# A New Simultaneity Method for Accelerated Observers in Special Relativity

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.

Well the "right now" at that moment (T+) according to all of the perpetually inertial observers at rest in her frame is when all of the synchronised clocks at rest in her frame display 40. All of them, including hers. So the "right now" at that moment would have her die at 40. That makes his answer of 26.67 incorrect.

Unless you want to tell me that your guy (saying if she dies now she'd be 26.67) and the PIO standing right next to him (saying if she dies now she'd be 40) can both be correct?

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.

Yes, and I already provided that diagram in post #85. Here it is again:

Note that at T+ his line of simultaneity points to her age being 40. Again, in SR, the slope of the LOS depends on the velocity. You can make up your own LOS slope method, but you can't call it SR.

Well the "right now" at that moment (T+) according to all of the perpetually inertial observers at rest in her frame is when all of the synchronised clocks at rest in her frame display 40. All of them, including hers. So the "right now" at that moment would have her die at 40.

That is HER conclusion. All perpetually-inertial observers moving with respect to her conclude that her clocks spread throughout space AREN'T synchronized with each other. They will say that at the instant "T+" in his life, she is NOT 40 years old. And he also says that she is NOT 40 years old then. He will say she is 26.67 years old then.

Unless you want to tell me that your guy (saying if she dies now she'd be 26.67) and the PIO standing right next to him (saying if she dies now she'd be 40) can both be correct?

That IS what special relativity says. Each observer is correct in the above statements, as far as their OWN perspective. And everyone's perspective is equally valid.

Yes, and I already provided that diagram in post #85.

Note that at T+ his line of simultaneity points to her age being 40.

That LOS you drew through the instant "T+" is not HIS line of simultaneity. It is the LOS of the PIO that he is stationary with. But he doesn't agree with that PIO for a period of time (sometimes for many years) after he accelerates. Anytime the pulse that he has just received travels partly in the left half of the Minkowsky diagram, and partly in the right half (which is true at his instant "T+"), he has to determine her current age when he receives that pulse by determining how much she aged during each of those two portions of the pulse. The PIO in the left half of the diagram determines her ageing in the portion of the pulse in the left half, and the PIO in the right half determines her ageing in the portion of the pulse in the right half. The traveler then ADDS those two amounts of ageing to get her TOTAL amount of ageing during the entire transit of the pulse. And to that he then adds her reported age when she transmitted the pulse to obtain her current age when he received the pulse. That procedure is what DEFINES my simultaneity method. It is described in detail in Section 8 of my paper.

That LOS you drew through the instant "T+" is not HIS line of simultaneity. It is the LOS of the PIO that he is stationary with.

It is the line of simultaneity (LOS) for the whole reference frame in that moment, and he is at rest in that reference frame. The line of simultaneity that you are using is from the out-bound reference frame which has a velocity of v=0.577c relative to her. He is no longer at rest in that reference frame, which is why it is a mistake on your part to assign that LOS to him. I understand that is your "new method" but it is not SR anymore if you do that.

Consider the following: Just as the stay-home twin dies (an event), she says that event (with her being t=40 years old) is simultaneous with her twin completing his deceleration to v=0.000c (also an event). Because he is at rest in her frame, he also has to say that his event (completing his deceleration) is simultaneous with her dying event. If he were still in the out-bound reference frame, with a velocity of v=0.577c relative to her, then there would be no requirement that the events which she considered simultaneous also had to be simultaneous according to him. But he is not at rest in that frame anymore.

In SR, simultaneity is frame-dependent. Simultaneity in SR is not dependent on subcategories of individual people. No people are even required in SR, only clocks.

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Mike,

Within one reference frame, if event A is simultaneous with event B, then event B is also simultaneous with event A. What you have is the event of her dying at t=40 simultaneous with him completing his deceleration (according to her), and him completing his deceleration also simultaneous with her being 26.67 (according to him), all within the same reference frame. It is nonsense.

