Second Opinion Needed: Time of Light Pulse Arrival

[Orodruin]

What is the time difference in the reference frame of A between the event on the world line of A that is simultaneous with the sending of the signal in B's rest frame and the event of A receiving the signal?

In B's frame, the signal is sent when the front of A's rod arrives. Since the rod rest length was 6 ly, its length in B's frame is 4.8 ly and at the same point in time in B's frame, A is therefore 4.8 ly away. The separation speed of the signal and A in B's frame is -1.6c and so it takes the signal 4.8/1.6 = 3 years to arrive in B's frame. The proper time elapsed for A between these events is time dilated and therefore equal to 3/1.25 = 2.4 years.

The time elapsed between the sending of the signal and the arrival of the signal based on A's simultaneity convention (ie, not B's) is 6 years.

 

[Jeronimus]

I fail to see how the introduction of yet another observer makes the scenario "simpler".

This is incorrect, A and B are still moving.It is unclear what you mean by this. The distance between A and B is changing in all frames and measuring "the same distance" is therefore inherently referring to "at the same time", but this has different meanings in the frames of A and B.

Introducing a 3rd observer does make this a lot simpler because it makes it easier to see the symmetry of the situation and understand that both A and B will have to arrive at the same measurements when they both do their measurements at same clock counts.

You were right about the 10s value however. That was a mistake.

I clarified what i meant by them measuring the same distance. When syncing their clocks the way i described it, using a 3rd observer which sees them both incoming at the same speed, then when they do measurements on the distance, they get the same results for same values on their clock count.

 

[david316]

The 4.8 ly is incompatible with the first statement that the distance between A and B at the time of emission in A's rest frame is 6 ly. The length contraction should be taken in the other direction if you consider how it is derived from the Lorentz transform. The result consistent with the first statement is 7.5 years. See #19.

You can also see this as follows: Let A carry 6 ly long stick ahead of him. The light signal is emitted when the other end touches B. While the stick in B's rest frame has length 4.8 ly, the events of the signal emission and the stick touching B are not simultaneous (they were simultaneous for A!)

Now, let B carry a 7.5 ly stick. Its length is 6 ly in A's rest frame and therefore A will emit the signal when he touches the other end at a distance of 7.5 ly in B's rest frame. It therefore takes the light 7.5 years to arrive.

How do I interpret this in terms of the distance being both 4.8 light years and 7.5 light years in B's rest frame?

 

[Orodruin]

How do I interpret this in terms of the distance being both 4.8 light years and 7.5 light years in B's rest frame?

Just as you need to define what you mean by time you need to define what you mean by "distance". This is intimately related to the definition of what "simultaneous" means.

 

[Dale]

The 4.8 ly is incompatible with the first statement that the distance between A and B at the time of emission in A's rest frame is 6 ly

I don't think that you and I disagree, but I think that we are making different assumptions about a poorly specified problem. From the revised description in the post I was responding to https://www.physicsforums.com/threads/second-opinion-needed.906688/#post-5710231 , the time and distance of emission is specified in B's frame.

In B's frame the worldline of B is $(t,0)$ and the worldline of A is $(t,0.6t-4.8)$ and a pulse of light emitted by A at $(0,-4.8)$ arrives at B at $(4.8,0)$.

Taking the Lorentz transform, in A's frame the worldline of B is $(t',-0.6t')$ and the worldline of A is $(t',-6.0)$. So at t'=0 they are indeed 6 ly away in A's frame.

However, A does not emit the pulse at t'=0 (A's frame). Instead, A emits the pulse of light at $(3.6,-6.0)$ in A's frame. This is what I was referring to about the disagreement.

 

[Orodruin]

Indeed, it is also the setting for OP's last problem statement for which I concluded 2.4 and 6 years, depending on the simultaneity convention.

 

[Jeronimus]

No matter how hard you try, this non-problem cannot be solved until we are told the clock count of B, A will measure when his clock count is at 0, or alternatively, the clock count of A, B will measure when his clock count is at 0.
Hence, whatever results are given here, can but only be false

I proposed a third observer C to do the syncing in such a way, it would allow to shed more light onto the core of the problem.

