Twin paradox initial acceleration

[flashprogram]

JesseM, I've heard of it. The order of non-causally related events can vary between observers, even be reversed or interpreted as simultaneous, iirc.

So it is not legitimate for you to claim that two clocks start off with the same time on them without specifying a frame and then making the claim that you can determine the correct frame by waiting until they unite to compare their elapsed times and assuming that the choice of frame is determined by nature and not by you.

Even if the clocks have different arbitrary times at the outset, all we have to do is establish a causal relation between the two objects, with this causal relation information can be exchanged, and on the basis of such exchanges, it can be determined that from that moment assuming all else remains constant, the clocks in the two objects differ in rate by a measurable proportion... and from such measure difference in speed can be inferred.

 

[ghwellsjr]

You are a master at making fuzzy statements. I can't tell what you are talking about. It would help if you would define your terms. What do you mean by causal relation--is that when two observers with a relative speed between them finally arrive together at the same location just long enough to exchange information?

 

[yogi]

If two clocks A and B travel at a constant relative velocity, which clock runs slow is a meaningless question. A second clock in the frame of A can be used to measure the time lapse of B clock and it will always appear to run slower when measured by the two clocks in the A frame, and the same is true for a second clock introduced in B frame to measure clocks in the A frame - as pointed out on a previous post, which clock runs slow depends upon in which frame the measurement is made. This is not an aging difference and therefore is not a paradox - there can be no age difference because the situation is symmetrical. Age difference only occurs when acceleration is involved somewhere during the time differential that defines the beginning and end of the experiment The pion in the lab is an example of real age difference because it has been accelerated from a rest position in the lab to near c velocity. This is a shrunk example of the one way twin paradox - you have acceleration following the initial synchronization of the pion clock in the lab frame (the pion changes from the lab frame to another frame in a jiffy or so) - but because the pion decay time is already known for at rest pions - only the lab clock and the distance before decay are needed to calculate the age of the traveling entity.

 

[flashprogram]

If two clocks A and B travel at a constant relative velocity, which clock runs slow is a meaningless question. A second clock in the frame of A can be used to measure the time lapse of B clock and it will always appear to run slower when measured by the two clocks in the A frame, and the same is true for a second clock introduced in B frame to measure clocks in the A frame - as pointed out on a previous post, which clock runs slow depends upon in which frame the measurement is made. This is not an aging difference and therefore is not a paradox - there can be no age difference because the situation is symmetrical. Age difference only occurs when acceleration is involved somewhere during the time differential that defines the beginning and end of the experiment The pion in the lab is an example of real age difference because it has been accelerated from a rest position in the lab to near c velocity. This is a shrunk example of the one way twin paradox - you have acceleration following the initial synchronization of the pion clock in the lab frame (the pion changes from the lab frame to another frame in a jiffy or so) - but because the pion decay time is already known for at rest pions - only the lab clock and the distance before decay are needed to calculate the age of the traveling entity.

But we've already seen the difference in clock rates will have measurable effects on things like half life, which will alter the composition of radioactive rocks or ships composed of such. Surely the physical composition of the ships cannot be frame dependent.

In previous posts related on this issue, others have commented that acceleration and deceleration need not be involved for effects to be measurable, for us to tell that clocks differ in rate of measuring time, and thus objects that are at constant speed and remain at such constant speed will experience different rates of 'aging'(passage of time) even while remaining at constant speed, if their speed differ.(example suppose we know the routes of the two ships, and put 2 messages with equal spacing along each such route. Between message one and message two of each route, the number of events in the two ships, say number of birthdays will vary between the two ships.)

Spontaneously created matter within a ship moving at high speed, close to C speed, if radioactive, will experience half life at a different rate(passing of time) as compared to the same matter created similarly in a slower ship.

 

[yogi]

But we've already seen the difference in clock rates will have measurable effects on things like half life, which will alter the composition of radioactive rocks or ships composed of such. Surely the physical composition of the ships cannot be frame dependent.

Spontaneously created matter within a ship moving at high speed, close to C speed, if radioactive, will experience half life at a different rate(passing of time) as compared to the same matter created similarly in a slower ship.

Measurements of half lives in the B frame made by clocks in the A frame will indicate a slower rate of decay in the B frame. Measurments of half lives in the A frame made by clocks in the B frame will indicate a slower rate of decay in the A frame

 

[ghwellsjr]

But we've already seen the difference in clock rates will have measurable effects on things like half life, which will alter the composition of radioactive rocks or ships composed of such. Surely the physical composition of the ships cannot be frame dependent.

In previous posts related on this issue, others have commented that acceleration and deceleration need not be involved for effects to be measurable, for us to tell that clocks differ in rate of measuring time, and thus objects that are at constant speed and remain at such constant speed will experience different rates of 'aging'(passage of time) even while remaining at constant speed, if their speed differ.(example suppose we know the routes of the two ships, and put 2 messages with equal spacing along each such route. Between message one and message two of each route, the number of events in the two ships, say number of birthdays will vary between the two ships.)

