Revised Twin Paradox: What's Wrong?

[dkgolfer16]

Thought experiment / story:

Albert the Alien sits atop a non-accelerating comet traveling 0.5c. He approaches earth, barely missing it, and passes on by. After he has passed Earth, he looks back toward it with his ultra-sensitive telescope and sees the face of Hyphy the Human. Hyphy the Human watches from her condo balcony with her ultra-sensitive telescope and sees the face of Albert the Alien. Suppose at this moment they are exactly the same age. It is love at first sight. One problem though. To Albert, Earth is moving away at 0.5c so time is slowing down for Hyphy, making her appear younger and younger relavitve him. To Hyphy, the comet is moving away at 0.5c so time is slowing down for Albert, making him appear younger and younger relative to her. After staring deeply into each other's eyes for a long time, both give up hope because they feel like the other is too good for them.

Question: What is wrong with this picture? Obviously time isn't slowing down for both. Also, notice that the original Twin paradox is resolved because the twin on the spaceship eventually accelerates, comes to a stop, and accelerates back up to a constant v and returns to earth. This does not occur here.

 

[Janus]

Nothing is wrong with the picture. According to each, the other is aging more slowly. It is a consequence of time being relative.

 

[paw]

Question: What is wrong with this picture?

Nothing wrong with this picture at all. That's exactly what SR is telling us. As long as they are both moving inertially neither one can make any special claim to be the one who is at rest. They need to share a spacetime event in order to compare ages in an objective fashion. Therefore your analysis is correct.

Now that's not to say that Albert can't calculate what would happen if he got into a rocket and traveled back to meet Hyphy. Albert would calculate that he would have to accelerate to do that and after he got back to Hyphy he would have aged less than she.

Similarly, if Hyphy got in a rocket and caught up with Albert she will have aged less than he.

And if they both got in rockets and set off after each other... well someone will probably write a country & western tune about it! ;^}

 

[RandallB]

Question: What is wrong with this picture?

Enough information is what is missing.
Without a turn around it needs a stationary string of Earth synchronized clocks strung out for light years along the path of the 0.5 c Comet(s) clocks. Plus a mini Comets on the same speed and path ahead of and behind Albert’s Comet each with a Comet synchronized clocks.
Now the observer on Earth or the Comet can directly watch time in the passing reference frame like numbers changing as you riff through a deck of cards.

NOW what does each observers know?

1) They can use their ultra-sensitive telescope and by accounting for the time delay of light traveling distances to confirm that all clocks in their frame of reference are synchronized to read the same time all the time; simultaneously.

2) They can directly observe from the passing clocks that Time in the other frame of reference is running FAST!

3) But they can also confirm by tracking anyone single clock in the other frame of reference by using their ultra-sensitive telescope and by accounting for the time delay of light to confirm that one clock is running SLOW!

4) Thus each observer can conclude from 2 & 3 that the in the other reference frame None of the other clocks are simultaneously reading the same time as any other clock in that other frame at any simultaneously point in time; ever.

The two observers insist that 5:00 happens simultaneously on every other clock in their own reference frame and they both consider the others frame of reference has clocks horribly out of synchronization. And between the two of them, they will not be able to agree on a standard for simultaneity; at least when there is any real distance between any two events they my wish to consider might happen at the same time.

Lack of simultaneity is the real lesson of SR and the twins.

 

[dkgolfer16]

Thanks for the help RandallB, Janus, paw. I understand my thought experiment now. Sorry for the elementary SR question but one last quick layman clarification:

In Albert's RF, he is aging faster. Let's say some time t passes where he is gazing into Hyphy's eyes. He finally takes a break from his telescope and calculates 10 years have passed. To Hyphy though, Albert is only 5 years older. Am I correct in concluding that both Albert and Hyphy's calculations are right?

