Gaining a Better Understanding of Special Relativity

[matheinste]

It's not anything particularly major. You spoke of what a twin "sees"; rather than what a twin calculates or infers.

What I really picked up on was the mention of "acceleration". Sometimes people think of something special happening during acceleration; but really all that matters is a change of reference frame. It's not really valid to speak of what happens to a remote twin "during" an acceleration of the other, because that implicitly brings up the notion of simultaneity, and that is a common source of errors.

The proper way to calculate the age of any twin is to integrate the proper time along their world line.

Cheers -- sylas

While this last fact is absolutely true for all realistic accelerations does it not cause a problem when the obviously unrealistic instantaneous accelerations are used, as they often are for instruction purposes.

Matheinste.

 

[sylas]

While this last fact is absolutely true for all realistic accelerations does it not cause a problem when the obviously unrealistic instantaneous accelerations are used, as they often are for instruction purposes.

Matheinste.

On the contrary! It is particularly the case of the instantaneous acceleration when the issue of what happens "during" acceleration is most stark. The turn around point is "simultaneous" with two different events for the remote twin; depending on which frame you use. The common error is to think that the traveling twin can calculate how much the remote twin ages during the outward trip, and calculate how much the remote twin ages during the return trip, and add. This is wrong, because of the simultaneity issue I mention.

Make it concrete. A traveling twin travels at 60% light speed to a star 6 light years away, and comes back at the same speed. The traveling twin at take off is in a frame where the star is approaching them at 60% light speed from a distance of 4.8 light years. In eight years elapsed time the star arrives at the traveling twin. (In the frame of the traveller, it is the star that is moving.) At the point of arrival, the traveler infer, correctly, that the stay at home twin is "now" 6.4 years of age, and is 4.8 light years distant. However, the light they see is coming from a point 3 light years distant, at which the twin is seen to be 4 years old.

Then magic happens, and the ship reverses direction. In the new frame, the remove twin is "now" 4.8 light years distant. However, this is a different "now", in a new reference frame, because of the change in planes of simultaneity. The light the traveller sees is the same light as before, but the point from which is came is now (in the new frame) 12 light years distant. The remote twin is still seen at an age of 4 years, but the remote twin is now approaching, and the traveler can infer (correctly) that the remote twin being "now" 4.8 light years distant must have traveled 7.2 light years since the light was emitted... which takes 12 years at 60% light speed. With time dilation of 1.25, the remote twin is "now" aged 9.6 years older then when the light was emitted, so they are "now" 13.6 years old.

Hence the turn around point is simultaneous with the remote twin being 4.8 years old in one instant, and a moment later in the new return frame, the turn around point is simultaneous with the remote twin being 13.6 years old.

Very confusing! This is not an ideal way to calculate the aging of the remote twin... it's better to integrate proper time over a worldline. But if you are careful, you can do it this way as well.

Cheers -- sylas

 

[George Jones]

Where does the doppler effect come in,now? I really didn't come across anything on the doppler effect while reading about the twin paradox--is there anything major I'm missing?

Try

https://www.physicsforums.com/showthread.php?p=2186296#post2186296.

 

[Dale]

While this last fact is absolutely true for all realistic accelerations does it not cause a problem when the obviously unrealistic instantaneous accelerations are used, as they often are for instruction purposes.

No, the spacetime interval is well-defined even in the case of instantaneous acceleration.

 

[matheinste]

Dalespam and Sylas,

I was mistakenly referring to the jump in the reading of the stay at home clock when compared with the travellers clock at the point of turnaround where the traveller changes reference frame instantaneously. For some unknown reason I was interpreting this as a jump in the traveller's proper time. My stupid mistake.

Matheinste.

 

[Urmi Roy]

I read up the post on https://www.physicsforums.com/showthread.php?p=2186296#post2186296
and also https://www.physicsforums.com/showthread.php?p=1384776#post1384776

both by George Jones and I think I sort of got it.

However, from what I understood, the main cause of dissymmetry of the out-going and home-coming trips of the traveling twin has its explanation in the doppler effect.

Whereas during the out-going trip the traveling twin observes a lesser frequency of rotation of the home-staying twin's seconds hand (on his clock), he observes a greater frequency of rotation while coming back home.

