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Author Topic:   How big is our Galaxy.
JustinC
Member (Idle past 4844 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 136 of 147 (281809)
01-26-2006 5:55 PM
Reply to: Message 132 by cavediver
01-24-2006 5:26 AM


Re: Relativistic vs Doppler (in a nutshell)
quote:
So in all cases - SR, cosmology and black holes - we have two completely separate effects: observational effects caused by Lorentz and doppler, and then we have shortening of the time-line caused by acceleration. In all cases - Twin's Paradox, cosmology and black holes - these two separate effects are totally confused, and leads to all sorts of misunderstandings.
I like this way of thinking about things, it really clears a lot up.
But if they are really completely different effects doesn't that make it a coincidence that when the twin is coming back to earth the observational effects will adjust the rate of his clock as to make it read what it should read based on the lengthening of his path through space-time?

This message is a reply to:
 Message 132 by cavediver, posted 01-24-2006 5:26 AM cavediver has replied

Replies to this message:
 Message 137 by Iblis, posted 01-26-2006 6:45 PM JustinC has replied
 Message 142 by cavediver, posted 01-27-2006 3:58 AM JustinC has not replied

  
Iblis
Member (Idle past 3896 days)
Posts: 663
Joined: 11-17-2005


Message 137 of 147 (281819)
01-26-2006 6:45 PM
Reply to: Message 136 by JustinC
01-26-2006 5:55 PM


Re: Relativistic vs Doppler (in a nutshell)
I hope you don't mind if I try to answer based on cavediver's demonstration of distinguishing out the different effects. If he corrects me I will get to learn something else so I would really appreciate it
Let's call the effect of acceleration through spacetime in respect to the observer's inertial frame the genuine time-dilation. This works rather like traveling northwesterly at a set speed, the more north you go the less west you go. Terrible analogy I know, but it helps visualize the whole four-dimensional thing better for me at least, the more northward I go the less futureward I go. The opposite effect will be deceleration, this stops but does not reverse the effects of the genuine time-dilation.
Distinct from that we have the doppler effect caused by traveling away from the observer, let's call this red-shift. The opposite effect will be blue-shift, this will reverse the effect of the red-shift.
A third effect to consider is the signal-delay, this is the one we mostly already understand. An object at rest (in respect to our inertial frame) at a distance 10 light years away will have its messages delayed by 10 years. Good so far?
Now let's try it out in practice. You hop in a spaceship and accelerate in such a way as to make a trip to the Centauri system 3ish light years away, traveling most of the trip at near-light speeds. Your acceleration causes you and your clock to experience a genuine time-dilation, it only takes you say 6 months of your personal time to get there. I am watching your signals back here on earth in mission-control, I see not only this genuine time-dilation but also another additional amount of clock-slowing which is illusory, caused by the red-shift. It also takes me longer and longer to receive your signals. At this point if I try to judge your "now" without the information needed to account for all the effects separately I will come to some very bad conclusions.
When you get to whichever of the Centauris, say 3 light years away, you decelerate into a normal orbit. At this point you are to all intents and purposes at rest again in respect to our original inertial frame. The red-shift decreases to normal, you keep the effect of the genuine time-dilation you have already experienced and stopped experiencing, and your messages are delayed by 3 years. At this point if I watch your clock it is ticking normally, but 3 years behind because of the signal delay and another 2.5 years behind because of the genuine time-dilation. I have a reasonably good chance of judging your "now" because I can subtract the 3 years representing your distance and the 2.5 years left over from the 6 months you log as experiencing during the trip.
You complete your brief mission, turn around and accelerate back. Again you experience genuine time-dilation due to your acceleration. But because you are moving towards me this time the primary effect I see is the blue-shift, this makes it look to me like your clock is running much faster, even though the genuine time-dilation is actually making it run somewhat slower. Also, there is less and less signal delay. Again I will have a bit of trouble judging your "now" under these circumstances, though slightly less trouble as time goes by rather than more and more because we are reducing rather than increasing the distortion of observation this time.
When you get back you decelerate, again stopping but not reversing the genuine time-dilation. The blue-shift cancels out the red-shift completely, the signal delay has been reduced to nothing much and then nothing at all as we meet. The only remaining effect is the genuine time-dilation you experienced as a result of your acceleration. For me it has been 6 years, for you 1 year. There's no coincidence, the illusions and delays have canceled out and what is left is the actual difference between our experience of time, the classic twins problem.
* have I got it yet? I should probably add a few days or months in to account for the fact that we can't quite travel at lightspeed, but I don't know how much extra to add to make the 6 months realistic so I have shamelessly glossed over that part of the problem
This message has been edited by Iblis, 01-26-2006 06:52 PM

This message is a reply to:
 Message 136 by JustinC, posted 01-26-2006 5:55 PM JustinC has replied

Replies to this message:
 Message 138 by cavediver, posted 01-26-2006 7:59 PM Iblis has replied
 Message 143 by JustinC, posted 01-27-2006 5:23 PM Iblis has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 138 of 147 (281832)
01-26-2006 7:59 PM
Reply to: Message 137 by Iblis
01-26-2006 6:45 PM


Re: Relativistic vs Doppler (in a nutshell)
I haven't had chance to read all of this yet, but I will later.
if he corrects me...
Ok, you asked for it
The Centauri system is 4.3 lyrs away !!!