 

[Janus]

Thanks for the help RandallB, Janus, paw. I understand my thought experiment now. Sorry for the elementary SR question but one last quick layman clarification:

In Albert's RF, he is aging faster. Let's say some time t passes where he is gazing into Hyphy's eyes. He finally takes a break from his telescope and calculates 10 years have passed. To Hyphy though, Albert is only 5 years older. Am I correct in concluding that both Albert and Hyphy's calculations are right?

According to Albert, at the moment he calculates the time he has aged 10 years and Hyphy has aged 5.
According to Hyphy, at the moment Albert calculates the time he has aged 10yrs and she has aged 20 yrs.

 

[RandallB]

In Albert's RF, he is aging faster. Let's say some time t passes where he is gazing into Hyphy's eyes. He finally takes a break from his telescope and calculates 10 years have passed. To Hyphy though, Albert is only 5 years older. Am I correct in concluding that both Albert and Hyphy's calculations are right?

Albert on the comet does not need to calculate how much time has passed he can see both times locally. He can read his clock directly as 5 years and see the clock passing by simultaneously reading 10 years. What he needs to calculate is how long he must wait to view through his telescope the event on Earth that occurred when clock reading 10 years in the Earth frame was recording his clock as running slow showing only 5 years and sending a report about it back to earth.

Note: based on the time dilations you have here I can see the Comet is traveling at 0.8 c wrt Earth not 0.5c

And when he eventually make that observation he can confirm by direct observation of the clock in his own reference frame that is passing next to Earth and reading 5 years he is looking at events that happened simultaneous with the event of his locally observing 5 years and 10 years on the two clocks years ago. He knows this because all the clocks in his frame have been carefully synchronized.
However he can also see that in fact the Earth clock is running slow only reading 2.5 years.

Obviously the Earth frame cannot be trusted to judge when things happen simultaneously!
But Earth has made the same judgment about the comet frame.

So NO they cannot both be viewed as “Correct” only that they are different.
More important under these conditions SR has no means to prove one as correct (preferred) over the other!
The point is inhabitants of both frames can see that as true.
Meaning we must doubt own frame of reference as being a correct judge of simultaneity.

 

[dkgolfer16]

Albert on the comet does not need to calculate how much time has passed he can see both times locally. He can read his clock directly as 5 years and see the clock passing by simultaneously reading 10 years. What he needs to calculate is how long he must wait to view through his telescope the event on Earth that occurred when clock reading 10 years in the Earth frame was recording his clock as running slow showing only 5 years and sending a report about it back to earth.

Note: based on the time dilations you have here I can see the Comet is traveling at 0.8 c wrt Earth not 0.5c.

Is there a quick solution you can post to show how you calculate this? Thanks. If not that's cool. Just curious.

Obviously the Earth frame cannot be trusted to judge when things happen simultaneously!
But Earth has made the same judgment about the comet frame.

So NO they cannot both be viewed as “Correct” only that they are different.

So they both can't be viewed as "Correct", but they also cannot both be view as "Incorrect"? I'm guessing this was the point of Einsteins own thought experiment where Lightening hit two ends of train simultaneously to the observer on the ground (in Earth's RF) but not to the observer in the train's RF.

 

[MeJennifer]

I'm guessing this was the point of Einsteins own thought experiment where Lightening hit two ends of train simultaneously to the observer on the ground (in Earth's RF) but not to the observer in the train's RF.

All the observer can claim with validity is that he received (light) signals from both events at the same time. That is something entirely different from saying that both events happened at the same time.

In spacetime there is no objective measure as to what event happens before another event. I think the significance of that is far more important than thinking in frame of references.

 

[matheinste]

Hello MeJennifer.

Quote:-

-----In spacetime there is no objective measure as to what event happens before another event.------

Perhaps i do not totaaly understand your point. If two events are caually related can we not infer that one event happened before or after another. Of course we may not observe it the same order in terms of light signal reception at our location.

I do understand that saying that two events are simultaneous is frame dependent and so practically meaningless, but sometimes helpful to me in trying to get a picture of things, although i could probably do without it.

Matheinste.