But,I have two questions related to this-
1. I read that the direction of relative velocity of two people who are traveling at relativistic speeds does not affect their observations--meaning moving towards each other or away from each other are equivalent in relativity-thats why the formula for the lorentz factor involves a squared quantity (the ratio of velocity of the object by the velociy of light is whole squared in the formula),so the sign of relative velocity does not matter.

However,as I said, the dissymetry seems to be hinged upon the fact that the traveling twin sees different things on his outward and home-ward journeys.

2. Is this an alternate explanation to the one in Virginia Tech or is it in accordance to it?

Then magic happens, and the ship reverses direction. In the new frame, the remove twin is "now" 4.8 light years distant. However, this is a different "now", in a new reference frame, because of the change in planes of simultaneity. The light the traveller sees is the same light as before, but the point from which is came is now (in the new frame) 12 light years distant. The remote twin is still seen at an age of 4 years, but the remote twin is now approaching, and the traveler can infer (correctly) that the remote twin being "now" 4.8 light years distant must have traveled 7.2 light years since the light was emitted... which takes 12 years at 60% light speed. With time dilation of 1.25, the remote twin is "now" aged 9.6 years older then when the light was emitted, so they are "now" 13.6 years old.

I had some problem understanding how the distance of the light source suddenly changed when the twin turns toward home and how the homestaying twin appears to be 4 years old for the distant star and what exactly happened just after that.

 

[Urmi Roy]

When I refer to the Virginia Tech website, I mean the one I gave in post number twentyfour of this thread,just in case anyone would like to refer to it.

 

[sylas]

1. I read that the direction of relative velocity of two people who are traveling at relativistic speeds does not affect their observations--meaning moving towards each other or away from each other are equivalent in relativity-thats why the formula for the lorentz factor involves a squared quantity (the ratio of velocity of the object by the velociy of light is whole squared in the formula),so the sign of relative velocity does not matter.

It does affect "observation" (what you see) and the Doppler effect deals with that. It does not effect the factor by which time is dilated. But as pointed out before, what you "see" is not the dilation, but includes also the effects of movement.

2. Is this an alternate explanation to the one in Virginia Tech or is it in accordance to it?

It's pretty dashed close to the same explanation. We may emphasize a few aspects differently, but I had a look and it considers many of the same things. Addendum. I especially like the way they show that it is not really acceleration that matters; only the change of frame of reference.

I had some problem understanding how the distance of the light source suddenly changed when the twin turns toward home and how the homestaying twin appears to be 4 years old for the distant star and what exactly happened just after that.

This is one of the basic things about relativity. There is no absolute notion of simultaneity. If you have two events A and B with a "time like" separation, then for some observers A is simultaneous with B, and for others A is before B and for others B is before A.

Consider the situation I described previously. A traveler flies at 60% light speed to a star 6 light years distant, and then reverses and returns. The trip takes 20 years according to the stay at home twin, but 16 years according to the traveling twin.

Now consider three events

• The stay at home twin is 4.8 years older.
• The stay at home twin is 10 years older.
• The stay at home twin is 13.6 years older.

Now... in the frame of reference of the stay at home twin, the arrival of the traveler at the star is simultaneous with event B. It takes another six years to "see" the arrival, of course, as the light takes that long to get back from the star and let you see it.

In the frame of reference of the outbound traveler, event A is simultaneous with the arrival at the star.

In the frame of reference of the inbound traveler, event C is simultaneous with the arrival at the star.

There's another event... D. The stay at home twin is 4 years older. This is the event that is "seen" by the traveler when they look back from the arrival event.

The distances to this event are given by Lorentz transformations. Taking the arrival event as the origin of all frames of reference, the event seen from turn around is at (-6, -6) in the stay at home frame; 6 light years distant and 6 years ago.

Now. The outbound twin has velocity 0.6c, and gamma factor is 1.25. Using the Lorentz transformations

$$\begin{align*} distance & = 1.25 ( -6 + 0.6 \times 6 ) \\ & = -1.25 ( 6 - 3.6 ) \\ & = -1.25 \times 2.4 \\ & = -3 \end{align*}$$​

The inbound twin has velocity -0.6, and the transformation gives

$$\begin{align*} distance & = 1.25 ( -6 - 0.6 \times 6 ) \\ & = -1.25 ( 6 + 3.6 ) \\ & = -1.25 \times 9.6 \\ & = -12 \end{align*}$$​

It is also interesting to look more carefully at what the traveler sees when they turn around. The remote stay at home twin was red shifted, and suddenly becomes blue shifted. Their angular size in the sky also reduces suddenly, by a factor of 4, because in the new frame the light is coming from 4 times further away.

