Twin Paradox: Explaining the Relativity of Aging

[spikenigma]

How do you determine which is older? Because they are separated you must use some simultaneity convention. Then the answer applies only to that frame.

as I said, they shoot light beams (or pulses if you want to be specific) at each other to communicate their clock rates

using this, they can calculate [x] years have passed on Earth and [y] years have passed on the rocket, and be in agreement at any given time

 

[matheinste]

reading through this thread has been interesting

instead of creating a new thread, I'd like to offer a little variation if I may:

A Rocket is an arbitrary distance from Earth, it accelerates up to a constant 0.7c

As the rocket hurtles past Earth at that constant speed, two twins are born, one on Earth and one on the rocket. Rocket-twin and Earth-twin know that they were both born at the same time.

They then communicate with each other with (VERY powerful lasers). Rocket-twin asserts that he is stationary and that the Earth is moving away from him at 0.7c, Earth-twin asserts that the Earth is stationary and Rocket-twin is moving.

If Rocket-twin is older than Earth-twin, doesn't that make Earth the preferred reference frame?

Why should the rocket twin be older. After the acceleration, which ends before the birth, they are both in inertial frames in relative motion and so any calculation of time elapsed is reciprocal.They will each "see" each others clock running slower than their own.

Matheinste.

 

[spikenigma]

Why should the rocket twin be older. After the acceleration, which ends before the birth, they are both in inertial frames in relative motion and so any calculation of time elapsed is reciprocal.They will each "see" each others clock running slower than their own.

Matheinste.

ok then, two further things for clarification:

1)

let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin. Which twin will be older/younger when he lands?

2)

during travel, why will each twin view the others clock as running more slowly than their own?

 

[Dale]

using this, they can calculate [x] years have passed on Earth and [y] years have passed on the rocket, and be in agreement at any given time

No, they will always be in disagreement unless they agree on a reference frame in which to do the calculations.

 

[matheinste]

ok then, two further things for clarification:

1)

let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin. Which twin will be older/younger when he lands?

2)

during travel, why will each twin view the others clock as running more slowly than their own?

1) The Earth twin will be older because he has remained inertial (for the purpose of this discussion) and so has traversed a longer spacetime interval and so accumulated more time on his clock than the spaceship twin.

2) Because that is what relativity says will happen.

Matheinste.

 

[yogi]

Why not just look at a one way trip where the ship doesn't return, but just comes to rest with Earth and stays there indefinitely?

The answer is the same (divided by two) and the reason for it is clearer.

Then just double that answer.

Quite right - you and I have tried previously to get this across when the twin trip analysis creeps into the forum - and as always no one seems to appreciate how simple it is to do the one way trip and double the answer

 

[spikenigma]

No, they will always be in disagreement unless they agree on a reference frame in which to do the calculations.

Earth

1) The Earth twin will be older because he has remained inertial (for the purpose of this discussion) and so has traversed a longer spacetime interval and so accumulated more time on his clock than the spaceship twin.

2) Because that is what relativity says will happen.

doesn't this then imply a preferred reference frame?, which was my original point

both twins know that an object that has accelerated will experience time dilation with reference to one that has not.

When they both meet up, they can conclude that it is in fact the rocket that has accelerated and not Earth, even though rocket-twin never underwent any acceleration during his lifetime

 

[matheinste]

Earth



doesn't this then imply a preferred reference frame?, which was my original point

both twins know that an object that has accelerated will experience time dilation with reference to one that has not.

When they both meet up, they can conclude that it is in fact the rocket that has accelerated and not Earth, even though rocket-twin never underwent any acceleration during his lifetime

Only preferred in the sense that one is inertial and the other is not. As far as physics is concerned there is nothing that makes this inertial frame stand out from the infinite number of other inertial frames.

Acceleration is not the cause of time dilation. Each twin will consider the other to have experienced time dilation because they are in relative motion with respect to each other.

For the twins to meet up again one of them must have undergone acceleration. As the Earth twin has remained inertial (for the purposes of this discussion) then the rocket twin must have undergone acceleration.The difference in ages is not directly due to acceleration but to the differences in spacetime paths due to the acceleration of the rocket twin.

I don't really want to get into a deep discussion of the twin "paradox" as it always causes a lot of grief.

Matheinste.

 

[Dale]

Earth

Then their answers will only apply to the Earth's frame. This reference frame is "prefered" only in the sense that they agreed to use it, it is not preferred in any physical sense. They could have picked any other inertial frame and the laws of physics would look the same (which is the physics meaning of a "prefered" frame).

 

[spikenigma]

Then their answers will only apply to the Earth's frame. This reference frame is "prefered" only in the sense that they agreed to use it, it is not preferred in any physical sense. They could have picked any other inertial frame and the laws of physics would look the same (which is the physics meaning of a "prefered" frame).

perhaps I'll clarify clearly what I mean

relativity (as far as I understand it) means that there is no preferred reference frame, i.e. if two bodies are moving at a constant velocity, no one body can say that it is the other is the one that is moving, or has moved and visa versa. It is supposed to be impossible to tell.

However, in the scenario, both of the twins can tell which one has accelerated - because one is older. Even though neither of them have ever undergone any acceleration

 

[JesseM]

perhaps I'll clarify clearly what I mean

relativity (as far as I understand it) means that there is no preferred reference frame, i.e. if two bodies are moving at a constant velocity, no one body can say that it is the other is the one that is moving, or has moved and visa versa. It is supposed to be impossible to tell.

However, in the scenario, both of the twins can tell which one has accelerated - because one is older. Even though neither of them have ever undergone any acceleration

Which scenario are you talking about? The one where the rocket travels past Earth at constant velocity and the two twins are born at the moment the rocket is next to Earth, then the rocket continues onward at constant velocity forever without turning around? In this case there is no objective truth about which twin is older, in the frame where the Earth is at rest the rocket-twin ages more slowly, in the frame where the rocket is at rest the Earth-twin ages more slowly. Are you familiar with the relativity of simultaneity? In the Earth frame it might be true that the event of the Earth-twin's 40th birthday is simultaneous with the event of the rocket-twin's 32nd birthday, while in the rocket frame it would then be true that the event of the Earth twin's 40th birthday is simultaneous with the event of the rocket-twin's 50th birthday, so in each frame the moving twin is only aging at 0.8 the rate of the at-rest twin. Only if you bring the twins back together to a single location in space will both frames have to agree on their respective ages at a single moment.

On the other hand, if you're talking about the scenario in post #53 where you said "let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin", in this case the rocket must have turned around at some point to travel back to Earth, so the rocket did accelerate in the rocket-twin's lifetime.

 

[alviros]

I can't understand why many of you, including "PF mentors", talk about acceleration.

According to https://www.physicsforums.com/library.php?do=view_item&itemid=166 "Time dilation does not depend on the acceleration of the clock."

 

[matheinste]

I can't understand why many of you, including "PF mentors", talk about acceleration.

According to https://www.physicsforums.com/library.php?do=view_item&itemid=166 "Time dilation does not depend on the acceleration of the clock."

I think it is often mentioned by questioners because they think tme dilation is related to acceleration and is mentioned by responders to explain that this is not the case.

It is alway mentioned in the twin "paradox" because it is an integral part of it in so much that for the twins to reunite acceleration must be involved. In the twins "paradox" it is thought necessary to point out that the difference in spacetime path length, which is ultimately the cause of the dfferential ageing, involves acceeration.

Matheinste

 

[JesseM]

I can't understand why many of you, including "PF mentors", talk about acceleration.

According to https://www.physicsforums.com/library.php?do=view_item&itemid=166 "Time dilation does not depend on the acceleration of the clock."