 

[dkgolfer16]

All the observer can claim with validity is that he received (light) signals from both events at the same time. That is something entirely different from saying that both events happened at the same time.

In the man on Earth's RF, the lightning hit the two ends of the train at same time t, let's call it t_c. If event A is the lightning hitting the front of the train and event B is lightning hitting the back of the train, and again both events happened at t_c how can we not say that the events happened at the same time? Remember we are only talking about the man on Earth's RF.

 

[MeJennifer]

What is wrong with the more accurate and less confusing assertion that the observer received signals from two separate events at the same time? To properly understand relativity I think it unwise to insist on Galilean reference frames that "have" the same time everywhere in that frame.

 

[dkgolfer16]

What is wrong with the more accurate and less confusing assertion that the observer received signals from two separate events at the same time? To properly understand relativity I think it unwise to insist on Galilean reference frames that "have" the same time everywhere in that frame.

It just seems like the next logical step (after asserting that the observer received signals from two separate events at the same time) is concluding that these events happened both at a particular time, t_c,in our case,and that therefore in their RF the events were simultaneous.

 

[RandallB]

… therefore in their RF the events were simultaneous.

from what you have learned and now know you can no longer make statement like that and need to be more careful about making a false at worst or misleading assertions. The one you are most likely to confuse is yourself as I believe you are here causing you to take “your eye of the ball”.
For two event separated by a distance in a common Ref Frame; you cannot say “therefore in their RF the events were simultaneous” since SR has shown you must idoubt your own frame of reference as being a correct judge of simultaneity the best you can say is “the events Appear To Be simultaneous”.

So the real question is can you establish, with any certainty and agreement between other frames if two separate events are actually occurring simultaneously. Said another way; can you establish a preferred frame of reference to use as a standard over your own Ref Frame.

Resolving an understanding of simultaneity is the real issue of SR & the Twins.

 

[dkgolfer16]

from what you have learned and now know you can no longer make statement like that and need to be more careful about making a false at worst or misleading assertions. The one you are most likely to confuse is yourself as I believe you are here causing you to take “your eye of the ball”.
For two event separated by a distance in a common Ref Frame; you cannot say “therefore in their RF the events were simultaneous” since SR has shown you must idoubt your own frame of reference as being a correct judge of simultaneity the best you can say is “the events Appear To Be simultaneous”.

So the real question is can you establish, with any certainty and agreement between other frames if two separate events are actually occurring simultaneously. Said another way; can you establish a preferred frame of reference to use as a standard over your own Ref Frame.

Resolving an understanding of simultaneity is the real issue of SR & the Twins.

I never said my reference frame was the "correct" judge of simultaneity. All I meant was that in my RF, standing beside the railroad track and not on the train, the two events occurred at exactly the same time, t_c. That fact is not debatable. Because to me the two events occurred at the exactly the same time, why can't I tell myself that the events occurred simultaneously? To you on the train, I understand they did not. But to me, they did so wouldn't I be lying to myself if I said they did not occur at the same time? Again this isn't saying that I am correct, it's only stating what I observed.

 

[Fredrik]

I never said my reference frame was the "correct" judge of simultaneity. All I meant was that in my RF, standing beside the railroad track and not on the train, the two events occurred at exactly the same time, t_c. That fact is not debatable. Because to me the two events occurred at the exactly the same time, why can't I tell myself that the events occurred simultaneously? To you on the train, I understand they did not. But to me, they did so wouldn't I be lying to myself if I said they did not occur at the same time? Again this isn't saying that I am correct, it's only stating what I observed.

"To me the two events occurred at the exactly the same time" means "In the inertial frame that everyone associates with my world line, the two events have the same time coordinate". It's a statement that's objectively true. The statement "In the inertial frame that everyone associates with the train's world line, the two events don't have the same time coordinate" is also objectively true. The statement "The events occurred simultaneously" is neither true nor false. It's nonsense, since it doesn't specify in which inertial frame the time coordinates of the events are equal.

Just make sure you always specify what frame you're talking about.