There are some spacetime diagrams for this example here, in [post=2199430]msg #50[/post] of thread "Twin paradox - a quick(ish) question", and there are diagrams to help explain the sudden change in angular size in [post=2217788]msg #21[/post] of thread "most basic of thought experiments in special relativity".

Note that for the stay at home twin, they "see" the turn around point when they have aged 16 years, and they see no change in angular size. The shift in angular size is a sure sign that you have changed your reference frame, even if you had somehow avoided noticing the infinite acceleration with a magic warp drive of some kind.

Cheers -- sylas

 

[Urmi Roy]

I'm trying to figure it all out in my head-it might take a while--since as everyone knows,it is all a little confusing, but do keep sending in any more opinions and views that you may be having,I'll be greatly benefited!

 

[Urmi Roy]

I've been working on this topic of the twin paradox for the last few days and after referring to the posts I received earlier and from references on other websites, I've finally come to a conclusion.

Here goes...

Firstly, the relativistic doppler effect (RDE)---this is basically a cumulative result of the classical doppler effect (CDE) and time dilation (TD) ,since Einstein first checked the CDE and found, when dealing with light waves, that it wasn't in accordance with his Special relativity (SR)and Maxwell's postulate for the constancy of the velocity of light,and so he edited the formula so that the modified formula gives result in accordance to SR--in other words, if we apply the classical relativity to a particular situation and then slightly modify the result by using lorentz transformation,we eventually get the same result that the RDE gives us.
(reference: http://redshift.vif.com/JournalFiles/V12NO1PDF/V12N1HAM.pdf)

In his post(https://www.physicsforums.com/showthr...76#post1384776 ), George states that the result,whether obtained by RDE or Lorentz transformation,is the same--it has to ,since the RDE was tailor-made for SR.

However,if we leave the formulae of RDE,and,as I said use CDE first,followed by time dilation formula,we see that the individual results for the doppler effect is 3 times more 'powerful' than time dilation effects.So, for a rapidly receding star, we would have TWO effects, Doppler and Time Dilation, both of which would cause us to see the spectral lines to be shifted toward the red end of the spectrum. Einstein made a Relativistic adjustment to the Doppler Effect equation to account for this Time Dilation effect.

If the star was rapidly moving toward us, The Doppler shift would be toward the BLUE end of the spectrum, while the Time Dilation shift would still be toward the red. Einstein's Relativistic Doppler formula calculates this, too, and gets a resulting red shift that is smaller that the non-Relativistic Doppler red shift would have been. It turns out that the Doppler effect is always at least three times as great as the Time Dilation effect, so Doppler always prevails.
(reference: http://mb-soft.com/public/reltvty1.html)

Now, as Sylas pointed out,in one of the previous threads, what we observe is nothing but the reception of light photons(I think page 3 of Twin paradox,a quick(ish) problem),time dilation is not what we see-the visual perception of light is governed by the doppler effect,since the doppler effect alone tells us about,'how' I may say,the light is received by us and thus it tells us exactly what we see.

In sylas' post(which is more elaborately dealt with in another thread,referring to https://www.physicsforums.com/showthread.php?p=2217788#post2217788), he dealt emmaculately with the observations of the twins--in which,therefore,the role of the doppler effect becomes very emminent.The reason why the star suddenly appears 12 light years away to the traveling twin, at the start of the outward journey,instead of the 6 light years that it appeared to be at in the star's rest frame, is basically due to the "way" in which light is recied or percieved---this is explained very well in the example of the pin-hole camera example,given by sylas(on https://www.physicsforums.com/showthread.php?p=2217788#post2217788).
In this example,it clearly states that the change in observation of objects,like the star,is all due to the way our perception of the light from the object changes, once there is relative motion.

