Twin Paradox: Explaining the Relativity of Aging

[john 8]

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. .

Hi JesseM. You are very thorough in your statements. I really want to be clear here. I think that you are a good terminal to talk to about many science subjects. You come across clear and concise. You use science as much as possible to explain your point of view. I like that. That is what is needed by more people who communicate on this forum.

I would like to narrow my debate, discussion between you and me. It tends to get a bit distracting trying to juggle many different conversations with different people. I am not going to ignore any other conversations or questions directed at me but I just want to have a one on one.

Having said all that, I have been asking if time is a physical thing as you know.

Let's just say that I am undecided as to the true physical reality of time. I could go either way. Now when I ask you if time is a physical thing what I am asking you is what your knowledge of time is, from what you have learned about time, do you think that time is a physical thing, that is what I am asking. So when I ask you a question regarding time I am not looking for an opinion, I am asking you to relay to me what the science of physics says about time.

As an example you said in the above quote that you would say time is an abstraction. I have seen some not so standard, simple kids dictionaries define time that way. I am not implying that what you said was childish, just that if you were to use that definition of time in a discussion on time dilation, what you would be saying is that an abstraction is dilating, now what kind of exact science is that?

You see opinions or incomplete, or simple definitions are not of much use because everyone has an opinion, and incomplete definitions raise more questions then they answer. I would like to go to the source, what does physics say that time is.

You see I have gone to many sources that contain data on time, standard dictionaries, physics books, books written by leading authorities in the field of physics, I have talked to people who teach physics, in all of this research I have not found any data that says time is a physical thing according to the definition of physical thing as defined by a physics book or standard dictionary. I have also not perceived any such force, energy, or object that is called time.

So when I pose the question is time physical, yes I get many responses from people that claim time is real, many people will say in their opinion time is real, or I think time is real and such, but when I ask these same people to tell me what physics says about time, and is time considered to be a real physical thing according to the field of physics. Well you can see by all of the gyrations people go through when asked that type of question by looking at the responses on this thread.

If you notice, there has not been one reference presented on this thread that states time is a physical thing according to physics.

Now I do not know if you believe in a god, but if you do, I am sure you have run into people who question your faith by asking you to prove your god is real, well you know that you can’t do that, your god is real to you according to what you believe and that is it.

Even if God is a real person, spirit, He is not real according to the physics definition of real. God is real according to the Christian definition of real. Those who think God is real and believe that He is real are doing so from the point of view of their religion and faith. God is in actuality real to some people, you can not deny that.

If you try to define God with the standards of physics you will run into trouble, if God is real or not has no bearing on physics at this time. Physics is what it is if God exist in this physical universe or not.

So this brings me back to my point. I am asking you if physics defines time as a real physical thing as it pertains to how it is used in physics. Physics uses the term time often, what definition of time are they using? If you think that time is a physical thing as defined by physics or any standard dictionary then please direct me to that reference.

Think of my question of time as not an attack, but just an inquiry. I have looked and found no evidence, that does not mean there is none to be found. You and others seem to disagree with my observation, so I am just asking you for the information that you have that says time is a physical thing according to the standards, teaching, laws of physics. Time is used in all physics books, what definition of the term time is being used, that’s all.

Einstein used time to describe many things and phenomenon, he gave no definition of time.

Einstein used human language to communicate his ideas and concepts to others, he picked the term time to rely an idea, if he did not feel it necessary to inform people of a specialized definition of time, then we are going to have to assume that he was satisfied with the way the world has already defined time.

If anyone today were to read the book on Relativity and they were not sure of what context Einstein was using the term time, that reader would normally turn to a good dictionary and find many different definitions of the term time, all depending on the context in which time was being used.

So that brings us back to what is time?

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.

I am defining physical the way it is defined in any standard dictionary or physics reference book. My definition of physical is the same as those.





john 8

 

[john 8]

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

No. Neither is there a force being applied to the train. (1st law)No. Neither is the train having a force applied to it (1st law)Relative to the train, yes.No. Neither does the embankment cause a force to be applied to the train. (1st law)Relative to my hand, yes.No, my brain is.This isn't "cause", it's logic. If A moves relative to B then B moves relative to A, by definition.No. The fact that A is moving relative to B does not imply that B (or A) caused the motion to occur.I never said that. I said the embankment was moving relative to the train. I never said how that motion was initiatedDon't understand the questionNeither. It is moving relative to the train. No more, no less. Any motion must be relative to something.Yes. I am talking about continuation of motion, not acceleration.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.