 

[russel_]

In the interests of clarifying things, and saving my sanity, I thought I'd offer some background on how this problem came about and hopefully clarify where the ambiguities may have been introduced.

It all started when this Scientific American article (https://www.scientificamerican.com/article/time-and-the-twin-paradox-2006-02/) came up in discussion - it claims to "explain" the twin paradox in terms of the time it takes for light to reach each observer. Now I claimed that this is misleading, because while the time delays might be interesting to consider in terms of what you'd actually "see", they are not relevant to the effects derived in Special Relativity. That is, time dilation and other effects are "real" and not just tricks due to how long it takes light to reach observers from distance events.

In order to demonstrate this, I pointed out that Einstein's original derivation let's observers have multiple clocks sitting in their frame of reference, all carefully synchronized with a clock next to them, and in this way the time it takes for light to reach each observer is eliminated (i.e., they measure the time of events in their frame by looking at their local clocks next to the event, no delay due to light propagation, or at least it's "cancelled").

This led to a number of progressively simpler thought experiments based on the twin paradox, trying to demonstrate this and other things that emerged in the process. Part of this involved having a fixed distance in A's frame (A was on Earth and the distance was to some star). Eventually we wound up with a situation like this:

A and B are two observers moving relative to each other at 0.6c
Two markers, 1 and 2, are stationary relative to A
As measured by A, the two markers are 6 light-years apart
When B's clock measures t = 0, B measures A as being next to marker 1 and himself as next to marker 2
When B's clock measures t = 0, B observers a pulse of light depart from A directed toward him

And the sticking point was how long it takes the light to reach B (3 years or 4.8 years?). I think that B would measure the distance between the markers as 4.8 light-years (the markers are stationary in A's rest frame, thus moving relative to B, so the 6 light-years apart markers are observed by B as length-contracted), but even if this is wrong, that doesn't matter for the next point: assuming he does measure the distance as 4.8 light-years, he will always measure the time it takes the light to reach him as 4.8 years by definition (or rather, by the two postulates of SR), regardless of the motion of A, or the motion of the markers, or anything else in the question - if the light starts 4.8 light-years away as measured his frame, it takes 4.8 years to reach him.

Now hopefully you can see why the 6 light-years was called a "proper distance". The distance originally referred to actual things at rest relative to A. Unfortunately I made the colossal blunder of suggesting that we remove the markers from the description (oops) because I wanted to whittle thing down to core ideas, in particular the one above: that if B measures the light starting 4.8 light-years away then it will always take 4.8 light-years to reach him, regardless of how we got to that distance and the motion of B relative to A or the markers.

The other ambiguity of "setting A's clock to t = 0"... I wasn't really paying attention to :). I don't think it's relevant to the point above, which I what I really care about, so I'm happy to let A set his clock to t = 0 whenever he likes, and whatever that means, and whether A and B see whatever event was used to set t = 0 on their clocks as being simultaneous, doesn't matter - if we just care about knowing when B measures the pulse of light departing and we have the specified positions above. Nonetheless I can see how this lax phrasing would further confuse things.

But at the end of the day the thing I care about most is that the statement above hold regardless of anything else in the problem: "if the light starts 4.8 light-years away as measured his frame, it takes 4.8 years to reach him"?

 

[Jeronimus]

Here is the initial post in the form of two x/t diagrams, as i would imagine you attempted to describe it, ignoring the inconsistencies with an attempt to point at what i believe you have not fully understood yet.

The magenta/light blue filled circle is Observer B. "He measures t=0" i assume to mean that he draws an x-t diagram where he places himself at x=0, t=0 and then goes on to map all other events within his reference frame onto the x-t diagram.

As you can see, observer B who in the left x-t diagram is at x=0, t=0 has a clock count of 10s currently.
He measures observer A to be at 6 lightseconds away of him, at x=6ls, t=0 with a clock count of 8s. Observer A is the white filled circle.