See my post #44 for an explanation of what is meant by this. The time dilation at any given instant depends solely on the the velocity in whatever frame you're using, the factor by which a moving clock is slowed down is always \sqrt{1 - v^2/c^2} where v is that clock's instantaneous velocity. However, if you have two worldlines that cross paths at two times t0 and t1, and you know the velocity as a function of time v(t) on each worldline, then you can do the integral \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt for both of them to find the total time elapsed on each worldline between the two points where they cross. If one worldline is inertial (constant value for v(t)) and the other involves some acceleration (the value of v(t) changes with t), it will always work out that when you do the integral above, you'll find that the total time elapsed is greater on the inertial worldline than the worldline that involved an acceleration. That's just a property of the way the integral works, and it's totally compatible with the idea that the time dilation at each moment depends solely on the velocity at that moment, not the acceleration.

If it helps, there's a direct analogy for this in ordinary Euclidean geometry. Suppose we have two paths on a 2D plane which cross at two points, and one is a straight-line path while the other involves some bending. Since we know a straight line on a 2D plane is the shortest distance between points, we know the straight-line path will have a shorter total length. But suppose we want to measure the length of each path by driving cars along them with odometers running to measure how far the cars have travelled. Suppose we also have an x-y coordinate system on this 2D plane, so we can talk about "the rate a car is accumulating distance as a function of its x-coordinate"--if you think about it, it's not hard to show that this is solely a function of the slope of the path at that point in the coordinate system you're using. If you know the function for the path in this coordinate system y(x), then the slope at x is defined by looking at a small interval from x to (x + dx), and seeing the amount dy that the y-coordinate of the path changes between those points, with the slope defined as dy/dx. Since dx and dy are assumed to be arbitrarily small, the path can be assumed to be arbitrarily close to a straight line between the points (x,y) and (x+dx,y+dy), so the distance accumulated on the car's odometer as it travels between those points is just given by the pythagorean theorem, it'll be \sqrt{dx^2 + dy^2}, which is equal to dx*\sqrt{1 + dy^2/dx^2}, and since the "slope" at a given coordinate S(x) is defined to be dy/dx, this means the distance accumulated on the car's odometer as it travels between these points can be written as dx * \sqrt{1 + S(x)^2}.

So, the ratio of (increment odometer increases)/(increment x-coordinate increases), i.e. "the rate the car is accumulating distance as a function of its x-coordinate", will just be \frac{dx*\sqrt{1 + S(x)^2}}{dx} which is just \sqrt{1 + S(x)^2}, purely a function of the slope. On the other hand, if you want to know how much distance accumulates on the odometer over a non-incremental change in the x-coordinate, say from some value x_0 to x_1, then we have to integrate the amount the odometer increases over each increment over the entire range from x_0 to x_1, giving the integral \int_{x_0}^{x_1} \sqrt{1 + S(x)^2} \, dx. Since we know a straight path is the shortest distance between two points, and we know straight implies constant slope, this means that if we have two different paths which cross once at x_0 and then again at x_1, and one has a constant S(x) while the other has a varying S(x), that means if we do the above integral for both paths the answer for the constant-slope path is guaranteed to be smaller.

Obviously all this is very closely analogous to the situation in relativity, where the rate a clock accumulates time as a function of the t-coordinate is just \sqrt{1 - v^2} (in units where c=1, like seconds and light-seconds), while the total time accumulated on a path with a specific v(t) is \int_{t_0}^{t_1} \sqrt{1 - v(t)^2} \, dt, and a path with constant v is guaranteed to have a longer total time than a path with a v that changes (the reason a straight path in SR is guaranteed to have the largest time while a straight path in geometry is guaranteed to have the shortest distance has to do with the fact that there's a plus sign in front of the geometric slope but a minus sign in front of the velocity in the two square roots).

 

[JM]

To Whom... I hoped for some substantive response to my posts before being sent off to read more. I have read more SR books and papers than I can remember, and my comments come from careful reading of them. At least Einstein, French, Taylor and Wheeler, Feynman, and Bondi. Nothing in these sources or in the sources mentioned in this thread addresses my concerns. I stand by my previous posts. I hope that you will also apply 'good faith' effort in response.
Here is a little more detail. Einsteins 1905 paper is based on the kinematics of rigid bodies. He says so in his introduction, and applies the principle in part 4, where he uses the equations for inertial motion in a straight line to determine the behavior of a clock moving in a closed curve consisting of a series of connected straight lines. Refering to Wikipedia-Kinematics, the definition of Kinematecs is 'A branch of classsical mechanics which describes the motion of objects without consideration of the causes leading to the motion.' It doesn't deny there are forces, it just defers their consideration to a later, Dynamic, analysis. This eliminates rockets etc. from possible explanation of Einsteins Twin/clock paradox, don't you think?
Einstein asserts that all inertial frames are equal, or in his terms from Relativity,1952, '... every motion must be considered only as a relative motion', and '...two forms,both of which are equally justifiable: (a) The carriage is in motion relative to the embankment.(b) The embankment is in motion relative to the carriage.' Notice that he has no trouble with the massive Earth being in motion. Thus for every result obtained with A at 'rest' and B in 'motion' there is an equal result with B at 'rest' and A in 'motion'. Thus my early post, when they reunite each twin thinks the other one is younger. I believe that this is what the 1905 paper says. How it's explained has not yet known, is it?

 

[JesseM]

Here is a little more detail. Einsteins 1905 paper is based on the kinematics of rigid bodies. He says so in his introduction, and applies the principle in part 4, where he uses the equations for inertial motion in a straight line to determine the behavior of a clock moving in a closed curve consisting of a series of connected straight lines. Refering to Wikipedia-Kinematics, the definition of Kinematecs is 'A branch of classsical mechanics which describes the motion of objects without consideration of the causes leading to the motion.' It doesn't deny there are forces, it just defers their consideration to a later, Dynamic, analysis. This eliminates rockets etc. from possible explanation of Einsteins Twin/clock paradox, don't you think?

All that matters is whether the path through spacetime is a "straight" inertial (constant velocity path, or one involving different velocities at different times (like 'a closed curve consisting of a series of connected straight lines). Knowing the path through spacetime is sufficient to determine the time elapsed by a clock that takes that path, and a "straight" path will always have a greater time elapsed than a non-straight one.

Einstein asserts that all inertial frames are equal, or in his terms from Relativity,1952, '... every motion must be considered only as a relative motion', and '...two forms,both of which are equally justifiable: (a) The carriage is in motion relative to the embankment.(b) The embankment is in motion relative to the carriage.' Notice that he has no trouble with the massive Earth being in motion. Thus for every result obtained with A at 'rest' and B in 'motion' there is an equal result with B at 'rest' and A in 'motion'.

All inertial frames are equal, but the situation is not symmetrical because one twin's path is not straight while the other is--all inertial frames will agree that one twin moved at constant velocity while the other changed velocities. And again, it's always true that a straight path has the greatest proper time, in much the same way that a straight line in 2D Euclidean geometry always has the shortest distance (see my previous post #64 for a discussion of this analogy).

Thus my early post, when they reunite each twin thinks the other one is younger.

Not if they calculate things from the perspective of an inertial frame, they won't--no matter which inertial frame you use, you'll always end up predicting that the inertial twin aged more than the twin that changed velocities midway through the trip.

Here's a simple example. Suppose twin A remains at rest on Earth (which for the sake of the problem we can assume is moving inertially rather than orbiting the Sun), while in the Earth's rest frame, twin B travels away from Earth at 0.6c for 25 years, then instantaneously turns around and travels back towards Earth at 0.6c for another 25 years. Thus twin A will be 50 years older when twin A returns, but because twin B experiences a time dilation factor of \sqrt{1 - 0.6^2} = 0.8 on both the outbound leg and the inbound leg, twin B only ages 25*0.8 = 20 years on the outbound leg and another 20 years on the inbound leg, for a total of 40 years.

