A New Simultaneity Method for Accelerated Observers in Special Relativity

[Mike_Fontenot]

When I first started to think about how much the home twin (she) ages during a light pulse's transit from her to the traveler (him) during his outbound leg, I was immediately struck by the fact that so MANY years pass during the lifetime of that pulse. So many years passing BEFORE his instantaneous velocity change occurs (IF it actually DOES finally occur). I was struck by the fact that she clearly does a LOT of ageing before we even KNOW if he goes through with his plan to change his velocity or not. That's when I started to suspect that my cherished belief in the CMIF method was doomed to the dustbin.

The Minkowski diagram I described in my last posting has two light pulses in it which only differ infinitesimally. But we can imagine that they are distinct pulses, with one slightly "to the right" of the other. But remember that, "to the right of" on the diagram ACTUALLY means "later in time than". We should keep in mind that the two pulses are actually moving along essentially the same line in space. We can imagine ourselves following along behind the second pulse, and we would see the two pulses infinitesimally close together, traveling that way for MANY years. For me, that mental image makes the CMIF method IMPOSSIBLE to believe. Her ages when each of those pulses were emitted differ only infinitesimally. And her ageing during the transit of each of those pulses differ only infinitesimally. So her ages when he receives the two pulses (which is the sum of her age at emission, plus her ageing during the transit) differ only infinitesimally. The CMIF method says that difference is FINITE and LARGE. I conclude that the CMIF method is invalid.

 

[Neddy Bate]

I would suggest studying the reference frame of the stay-home twin, because there is no question about how she ages in that frame. For example, in Mike's scenario, it is indisputable that she is 40 years old in that reference frame, at the time when the traveling twin does his instantaneous acceleration.

Also, in the reference frame of the stay-home twin, we can place a stationary clock at any location we choose, and synchronise it to the stay-home twin's clock. Let us imagine one located at the location where the traveling twin does his instantaneous acceleration, which is 23.09 light years away from the stay-home twin. Thus that clock would also display a time of 40 years when the traveling twin does his instantaneous acceleration. And if there were a person standing in that location, looking at that clock displaying 40 years, that person could know her age at that time is 40 years old, even though he cannot see her actually being 40 years old at that moment. All he would have to know is that the clock near him is synchronised to her clock & age in that reference frame, and that he is stationary with respect to that frame.

Can we all agree to that much?

If so, then all we have to do is let the traveling twin instantaneously accelerate to v=0.000c at that location, and he can then know the stay-home twin is 40 years old by simply standing there and looking at the clock which is located there, knowing it was synchronised to her clock. There is no way anyone can prove that he would be wrong to do that, because it is the definition of the words "synchronised clocks" in that reference frame.

 

[Neddy Bate]

And her ageing during the transit of each of those pulses differ only infinitesimally.

That is where you go wrong. A person traveling v = +0.577c with respect to her, and a person traveling v = -0.577c with respect to her will calculate vastly different amounts of her aging during the transit of the pulses. Just because both pulses contain essentially the same information about the age she was when she sent them, does not mean that she must have aged the same amount during the transit of both pulses, according to them.

One says he is getting closer to her, and the other says he is getting farther away from her. They must calculate different distances that the pulse had to travel. This is simple stuff, Mike. When you get closer to something, the distance between you and it gets smaller over time. When you get farther away from something, the distance between you and it gets larger over time.

Will you just say that it is "obvious" to you that those two people would calculate the same distance that the pulse had to travel? If not, then don't say that it is "obvious" to you that her ageing during the transit of each of those pulses would differ only infinitesimally. It does not follow from the fact that her ages at the times of emission of each of those pulses differ only infinitesimally.

 

[phyti]

Mike;

The intent of the simple 'twin' scenario was to analyze only the constant speed (inertial) portions of the motion, and disregard everything else.
The problem in your case is focusing on the reversal, and not allowing B and C enough time to make the necessary measurements to apply the (green) axis of simultaneity (aos).