Observer A however, CANNOT measure the distance to the _instance_ of observer B with a clock count of 10s. As you can see from the right x-t diagram, which is A's reference frame, observer B with a clock count of 10s is not on the simultaneous axis of A.
That instance of observer B with a clock count of 10s is at about x'~ -7.5ls, t' ~ -4.5s (won't calculate the exact values), where the magenta/light blue filled circle is on the right diagram.

Instead, the instance of B which has a clock count of 13.6s(deep blue filled circle), located at the spacetime position of x'=4.8ls, t'=0 is simultaneous to the instance of A with a clock count of 8 seconds when observed from within A's reference frame.

And once again, the instance of observer B with a clock count of 13.6s, won't be able to measure the distance to observer A with a clock count of 8 seconds, because that instance of A is NOT simultaneous to this instance of B.
Instead it will be the instance of A which i marked as a pink filled circle which the instance of observer B with a clock count of 13.6s will observer as simultaneous to himself...

I hope you get the idea now.

As for the question for how many seconds it will take for the light beam to reach B when shot by A at a distance of 4.8ly, Dale already answered this correctly. 4.8 years of course, but i doubt that this was what you were trying to _really_ figure out.

That light beam in the diagrams would be the orange line. I used lightseconds instead of years because it would require too much editing.Those spacetime diagrams are taken from a screenshot of my twin paradox simulation. You might want to check it out here and download the code if you want to run it yourself (link is in the description).



maybe this will lift some of the confusion, hopefully not add to it :D

 

[russel_]

As for the question for how many seconds it will take for the light beam to reach B when shot by A at a distance of 4.8ly, Dale already answered this correctly. 4.8 years of course, but i doubt that this was what you were trying to _really_ figure out.

I'm pretty sure it is :)

Of course there are other things around it but the originating dispute was over - assuming B measures a 4.8 light-year distance & light departing at t = 0 - whether 3 years could possibly be correct. That's why the last three statements in the original problem explicitly gave t = 0 and 4.8 light-years as the distance for B's measurements. I couldn't think of a better explanation of why the 4.8 years answer immediately follows from this other than "Because the speed of light is constant and B is stationary in his own frame", and I was simply hoping someone would either have a more convincing explanation or at least back that up (i.e., Dale's response).

All the other issues raised here have resulted from removing the markers at the last minute so that the distance became ambiguous, coupled with the extraneous specification of t = 0 on A's clock.

 

[Ibix]

@david316 @russel_: The problem with your thought experiment is that the relativity of simultaneity means that A and B don't agree on when the experiment starts for the other person. If A calculates the time at which B is six light years away and sends a signal to B, then B looks at his clock when he receives the signal and subtracts six years he will not agree that A was six light years away then.

This is a general problem: there is no unique way to define what "at the same time" means for separated observers. Talking about "proper distance" doesn't save you because the proper distance is just the distance between two objects in their rest frame - and A and B are moving with respect to each other, so they don't have a rest frame (A has one, B has one, but they're not the same frame) so proper distance is not defined here. So your thought experiment is ambiguous. And you haven't realized that, so your thinking is subtly self-contradictory, and that is why you can't resolve it.

The twin paradox is a way to avoid the ambiguities by starting and finishing with both observers in the same place. The Scientific American article you linked therefore doesn't go into the ambiguities you introduced by trying to simplify things. It's not saying that relativistic effects are caused by lightspeed delays. Rather, it's using lightspeed delays to show that "acceleration causes the age difference" is not correct (or not complete, at least). The observations each twin makes of the other are different in many ways, not just that "one of them turns round".

In many ways the "exchanging light signals" explanation is very good because it deals solely in what each twin sees, not in how they interpret what they see. But I find the geometric explanation to be better. Follow the "Insights author" link on Orodruin's profile page to read his article on that.

 

[Ibix]

All the other issues raised here have resulted from removing the markers at the last minute so that the distance became ambiguous, coupled with the extraneous specification of t = 0 on A's clock.

All of the issues stem from "synced at t=0" which is an ambiguous statement unless the clocks are at the same place at t=0, which they aren't.

Re-reading the initial problem statement I suspect it is possible to resolve it if you set t=0 (or some other agreed value) when A and B meet.