Now consider things from the perspective of a different inertial frame, the one where twin B is the one who's at rest during the outbound leg, while twin A moves away at 0.6c. In this frame twin B remains at rest for 20 years, but then instantaneously accelerates to catch up to A while A continues to move away at 0.6c--using the formula for addition of relativistic velocities, in this frame B must have a velocity of (0.6c + 0.6c)/(1 + 0.6*0.6) = 1.2c/1.36 = 0.88235c during the inbound leg. At the moment B turns around in this frame, A has been traveling away from B at 0.6c for 20 years, so A is 0.6*20 = 12 light-years away at this moment. With A continuing to move away at 0.6c and B moving at 0.88235c to catch up, the distance between B and A will be shrinking at a rate of (0.88235c - 0.6c) = 0.28235c in this frame, so it'll take another 12/0.28235 = 42.5 years for B to catch up with A. During this leg B is experiencing a time dilation factor of \sqrt{1 - 0.88235^2} = 0.4706, so B only ages 42.5*0.4706 = 20 years during the second leg of the trip. Meanwhile A was moving at 0.6c during both the first leg which lasted 20 years and the second leg which lasted 42.5 years, a total of 62.5 years in this frame, and A's time dilation factor was \sqrt{1 - 0.6^2} = 0.8, so A aged 0.8*62.5 = 50 years in this frame. So you see that even when we calculate things in a totally different frame, we still find the same conclusion as before: A aged a total of 50 years between B leaving and B returning, while B aged 20 years during the first leg of the trip and 20 years during the second leg, for a total of 40 years.

 

[Al68]

Why not just look at a one way trip where the ship doesn't return, but just comes to rest with Earth and stays there indefinitely?

The answer is the same (divided by two) and the reason for it is clearer.

Then just double that answer.

Quite right - you and I have tried previously to get this across when the twin trip analysis creeps into the forum - and as always no one seems to appreciate how simple it is to do the one way trip and double the answer

I guess it's just more interesting to do it the hard way. The thing is, showing two separate one way trips (correctly) would completely eliminate every objection I've seen to the standard resolutions.

 

[Dale]

Einstein asserts that all inertial frames are equal, ... Thus my early post, when they reunite each twin thinks the other one is younger.

One of the twins was inertial and the other was non-inertial, they both agree which one is younger.

 

[MikeLizzi]

Just shadowing this thread. Did it ever occur to you folks who are so proficient in relativity that the reason you never convince anybody is because YOU don't get it? Round trip or one way, there has to be acceleration involved. You know that the acceleration phase does not alter the result, differential aging. But the burden is on you to show that.

These threads are taking sincere skeptical people and turning them into cynical people hostile to physics. Not a good idea when some of them get into position to vote on funding physics research.

 

[JesseM]

Just shadowing this thread. Did it ever occur to you folks who are so proficient in relativity that the reason you never convince anybody is because YOU don't get it? Round trip or one way, there has to be acceleration involved. You know that the acceleration phase does not alter the result, differential aging. But the burden is on you to show that.

What do you mean "the acceleration phase does not alter the result, differential aging"? It is certainly true that if one twin accelerates and the other doesn't, the inertial one will always have accumulated more age than the accelerated one when they reunite. Do you just mean that the inertial twin's extra age does not all accumulate during the actual period of acceleration? If so, this is certainly true, but once again I think the geometric analogy makes things pretty clear. If you have two paths between points A and B on a 2D plane, one a straight-line path and the other a path consisting of two straight segments at different angles joined by a short bend (change in slope, analogous to change in velocity), then if two cars drive along both paths from A to B with odometers running, the car on the bent path will have accumulated more distance when they meet at point B. However, it's not true that the odometer of the car driving on the bent path accumulated all the extra distance during the brief phase it was driving along the bend in the bent path--it's odometer didn't suddenly jump forward by a large amount during this phase--rather the greater length of the bent path is a consequence of its overall geometry. If you want to understand rigorously what is meant by the "geometry" of the paths you have to get into a lot of math, but we all understand intuitively that a straight line is the shortest distance between two points in a 2D plane, and that if you compare a straight-line path with a path consisting of two straight segments joined by a bend, the extra length of the non-straight path is not just due to the length of the bent part. In relativity everything about proper time along worldlines maps pretty directly to statements about distance along paths in Euclidean geometry (as I showed in post #64); you can also verify that different inertial frames will all agree about the time along an inertial path and a non-inertial path even if the acceleration is made instantaneously brief so no proper time accumulates during the acceleration itself (as I showed with an example in post #66).

 

[Dale]

Hi MikeLizzi, you are certainly more than welcome to join in and see if you can provide a better explanation. The best pedagogical approach is not obvious, so it is a place where you can definitely contribute.

Round trip or one way, there has to be acceleration involved.

That is simply not true. You can easily have "one way" trips that are purely inertial.

 

[Al68]

You can easily have "one way" trips that are purely inertial.

I think he was referring to my statement about one way trips that were each equivalent to half of the twins paradox, which would have to involve acceleration.

 

[JM]

To MikeLizzi: Not hostile to physics, just to this forum. It's a waste of time to post when all you get is the 'acceleration' explanation no matter what you say.

To whom 2... Please respond specifically to the following: 1. Einsteins 1905 paper is based on Kinematics, 2. Kinematics excludes external forces, accelerations and response to them, 3.Einsteins formula for the traveling clock/twin is based on the relation between two inertial coordinate frames, 4. so what are you trying to accomplish with the accelerations etc?

 

[JesseM]

To MikeLizzi: Not hostile to physics, just to this forum. It's a waste of time to post when all you get is the 'acceleration' explanation no matter what you say.

You aren't just getting the answer "acceleration", you're getting a more nuanced answer; the rate a clock is slowed down at any instant in a given frame \sqrt{1 - v^2/c^2} is determined solely by its velocity in that frame and not by its acceleration, but this means that if you want the total time elapsed on a clock between two times t_0 and t_1 in a frame, and you know its velocity as a function of time v(t), you must do the integral \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt. If you pick two paths that cross at points t_0 and t_1, one of which has a constant v(t) and the other of which has a v(t) that changes (an acceleration), the integral has the property that it will always give a larger value for the one with constant v(t) than the one with changing v(t). Are you willing to address specifically what part of this answer you disagree with or don't understand?

To whom 2... Please respond specifically to the following: 1. Einsteins 1905 paper is based on Kinematics, 2. Kinematics excludes external forces, accelerations and response to them

Kinematics excludes the cause of acceleration (forces) but it certainly does not exclude acceleration itself. Wikipedia defines kinematics as "a branch of classical mechanics which describes the motion of objects without consideration of the causes leading to the motion". Acceleration is a type of motion, namely motion where the velocity is changing as a function of time. The wikipedia article on kinematics has a section on constant acceleration, for example.

3.Einsteins formula for the traveling clock/twin is based on the relation between two inertial coordinate frames

Yes, and the integral \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt is written in terms of the coordinates of an inertial frame, not an accelerating frame. You can certainly use an inertial frame to describe the behavior of an object that is moving non-inertially, and Einstein does so in the 1905 paper, for example in section 4 where he considers the time elapsed by a clock at the equator of a rotating planet (rotation is a type of acceleration, since constant velocity implies constant speed and constant direction, while motion in a circle involves constantly changing direction).

Since you asked for a specific response, I hope you will respond specifically to these points as well.

 

[Dale]

To MikeLizzi: Not hostile to physics, just to this forum. It's a waste of time to post when all you get is the 'acceleration' explanation no matter what you say.

To whom 2... Please respond specifically to the following: 1. Einsteins 1905 paper is based on Kinematics, 2. Kinematics excludes external forces, accelerations and response to them, 3.Einsteins formula for the traveling clock/twin is based on the relation between two inertial coordinate frames, 4. so what are you trying to accomplish with the accelerations etc?