The graphic shows B doing the outbound portion, and C doing the inbound portion. The coordinate transformations are based on a common origin. For that reason, the C portion is rotated 180 deg and compared to the B portion. The film is run in reverse, with the A and C clocks decreasing from the origin.
It's obvious the 2 portions are mirror images.
With the reversal distance x = 24 at A40, time to intercept B backward is 24/1.6=15t.
Time to intercept B forward is 24/.4=60t.
Light path is B20, A40, B80. B assigns A40 to B50.
B concludes A clock rate is .8 B clock rate.
Since the common origin for A and C is the reunion, the C clock is set to C80.
C accumulates -50 t while A accumulates -40 t.
There is reciprocal time dilation for B and C.
There is no 'missing time'.

 

[Mike_Fontenot]

[...]

Here's what I wrote early (MST) this morning (but didn't post then):
_________________

The entire lifetime of the first pulse is in his past when he instantaneously changes his velocity. And the lifetime of that pulse is many years. Her ageing during the transit of that pulse is part of history ... no one can change that amount of her ageing. And her age when she transmitted that pulse is also an unchangeable fact. So the sum of those two facts, which is her current age immediately before his velocity change, is also a fact which cannot change.

And my last posting shows that the two pulses differ only infinitesimally. They both exist for many years, and are only infinitesimally different. Up until the instant that he changes his velocity, the amount she has aged during the transit of the pulses is essentially the same ... the difference is only infinitesimal.

But what about the second pulse (which he receives immediately after he changes his velocity)? My last posting showed that when he receives the first pulse, the second pulse is itself almost complete. Most of her ageing during the entire second pulse has already happened when he receives the first pulse. The only part of the second pulse which hasn't happened yet, when he accelerates, is the last infinitesimal part.
__________________

I now see that I haven't successfully proved the above sentence with the phrase I've now highlighted in red. I haven't been able to prove that she can't age by a large finite amount during that infinitesimal remaining part of the second pulse. And I'm beginning to suspect now that it CAN'T be proven.

So where does that leave me? It leaves me with having defined a new simultaneity method that has some very nice properties. It is causal (like the CMIF method), it produces an Age Correspondence Diagram (ACD) that has no discontinuities, is piecewise-linear, never decreases (so she never gets younger, according to him), and is easy and quick to obtain. So people who are horrified about instantaneous (and especially negative) ageing will probably like it. But I can't (and probably never will be able to) prove that the CMIF method is incorrect, or that my method is correct.

However, I DO believe that there IS only one correct simultaneity method for the accelerated observer. I DON'T accept that either method is equally good. And I don't accept that simultaneity at a distance is meaningless. That is based on my philosophical belief that she doesn't cease to exist whenever they are separated, and IF she still exists, she MUST be doing something specific "right now". And if so, she MUST have a specific age right now, because her brain at each instant of her life contains a record of what she was doing at that instant. So, I believe that EITHER the CMIF method, OR my method, is correct, but they aren't BOTH correct. We just don't know which one is the correct one. I reject the Dolby&Gull method, and the Minguizzi method, because they are non-causal, and special relativity (at least Einstein's version of it) is causal. So, as for now, the CMIF method and my method are "the only games in town".

 

[Neddy Bate]

So where does that leave me? It leaves me with having defined a new simultaneity method that has some very nice properties. It is causal (like the CMIF method), it produces an Age Correspondence Diagram (ACD) that has no discontinuities, is piecewise-linear, never decreases (so she never gets younger, according to him), and is easy and quick to obtain. So people who are horrified about instantaneous (and especially negative) ageing will probably like it. But I can't (and probably never will be able to) prove that the CMIF method is incorrect, or that my method is correct.

Well this is progress at least. I was a little concerned that you thought you had proven that a guy who had recently decelerated from v=+0.577c to v=0.000 would be absolutely wrong to simply adopt the simultaneity convention of the stay-home twin. I mean if everyone else in that frame says she is 40 because all syncrhonised clocks in that frame are simultaneously displaying the time 40, then how could he possibly be wrong to accept that? The answer is that of course he would not be wrong to accept that.