 

[Jeronimus]

I'm pretty sure it is :)

Of course there are other things around it but the originating dispute was over - assuming B measures a 4.8 light-year distance & light departing at t = 0 - whether 3 years could possibly be correct. That's why the last three statements in the original problem explicitly gave t = 0 and 4.8 light-years as the distance for B's measurements. I couldn't think of a better explanation of why the 4.8 years answer immediately follows from this other than "Because the speed of light is constant and B is stationary in his own frame", and I was simply hoping someone would either have a more convincing explanation or at least back that up (i.e., Dale's response).

All the other issues raised here have resulted from removing the markers at the last minute so that the distance became ambiguous, coupled with the extraneous specification of t = 0 on A's clock.

What could be more convincing than using the most fundamental explanation? One of the two postulates SR is grounded upon.

If someone at 4.8 lightyears away of you shoots a lightbeam towards you, then the light coming towards you will be traveling at c ~ 300000km/s. If it did not do that, then we could throw SR into the trash bin because all you need to derive the formulas of SR mathematically is the postulate of light always traveling at 300000km/s independent of which inertial frame of reference you observe it from.

That and the first postulate, stating that the laws of physics are the same in every inertial frame of reference. Basically, that no IFR is special compared to another.

So of course it will be 4.8 years. Can you imagine a scenario where it would take longer or less than 4.8 years without violating one of the most fundamental rules of SR - light always traveling at c in a vacuum absent of gravity?

 

[russel_]

All of the issues stem from "synced at t=0" which is an ambiguous statement unless the clocks are at the same place at t=0, which they aren't.

Re-reading the initial problem statement I suspect it is possible to resolve it if you set t=0 (or some other agreed value) when A and B meet.

Well, the "synced at t=0" statement wasn't in the original (pre-forum) problem statement, so in this regard I claim innocence :).

 

[Jeronimus]

Well, the "synced at t=0" statement wasn't in the original (pre-forum) problem statement, so in this regard I claim innocence :).

You are guilty of adding too much detail and wording it badly however. The problem could be stated as follows:There are two observers A & B traveling at a relative speed of v= 0.6c towards each other.

At a distance of 6 lightyears, there is an object O which is at rest, relative to observer A.

Observer B measures the distance between O and A to be 4.8 lightyears (length contraction).

Observer B measures/calculates A shooting a lightbeam towards him, just as he passes by object O (simultaneously as measured/calculated by observer B).

how long will it take for the lightbeam to reach observer B? 4.8y of course.

How long would it take for the lightbeam to reach observer B, from observer's A perspective? This is a much more difficult question!(and much closer to the value you hoped for)

Never mind, it does not seem to be a secret anymore. I just calculated it to be 2.4 years, a value my eye already caught in some post earlier i did not fully read.

 

[russel_]

(and much closer to the value you hoped for)

Except that the value I was hoping & arguing for was 4.8, you may have missed the different usernames?

 

[Ibix]

Well, the "synced at t=0" statement wasn't in the original (pre-forum) problem statement, so in this regard I claim innocence :).

If I understand the problem statement right, A emits the pulse when he is 4.8ly distant from B as measured in B's frame. This is the time B is calling zero, so obviously, B's clock will read 4.8 years when he receives the pulse. This is 3.2 years before the two ships meet up, which happens at 8 years on B's clock.

I think A set his clock to zero when, according to A, B was 6ly distant. A emits the pulse when his clock reads 3.6 years and says it was received at 6 years. His clock reads 10 years when the two ships meet up.

Note that A and B will agree what A's clock reads when A emits the pulse and what B's clock reads when B receives the pulse. They will not agree what B's clock reads when A emits the pulse, nor what A's clock reads when B receives the pulse. This is the relativity of simultaneity.

Note also that one would normally use the Lorentz transforms to relate the coordinates of events in A and B's frames. You can't do that in this case without some careful thought about where the origin of coordinates is - it isn't in the obvious place (where the two ships meet), so careless application will give you the wrong answer.