This message is a reply to:
 Message 137 by Iblis, posted 01-26-2006 6:45 PM Iblis has replied

Replies to this message:
 Message 139 by Iblis, posted 01-26-2006 8:21 PM cavediver has replied

  
Iblis
Member (Idle past 3896 days)
Posts: 663
Joined: 11-17-2005


Message 139 of 147 (281838)
01-26-2006 8:21 PM
Reply to: Message 138 by cavediver
01-26-2006 7:59 PM


Re: Relativistic vs Doppler (in a nutshell)
Oh fine, I'm leaving it because it doesn't affect the principle and as a permanent record of what a big dope I am then It can be an as-yet-undiscovered white dwarf only barely in that system to be named Big Dope Centauri, exactly 3 light years away and so on
I'm more concerned about the fact that in my scenario the home observer sees the 3 year journey out, experienced by the astronaut as 6 months, as taking up the full 6 years. The clock ticks are normal during the mission, which has to take only an hour or so in order to keep my arithmetic pretty straight. Then the home observer sees the entire 3 year journey back crammed into another hour or so, or whatever the gap in my math is, by the blue-shift, though the astronaut experiences it as the same 6 months it took to get there in the first place.
Even assuming this is correct I probably ought to have conjured up a better example that isn't so freaking unbelievable

This message is a reply to:
 Message 138 by cavediver, posted 01-26-2006 7:59 PM cavediver has replied

Replies to this message:
 Message 140 by cavediver, posted 01-27-2006 3:28 AM Iblis has replied
 Message 141 by cavediver, posted 01-27-2006 3:49 AM Iblis has not replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 140 of 147 (281920)
01-27-2006 3:28 AM
Reply to: Message 139 by Iblis
01-26-2006 8:21 PM


Re: Relativistic vs Doppler (in a nutshell)
Ok, read it now.
Apart from the 3 lyrs, it seems spot on. I usually give a slightly more extreme gamma so the astronaut gets there in a week; it just separates the home time and the astronaut time a little better.
I'm more concerned about the fact that in my scenario the home observer sees the 3 year journey out, experienced by the astronaut as 6 months, as taking up the full 6 years. The clock ticks are normal during the mission, which has to take only an hour or so in order to keep my arithmetic pretty straight. Then the home observer sees the entire 3 year journey back crammed into another hour or so, or whatever the gap in my math is, by the blue-shift, though the astronaut experiences it as the same 6 months it took to get there in the first place.
Freaky isn't it But totally correct. And I must say that your paragraph above is a wondefully succint statement of the facts...
Essentially the astronaut is cruising back with his own photons only slightly outpacing him. If something heads towards us at c, the first we know is when that something arrives! Not good if it's something bad...
Even assuming this is correct I probably ought to have conjured up a better example that isn't so freaking unbelievable
No, I would say this is pretty mundane for Relativity
Now tell me what the astronaut experiences during his journey... he travels "3" lyrs in what he experiences as 6 months. That sounds like 6c (just under Warp 2 ) Does he think he is travelling faster than light?
This message has been edited by cavediver, 01-27-2006 03:31 AM

This message is a reply to:
 Message 139 by Iblis, posted 01-26-2006 8:21 PM Iblis has replied

Replies to this message:
 Message 145 by Iblis, posted 01-27-2006 8:10 PM cavediver has not replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 141 of 147 (281921)
01-27-2006 3:49 AM
Reply to: Message 139 by Iblis
01-26-2006 8:21 PM


A quick aside on Superluminal Jets
Your story just reminded me of the phenomenon of superluminal jets so I thought I'd mention them...
We observe jets of luminous material ejected from quasars and other active galactic nuclei (AGNs). These are wonderful because we can see them move in real time (well, over a month to a few years), which is mind blowing for something that is 100s of millions to billions of lyrs away. The upset was that in the order of a month to a year, these jets were moving across an arc of sky equivalent to hundreds (or thousands) of lyrs. There was some real belief that these jets proved superluminary travel was possible! I'm sure you can probably still find today some wacko sites trying to use them as "proof".
The fact is these jets are not travelling radially to the AGN (wrt us) but are travelling almost directly towards us at close to c. The slight offset gives rise to the observed sideways motion, and the enormous blueshift is what makes it look like the jet is making that sideways motion in just a matter of months.
This is exactly as you described your homeward bound astronaut: we see him take an hour to journey 3 lyrs!