If you want a non-acceleration explanation for the twin's paradox then you are probably going to have to look past Einstein to the http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_spacetime.html" of Minkowski. That is the approach I favor for a variety of reasons including the fact that it is easily generalizable to purely inertial scenarios (GR or a series of "one-way" trips). As JesseM mentioned, kinematics includes acceleration as did all of Einstein's early explanations.

 

[yogi]

Post 75 - The Minkowski approach is nothing more than the invariance of the interval applied to the one way trip per post 72. In the usual setting, put forth by Einstein in his 1905 paper, he starts with both clocks getting synchronized in the same frame at rest - then one gets put in motion - so there is an incidental acceleration (but it was not meant to be a factor in the outcome). It was simply a necessary circumstance to get one of the clocks in motion. Einstein knew the answer he wanted which was an actual time difference on the two clocks - there is no question which clock logged the most time - everyone agrees - it was the clock that remained at rest on Earth which is the same as an Alpha Centuri clock in the same frame as the Earth - but the time difference is not the result of one clock being put in motion - you can do the experiment by having one clock already in motion as it passes by the Earth clock on its way to Alpha Centuri at a high constant speed. Sync it with the Earth clock during flyby - when it arrives at Alpha Centuri it will read less than a clock on alpha Centure that has remained in sync with the Earth clock

 

[john 8]

To Whom... I hoped for some substantive response to my posts before being sent off to read more. I have read more SR books and papers than I can remember, and my comments come from careful reading of them.

I sectioned off this quote of yours to point out that you say that you have read much on the topic of SR, and that you read them carefully. Now I do not know how old you are or to what degree of education you have had, but I am very suspect of your assertion that you have read data on SR with care. I normally do not take a tone that I am going to take with you on what you have said, but I need to point out to you that you have either not carefully read data concerning SR, or you have not been careful in what you write regarding SR.

My point being this following quote:

Thus for every result obtained with A at 'rest' and B in 'motion' there is an equal result with B at 'rest' and A in 'motion'. Thus my early post, when they reunite each twin thinks the other one is younger. I believe that this is what the 1905 paper says. How it's explained has not yet known, is it?

Do you actually read what you write? You say that when the twins reunite they think the other one is younger. In the twin paradox when the twins reunite they see each other and notice from physical changes that aging has occurred in one of the twins, what is this reunite and thinks one is younger, wow, what a misunderstanding on your part.

Next is this quote:

I believe that this is what the 1905 paper says. How it's explained has not yet known, is it?

If you read about something your intension is to gain a better understanding of that subject. Right?
So how can you say that you carefully read data on SR and then walk away from Einstein’s writing with no more than a belief. Einstein did not write something that was to be believed in, it was a scientific theory, not some belief. Maybe you did not mean to use the word believe, that is why I asked if you actually read what you write or were careful about what you write.

Sorry about being so picky, but this is a science form and you really have to be specific in what you say.

One last point.

Einstein asserts that all inertial frames are equal, or in his terms from Relativity,1952, '... every motion must be considered only as a relative motion', and '...two forms, both of which are equally justifiable: (a) The carriage is in motion relative to the embankment.(b) The embankment is in motion relative to the carriage.'

I am familiar with this example that Einstein uses to describe relative motion and frames of reference.
I only say this because I am going to point something out in this example and have you think about it.

Now I am sure that you are familiar with Newton’s three laws of motion. I want to direct your attention to the first law. For those of you reading this who are unfamiliar with Newton’s first law I will I will list it for you. Mind you this is paraphrased, you can look up all the laws on the web if you like.

The first law states: 1. A physical body will remain at rest unless an external force acts on it, a physical body will continue to move at a constant velocity in a straight path, unless an external force acts upon it.


In essence it takes the application of force or energy to cause a change in a physical body.

Now with that in mind let's look at this train and embankment example that Einstein talks about in his book.

When the train moves relative to the embankment that train is having a force applied to it in order for it to move. No force, no motion. Correct?

A passenger on this train that is moving in a straight line at a constant velocity will not notice that he is in motion, but he will see the embankment pass by as he sits on the moving train. And so the passenger could conclude that the embankment is moving and he is at rest.

Now we know that the train is moving because a force is being applied to it. Even if the passenger does not notice the motion of the train, the train is moving because it is being acted upon by a force. The motion of the train is not determined by a passengers perception of motion. The train is moving whether the passenger perceives it or not.

Now for this passenger to think that the embankment is moving and not him would be a mistake. The embankment is not moving because there is no force being applied to move the embankment. Just because the embankment appears to be moving does not make it so.

So those of you who are now reading this, chomping at the bit to say I am wrong about this whole frame of reference concept, you will have to show the force being applied to the embankment. There is none. The state of that embankment or any object that the moving train passes by will not change because a passenger mistakenly perceives it to be so.

A guy driving by a house in a car will not cause that house to move.

So all of the descriptions that Einstein made about frames of reference in his book do not change the basic laws of nature. In order to move an object you have to apply a force to it.

Anyone is free to give an example of how an object that is moving due to an application of force will in fact cause another object that is at rest due to absence of force being applied to it to move. Objects do not actually move because someone thinks it is moving. The object may appear to be moving to someone, if no force is being applied to that object then the object is not moving or being changed.

Go ahead and defend Einstein, I know that I have struck a nerve with some of you.

Alright, now let's get to the actual topic of this thread. The twin paradox and time dilation. I wrote about this in the thread entitled time dilation so I will just copy and paste it here because it is applicable.



In regards to time dilation there are a few outpoints that need to be resolved. In order for the phenomenon of time dilation to be taken seriously as an actual event we need to establish what a clock is and its function and establish if time is a physical thing or not.

First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock? Yes/No

If No, than please explain or give a reference on how a clock can move or change without any energy being involved.

If yes, than what types of energy can be used to motivate the machine called a clock?

Can electricity be used? Yes

Can spring tension be used? Yes

Can the motion of mass (as in a water clock, an atomic clock) be used? Yes

I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.

You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.

If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.

In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.

So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.

If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing or a form of energy is absurd.

Physics does not define or recognize time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.

You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.

Let the discussion begin.

 

[DrGreg]

Now we know that the train is moving because a force is being applied to it. Even if the passenger does not notice the motion of the train, the train is moving because it is being acted upon by a force. The motion of the train is not determined by a passengers perception of motion. The train is moving whether the passenger perceives it or not.

Now for this passenger to think that the embankment is moving and not him would be a mistake. The embankment is not moving because there is no force being applied to move the embankment. Just because the embankment appears to be moving does not make it so.

There isn't just a forward force acting on the train from the engine. There are lots of other forces too, such as air resistance, friction in the wheel-bearings and so on. When you add up all the forces acting on the train, the total force is exactly zero (assuming constant velocity). This isn't even relativity, it's elementary Newtonian mechanics. You said it yourself:

The first law states: 1. A physical body will remain at rest unless an external force acts on it, a physical body will continue to move at a constant velocity in a straight path, unless an external force acts upon it.

 

[matheinste]

I sectioned off this quote of yours to point out that you say that you have read much on the topic of SR, and that you read them carefully. Now I do not know how old you are or to what degree of education you have had, but I am very suspect of your assertion that you have read data on SR with care. I normally do not take a tone that I am going to take with you on what you have said, but I need to point out to you that you have either not carefully read data concerning SR, or you have not been careful in what you write regarding SR.

My point being this following quote:

Do you actually read what you write? You say that when the twins reunite they think the other one is younger. In the twin paradox when the twins reunite they see each other and notice from physical changes that aging has occurred in one of the twins, what is this reunite and thinks one is younger, wow, what a misunderstanding on your part.