Thank you very much for your reply. you really put some effort into it. I asked you many questions and quite frequently people do not respond to all of them.

In order to keep this short I will try to ask only a few questions. First I would like to say that I have read many books on Relativity and the basic concepts just don’t jive. Maybe I have a misunderstanding, that is why I am on this thread.

I would really like to get Relativity straight if I have a misunderstanding. I would like to take one concept at a time, and start with the basic concept of frames of reference.

Here is my understanding of physics before Einstein. According to Newton’s 1st law of motion it will take energy, or a force to cause a object that is in a state of rest, or experiencing a balance of forces (as in a ball being supported by a spring), the force of gravity is pulling the ball down, the spring is pushing the ball up, there is a balance of force and the ball is not moving from point A to point B.

Correct so far?


Now in order to cause a change in an object, energy or force has to be applied. If an object is existing in one state, in order to cause a change in that object, energy has to be applied to that object.

Correct so far?

I say that Newton’s laws of motion work in all situations involving energy and objects, no exceptions.

Correct so far?


I want to ask you about frames of reference, but I want to make sure that we are in agreement on what I have stated so far.

Thank You.

John 8

 

[DrGreg]

Thank you very much for your reply. you really put some effort into it. I asked you many questions and quite frequently people do not respond to all of them.

In order to keep this short I will try to ask only a few questions. First I would like to say that I have read many books on Relativity and the basic concepts just don’t jive. Maybe I have a misunderstanding, that is why I am on this thread.

First of all I'd like to say I very much welcome what I perceive to be a change of tone in your responses, to both myself and to JesseM.

I think some people won't give direct answers to posts in which you ask many questions because they think the whole post is based on a misunderstanding, and they want to correct that misunderstanding directly instead of giving detailed answers to every question.

The impresssion you have given so far, whether you intended to or not, was that you weren't really listening to the answers, that you were simply telling us all "what science says" (and actually getting it wrong in the process). I say this to you, not out of any personal disrepect, but simply to try and explain why you've had such a bad response from most people so far.

I would really like to get Relativity straight if I have a misunderstanding. I would like to take one concept at a time, and start with the basic concept of frames of reference.

Here is my understanding of physics before Einstein. According to Newton’s 1st law of motion it will take energy, or a force to cause a object that is in a state of rest, or experiencing a balance of forces (as in a ball being supported by a spring), the force of gravity is pulling the ball down, the spring is pushing the ball up, there is a balance of force and the ball is not moving from point A to point B.

Correct so far?

Yes. In fact we say (in Newtonian physics) the upward force and downward force exactly cancel each other out, so the total force acting on the object is zero and it doesn't move. Energy is not the same thing as force. It requires energy to move a force through a distance; if you apply a force but nothing moves, no energy is used. The force of the spring does not imply any energy (unless the object moves).

Now in order to cause a change in an object, energy or force has to be applied. If an object is existing in one state, in order to cause a change in that object, energy has to be applied to that object.

Correct so far?

That is a bit too vague for me to agree to. A "change of state" could mean many things; whether that actually requires energy or force would depend on what exactly you mean. It's certainly true that a change in velocity, a change of spin, a change of temperature are all things that require a transfer of energy either into or out of the object.

I say that Newton’s laws of motion work in all situations involving energy and objects, no exceptions.

Correct so far?

Provided the laws are applied correctly (and ignoring relativistic corrections to Newton's laws), yes.

I want to ask you about frames of reference, but I want to make sure that we are in agreement on what I have stated so far.

Thank You.

John 8

I will just point out that all the answers I gave above are assuming that we choose just one inertial frame of reference and stick with it. It is possible for an object's velocity to "change" simply by measuring it in a different frame. If a train is slowly moving at 5mph, and I walk forward at 5mph relative to the train, then I am moving at 10mph relative to the ground. If someone else jumps off the train while it is moving, my velocity, relative to that person, has increased from 5mph to 10mph. But no force or energy has been applied to me.

On a general point, you have often said things like

I am defining physical the way it is defined in any standard dictionary or physics reference book. My definition of physical is the same as those.

The problem is that there are lots of different dictionaries and physics reference books. They will all use different wordings when they define things. If you want to refer to someone else's definition, you need to tell us, explicitly, word-for-word, precisely what that definition is, and precisely which book you got it from, otherwise we genuinely don't know what you are talking about and so we cannot make any sensible comment about it.

 

[JesseM]

Having said all that, I have been asking if time is a physical thing as you know.

