Special Relativity question

[ralfcis]

Here is the STD:

Alice leaves Bob at .6c and stops after 4 years her time and sends a pink light signal to Bob who receives it at t=8 thereby ending the spacetime path. At this point Bob has aged 5 to 8 yrs and Alice 4 to 7 in the 3 years it has taken the light to reach Bob. Alice has aged 1 yr less than Bob during that time but how much less has she aged per year of the 3 yr light journey.

[BurtJordaan]

Ralf, you have already answered the question in your: "At this point Bob has aged 5 to 8 yrs and Alice 4 to 7 in the 3 years it has taken the light to reach Bob". Are you asking if this was correct?

[Faradave]

This thread may have originated in context elsewhere. As stated here, there does not appear to be any acceleration (force) involved. Thus, as per Special Relativity, differences in aging are mutually seen (often described as "reciprocal"). Though it can be surmised, you should specify which frame you are adopting.

[BurtJordaan]

The "stops" says that Alice decelerated to a stop (relative to Bob), although the "leaves" could have been without acceleration. Relativity don't care about what happened before the test scenario started...

[ralfcis]

Faradave you're still confusing age difference with reciprocal time dilation. The age difference is not mutual.
Jorrie, the answer I'm trying to get from relativity is how much Alice is aging less than Bob for every year from t'=4 to t'=7. Brian Greene says the swing of Alice's line of present is what causes an instantaneous age difference right at t'=4. I know that's not true because if you make the stop brief and then allow her to continue at .6c, the age difference does not stick. In my ralfativity 2.0 thread I've tried to reason out how much less Alice actually ages per year but the tally is only .75 yrs in 3 years or -.25 yrs per year when the correct answer should be -.333 yrs/yr. The reasoning behind this is before t'=4 (t=3.2) there can be no age difference accumulating because they are in constant .6c relative velocity. There can also be no age difference accumulating after t'=7 (t=8) because they are in constant 0 relative velocity. I can get the correct answer that Alice has aged 1 yr less at the end of the spacetime path but I can't get how she accumulates this difference over the 3 years. I'm just wondering if relativity gets the correct answer and if so, how does it do it.

P.S. Hey hold on I just got an idea. I should do the STD with Alice stopping for a year and then continuing at .6c to see how much less she ends up aging that way.

[Faradave]

"stops" says that Alice decelerated

Agreed. My mistake (I hadn't seen a curve in the worldline).

The age difference is not mutual.

While a "difference" is always mutual, in view of above, I concede your point. There was a force acting on Alice, which caused her to change reference frames and age differently in the process. By Newton's 3rd Law, there would be an equal and oppsite force acting (effectively) on the rest of the universe, but its acceleration would be immeasurably small.

I expect that if you make Alice stop (and start again), there must be aging consequences for each change in reference frame. But you're in good hands so, I'll stop interfering.

[ralfcis]

Here's the STD for Alice stopping 1 yr then continuing at .6c. I'm still getting the wrong answer that she is losing .25 Alice yrs (or .2 Bob yrs) wrt Bob's age for 1 yr stop. So a 3 yr stop tallies to .75 yrs younger when the correct answer should be 1 yr younger over 3 yrs.

The bold pink lines are the light signals from Alice that a change in relative velocity has been made. The bold red lines show at the stop that she was 4 three yrs ago (pink line travel time) and Bob was 5 in Bob yrs which is 4 Alice yrs. Bob would have been 8 (or 10 equivalent Alice yrs) if no stop had been made but instead he ends up .2 yrs older (or Alice has aged .25 yrs less than Bob in Alice yrs due to the 1 yr stop). This just doesn't make sense to me.

[BurtJordaan]

Brian Greene says the swing of Alice's line of present is what causes an instantaneous age difference right at t'=4. I know that's not true because if you make the stop brief and then allow her to continue at .6c, the age difference does not stick.

Yea, but a brief stop and then acceleration again swings the line in the opposite direction, so you will end with a negligible observable age difference. 'Observable' is the key word, and for any age difference, your two parties must agree, which they can only do when they end up in the same inertial frame for 3 years or more, as you said.

Relativity does not actually say "when" the age difference happened, only that the (absolute) difference over the scenario was so much. The "when" depends on who observes it from where, so it cannot be absolute.

[ralfcis]

but my example with the 1yr stop matches the age difference for 1 out of the 3yr stop. So you're saying there's absolutely no mathematical extrapolation that can be drawn from this. .25 yrs less is correct for a 1 yr stop and 1 yr less is correct for a 3 yr stop. Why? What's going on internally that's causing this difference?