I will not go into the detailed description of sylas' example,but I found a simpler approach to it(which does not,however deal with what the twins individually see).
Suppose there is a pulsar (flashing star) at a certain distance from earth,which to an earthbound observer flashes 1 time per sec.Now, a twin moves staright toward this puslar,leaving earth, and due to doppler effect,observes a greater frequency of light,2 flashes per second,and when he returns home,observes a lower frequency of 0.5 flashes per sec (=1 flash per 2 secs).
The earthbound observer sees 20 flashes from the beginning of the other twin's journey to the instant that he reaches home--so the journey took 20 seconds to the earthbound observer.
However, to the traveling twin,he sees 16 flashes while going and only 4 while coming. Thus, the outward journey took him (in his reference frame) 8 secs and so did the return journey(this comes from the different frequencies observed by him during the journey.)

Thus, by the end of the trip,the traveling twin thinks he is 16 secs old,but the earthbound observer thinks he is 20 secs old.(reference: )

This is a much more simplified version of sylas',explanation,but its purely in the point of view if the doppler effect,just like sylas said.

The explanation in the Virginia Tech website ( link provide in post 24 of this thread),is,on the other hand completely in terms of lorentz transformation---but,as George Jones said, they end up to the same result.

Now, coming to my original question, the twin paradox is very different from the train-tunnel experiment because --in the train-tunnel experiment,the two observers are only receding from each other,whereas in the twin paradox,the twins first reced from each other,then move toward each other---and,thanks to the doppler effect,they 'recieve' the light waves responsible for the visual perceprtion of these events,very differently on either journey.
The explanation on the Virginia Tech website described the entire story based on time dilation and length contraction only--that was just an alternate,but equivalent description.

sylas also stated in one of his posts that "Furthermore, the star ship passengers KNOW that that they are the ones who have changed perspective -- not the remote star -- because the star cannot have moved a large distance in negligible time. They must be looking at it from a new frame of reference. " (pg 1 https://www.physicsforums.com/showthread.php?p=2217788#post2217788)

He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.

This is what I think it is all about,please tell me if my basic concepts are alright,even if I haven't gone into the details.

 

[sylas]

He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.

This is what I think it is all about,please tell me if my basic concepts are alright,even if I haven't gone into the details.

Thanks for the comments, I'm glad it helped. My accounts got a bit too long sometimes.

As with many essentially mathematical problems, there are many ways to get the correct solution. For example... the angular size of the image in a moving pinhole camera is reduced when the camera reverses direction to approach the object being viewed. You can derive the reduced size of the image in two ways that appear superficially different, but are actually equivalent, and refer to different equally valid points of view.

• The image is reduced because the photons have a shorter path from the pinhole to the light detector at the rear of the camera, now that that the rear of the camera is moving towards, rather than away, from the photon stream. (Point of view of a stationary observer beside the reversing camera.)
• The image is reduced, because the photons are now coming from much further away. (Point of view of a photographer, who is reversing direction along with their camera, and is in a new frame of reference.)

You can tell when you have moved into a new reference frame by experiencing a sudden acceleration, OR by observing a sudden change in the distances to remote objects you are observing.

The crucial point to note... it matters not a scrap whether the object is "massive" or not. No object, massive or otherwise, is transported 9 light years in a moment. Therefore the new distance is not because the object moved, but because you changed your direction in spacetime... you moved into a new frame of reference and THAT caused the change in distance.

There are other ways you can tell you were the one moving. If you have been unable to maintain observations of the remote twin, but you find on return that they have aged more than you did... then you must have been moving non-inertially. If you have been able to maintain observations of redshift and blueshift of the remote twin, then equal amounts of time of an equal and opposite redshift/blueshift is a sure sign that you were the one who reversed direction. And so on.

In brief... there are all kinds of differences between the two twins in the thought experiment where one goes out and returns at relativistic velocity while the other remains at rest, and this lack of symmetry includes differences in what they experience in acceleration, in what they observe looking at their remote partner, and in how they age. The differences can be calculated, consistently, with special relativity. There's no paradox when you actually apply the physics to the problem (and I realize you aren't claiming a paradox!) ... it is simply a case of getting one's head around how relativity works.

Cheers -- sylas

 

[Urmi Roy]

Well,very cautiously, I would like to ask sylas and everyone else who has been kind enough to read this thread if you think whatever I said was 'basically' correct,since sylas didn't really point out any mistakes in the last post...have I finally got somewhere on the right track?