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The line of simultaneity that you are using is from the out-bound reference frame which has a velocity of v=0.577c relative to her.

No. I'm not using that LOS (the LOS of the PIO of the outbound leg ... what I call the OCMIO in Section 8). And I'm not using the PIO of the v = -0.57735 worldline, or the PIO of the v = 0 worldline of your new scenario. The CMIF method requires that the accelerating traveler (he) must ALWAYS agree with the PIO who is currently stationary and co-located with him. That is the ASSUMPTION that the CMIF method makes in its definition. It is NOT an assumption that SPECIAL RELATIVITY makes. It is NOT the assumption that my method makes.

My method requires him to make use of the LOS's of TWO DIFFERENT PIO's. One of those PIO's is co-located with him BEFORE his velocity change, and the other is co-located with him AFTER his velocity change. The first PIO determines how much she ages during the portion of the pulse that occurs BEFORE the velocity change (according to the home twin (her)). The second PIO determines how much she ages during the portion of the pulse that occurs AFTER the velocity change (according to her). The traveler ADDS those two amounts of her ageing to get her total ageing during the entire pulse. And to that, he adds her age when she sends the pulse, to get her current age when he receives the pulse. THAT is the definition of my method.

Neither the CMIF method, nor my method, is MANDATED by special relativity. Special relativity is SILENT on how to determine the current age of a distant person, according to an accelerating observer. Both methods are internally consistent. We are free to choose either method. My philosophical feelings compel me to believe that there is only one CORRECT simultaneity method. But there is no way to know whether that one correct method is the CMIF method, or my method, or some other currently unknown (causal) method.

Within one reference frame, if event A is simultaneous with event B, then event B is also simultaneous with event A. What you have is the event of her dying at t=40 simultaneous with him completing his deceleration (according to her), and him completing his deceleration also simultaneous with her being 26.67 (according to him), all within the same reference frame.

If she ACTUALLY dies when she is 40 (which is a fact that you are free to SPECIFY in the scenario, and everyone must then agree with that), then he will say that she died at 40, WELL AFTER he changed his velocity (because he says that she was 26.67 when he changed his velocity, and therefore she was still quite alive then).

Neither the CMIF method, nor my method, is MANDATED by special relativity. Special relativity is SILENT on how to determine the current age of a distant person, according to an accelerating observer.

This is incorrect. SR is built on the premise that the speed of light is constant in all non-accelerating reference frames. From that premise, it was derived that time dilation must occur. More specifically, time dilation in which the rate of a relatively moving clock at constant velocity v would tick at a rate of exactly 1/gamma the rate of relatively stationary clocks, where gamma = 1 / √(1 - (v²/c²)). That means the traveler must consider the stay-home twin's clock to tick slower than his own on both the out-bound non-accelerating leg of his journey, and the inbound non accelerating leg of his journey. You method violates all of that.

I have already told you that in this thread. Your answer was that SR allows exceptions to be made for people who have recently accelerated. However, you have never cited any reference to anything that supports that.

I have cited this before, and granted it is just Wiki, but it is better than the nothing that you have cited:

https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation
"Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest in his frame of reference. This case is sometimes called special relativistic time dilation."

https://en.wikipedia.org/wiki/Inertial_frame_of_reference
"An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity."

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This is incorrect.

I stand by everything I said in my recent posts.

SR is built on the premise that the speed of light is constant in all non-accelerating reference frames.

That is only true for all PERPETUALLY INERTIAL reference frames.

From that premise, it was derived that time dilation must occur. More specifically, time dilation in which the rate of a relatively moving clock at constant velocity v would tick at a rate of exactly 1/gamma the rate of relatively stationary clocks, where gamma = 1 / √(1 - (v²/c²)).

That is true for two perpetually inertial frames moving at a relative velocity v. There is no distinction between
the "relatively moving" clock and the "relatively stationary" clock. Each frame will say the clocks in the other frame are ticking at a slower rate. It is entirely symmetrical.

