Relativistic Red Shift - A New Interpretation

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 extremely distant 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.


Consider for a moment the Twins Paradox of Special Relativity. This is where twin brothers grew up on Earth. One stays on Earth and the other goes in a spaceship at nearly the speed of light to Alpha Centauri, says Hi, and immediately returns. Since A.C. is 4.3 Light Years away, the brother on Earth will have aged about 8.6 years during the trip. But, due to the Time Dilation (or Time Dilatation) consequence of Special Relativity, the traveling brother would only have aged a few weeks for EACH trip and would come back more than 8 years younger than his twin! From his point-of-view, he did not exceed the speed of light in doing this, because he would have seen the distance as seeming to be much shorter, a trip that logically took a few weeks to travel.

The Equivalence of Relativity also says that each brother would not be aware of anything unusual, in any experiment. Therefore the traveling brother would be in a totally self-consistent frame of reference. Any experiment he does would give him results identical to a similar experiment done by his brother on Earth. His clocks would seem (to him) to run properly and his body would seem to age normally. His perception would be that the DISTANCE to A.C. was much shorter than we perceive it to be, and so the trip of a few weeks would seem logical to him.

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The only unusual part would be if the brother on Earth had a very strong telescope to be able to watch his traveling brother's activities, where they would seem to be happening in slow motion, due to the Time Dilation. Everything happening aboard the space ship would appear (to the Earth-bound twin) to have slowed.

Now, consider that the traveling brother had a Cesium Clock, based on molecular vibration. He would see it as having its atoms vibrating at the expected rate, and thereby keeping correct time (in his reference frame). The Earth-based observer would see it as having its atoms vibrating more slowly, and therefore keeping an apparently slowed time base, consistent with the apparent slowing of time he observes for everything on the spacecraft. The significant point here is that the atoms would appear to Earth to be vibrating more slowly than they would appear in the rest frame of the atoms.

Now say that the traveling twin also has some glowing Hydrogen gas. When he makes a spectrum of it he sees the standard expected spectrum lines of Hydrogen (with the correct rest-frame wavelengths). The Earth-based observer, taking a spectrum of the light from that same glowing Hydrogen gas, would see those lines as shifted to the red end of the spectrum, due to the apparent effect of the vibration of the atoms/electrons being slowed down due to the Time Dilation effect.

This is a previously undescribed relativistic Red Shift. Near the speed of light, this effect becomes quite significant.

This is NOT just another view of Relativistic Doppler Red Shifts. This can quickly be assured. Doppler Shifts are to the red for receding sources and to the blue for approaching sources. This Dilation Shift is to the red WHETHER THE SOURCE IS RECEDING OR APPROACHING. The effect being described here is a separate and previously undescribed phenomenon.

This means that, for approaching sources, there are two potentially large effects which oppose each other: The Doppler Shift is blue-ward and the Dilation Shift is red-ward. Since the Doppler effect is always larger, this creates the net effect of a Blue Shift, but smaller than previously thought, especially at relativistic velocities. For receding sources, the two effects are additive since they are both Red Shifts. The Dilation Red Shift effect can be as large as 30% of the magnitude of the Relativistic Doppler Shift. This means that for an empirically measured Red Shift, only about 3/4 of it (in that situation) can be attributed to Relativistic Doppler Shift This implies significantly reduced velocities of recession of distant galaxies. This is irrespective of the precise value of the Hubble constant. There are numerous implications of this modification, including much smaller dimensions for the Universe, and some alterations to the scatter chart graphs on which the Hubble Constant is determined.

This Time Dilation Red Shift is also not dependent on whether the atoms/electrons of Hydrogen were vibrating along the line-of-sight or perpendicular to it because the apparent passage of time, being slowed, is the base cause of the effect. Irrespective of the orientation of the atoms, time would appear to pass more slowly and therefore the apparent frequency and speed of the atoms and electrons must be slowed.

The Relativistic Gravitational Red Shift and the other known effects still remain valid, but those other effects are generally MUCH smaller than this Dilation Red Shift.


More Technically

Soon after Albert Einstein developed the Theory of Special Relativity, science realized that there was a necessary phenomenon of Time Dilation (or dilatation). This phenomenon is where there is an apparent slowing of the passage of time when observing an object that is moving at relativistic velocity relative to the observer. The phenomenon is well documented, and experimentally confirmed, as during early manned orbital space flights, when atomic clocks were carried on the flights to confirm it.

In their rest-frame, hydrogen atoms and their electrons oscillate at unique natural frequencies. A result 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

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.

In the case of the glowing Hydrogen, which is moving away from us at a velocity near the speed of light, the individual atoms and electrons of Hydrogen would appear to move more slowly, electron orbital energies would seem smaller, and transitions from one state to another (during ionization) would appear to involve smaller net quantities of energy. This would have two separate effects, when viewed from Earth. The time interval between all viewed oscillation cycle maxima would appear to be longer when viewed from Earth, which would manifest itself as slower oscillations, and therefore lower observed frequencies, and therefore a Red Shift. The apparent velocity of the individual Hydrogen atoms would also 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. Time Dilation appears to slow the passage of time for both receding and approaching objects.

Molecules, atoms and electrons 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 still 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.


Calculations

The relativistic Doppler effect is given by:

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

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

For an object ACTUALLY 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:

equation-b

For an object ACTUALLY 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

For an object ACTUALLY 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

[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(TDf))/(log(2)) ]


Currently, if an observed Red Shift has z = 1.32, it is assumed that, by assuming the entire effect to be relativistic Doppler, the velocity of recession, v = 0.687. This argument is showing that it is actually somewhat slower, at v = 0.600, because roughly 1/4 of the observed effect is actually due to Time Dilation Red Shift. The effect is very important.


Observed
z
(Old)
Calculated
Recessional
Velocity
/c
Doppler
Only
Revised
Calculated
Recessional
Velocity
/c
Doppler
+Dilation
Percent of
total effect
being Doppler
0.0010.0010.00199.93%
0.010.0100.01099.3%
0.100.0950.09093%
0.500.3850.33483%
1.000.6000.51877%
2.000.8000.71974%
3.000.8830.82273%
4.000.9230.87973%
5.000.9460.91374%
7.000.9690.95176%


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 an observed 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 could be 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 again be 1.0 octave, and the Time Dilation Red Shift would again 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 Submitted 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, Theoretical Physicist, Physics Degree from Univ. of Chicago