 

[dkgolfer16]

"To me the two events occurred at the exactly the same time" means "In the inertial frame that everyone associates with my world line, the two events have the same time coordinate". It's a statement that's objectively true. The statement "In the inertial frame that everyone associates with the train's world line, the two events don't have the same time coordinate" is also objectively true. The statement "The events occurred simultaneously" is neither true nor false. It's nonsense, since it doesn't specify in which inertial frame the time coordinates of the events are equal.

Just make sure you always specify what frame you're talking about.

I think that is what I've been trying to say all along. I just don't see what is wrong with the statement "The events occurred simultaneously in my RF" (assuming I am the person standing beside the train). How is that nonsense? How would I better describe the event? Should I say "Event A (Lightening hitting the front of the train) occurred at t_c and Event B (Lightening hitting the back of the train) occurred at t_c"? In my RF, what is the difference between these two statements?

 

[Fredrik]

I just don't see what is wrong with the statement "The events occurred simultaneously in my RF"

There's nothing wrong with it.

 

[dkgolfer16]

Ok cool. One last thought...

Suppose my friend is standing directly behind me. Remember we have established in my RF Event A and Event B were simultaneous and occurred at time, t_c. My friend directly behind me (he plays in the NBA and is a foot taller) has a clear view of event A and event B. He too concludes the two events were simultaneous, but at a slightly later time, t_d because he is slightly further away. We both conclude that the same event was simultaneous in our respective RF's.

So can two observer's viewing the same event both conclude that in their RF's the same event occurred simultaneously?

 

[Fredrik]

My friend directly behind me (he plays in the NBA and is a foot taller) has a clear view of event A and event B. He too concludes the two events were simultaneous, but at a slightly later time, t_d because he is slightly further away.

That's not how it works. Since you guys are moving at the same velocity, you will always agree about which events are simultaneous.

If on the other hand your friend's velocity in your frame is v, then the slope of his world line in a spacetime diagram representing your frame is 1/v, and the slope of his simultaneity lines is v. (Otherwise the speed of light wouldn't be the same in his frame). As you described it, v=0, and his simultaneity lines are the same as yours.

 

[Mentz114]

Fredrik,

If on the other hand your friend's velocity in your frame is v, then the slope of his world line in a spacetime diagram representing your frame is 1/v, and the slope of his simultaneity lines is v. (Otherwise the speed of light wouldn't be the same in his frame). As you described it, v=0, and his simultaneity lines are the same as yours.

Forgive me if I'm misunderstanding you, but you've said this in two threads.

The hyperbolic angle between a worldline and the time-axis in a space-time diagram in Minkowski space is R=tanh^-1(v/c).

If the slope were 1/v then it would be infinite in the rest-frame.

M

 

[RandallB]

I think that is what I've been trying to say all along. I just don't see what is wrong with the statement "The events occurred simultaneously in my RF"

No. It’s wrong because it allows the assumption that they did in an absolute sense actually happen at the same time. You have no evidence for that. You only know that separate clocks in your ref frame at those two events read exactly the same time, but you’ve already demonstrated that no Frame under these conditions can confirm their clocks are correctly synchronized with something like an “Absolute Time”. So yes there is a big difference between your statement verses "The events appear to have occurred simultaneously in my RF" .

If you insist on allowing yourself to think of your frame as a “preferred frame” in this manner then you must allow observers in other frames the same privilege. That ultimately allows for more than one “preferred” frame; which can quickly lead to unjustified fantasies of “backwards time”.

Your only being alerted about sloppy statements because of the adverse thinking & conclusions that can grow from not being clear on these tricky issues with yourself. What SR – twins is making clear is that there can only be one Absolute Time and one preferred frame, but the Einstein SR simultaneity issue here (Twins Trains etc.) prevents us from knowing which frame if any might be that frame.

What you can know from SR and these examples will not even tell you for sure if something like a preferred frame even exists or not; for many that is still a debatable opinion.