Next is this quote:





If you read about something your intension is to gain a better understanding of that subject. Right?
So how can you say that you carefully read data on SR and then walk away from Einstein’s writing with no more than a belief. Einstein did not write something that was to be believed in, it was a scientific theory, not some belief. Maybe you did not mean to use the word believe, that is why I asked if you actually read what you write or were careful about what you write.

Sorry about being so picky, but this is a science form and you really have to be specific in what you say.

One last point.



I am familiar with this example that Einstein uses to describe relative motion and frames of reference.
I only say this because I am going to point something out in this example and have you think about it.

Now I am sure that you are familiar with Newton’s three laws of motion. I want to direct your attention to the first law. For those of you reading this who are unfamiliar with Newton’s first law I will I will list it for you. Mind you this is paraphrased, you can look up all the laws on the web if you like.

The first law states: 1. A physical body will remain at rest unless an external force acts on it, a physical body will continue to move at a constant velocity in a straight path, unless an external force acts upon it.


In essence it takes the application of force or energy to cause a change in a physical body.

Now with that in mind let's look at this train and embankment example that Einstein talks about in his book.

When the train moves relative to the embankment that train is having a force applied to it in order for it to move. No force, no motion. Correct?

A passenger on this train that is moving in a straight line at a constant velocity will not notice that he is in motion, but he will see the embankment pass by as he sits on the moving train. And so the passenger could conclude that the embankment is moving and he is at rest.

Now we know that the train is moving because a force is being applied to it. Even if the passenger does not notice the motion of the train, the train is moving because it is being acted upon by a force. The motion of the train is not determined by a passengers perception of motion. The train is moving whether the passenger perceives it or not.

Now for this passenger to think that the embankment is moving and not him would be a mistake. The embankment is not moving because there is no force being applied to move the embankment. Just because the embankment appears to be moving does not make it so.

So those of you who are now reading this, chomping at the bit to say I am wrong about this whole frame of reference concept, you will have to show the force being applied to the embankment. There is none. The state of that embankment or any object that the moving train passes by will not change because a passenger mistakenly perceives it to be so.

A guy driving by a house in a car will not cause that house to move.

So all of the descriptions that Einstein made about frames of reference in his book do not change the basic laws of nature. In order to move an object you have to apply a force to it.

Anyone is free to give an example of how an object that is moving due to an application of force will in fact cause another object that is at rest due to absence of force being applied to it to move. Objects do not actually move because someone thinks it is moving. The object may appear to be moving to someone, if no force is being applied to that object then the object is not moving or being changed.

Go ahead and defend Einstein, I know that I have struck a nerve with some of you.

Alright, now let's get to the actual topic of this thread. The twin paradox and time dilation. I wrote about this in the thread entitled time dilation so I will just copy and paste it here because it is applicable.



In regards to time dilation there are a few outpoints that need to be resolved. In order for the phenomenon of time dilation to be taken seriously as an actual event we need to establish what a clock is and its function and establish if time is a physical thing or not.

First thing that needs to be established is the exact way in which a clock is motivated to move or count off numbers. Is energy being applied to it in some manner to motivate this machine called a clock? Yes/No

If No, than please explain or give a reference on how a clock can move or change without any energy being involved.

If yes, than what types of energy can be used to motivate the machine called a clock?

Can electricity be used? Yes

Can spring tension be used? Yes

Can the motion of mass (as in a water clock, an atomic clock) be used? Yes

I am sure some of you could think of other ways in which energy can be used to motive a clock, but in all of these different types of energy that can be thought of that in actuality cause a change in a clock, is time an energy that can be detected by a clock or has the ability to change the workings of this machine known as a clock.

You see the question of time dilation can only be answered when it has been established what causes a change in any clock and is time an actual physical thing that has the ability to cause change in a clock.

If you say that time is indeed is a physical thing and can actually influence the workings of a clock, then you would have to explain how this occurs. It has not been described in any writings on this planet.

In order for there to be a physical occurrence of time dilation, time would have to be a form of energy and you would need to have a physical measuring device that is capable of detecting this form of energy called time.

So. To those of you who think that time dilation is an actual physical occurrence, can you explain how this phenomenon works, or at least show a reference that explains it.

If you say that experiments on time dilation have been done to prove the occurrence. Let me remind you that two machines that go out of synch after being moved around only goes to show that machines can go out of synch, saying that this out of synch occurrence is due to some influence of a thing that physics has never defined as a thing or a form of energy is absurd.

Physics does not define or recognize time as a form of energy, yet it takes energy to change a clock. So in order to have the occurrence known as time dilation to be an actual physical phenomenon time has to be a form of energy. You cannot have it both ways.

You can argue and protest all that you like. Science does not recognize time as a form of energy. Time dilation involves the notion that this thing called time is being dilated, and the only way to measure this dilation is with a machine known as a clock. Clocks are only motivated by energy. So in order for this time thing to influence a clock this time thing has to be a form of energy.

Let the discussion begin.

Any elementary textbook on Special Relativity or even Wikipedia explains these things to the stisfaction of the vast majority of people, some of who, unlike me, are very intelligent and not easily taken in. .

Matheinste.

 

[john 8]

There isn't just a forward force acting on the train from the engine. There are lots of other forces too, such as air resistance, friction in the wheel-bearings and so on. When you add up all the forces acting on the train, the total force is exactly zero (assuming constant velocity). This isn't even relativity, it's elementary Newtonian mechanics. You said it yourself:

Right, so do you think that the embankment is moving?

 

[john 8]

Any elementary textbook on Special Relativity or even Wikipedia explains these things to the stisfaction of the vast majority of people, some of who, unlike me, are very intelligent and not easily taken in. .

Matheinste.

So do these textbooks define time? Is time an energy or not? What do these textbooks say about the nature of time to your satisfaction? After reading these textbooks what is your understanding of time. You have completely ignored what I wrote. All you have to do is provide evidence from any of these textbooks or wikipedia that time is some form of energy.

What I have stated about time dilation is completely logical and follows the laws of nature. Time has to be a form of energy in order to exist and have some effect on a clock. You have ignored the question and obvious outpoint that I have brought up by saying that it is explained in textbooks and wikipedia.

Fine, show me. Show me the explanation of time motivating a clock.

I have given a complete logical explanation of how time dilation is not an actual physical phenomenon. If you disagree than give me your explanation. Your rebuttal to my explanation is lacking facts. If you disagree then explain why.

Does your understanding of subjects depend on majority rule? The more that believe it the truer it is.

Come on, use some science, that is what this form is for. Please try again.

Do you think or do these textbooks say time is a form of energy?

Anybody else up to the challenge?

 

[DrGreg]

Right, so do you think that the embankment is moving?

Relative to the train, yes.

 

[JesseM]

So do these textbooks define time? Is time an energy or not? What do these textbooks say about the nature of time to your satisfaction? After reading these textbooks what is your understanding of time. You have completely ignored what I wrote. All you have to do is provide evidence from any of these textbooks or wikipedia that time is some form of energy.

What I have stated about time dilation is completely logical and follows the laws of nature. Time has to be a form of energy in order to exist and have some effect on a clock. You have ignored the question and obvious outpoint that I have brought up by saying that it is explained in textbooks and wikipedia.

The ideas of time "having an effect on clocks" or time being "energy" don't appear to make much sense. In SR it is a clock's velocity in a particular inertial frame that corresponds to how much it slows down in this frame, and there is also no frame-independent "objective" truth about whether a clock is running slow at any moment--in a frame where the clock is in motion it is running slow, in a frame where the same clock is at rest it's ticking at the normal rate, both are equally valid perspectives. There are objective frame-independent truths about what two clocks read when they cross paths at a single location, though, so it is true that if two clocks cross paths once and then cross paths again later, and one of the two clocks moved inertially between these two crossings (constant speed and direction) while the other accelerated at some point (changed speed or direction), then the one that accelerated will have elapsed less time in total between the two meetings. This is similar to the fact that on a 2D surface, if you have two cars whose paths cross at two points, and one was moving in a straight line between the crossings while the other changed directions at some point, then the one that changed directions will have elapsed a larger amount on its odometer (which measures distance traveled on the plane rather than time) between the two crossings, since a straight line is the shortest distance between points on a plane--see my discussion of this analogy in post #64 on this thread.

