The twin paradox

[michel123456]

The abrupt change is a result of the difference in light delay. While the object is traveling toward you, each photon bouncing off of it is starting a little closer to the Earth, so it will have slightly less travel time than the last photon to bounce off of the object, and will arrive on Earth sooner after the previous one than it left.

 

When the object is traveling away from Earth, each successive photon is slightly farther away from Earth, so it has to travel farther and the gap between when the first arrives and the second arrives will be slightly longer than the gap between the first and second bouncing off the object.

 

This creates the illusion that objects moving toward you are faster than they really are, and objects moving away from you are slower than they really are, though it's only really noticeable at large fractions of light speed.

 

When the object reaches you, it transitions from the blue-shift "sped up" appearance to the red-shifted "slowed down" appearance, which creates the illusion of rapid deceleration even though the object is still actually traveling along an inertial path and doesn't feel any net forces.

All that is O.K.

But the "blueshift rate" is not the same as the "redshift rate". The one is not the reverse of the other.

I mean, if one made a graph of the "apparent velocity", this graph has an abrupt change at the observer.

In our E.T. example, the "apparent velocity" (of the image) is 1000LY/1 day when coming and 1000LY/365001 days when leaving (if i understand clearly). That is 365001 times slower.

Edited May 20, 2013 by michel123456

[swansont]

All that is O.K.

But the "blueshift rate" is not the same as the "redshift rate". The one is not the reverse of the other.

I mean, if one made a graph of the "apparent velocity", this graph has an abrupt change at the observer.

In our E.T. example, the "apparent velocity" (of the image) is 1000LY/1 day when coming and 1000LY/365001 days when leaving (if i understand clearly). That is 365001 times slower.

 

There is no reason to expect it to be "the reverse", because it's an inverse relation. If the Doppler shift is a factor of 2 when approaching, it's 1/2 when receding. Same factor of 2, but dividing instead of multiplying.

[md65536]

In our E.T. example, the "apparent velocity" (of the image) is 1000LY/1 day when coming and 1000LY/365001 days when leaving (if i understand clearly).

No, you're forgetting that light from the receding object is also delayed.

[michel123456]

No, you're forgetting that light from the receding object is also delayed.

How much time will take the light signal from the arrival to come to Earth? At least 1000 years (365000 days)

[md65536]

How much time will take the light signal from the arrival to come to Earth? At least 1000 years (365000 days)

Plus 365001 days measured on Earth for ET to get there equals...

[michel123456]

Right. 730001 days.

[michel123456]

---------------------------------------------------

That is a ratio 1/730001 between the image coming and the image leaving!

With the "real" object in between the 2 "apparent velocities", coinciding with its own image at the observer, at the "correct" mathematical velocity

[md65536]

---------------------------------------------------

That is a ratio 1/730001 between the image coming and the image leaving!

 

 

With the "real" object in between the 2 "apparent velocities", coinciding with its own image at the observer, at the "correct" mathematical velocity

So you see that it all works out. If it comes in very near the speed of light, there is little difference between the timing of it and light (according to the astronomer). If it goes out near the speed of light, it takes about twice the time of light, because the object has to get out there and the light has to come back in.

 

The object starts and ends at the same distance from Earth; the two events have the same delay of light. So the change in delay averages to 0 and on average it appears to travel at velocity v: (365000+365000) light-days traveled / (1 + 730001) days watched = 0.99999726 light days per day.

 

This is true in SR.

As long as we're using only one observer and clock, it's also true in classical physics, where the speed of light is c (eg. unaffected by ship's velocity, or signals are sent from markers at rest, or Earth is at rest in an aether).

Edited May 21, 2013 by md65536

[michel123456]

So you see that it all works out. If it comes in very near the speed of light, there is little difference between the timing of it and light. If it goes out near the speed of light, it takes about twice the timing of light, because the object has to get out there and the light has to come in.

 

The object starts and ends at the same distance from Earth; they both have the same delay of light. So the average timing will appear to be v: (365000+365000) light-days traveled / (1 + 730001) days watched = 0.99999726 light days per day.

 

This is true in SR.

As long as we're using only one observer and clock, it's also true in classical physics, where the speed of light is c (eg. unaffected by ship's velocity, or signals are sent from markers at rest, or Earth is at rest in an aether).