Spontaneously created matter within a ship moving at high speed, close to C speed, if radioactive, will experience half life at a different rate(passing of time) as compared to the same matter created similarly in a slower ship.

Flashprogram, one problem with using radioactive rocks is that the radiation they give off is proportional to their initial size so determining their age or their aging rate from just the radiation is almost impossible so let's consider another object, totally imaginary, something like a pulsar except much smaller, that gives off a very bright flash of light at a regular interval, say once per second. And let's imagine that two exactly identical such objects exist and that one of them is traveling at 60% of the speed of light directly toward the other one which is stationary. Now let's also consider that each one can see the flashes from the other one and have been doing so for a very long time and that they are still very far apart from each other. Isn't this very much like the scenarios that you have been devising?

Now here's the question for you: How will each object observe the rate of the flashes from the other object compared to their own flash rate?

 

[flashprogram]

Now here's the question for you: How will each object observe the rate of the flashes from the other object compared to their own flash rate?

It would seem that one would see a higher number of flashes than the other, unless I'm missing something. It would seem that if you sped the object up arbitrarily close to C, it will experience the passage of time at a very slow rate during any interval of travel.

Say the following, we can put an even simpler example:

Two ships are headed to pass a destination say X.X lightyears away, they start from the same origin, and they're both covering the same distance(as previously measured by stationary observers at the origin and destination points). One ship is traveling at .9c, the other is traveling arbitrarily close to C(e.g. .999999999999...c). As they pass the destination they leave a message of what happened during the trip(a log of activities.).

It can be seen that as the two ships were traveling very close to C, from the observers at the destination's perspective they covered the distance within a similar span of time.

The log shows that on one ship the traveler only managed to view a single episode of 'LOST', the other ship shows a year's worth of activities in the log. How can there be any argument regarding which ship had more events and thus had faster rate of the passage of time, and which had a slower rate?

 

[ghwellsjr]

It would seem that one would see a higher number of flashes than the other, unless I'm missing something. It would seem that if you sped the object up arbitrarily close to C, it will experience the passage of time at a very slow rate during any interval of travel.

No, they would each measure the other one's flashes as occurring at exactly double the rate of their own. This is an example of Relativistic Doppler. And the faster the one ship is going, the higher the ratio they both measure of the other one's flashes compared to their own.

Say the following, we can put an even simpler example:

Two ships are headed to pass a destination say X.X lightyears away, they start from the same origin, and they're both covering the same distance(as previously measured by stationary observers at the origin and destination points). One ship is traveling at .9c, the other is traveling arbitrarily close to C(e.g. .999999999999...c). As they pass the destination they leave a message of what happened during the trip(a log of activities.).

It can be seen that as the two ships were traveling very close to C, from the observers at the destination's perspective they covered the distance within a similar span of time.

The log shows that on one ship the traveler only managed to view a single episode of 'LOST', the other ship shows a year's worth of activities in the log. How can there be any argument regarding which ship had more events and thus had faster rate of the passage of time, and which had a slower rate?

This is correct in your implied stationary rest frame (except maybe for your statement about them both covering the distance in a similar span of time, since one of them is very close to C while the other one is only .9c, but I don't think this adversely affects your scenario).'

By the way, you have finally specified a scenario with enough details to unambiguously interpret what is going on. Good for you.

However, in the rest frame of the "faster" ship, the destination is traveling toward him at almost the speed of light and wasn't very far away (because of length contraction) and it only took one hour to get to him, whereas the other ship is traveling away from him and is "running away" from the approaching destination so even though the "faster" ship sees the "slower" ship as having time-dilated clocks, it still takes a year of the "slower" ship's time for the destination to catch up to him.

And from the rest frame of the "slower" ship, the destination is traveling toward him at .9c and takes a year to get to him but the "faster" ship is traveling at almost the speed of light toward the destination and even though the "slower" ship sees the "faster" ship's clock as running slower than his own, it still takes one hour of the "faster" ship's clock to reach the approaching destination.

So the issue of which had more events is different from the issue of the rate of the passage of time because you are overlooking the effect of length contraction. In a given frame, a clock can be running at a normal rate but the distance covered is very short and so the number of events can be very small.

 

[flashprogram]

Hmmm...

That relativistic doppler effect is very strange, almost like an escape clause. Yeah while you traveled a million light years from a distant galaxy, and your flashing machine which flashes each frame you manage to watch of a single 'lost' episode to us(you just managed to finish just a single episode during all this travel), and Earth has been using the identical flashing machine to loop the episode for a million years... there's this weird effect, and tada gotcha relativistic doppler effect meddles in and you got nothing.

