Naked Science Forum
On the Lighter Side => New Theories => Topic started by: hamdani yusuf on 17/09/2023 08:30:13
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This is a slightly modified twin paradox to distinguish the effects of relative speeds and acceleration.
Twin A started a journey to Alpha Centauri 4 light years away in a space ship moving at 0.4c. He is expected to arrive 10 years later, according to earth observer.
Twin B stayed home to improve the space ship, so he can go to Alpha Centauri 5 years later at 0.8 c.
Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously. Does special theory of relativity predict the same?
How old are they when they meet up at Alpha Centauri?
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This is a slightly modified twin paradox to distinguish the effects of relative speeds and acceleration.
In a different inertial reference frame (one in which both stars are moving at -0.4c), this is pretty much exactly the twin paradox, with twin A being stationary the entire time, and twin B going out and back, albeit at 0.4c only outbound, and faster on the return.
OK, so this is trivially computed in the Earth frame. The resolution for any exercise in special relativity is to simply choose a frame (we'll pick Earth since Earth time was specified), all you need to do is compute the dilation factor due to the speed relative to that frame. This is computed (in natural units) with
λ = 1/√(1-v2)
Twin A started a journey to Alpha Centauri 4 light years away in a space ship moving at 0.4c is expected to arrive 10 years later, according to earth observer.
OK, so in Earth frame, λ=1.091 so 10 / 1.091 = 9 years 2 months elapsed time for twin A.
Twin B stayed home to improve the space ship, so he can go to Alpha Centauri 5 years later at 0.8 c.
0.8c yields a λ of 1.667 so 5 years at home and 3 during the trip, so 8 total. Not so hard, right? You can do this yourself without asking each and every time.
Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously.
Classical in what sense? Classical physics refers to non-quantum physics. I think you mean Newtonian physics, not classical. Yes, every theory (including Newtonian) says they get there simultaneously. This is an objective fact, true in any reference frame.
How old are they when they meet up at Alpha Centauri?
As computed above, 9y2m and 8y respectively.
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As computed above, 9y2m and 8y respectively.
Thanks for the answers.
Do we get the same answers if the calculations are made from the perspectives of the travelling twins?
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As computed above, 9y2m and 8y respectively.
Thanks for the answers.
Do we get the same answers if the calculations are made from the perspectives of the travelling twins?
Yes.
Because the alternative would be a contradiction.
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None of these phenomena are paradoxes, they are just somewhat counterintuitive when given a cursory examination. Once one does the maths, all becomes clear.
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None of these phenomena are paradoxes, they are just somewhat counterintuitive when given a cursory examination. Once one does the maths, all becomes clear.
Have you done the calculations?
Do you use length contraction for the distance?
Do you use relativistic velocity addition?
Do you use Doppler effect?
What's the formula necessary to get the same answers as calculated from earth perspective?
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What's the formula necessary to get the same answers as calculated from earth perspective?
Using the equations from special relativity, you will find that there are no actual paradoxes as paul cotter said.
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1/√(1-vsq/csq) is all you need. I did not calculate this scenario, Halc had already done so and thus there was no need. With all due respect, and I mean this sincerely, I believe you, Hamdani, look at too many videos and get confused messages from these. A reliable physics textbook would clear up any doubts you may have.
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Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c. Length contraction reduces the duration of the journey from 10y to 9y2m. It's what his clock will show when Alpha Centauri arrive at his location.
Meanwhile, twin B moves away to the other direction at the same speed. Then at half way, he returns to A's position. Somehow, B's clock will age less than A's when they meet, ie 8y.
Now, how would it look like from B's perspective?
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Let's describe the same case from twin A's perspective. He stays in his own reference frame
Just for some terminology, 'perspective' is a point of view. I think you mean his frame, or more specifically, the frame in which twin A is stationary, so we can call it 'frame A'. Frame E was the one where Earth is stationary. Everybody is in all frames, so there is no way to exit it, so 'stays in' should read 'is stationary in'.
As for perspective, two people stationary relative to each other still have different perspectives since they're not in the same place and thus see different things. The twins scenario isn't about perspectives, or even about twins for that matter. The twins is just a funny way to emphasize that people can act as clocks.
while Alpha Centauri moves closer at 0.4c. Length contraction reduces the duration of the journey from 10y to 9y2m.
Length contraction is about length, not time. Earth and AC are 9.166 light years apart in that frame. That's length contraction. AC needs to travel that distance to where 'twin A' is, so yes, you are correct in that the journey taken by AC is of length 9 1/6 light years.
It's what his clock will show when Alpha Centauri arrive at his location.
Yes, exactly.
Meanwhile, twin B moves away to the other direction at the same speed.
Riding 'spaceship Earth' away from twin A at the speed of 0.4c.
Then at half way, he returns to A's position.
Half way to what? No, he simply rides Earth for 5 of his years. λ=1.091 for 0.4c, remember? So that's going to take 5λ years in the frame we're using, which is 5.455 years. 5.455 years at 0.4c takes him 2.182 ly away from where he started, which isn't particularly halfway to anything.
Somehow, B's clock will age less than A's when they meet, ie 8y.
We know that took 5.455 to get to turnaround (in frame A), so that leaves 9.167 = 5.455 = 3.712 years to get back. Clearly he'll be going faster on the return than on the way out.
2.182 ly / 3.712 years is 0.588c which is his return speed in frame A. It's that easy.
λ = 1/√(1-v2), so at that speed, λ is 1.236. To verify, 3.712 / λ = 3, so he ages 3 years during the 2nd leg, which is what we got in the first example.
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Half way to what?
Halfway of A's journey, calculated from earth's perspective.
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Somehow, B's clock will age less than A's when they meet, ie 8y.
We know that took 5.455 to get to turnaround (in frame A), so that leaves 9.167 = 5.455 = 3.712 years to get back. Clearly he'll be going faster on the return than on the way out.
2.182 ly / 3.712 years is 0.588c which is his return speed in frame A. It's that easy.
λ = 1/√(1-v2), so at that speed, λ is 1.236. To verify, 3.712 / λ = 3, so he ages 3 years during the 2nd leg, which is what we got in the first example.
How do you get 8y as B's age when calculated from A's perspective?
Now, how would it look like from B's perspective?
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B is not inertial.
Is A inertial?
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I think it would be best to work your way backwards, computing the second leg first, and then the prior leg of the journey. You know most of the relevant numbers from the posts above, such as how fast is twin A is moving relative to this frame, and how long (his clock) it takes him to do it. Start with that. All you need is the one formula (which involves a square root, scary...), and the rest can be done with a 4-function calculator.
Should we calculate the Doppler effect to get the correct answer?
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Would it make a difference whether those twins stop at the end of the journey, or continue going at their travelling velocity, or turn around to return to the earth, as measured by earth observer?
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We know that took 5.455 to get to turnaround (in frame A), so that leaves 9.167 = 5.455 = 3.712 years to get back.
2.182 ly / 3.712 years is 0.588c which is his return speed in frame A. It's that easy.
λ = 1/√(1-v2), so at that speed, λ is 1.236. To verify, 3.712 / λ = 3, so he ages 3 years during the 2nd leg, which is what we got in the first example.
How do you get 8y as B's age when calculated from A's perspective?
By adding 3 to the 5 subjective years he took on the outbound trip.
5 years was given in the description. 3 was computed as per the bit that you quoted, 3.712 years / λ where λ is computed to be 1.236 for the return leg.
Now, how would it look like from B's perspective?
B is not inertial. Yes, he has a perspective, but he doesn't define any one inertial frame, so you need to be more specific. You probably want the frame in which his 2nd leg has him stationary since the 1st leg frame is the same one as Earth/AC, and we already did that one.
Go through steps similar to above and you can do it yourself. In that frame, A moves towards the destination at constant speed, and B and Earth move toward it at some higher speed, both getting there simultaneously and before twin A. At that point, twin B stops, waiting for both A and AC to get to him simultaneously, but at different speeds..
I think it would be best to work your way backwards, computing the second leg first, and then the prior leg of the journey. You know most of the relevant numbers from the posts above, such as how fast is twin A is moving relative to this frame, and how long (his clock) it takes him to do it. Start with that. All you need is the one formula (which involves a square root, scary...), and the rest can be done with a 4-function calculator.
Is A inertial?