What you find perfectly logic and consistent I find amazing.

For example, it means that if you take a movie of an object coming and leaving, and then reverse the movie, you will not observe the same thing. The image of the phenomena is not time reversible!

Speaking of motion, I find that amazing.

[md65536]

What you find perfectly logic and consistent I find amazing.

For example, it means that if you take a movie of an object coming and leaving, and then reverse the movie, you will not observe the same thing. The image of the phenomena is not time reversible!

Speaking of motion, I find that amazing.

No, if you reverse a movie it will take the same length as the movie! It's a 1 day movie of incoming ship and incoming photons. Reversed it would be a 1 day movie of outgoing ship and outgoing photons.

 

So for example, if you watch the ship leaving you over 730001 days, and you sent a signal after 1 day, ET would get your signal at the same time that it arrives at its destination (after it travels for 365000 additional days by your watch). The difference in time that it takes a ship at v=365000/365001 to travel 365000 light-days, vs light, is 1 day, whether it's incoming or outgoing.

 

 

Edit: Or if you mean that a movie of reverse action will not appear the same as a reversed movie, then yes that's true. A movie of either forward or reversed action will still require incoming photons, so appearance is not time-symmetric reversal of observations are not the same as observations of reversed phenomena. Or something.

Edited May 21, 2013 by md65536

[michel123456]

No, if you reverse a movie it will take the same length as the movie! It's a 1 day movie of incoming ship and incoming photons. Reversed it would be a 1 day movie of outgoing ship and outgoing photons.

1 day movie of outgoing object, and that is not what we observe.

(...)

 

Edit: Or if you mean that a movie of reverse action will not appear the same as a reversed movie, then yes that's true. A movie of either forward or reversed action will still require incoming photons, so appearance is not time-symmetric.

I don't understand clearly your sentence but yes, appearance is not time-symmetric. The reversed movie would show 1 day outgoing object going 1000LY away and that is not what we observe.

 

-----------------

It is obvious on the last diagram. The left side is totally different from the right side.

I find that mind blowing.

Edited May 21, 2013 by michel123456

[Delta1212]

I'm not sure time asymmetry is really the proper term to use, but yes, something moving away from you doesn't just look like something moving toward you shown in reverse.

[md65536]

The reversed movie would show 1 day outgoing object going 1000LY away and that is not what we observe.

Another way to put it is that a reversed movie reverses causality. You see effects happen before their causes. You see ET leaving before it leaves. The movement of photons is reversed with everything else.

 

Having ET pass us by and recede is not the same as reversing all of time.

I find that mind blowing.

Perhaps that, rather than simple understanding, is what you're looking for?

[tar]

Spacetime diagram folk.

 

OK, suppose I get the math, but do not accept the answer. Every thing works out on the shift or transform from the one reference frame to the other, with the exception of sensibility. The "figuring" or "measuring" is done based on prior knowledge, and subsequent "forgetting" of the proper distances and times, and the replacement with new observations when required.

 

What if we take a known clock, like a pulsar, and put it at a great enough distance away, that both the traveler and the stay at home see it in a direction 90 degrees from the direction of travel out and back. If the traveler would "measure" his distance and time off of this clock, would not everything work out to be the same time and the same length of trip, in lys and in years, for both the stay at home, and the traveler? So what exactly has been contracted and dilated?

 

Regards, TAR2

 

Or for the 1000 ly away waver, suppose both the waver and the Earth observer, both had figured out when the pulsar first ticked, and both knew how many ticks it was on at any point. Let's say the traveler held up a sign,"one zillion and three", when the traveler waved. The Earth observer's count at the time of seeing the sign, should be one zillion and three plus 1000 years worth of ticks. The next day, when the traveler arrives, HIS count is one zillion and three, plus 1000 years and a day worth of ticks. Same as the Earth observer. Took him 1000 years and a day, to make the trip of 1000 lys. No length contraction or time dilation required.

 

Except, at the halfway point, when he holds up the "one zillion and three plus 500 years worth of ticks" sign, the Earth bound observer would have to figure he aged 500 years, and traveled 500 lys in 12 hours. and we are back to michel123456's issue of "speed of approach".