So the issue of which had more events is different from the issue of the rate of the passage of time because you are overlooking the effect of length contraction. In a given frame, a clock can be running at a normal rate but the distance covered is very short and so the number of events can be very small.

The length contraction while a true phenomena I'd heard about, is still a bit tricky to picture, how about the following:

What happens if we imagine that instead of empty space, this is a very long road with identical houses at equal distances along the way(say a large neighborhood), and instead of spaceships we have very fast runners(same .9c and .9999...c). One runner breaks the mailboxes on the left and the other the mailboxes on the right. The runners reach house number 1 Trillion, and drop a message*(the message says the point at which they got while watching an identical video on their ipad.).

They each broke 1 Trillion mailboxes and passed along one trillion houses, yet at house 1T, one managed to see the whole video while the other did not. By measure of houses passed by and broken mailboxes, it would seem the length is the same even if the runners measure the road contracted to different extents.

 

[ghwellsjr]

I think you're catching on.

 

[flashprogram]

The effect of acceleration is proportional to the distance between the twins. At the start and end of the trip, this distance is zero.

if this is so instantaneous travel could land you anywhere and would require a practically infinite energy source, good luck finding that! Since antiquity it has been searched, and no one is supposed to have found it hence, the red queen dilemma... constant progress while appearing to show zero progress.

 

[Mueiz]

Hi,

I've seen many variations of explanations of the twin paradox using special relativity, but i haven't yet seen an explanation that bothers to take into account the initial acceleration of the traveling twin away from planet Earth. Is it safe to say that this can be neglected? And, also, if the traveling twin were to accelerate away from Earth and then decelerate onto the distant planet and then stay there without coming back, would he still be younger than his twin at home?

Thanks for any help that anyone can provide!

acceleration and deceleration effects can not be the resolution of the so called twin paradox because we can make the interval of uniform motion long enough to neglct the effects of acceleration and deceleration.
There is no twin paradox if we look from one frame of reference...each of the twin will see that the other is younger ..when we ask ''who is younger?'' we must chose a frame .

 

[ghwellsjr]

Hi,

I've seen many variations of explanations of the twin paradox using special relativity, but i haven't yet seen an explanation that bothers to take into account the initial acceleration of the traveling twin away from planet Earth. Is it safe to say that this can be neglected? And, also, if the traveling twin were to accelerate away from Earth and then decelerate onto the distant planet and then stay there without coming back, would he still be younger than his twin at home?

Thanks for any help that anyone can provide!

acceleration and deceleration effects can not be the resolution of the so called twin paradox because we can make the interval of uniform motion long enough to neglct the effects of acceleration and deceleration.
There is no twin paradox if we look from one frame of reference...each of the twin will see that the other is younger ..when we ask ''who is younger?'' we must chose a frame .

This is true, we must choose a frame to decide who is younger, but if we limit ourselves to the frame in which they both started out at rest and both ended up at rest, then the twin that traveled to the distant planet will be younger and they will both eventually see and agree that he is younger although while he is traveling, they will both see the other one as younger.

While traveling, due to relativistic doppler, they will both symmetrically see the other one as aging at a younger rate. When the traveling twin stops on the distant planet, he immediately begins to see his twin age at the same rate as himself but his twin back on Earth will continue to see the traveling twin aging at the same lower rate until he eventually sees that his twin has stopped traveling and begins aging at the same rate as himself. Since they are now both stationary in the same frame, according to Special Relativity, we can compare their ages and the traveling twin will be younger in that frame.

 

[HarryWertM]

From Meir Achuz' post no. 4...

The effect of acceleration is proportional to the distance between the twins.

Huh?? Meir [or anybody], can you show equations or web sites to support this statement?

 

[PAllen]

From Meir Achuz' post no. 4...

Huh?? Meir [or anybody], can you show equations or web sites to support this statement?

This sounds like a distorted version of one way of talking about differential aging. In a real gravitational field, the further apart two clocks are in the gravity gradient, the larger the difference in their aging. If one uses a non-inertial frame, with metric modeling inertial force as gravity, you also see that the further apart two observers are (in the direction of acceleration), the greater the difference in clock rate. It is possible to explain almost all twin variants this way, but I don't find it the most natural way (personally).

 

[Ich]

can you show equations or web sites to support this statement?

If you have the traveling twin at distance d change her velocity by dv, the "simultaneous" event at the origin shifts by dt = -dv*d, which is the essence of Meir Achuz' statement.
You can derive this from the Lorentz transformations by first solving for t' at the event t=0, x=d, then solving for t at the event t', x=0.

 

[Mike_Fontenot]

From Meir Achuz' post no. 4...

"The effect of acceleration is proportional to the distance between the twins."


Huh?? Meir [or anybody], can you show equations or web sites to support this statement?

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7