Let's just say that I am undecided as to the true physical reality of time. I could go either way. Now when I ask you if time is a physical thing what I am asking you is what your knowledge of time is, from what you have learned about time, do you think that time is a physical thing, that is what I am asking. So when I ask you a question regarding time I am not looking for an opinion, I am asking you to relay to me what the science of physics says about time.

The problem is I still don't know what is meant by the words "physical thing". It is not a technical term that's used in physics, certainly. Perhaps you have given a definition earlier on the thread; if so, could you repost it?

As an example you said in the above quote that you would say time is an abstraction. I have seen some not so standard, simple kids dictionaries define time that way. I am not implying that what you said was childish, just that if you were to use that definition of time in a discussion on time dilation, what you would be saying is that an abstraction is dilating, now what kind of exact science is that?

But as I said, time is an abstraction from the fact that we can build physical clocks which tick at a constant rate relative to one another when they are next to each other, so when we talk about "time dilation", this is itself an abstraction from the fact that physical clocks can be measured to show fewer elapsed ticks when they are in motion relative to other clocks. If you can use the mathematics of time dilation to make accurate quantitative predictions about the behavior of clocks, isn't that an "exact science" regardless of whatever philosophical issues you may bring up with time being an "abstraction"?

I should also point out that when I refer to time being an abstraction, this isn't a unique feature of time specifically, I would say that any physical quantity which appears in the equations of physics, like distance or energy or mass or force, is also an abstraction. You determine the "mass" of a physical object by looking at readings on a scale or other mass-measuring device, just like you determine the "time" between two events by looking at readings on a clock. I could go even further and say that any of the particles that appear in particle physics is also an abstraction--the only way to detect a particle like an electron is to note that the readings of certain detectors (curling paths in a bubble chamber, for example) can be predicted in a quantitative way by mathematical models which include abstract mathematical elements called "electrons". So, to me they are all abstractions from real physical instrument readings. That doesn't mean they aren't also "real", just that since we have no way to experience them directly in a way that doesn't depend on comparing instrument readings to an abstract mathematical model (unlike, say, the planet Mars, which we can see pictures of that reveal all sorts of idiosyncratic features that are a consequence of its history and can't be predicted from physics models alone), then for us we can know them only as abstract elements of mathematical models which make accurate predictions about instrument-readings.

This is why, as I said in post #101 on the Fabric Of Spacetime thread, I think that fundamentally physics is fundamentally just about coming up with mathematical models that make accurate quantitative predictions, that any additional significance we assign to the mathematical models--how we visualize certain mathematical elements like forces or particles or time, or whether we consider them "real"--is just a matter of personal beliefs and intuitions, whether we're right or wrong about these things isn't something that can be settled by science, and so there is no scientific basis for telling anyone else they should think about the models in the same way. Did you read the long quote by Feynman I posted there, and if so do you have any thoughts? As he pointed out, it's not that it's useless to conceptualize theories of physics as something more than pure mathematics, since visualizations and such may help physicists get better intuitions and may even aid in coming up with new improved mathematical models. But all that can actually be tested experimentally is which model makes the best quantitative predictions, so if two physicists are using the same mathematical model but conceptualize it in different ways, there's no experimental evidence that can settle this. What's more, the history of 20th century physics has taught physicists to be very cautious about getting too attached to any particular way of conceptualizing a mathematical model, because often it has happened that one model has turned out to be just an approximation for an improved model whose elements are different enough that they can't really be conceptualized in the same way (for example, the forces acting instantaneously at a distance in Newtonian gravity were replaced by the idea of mass causing local curvature in spacetime in general relativity), and yet all the successful quantitative predictions of the old model can be replicated by the new model.

You see I have gone to many sources that contain data on time, standard dictionaries, physics books, books written by leading authorities in the field of physics, I have talked to people who teach physics, in all of this research I have not found any data that says time is a physical thing according to the definition of physical thing as defined by a physics book or standard dictionary. I have also not perceived any such force, energy, or object that is called time.

But do you have any sources written by physicists that use words like "physical thing" and define what they mean in any precise, experimentally-testable way? This sounds to me like a philosophical question about ontology, outside the domain of science. Again, all physics theories can do is give you mathematical models for making predictions about the readings of various physical instruments, I can't think of any conceivable way that you could determine scientifically which elements of the abstract mathematical model are "real physical things" and which are not--can you?

If you notice, there has not been one reference presented on this thread that states time is a physical thing according to physics.

