redshift and special relativity

[Heretik]

Consider a spacecraft travelling through the cosmos at a constant high speed, say .87c, and vector. It should be experiencing time dilation to about half normal (stationary) time. Ie, 1 sec to it would be experienced as 2 seconds to all stationary observers regardless of their orientation to the spacecraft. By that I mean regardless whether the observers are behind, beside or ahead of the spacecraft. The craft is broadcasting light and other electro-magnetic radiation from within itself as it is travelling. Because of time dilation this EM radiation would be observed as redshifted by all (stationary to the Cosmos) observers. In addition to this, the fact that it is moving changes the wavelength of the EM radiation that reaches the observers due to the well known Doppler effect. Where the observer is situated will determine how that wavelength is changed. For example, to an observer behind the craft the EM radiation will be redshifted. To an observer in front of the craft the EM radiation will be blueshifted and the observer that is beside the craft for the briefest of moments that the craft is actually beside the observer, he will notice no frequency change. Ok, it will be blueshifted changing to redshifted the instant it goes past. The point here is that to the observer in front, the EM radiation would be redshifted first due to time dilation, then blueshifted because of the Doppler effect. This would cancel out the redshift resulting in no net frequency change. Therefore there should be no observable blueshifts in the the universe. However astronomers do observe some blueshifts. Why is this? Could it be that there is no time dilation due solely to velocity? Or could it be that at a given speed the Doppler effect more than compensates for the time dilation giving a net blueshift. Somebody do the Math!!

Edited November 19, 2010 by Heretik

[between3and26characterslon]

Consider a spacecraft travelling through the cosmos at a constant high speed, say .87c, and vector. It should be experiencing time dilation to about half normal (stationary) time. Ie, 1 sec to it would be experienced as 2 seconds to all stationary observers regardless of their orientation to the spacecraft. By that I mean regardless whether the observers are behind, beside or ahead of the spacecraft. The craft is broadcasting light and other electro-magnetic radiation from within itself as it is travelling. Because of time dilation this EM radiation would be observed as redshifted by all (stationary to the Cosmos) observers. In addition to this, the fact that it is moving changes the wavelength of the EM radiation that reaches the observers due to the well known Doppler effect. Where the observer is situated will determine how that wavelength is changed. For example, to an observer behind the craft the EM radiation will be redshifted. To an observer in front of the craft the EM radiation will be blueshifted and the observer that is beside the craft for the briefest of moments that the craft is actually beside the observer, he will notice no frequency change. Ok, it will be blueshifted changing to redshifted the instant it goes past. The point here is that to the observer in front, the EM radiation would be redshifted first due to time dilation, then blueshifted because of the Doppler effect. This would cancel out the redshift resulting in no net frequency change. Therefore there should be no observable blueshifts in the the universe. However astronomers do observe some blueshifts. Why is this? Could it be that there is no time dilation due solely to velocity? Or could it be that at a given speed the Doppler effect more than compensates for the time dilation giving a net blueshift.

 

"(stationary to the Cosmos)" first off there is no such thing as stationary to the Cosmos, they are stationary within a frame of reference (read about relativity principle for further explanation)

 

2nd "The point here is that to the observer in front, the EM radiation would be redshifted first due to time dilation, then blueshifted because of the Doppler effect" If red shift is due also to Doppler then the problem goes away.

Edited November 19, 2010 by between3and26characterslon

[Spyman]

... Because of time dilation this EM radiation would be observed as redshifted ...

No, I don't think so, the speed of light is constant for all observers and therefore the EM radiation is in itself independent of the speed of the emitter.

 

Any "standby" observers will only observe Relativistic Doppler Red/Blue-shift from the spacecraft.