A is moving at constant velocity for the duration of the exercise, so yes, A is inertial. Sure, there is acceleration at one end or both, but no duration is spent at those alternate velocities, so those zero-duration periods are irrelevant to what the respective clocks (ages) say when compared at the reunion event.
Should we calculate the Doppler effect to get the correct answer?
Doppler effect only concerns a perspective, a point of view, but not a frame since a point of view is frame independent. What a particular observer sees cannot be calculated until you know what is, and if you already know what is, the correct answer is already in your hands.
So no. Computing Doppler (or worrying about observers at all) is useless for this exercise. Use the techniques shown above. Use the values you already know and it is simple to figure the missing ones. The only formula needed is the one given. Ditch the fact that there are twins at all and just assume clocks are taking the trips indicated, on ships with no windows while we're at it.
Would it make a difference whether those twins stop at the end of the journey, or continue going at their travelling velocity, or turn around to return to the earth, as measured by earth observer?
Nothing you do at a given moment in time can effect what your own clock says at that moment in time. In fact, I said above that time dilation is all about speed relative to a specific frame, so accelerations don't matter anywhere. All that matters is that you pick a frame and figure out the speed of each clock in that frame, and for how long it travels at that speed. The one formula that is needed (quoted several times above) takes speed as an input, and makes no reference to acceleration.
So no, any acceleration done at the final event cannot effect the comparison of ages(times on the clocks) in each other's presence at the reuniting event. One cannot make a clock jump in time except by just setting it to a different value, such as I need to do on my microwave every time I get a power glitch.
Similarly, one's future plans (say a trip back to Earth or not) cannot effect the result of a comparison at a given event. If it did, that would be backwards causality.
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Nothing you do at a given moment in time can effect what your own clock says at that moment in time.
Can it change what a relatively moving observer see on our accelerating clock?
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All that matters is that you pick a frame and figure out the speed of each clock in that frame, and for how long it travels at that speed. The one formula that is needed (quoted several times above) takes speed as an input, and makes no reference to acceleration.
Change of reference frame requires acceleration. It's the cause of asymmetric time dilation in twins paradox.
Without it, no twin can conclude that the other twin is older than himself.
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No. The acceleration is irrelevant other than providing the SPEED at which relativistic effects occur.
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No. The acceleration is irrelevant other than providing the SPEED at which relativistic effects occur.
You're saying no, except yes.
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Halc kindly did the calculation for you and the method he used gives any answer you could possibly need. Acceleration does not occur in the equation he used and is irrelevant.
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Nothing you do at a given moment in time can effect what your own clock says at that moment in time.
Can it change what a relatively moving observer see on our accelerating clock?
No. Change requires time, not acceleration.
All that matters is that you pick a frame and figure out the speed of each clock in that frame, and for how long it travels at that speed. The one formula that is needed (quoted several times above) takes speed as an input, and makes no reference to acceleration.
Change of reference frame requires acceleration.
I said no such thing. If you're going to ignore my posts, then fine. The effort seems unproductive.
A reference frame is a mental abstraction, the assignment of coordinates to events, nothing more. I can change that abstraction any time I want without acceleration. For instance, when driving in my car, I tend to use the rotating frame of the road under me when considering navigation, speed limits, and such. But when I reach for my coffee in the cup holder, I immediately change reference frames to that of the car since that is the most pragmatic frame for the task. That change of reference frame required no acceleration at all.
It's the cause of asymmetric time dilation in twins paradox.
Time dilation is perfectly symmetric in flat spacetime, so that cannot be 'the cause'. The simplest 'cause' of dilation in flat spacetime is speed relative to a specific inertial frame. That's it. The formula I gave makes no mention of acceleration, so it can be entirely dismissed. Doing it via acceleration works, but is vastly more complicated.
Without it, no twin can conclude that the other twin is older than himself.
This is also incorrect since the conclusion is abstract (mental, not physical) unless they are in each other's presence, in which case it is called 'differential aging', which is the unequal comparison of clocks physically in each other's presence.
The acceleration is irrelevant other than providing the SPEED at which relativistic effects occur.
Exactly.
This topic seems unproductive since the OP refuses to actually accept any of the answers. I might still answer some if they show otherwise.
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Halc kindly did the calculation for you and the method he used gives any answer you could possibly need. Acceleration does not occur in the equation he used and is irrelevant.
We can easily remove any parameter from equations. The problem is do they still give the correct answer?
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This is also incorrect since the conclusion is abstract (mental, not physical) unless they are in each other's presence, in which case it is called 'differential aging', which is the unequal comparison of clocks physically in each other's presence.
Do you mean that A's clock will be equal to B's clock at the destination point?
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Yes, one can remove any parameter from any equation. However, the equation then loses it's integrity and any answers obtained will be utterly meaningless.
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Yes, one can remove any parameter from any equation. However, the equation then loses it's integrity and any answers obtained will be utterly meaningless.
Without acceleration, A and B's observations should be symmetrical.
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In your initial query you specified a speed of 40% the speed of light. Obviously acceleration is needed to achieve these speeds but acceleration does NOT figure in the subsequent calculation. This has been explained to you several times and at this point I give up-i'm out.
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In your initial query you specified a speed of 40% the speed of light. Obviously acceleration is needed to achieve these speeds but acceleration does NOT figure in the subsequent calculation. This has been explained to you several times and at this point I give up-i'm out.
The problem in discussion on special theory of relativity is many people thinking different things as if they are the same.
Here is the problem statement.
This is a slightly modified twin paradox to distinguish the effects of relative speeds and acceleration.
Twin A started a journey to Alpha Centauri 4 light years away in a space ship moving at 0.4c. He is expected to arrive 10 years later, according to earth observer.
Twin B stayed home to improve the space ship, so he can go to Alpha Centauri 5 years later at 0.8 c.
Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously. Does special theory of relativity predict the same?
How old are they when they meet up at Alpha Centauri?
There are three observers here: earth observer, twin A, and twin B. The only observer stays in his frame of reference is the earth. A and B accelerate once. They are seperated for a while, but eventually reunite.
Most people have no difficulty in using earth earth reference frame to calculate relativistic effects. But they start to disagree when they are asked to make the calculation from the travelling twin's frame of reference.
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For sanity check, we can add other twins C and D with similar journey to twin B. They make journey from earth to Alpha Centauri at 0.8c. Only starting time is different. C started the journey at the same time as A, and then wait on Alpha Centauri until meeting time with A. D starts the journey 2.5 years after A and C left, and then wait on Alpha Centauri until meeting time. B, C, and D should have the same age when A arrives at the destination point.
A should also get the same results when they are calculated in his frame of reference.
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Most people have no difficulty in using earth earth reference frame to calculate relativistic effects. But they start to disagree when they are asked to make the calculation from the travelling twin's frame of reference.
People who have even a basic understanding of relativity don't disagree.
For sanity check,
Why do you need a sanity check?
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People who have even a basic understanding of relativity don't disagree.
Are you sure? Do you know that Einstein himself changed his mind several times on this issue?
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Why do you need a sanity check?
To make sure the consistency of our arguments and assumptions.
According to A, twin B and C only change their frame of reference once. While D has to change twice. Yet, symmetry requires that all of them have the same age.
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Are you sure?
Yes.
You received the correct answer to your question, so I don't really understand where your confusion is coming from.
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According to A, twin B and C only change their frame of reference once.
I don't understand your confusion, especially since it is your scenario.
You should stop referring to inertial frames as frames of reference, using the wrong terminology can lead to additional confusion.
In your scenario twin A starts in the earths inertial frame and then accelerates to a new inertial frame. He then decelerates to Alpha Centauri's inertial frame, so in your example there are 2 inertial frame changes. Twin B does exactly the same number of inertial frame changes. Observer A, B and C all agree on the number of changes in inertial frames of A and B.
I am not going to address observer D since this was not part of the original scenario, it is unnecessary and it only is going to cloud the issue.
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Are you sure?
Yes.
You received the correct answer to your question, so I don't really understand where your confusion is coming from.
What makes you think that they are correct?
The confusion comes from asymmetrical results produced by symmetrical situations.
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In your scenario twin A starts in the earths inertial frame and then accelerates to a new inertial frame. He then decelerates to Alpha Centauri's inertial frame, so in your example there are 2 inertial frame changes. Twin B does exactly the same number of inertial frame changes. Observer A, B and C all agree on the number of changes in inertial frames of A and B.