That means the traveler must consider the stay-home twin's clock to tick slower than his own on both the out-bound non-accelerating leg of his journey, and the inbound non accelerating leg of his journey.

No, it doesn't. The traveler is NOT a perpetually inertial observer . None of the above applies to him.

https://en.wikipedia.org/wiki/Time_dilation#Velocity_time_dilation
"Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to him will be measured to tick slower than a clock that is at rest in his frame of reference. This case is sometimes called special relativistic time dilation."

Wiki doesn't define what they mean by "an inertial frame of reference". There statement is true only for the case of a perpetually inertial frame of reference.

That is only true for all PERPETUALLY INERTIAL reference frames.

Being perpetually inertial is not a requirement. Citation please, or else you made it up.

That is true for two perpetually inertial frames moving at a relative velocity v. There is no distinction between
the "relatively moving" clock and the "relatively stationary" clock. Each frame will say the clocks in the other frame are ticking at a slower rate. It is entirely symmetrical.

That is all true, except your requirement that the frames be "perpetually inertial" is not actually a requirement. You made that up. If not, citation please.

The traveler is NOT a perpetually inertial observer . None of the above applies to him.

Being perpetually inertial is not a requirement. Citation please, or else you made it up.

Wiki doesn't define what they mean by "an inertial frame of reference". There statement is true only for the case of a perpetually inertial frame of reference.

Again, being perpetually inertial is not a requirement. But even if it was, the whole stay-home twin's frame can be perpetually inertial, even while containing the traveler who has decelerated from v=0.577c to v=0.000c. So I am requesting another citation from you. Cite any reference to a person or other object not being considered to be inertial, even while they are at rest in a perpetually inertial frame of reference.

I just added the age correspondence diagram (ACD) for my simultaneity method to the bottom of the new stuff on my webpage (before the old stuff starts). And immediately below that diagram, I've indicated how the ACD's of the CMIF, D&G, and Minguzzi simultaneity methods (and also the ACD of the home twin's simultaneity method (the time dilation equation (TDE))) are different from my ACD.

The advantage of my method over the CMIF method is that mine has no discontinuities, and no possibility of any negative ageing by the home twin (according to the accelerating traveler). That negative ageing of the CMIF method bothers quite a few physicists, because it causes the correspondence between the twins' ages to NOT be one-to-one (i.e., not a "chart").

The advantage of my method over the CMIF method is that mine has no discontinuities, and no possibility of any negative ageing by the home twin (according to the accelerating traveler). That negative ageing of the CMIF method bothers quite a few physicists, because it causes the correspondence between the twins' ages to NOT be one-to-one (i.e., not a "chart").

I'm looking forward to you finding out whether any physicists are bothered by the idea that simultaneity is "person-dependent" in your method, rather than "frame-dependent" as it is in the CMIF method. I can't imagine telling a physicist with a straight face that you think a certain person at rest in an inertial frame has a different simultaneity than the rest of the frame that they are stationary in, just because that person did something in the past. But "you do you" as they say.

I'm looking forward to you finding out whether any physicists are bothered by the idea that simultaneity is "person-dependent" in your method, rather than "frame-dependent" as it is in the CMIF method.

I think the terms "person dependent" and "frame dependent" are completely synonymous. The person (the traveling twin, who sometimes accelerates) HAS a reference frame. In his frame, he is perpetually at the spatial origin. The time axis of that frame is his current age. The spatial axis in that frame gives him the distance to all other people (in the assumed one-dimensional space). His "frame" tells him the current age of the home twin. That's all it needs to do (plus a few other things that might sometimes be of interest, like their current separation, or their (instantaneous) relative velocity).