[Janus]

Consider a spacecraft travelling through the cosmos at a constant high speed, say .87c, and vector. It should be experiencing time dilation to about half normal (stationary) time. Ie, 1 sec to it would be experienced as 2 seconds to all stationary observers regardless of their orientation to the spacecraft. By that I mean regardless whether the observers are behind, beside or ahead of the spacecraft. The craft is broadcasting light and other electro-magnetic radiation from within itself as it is travelling. Because of time dilation this EM radiation would be observed as redshifted by all (stationary to the Cosmos) observers. In addition to this, the fact that it is moving changes the wavelength of the EM radiation that reaches the observers due to the well known Doppler effect. Where the observer is situated will determine how that wavelength is changed. For example, to an observer behind the craft the EM radiation will be redshifted. To an observer in front of the craft the EM radiation will be blueshifted and the observer that is beside the craft for the briefest of moments that the craft is actually beside the observer, he will notice no frequency change. Ok, it will be blueshifted changing to redshifted the instant it goes past. The point here is that to the observer in front, the EM radiation would be redshifted first due to time dilation, then blueshifted because of the Doppler effect. This would cancel out the redshift resulting in no net frequency change. Therefore there should be no observable blueshifts in the the universe. However astronomers do observe some blueshifts. Why is this? Could it be that there is no time dilation due solely to velocity? Or could it be that at a given speed the Doppler effect more than compensates for the time dilation giving a net blueshift. Somebody do the Math!!

 

Somebody has already done the math.

 

For Doppler shift where Relativistic effects are ignored, you use the expression:

 

[math]\left( 1-\frac{v}{c} \right )[/math]

 

Relativistic Doppler shift (after taking all relativistic effects into account) is found by:

 

[math]\sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}[/math]

 

Where v is positive when the source is moving away from you.

 

This formula always gives a blueshift when the source is moving towards you.

Edited November 19, 2010 by Janus

[IM Egdall]

Take a look at the wikipedia link:

 

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

 

Hope it helps.

Edited November 19, 2010 by I ME

[Heretik]

"(stationary to the Cosmos)" first off there is no such thing as stationary to the Cosmos, they are stationary within a frame of reference (read about relativity principle for further explanation)

 

2nd "The point here is that to the observer in front, the EM radiation would be redshifted first due to time dilation, then blueshifted because of the Doppler effect" If red shift is due also to Doppler then the problem goes away.

 

 

1st Yeah, I knew I'd get into trouble for putting it that way. Delete "stationary to the Cosmos" and insert " the observers are all stationary to each other and the craft is travelling .87c relative to the observers"

 

2nd The redshift referred to is because the craft producing the light/EM radiation is travelling at a relativistic speed (.87c) relative to all the observers which would reduce all onboard processes to about half the clock speed experienced by all the observers. The Doppler effect is a seperate effect caused by the observed shortening of the wavelength of transmitted EM radiation if the craft is coming towards an observer or the observed lenghtening of the wavelength if it is going away from the observer.

 

Somebody has already done the math.

 

For Doppler shift where Relativistic effects are ignored, you use the expression:

 

[math]\left( 1-\frac{v}{c} \right )[/math]

 

Relativistic Doppler shift (after taking all relativistic effects into account) is found by:

 

[math]\sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}[/math]

 

Where v is positive when the source is moving away from you.

 

This formula always gives a blueshift when the source is moving towards you.

 

Thanks for that Janus.

 

No, I don't think so, the speed of light is constant for all observers and therefore the EM radiation is in itself independent of the speed of the emitter.

 

Any "standby" observers will only observe Relativistic Doppler Red/Blue-shift from the spacecraft.

 

 

1; The speed of light is not in question. From the instant that each individual photon of light leaves the spacecraft and travels the distance from where it left the craft to where the observer happens to be it travels at 186000 miles/sec.

 

2; I see the terms "Relativistic" and "Doppler" as two completely separate processes, "Relativistic" always resulting in a redshift and "Doppler" resulting in a redshift if going away from the observer and a blueshift if going towards an odserver.

 

Take a look at the wikipedia link:

 

http://en.wikipedia...._Doppler_effect

 

Hope it helps.

 

 

It's a great article. Thanks

[between3and26characterslon]

 

 

2nd The redshift referred to is because the craft producing the light/EM radiation is travelling at a relativistic speed (.87c) relative to all the observers which would reduce all onboard processes to about half the clock speed experienced by all the observers. The Doppler effect is a seperate effect caused by the observed shortening of the wavelength of transmitted EM radiation if the craft is coming towards an observer or the observed lenghtening of the wavelength if it is going away from the observer.