I am not going to address observer D since this was not part of the original scenario, it is unnecessary and it only is going to cloud the issue.
So, you are not confused if the problem can be simplified to 0 or 1 inertial frame change, but you start to get confused with 2 or more inertial frame changes. Cmiiw.
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What makes you think that they are correct?
Because the answers are derived from the equations of special relativity which have been shown to always agree with observation and experimentation.
The confusion comes from asymmetrical results produced by symmetrical situations.
If this confuses you, I suggest that you research special relativity. There are several very good online courses that are free. These are real course from colleges like Stanford and MIT.
So, you are not confused if the problem can be simplified to 0 or 1 inertial frame change, but you start to get confused with 2 or more inertial frame changes.
No, your scenario is a very straight forward relativity problem and not confusing at all. You are the one that is claiming this is confusing and unclear. So just let me repeat; the correct answers were given in reply #1 and reply #3.
Do you agree that these answers are correct or do you see a problem with the answers?
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No, your scenario is a very straight forward relativity problem and not confusing at all. You are the one that is claiming this is confusing and unclear. So just let me repeat; the correct answers were given in reply #1 and reply #3.
Do you agree that these answers are correct or do you see a problem with the answers?
You don't seem to understand the core problem in twin paradox situations. Time dilation observed by a relatively moving observer is just half of the problem. The other half is asymmetrical results between the twins, which means that one of them will observe time contraction of the other twin, instead of time dilation. It's the cause of this supposed asymmetry which created disagreement among physicists.
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You don't seem to understand the core problem in twin paradox situations. Time dilation observed by a relatively moving observer is just half of the problem. The other half is asymmetrical results between the twins, which means that one of them will observe time contraction of the other twin, instead of time dilation. It's the cause of this supposed asymmetry which created disagreement among physicists.
I do understand the core issue that makes it appear to be a paradox. But it's not actually a paradox and there is no disagreement between physicists. The asymmetry is due to one twin changing reference frames. No confusion if you understand this.
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The asymmetry is due to one twin changing reference frames.
How much difference is caused by the changing reference frames?
Is it quantifiable?
Is there any other causes?
If there are more than one changes of reference frames, what difference do those extra changes cause?
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How much difference is caused by the changing reference frames?
Reread reply #1
Is it quantifiable?
Yes, reread reply #1.
Is there any other causes?
No.
If there are more than one changes of reference frames, what difference do those extra changes cause?
It seems you do not know what a inertial frame is. If something is moving at a velocity that is different than you, then it is in a different inertial frame.
In your example the twins left earth, this was the first change of inertial frame. The twins move at a constant velocity and then stop and meet up at Alpha Centauri, that is the second inertial frame change.
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How much difference is caused by the changing reference frames?
Reread reply #1
Is it quantifiable?
Yes, reread reply #1.
Is there any other causes?
No.
If there are more than one changes of reference frames, what difference do those extra changes cause?
It seems you do not know what a inertial frame is. If something is moving at a velocity that is different than you, then it is in a different inertial frame.
In your example the twins left earth, this was the first change of inertial frame. The twins move at a constant velocity and then stop and meet up at Alpha Centauri, that is the second inertial frame change.
You misunderstood my questions and Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"
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You misunderstood my questions and Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Sorry, I must be misremembering the questions and answers, I will go back and check.
No, I did not misremember, it is very clear that in the OP you asked 2 questions and reply #1 answered those questions.
Question 1: Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously. Does special theory of relativity predict the same?
Answer: Classical in what sense? Classical physics refers to non-quantum physics. I think you mean Newtonian physics, not classical. Yes, every theory (including Newtonian) says they get there simultaneously. This is an objective fact, true in any reference frame.
Question 2: How old are they when they meet up at Alpha Centauri?
Answer: As computed above, 9y2m and 8y respectively.
I did in fact understand your 2 questions which were quite clear. I also understand the answers Halc gave and I agree with those answers.
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Half way to what? No, he simply rides Earth for 5 of his years. λ=1.091 for 0.4c, remember? So that's going to take 5λ years in the frame we're using, which is 5.455 years. 5.455 years at 0.4c takes him 2.182 ly away from where he started, which isn't particularly halfway to anything.
It's may not be a critical issue, but Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.
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Sorry, I must be misremembering the questions and answers, I will go back and check.
No, I did not misremember, it is very clear that in the OP you asked 2 questions and reply #1 answered those questions.
Reply#1 answered time dilation experienced by twin A and B as observed/calculated by earth observer.
No paradox is found here, because it only described half of the story.
Reply#9 answered time dilation experienced by twin B as observed/calculated by twin A.
Here, twin A is treated as in a single inertial frame of reference.
Reply#15 is supposed to answer time dilation experienced by twin A as observed/calculated by twin B. But he refused to give numeric result, on the account that twin B switched his frame of reference.
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The video below tries to solve twin paradox using acceleration.
But this video below doesn't touch the paradox yet. It only describe time dilation observed by earth twin, without being bothered by travelling twin's perspective.
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Reply#1 answered time dilation experienced by twin A and B as observed/calculated by earth observer.
No paradox is found here, because it only described half of the story.
The answer is also as observed/calculated by the twins. You need to understand this part before moving on.
Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c.
This statement is incorrect. Twin A does not stay in his own constant inertial frame. He starts in earths frame, accelerates to the cruising frame then decelerates to Alpha Centauri's frame. Twin A knows that he is accelerating away from earth and it is not earth accelerating away from him. Twin A, twin B and the earth all agree that twin A is the one that accelerates.
The problem with your threads in general is you ask a question and receive an answer that you don't fully understand. Instead of asking questions to clarify the original answer you ask questions that further complicate the issue which then leads to more complications until you are so confused that you deduce no one understands anything. That ain't a good way to learn.
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This is also incorrect since the conclusion is abstract (mental, not physical) unless they are in each other's presence, in which case it is called 'differential aging', which is the unequal comparison of clocks physically in each other's presence.
Do you mean that A's clock will be equal to B's clock at the destination point?
No. 8y is not equal to 9y 2m. Why would you suggest otherwise?
So, you are not confused if the problem can be simplified to 0 or 1 inertial frame change, but you start to get confused with 2 or more inertial frame changes. Cmiiw.
As I said before, doing it via frame changes just adds complications, requiring multiple formulas, some of those being more complicated.
Using what I showed, no frame change is made ever. You pick just one and stick with it.
The confusion comes from asymmetrical results produced by symmetrical situations.
The situation was never symmentrical, and if it is (like the one in one of your recent threads), then the result is very much symmetrical. But adding more characters just adds more complications which is inadvisable if you cannot in any way understand even the simplest case.
How much difference is caused by the changing reference frames?
None actually, since a change of reference frame is a mental abstraction, not physical. A mental change doesn't in any way alter what actually happens.
The other half is asymmetrical results between the twins, which means that one of them will observe time contraction of the other twin, instead of time dilation.
There is no such thing as 'time contraction'. There is time dilation, but you speak of this time contraction as if it is something different.
t's the cause of this supposed asymmetry which created disagreement among physicists.
You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.
Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"
I didn't touch on a paradoxical part because there isn't one.
The misunderstanding can be best avoided if we avoid switching inertial frames altogether, as I suggested in post 1.It only leads to confusion if you don't understand how to do it right, and doing it right that way is considerably more complicated than sticking to one frame as I suggested.
Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.
I stand corrected on that one
Reply#15 is supposed to answer time dilation experienced by twin A as observed/calculated by twin B. But he refused to give numeric result, on the account that twin B switched his frame of reference.
I instead encouraged you to work it out yourself. Even an attempt with mistakes would have been a learning experience, and we could have helped. But you declined since apparently learning anything isn't your goal. Hence my not bothering to reply much anymore.
The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.
The video below tries to solve twin paradox using acceleration.
But this video below doesn't touch the paradox yet. It only describe time dilation observed by earth twin, without being bothered by travelling twin's perspective.
The first is a terrible video. It has many errors, such as asserting that they see each other age more slowly, which is only true when they watch each other recede. The twins scenario is not in any way about what anybody sees. Then they try to explain things via gravity which is utterly wrong. This is a special relativity scenario in which gravity is never taken into consideration.
The second video isn't much better. It say 'time slows down as you approach the speed of light'. That's just wrong. 'I move at nearly light speed relative to a muon created in the upper atmosphere. It doesn't make time slow down to me. He then attempts to reference an invalid frame of a light-like worldline, which is obfuscation at best, and wrong at worst. He never actually gets back to the twins after that.