What is of interest in the current thread are the characteristics of the 4 simultaneity methods: CMIF, my method, D&G's method, and Minguzzi's method (and also the simultaneity method of the home twin (which is HER conclusion about the correspondence between their ages during the trip). (Believe it or not, I've been told by more than one physicist that the best thing for a relativistic space traveler to do is to adopt the simultaneity view of the people back on earth during his trip).

The disadvantage of the D&G method, and the Minguzzi method, is that they violate the principle of causality. A further disadvantage of Minguzzi's method is that determining it's ACD is very time-consuming, because there are no straight lines after the velocity change ... it's ACD is a curved line with a continuously changing slope, all the way from the velocity change to the reunion. And it can only be computed by drawing a different Minkowski diagram for EACH instant of the traveler's life that you'd like to know the corresponding current age of the home twin for.

The main disadvantage of the CMIF method is that it predicts that the home twin gets YOUNGER when the traveler accelerates AWAY from her (when their separation is sufficiently great). That results in their corresponding ages not having a one-to-one relationship, which means that the CMIF's ACD isn't a "chart", and that bothers a lot of physicists. And the fact that the CMIF's ACD is discontinuous bothers some physicists.

The only disadvantage you raised for my method is that it says that an observer who has accelerated will not agree about the home twin's age (for some period of time (sometimes many years) after his acceleration), with a perpetually-inertial observer who is co-located and co-stationary with him. That apparently bothers you a LOT. In fact, you seem to think his need to ALWAYS agree with the perpetually-inertial observer, whom he is riding along with, is MANDATED by special relativity. It is NOT. It is AN ASSUMPTION (the DEFINING assumption) of the CMIF method. It is not true in ANY of the other three simultaneity methods besides the CMIF method.

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Mike,

If you don't mind, I'd like to look one more time at this idea of yours. You admit that you have not proved the CMIF wrong, so at this point in time, I assume you think the CMIF and your method are both equally viable.

Let's please look at this simple case again, where the traveler decelerates from v=+0.577c to v=0.000c with respect to the home twin:

Consider the moment of time immediately after the traveler has decelerated. In that moment, he sends her a light signal message that says, "Hi Sister, I have decelerated, so I am motionless with respect to you. I am currently located 23.09 light years away from you, and using the Fontenot method I predict that you are currently 26.67 years old. This is remarkable because using the CMIF method I would have predicted you were currently 40.00 years old. Luckily there is no way to tell which is correct."

She receives those two conflicting age predictions at the time when she is 63.09 years old, and tries to determine which one of the two is correct. Knowing the speed of light is 1 light year per year, she subtracts the distance the signal traveled (23.09) from her current age (63.09) and gets the following result: 63.09-23.09=40.00. She determines that the CMIF method was correct, and the Fontenot method was wrong.

Now how are you going to try to explain to her that both predictions can be considered equally correct? Are you going to tell her the speed of a light signal sent by someone who recently decelerated might not be 1 light year per year? Do you really think that physicists would prefer that idea?

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If you don't mind, I'd like to look one more time at this idea of yours. You admit that you have not proved the CMIF wrong, so at this point in time, I assume you think the CMIF and your method are both equally viable.

I suspect that it is impossible to tell which method is correct and which is incorrect. Philosophical considerations lead me to believe that one of them is correct, and the other is incorrect. But I can't know which is which. So all I can do is consider the advantages and disadvantages of the four simultaneity methods, and I conclude my method wins that contest.

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She determines that the CMIF method was correct, and the Fontenot method was wrong.

Actually, she says we BOTH have been wrong for the ENTIRE trip before your modified velocity change occurred. So I don't lose a lot of sleep worrying about whether she thinks I'm wrong or not. She will agree with you for the rest of your scenario. (She wouldn't have agreed with you EVER in the scenario I specified, except for a single instant if you consider that the traveler's velocity has to be zero for a single instant between its change from +v to -v). EVENTUALLY, she will also agree with me (in your modified scenario), because eventually the traveler begins to agree with the perpetually-inertial co-located and mutually-stationary observer. But I don't associate any value at all with her agreement or disagreement with me.