 

[dkgolfer16]

No. It’s wrong because it allows the assumption that they did in an absolute sense actually happen at the same time. You have no evidence for that. You only know that separate clocks in your ref frame at those two events read exactly the same time, but you’ve already demonstrated that no Frame under these conditions can confirm their clocks are correctly synchronized with something like an “Absolute Time”. So yes there is a big difference between your statement verses "The events appear to have occurred simultaneously in my RF" .

If you insist on allowing yourself to think of your frame as a “preferred frame” in this manner then you must allow observers in other frames the same privilege. That ultimately allows for more than one “preferred” frame; which can quickly lead to unjustified fantasies of “backwards time”.

Your only being alerted about sloppy statements because of the adverse thinking & conclusions that can grow from not being clear on these tricky issues with yourself. What SR – twins is making clear is that there can only be one Absolute Time and one preferred frame, but the Einstein SR simultaneity issue here (Twins Trains etc.) prevents us from knowing which frame if any might be that frame.

What you can know from SR and these examples will not even tell you for sure if something like a preferred frame even exists or not; for many that is still a debatable opinion.

Ok got it. So if the events A & B did occur at t_c in my RF I should describe it as simply they occurred at t_c. Describing them as occurring simultanously implies that my RF alone is the measure of absolute time. Thanks Randell.

Just out of curiousity, you said SR doesn't tell you if a preferred frame even exists or not and that this is a debatable opinion. Since SR doen't clarify this, have efforts been to prove or disprove this? Like you said it is an opinion so probably it isn't possible but just curious.

 

[Fredrik]

Fredrik,

Forgive me if I'm misunderstanding you, but you've said this in two threads.

The hyperbolic angle between a worldline and the time-axis in a space-time diagram in Minkowski space is R=tanh^-1(v/c).

If the slope were 1/v then it would be infinite in the rest-frame.

M

When I said "slope" I meant it as in "the slope of the line y=kx+m is k". So think "derivative" not "angle". What I called the "slope" of the world line of an object moving with speed v is just $\Delta t/\Delta x=1/v$.

Edit: Is my use of the word "slope" confusing? Did you guys (not just Mentz) think I meant something other than what I meant? I'd like to know if I need to change the way I explain these things.

 

[RandallB]

Like you said it is an opinion so probably it isn't possible but just curious.

What is or is not possible can often also be a matter of opinion. IMO the Science of Astrophysics goes beyond the ability of this example and can do this. However others have strong opinions that it cannot. Well beyond the scope and level of this thread.

 

[Fredrik]

I just don't see what is wrong with the statement "The events occurred simultaneously in my RF"

It’s wrong because it allows the assumption that they did in an absolute sense actually happen at the same time.
...
So yes there is a big difference between your statement verses "The events appear to have occurred simultaneously in my RF" .

In my opinion, "the events appear to have occurred simultaneously in my RF" is a lot worse than "the events occurred simultaneously in my RF". I don't think the first suggests that they were simultaneous in an absolute sense. I think it suggests the opposite. A person who wants to suggest that the simultaneity is absolute wouldn't include the words "in my RF". To me, this statement is 100% synonymous with "the events have the same time coordinate in my coordinate system".

The problem I have with the other statement is that I think it suggests that relativistic effects are just some kind of illusions.

 

[dkgolfer16]

Sorry but I actually have another question. I couldn't find it in another thread. I will refrain from using the term simultaneous for it seems to only get me in trouble.

Imagine your typical xyz coordinate system (z vertical, y horizontal, x normal to page) located in an inertial RF. Event A happens at (0,3,0,t_c). Event B at (0,-3,0,t_c). The points (10,0,0), (-10,0,0), (0,0,10), (0,0,-10) all experience the events at some time, t_d and all agree both events took place at the same time, t_d because they are all on the same clock. So everytime a single point in space experiences two events occurring at the same time, there are exactly 3 other points in space that would also agree?

I hope this makes sense but I can clarify if needed.