There are good videos out there, but hunting down bad ones seems a favored pasttime to those that don't want to learn. Take the advice of other posters and find a good physics text if you actually want to learn this, which I suspect you don't. Stay away from you-tube, pop sites, and especially social media.
Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c.
This statement is incorrect. Twin A does not stay in his own constant inertial frame. He starts in earths frame, accelerates to the cruising frame then decelerates to Alpha Centauri's frame.
His statement is pretty much my words from post 9. The statement doesn't suggest that any planet undergoes any acceleration. I was talking about the frame in which A is stationary for the entire duration of the exercise. Everybody 'stays in' this frame since it is impossible to exit an inertial frame. To 'be in' a frame is simply to have valid and unique coordinates to your event in that frame. So acceleration doesn't necessarily cause a change of frame, since a frame is simply an abstract choice, and the simplest choice is to never switch frames. So the other players (planets, twin B) are still in this frame, they're just not stationary relative to it.
Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.
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Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.
I agree.
I am trying to help Hamdani understand this but it is very difficult because he asks question after question either ignoring or not understanding the answers. I have no idea if he even understood the original answer in reply #1.
It almost seems that his goal is to sow confusion, I doubt that is the actual goal but that seems to be what happens in all his posts.
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How does he know?
Twin A knows that he is accelerating away from earth and it is not earth accelerating away from him.
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The problem with your threads in general is you ask a question and receive an answer that you don't fully understand.
I received several different answers and tried to figure out which one is the most correct. Your problem is inability to distinguish them and think that they are the same. You can't come up with a solution if you can't even identify the problem in the first place.
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How does he know?
I assume you are asking how does the twin know he is the one accelerating. So again we are moving even farther away from the original question which I am not sure you ever understood the answer.
All inertial observers agree the twin is the one accelerating since acceleration is absolute. Or to put it more simply the twin can feel himself accelerate or he can read an accelerometer telling him he is accelerating.
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acceleration is absolute.
Where did you get that from?
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I received several different answers
The answers seem consistent to me. I think you may only be happy when your confused.
You cannot learn special relativity on a forum. As I suggested earlier if you really want to understand SR, look up "SR Stanford" or "SR Yale" on Youtube, both are quite good overviews.
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No. 8y is not equal to 9y 2m. Why would you suggest otherwise?
What does this mean?
the conclusion is abstract (mental, not physical)
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There is no such thing as 'time contraction'. There is time dilation, but you speak of this time contraction as if it is something different.
Twin A finds twin B as younger than himself, hence he says that B experience time dilation.
On the other hand, Twin B finds twin A as older than himself, hence he says that A experience time contraction.
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acceleration is absolute.
Where did you get that from?
Physics...
Here is a link from the University of California https://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html#:~:text=Velocities%20are%20relative%20but%20acceleration,space%2Dtime%20is%20always%20flat. (https://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html#:~:text=Velocities%20are%20relative%20but%20acceleration,space%2Dtime%20is%20always%20flat.)
From the link:
Velocities are relative but acceleration is treated as absolute. In general relativity all motion is relative. To accommodate this change, general relativity has to use curved space-time. In special relativity space-time is always flat.
If you want to discuss your original question I am willing to do that but I am done with you dragging this discussion "into the weeds".
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The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.
What does it mean, unambiguously?
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You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.
Not just a different way, but different interpretation of the cause.
Lorentz' relativity interpretes time dilation is caused by relative motion against stationary aether. Thus no paradox is generated. Clocks stationary to the aether tick the fastest.
Einstein's 1905 Relativity dismissed aether, hence the paradox came up. Since there is no more universal reference, it's no longer clear which clock ticks faster.
Einstein's 1921 relativity reintroduced aether, with some modifications. It no longer carries some physical characteristics. It was then renamed to space-time continuum.
It seems like not many of us are aware of those distinction. But we can't just erase history of science.
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What does it mean, unambiguously?
What about Halc's answer did you find ambiguous?
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Twin A finds twin B as younger than himself, hence he says that B experience time dilation.
No. While in relative motion they both consider/know that time is slow for the other. That's what is called "Time dilation".
And it goes both ways - it's reciprocal. After all, that is what puts "paradox" in "twins' paradox". (But to be clear, it's not actually a paradox, there's is no argument about that. The term comes from a naive partial understanding.)
On the other hand, Twin B finds twin A as older than himself, hence he says that A experience time contraction.
That one turns out a different age than the other is usually called "differential aging".
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As I said before, doing it via frame changes just adds complications, requiring multiple formulas, some of those being more complicated.
Using what I showed, no frame change is made ever. You pick just one and stick with it.
If you dismiss frame changes, you should get reciprocal time dilation. And there will be nothing to tell which twin is the younger when they reunite.
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The situation was never symmentrical, and if it is (like the one in one of your recent threads), then the result is very much symmetrical. But adding more characters just adds more complications which is inadvisable if you cannot in any way understand even the simplest case.
I'll get to the symmetrical version of this problem later, after we sort out some of current scenario at hand.
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I didn't touch on a paradoxical part because there isn't one.
The misunderstanding can be best avoided if we avoid switching inertial frames altogether, as I suggested in post 1.It only leads to confusion if you don't understand how to do it right, and doing it right that way is considerably more complicated than sticking to one frame as I suggested.
I just want to know how to do it right, and what makes it hard to explain.
STR requires that all inertial frames are equally valid frame of reference. Let's see if it can be satisfied. If you dismiss it, you are no longer using STR.
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The first is a terrible video. It has many errors, such as asserting that they see each other age more slowly, which is only true when they watch each other recede. The twins scenario is not in any way about what anybody sees. Then they try to explain things via gravity which is utterly wrong. This is a special relativity scenario in which gravity is never taken into consideration.
Minutephysics' video also depicts both twins see each other age more slowly during constant velocity motion. Only when the travelling twin turns around, he sees the staying twin ages much faster. He mentions acceleration as the cause, instead of gravity. But GR says they are equivalent.
Then on returning leg, travelling twin sees staying twin to age more slowly again.
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The second video isn't much better. It say 'time slows down as you approach the speed of light'. That's just wrong. 'I move at nearly light speed relative to a muon created in the upper atmosphere. It doesn't make time slow down to me. He then attempts to reference an invalid frame of a light-like worldline, which is obfuscation at best, and wrong at worst. He never actually gets back to the twins after that.
He is one of the most famous astrophysicist and science communicator at present. If even he fails to get it right, it's no wonder that many others also fail.
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There are good videos out there, but hunting down bad ones seems a favored pasttime to those that don't want to learn. Take the advice of other posters and find a good physics text if you actually want to learn this, which I suspect you don't. Stay away from you-tube, pop sites, and especially social media.
The format of the information source should not prevent the content to be delivered correctly. IMO, the video format is much richer than paper printout for its ability to show motion and audio information simultaneously. Interactive video/simulation would be better.
If you think there are good videos, you can just put the link here, so we can compare with the bad ones and analyze what makes them better.
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Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.
I agree.
I am trying to help Hamdani understand this but it is very difficult because he asks question after question either ignoring or not understanding the answers. I have no idea if he even understood the original answer in reply #1.
It almost seems that his goal is to sow confusion, I doubt that is the actual goal but that seems to be what happens in all his posts.
You agree with Halc, but disagree with me, even when what we say is the same thing. It seems like you are the one who's confused.
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Ignoring, yes. Understanding seems not to be his goal, and most can see that and simply stop responding to the brick wall.
I chimed in because we all this talk of acceleration requiring a change of frames was running contrary to my suggestion to keep things simple and never choose to switch frames. Hamdani pays enough attention to notice when we give non-unified answers. So his goal is perhaps to find the differences between the ways different people correctly approach the same problem, and then spin those differences as contradictory, which they are of course not.
Without frame switching, both twins are equally valid observers, and there would be no physical age difference between the twins. The discrepancy in observed age would be fully covered by relativity of simultaneity.
Professional physicists commonly say that it's the frame switching which causes the age difference. Some say that it's the same as acceleration, while some other say that acceleration is not necessary, hence treating frame switching differently than acceleration.
Some critics of STR say that the confusion is caused by many supporters of STR have their own versions of the theory which are incompatible with one another, but claim that they are the standard STR.