 

[john 8]

Originally Posted by john 8


“Right, so do you think that the embankment is moving?”

Relative to the train, yes.

If the train has no force being applied to it, it will not move. Add enough force and the train will move.

When the train is moving, is there a force being applied to the embankment to move it?

Is the embankment having a force applied to it?


If the train is moving along the embankment and all of the windows are blacked out so no one on the train can see the embankment, is the embankment moving?

Does a moving train cause a force to be applied to the embankment?


When you take your hand and move it over a book are you causing that book to move? Is the book causing your hand to move?


Does the actual action of one object moving cause another object to move? If so, how far does this field of influence spread out from a moving object?

Right now there are cars, planes ships, stars, people, animals, planets, baseballs, fish, there are so many object moving right now in a different frame of reference to me. Which way and how fast am supposed to be moving relative to them. Are you saying that all moving objects have a physical effect on all other objects?

Do you honestly think that the train is physically moving the embankment? Yes/No

It can appear that the embankment is moving, but in reality is the embankment being forced to move?

The embankment is either physically moving in space relative to a starting point and an ending point, or it is not actually moving it just appears to be doing so. Which is it according to the laws of nature?

DrGreg, tell me if you think that all it takes to move an object is to move past it at a constant velocity in a straight line.

Is the embankment actually moving according to the laws of physics

 

[john 8]

The ideas of time "having an effect on clocks" or time being "energy" don't appear to make much sense. In SR it is a clock's velocity in a particular inertial frame that corresponds to how much it slows down in this frame, and there is also no frame-independent "objective" truth about whether a clock is running slow at any moment--in a frame where the clock is in motion it is running slow, in a frame where the same clock is at rest it's ticking at the normal rate, both are equally valid perspectives. There are objective frame-independent truths about what two clocks read when they cross paths at a single location, though, so it is true that if two clocks cross paths once and then cross paths again later, and one of the two clocks moved inertially between these two crossings (constant speed and direction) while the other accelerated at some point (changed speed or direction), then the one that accelerated will have elapsed less time in total between the two meetings. This is similar to the fact that on a 2D surface, if you have two cars whose paths cross at two points, and one was moving in a straight line between the crossings while the other changed directions at some point, then the one that changed directions will have elapsed a larger amount on its odometer (which measures distance traveled on the plane rather than time) between the two crossings, since a straight line is the shortest distance between points on a plane--see my discussion of this analogy in post #64 on this thread.

If you think that the idea of time having an effect on clocks does not appear to make much sense, then what do clocks measure and how are they motivated? If clocks do not measure this thing called time then what are clocks doing?


So is time a physical thing? Yes/No

I have been asking this question over and over and still no proof that time is a physical thing. Does anyone see this? Come on people, all I am asking for is scientific evidence. Stop with all the rhetoric and run around and provide evidence that time is a physical thing.

Let me ask you, did you in the above quote give evidence that time is a physical thing? Yes/No.

If so please point it out because I do not see any.

 

[JesseM]

If you think that the idea of time having an effect on clocks does not appear to make much sense, then what do clocks measure and how are they motivated? If clocks do not measure this thing called time then what are clocks doing?

Well, I'd say time is an abstraction based on the fact that we see various physical objects which exhibit regular cycles (like the atomic oscillations that atomic clocks are based on) such that when the objects are next to each other the ratio of their cycles remains constant. For example, if I have an atomic clock based on oscillations of cesium 133 atoms, and a spring clock which ticks in the units we label as "seconds", then if you place them next to each other on Earth you'll find the atomic clock always registers around 9,193 billion ticks between each tick of the spring clock (it will depend on how good the spring clock is of course, nowadays a second is supposed to correspond to exactly 9192631770 oscillations of such a cesium 133 clock). If you take a second atomic clock/spring clock pair which is physically identical to the first and take them on a relativistic journey through space and then return them to Earth, the pair that took the journey will have registered less ticks than the pair that remained on Earth, but the ratio between the number of ticks registered on the atomic clock that took the journey and the number of ticks registered on the spring clock that took the journey should still be about 9,193:1, assuming both clocks were next to each other as they traveled so their velocity at each moment (in whatever frame we choose) would have been the same. From this you can abstract that all paths through spacetime have a certain "proper time" along them, different clocks will divide the proper time into different increments but the ratio between ticks of different clocks should stay the same as long as they take the same path through spacetime.

You could say something pretty analogous for "distance" on a 2D surface as an abstraction of what instruments like odometers measure when they take particular paths on this surface. There are various ways you could construct an odometer--one might be based on number of revolutions of a car's wheel, another might be keeping track of how quickly marks on the ground are passing the car at each moment, another might actually be laying down a trail of measuring-tape behind the car--but whatever increments each one is using, if you put them together in the same car the ratio of the number of increments each one measures as the car travels should be pretty close to constant (depending on how accurate they are), regardless of what path the car takes. And if we send two cars on different paths between points A and B, one car's group of odometers may measure different numbers of increments between A and B than the other car's group of identical odometers, yet the ratio of type-1-odometer-increments to type-2-odometer-increments will be the same for both cars, so we say that the two paths had different "distances" which each odometer divided up into different increments.

However, though we may say based on this that clocks "measure time" along paths through spacetime and odometers "measure distance" along paths on a 2D surface, I don't think that's quite the same thing as saying "time has an effect on clocks" or "distance has an effect on odometers...I guess it depends on what you mean by "effect" though. Certainly it wouldn't make sense to treat distance or time as things that are supplying energy to clocks or odometers though.

So is time a physical thing? Yes/No

Could you define what you mean by "physical"? The time along a path through spacetime is at least "physical" if you just mean "there's a well-defined physical procedure for determining the amount of 'time' on a path through spacetime, and this procedure gives a frame-invariant answer", but you seem to be implying something more when you suggest that time is physical and therefore must have energy. It would also help if you told me whether you think "distance" is a "physical thing" or not.

 

[DrGreg]

If the train has no force being applied to it, it will not move. Add enough force and the train will move.

There is confusion here over the meaning of the word move. When I say "the train moves relative to the embankment", I mean it continues to move at a constant velocity. I don't mean it begins to move from being at rest -- I would call that "acceleration" rather than movement, to avoid confusion.

You quoted Newtons Laws in an earlier post. Let me remind you:

1. A body persists its state of rest or of uniform motion unless acted upon by an external unbalanced force
2. The net force on an object is equal to the mass of the object multiplied by its acceleration
3. To every action there is an equal and opposite reaction

Therefore for an object to move (i.e. continue moving) no force is required. Forces cause acceleration i.e. a change of motion.

When the train is moving, is there a force being applied to the embankment to move it?

No. Neither is there a force being applied to the train. (1st law)

Is the embankment having a force applied to it?

No. Neither is the train having a force applied to it (1st law)

If the train is moving along the embankment and all of the windows are blacked out so no one on the train can see the embankment, is the embankment moving?

Relative to the train, yes.

Does a moving train cause a force to be applied to the embankment?

No. Neither does the embankment cause a force to be applied to the train. (1st law)

When you take your hand and move it over a book are you causing that book to move?

Relative to my hand, yes.

Is the book causing your hand to move?

No, my brain is.

Does the actual action of one object moving cause another object to move? If so, how far does this field of influence spread out from a moving object?