However, I DO believe that there IS only one correct simultaneity method for the accelerated observer. I DON'T accept that either method is equally good. And I don't accept that simultaneity at a distance is meaningless. That is based on my philosophical belief that she doesn't cease to exist whenever they are separated, and IF she still exists, she MUST be doing something specific "right now". And if so, she MUST have a specific age right now, because her brain at each instant of her life contains a record of what she was doing at that instant. So, I believe that EITHER the CMIF method, OR my method, is correct, but they aren't BOTH correct. We just don't know which one is the correct one. I reject the Dolby&Gull method, and the Minguizzi method, because they are non-causal, and special relativity (at least Einstein's version of it) is causal. So, as for now, the CMIF method and my method are "the only games in town".

Well then you can choose the method where the guy who had recently decelerated from v=+0.577c to v=0.000 simply adopts the simultaneity convention of the stay-home twin, because all syncrhonised clocks in that frame are simultaneously displaying the time 40, so she must be 40 years old. Or you can choose the method where he has to be the only one who doesn't accept that, and who says she is 26.67 years old, even though that is not true according to all of the synchronised clocks in that frame. I would choose the CMIF method.

 

[Mike_Fontenot]

[...]
Or you can choose the method where he has to be the only one who doesn't accept that, and who says she is 26.67 years old, even though that is not true according to all of the synchronised clocks in that frame. I would choose the CMIF method.

I can't tell from the above whether or not you agree that there is no way to tell which of the two causal simultaneity methods (CMIF or mine) is true and which is not. It sounds like you might be arguing that my method can't be true, because it disagrees with the clocks that are synchronized in her frame. If so, I disagree. Just as a perpetually-inertial observer moving wrt her would say that her clocks AREN'T synchronized, my method also says that her clocks aren't (always) synchronized. My method says that for a while after an observer accelerates, he will disagree with a perpetually-inertial observer (PIO) who is co-located and stationary with him (and that disagreement can last for many years). But after a sufficiently long (and well defined) time, he WILL once again agree with the PIO unless and until he next changes his velocity).

 

[Neddy Bate]

I can't tell from the above whether or not you agree that there is no way to tell which of the two causal simultaneity methods (CMIF or mine) is true and which is not. It sounds like you might be arguing that my method can't be true, because it disagrees with the clocks that are synchronized in her frame.

I'm not actually arguing that yet, but I suspect that I will be soon. However, first I'd like to understand exactly what your method is claiming to be true.

For example, after the guy decelerates from v=0.577c to v=0.000c, he is standing there at rest in her reference frame. There can be a stationary clock located there which is synchronised to her clock, which he can plainly see displays 40 years.

If someone were to ask him at that moment, "What age would she be if she died right now?" and he were to answer 26.67 years, what does that mean? Does it mean that he thinks her dead body would be 26.67 years old because he thinks she would have died when her clock displayed 26.67? Or does it mean that he thinks her dead body would be 40.00 years old but his "right now" is somehow behind in time, back when her clock displayed 26.67 but she doesn't actually die until her clock displays 40? Or is there some other explanation to what it all means?

SR says that if someone were to ask a perpetually inertial observer in that location at that moment, "What age would she be if she died right now?" they would answer 40.00 years, and her dead body would actually be 40.00 years old, and they would end up being correct. So at least that method has a practical value, and makes intuitive sense.

If so, I disagree. Just as a perpetually-inertial observer moving wrt her would say that her clocks AREN'T synchronized, my method also says that her clocks aren't (always) synchronized. My method says that for a while after an observer accelerates, he will disagree with a perpetually-inertial observer (PIO) who is co-located and stationary with him (and that disagreement can last for many years). But after a sufficiently long (and well defined) time, he WILL once again agree with the PIO unless and until he next changes his velocity).

Yes, I understand that your method has that bizarre feature, but let's set that aside, and focus on my very practical questions above.

 

[Mike_Fontenot]

I'm not actually arguing that yet, but I suspect that I will be soon. However, first I'd like to understand exactly what your method is claiming to be true.