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As I said, his goal doesn't seem to be to give the appearance of understanding anything.
Understanding how nature works accurately is an instrumental goal to achieve the universal terminal goal.
I'll just let ideas to come up, and then let natural selection to do its job. Shutting down ideas prematurely can prevent us from getting the correct answer. We need reasons to accept or reject ideas.
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Possibly there's some talking past each other in regards to "frame switching".
You are right (in short) that the explanation of the (not) paradox is that the scenario is not symmetrical, the reason for that being one observer remaining in a single frame, and the other not. *
But there's another kind of "frame switching" ... someone trying to analyse the thought experiment who willy-nilly flips from frame to frame (Alice, Bob going, Bob returning ...) without rigour and confusing themselves and everyone reading their words.
(* I prefer the triplet version: B passes A, later C passes B, back towards and eventually passing A. Nobody accelerates ever. Makes it clearer, I think, especially in the "frame switching" sense.)
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You agree with Halc, but disagree with me, even when what we say is the same thing
When did I do that?
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You agree with Halc, but disagree with me, even when what we say is the same thing
When did I do that?
This statement is incorrect. Twin A does not stay in his own constant inertial frame.
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I asked Google Bard about Twins Paradox.
What is the twin paradox?
The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.
The paradox centers on the contention that, in relativity, either twin could regard the other as the traveler, in which case each should find the other younger?a logical contradiction. This contention assumes that the twins' situations are symmetrical and interchangeable, an assumption that is not correct.
The key to understanding the twin paradox is to realize that the twins' situations are not symmetrical. The traveling twin undergoes acceleration during the turnaround phase of the journey, while the stay-at-home twin does not. This asymmetry is what allows for the difference in aging.
Another way to think about it is that the traveling twin's worldline is not a straight line in spacetime, but rather a curved line. The stay-at-home twin's worldline, on the other hand, is a straight line. This difference in worldlines is what accounts for the difference in aging.
The twin paradox has been experimentally verified using atomic clocks. In one experiment, two atomic clocks were synchronized and then one was flown around the Earth on a jet aircraft. When the clock was returned, it was found to have lost a tiny fraction of a second. This was due to the time dilation effect predicted by special relativity.
The twin paradox is a fascinating example of how special relativity can lead to counterintuitive results. It is also a reminder that the universe is not as simple as it seems.
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Quote from: Origin on Today at 05:09:24
Quote from: hamdani yusuf on Today at 03:16:06
You agree with Halc, but disagree with me, even when what we say is the same thing
When did I do that?
Quote from: Origin on Yesterday at 13:19:58
This statement is incorrect. Twin A does not stay in his own constant inertial frame.
Halc pointed out that what I said was incorrect. I was agreeing with him.
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You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.
Not just a different way, but different interpretation of the cause.
But one interpretation of 'the cause' doesn't invalidate any of the others. Personally I don't think there is a cause. Asking for one is like asking what causes a table to be longer than it is wide. It is perhaps caused by which dimension one decides to designate as the length.
Lorentz' relativity interpretes time dilation is caused by relative motion against stationary aether. Thus no paradox is generated.
But that's pretty much the answer I gave in post 1, except without the aether, which has no method of detection. Instead there is just a preferred frame. You choose one, and exactly like the Lorentz case, no paradox is generated.
Einstein's 1905 Relativity dismissed aether ...
Since there is no more universal reference, it's no longer clear which clock ticks faster.
Nobody ever claimed that a clock ticked faster. Your problem for suggesting otherwise, but don't blame relativity theory when making such a blunder.
Einstein's 1921 relativity reintroduced aether, with some modifications. It no longer carries some physical characteristics. It was then renamed to space-time continuum.
'Spacetime' was coined by Minkowski in 1908. Einstein never wrote the term "space-time continuum:, which seems to be a pop term introduced as early as 1930 in a fiction story. I am unaware of a physics paper that uses the term ever, but if you have a quote from Einstein, that would really help illustrate that you're not just making up your own facts. And no, he never reintroduced aether either, but GR does introduce a preferred (non-inertial) frame relative to which cosmological time (adjusted for potential) is constant at simultaneous events, something that can be measured since cosmological time is an empirical measurement. None of that has anything to do with a proposal of a medium through which light travels.
If you dismiss frame changes
Nowhere do I dismiss them. I just said that computations are more complex if you choose to do them. Please try to actually read what I say and not make up your own crank story about what you hoped I said. The computation in posts 1 and 9 did no frame changes, and they both arrived at the same answer of 8 and 9 1/6 and they did it with only the one equation instead of several that would have been required to do the same thing with frame changes.
I just want to know how to do it right
This is very apparently a lie. If you wanted to know how to do it, there are many correct ways to do so, but I illustrated probably the easiest way. I invited you to work out yourself how to do it in the frame of the B's 2nd leg. That's how you learn, by doing, or at least attempting. You declined. You show no indication of wanting to learn how to do it, so the above statement is false.
It is this obvious lack of desire to learn that makes myself and other ignore the majority of any of your posts.
Prove me wrong and attempt the calculation using the 3rd frame and the numbers already provided in posts 1 & 9.
STR requires that all inertial frames are equally valid frame of reference.
That it does, but it doesn't say you are required to use them all. You can if you want, but it's a lot more work since transformations are required every time you change frames.
Minutephysics' video also depicts both twins see each other age more slowly during constant velocity motion. Only when the travelling twin turns around, he sees the staying twin ages much faster.
If it doesn't say that each of them sees the other twin age faster when approaching, then the video is wrong.
An explanation based on what people see is not wrong, but again, more complicated than this simple situation needs to be. You again need more than one formula to get the correct answers.
He mentions acceleration as the cause, instead of gravity. But GR says they are equivalent.
This is wrong, and the video is wrong if it says this. GR says the two are equivalent only locally, not over any significant distance. The two are very distinguishable over distance.
The problem with using videos for education is so many of the videos have no peer review.
The format of the information source should not prevent the content to be delivered correctly.
No, it shouldn't, but only peer review helps ensure the content is correct, and almost no video undergoes such review. I've pointed out blatant errors in videos by very respected, famous and popular authors.
If you think there are good videos, you can just put the link here
I've never had the time to search for good ones, and I've never chosen any to do the actual learning.
Watch out for any video that claims to be the one correct way to explain the situation.
Without frame switching, both twins are equally valid observers
First of all, it is you that needs to do frame switching or not, not the twins, who require no more intelligence than the ability to read the clock that's strapped to their wrist.
Secondly, all people and devices for that matter are valid observers. Frame switching doesn't somehow cancel the ability of a thing to make a measurement, but in the twins scenario, the only measurement is the local consultation of one's watch. There are other scenarios where actual observation beyond clock watching is necessary, but the twins scenario doesn't require observers at all. It can be (and has been) done by just zooming clocks around without people serving any purpose other than that of a courier.
confusion is caused by many supporters of STR have their own versions of the theory which are incompatible with one another, but claim that they are the standard STR.
There is one STR, and it is mathematically perfect, meaning it cannot be falsified from an armchair, only by empirical means. If somebody actaully alters the theory, that person is wrong, but most just convey the concepts in different ways. I've seen no wrong replies to you for instance. You're the only one making blatantly incorrect assertions.
I asked Google Bard about Twins Paradox.
Should be entertaining since it, like chatGPT, uses all the disinformation online as part of its training material. I would never trust an answer from a chatbot.
What is the twin paradox?
Bad start. You didn't ask about your scenario specifically (asking it for the ages at the end of your experiment in the OP, nor did you ask it about 'the cause' of the differential aging. So you're now asking a far more generic question. But you're in luck since it does directly attribute the potential differential aging to asymmetry, and the asymmetry to non-symmetric acceleration. So the answer is actually quite good this time. It says that asymmetry 'allows for' differential aging, but correctly doesn't go so far as to say it causes it, since there are plenty of asymmetric situations where there is no differential aging.
Another way to think about it is that the traveling twin's worldline is not a straight line in spacetime, but rather a curved line. The stay-at-home twin's worldline, on the other hand, is a straight line. This difference in worldlines is what accounts for the difference in aging.
This is quite close to the explanation I gave in the 'what is the cause' topic that has so many of your posts.
This answer is less intuitive and more complicated, but also more generic (can be applied to any situation), something not true of the first explanation.