 

 

 

The frequency of the light emitted from the space craft is the same in all directions (as if the craft were stationary and the observers moving). The frequency of the light recieved by the observers would differ due to Dopler effect. The light would be equally redshifted in all directions due to time dilation and then, due to Dopler effect, blue shifted in front of the craft and red shifted further behind the craft.

[Heretik]

The frequency of the light emitted from the space craft is the same in all directions (as if the craft were stationary and the observers moving). The frequency of the light recieved by the observers would differ due to Dopler effect. The light would be equally redshifted in all directions due to time dilation and then, due to Dopler effect, blue shifted in front of the craft and red shifted further behind the craft.

 

 

I think we approximately agree with each other...

[Spyman]

1; The speed of light is not in question. From the instant that each individual photon of light leaves the spacecraft and travels the distance from where it left the craft to where the observer happens to be it travels at 186000 miles/sec.

 

2; I see the terms "Relativistic" and "Doppler" as two completely separate processes, "Relativistic" always resulting in a redshift and "Doppler" resulting in a redshift if going away from the observer and a blueshift if going towards an odserver.

You didn't seem to understand my point, let's put it this way:

 

Can you explain how the photons in a lightray manages to get "time dilated" by bouncing of the spacecraft ?

 

AFAIK there is no time dilation for the EM radiation itself, since the photons already travel at the speed of light they don't experience time at all, thus their time can't be slowed down any more so they shouldn't be affected by the speed of the craft.

[Heretik]

You didn't seem to understand my point, let's put it this way:

 

Can you explain how the photons in a lightray manages to get "time dilated" by bouncing of the spacecraft ?

 

AFAIK there is no time dilation for the EM radiation itself, since the photons already travel at the speed of light they don't experience time at all, thus their time can't be slowed down any more so they shouldn't be affected by the speed of the craft.

 

 

I'm sorry but you didn't seem to understand my point! If you'll re-read my scenario you'll see that the space craft is, "broadcasting light and other EM radiation from within itself", not reflecting light. In other words it has flood lights and a radio transmitter scattering light and other EM radiation 360 degrees. The light and other EM radiation that it is manufacturing is, according to Einstein's theory of special relativity, running slow compared to the observers who are passing/being passed at .87 the speed of light relative. In fact, at that relative speed all that happens on board the craft is happening at about half speed, according to the observers. This has no effect on the speed of light from anyones point of view. What it does do is slow down the freguency of the light/Em Radiation reaching the observers. That is, a barely visable violet light would be seen as a barely visable dull red. The frequency of this light/EM radiation is further modified, according to the observers, by the Doppler effect. This means that the observers behind the craft see the light/EM radiation as having a lower frequency than the observers in front of the craft. The dull red would become an invisable infra-red to the rear observers and to the observers in front, the dull red would become an invisable ultra-violet. This effect is commonly called redshift and blueshift. If the craft WAS reflecting light produced by the observers, the reflected light would only be subject to the Doppler effect, from the point of view of the observers.

Edited November 22, 2010 by Heretik

[Spyman]

Well, as a manner of fact I did understand your point, but I was simply wrong.

 

 

Let's see if I can get it right this time:

 

[math]v = -0.87c[/math] When the spacecraft is moving towards the observer.

 

[math]z_{Doppler} = \left( 1+\frac{v}{c} \right )-1 = -0.87[/math]

 

[math]z_{Dilation} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1 = 1[/math]

 

[math]z_{Relativistic Doppler} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}*\left( 1+\frac{v}{c} \right )-1 = -0.74[/math]

 

And now a check if the result is correct:

 

[math]Redshift = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1 = -0.74[/math]

 

(Redshift formulaes from here: http://en.wikipedia.org/wiki/Redshift)

 

It appears as the two different factors from Doppler effect and Time Dilation are not equal, instead the Doppler effect from speed seems more dominant, so that they together always result in a net blueshift if the objects are moving towards each other.

Edited November 23, 2010 by Spyman

[Heretik]

Well, as a manner of fact I did understand your point, but I was simply wrong.

 

 

Let's see if I can get it right this time:

 

[math]v = -0.87c[/math] When the spacecraft is moving towards the observer.

