantly altered.

There are many other consequences of this adjustment in explaining the Red Shifts we observe. Confirmation of the validity of this Dilation effect modification will likely affect many astrophysics disciplines.

Another interesting consequence exists. For light sources moving toward us, the light has a Blue Shift due to relativistic Doppler, but ALSO has a (smaller) Red Shift due to Time Dilation. The net effect IS an observed Blue Shift, but of MUCH smaller extent than would otherwise seem the case. Using some of the numbers mentioned above, but for an approaching source at 0.6c, the Doppler Blue Shift would be 1.0 octave, and the Time Dilation Red Shift would be 0.32 octave. The observed Blue Shift would be 0.68 octaves and not 1.0 octave as previously expected. This suggests that there may be objects coming toward us at higher velocities than previously thought.

The Second New Major Relativistic Consequence of Time Dilation

As has been pointed out above, the apparent resultant effect on atoms due to Time Dilation is that they appear to be moving at lower velocities than they would appear to have in their rest-state. The very definition of temperature is a description of the average velocity of the constituent atoms of the material.

This means that the lower apparent average atom velocity gives us received light that appears to come from a source of lower surface temperature than it actually is. The actual object surface temperature can be substantially higher. Consider an object that is moving away from us at an ACTUAL velocity of 0.87c. For this recessional velocity, Time Dilation makes time appear to pass at exactly half of its normal rate. Molecular and atomic velocities would therefore be half, as well. This means that effectively, we would see an object that indicates a surface temperature of half its actual rest-frame value.

Any text on thermodynamics tells that blackbody radiation rates go as the fourth power of the absolute temperature (the Stefan-Boltzmann law). This means that the object in question is actually radiating 16 times as much energy as previously thought.

This object would have an observed z = 3.8. (2.8 due to Relativistic Doppler and 1.0 due to Dilation). If the object had a higher total z than that, this temperature and radiation effect is even greater. An object that had z = 2.0 due to Dilation would be actually radiating 256 times as much energy as previously thought.

Conclusion

The two new consequences of considering Time Dilation have a cumulative effect. The z = 3.8 object we just considered is therefore only about two-thirds as far away (per the adjustment to Red Shift analysis presented above), and it is likely to actually be radiating 16 times as much energy as previously thought. The observed amounts of radiation received are therefore indications of 36 times as much energy actually being emitted by the object. This is a significant effect, and may now allow conventional physics to explain such a source, as it is not as far beyond traditional theory as previously thought. It may turn out to be less necessary to resort to exotic explanations for such objects, such as black holes.

First Developed, Apr 1989,
First Presented for Journal publication, Jun 1989, (but not accepted)
First Published on the Web: Jun 8, 1997,
Occasionally slightly revised since.

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C Johnson, BA Physics, Univ. of Chicago
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