The twin paradox has been experimentally verified using atomic clocks. In one experiment, two atomic clocks were synchronized and then one was flown around the Earth on a jet aircraft. When the clock was returned, it was found to have lost a tiny fraction of a second. This was due to the time dilation effect predicted by special relativity.
This part is a little off, since GR was needed to predict the results. The entire experiment took place at various altitudes in a gravity well. SR was not up to making any prediction better than the fact that the westbound clock would accrue more time than the eastbound one.
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But one interpretation of 'the cause' doesn't invalidate any of the others. Personally I don't think there is a cause. Asking for one is like asking what causes a table to be longer than it is wide. It is perhaps caused by which dimension one decides to designate as the length.
The cause is how people commonly define length and width.
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Quote from: Origin on Today at 05:09:24
Quote from: hamdani yusuf on Today at 03:16:06
You agree with Halc, but disagree with me, even when what we say is the same thing
When did I do that?
Quote from: Origin on Yesterday at 13:19:58
This statement is incorrect. Twin A does not stay in his own constant inertial frame.
Halc pointed out that what I said was incorrect. I was agreeing with him.
The statement you said to be incorrect is Halc's statement which I paraphrased. Which means you didn't agree with him.
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And no, he never reintroduced aether either,
He used the word ether in his lecture in 1920. You can't just deny history.
"According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time"
He just modify some of its characteristics to comply with known experimental results.
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GR says the two are equivalent only locally, not over any significant distance.
How much distance is considered significant?
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This is wrong, and the video is wrong if it says this. GR says the two are equivalent only locally, not over any significant distance. The two are very distinguishable over distance.
The problem with using videos for education is so many of the videos have no peer review.
I've never had the time to search for good ones, and I've never chosen any to do the actual learning.
Watch out for any video that claims to be the one correct way to explain the situation.
It seems like the confusion is more common than what we think.
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It seems like the confusion is more common than what we think.
Just in the popsci world. As I said before if you want to learn the physics relativity go to a university site that has open courseware and do the course.
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I've never had the time to search for good ones, and I've never chosen any to do the actual learning.
Watch out for any video that claims to be the one correct way to explain the situation.
How could you say this previously?
There are good videos out there, but hunting down bad ones seems a favored pasttime to those that don't want to learn. Take the advice of other posters and find a good physics text if you actually want to learn this, which I suspect you don't. Stay away from you-tube, pop sites, and especially social media.
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It seems like the confusion is more common than what we think.
Just in the popsci world. As I said before if you want to learn the physics relativity go to a university site that has open courseware and do the course.
Do you mean like this one?
It shows that time dilation is reciprocal, until the switch of reference frame. The explanation is similar to Minutephysic's video.
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nor did you ask it about 'the cause' of the differential aging.
I asked about it as well, but the answer is even worse. It doesn't explain why the travelling twin can't just think that he is the stationary one, while the earth twin is the one in motion.
The twins age differently because of a phenomenon called time dilation. Time dilation is a consequence of special relativity, which is a theory of physics that describes how space and time are interwoven and how they are affected by the motion of objects.
According to special relativity, time passes more slowly for objects that are moving at high speeds. This is because the faster an object moves, the more its length is contracted and the more its time is dilated.
In the twin paradox, the traveling twin is moving at a high speed relative to the stay-at-home twin. This means that the traveling twin's time will pass more slowly than the stay-at-home twin's time. As a result, when the traveling twin returns to Earth, they will have aged less than the stay-at-home twin.
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If it doesn't say that each of them sees the other twin age faster when approaching, then the video is wrong.
The video from MIT Opencourseware doesn't say that.
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I also asked this to Google Bard.
what makes earth twin age faster than travelling twin, when we analyze from travelling twin's frame of reference?
From the traveling twin's frame of reference, the Earth twin appears to be accelerating during the turnaround phase of the journey. This is because the Earth twin is moving relative to the traveling twin, and the traveling twin sees the Earth twin as changing its direction of motion.
Acceleration breaks the symmetry of the situation. The traveling twin does not accelerate during the turnaround phase, while the Earth twin does. This asymmetry is what allows for the difference in aging.
Another way to think about it is that the Earth twin's worldline is not a straight line in spacetime, but rather a curved line. The traveling twin's worldline, on the other hand, is a straight line. This difference in worldlines is what accounts for the difference in aging.
The traveling twin can use this asymmetry to explain why the Earth twin has aged more. They can argue that the Earth twin's acceleration has caused their time to run faster.
This explanation is consistent with special relativity. Special relativity allows for different observers to measure different amounts of time for the same event, depending on their relative motion.
It is important to note that the traveling twin's explanation is not the only possible explanation for the difference in aging. The Earth twin can also give an explanation from their own frame of reference. They can argue that the traveling twin's time has run slower because they have been moving at a high speed.
Both explanations are valid, and they are both consistent with special relativity. The key to understanding the twin paradox is to realize that the twins' situations are not symmetrical. The traveling twin undergoes acceleration during the turnaround phase of the journey, while the stay-at-home twin does not. This asymmetry is what allows for the difference in aging.
The boldened sentence raises a question. Does acceleration cause an object's time to speed up or slow down instead?
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The questions and answers quoted below are by Google Bard itself, as additional information when I asked what makes travelling twin age slower than earth twin, when we analyze from earth twin's frame of reference?
From the Earth twin's frame of reference, the traveling twin is moving at a high speed relative to them. According to special relativity, time passes more slowly for objects that are moving at high speeds. This is called time dilation.
Therefore, the Earth twin will observe that the traveling twin has aged less than them when they return to Earth. This is because the traveling twin's time has been dilated due to their high speed of motion.
The amount of time dilation that occurs depends on the speed of the object and the distance that it travels. For example, if the traveling twin travels at half the speed of light for 10 years, they will have aged only 5 years when they return to Earth.
Why does the traveling twin not experience time dilation from their own frame of reference?
This is a common question, and the answer is that the traveling twin does not experience time dilation from their own frame of reference because they are not accelerating. Acceleration breaks the symmetry of the situation, and it is what allows for the difference in aging between the twins.
The traveling twin is moving at a constant speed for the majority of their journey. It is only during the turnaround phase of the journey that they accelerate. However, this acceleration is enough to break the symmetry and cause the traveling twin to age less than the Earth twin.
How to explain this to the traveling twin?
The Earth twin can explain to the traveling twin that their time has been dilated due to their high speed of motion. They can also explain that the traveling twin does not experience time dilation from their own frame of reference because they are not accelerating.
The traveling twin may find this explanation difficult to believe, because they will feel like they have experienced the same amount of time as the Earth twin. However, this is due to the effects of special relativity.
The traveling twin can verify the Earth twin's explanation by comparing their clocks to the clocks on Earth. They will find that their clocks have fallen behind the clocks on Earth. This is due to the time dilation effect.
The twin paradox is a challenging concept to understand, but it is an important one in special relativity. It demonstrates that time is not absolute, but rather relative to the observer's frame of reference.
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I asked Bard, has Michelson-Morley experiment been replicated in ISS?
To the best of my knowledge, the Michelson-Morley experiment has not been replicated on the International Space Station (ISS). This is likely because the experiment is quite complex and requires a very stable platform to be successful. The ISS is in a microgravity environment, which can make it difficult to achieve the stability required for the experiment.
However, there have been other experiments conducted on the ISS that have tested the Michelson-Morley hypothesis. For example, in 2009, scientists conducted an experiment using optical resonators that confirmed the absence of any aether wind at the 10−17 level.
The Michelson-Morley experiment was a landmark experiment that helped to pave the way for Einstein's theory of special relativity. The experiment showed that the speed of light is the same for all observers, regardless of their motion. This result was unexpected at the time, and it led to a fundamental shift in our understanding of space and time.
Despite the fact that the Michelson-Morley experiment has not been replicated on the ISS, the results of the experiment have been replicated many times on Earth. These results have been confirmed with ever-increasing precision, and they provide strong evidence for the validity of special relativity.
I find that the underlined statement is rather odd.
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There is one STR, and it is mathematically perfect, meaning it cannot be falsified from an armchair, only by empirical means. If somebody actaully alters the theory, that person is wrong, but most just convey the concepts in different ways. I've seen no wrong replies to you for instance. You're the only one making blatantly incorrect assertions.