You're right, there is a difference between the two examples. At the end of 3 yrs Alice and Bob have agreed that their relative velocity has changed from .6c to 0 with a different result that would occur if Alice returned to .6c after the 3 yrs. I assume that scenario would mean .75yrs difference between the two. That's a very interesting phenomenon (I'll have to check it). It would mean the per yr age difference within a multi-yr stop differs depending on subsequent velocity changes. But it's not some random value. It appears to be .333 yrs less per yr without a 2nd velocity change and .25 yrs less per yr with a return to he original relative velocity which takes a certain amount of extra time to process.

[ralfcis]

Yup that's the answer. As you can see the spacetime path ends differently with Bob being 8.6 when Alice is 10 which equates to Alice being .75 yrs younger than Bob and not 1 yr younger if she had remained at 0 relative velocity. So the idea of cumulative age difference is only apparent if the initial relative velocity is returned to. That's not reliable so I will alter the next STD to make determining age difference clear.

[ralfcis]

There's still a problem. I can show how much less Alice ages for a single year if she returns to .6c after that year but I can't show how much less Alice ages for a single year if she remains stopped. In fact the STD shows just before Alice turns 4, Bob is equivalently 4 in Alice years but just after 4, Bob is instantaneously 1 yr older than Alice. The lines of present overlap which means the times are instantaneous present, there is no relativity of simultaneity between Alice and Bob because v=0 and the formula for simultaneity is vx/c. So an instantaneous present exists between them when either x=0 or v=0. Age difference cannot be instantaneous, it makes no physical sense. Maybe if I look at it from the perspective that Bob takes off at .6c to match Alice's speed to create 0 relative velocity. Maybe that will get rid of this anomaly.

[JMP1958]

There's still a problem. I can show how much less Alice ages for a single year if she returns to .6c after that year but I can't show how much less Alice ages for a single year if she remains stopped. In fact the STD shows just before Alice turns 4, Bob is equivalently 4 in Alice years but just after 4, Bob is instantaneously 1 yr older than Alice.

I'm not quite clear what you mean by Bob being equivalently 4 in "Alice years". According to Alice, After 4 years of her time, Bob will be 0.8 years younger than she is before the acceleration and 1 year older after.

The lines of present overlap which means the times are instantaneous present, there is no relativity of simultaneity between Alice and Bob because v=0 and the formula for simultaneity is vx/c. So an instantaneous present exists between them when either x=0 or v=0. Age difference cannot be instantaneous, it makes no physical sense. Maybe if I look at it from the perspective that Bob takes off at .6c to match Alice's speed to create 0 relative velocity. Maybe that will get rid of this anomaly.

The "anomaly" is merely the result of making the non-physical assumption of an instantaneous velocity change. When you do this you are saying that Alice undergoes an infinite acceleration over a 0 time duration. In reality, the acceleration can be as high a value as we want for as short an interval as we want, but it will always have to occur over some non-zero time period.
At the onset of this period, Bill will be 0.8 years younger than Alice, and during the acceleration would age 1.8 years over that short, but not zero time length. As a result, you never get a situation where Alice would determine Bob's age as having two different values.

Anytime we assume an "instantaneous" change in velocity, what we are really doing is just assuming an acceleration period that is so short in duration that is doesn't significantly effect the outcome.

For example, if Alice accelerates at ~2.079e16 m/s² for 1 nanosecond of her time, she will cause a 0.6c difference in her velocity with respect to Bob. According to Bob, she will have been under acceleration for ~1.1 nano second to make that same velocity change. But when we are dealing with trips that take years, that 0.1 nanosecond difference is insignificant. But it does mean that according to Alice there is a 1 nanosecond period of transistion between Bob being 0.8 years younger than she is and being 1 year older.

[mitchellmckain]

Alice leaves Bob at .6c and stops after 4 years her time and sends a pink light signal to Bob who receives it at t=8 thereby ending the spacetime path. At this point Bob has aged 5 to 8 yrs and Alice 4 to 7 in the 3 years it has taken the light to reach Bob. Alice has aged 1 yr less than Bob during that time but how much less has she aged per year of the 3 yr light journey.

According to Bob, Alice travels a distance 3ly for 5 years. The light thus takes 3 years to get to Bob and he will be 8 years older. We can suppose that this signal includes Alice's report that she is only 4 years older when she sent the signal.

There's still a problem. I can show how much less Alice ages for a single year if she returns to .6c after that year but I can't show how much less Alice ages for a single year if she remains stopped.

Alice can send a message back to Bob every year reporting her age. Thus each year she is "stopped" (i.e. in the same inertial frame as Bob), Bob will receive a message each year after the first one and will then be able to see that Alice is aging a year each time, the same as Bob.

When Alice resumes her journey away from Bob at .6c, if she keeps sending her yearly reports of her increased age. When does Bob receive them? Each year according to Alice, she is .36ly farther away by her own measure. Bob receives these at 1.73 intervals and can then calculate backwards to conclude that these messages were each sent at 1.25 year intervals at .48ly farther away each time. And thus he can conclude that Alice is aging .8 years for each year of his own but only on the assumption that Alice will return to his own inertial frame, otherwise it makes no sense.