Edited May 22, 2013 by tar

[Delta1212]

What if we take a known clock, like a pulsar, and put it at a great enough distance away, that both the traveler and the stay at home see it in a direction 90 degrees from the direction of travel out and back. If the traveler would "measure" his distance and time off of this clock, would not everything work out to be the same time and the same length of trip, in lys and in years, for both the stay at home, and the traveler? So what exactly has been contracted and dilated?

No. No matter how far away or where the pulsar is positioned, it will be moving with respect to one or both of the travel/stay-at-home. As such, regular old time dilation applies and they will measure the pulsar as "ticking" at different rates.

 

Time dilation is not the same thing as Doppler shift.

[Janus]

Spacetime diagram folk.

 

OK, suppose I get the math, but do not accept the answer. Every thing works out on the shift or transform from the one reference frame to the other, with the exception of sensibility. The "figuring" or "measuring" is done based on prior knowledge, and subsequent "forgetting" of the proper distances and times, and the replacement with new observations when required.

 

What if we take a known clock, like a pulsar, and put it at a great enough distance away, that both the traveler and the stay at home see it in a direction 90 degrees from the direction of travel out and back. If the traveler would "measure" his distance and time off of this clock, would not everything work out to be the same time and the same length of trip, in lys and in years, for both the stay at home, and the traveler? So what exactly has been contracted and dilated?

 

Regards, TAR2

The stay at home and traveler cannot both see the light coming from a direction of 90 degrees to the direction of travel. The traveler will see pulses coming from some angle in front of him due to the aberration of light. He also will see the pulses blue-shifted by a factor of gamma. Thus, if the Stay at home twin sees 365,000 pulses in one year at a rate of 1000 pulse per day while the traveler travels out and back at 0.866c, the traveler will see 365,000 pulses in 1/2 year at a rate of 2000 pulses a day. Edited May 22, 2013 by Janus

[md65536]

No. No matter how far away or where the pulsar is positioned, it will be moving with respect to one or both of the travel/stay-at-home. As such, regular old time dilation applies and they will measure the pulsar as "ticking" at different rates.

 

Time dilation is not the same thing as Doppler shift.

That's an interesting twist I usually avoid thinking about!

 

Edit: And after reading the preceding post by Janus, I realize the following is in error:

 

Moving 90 degrees relative to something is transverse motion and the transverse Doppler effect applies again. Based on a reply in another thread (http://www.scienceforums.net/topic/75019-gravitational-redshift-and-length-contraction-factors/#entry744881), I think that the relativistic Doppler effect is time dilation combined with (multiplied by) a pseudo-classical Doppler shift of light. With transverse motion, there's no classical Doppler shift, so you get only the effect of time dilation, which is why the transverse Doppler effect is 1/gamma -- perhaps this is false due to aberration??

 

So you'd see the pulsar's clock tick at its actual rate of 1/gamma compared to yours, redshifted due to time dilation but not due to any change in delay of light. In a way, this would give you a sense of what time dilation "really looks like." Edit: or... quite the opposite!

 

Now I'm not sure now if the transverse Doppler effect applies, but if it does and is applied correctly it predicts what Janus said...

Edited May 22, 2013 by md65536

[tar]

Delta1212,<br /><br />Well yes, but if the pulsar ticks 1,495,203,938 times and then blows up, there are a finite, and definite amount of ticks which it has accomplished. Anybody, anywhere, moving at any speed, toward, away from or tangent to the pulsar, if they saw the first tick, and the explosion, would agree with anyone else that saw the whole thing, that it ticked 1,495,203,938 times. There is nowhere for the ticks to go but toward everywhere else. They all have to be accounted for, by two "nearby" and longlived observers, in the end. The count has to be the same. If the two parties are on different counts whenn they are close or far, that is understandable. If they approach the pulsar the count should quicken, if they depart from the pulsar the count slows, but whenever they get together, at the same spot, the count should be the same.<br /><br />Regards, TAR2

 

Janus, on 22 May 2013 - 15:10, said:

The stay at home and traveler cannot both see the light coming from a direction of 90 degrees to the direction of travel. The traveler will see pulses coming from some angle in front of him due to the aberration of light. He also will see the pulses blue-shifted by a factor of gamma. Thus, if the Stay at home twin sees 365,000 pulses in one year at a rate of 1000 pulse per day while the traveler travels out and back at 0.866c, the traveler will see 365,000 pulses in 1/2 year at a rate of 2000 pulses a day.