This message is a reply to:
 Message 139 by Iblis, posted 01-26-2006 8:21 PM Iblis has not replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 142 of 147 (281922)
01-27-2006 3:58 AM
Reply to: Message 136 by JustinC
01-26-2006 5:55 PM


Re: Relativistic vs Doppler (in a nutshell)
Hi Justin, glad you liked the discussion. It's not really a coincidence. There is a real part - the length of the space-time path, known as the Proper Time of the asttronaut - and there are distorted observations of the path. As the astronaut and observer come back to rest wrt each other back on Earth, there are no more distortions.
I think Iblis' summing up paragraph in Message 139 says it all. The observer really has no clue what is going on until the astronaut stops accelerating (at Centauri or back on Earth) The combination of Doppler and Lorentz severely screws up observations.
This message has been edited by cavediver, 01-27-2006 03:58 AM

This message is a reply to:
 Message 136 by JustinC, posted 01-26-2006 5:55 PM JustinC has not replied

  
JustinC
Member (Idle past 4844 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 143 of 147 (282034)
01-27-2006 5:23 PM
Reply to: Message 137 by Iblis
01-26-2006 6:45 PM


Re: Relativistic vs Doppler (in a nutshell)
So if I were to imagine this on a space-time diagram, with instant accelerations, it would look like a four sided polygon with two sides parallel and the others sides symmetrical. I don't if that is a good way to describe it, but I think you know what shape I'm thinking of. Then, since the the twin takes a longer route to get back to the reference frame he started at (the part of the diagram that runs parallel with the original twin), his clock will read less time compared to the twin who just stayed in his refernce frame. Is this correct?
So is the maxim, "The longer the path one takes to get to a particular reference frame, the less time there clock will read compared to someone who took a shorter path to get to that reference frame."

This message is a reply to:
 Message 137 by Iblis, posted 01-26-2006 6:45 PM Iblis has replied

Replies to this message:
 Message 144 by Iblis, posted 01-27-2006 6:41 PM JustinC has not replied

  
Iblis
Member (Idle past 3896 days)
Posts: 663
Joined: 11-17-2005


Message 144 of 147 (282039)
01-27-2006 6:41 PM
Reply to: Message 143 by JustinC
01-27-2006 5:23 PM


shout out to the Illuminati
Yes, an isosceles trapezoid is what you are imagining. (In gringo, in anglo it would be a trapezium.) Keeping in mind how little time I allowed for the actual scoring of the Big Dope, what you will imagine is just short of a triangle.
A good example of an isosceles trapezoid is the face of the Pyramid on the Great Seal, the Eye not being considered as part of the structure.
Isosceles Trapezoid -- from Wolfram MathWorld
And yes, the longer the route through spacetime (i e the more of it is space) the less of it is time. We need relatively great spatial distances in conjunction with short periods of time in order for the difference to have much significance though. (More on that part in a bit I expect)

This message is a reply to:
 Message 143 by JustinC, posted 01-27-2006 5:23 PM JustinC has not replied

  
Iblis
Member (Idle past 3896 days)
Posts: 663
Joined: 11-17-2005


Message 145 of 147 (282048)
01-27-2006 8:10 PM
Reply to: Message 140 by cavediver
01-27-2006 3:28 AM