In fact the STD shows just before Alice turns 4, Bob is equivalently 4 in Alice years but just after 4, Bob is instantaneously 1 yr older than Alice. The lines of present overlap which means the times are instantaneous present, there is no relativity of simultaneity between Alice and Bob because v=0 and the formula for simultaneity is vx/c. So an instantaneous present exists between them when either x=0 or v=0. Age difference cannot be instantaneous, it makes no physical sense. Maybe if I look at it from the perspective that Bob takes off at .6c to match Alice's speed to create 0 relative velocity. Maybe that will get rid of this anomaly.

This is all nonsense.

Before Alice stops there are two inertial frames involved: Alice's and Bobs. In Bob's inertial frame 5 years have passed and Alice has traveled 3ly. In Alice's inertial frame 4 years have passed and she has traveled (that is Bob is now at a distance of) 2.4ly. When Alice comes to a sudden stop then there is only Bob's inertial frame where she has traveled 3ly and she is 1 year younger because of time dilation..

However if instead of Alice stopping, we have Bob accelerate to .6c in the direction of Alice, then we have only Alice's inertial frame where she has traveled 2.4ly in 4 years. It only works if Bob does this when only 3.2 years have passed for him and thus when Alice has traveled only 1.92ly according to him. Then he finds out that the distance of 1.92ly was in fact a distance of 2.4ly in Alice's inertial frame times a length dilation factor of 0.8. He will also notice that he has aged only 3.2 years compared to the 4 years which Alice has aged. If Bob waits any longer than 3.2 years, then he will have to conclude that the first message from Alice was already en-route (according to his new inertial frame) when he accelerated.

[BurtJordaan]

The "anomaly" is merely the result of making the non-physical assumption of an instantaneous velocity change.

Yes, and apart from that, also the nonphysical assumption that Bob can know instantly that Alice has changed relative speed. Relativity is all about observables - strictly speaking, we must wait until the whole scenario has played out and Alice and Bob are either co-located momentarily, or stationary in the same inertial frame for long enough to allow two-way clock-sync/desync observations.

This means that Ralf's "stop for a year and then proceed" does not yield a valid, frame independent age comparison in his scenario. Yes, we can pre-process, post-process and make all sort of interim measurements and predictions, but in the end proper observation is king.

[ralfcis]

Yes, and apart from that, also the nonphysical assumption that Bob can know instantly that Alice has changed relative speed

No matter how slow you make the velocity change, the age difference is still being caused by the sweep of the line of present which means age difference is being caused by acceleration. If Alice crashed on a planet 3 ly away and sent out a light signal just seconds before the crash and a light signal followed from the planet of when she crashed, that would be the source of the anomaly I described. Alice would suddenly be 1 yr younger than Bob at the time of her death and the same age as Bob seconds earlier.

Of course he would only know that 3 yrs later and be able to post process the result. Until then he would think he is still going at .6c relative velocity. My mistake was the sweep of the line of present causing the age difference at the beginning. The sweep is seen by Bob later. You are wrong about the analysis of Alice's stop and restart, I have considered all the information if you'd just look at the STD the result is valid..

Moderator's note: Ill-informed comment about Mitch and Positor removed.

[BurtJordaan]

Before Alice stops there are two inertial frames involved: Alice's and Bobs. In Bob's inertial frame 5 years have passed and Alice has traveled 3ly. In Alice's inertial frame 4 years have passed and she has traveled (that is Bob is now at a distance of) 2.4ly.

Exactly. It depends on who is looking from where. Alice surely knows her own age then, but she has no knowledge of Bob's aging at that point and neither does Bob know what Alice's aging has been up to then. Proper aging cannot be a coordinate dependent quantity.

Your (correct) dealing with the coordinate dependent aspects does not quite help Ralf - he seems to have a 'lock-on' to proper aging differences and is on a quest to find out why I said that relativity does not tell us where the proper aging difference happens during the scenario that he has sketched.

[BurtJordaan]

No matter how slow you make the velocity change, the age difference is still being caused by the sweep of the line of present which means age difference is being caused by acceleration. If Alice crashed on a planet 3 ly away and sent out a light signal just seconds before the crash and a light signal followed from the planet of when she crashed, that would be the source of the anomaly I described. Alice would suddenly be 1 yr younger than Bob at the time of her death and the same age as Bob seconds earlier.

Ralf, you started this thread off as if you understand the difference between proper- and coordinate-aging. But here you are 'boots and all' back into ascribing coordinate system dependent "aging" as if it is proper aging. The "sweep of the line of present" has nothing to do with aging. And acceleration itself does not cause age differences. Non-equivalent spacetime paths do.