This isn't "cause", it's logic. If A moves relative to B then B moves relative to A, by definition.

Right now there are cars, planes ships, stars, people, animals, planets, baseballs, fish, there are so many object moving right now in a different frame of reference to me. Which way and how fast am supposed to be moving relative to them. Are you saying that all moving objects have a physical effect on all other objects?

No. The fact that A is moving relative to B does not imply that B (or A) caused the motion to occur.

Do you honestly think that the train is physically moving the embankment? Yes/No

I never said that. I said the embankment was moving relative to the train. I never said how that motion was initiated

It can appear that the embankment is moving, but in reality is the embankment being forced to move?

Don't understand the question

The embankment is either physically moving in space relative to a starting point and an ending point, or it is not actually moving it just appears to be doing so. Which is it according to the laws of nature?

Neither. It is moving relative to the train. No more, no less. Any motion must be relative to something.

DrGreg, tell me if you think that all it takes to move an object is to move past it at a constant velocity in a straight line.

Yes. I am talking about continuation of motion, not acceleration.

Is the embankment actually moving according to the laws of physics

Relative to the train, yes.

Everything I've said above follows from Newton's theories, never mind Einstein. Before you come here criticising relativity, you really ought to find out something about pre-relativity science first.

 

[spikenigma]

Which scenario are you talking about? The one where the rocket travels past Earth at constant velocity and the two twins are born at the moment the rocket is next to Earth, then the rocket continues onward at constant velocity forever without turning around?

In this case there is no objective truth about which twin is older, in the frame where the Earth is at rest the rocket-twin ages more slowly, in the frame where the rocket is at rest the Earth-twin ages more slowly. Are you familiar with the relativity of simultaneity?

In the Earth frame it might be true that the event of the Earth-twin's 40th birthday is simultaneous with the event of the rocket-twin's 32nd birthday, while in the rocket frame it would then be true that the event of the Earth twin's 40th birthday is simultaneous with the event of the rocket-twin's 50th birthday, so in each frame the moving twin is only aging at 0.8 the rate of the at-rest twin.

Only if you bring the twins back together to a single location in space will both frames have to agree on their respective ages at a single moment.

I think I understand what you are saying, but I need clarification. Let's say on their 40th birthday they both freeze their bodies. For the purposes of this discussion, perfect freezing

The rocket then returns to Earth, they then both unfreeze and they compare their ages

is one twin older?

On the other hand, if you're talking about the scenario in post #53 where you said "let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin", in this case the rocket must have turned around at some point to travel back to Earth, so the rocket did accelerate in the rocket-twin's lifetime.

I wanted to leave any accelerational effects out of my area of this discussion, so I'll leave the 'coming back slowly' area

 

[matheinste]

So do these textbooks define time? Is time an energy or not? What do these textbooks say about the nature of time to your satisfaction? After reading these textbooks what is your understanding of time. You have completely ignored what I wrote. All you have to do is provide evidence from any of these textbooks or wikipedia that time is some form of energy.

What I have stated about time dilation is completely logical and follows the laws of nature. Time has to be a form of energy in order to exist and have some effect on a clock. You have ignored the question and obvious outpoint that I have brought up by saying that it is explained in textbooks and wikipedia.

Fine, show me. Show me the explanation of time motivating a clock.

I have given a complete logical explanation of how time dilation is not an actual physical phenomenon. If you disagree than give me your explanation. Your rebuttal to my explanation is lacking facts. If you disagree then explain why.

Does your understanding of subjects depend on majority rule? The more that believe it the truer it is.

Come on, use some science, that is what this form is for. Please try again.

Do you think or do these textbooks say time is a form of energy?

Anybody else up to the challenge?

I do not think that time is a form of energy. However, how one describes/explains time is a subject to much philosophcal speculatio and I do not have any answers. Time is of course of much use in physics and so I will continue to use it despite my lack of a fundamental understanding.

My reference to textbooks was because at the point in the thread at which I made the comment you showed a lack of understaning, whch has continued since, about such basic points of SR as that which the train and embankment thought experiment explain.

I have no interest in a discusson about time. I have read much by heavyweights such as Reichenbach, Weyl, Eddington etc. but remain unenlightened. I hope eventually that you find an answer to satisfy you.

Matheinste

 

[JesseM]

I think I understand what you are saying, but I need clarification. Let's say on their 40th birthday they both freeze their bodies. For the purposes of this discussion, perfect freezing

The rocket then returns to Earth, they then both unfreeze and they compare their ages

is one twin older?

The Earth twin is older in years he has existed according to a clock that's been next to him since birth (as compared with a clock that's been next to the rocket twin since his own birth), but obviously not older in appearance or psychological age if they were both frozen at 40. In relativity the fundamental thing physicists are interested in is time elapsed on ideal clocks that take different paths through spacetime, though, talking about "aging" is just used as a kind of shorthand.

 

[spikenigma]

The Earth twin is older in years he has existed according to a clock that's been next to him since birth (as compared with a clock that's been next to the rocket twin since his own birth), but obviously not older in appearance or psychological age if they were both frozen at 40. In relativity the fundamental thing physicists are interested in is time elapsed on ideal clocks that take different paths through spacetime, though, talking about "aging" is just used as a kind of shorthand.

makes perfect sense, thankyou

 

[yogi]

One need not contemplate long voyages - two twin pion particles in the lab will exhibit vastly different decay rates if one is moving at a relatively high speed wrt the other - clocks attached to the particles will run at different rates and log different total times for the same spacetime interval. One particle is aging less even though neither particle has left the room during the experiment - this is an example of a local one way voyage - and as per previous posts - you can double the answer to get the result if one pion turned around and zipped back to its starting point before decaying

 

[JM]

In response to post 74:
Thank you JesseM for your answers to my concerns.
I don't disagree with the first paragraph. The integral reduces to Einsteins result when v is constant and higher terms are omitted from the expansion of the radical. It's hard for me to see what variable speed will do to the result. It appears that its the addition of a new factor, variable speed, to relativity rather than a method to determine whether a frame is not inertial.
You are right, kinematics in general includes acceleration. I was thinking of a more restricted application. In any case I think the 1905 paper excludes acceleration.
Lets look at par.4 of the 1905 paper. It formulates the moving clock problem and then calculates the amount by which the moving clock is slow. The analysis starts with the time transform equation given immediately before par. 4. The position of the clock at the origin of the moving axes is identified, x =vt, this is entered into the time equation and the result simplified. The moving clock appears to be slow by t v squared/2csquared. It is then argued that a clock moving at constant ( speed ) along a closed curve will be also slow by this same amount. There is an implicit assumption here that the behavior of the moving clock is the same when moving along the closed curve as it is when moving along a straight inertial line that was used to derive the time equation. Thus this analysis excludes the external force needed to restrain the clock to move along the curved line and the resulting acceleration. This reasoning convinces me that both clocks/twins are represented as inertial by the 1905 analysis, and that there is no need to introduce rockets or acceleration to explain the results.

 

[JesseM]

In response to post 74:
Thank you JesseM for your answers to my concerns.
I don't disagree with the first paragraph. The integral reduces to Einsteins result when v is constant and higher terms are omitted from the expansion of the radical. It's hard for me to see what variable speed will do to the result. It appears that its the addition of a new factor, variable speed, to relativity rather than a method to determine whether a frame is not inertial.

