Is the Sun invisible at relativistic speeds? Part II

[tionis]

We can see that the spherical sun, at rest in some frame, is not spherical in a moving frame, due to Lorentz contraction. The light emitted from the sun is also affected by the Lorentz transform, being squashed in a similar manner.

https://www.youtube.com/watch?v=JQnHTKZBTI4


Pervect, on this^^ video, from 5:08 - 5:18, they say that:

another property of aberration is that it preserves circles, that is - a sphere will always present a spherical outline to any observer regardless of their relative motion.

Is that wrong?

 

[Russell E]

On this video they say that: "another property of aberration is that it preserves circles, that is - a sphere will always present a spherical outline to any observer regardless of their relative motion." Is that wrong?

The video is correct, and what pervect said is also correct. They are describing two different things. The video is talking about the visual image of a moving object, which consists of light reaching the observer's eye that has traveled different amounts of time to reach the eye (because different points on the sphere are at slightly different distances), so the visual image is not an "instantaneous" representation of the object (where "instantaneous" is defined in terms of the observer's rest frame inertial coordinates). In contrast, Pervect was describing the true shape of the sphere at a single instant (where, again, "instant" is defined in terms of the observer's rest frame coordinates). It is an interesting fact (first discussed by Terrell and Penrose back in the 1950's) that although a spherical object is fore-shortened into an ellipsoid in terms of relatively moving coordinates, the optical image at any point always remains circular.

 

[tionis]

OK, thanks lol. So, are you guys both in agreement that the Sun does eventually disappear from view given enough speed?

 

[tionis]

Hey, I have a question: what does a Doppler shift greater or less than unity means?

 

[Dale]

By the way, tionis, we shouldn't be talking about "invisible" or "disappear". It simply goes black, but it remains opaque and not invisible.

 

[DrGreg]

Hey, I have a question: what does a Doppler shift greater or less than unity means?

That should, strictly speaking, be called "Doppler factor" rather than "Doppler shift": the ratio of observed frequency to source frequency.

So a Doppler factor greater than unity means blue shift.

A Doppler factor less than unity means red shift.

 

[tionis]

By the way, tionis, we shouldn't be talking about "invisible" or "disappear". It simply goes black, but it remains opaque and not invisible.

Yes, but for the purpose of our animation, we need to know if the Sun becomes indistinguishable (invisible to the human eye) from the background space once we accelerate the ship close to c. Bear in mind that we start from a distance of 4ly, but by the time we are done with our trip, we'll be a lot closer to the Sun. Do you maintain that as soon as we reach the desired speed (incredibly close to c) the Sun will remain ''opaque'' all throughout our trip even though we are getting closer and closer?

That should, strictly speaking, be called "Doppler factor" rather than "Doppler shift": the ratio of observed frequency to source frequency.

So a Doppler factor greater than unity means blue shift.

A Doppler factor less than unity means red shift.

So ''unity'' means shift?

 

[Doc Al]

So ''unity'' means shift?

Unity means 1.

 

[tionis]

Unity means 1.

Doc Al, so when someone says a ''Doppler shift greater or less than unity,'' he means a shift < or> than 1 what? The speed of light?

 

[Doc Al]

Doc Al, so when someone says a ''Doppler shift greater or less than unity,'' he means a shift < or> than 1 what? The speed of light?

The Doppler factor, as used by DrGreg, is a ratio of frequencies. It has no units. So when he says that that factor is greater or less than unity, he means greater or less than 1. Period.

 

[Russell E]

By the way, tionis, we shouldn't be talking about "invisible" or "disappear". It simply goes black, but it remains opaque and not invisible.

There's a valid distinction between "invisible" in the sense of "transparent", versus in the sense of "completely dark". However, in this context it's a moot point, because in the limit as the speed approaches c the apparent size of the Sun goes to zero, so the distinction between transparent or opaque doesn't matter. (Also note that on a per-area basis it actually gets brighter.)

 

[pervect]

Yes, but for the purpose of our animation, we need to know if the Sun becomes indistinguishable (invisible to the human eye) from the background space once we accelerate the ship close to c. Bear in mind that we start from a distance of 4ly, but by the time we are done with our trip, we'll be a lot closer to the Sun. Do you maintain that as soon as we reach the desired speed (incredibly close to c) the Sun will remain ''opaque'' all throughout our trip even though we are getting closer and closer?

I'm not sure what you mean by "opaque". And the answer is - probably not for the entire trip, no. This is the first time in the thread that a "trip" has even been mentioned. It's a good thing we dragged this minor little detail out of you, finally.

The details of what you'd see on a trip depends on how fast you are moving - which hasn't been specified either. There is also the issue of whether or not the sun acts as a black body. Consulting wiki, http://en.wikipedia.org/wiki/File:Solar_Spectrum.png, the sun's spectrum appears to be a good fit to a black body out to 2500nm. Since the visual range is around 500 nm, we can say there shouldn't be any issues up to a doppler factor of 5:1.

There's no reason I can think of that there would be issues at higher doppler factors, but the matter should be investigated. The first step of the investigation would be to specify exactly what the speed you're moving at (so as to get the corresponding doppler factor).

 

[tionis]

The first step of the investigation would be to specify exactly what the speed you're moving at (so as to get the corresponding doppler factor).

Rusell E mentioned a v = 0.999999973. Is that the magic number to make the Sun invisible?

 

[Dale]

we need to know if the Sun becomes indistinguishable (invisible to the human eye) from the background space once we accelerate the ship close to c.

Nobody has addressed the question of distinguishing the sun from the background. The cosmic microwave background radiation is also a blackbody. As you reach ultra relativistic speeds it will become bright also.

 

[pervect]

Nobody has addressed the question of distinguishing the sun from the background. The cosmic microwave background radiation is also a blackbody. As you reach ultra relativistic speeds it will become bright also.

It's been alluded to, nobody has worked out the details. We can say that at a doppler factor as low as about 2200, the temperature of the CMB in the directon of motion will be the same as that of the sun. Which is a lot lower doppler factor than some of the rather extreme numbers that have been thrown around already.

The CMB transforms differently than the light from a star. I suspect we could have another thread as long and confused as this one working out (or failing to work out, or working out via means that are unfortunately not familiar to most readers of the thread and thus not convicing them) the details.

 

[tionis]

Nobody has addressed the question of distinguishing the sun from the background. The cosmic microwave background radiation is also a blackbody. As you reach ultra relativistic speeds it will become bright also.

That is an interesting question. I hope someone delves into it. Maybe there is a breakdown in the continuum description at sufficiently high speeds. Since you can only see integer number of CMB photons, then at some point you either see a photon or not.

 

[Vanadium 50]

Nobody has addressed the question of distinguishing the sun from the background. The cosmic microwave background radiation is also a blackbody. As you reach ultra relativistic speeds it will become bright also.

Yes, but not as bright. More specifically, I believe there is no frame where the temperature of the CMB just past the limb of the sun and the limb of the sun are radiating as if they were at the same T.