 

[Mister T]

- it claims to "explain" the twin paradox in terms of the time it takes for light to reach each observer. Now I claimed that this is misleading, because while the time delays might be interesting to consider in terms of what you'd actually "see", they are not relevant to the effects derived in Special Relativity. That is, time dilation and other effects are "real" and not just tricks due to how long it takes light to reach observers from distance events.

But the delay due to light travel time is not a trick, it's real and to understand it you need to account for time dilation. You might gain some insight by reviewing the short and simple derivation of the relativistic Doppler effect. In the example cited $\beta=0.6$ so we have for the reativistic Doppler effect factor $$\sqrt{\frac{1+\beta}{1-\beta}}=\sqrt{\frac{1+0.6}{1-0.6}}=\sqrt{\frac{1.6}{1-0.6}}=2.$$ Thus each twin sees the other's clock running fast (or slow) by factor of 2 when they are approaching (or receding from) each other.

Search for Hewitt's Twin Trip on YouTube. He uses the same speed of $0.6 c$ in his example, but instead of watching each other's clock, the twins send each other pulses of light.

 

[Orodruin]

But the delay due to light travel time is not a trick, it's real and to understand it you need to account for time dilation. You might gain some insight by reviewing the short and simple derivation of the relativistic Doppler effect. In the example cited $\beta=0.6$ so we have for the reativistic Doppler effect factor $$\sqrt{\frac{1+\beta}{1-\beta}}=\sqrt{\frac{1+0.6}{1-0.6}}=\sqrt{\frac{1.6}{1-0.6}}=2.$$ Thus each twin sees the other's clock running fast (or slow) by factor of 2 when they are approaching (or receding from) each other.

Search for Hewitt's Twin Trip on YouTube. He uses the same speed of $0.6 c$ in his example, but instead of watching each other's clock, the twins send each other pulses of light.

Just to point out that this becomes even clearer if one takes the Bondi k-calculus approach to introducing relativity. I have not used in any course myself, but mainly because the course I teach is not at introductory level and students are expected to have more prerequisites. If teaching laymen today, I would probably start from there.

 

[russel_]

But the delay due to light travel time is not a trick, it's real and to understand it you need to account for time dilation.

That isn't what I said - I didn't say the light travel time wasn't real or is a trick, I said time dilation itself is real and not a trick - there is a logical difference. I understand the article wasn't exactly denying that either but I just said it could be misleading - in the sense that it could lead people to that conclusion if they didn't already know better. I don't know how that wasn't clear.

 

[Ibix]

Actually, you can adjust time dilation freely by changing your interpretation of what causes the Doppler effect. You can't make the Doppler effect go away, nor can you make differential aging (as in the twin paradox) go away. In some senses they are more fundamental than time dilation and length contraction.

 

[russel_]

Actually, you can adjust time dilation freely by changing your interpretation of what causes the Doppler effect. You can't make the Doppler effect go away, nor can you make differential aging (as in the twin paradox) go away. In some senses they are more fundamental than time dilation and length contraction.

Well that certainly is interesting, though probably beyond my current ability to fully understand! My understanding comes only from, in order, "layman" books (like Epstein's Relativity Visualized), followed by half-read undergraduate textbooks, followed by a staggered reading of Einstein's original paper.

 

[david316]

No. You are still failing to specify what "at the same time" means as requested in #2. You need this to give the problem meaning.

You can do this in several ways, for example:

When the distance between A and B in A's reference frame is 6 light-years, A sends a signal to B. What is the time difference between this event and B receiving the signal in the reference frame of B?

Alternatively:

When the distance between A and B in A's reference frame is 6 light-years, A sends a signal to B. What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

These are different questions with different answers.

There is no such thing as a "stationary" reference frame. Reference frames can only be moving or at rest relative to some object or other reference frame. This is true in classical mechanics as well as SR.

Thank you Orodruin for your phasing of the two questions and you subsequent answers. They clarified how I should be posing the question. Would below be a better way to phase it?

Two observers, A and B, are traveling towards each other at a relative speed of 0.6c.