For example, after the guy decelerates from v=0.577c to v=0.000c, he is standing there at rest in her reference frame. There can be a stationary clock located there which is synchronised to her clock, which he can plainly see displays 40 years.

Yes, that clock displays 40 years, immediately before and immediately after he changes his relative velocity to zero. He knows that she was 26.67 years old just an instant in his life ago, and he knows she is STILL 26.67 years old at this infinitesimally later instant. So he disagrees with that clock at that instant. However, he WILL immediately see that the amount of his disagreement with that clock about her current age linearly decreases as he ages, and that linear decrease will continue until he eventually agrees with that clock. After that point of agreement occurs, he will continue to agree with that clock, unless and until he changes his relative velocity again.

The basic assumption that DEFINES the CMIF method is that an accelerating observer will always agree with the PIO who is currently stationary wrt him, even if that stationary state is only momentary. My method makes no such assumption. My method is defined differently, as given on my webpage.

 

[Neddy Bate]

Yes, that clock displays 40 years, immediately before and immediately after he changes his relative velocity to zero. He knows that she was 26.67 years old just an instant in his life ago, and he knows she is STILL 26.67 years old at this infinitesimally later instant. So he disagrees with that clock at that instant. However, he WILL immediately see that the amount of his disagreement with that clock about her current age linearly decreases as he ages, and that linear decrease will continue until he eventually agrees with that clock. After that point of agreement occurs, he will continue to agree with that clock, unless and until he changes his relative velocity again.

The basic assumption that DEFINES the CMIF method is that an accelerating observer will always agree with the PIO who is currently stationary wrt him, even if that stationary state is only momentary. My method makes no such assumption. My method is defined differently, as given on my webpage.

Yes, I understand that. But I asked some questions about the implications which you seem to have avoided or ignored:

If someone were to ask him at that moment, "What age would she be if she died right now?" and he were to answer 26.67 years, what does that mean? Does it mean that he thinks her dead body would be 26.67 years old because he thinks she would have died when her clock displayed 26.67? Or does it mean that he thinks her dead body would be 40.00 years old but his "right now" is somehow behind in time, back when her clock displayed 26.67 but she doesn't actually die until her clock displays 40?

But you don't have to answer, I think I can figure it out by just looking at the moment before he decelerated, when his velocity was still 0.577c. If someone were to ask him at that moment, "What age would she be if she died right now?" and he were to answer 26.67 years, that would mean that she would have died when she was 26.67 and never lived to see 40.00. So, I suppose it is the same with your guy after he decelerates, he would expect her body to be 26.67 years old, and then when he saw her in the casket looking like a 40 year old, he would realize that he was simply wrong.

 

[Mike_Fontenot]

[...]

Bringing her death into it is a red herring. But if you DO want to talk about her death, you have to specify what her age at death WAS. (Her age at death is an EVENT that all observers must agree on.) Go ahead and specify that, and then I'll answer your questions about it's effect on our argument.

 

[Neddy Bate]

Bringing her death into it is a red herring. But if you DO want to talk about her death, you have to specify what her age at death WAS. (Her age at death is an EVENT that all observers must agree on.) Go ahead and specify that, and then I'll answer your questions about it's effect on our argument.

It is an event which occurs simultaneously with all of the synchronised clocks in her frame displaying 40 years, at the moment just after the traveler decelerated to v=0.000c. So, using your method, the traveler says she dies at 26.67 years, while everyone else at rest in that frame says she dies at 40 years. Who is correct and who is wrong? They can't all be correct, can they?

 

[Mike_Fontenot]

It is an event which occurs simultaneously with all of the synchronised clocks in her frame displaying 40 years, at the moment just after the traveler decelerated to v=0.000c. So, using your method, the traveler says she dies at 26.67 years, while everyone else at rest in that frame says she dies at 40 years. Who is correct and who is wrong? They can't all be correct, can they?

You're still not getting it. First, you have to decide what you want her year of death to be ... it's an arbitrary decision on your part. Once you specify her age at death, it's an event that everyone must agrees on. So decide how old you want her to be when she dies, and tell me what that age of death is.