Janus,

 

But what if the traveler's definition of a day is 1000 ticks of the pulsar? How could he figure it pulsed 2000 times every time it pulsed 1000 times? If he counted 365000 pulses, not only would he know he was gone a year, but he would figure he went the actual distance that he went, in the actual time it took him.

 

Another ancillary question that arose in my muses on this topic. When the cesium clock in Colorado ticks to 100,000, what does a synchronized cesium clock on the other side of the planet read at that moment? Is the time it takes electrical/radio signals to reach from one to the other added, subtracted, or conventionally dealt with in some certain way?

 

Regards, TAR2

 

I will have to read up on that abberation of light thing.

[Delta1212]

You can't define time in one frame by the number of clock ticks in another frame. Both frames will read a single clock tick the same number of times, but won't agree on how much time passed between ticks.

 

For instance, if you define a "day" as 1000 pulses of the pulsar, the pulsar obviously won't pulse a different number of times per day, by definition, but each frame is going to wildly disagree on how long a day is. Going by that definition of a day, one frame might experience a day (ie 1000 pulsar ticks) in a span roughly equivalent to what we think of as a day, while someone in the other frame lives out their entire life and dies of old age before "tomorrow" arrives.

 

Labeling 1000 ticks of a clock in one frame as one unit of time in every frame that can see that clock doesn't suddenly make all of the frames agree on the elapsed time, it just means they disagree on how long that unit lasts. Calling it a day doesn't mean it will last a day in every frame, and saying every frame experienced one "day" doesn't mean anything if they don't agree on how long a day is.

[md65536]

Delta1212,<br /><br />Well yes, but if the pulsar ticks 1,495,203,938 times and then blows up, there are a finite, and definite amount of ticks which it has accomplished. Anybody, anywhere, moving at any speed, toward, away from or tangent to the pulsar, if they saw the first tick, and the explosion, would agree with anyone else that saw the whole thing, that it ticked 1,495,203,938 times.

That's accounted for in the example. Both the inertial twin and traveler see 365,000 pulses. If that's all there were, and then it blew up, that's all anyone would see. Inertial twin saw 365,000 pulses while aging 1 year, and the traveler saw 365,000 pulses while aging 0.5 years.

I will have to read up on that abberation of light thing.

After a cursory glance at that topic, one way to see that Janus is right is to consider the perspective of the traveler in its rest frame. In this frame, the pulsar has a relative velocity pointing "backward" of the direction the traveler is facing. If the pulsar is far away, and light from it comes in "now" at 90 degrees, then the pulsar was directly to the side when that light *left* it, so the pulsar must have traveled a great distance "backward" while the light was incoming. However if we establish that the pulsar really is directly to the side "now", but that light from it has still taken a long time to reach us---just shift what we observe of the pulsar forward---it must appear to be coming from a forward direction.

 

The animation here shows what I mean: https://en.wikipedia.org/wiki/Aberration_of_light#Relationship_to_Light-Time_Correction_and_Relativistic_Beaming

Edited May 23, 2013 by md65536

[michel123456]

That's accounted for in the example. Both the inertial twin and traveler see 365,000 pulses. If that's all there were, and then it blew up, that's all anyone would see. Inertial twin saw 365,000 pulses while aging 1 year, and the traveler saw 365,000 pulses while aging 0.5 years.After a cursory glance at that topic, one way to see that Janus is right is to consider the perspective of the traveler in its rest frame. In this frame, the pulsar has a relative velocity pointing "backward" of the direction the traveler is facing. If the pulsar is far away, and light from it comes in "now" at 90 degrees, then the pulsar was directly to the side when that light *left* it, so the pulsar must have traveled a great distance "backward" while the light was incoming. However if we establish that the pulsar really is directly to the side "now", but that light from it has still taken a long time to reach us---just shift what we observe of the pulsar forward---it must appear to be coming from a forward direction.

 

The animation here shows what I mean: https://en.wikipedia.org/wiki/Aberration_of_light#Relationship_to_Light-Time_Correction_and_Relativistic_Beaming

 

This diagram?

 

I don't understand (again)

Take the left part.

Can the source (the yellow dot) observe the light beam that goes to the white dot? the answer is: NO.

For the source to observe the reflect of its own light (putting a mirror on the white dot), one has to take the right diagram and put it upside-down on the left one.