Which assertions are incorrect? What are the correct ones?
https://www.quora.com/Why-did-Einstein-write-Since-the-mathematicians-have-invaded-the-theory-of-relativity-I-do-not-understand-it-myself-anymore-After-all-GR-relies-heavily-on-mathematics
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I asked Bard, has Michelson-Morley experiment been replicated in ISS?
If you ask a chat bot a question, it will chat with you, what it chats about may or may not be true, it's just chatting.
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The video from MIT Opencourseware doesn't say that.
I guess the lecture wasn't discussing the doppler effect then, was it.
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I asked Bard, has Michelson-Morley experiment been replicated in ISS?
If you ask a chat bot a question, it will chat with you, what it chats about may or may not be true, it's just chatting.
Do you have any source refuting Bard's answer?
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The video from MIT Opencourseware doesn't say that.
I guess the lecture wasn't discussing the doppler effect then, was it.
The lecture was discussing twin paradox. The lecturer didn't think that doppler effect was necessary to explain it.
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The lecture was discussing twin paradox. The lecturer didn't think that doppler effect was necessary to explain it.
It isn't. It is necessary to consider the doppler effect to answer some of your questions though.
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The lecture was discussing twin paradox. The lecturer didn't think that doppler effect was necessary to explain it.
It isn't. It is necessary to consider the doppler effect to answer some of your questions though.
Which one?
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there are plenty of asymmetric situations where there is no differential aging.
Can you show an example?
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Which one?
The questions involving what you see when one twin is moving towards you or away from you.
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Which one?
The questions involving what you see when one twin is moving towards you or away from you.
Is it from another thread?
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Is it from another thread?
No.
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Is it from another thread?
No.
Which post is it?
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The videos from Stanford are longer, but they also say that you haven't even described the problem yet until it's analyzed from traveling twin's perspective, let alone providing a possible solution.
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You are right (in short) that the explanation of the (not) paradox is that the scenario is not symmetrical, the reason for that being one observer remaining in a single frame, and the other not. *
In the scenario here, all travelling twins accelerate exactly once. They also decelerate exactly once.
The trajectories of twins B, C, and D have translational symmetry.
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That's an amazingly dishonest trimming of my post, which completely removes the point.
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That's an amazingly dishonest trimming of my post, which completely removes the point.
You should read the title of this thread.
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That's an amazingly dishonest trimming of my post, which completely removes the point.
You should read the title of this thread.
You should read the posts in the thread. (Including your own!)
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That's an amazingly dishonest trimming of my post, which completely removes the point.
You should read the title of this thread.
You should read the posts in the thread. (Including your own!)
What's the point you tried to make in your post?
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Here's the diagram in the perspective of stationary earth, midway, or Alpha Centauri.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34113)
The diagram was made in Power point.
The yellow square is 10x10 cm, which represent 10 years in vertical axis, and 10 light years in horizontal axis.
Red line represents light trajectory.
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The next diagram will describe the same events in A's perspective. It's done by rotating time, as explained in the video below.
The Twins Paradox Primer (Rotating TIME!)
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Here's the result.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34115;image)
The size of the yellow square is 9.165 cm, which represents the A's travel time in his own frame of reference, which is around 9.165 years.
Note that A meets D at the midway point at half way of his journey. A also arrive at Alpha Centauri at the same time as B.
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Here are the perspective of B, C, and D while they are travelling. The size of yellow squares are 3x3 cm, representing 3 years and 3 light years.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34117;image)
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34119;image)
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34121;image)
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Note that diagrams with rotated time preserve the Orthogonality of space-time axes of the earth and Alpha Centauri frame (see the midway arrow and dashed grey line connecting earth and Alpha Centauri). The closer the speed of travelling twin to the speed of light, the space-time axes of the stationary frame get closer to the light cone in the rotated space-time diagram.
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Here's the result.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34115;image)
The size of the yellow square is 9.165 cm, which represents the A's travel time in his own frame of reference, which is around 9.165 years.
Note that A meets D at the midway point at half way of his journey. A also arrive at Alpha Centauri at the same time as B.
According to A, both B and C switch their reference frame once, while D switchs twice. But they must have the same age, due to symmetry.
It means that each frame switch of D only produces half amount of age difference, compared to each frame switch of B or C. It also means that the age difference depends on the distance between the subject and the switching frame observer.
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(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=86510.0;attach=34117;image)
During the launch, twin B lit up a powerful flash light going everywhere spherically. According to B, the light will get to Alpha Centauri after twin C arrives there, but before twin D arrives there.
But according to observer on Alpha Centauri, the flash light will not be received before both C and D have arrived.
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So have you figured out it is not really a paradox?
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So have you figured out it is not really a paradox?
I don't think so. Have you?
If you are referring to my latest post, then at least one of the observers must be false. Do you know which one? Why is it?
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If you are referring to my latest post, then at least one of the observers must be false. Do you know which one? Why is it?
I'm not referring to any post in particular, I was just wondering if you have figured out that there is not really a paradox.
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If you are referring to my latest post, then at least one of the observers must be false. Do you know which one? Why is it?
I'm not referring to any post in particular, I was just wondering if you have figured out that there is not really a paradox.
Did you take it for a reason?
Or did you take it by faith?
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Did you take it for a reason?
Or did you take it by faith?
You are not very good at answering questions. I will assume you have not come to the conclusion that there is no real paradox.
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Did you take it for a reason?
Or did you take it by faith?
You are not very good at answering questions. I will assume you have not come to the conclusion that there is no real paradox.
You're too good at answering questions. You already knew the answer even before the question was properly described yet.
Unfortunately, you can't explain how you got that answer.
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Unfortunately, you can't explain how you got that answer.
It has been explained, you are resisting learning.
I believe every source you have cited here says the traveling twin is the one that ages more. That means none of your sources see a paradox, but for some reason you're not sure.
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Unfortunately, you can't explain how you got that answer.
It has been explained, you are resisting learning.
I believe every source you have cited here says the traveling twin is the one that ages more. That means none of your sources see a paradox, but for some reason you're not sure.
I discussed standard twin paradox problem in someone else's thread. Basically, the common explanations employ time rotation as explained by minutephysics' video. Videos from Harvard and MIT use similar explanation.
Here I want to test the generality of that explanation. Is it still useful to explain some varieties of the problem? Where's the boundaries that the explanation stops working?
Is it compatible with other physics principles that are widely accepted?
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Basically, the common explanations employ time rotation as explained by minutephysics' video. Videos from Harvard and MIT use similar explanation.
The time rotation thing lends itself nicely to video. It is hardly the simplest explanation, but it very much is a valid one.
But it needs to do a Lorentz rotation, not a Euclidean rotation like you're doing with all your pictures posted above. Those produce contradictory observations, as you have noted.
For instance, in your pictures in post 110, all the ships B,C,D age about 4.5 years, not 8. That's a contradiction since any observation (like everybody's age at the final event) should be a frame independent thing.
Here I want to test the generality of that explanation.
That explanation generalizes to any special relativity situtation, but not to any situation involving gravity. The more simple explanation I posted also applies only to SR, but in the other thread you mention I gave a geometric explanation that works in all cases, but is beyond your ability to learn.
Is it still useful to explain some varieties of the problem?
Again, so long as it doesn't involve gravity.
According to A, both B and C switch their reference frame once, while D switchs twice. But they must have the same age, due to symmetry.
Pretty strong evidence that it isn't acceleration (or frame changes as you call them) that causes the age differential. That's been said repeatedly, but you don't accept it. A ship could continuously stop and start, each time moving at 0.8c for a short time and then pausing again, hundreds of times before getting to the end. He'll age 8 years just like all the others except A who travels at a different speed than the others. It's about speed, and not at all about acceleration. I've said that from the beginning.
It also means that the age difference depends on the distance between the subject and the switching frame observer.
This statement is surprisingly correct. Similar to moment of inertia, the term is called moment-of-acceleration, where the effect is acceleration (in the direction of the 'subject') leveraged by the distance (as measured in the subject frame) to the acceleration event from the subject.
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The time rotation thing lends itself nicely to video. It is hardly the simplest explanation, but it very much is a valid one.
But it needs to do a Lorentz rotation, not a Euclidean rotation like you're doing with all your pictures posted above. Those produce contradictory observations, as you have noted.
For instance, in your pictures in post 110, all the ships B,C,D age about 4.5 years, not 8. That's a contradiction since any observation (like everybody's age at the final event) should be a frame independent thing.