 

[Neddy Bate]

You're still not getting it. First, you have to decide what you want her year of death to be ... it's an arbitrary decision on your part. Once you specify her age at death, it's an event that everyone must agrees on. So decide how old you want her to be when she dies, and tell me what that age of death is.

You should be able to figure it out from the given facts. She dies simultaneously with all of the synchronised clocks in her frame displaying 40 years. That includes the clock which I have strategically placed 23.09 light years away from her, so that it would be right in front of the decelerated traveler's eyes. He can see it displaying 40, and knows it has been synchronised to her clock, and he knows he is motionless with respect to it. Then he is asked how old she would be if she died right now. All he has to do is look at that clock and answer 40 years, right? What other option does he have?

 

[Mike_Fontenot]

[...]
She dies simultaneously with all of the synchronised clocks in her frame displaying 40 years.
[...]

OK, so you've FINALLY specified that she dies at age 40. When he says at the turnaround that she is 26.67 years old, she hasn't died yet. Once he concludes that she is 40 years old (which occurs roughly in the middle section of the Age Correspondence Diagram (ACD), when he is in his high 30's) for the scenario that I have specified, she dies then (although he won't know that until he receives an image of her, showing her age at death at age 40, which he receives much later). Similarly, the PIO at the turnaround who is stationary wrt her, won't know that she died at age 40 until much later.

Whenever he concludes that she is currently older that 40, say 50 years old, that just means that she has been dead for 10 years then (although he won't now that until much later).

The whole death thing is a red herring, of no consequence.

 

[Mike_Fontenot]

I just finished applying my method to your different scenario (where his velocity is instantaneously changed to zero (and kept there), instead of my scenario's change to -0.57735. The Minkowski diagram for your scenario is the same as for my scenario, up until the velocity change. But in your scenario, his worldline after the velocity change is just a horizontal line that goes on forever. Immediately after he changes his velocity to zero, she transmits a pulse giving her age as 40. And you have specified that she dies at that instant. When he receives that pulse, he finally starts agreeing with the the PIO co-located and stationary with him. Before that, and starting when he changed his velocity to zero, he disagreed with the PIO (although the amount of his disagreement linearly decreased as he continued to age). He was 32.66 years old when he changed his velocity to zero. He says she was 26.67 years old then. She says she was 40 then. He receives that pulse when he is 55.75 years old, and that pulse shows him that she had just died when she transmitted that pulse. He says she would have been 63.094 years old when he received that pulse, if she hadn't died at 40. From then on, he would say that he and she were ageing at exactly the same rate, if she hadn't died.

With the above information, the Age Correspondence Diagram (ACD) can be drawn. I plotted it on some home-made graph paper. As always, my method gives an ACD that consists of three connected straight-line segments ... i.e., it is piecewise linear with no discontinuities. The first segment is always trivial to get, merely from the time-dilation equation (TDE). It starts at the origin (zero for each of their ages), and has a slope of 1/gamma_1 = 0.8165. He is 32.66 and she is 26.67 at the end of that first segment. Then, the middle segment has a slope of 1.57735. The middle segment ends when he is 55.75 and she is 63.094. (The end of the middle segment is when he received the her pulse). Finally, the third segment has a slope of 1.0.

I ordinarily construct the ACD graphically, using information I get from the Minkowski diagram. That's what I did this time also. It gave me a slope for the middle segment that was roughly 1.577. But then I CHECKED that result, using the analytical equation I give for the middle slope near the end of Section 10 of my paper. For this scenario, that equation says the slope is (1 + v_1), which is equal to 1.57735.

 

[phyti]

Mike;
The problem is not really about twins, but clocks and light.
A and B are complete strangers.
Fig.1:
A sends a signal to B and triggers a clock signal E1, and receives it at t2.
She only knows where B was at t1 and what his clock indicated then.
She has no knowledge of events after E1, as indicated by the '?'.
Fig.3, as described by a 3rd observer U:
B sends a signal to A and triggers a clock signal E2, and receives it at t2.
The red lines transform Bt values to At values based on time dilation.
Fig.2, as described by a 3rd observer U:
B only knows where A was at t1 and what her clock indicated then.
Be has no knowledge of events after E2, as indicated by the '?'.