Actually, she says we BOTH have been wrong for the ENTIRE trip before your modified velocity change occurred. So I don't lose a lot of sleep worrying about whether she thinks I'm wrong or not.

Okay, fair enough. But before giving up on this line of thought, let's take a quick look at the message he would send to her the moment before he decelerates. In that case, he would say the following:

"Hi Sister, you are moving away from me with a speed of 0.577c, so of course we are not going to agree on any frame-dependent measures. For example, your distance marker showing 23.09 light years is passing right next to me at this moment, so you probably think the distance between us is 23.09 light years, but to me all of your distance markers are length contracted, so to me the distance between us is currently 23.09/1.2247=18.85 light years. So, using my own frame of reference I would predict you are currently 26.67 years old, but I know you will disagree, however if I use yours instead, I would predict you are currently 40.00 and I believe you will agree to that."

Now that last line could be a way for you and I to come to an agreement of some sort. Let me add that last line to the message he would send after he decelerates. It would be as follows:

"Hi Sister, I have decelerated, so I am motionless with respect to you, and I am currently located 23.09 light years away from you. So, using the Fontenot method and my own personal* frame of reference, I would predict you are currently 26.67 years old, but I know you will disagree, however if I use your personal* frame of reference instead, I would predict you are currently 40.00 and I believe you will agree to that."

*Note that I had to add the word "personal" because after he decelerates, SR says he is in the same frame of reference that she is, because their relative velocity is v=0.000c at that point. (Notice that they are able to agree that their separation distance is 23.09 light years now, unless you disagree?) You should at least be able to see that your method makes a distinction between different people's *personal* frames of reference, instead of relying on relative velocity. If you are okay with that, then I am also, but it is a departure from what is normally done in SR.

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[...] because after he decelerates, SR says he is in the same frame of reference that she is, because their relative velocity is v=0.000c at that point.

I disagree that "SR says that". In my method, Her frame and His frame are different before the velocity changes to zero, and they are DIFFERENT for some (well-defined) period after the velocity change to zero. SR doesn't forbid that.

I actually haven't given any thought to the question of how their separation (according to him) in my method varies with his age. I really haven't had any interest in that question, because what is important to me is the correspondence between their ages, according to him. I.e., it's the ACD that is important to me. But I'll give the question of separation, according to him, some thought when I can.

I disagree that "SR says that".

In that case, I suggest you study the concept of "rest frame".

https://en.wikipedia.org/wiki/Rest_frame

"In special relativity the rest frame of a particle is the coordinate system (frame of reference) in which the particle is at rest."

"In both special relativity and general relativity it is essential to specify the rest frame of any time measurements, as the time that an event occurred is dependent on the rest frame of the observer."

In my method, Her frame and His frame are DIFFERENT for some (well-defined) period after the velocity change to zero.

I know, that is one of your method's problems.

SR doesn't forbid that.

Yes it does. The whole SR theory, (and even Galilean relativity), are built on the idea of reference frames and their relative motion. The velocity v that is used in the Lorentz transforms, (and Galilean transforms), is the relative velocity between reference frames. A person at rest in a reference frame is just another point of interest in that frame. You don't get to make exceptions because it wasn't perpetually inertial. Perpetuality was never part of it at all.

I actually haven't given any thought to the question of how their separation (according to him) in my method varies with his age. I really haven't had any interest in that question, because what is important to me is the correspondence between their ages, according to him. I.e., it's the ACD that is important to me. But I'll give the question of separation, according to him, some thought when I can.

Okay, but I would suggest starting with the basics. Get a book or website on SR that uses light clocks, and shows you how the time dilation RATE (1/gamma) is derived from them. From there, it should become clear that the RATE of the home twin's clock on the inbound leg of the twin 'paradox' must be 1/gamma according to the traveler. That alone is enough to tell you that the CMIF is the only simultaneity method that works.