That's because "physical thing" is not a term that is used in physics. Can you present any reference that states that any quantity or entity that appears in physics models is a "physical thing", whether energy or distance or electrons?

I am defining physical the way it is defined in any standard dictionary or physics reference book. My definition of physical is the same as those.

Dictionaries only define things in terms of how they are used in everyday life, and everyday usage is often fuzzy at the edges and determined more by consensus than any clear definitions (for example, precisely what range of temperatures would qualify as 'hot'?) Do you have any sources that define "physical" in a more precise sense that would allow us to tell whether something qualifies just by checking its properties against the definition? Can you find any physics textbooks or other sources written by professional physicists that give rigorous definitions for this word?

 

[JM]

JesseM' Hello again. Re your post 100. I think there is great difficulty separating the conditions observed in the twins journey from the conditions used in the analysis.
You said '... you can calculate the time elapsed on each segment using the time dilation equation and then just add the two times..."
If you use this procedure aren't you excluding any external forces or accelarations from your analysis?
The time dilation equation was derived for two coordinate systems in constant relative velocity v. If you use this equation as you said aren't you treating the two clocks as inertial? If they are both inertial aren't they indistinguishable, as The-genius suggested in his first post? If you wanted to have one clock to be non-inertial wouldn't you have to use a time dilation equation that was derived for non-inertial conditions?
So the analysis you propose ignores turn around effects and treats both clocks as inertial, just as the 1905 paper does. So what is the purpose of insisting that one clock is not inertial, again?
So I do agree that one clock changes velocity in the journey described, but I also assert that this change of velocity is not represented in the actual equations used for the analysis.
The various pieces of our discussion of this topic are scattered along this long thread, would it be useful to gather them all together?

 

[JesseM]

JesseM' Hello again. Re your post 100. I think there is great difficulty separating the conditions observed in the twins journey from the conditions used in the analysis.
You said '... you can calculate the time elapsed on each segment using the time dilation equation and then just add the two times..."
If you use this procedure aren't you excluding any external forces or accelarations from your analysis?
The time dilation equation was derived for two coordinate systems in constant relative velocity v. If you use this equation as you said aren't you treating the two clocks as inertial?

I'm saying one clock has a polygonal path consisting of different inertial segments--for example, the clock might have moved at constant velocity 0.6c in one direction for 20 years, then instantaneously changed velocity so it was moving at velocity 0.8c in the opposite direction, and continued at this constant velocity for another 15 years. Einstein talked about this sort of polygonal path in section 4 of the 1905 paper. Are you disagreeing that in SR we should be able to calculate the total time elapsed on this sort of polygonal path just by using the time dilation equation to calculate the time elapsed on each segment, i.e. 20*sqrt(1 - 0.6^2) + 15*sqrt(1 - 0.8^2), which gives a sum of 25 years? The acceleration phase between these two inertial phases is assumed to be instantaneous, so it shouldn't cause any sudden change in the clock's reading. The only way this sort of sum wouldn't give the right answer is if the clock had some kind of "memory" that it had been accelerated which affected its rate of ticking, so even if on the second segment it was traveling right next to a clock that had been moving inertially at 0.8c for all time, somehow its past history would make it so that its rate of ticking didn't match that of the inertial clock it was traveling alongside. Perhaps this wouldn't explicitly contradict either of the 2 basic postulates of SR, but the fact that a clock's time dilation is predicted purely by its velocity is something that can be tested experimentally, I think to a pretty high degree of accuracy.

So the analysis you propose ignores turn around effects and treats both clocks as inertial, just as the 1905 paper does. So what is the purpose of insisting that one clock is not inertial, again?

The 1905 paper doesn't ignore acceleration, rather in section 4 Einstein is effectively proposing the postulate that any accelerated path can be taken as the limit of a polygonal path as the length of the segments goes to zero, along with the postulate that for a polygonal path with instantaneous accelerations we can assume the instantaneous accelerations don't change the reading so the time elapsed is just the sum of the time elapsed on each segment. It's true that these postulates might not follow directly from the two basic postulates of SR, but they certainly seem pretty plausible as additional postulates if you accept the basic SR postulates, and ultimately the real test of both the basic SR postulates and these additional postulates is experimental evidence, which supports all of them quite well.