In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

Answer = 3 years ... (i hope)

What is the time difference in the reference frame of A between the sending of the signal in A's rest frame and the event on the world line of A that is simultaneous with the event of B receiving the signal?

Answer = 6 years ... (i hope)

In A's frame of reference, when B is 6 light-years away, A sends a photon to B. What is the time difference between this event and B receiving the signal in the reference frame of B?

Answer = 7.5 years ... (i hope)

And a final question:

Two observers, A and B, are traveling relative to each other at a relative speed of 0.6c.

In A's frame of reference, there is a ruler that is 4.8 light years long.

In A's frame of reference how long would it take a photon of light to travel the length of the ruler?

Answer = 4.8 years ... ( I hope)

In B's frame of reference there is a ruler. Said ruler measures 4.8 light long in A frame's of reference. How long would it take a photon to travel the length of the ruler in B's frame of reference?

Answer = 6 years ... (i hope... still feeling shaky)

 

[Ibix]

In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

Answer = 3 years ... (i hope)

Yes.

What is the time difference in the reference frame of A between the sending of the signal in A's rest frame and the event on the world line of A that is simultaneous with the event of B receiving the signal?

Answer = 6 years ... (i hope)

3.75 years ($\gamma$ times your last answer).

In A's frame of reference, when B is 6 light-years away, A sends a photon to B. What is the time difference between this event and B receiving the signal in the reference frame of B?

Answer = 7.5 years ... (i hope)

Yes.

 

[david316]

Yes.

3.75 years ($\gamma$ times your last answer).
Yes.

Make sense. Thanks.

 

[Orodruin]

What is the time difference in the reference frame of A between the sending of the signal in A's rest frame and the event on the world line of A that is simultaneous with the event of B receiving the signal?

Answer = 6 years ... (i hope)

3.75 years (γγ\gamma times your last answer).

The easier way of seeing this is: The distance between B and the signal decreases at speed 1.6c and so the result is 6/1.6 = 3.75 years. Everything in the problem refers to frame A and so there is no reason to involve anything from B (except its velocity relative to A).

 

[robphy]

Thank you Orodruin for your phasing of the two questions and you subsequent answers. They clarified how I should be posing the question. Would below be a better way to phase it?

Two observers, A and B, are traveling towards each other at a relative speed of 0.6c.

In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

Answer = 3 years ... (i hope)

What is the time difference in the reference frame of A between the sending of the signal in A's rest frame and the event on the world line of A that is simultaneous with the event of B receiving the signal?

Answer = 6 years ... (i hope)

In A's frame of reference, when B is 6 light-years away, A sends a photon to B. What is the time difference between this event and B receiving the signal in the reference frame of B?

Answer = 7.5 years ... (i hope)

Here's a diagram I made with my GeoGebra tool: https://www.geogebra.org/m/HYD7hB9v# .
It's an ordinary Minkowski diagram with light-clock diamonds supplementing worldlines (and other segments on a spacetime diagram)
(See my Insight for details: https://www.physicsforums.com/insights/relativity-rotated-graph-paper/ )

It's probably similar to what @Jeronimus drew in his earlier post #44
assuming the situation there is the same as is quoted above---I didn't follow this thread from the beginning.

Since you chose a relative velocity with a rational Doppler k-factor,
you could easily sketch this on graph paper and obtain precise values--by counting boxes--, assuming decent drafting skills, fairly easily.
(With merely rational relative velocities, a little more drafting skill is needed..
or else a little more abstraction by thinking in terms of square-intervals rather than counting ticks on a worldline.)

Note: no need to draw another spacetime diagram for the other frame.
But if you want to, you could easily perform the Lorentz transformation visually
by restacking the corresponding transformed diamonds on the graph paper.

With this spacetime diagram, you can then use it (in particular, the triangles) to "explain" various approaches to get the results...
use "spacetime trigonometry" [shameless pitch] or 4-vector methods or "relativistic formulas" and "Lorentz transformations" or k-calculus methods or radar methods.