A and B can calculate based on assumptions as to elapsed time, but the conclusions are still speculations.

I think perspective has been lost when considering the fantasy world of fractional light speeds. If we consider aircraft speeds in human activity, radar tracks them in milliseconds. The delay between an event and perception of the event is insignificant.

Why don't you have graphics on your site?

 

[Mike_Fontenot]

Why don't you have graphics on your site?

How do YOU produce graphics?

 

[Neddy Bate]

OK, so you've FINALLY specified that she dies at age 40. When he says at the turnaround that she is 26.67 years old, she hasn't died yet. Once he concludes that she is 40 years old (which occurs roughly in the middle section of the Age Correspondence Diagram (ACD), when he is in his high 30's) for the scenario that I have specified, she dies then

Okay, so you admit that when he is standing at rest in her frame, and by your method thinks she is 26.67, if someone were to ask him, "If she were to die right now, what age would she have died?" He can't answer 26.67 and be correct. Instead he has to stand there and wait until later, when he finally thinks she is 40.

However, if at that later time someone were to ask him, "If she were to die right now, what age would she have died?" He still can't answer 40 and be correct, because she would be older than 40 by that time, if she had lived.

Below is the mathematical error that he is making at the moment he decelerates to v=0.000c and is at rest in her frame, thinking she is 26.67:
1. The message pulse she sent which arrives to him at that moment shows her to be 16.91 (true).
2. The amount he thinks she aged during the transit of that pulse is 9.76 (false).
3. He adds the two (16.91 + 9.76) and concludes she is 26.67 (false).

Below is the correct mathematical calculation that he should be making at that time:
1. The message pulse she sent which arrives to him at that moment shows her to be 16.91 (true).
2. The amount he thinks she aged during the transit of that pulse is 23.09 (true).
3. He adds the two (16.91 + 23.09) and concludes she is 40 (correct).

 

[Mike_Fontenot]

Okay, so you admit that when he is standing at rest in her frame, and using your method he thinks she is 26.67,

Yes, that is what my method says.

if someone were to ask him, "If she were to die right now, what age would she have died?" He can't answer 26.67 and be correct.

If someone asked him that exact question, he would say "IF she were to die right now, she would die at age 26.67, because that IS her age right now.

Below is the mathematical error that he is making at the moment he decelerates to v=0.000c and is at rest in her frame, thinking she is 26.67:
1. The message pulse she sent which arrive to him at that moment shows her to be 16.91 (true).

More accurately,
1. The message pulse she sent which he received at that moment shows her to have been 16.91 when she transmitted the pulse (true).

2. The amount he thinks she aged during the transit of that pulse is 9.76 (false).

That's TRUE, not FALSE, for the pulse that arrives at "T-", infinitesimally BEFORE he changes his velocity to zero, because that pulse is ENTIRELY in the left half of the diagram, so the LOS of slope 1/o.57735 can be used. For the pulse which arrives at "T+", infinitesimally AFTER he changes his velocity to zero, the two-part procedure that I describe in Section 8 of my paper must be used. The portion of that second pulse that is in the left half of the diagram (which is all of it except for the last infinitesimal part) can be analyzed with the same LOS as was used for the entire previous pulse. The portion of the second pulse that is in the RIGHT half of the diagram uses the LOS of the new velocity. The new velocity is zero, so the corresponding LOS is a vertical line. But the answer to the question, "How much does she age during that remaining portion of the pulse" is "she ages only by an infinitesimal amount", because the time lapse between the point "T" and the point "T-" is infinitesimal. So there is no finite change in her age between "T-" and "T+". But as subsequent pulses (which are partly in the left half and partly in the right half of the diagram) are analyzed, there is a FINITE time that the pulses are in the right half of the diagram, and that causes her age to continuously and linearly increase as he ages, as long as the pulses are only partly in each half of the diagram.

The above two-part procedure is explained in detail in Section 8 of my paper. It's pretty clear that you haven't understood my method yet.