I won't mind waiting a few days,if it takes a while to go through my enormous post and have a quick glance at the references I provided.

 

[Urmi Roy]

Could someone spare just a little time in ascertaining whether post no. 45 doesn't have any conceptual mistakes---I need move ahead with my study of special relativity, which I can do only when I'm certain that I 've got this section right.

 

[JesseM]

sylas also stated in one of his posts that "Furthermore, the star ship passengers KNOW that that they are the ones who have changed perspective -- not the remote star -- because the star cannot have moved a large distance in negligible time. They must be looking at it from a new frame of reference. " (pg 1 https://www.physicsforums.com/showthread.php?p=2217788#post2217788)

He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.

It is not necessary to look at outside objects to judge if you've accelerated in SR, you can tell using an accelerometer--if you accelerate you'll feel G-forces and the accelerometer will register this, while inertial observers in SR will always feel weightless.

 

[Urmi Roy]

It is not necessary to look at outside objects to judge if you've accelerated in SR, you can tell using an accelerometer--if you accelerate you'll feel G-forces and the accelerometer will register this, while inertial observers in SR will always feel weightless.

I was actually assuming the ideal case where the acceleration is instantaneous and its perception is negligible.

What do you think of the rest of the explanation--do you approve of it?

 

[Al68]

He says that in the case of the twin paradox,we can tell which person is moving,as opposed to other situations in SR where due to relative uniform motion,we can't tell which person is moving and which isn't---but this is again,not due to any breach of the laws of SR,but it is due to a common sense explanation,that a massive nonliving object like a star can't move all of a sudden. If we lacked this common sense,or if the star had the capability to move,like a giant living object,we could not have told who actually is moving.

Every star in the sky is "moving". Unless you mean "accelerating" instead of moving. In that case, of course an observer could tell if he accelerated even if he couldn't feel it (because he was a robot with no accelerometer, for example) because his change of motion would be relative to not just one star, but every star in the universe. He could tell he wasn't at rest in an inertial frame because every other object in the universe would have accelerated (relative to him) with no force acting on them.

 

[JesseM]

I was actually assuming the ideal case where the acceleration is instantaneous and its perception is negligible.

Even if we assume non-ideal accelerometers which can't detect this, you could detect the acceleration in other ways. Suppose in the middle of a rocket you let go of a ball, and since everything inside is weightless the ball just hangs there, not moving closer to any of the walls (from the perspective of a frame where the rocket is moving, the ball is moving inertially with the same velocity). But now if the rocket instantaneously accelerates, since no part of it is in contact with the ball the acceleration is not imparted to the ball, so the ball continues to move inertially at the same velocity as before, meaning from the perspective of an observer in the rocket the ball has suddenly stopped being at rest relative to the walls and is now moving towards one of the walls at great speed.

What do you think of the rest of the explanation--do you approve of it?

Looks fine to me.

 

[Urmi Roy]

Even if we assume non-ideal accelerometers which can't detect this, you could detect the acceleration in other ways. Suppose in the middle of a rocket you let go of a ball, and since everything inside is weightless the ball just hangs there, not moving closer to any of the walls (from the perspective of a frame where the rocket is moving, the ball is moving inertially with the same velocity). But now if the rocket instantaneously accelerates, since no part of it is in contact with the ball the acceleration is not imparted to the ball, so the ball continues to move inertially at the same velocity as before, meaning from the perspective of an observer in the rocket the ball has suddenly stopped being at rest relative towards the walls and is now moving towards one of the walls at great speed.

Hmm...It seems that if we analyse with a little bit of logic,there may be loads of ways to detect acceleration! Thanks for this particular idea.

Looks fine to me.

I'm really grateful,it's a big load off my mind,now!

 

[Urmi Roy]

Sorry to bother you all with this thread after a long time,but I have some small,but essential points to clear up...

1.Is it that in the real world a velocity of greater than 'c' is not attainable or any velocity greater than or equal to c is not attainable?

2. Since the lorentz contraction factor depends on the square of the ratio of the relative velocity by the velocity of light,is the magnitude of length contraction independant of the direction of relative motion?

3. In the formula for the addition of velocities,the lorentz factor(gamma) cancels out--does this imply anything very important?
(I mean the formulae derived in the page http://theory.uwinnipeg.ca/mod_tech/node137.html)