Warp Drive (in the nutshell)
Now tell me what the astronaut experiences during his journey... he travels "3" lyrs in what he experiences as 6 months. That sounds like 6c (just under Warp 2 ) Does he think he is travelling faster than light?
Depends how he measures and what he sets his standards at. No, he never thinks he is traveling faster than any actual light, that's the rough part for me, I will try to wrap my mind around it in a minute.
But first, let's say he considers c to be 186000ish miles per second. If he has a "speedometer" display that uses some accurate method to measure the distance he has traveled, continuously corrected parallax or somesuch, and then divides it by his proper time, he certainly thinks he is traveling at 6c just as you described. He could have another speedometer that calculated "real time" using every fact at his disposal, that might show his real speed.
It's when we get to "the speed of light" part that it gets tricky and my maths start to fail me. He continues to observe or measure light as traveling at 186,000ish miles per second no matter how fast he goes, just as if he were standing still. If it were as simple as I would like, that would mean he now measures it as traveling at 7c. That would only be the light traveling in the same direction as him though, the light traveling in the opposite direction as him would be going at 5c by the same logic. And sideways? Geez, it would vary accordingly.
And as I have mentioned before this logic is wrong Wrong WRONG. According to what I understand, it never varies, neither forward or backwards nor sideways, the speed of the actual light is always measured the same, the actual variance is the doppler stuff we have been yammering about, the stretching of the wavelengths, this is how light deals with its own "proper time", by keeping it at 0 no matter what.
How the heck do I visualize that?
* yeah side note, I'm glad you mentioned the "warp speed" thing, Roddenberry actually consulted with various popular science types while planning the original Trek. He wanted things to look and sound "realistic" even when we got around to actually traveling in space on a grander scale.
This is why, for example, the Enterprise looks the way it does. When he asked about potential "artificial gravity" strategies, of course they only had the 2, normal acceleration and centrifugal force (circular acceleration). They showed him drawings of the usual stuff, a big space station shaped like a wheel and a big continuous-drive fusion system shaped like one pipe for the passengers with some other pipes for the engines. Stick 'em together and write NCC-1701 across the bow, there we are.
Anyway the cubic measurement we call "warp speed" now was offered up as what might be a convenient way to measure apparent average speed when crossing various distances at 1g of continuous acceleration, it's the kind of thing we would want because it wouldn't go off the scale as quickly as some sort of distance/time measurement like "miles per hour" or "light years per year". Some of the early versions of the pilot script still had this logic in it, but it was a bit too abstruse for the Desilu and Paramount writers to pay it much mind.
Still when you watch the scene in "The Menagerie" where the supposed settler is talking with Pike about his "Time Warp" drive, or when you look at the background history where Zefram Cochrane is said to have first tested his invention by achieving some minor fraction on a trip past Pluto before venturing off to Promixa or Alpha, remember that these ideas were born out of the perfectly-realistic engineering implications inherent in a 1g continuous-acceleration system.

This message is a reply to:
 Message 140 by cavediver, posted 01-27-2006 3:28 AM cavediver has not replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 146 of 147 (408062)
06-30-2007 10:14 AM
Reply to: Message 110 by Percy
01-19-2006 8:16 PM


Re: Relativistic vs Doppler
cavediver writes:
No, no, no. The cosmological doppler IS relativistic. It cannot be otherwise. Please do not use "relativistic" to mean SR effects, especially as there are no SR effects in cosmology, only approximations to SR effects which come from the GR metric... precisely where the cosmological redshift and gravitational redshift originate.
Don't use relativistic to mean SR effects? So even though SR is short for Special Relativity, you're saying its effects shouldn't be described as relativistic. I know you qualified that to the cosmological context, but still.
I appreciate that it's difficult to find sufficient time to explain complex and easily misunderstood topics, and I appreciate that you're making the effort, but you haven't given me much to go on. I suppose I could memorize what you're saying so I could parrot it back, but my goal is understanding, not mimicry. Perhaps you could point me to a readily available layperson's book that has a chapter describing what you're trying to explain to me.
Well, only 18 months to get back to this
I was trying to explain Cosmological redshift from a different POV ovet at IIDB and it reminded me of our discussion early last year. So I thought I'd bring it over here (especially as BB&C has been SO dry this last year) to try out on you!
quote:
First off we are interseted in red-shift as a change in frequency, not wave-length.
Wave-length makes us think of an actual extended wave in space, extended in the direction of travel. It sort of makes sense that if space is stretching, this will stretch the wave, thus creating a red-shift. Trouble is, there is no extended distance in the direction of travel. There is actually zero distance between the emission and absorption of the photon (complete Lorentz contraction), and likewise no time passes (complete time dilation). So wave-length is not much good for thinking about red-shift.
Back to frequency - frequency obviously requires reference to the local time and this is goverened by the local light cone at the point of emission. However, at absorption, that frequency is going to be measured with reference to the local light cone at the point of absorption. The photon by virtue of travelling at c is essentially overlapping these two light cones and allowing them to be compared. The difference between these light cones is what is being measured by the change in frequency of the photon - hence red-shift.

This message is a reply to:
 Message 110 by Percy, posted 01-19-2006 8:16 PM Percy has not replied

  
Phat
Member
Posts: 18262
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.1


Message 147 of 147 (438352)
12-04-2007 7:52 AM
Reply to: Message 44 by cavediver
01-14-2006 4:37 AM


Galaxies as Frisbees
Just out of curiosity, when is the latest model of the Space Telescope set to be in place?
Also....how much better will the new Space Telescope be in relation to its predecessor?
Im wondering if we will ever be able to peer right into the point of Origin in space time itself.....perhaps a giant Eye will be looking back at us!

This message is a reply to:
 Message 44 by cavediver, posted 01-14-2006 4:37 AM cavediver has not replied

  
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