The rest of what you wrote is not worth commenting on. I'm not going to be drawn into a long "quote/misquote/out-of-context" debate again. Get your physics straight or stick to the personal theories section.

[ralfcis]

I understand your words but how about some math to go with them? That was the original question, why is there a difference between the accumulating age difference and the final age difference. I'd venture to guess from others responses that it isn't even known that there's a difference between time dilation and age difference. You said and have always said relativity can't determine any age difference accumulation before the stop of the spacetime path. But then you said my stop and restart answer was wrong and that was a complete spacetime path. So what is your math answer for that example in the math that you use? I'm positive our answers agree. I can show you my math step by step if the single STD is too overwhelming. You can point out the exact spot where I supposedly go wrong. If I could see your math, maybe I'll finally learn something. If you are going to kick me off for posing a question could you please tack this thread on my ralfativity 2.0 thread, there's still some good info here to help me in my quest to prove the accumulating age difference can match the final age difference. I'll concede defeat once I exhaust all math avenues.

[BurtJordaan]

Ralf, the math of propertime is well written up. Wikipedia's article is pretty good. No need to repeat anything here, except the caveat that is mentioned up front: "The proper time interval between two events on a world line is the change in proper time."

Sorry I posted it incomplete by accident. The rest will follow.

The key words here are "between two events on a world line". This means it determines the accumulation of time (or age) for single observer as it travel between two events, gradually along the spacetime path of that observer. It has nothing to say about the age accumulation of any observer that is not present at both events.

This, taken to its logical conclusion, answers all the issues that you have with SR.

[ralfcis]

That's great. I plugged in the numbers for my stop/restart STD and I get the same answer as my math gives. No I'm lying of course. You've given me the typical blow off answer of go read a book on relativity and your answer will be there.) But 'm looking for the math that shows if Alice stops for 3 years and she'll end up 1 yr younger than Bob at the end of those 3 years, how much younger is she for each of those 3 years. You're saying that's unknowable, there is no progression of age difference. Aging is a physical phenomenon, it can't just suddenly appear out of nowhere. The light signal from Alice at t'=4 is used by Bob at t=8 to post process that he was 5 when Alice was 4 from any perspective. This is no longer a coordinate value at this point, it is 2 ages being compared in the god's eye instantaneous present. This means that Alice went immediately from being the same age as Bob (because they were engaged in constant relative velocity) to 1 year younger.Can I can prove that here without you claiming perspectives are getting mixed up and so is coordinate and proper time?

[BurtJordaan]

Bob is never present at the two events that concern Alice, so his aging is indeterminate for those two events. After 3 years of her stopping, Alice and Bob are still at two different events, but now they had time to exchange signals and could determine that they now share a mutual inertial frame and hence a shared definition of simultaneity. This, for the first time, allows a proper aging difference of 1 year to be established.

For Alice it means 1 year difference in 7 years and for Bob it is 1 year difference in 8 years. Where it happened, neither can tell. Post-processing depends on arbitrary choice of reference frames and it is hence not a coordinate-independent result.

[BurtJordaan]

Can I can prove that here without you claiming perspectives are getting mixed up and so is coordinate and proper time?

No, not here, because that will constitute flawed physics. Feel free to do that under the 'personal' section.

[ralfcis]

They can establish through post processing that they had a shared definition of simultaneity at t'=4. True Bob thought his relative velocity at this point was .6c all the way up to t=8. But Alice knew they were at 0 relative velocity. Her lines of present went horizontal at this point and aligned with Bob's lines of present which is a fact he could post process. So the formula for simultaneity is vx/c. If x=0, the two are co-located and hence share an instantaneous present and a valid age comparison can be made. But if math is to be believed, the formula also offers a shared simultaneity at a distance if the relative velocity between the two is zero. Does that not also mean a valid age difference can be established? Mitch thinks that math result is nonsense. What do you think?

P.S. The physics dictates a valid age comparison must wait until the light delay between them is overcome. But where does that say so in the formula for simultaneity?

[ralfcis]

Flame post deleted.

[BurtJordaan]

They can establish through post processing that they had a shared definition of simultaneity at t'=4. True Bob thought his relative velocity at this point was .6c all the way up to t=8. But Alice knew they were at 0 relative velocity.

Exactly. This is a coordinate-choice dependent view (Alice's or Bob's), which is exactly what we are trying to tell you: it does not represent aging differences.

Relativity is applied math, not merely math. The key is to know what is valid for which physical situation. A physical intuition is required, which is best learned by reading and listening to those that already have acquired that to some degree.

[BurtJordaan]

Ralf, you have been given the answer to your original question multiple times from a relativity p.o.v.

If you have other ideas, go to your personal theories. Thread closed.