It's not really a significantly new idea from the ones expressed in the 1905 paper, this sort of integral is what Einstein was alluding to in the last paragraph of section 4 when he wrote "If we assume that the result proved for a polygonal line is also valid for a continuously curved line...". To elaborate, if you have a polygonal path made up of three constant-velocity segments joined by instantaneous accelerations, with the three segments having velocities v_1, v_2, and v_3 in some inertial frame, and the lengths of time that each segment lasted for in that frame being \Delta t_1, \Delta t_2, and \Delta t_3, then to find the total time elapsed on a clock that traversed this polygonal path, do you agree that you'd just look at the sum (\Delta t_1 * \sqrt{1 - v_1^2 /c^2}) \, + \, (\Delta t_2 * \sqrt{1 - v_2^2 /c^2}) \, + \, (\Delta t_3 * \sqrt{1 - v_3^2 /c^2})? If so, then you should be able to see why if instead we have a polygonal path made up of some large number N of segments, the total time elapsed by a clock following this path would be given by the sum \sum_{i=1}^N (\Delta t_i * \sqrt{1 - v_i^2 /c^2}). For any continuously curved path, you can always approximate it using a series of straight segments, and if you choose the segments so that they all last the same time \Delta t, then the time elapsed on this approximate path is \sum_{i=1}^N (\Delta t * \sqrt{1 - v_i^2 /c^2}). In the limit as the time of each segment in the approximation approaches zero, the difference between the approximation and the original curved path also approaches zero, and since an integral is just a limit of this sort of sum but with dt taken to be infinitesimally small, this means that the time on the continuous curve must be \int \sqrt{1 - v(t)^2 / c^2} \, dt.

You are right, kinematics in general includes acceleration. I was thinking of a more restricted application. In any case I think the 1905 paper excludes acceleration.
Lets look at par.4 of the 1905 paper. It formulates the moving clock problem and then calculates the amount by which the moving clock is slow. The analysis starts with the time transform equation given immediately before par. 4. The position of the clock at the origin of the moving axes is identified, x =vt, this is entered into the time equation and the result simplified. The moving clock appears to be slow by t v squared/2csquared. It is then argued that a clock moving at constant ( speed ) along a closed curve will be also slow by this same amount.

But why do you say the analysis excludes acceleration? Do you understand that even if speed remains constant, any change in direction is a type of acceleration, so the example in section 4 of a clock moving in a circle because it's on the equator of a rotating sphere would necessarily be a problem involving acceleration?

Thus this analysis excludes the external force needed to restrain the clock to move along the curved line and the resulting acceleration.

It's true that the cause of the acceleration is not relevant, but his analysis does suggest we can use time dilation to calculate the time elapsed on clocks whose velocity is not constant.

This reasoning convinces me that both clocks/twins are represented as inertial by the 1905 analysis, and that there is no need to introduce rockets or acceleration to explain the results.

Both twins cannot be inertial, since if they are at first moving apart but later moving back towards one another, one of them must have changed direction. Of course you can treat the non-inertial twin as taking a polygonal path consisting of two inertial segments at different velocities (different directions if not different speeds) joined by an instantaneous acceleration, but the fact remains that if one twin moves at constant velocity from beginning to end while the other twin changes velocity at some point on the journey, it will always be the inertial twin whose clock has elapsed more time when they reunite. Do you disagree?

 

[JM]

JesseM. Thanks again. Sorry I can't reply now, the system claims I am not logged in and erases my reply, so I would have to retype. Do you know how to work the system when your reply is long?

 

[JM]

Hey there The-Genius, are you still listening? I have a question for you. You say you heard about A and B and think they can't be different ( my parahprase). Can you say where you got your ideas?

 

[JM]

JesseM, reply to your recent post. I agree with your first point re the integral.
Re the second point: When Einstein used the equation for inertial frames to find time, he replaced his curved line at constant v with a straight line, thus with no acceleration.
Re the third point: yes, but time dilation also occurs for two inertial frames, as shown earlier in his paper.
Re your last point: I think you are commenting on what we know about the physics of the motion, forces and accelerations are surely present. But what Einstein did was to exclude them by his choice of equations. This is ok in a kinematic analysis, in the restricted sense.

 

[JesseM]

JesseM. Thanks again. Sorry I can't reply now, the system claims I am not logged in and erases my reply, so I would have to retype. Do you know how to work the system when your reply is long?

I think when you log in you have the option to click something that says "stay logged in" and that way it shouldn't log you out. But another option is just to copy your reply before you hit "submit reply", and that way if it erases it, you can just log in again and paste in your response and submit it right away.

JesseM, reply to your recent post. I agree with your first point re the integral.
Re the second point: When Einstein used the equation for inertial frames to find time, he replaced his curved line at constant v with a straight line, thus with no acceleration.

By "find time" you mean the time dilation equation? If so I agree that you derive the time dilation equation by looking at two events on a straight line segment, although this segment can be infinitesimally short.

Re the third point: yes, but time dilation also occurs for two inertial frames, as shown earlier in his paper.

By "third point" you mean my statement "It's true that the cause of the acceleration is not relevant, but his analysis does suggest we can use time dilation to calculate the time elapsed on clocks whose velocity is not constant."? If so, yes, I wasn't denying that you can also calculate the time dilation on clocks whose velocity is constant, in fact that's the easiest case.

Re your last point: I think you are commenting on what we know about the physics of the motion, forces and accelerations are surely present. But what Einstein did was to exclude them by his choice of equations. This is ok in a kinematic analysis, in the restricted sense.

But just talking about constant-velocity motion is not sufficient if you want to analyze the twin paradox, which is the main subject of the thread. Do you agree that in order for two twins to start out at the same position, then move apart, then later reunite, at least one of them has to change velocities at some point in his journey? (assuming we are analyzing things from the perspective of an inertial frame) And if so, do you agree that if one twin maintains a constant velocity between the event of the twins departing and the event of the twins reuining, while the other twin changes velocity at some point, then these facts are enough to guarantee that the constant-velocity twin will have aged more when they reunite, regardless of the specific velocities and times involved?

 

[JM]

JesseM. Thanks again for your reply.
"...at least one of them has to change velocity..." Yes. In the path of '1905' the moving clock moves at constant speed, but changes velocity from 'moving away' to 'moving back'.
" ...constant velocity motion is not sufficient...' I read the 1905 paper to be limited to constant velocity motion, by virtue of the use of the time equation for such motion to calculate the time for the closed path. I assume you are extending that analysis.
"...facts are enough to guarantee..." I can't comment on this because I haven't seen the analysis that leads to this conclusion.

I have enjoyed our exchange of ideas given in the spirit of friendship. I would like to continue but feel it's time to step back and try to digest this lengthy thread. I plan to monitor this thread for comments from you, or others , whom we seem to have lost.

Peace, and best wishes.

 

[JesseM]

JesseM. Thanks again for your reply.
"...at least one of them has to change velocity..." Yes. In the path of '1905' the moving clock moves at constant speed, but changes velocity from 'moving away' to 'moving back'.
" ...constant velocity motion is not sufficient...' I read the 1905 paper to be limited to constant velocity motion, by virtue of the use of the time equation for such motion to calculate the time for the closed path. I assume you are extending that analysis.

But you just said above that the clock "changes velocity from 'moving away' to 'moving back'", so you seem to agree that both twins don't have a constant velocity throughout the journey. The path involves two segments which individually have constant velocity, and thus you can calculate the time elapsed on each segment using the time dilation equation and then just add the two times to get the total time elapsed, but the entire path does not involve a single constant velocity, that's all I meant by "constant velocity motion is not sufficient". If each clock moves at a single constant velocity forever, then they will just move away forever after passing each other so they can't compare their clocks on two different meetings.

"...facts are enough to guarantee..." I can't comment on this because I haven't seen the analysis that leads to this conclusion.

A simple way to prove it is to note that all frames will agree on the time elapsed on the two clocks between their meetings, so you can just analyze things from the frame where the inertial clock is at rest, and since the other clock will have a nonzero velocity for at least part of its trip in this frame, it will tick slower than the inertial clock during those parts of its trip and thus will have elapsed less total time when they reunite.