 

[Mister T]

That isn't what I said - I didn't say the light travel time wasn't real or is a trick, I said time dilation itself is real and not a trick - there is a logical difference. I understand the article wasn't exactly denying that either but I just said it could be misleading - in the sense that it could lead people to that conclusion if they didn't already know better. I don't know how that wasn't clear.

Right. I didn't mean to imply that you had said that. I was in effect offering a response to the "someone" who may have been mislead.

As soon as I saw the Bondi quote under the title of the Sci Am article and began to read it I immediately thought about and compared that analysis of the twin trip to one employing an exchange of (Doppler-shifted) light signals between the twins. When first encountered that analysis seems to gloss over time dilation and the point I was making is that time dilation is part of the explanation of the Doppler shift.

More to the point, the time differences explained using light signal travel time are a direct consequence of the fact that the speed of the signals is independent of the speed of either twin.

That is perhaps at least part of what @Ibix referred to when he responded:

Actually, you can adjust time dilation freely by changing your interpretation of what causes the Doppler effect. You can't make the Doppler effect go away, nor can you make differential aging (as in the twin paradox) go away. In some senses they are more fundamental than time dilation and length contraction.

 

[Jeronimus]

Thank you Orodruin for your phasing of the two questions and you subsequent answers. They clarified how I should be posing the question. Would below be a better way to phase it?

Two observers, A and B, are traveling towards each other at a relative speed of 0.6c.

In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

Answer = 3 years ... (i hope)

What is the time difference in the reference frame of A between the sending of the signal in A's rest frame and the event on the world line of A that is simultaneous with the event of B receiving the signal?

Answer = 6 years ... (i hope)

In A's frame of reference, when B is 6 light-years away, A sends a photon to B. What is the time difference between this event and B receiving the signal in the reference frame of B?

Answer = 7.5 years ... (i hope)

And a final question:

Two observers, A and B, are traveling relative to each other at a relative speed of 0.6c.

In A's frame of reference, there is a ruler that is 4.8 light years long.

In A's frame of reference how long would it take a photon of light to travel the length of the ruler?

Answer = 4.8 years ... ( I hope)

In B's frame of reference there is a ruler. Said ruler measures 4.8 light long in A frame's of reference. How long would it take a photon to travel the length of the ruler in B's frame of reference?

Answer = 6 years ... (i hope... still feeling shaky)

I wasn't sure how you arrived at 3 and 6 years, going by the description you gave.

For example:

"In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference in the reference frame of B between the event on the world line of B that is simultaneous with the sending of the signal in A's rest frame and the event of B receiving the signal?

Answer = 3 years ... (i hope)"

and...

"In A's frame of reference, when B is 6 light-years away, A sends a photon to B.

What is the time difference between this event and B receiving the signal in the reference frame of B?

Answer = 7.5 years ... (i hope)"

...are equivalent descriptions to me. Both would result in 7.5years, not 3 years. After drawing it, i realized that in the former case, you are asking for the time difference between the event of a light signal reaching B that was sent by A when he observed B to be at 6 lightyears away of him (light blue/magenta filled circle), and the event when A sent a signal towards B, when B observed A to be at 4.8 lightyears away. Or alternatively, when A observed B to be at 3.75 lightyears away (the blue filled circle).

Here is a more complete drawing of the situation, which will hopefully shed some light on this

 

[david316]

In the interests of clarifying things, and saving my sanity, I thought I'd offer some background on how this problem came about and hopefully clarify where the ambiguities may have been introduced.

It all started when this Scientific American article (https://www.scientificamerican.com/article/time-and-the-twin-paradox-2006-02/) came up in discussion - it claims to "explain" the twin paradox in terms of the time it takes for light to reach each observer. Now I claimed that this is misleading, because while the time delays might be interesting to consider in terms of what you'd actually "see", they are not relevant to the effects derived in Special Relativity. That is, time dilation and other effects are "real" and not just tricks due to how long it takes light to reach observers from distance events.

I made the claim... not sure if I should admit it...