My diagrams for B, C, D perspectives are only during their travelling period, which are 3 years. Non-travelling period are still 5 years.
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Pretty strong evidence that it isn't acceleration (or frame changes as you call them) that causes the age differential. That's been said repeatedly, but you don't accept it. A ship could continuously stop and start, each time moving at 0.8c for a short time and then pausing again, hundreds of times before getting to the end. He'll age 8 years just like all the others except A who travels at a different speed than the others. It's about speed, and not at all about acceleration. I've said that from the beginning.
Your explanation seem to employ absolute reference frame which can be used to measure speeds of other reference frames.
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Your explanation seem to employ absolute reference frame which can be used to measure speeds of other reference frames.
No where does he say or even imply an absolute reference frame. I'm at a loss to see where you came up with that idea.
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Your explanation seem to employ absolute reference frame which can be used to measure speeds of other reference frames.
No where does he say or even imply an absolute reference frame. I'm at a loss to see where you came up with that idea.
That's a logical implication of Lorentz' relativity theory, which differentiate it from Einstein's special relativity.
In Lorentz' relativity, A objectively ages less than earth observer or Alpha Centauri observer. A never measure/calculate earth/Alpha Centauri observers to age less than himself.
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Your post was indeed not particularly offensive since it for the most part contains frame references, but then the causal language starts creeping in and you start asserting that somebody's choices has a physical effect on somebody far away, which is very much 'another theory'.
That's what's described in the videos by Minutephysics, MIT OCW, and Stanford professor. Right BEFORE the turn around, the travelling twin measured that the earth twin is younger than him. Right AFTER the turn around, the travelling twin measured that the earth twin is older than him.
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That's what's described in the videos by Minutephysics, MIT OCW, and Harvard professor. Right BEFORE the turn around, the travelling twin measured that the earth twin is younger than him. Right AFTER the turn around, the travelling twin measured that the earth twin is older than him.
No video was referenced. Where is this asserted? What video, what timestamp?
In particular, exactly what measurement does the twin perform that lets him know this, all without presuming the answer to his measurement before he performs it? If the video does not mention a way to actually measure this, then the claim falls flat.
No where does he say or even imply an absolute reference frame. I'm at a loss to see where you came up with that idea.
That's a logical implication of Lorentz' relativity theory, which differentiate it from Einstein's special relativity.
Yes, LET has completely different premises than does SR, making it a different theory, or different interpretation at least. Funny thing is that the simplified method I explained at the beginning of this topic works in LET just as well as it does in SR. That's not true for most explanations.
As for 'the exact cause of the dilation' as the one topic asked, dilation isn't something that is caused. It can be explained by various methods, so there is no one correct explanation, and the existence of any one alternate explanation does not in any way invalidate the others. You seem bent on finding the most convoluted explanation out there, with bonus points if it's actually wrong.
In Lorentz' relativity, A objectively ages less than earth observer or Alpha Centauri observer. A never measure/calculate earth/Alpha Centauri observers to age less than himself.
All this is blatantly false. LET neither asserts nor concludes any of these things. I'm not saying LET is wrong. I'm only saying you are.
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Your post was indeed not particularly offensive since it for the most part contains frame references, but then the causal language starts creeping in and you start asserting that somebody's choices has a physical effect on somebody far away, which is very much 'another theory'.
That's what's described in the videos by Minutephysics, MIT OCW, and Harvard professor. Right BEFORE the turn around, the travelling twin measured that the earth twin is younger than him. Right AFTER the turn around, the travelling twin measured that the earth twin is older than him.
I'm sorry, it should be Stanford, instead of Harvard. But it should not change my points.
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No video was referenced. Where is this asserted? What video, what timestamp?
It's in the third video from Stanford professor, at around 9:00 time stamp.
The numeric values may be different, but the point is the same.
The videos from Stanford are longer, but they also say that you haven't even described the problem yet until it's analyzed from traveling twin's perspective, let alone providing a possible solution.
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As for 'the exact cause of the dilation' as the one topic asked, dilation isn't something that is caused.
It's not the cause of dilation that's asked. It's the cause of age difference. Why one twin's calculations are correct, while the other are false, when they move relative to each other without involving absolute frame of reference.
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All this is blatantly false. LET neither asserts nor concludes any of these things. I'm not saying LET is wrong. I'm only saying you are.
LET uses aether as frame of reference. Time dilation occurs in objects moving relative to it.
In the twin paradox case, earth and the destination star don't experience time dilation, which means they are stationary in the aether frame when analyzed using LET.
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In particular, exactly what measurement does the twin perform that lets him know this, all without presuming the answer to his measurement before he performs it? If the video does not mention a way to actually measure this, then the claim falls flat.
It's a thought experiment, hence every stated measurement is actually a calculation based on chosen model and assumptions.
It seems that your understanding of twin paradox is not mainstream among current physics community.
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It's the cause of age difference. Why one twin's calculations are correct, while the other are false, when they move relative to each other without involving absolute frame of reference.
That has been answered.
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It's the cause of age difference. Why one twin's calculations are correct, while the other are false, when they move relative to each other without involving absolute frame of reference.
That has been answered.
Do you agree with mike's answer from his thread?
[Mod edit: Topic split from https://www.thenakedscientists.com/forum/index.php?topic=86033
Please do not post personal relativity conjecture in the main sections of the forum]
The Twin "Paradox" is very simple to analyze. Here is how to do it:
The home twin is older that the traveling twin at their reunion. The home twin (she) is ALWAYS inertial, so she can immediately compute the traveling twin's (his) current age from the time dilation equation (TDE): she says his current age is equal to her current age, divided by gamma:
gamma = 1 / { sqrt [ 1 - ( v * v ) ] } .
For example, for v = +-0.866 ly/y, gamma = 2.0 .
So SHE says that, during his entire trip, he is always ageing half as fast as she is. So, in the case where he ages by 20 years on each of the two legs of his trip, she says that he is 40 at their reunion, and she is 80. And everyone must agree with that.
But how does HE describe their ages DURING the trip? He obviously has to agree with her about their respective ages at the reunion (because they are standing together right there, motionless, looking at each other). But what does HE say about their two ages at other times during his trip? Everyone DOES agree that he is 20 years old during his turnaround. But what does HE say about her age immediately BEFORE and immediately AFTER his turnaround?
He can also use the time dilation equation (TDE) immediately before his turnaround. From that, he concludes that, since he is 20 years old then, she is 10 years old then.
He also knows that, since he ages 20 years during his return trip, she must age 10 years during his return trip. So, if that were all that happens to her age during his trip (according to him), she would only be 20 years old at their reunion, when he is 40 years old. But she's NOT 20 years old then ... he can see with his own eyes that she is 80 years old then. Somewhere during his trip, she HAD to age an additional 60 years, according to him. WHERE did that extra ageing by her, according to him, occur? There is only one possible place it could have occurred: it HAD to have occurred during his instantaneous turnaround, because during ALL the rest of his trip, he knows she was ageing only half as fast as he was.
For this simplest scenario, that's all you need to know to solve "the paradox". More complicated scenarios require that you know how to COMPUTE her instantaneous age-changing (according to him). There is a simple equation that allows you to do that (and also a graphical technique that you can use to do it), but neither of those is needed for this simplest scenario.
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Do you agree with mike's answeranswer from his thread?
Sure that is one explanation.
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Do you agree with mike's answeranswer from his thread?
Sure that is one explanation.
Good. That's an important step to discuss the case described in this thread.
Can we use that explanation for the cases described in this thread? What does it predict?
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That's an important step to discuss the case described in this thread.
Can we use that explanation for the cases described in this thread?
Please pay attention, I just said you could in my last post!
What does it predict?
Seriously? It predicts the same answer that has been shown several times in this thread.
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The time rotation thing lends itself nicely to video. It is hardly the simplest explanation, but it very much is a valid one.
But it needs to do a Lorentz rotation, not a Euclidean rotation like you're doing with all your pictures posted above. Those produce contradictory observations, as you have noted.
For instance, in your pictures in post 110, all the ships B,C,D age about 4.5 years, not 8. That's a contradiction since any observation (like everybody's age at the final event) should be a frame independent thing.
How should the Lorentz' rotation be drawn? How could it avoid producing contradictory observations?
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There are plenty of web sites that explain how, but they're not videos, but I'm sure there's something on youtube that actually does it.
I don't mind to use sources with various formats, not just videos.
What makes you sure?