Does that make sense?

[DimaMazin]

This diagram?

 

I don't understand (again)

Take the left part.

Can the source (the yellow dot) observe the light beam that goes to the white dot? the answer is: NO.

For the source to observe the reflect of its own light (putting a mirror on the white dot), one has to take the right diagram and put it upside-down on the left one.

Does that make sense?

Edited May 23, 2013 by DimaMazin

[Janus]

 

This diagram?

 

I don't understand (again)

Take the left part.

Can the source (the yellow dot) observe the light beam that goes to the white dot? the answer is: NO.

For the source to observe the reflect of its own light (putting a mirror on the white dot), one has to take the right diagram and put it upside-down on the left one.

Does that make sense?

If you put a mirror on the White dot, then what the left part will show is the light coming straight down, hitting the white dot and then retracing its path straight up and returning to the source.

 

The right side (according the white dot) has the light coming in a an angle from the right, bouncing off at an angle to the left, and intercepting the yellow dot as it travels to the left.

[tar]

Janus,

 

Well thankyou, I think its beginning to sink in, again. That is what is "meant" by time dilation.

 

Except I still am confused about all the laws of physics applying equally in any inertial reference frame. It seems that some do and some don't. Not ALL clocks are ticking as they should. The pulsar is not ticking in sync with the cesium wristwatch on the traveller's wrist. The speed of light remains constant, and does not carry with it, the velocity of the ship when light is reflected off or emitted from the ship, but the speed of incoming light, seems to vary, depending on whether you are figuring it, from the traveler's point of view and notion of time, or from the "standard" reference frame of the Sun and its environs, that we have fairly well modeled. Its in this, that I remain perplexed, as to what to call a distance, and what to call a time.

 

Judging by the aberration thing, the view of the traveler would be quite disparate from the view of the same "local" area of the Milky Way, taken while stationary in the Sun's frame of reference. The traveler, if he was familiar with the model of the Milky Way, formed while considering the Sun as a frame of reference holder, would surely notice everything happening and be able to translate what he saw, back into consideration of the Sun's reference frame. He would know for instance, that he could not travel what was a lightyear's distance in the Sun's reference frame, in less than a year, no matter how fast he went. If he were to reach a spot, known to be a lightyear away from Earth, in what seemed to him to be only six months, he would also realize that he had made a trip away from Earth's "now" and a trip to the "now" of the distant point, which is one year, light travel time away from Earth. If he would stop for a breath and a muse at this point, he would realize that even if he traveled back at the full speed of light, he would not be able to make it back to the Sun's now, in less than a year. Why would he not figure his measurements and experiences were true and consistent with the Sun's frame of reference, and his age was consistent with the age of everything in the Sun's frame of reference, and he was displaced in position from the Earth, one year's worth?

 

Regards, TAR2

[Delta1212]

You have to understand what is meant by a law of physics. It means that the same rules apply no matter what (inertial) frame you are in, but certain things are not rules. There is no rule that clocks in different frames must tick at the same rate as yours. In fact, the rule, applied to all frames, is the opposite. Every frame will measure the clocks in every other frame as being slower. It's counter-intuitive at first glance, but it's a consistent rule across every frame.

 

Similarly, it is not a rule that every frame will measure the same difference in speed between light and any given moving object (e.g. See light as traveling at c + the velocity of the source). It is a rule that every frame will observe light traveling at exactly c (in a vacuum).

 

Knowing that these rules apply in every frame the same way allows us to figure out what events "look like" in that frame, even when we are not currently in it. So if you were to travel one lightyears distant, you could calculate how much time would have passed on Earth should you turn around and travel back, and you could determine that the distance you traveled is greater as seen from Earth than as seen by you, and consequently took more time as seen from Earth than as experienced by you. And you could decide that Earth's frame is valid, and that your time was dilated rather than theirs. Until you actually turn around (and, by accelerating, cease to be in an inertial frame) the Earth could say the same thing about you.

 

There is nothing stopping any frame from treating any other frame as "standard" and, by applying the rules, coming out with a model of how things look that is perfectly consistent with the experiences of its own frame. Because every frame can do this with every other frame, there is no uniquely "standard" frame, and everything is, well, relative.

 

Observations from different frames may not be identical, but they will always be consistent with each other when you know the rules by which they operate.