"During the trip to the star both the traveller and homebody would view each other clocks as running slow. But when the traveller gets to the star the travellers clock would have elapsed 6 years and the travellers clock would have elapsed 10 years. This doesn’t make sense although it must be correct. It only makes sense if you say that it is not possible to know two events at the same time which is the basis of space-time. Hence you need to take into account the time traveled in order to observe the clocks or else it doesn’t work. "

lets pretend I said this:

"During the trip to the star both the traveller and homebody would view each other clocks as running slow. But when the traveller gets to the star the travellers clock would have elapsed 6 years and the travellers clock would have elapsed 10 years. This doesn’t make sense although it must be correct. It only makes sense if you take into account the time traveled in order to observe the clocks or else it doesn’t work. "

Then, I constructed an example with all sorts of problems to try and demonstrate this... now I am lying awake at night thinking about SR...

 

[Mister T]

Consider the event "traveler arrives at star" and the event "home clock reads 10 years". Saying that the first one happened when the second one happened is not a meaningful assertion. The two events occur in different places, so if they're simultaneous to one of the twins they won't be simultaneous to the other.

If, however, the two events occur at the same place, then such a statement is meaningful. Because it will be true for all observers.

 

[david316]

Consider the event "traveler arrives at star" and the event "home clock reads 10 years". Saying that the first one happened when the second one happened is not a meaningful assertion. The two events occur in different places, so if they're simultaneous to one of the twins they won't be simultaneous to the other.

If, however, the two events occur at the same place, then such a statement is meaningful. Because it will be true for all observers.

Accepted. What I meant is:

During the trip to the star both the traveller and homebody would view each other clocks as running slow. But when the traveller gets to the star, in the travellers frame of reference his clock would have elapsed 6 years. In the event on the world line of the home body that occurs simultaneously with the event of the traveller arriving at the star, the homebody's clock would have elapsed 10 years. So both view each others clocks running slow, and at the event described above, both clocks read 6 and 10 years. It only makes sense if you accept that in order for each observer to observe the others clock, the observation between the observers is limited by the speed of light and the distance required to travel in the respective rest frame.

 

[david316]

Is the statement below correct, in the context of SR not GR ... I'm not liking my odds...

"Two people will only disagree on the time of a single clock if you limit information travel by the speed of light and one person is traveling relative to the other. "

 

[russel_]

Is the statement below correct, in the context of SR not GR ... I'm not liking my odds...

"Two people will only disagree on the time of a single clock if you limit information travel by the speed of light and one person is traveling relative to the other. "

I suspect someone will take exception to the notion of a "single clock"! I say this because the observers have different clocks (different frames), and while a single event could be used to set both to "0", I don't think that really gets at the matter. Maybe the statement below would be as good? Here the "clock" is replaced with an event, and you need two of them so the observers can make a comparison (i.e., the spacing and coincidence of events is what defines our underlying notion of time).

"Two people will only disagree on the simultaneity of two events at different locations if you limit information travel by the speed of light and one person is traveling relative to the other."

And I hazard to say that, at least as I understand it, this is not true: they can disagree even after taking into account the time it took the information to travel. They literally observe (not just "see") parts of space arriving at various times differently than the other does. We'll see what others say...

 

[david316]

I suspect someone will take exception to the notion of a "single clock"! I say this because the observers have different clocks (different frames), and while a single event could be used to set both to "0", I don't think that really gets at the matter. Maybe the statement below would be as good? Here the "clock" is replaced with an event, and you need two of them so the observers can make a comparison (i.e., the spacing and coincidence of events is what defines our underlying notion of time).

"Two people will only disagree on the simultaneity of two events at different locations if you limit information travel by the speed of light and one person is traveling relative to the other."

And I hazard to say that, at least as I understand it, this is not true: they can disagree even after taking into account the time it took the information to travel. They literally observe (not just "see") parts of space arriving at various times differently than the other does. We'll see what others say...

Yip. In my sleep deprived state I think I agree with what you think I think. i.e.

"In the framework of special relativity, two people will only disagree on the simultaneity of two events at different locations if you limit information travel by the speed of light and one person is traveling relative to the other."

I still think this true but I accept my knowledge in this area has been proved to be vastly lacking and hence won't be surprised if its wrong!