 

[math]z_{Doppler} = \left( 1+\frac{v}{c} \right )-1 = -0.87[/math]

 

[math]z_{Dilation} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1 = 1[/math]

 

[math]z_{Relativistic Doppler} = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}*\left( 1+\frac{v}{c} \right )-1 = -0.74[/math]

 

And now a check if the result is correct:

 

[math]Redshift = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}-1 = -0.74[/math]

 

(Redshift formulaes from here: http://en.wikipedia.org/wiki/Redshift)

 

It appears as the two different factors from Doppler effect and Time Dilation are not equal, instead the Doppler effect from speed seems more dominant, so that they together always result in a net blueshift if the objects are moving towards each other.

 

 

Thanks for that, Spyman.

 

Now, I could be wrong but I suspect that we only have half the equation. When a body(A) is travelling at a very high speed relative to another body(B ), the light it produces is redshifted. Also the light produced by body(B ), obviously also travelling at a very high speed relative to body(A), is also redshifted. When something is producing redshifted light it follows that when receiving light from other sources, the received light should be blueshifted. Therefore the redshifted light produced by (A) should be blueshifted when received by (B ), and the redshifted light produced by (B ) should be blueshifted on receival by (A). That means that the relativistic component of the light received by (A) and (B ) from each other is a big, fat, Zero. This leaves only the Doppler shifted light to explain the red/blue shifts observed. Maybe the observable universe is expanding at a different rate to what we thought.

Edited November 28, 2010 by Heretik

[Spyman]

No, I think we have both parts, each observer will see the others light redshifted in his own frame.

 

Reciprocity

Sometimes the question arises as to how the transverse Doppler effect can lead to a redshift as seen by the "observer" whilst another observer moving with the emitter would also see a redshift of light sent (perhaps accidentally) from the receiver.

 

It is essential to understand that the concept "transverse" is not reciprocal. Each participant understands that when the light reaches her/him transversely as measured in terms of that person's rest frame, the other had emitted the light aftward as measured in the other person's rest frame. In addition, each participant measures the other's frequency as reduced ("time dilation"). These effects combined make the observations fully reciprocal, thus obeying the principle of relativity.

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

 

 

Cosmological Redshift is not thought to be due to doppler but instead caused by space expanding.

 

Expansion of space

In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blue shifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blue shifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. Hubble's law of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a metric expansion of space. As a result, photons propagating through the expanding space are stretched, creating the cosmological redshift.

 

There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a local Doppler-effect redshift. Rather than cosmological redshifts being a consequence of relative velocities; instead, the photons increase in wavelength and redshift because of a feature of the spacetime through which they are traveling that causes space to expand. Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3 × 10⁸ m/s, but this does not imply that the galaxies move faster than the speed of light at their present location which is forbidden by Lorentz covariance.

http://en.wikipedia.org/wiki/Redshift

[Heretik]

No, I think we have both parts, each observer will see the others light redshifted in his own frame.

 

Reciprocity

Sometimes the question arises as to how the transverse Doppler effect can lead to a redshift as seen by the "observer" whilst another observer moving with the emitter would also see a redshift of light sent (perhaps accidentally) from the receiver.

 

It is essential to understand that the concept "transverse" is not reciprocal. Each participant understands that when the light reaches her/him transversely as measured in terms of that person's rest frame, the other had emitted the light aftward as measured in the other person's rest frame. In addition, each participant measures the other's frequency as reduced ("time dilation"). These effects combined make the observations fully reciprocal, thus obeying the principle of relativity.

http://en.wikipedia...._Doppler_effect

 

 

Cosmological Redshift is not thought to be due to doppler but instead caused by space expanding.

 

Expansion of space

In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blue shifts of galaxies beyond the Milky Way. They initially interpreted these redshifts and blue shifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. Hubble's law of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a metric expansion of space. As a result, photons propagating through the expanding space are stretched, creating the cosmological redshift.

 

There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a local Doppler-effect redshift. Rather than cosmological redshifts being a consequence of relative velocities; instead, the photons increase in wavelength and redshift because of a feature of the spacetime through which they are traveling that causes space to expand. Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3 × 10⁸ m/s, but this does not imply that the galaxies move faster than the speed of light at their present location which is forbidden by Lorentz covariance.

http://en.wikipedia.org/wiki/Redshift

 

Yes, I expect so. What a pity that it is SO difficult to directly experiment with these topics. It is fun to think about them, though.