 

[Fredrik]

Imagine your typical xyz coordinate system (z vertical, y horizontal, x normal to page) located in an inertial RF. Event A happens at (0,3,0,t_c). Event B at (0,-3,0,t_c).

I understand what you're saying so far.

The points (10,0,0), (-10,0,0), (0,0,10), (0,0,-10) all experience the events at some time, t_d and all agree both events took place at the same time, t_d because they are all on the same clock.

This is where you lost me. What do you mean by "experience"? Are you talking about events where some sort of signal with information about A and B reach those positions in space?

So everytime a single point in space experiences two events occurring at the same time, there are exactly 3 other points in space that would also agree?

Agree about what? The time coordinates of events A and B? A coordinate system is just a function that assigns four numbers to each event, and if it this one assigns the time coordinate t_C to those two events, that's the end of if. There's no way that other positions in space can affect that asssignment.

 

[Dale]

Sorry but I actually have another question. I couldn't find it in another thread. I will refrain from using the term simultaneous for it seems to only get me in trouble.

Imagine your typical xyz coordinate system (z vertical, y horizontal, x normal to page) located in an inertial RF. Event A happens at (0,3,0,t_c). Event B at (0,-3,0,t_c). The points (10,0,0), (-10,0,0), (0,0,10), (0,0,-10) all experience the events at some time, t_d and all agree both events took place at the same time, t_d because they are all on the same clock. So everytime a single point in space experiences two events occurring at the same time, there are exactly 3 other points in space that would also agree?

I hope this makes sense but I can clarify if needed.

Are you talking about observers at those four points receiving light signals from events A and B? If so, don't forget that the event of a signal being emitted is distinct from the event of a signal being recieved, and each observer accounts for the finite speed of light in determining the time of emission.

Also, there are an infinite number of events on the intersection of two light cones.

 

[dkgolfer16]

Sorry I'll try to explain the idea in a different way.

Back to the train example. Instead of being on top of the train, Person 2 is on the opposite side of the track, straight across from the original Person 1 in the classical example. Each is 10 meters away from the track and are the same height. In the classical example, Person 1 concludes Event A and Event B (lightening hitting front and back of train) occur at the same time, let's call it t_d. Why wouldn't person 2 conclude they both occurred at t_d as well?

 

[MeJennifer]

Sorry I'll try to explain the idea in a different way.

Back to the train example. Instead of being on top of the train, Person 2 is on the opposite side of the track, straight across from the original Person 1 in the classical example. Each is 10 meters away from the track and are the same height. In the classical example, Person 1 concludes Event A and Event B (lightening hitting front and back of train) occur at the same time, let's call it t_d. Why wouldn't person 2 conclude they both occurred at t_d as well?

Because person 1 and person 2 are in motion.

 

[dkgolfer16]

Because person 1 and person 2 are in motion.

Not relative to each other. They are in the same RF as the light

 

[MeJennifer]

Not relative to each other.

Perhaps I misread. If 1 and 2 are not in motion with respect to each other and their distances to the events are identical then each will measure the same time interval between information coming from event A and B.

 

[dkgolfer16]

So then whenever two events take place and are measured to have occurred at the same time (call it t_d as usual), there are always exactly 3 other locations (in the same RF that the original measurement was taken) that would conclude that these two events occurred this time, t_d?

 

[Dale]

So then whenever two events take place and are measured to have occurred at the same time (call it t_d as usual), there are always exactly 3 other locations (in the same RF that the original measurement was taken) that would conclude that these two events occurred this time, t_d?

No, there are an infinite number of locations. If an observer determines that in his reference frame events A and B occurred simultaneously then all other observers at rest wrt the first also determine the events occurred simultaneously. The positions don't matter, only the fact that they are at rest wrt each other.

The reason that the positions don't matter is that each observer is intelligent and will account for the finite speed of light in determining when events A and B occured. This is why you can interchangably talk about a reference frame being a single observer accounting for finite light speed, or a system of an arbitrary number of observers all at rest wrt each other and using synchronized clocks.