 

[JM]

To whom...
This has been a long thread. It may be useful to gather the features of SR that apply to the twin paradox as descrebed in par. 4 of the 1905 paper " on the Electrodynamics of Moving Bodies'.
A.The path of the moving clock is given as a constant speed motion along a closed path of connected straight line segments beginning at, and endding at, the same point. The path is describes as 'polygonal' which suggestrs many more than two segments.
B. The time of the moving clock is calculated by entering the expression x = vt, representing the position of the clock at the origin of the moving coordinates, into the Lorentz equation relating 'moving' time to 'stationary' time. These transfforms were derived under the condition that both coorddinates are inertial, i.e. moving in a straight line at constant relative speed v. The use of this transform implies the following assumptions:
1.The behavior of the moving clock when moving along the polygonal patthis the same as when moving along a straight inertial line,
2.The forces required to constrain the clock to the polygonal line and any accelerations are excluded from the analysis. This is consistent with the kinematic procedure named in the introduction of the paper.
3. Both coordinates/clocks are represented as inertial for the polygonal path, as they are for the straight line.
C. This last condition, along with the idea that there is no location of absolute rest, allows each twin/clock equal entitlement to consider himself to be at rest.
D. The original question for this thread was whether it is possible to determine who went for the trip and who didn't. The answer, according to the 1905paper, is no. Each twin caan equally consider himself to be at rest and the other one to be traverling.

 

[Ich]

The answer, according to the 1905paper, is no.

The answer, according to the 1905 paper, is yes. It's explicitly given.
The answer, according to your understanding, may be no. But then, that's wrong.

 

[ZikZak]

D. The original question for this thread was whether it is possible to determine who went for the trip and who didn't. The answer, according to the 1905paper, is no.

Let's see if that is, in fact, true.

...if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B...

if one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be 1/2 tv^2/c^2 second slow.

No, it looks like you are reading the Bizarro Version of the 1905 paper, because in the real 1905 paper, Einstein explicitly states which clock arrives reading behind the other. Please stop putting (wrong) statements into Einstein's mouth. He is not here to defend himself.

 

[JesseM]

To whom...
This has been a long thread. It may be useful to gather the features of SR that apply to the twin paradox as descrebed in par. 4 of the 1905 paper " on the Electrodynamics of Moving Bodies'.
A.The path of the moving clock is given as a constant speed motion along a closed path of connected straight line segments beginning at, and endding at, the same point. The path is describes as 'polygonal' which suggestrs many more than two segments.

Sure it does, I was just picking an example of a polygonal path with two segments to make writing out the sum easier. I'm sure if Einstein postulated that we can just calculate the elapsed time on each segment using time dilation and add them together to get total time elapsed in the case of a polygonal path with many segments, he'd say the same about a polygonal path with just two segments--do you disagree?

As a matter of fact, in this paragraph below from section 4 he seems to be talking about a clock A that's originally at rest relative to B and then is accelerated once, moving inertially at constant velocity v towards B after the acceleration--that would in fact be a polygonal path with two segments.

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by (1/2)*tv^2/c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

B. The time of the moving clock is calculated by entering the expression x = vt, representing the position of the clock at the origin of the moving coordinates, into the Lorentz equation relating 'moving' time to 'stationary' time.

You could use the full Lorentz transformation for the event (t, vt) to find the time t' of that event in the moving frame (assuming the clock was initially at (0,0)), but you can also just use the time dilation equation t_{your frame} = t_{moving clock} / sqrt(1 - v^2/c^2), which you can rearrange to solve for time on the moving clock if you know the time t in your frame: t_{moving clock} = t_{your frame} * sqrt(1 - v^2/c^2). Of course the time dilation equation is derived directly from the Lorentz transformation, so this is just a shortcut.

These transfforms were derived under the condition that both coorddinates are inertial, i.e. moving in a straight line at constant relative speed v. The use of this transform implies the following assumptions:
1.The behavior of the moving clock when moving along the polygonal patthis the same as when moving along a straight inertial line,

Yes, more specifically, the assumption is that during each segment of the polygonal path, the clock would be ticking at the same rate as a clock at rest next to it that had been moving inertially for all time.

2.The forces required to constrain the clock to the polygonal line and any accelerations are excluded from the analysis. This is consistent with the kinematic procedure named in the introduction of the paper.

Yes, given that the accelerations are instantaneously brief in the case of a polygonal path, it seems reasonable to postulate that the accelerations won't cause any sudden jump in the clock reading. And in any case, the postulate that the rate of ticking at each moment depends solely on the velocity at each moment is a testable one, and experimentally it seems to be true.

3. Both coordinates/clocks are represented as inertial for the polygonal path, as they are for the straight line.

What do you mean? Each segment is inertial, but the entire polygonal path is clearly not inertial, since the clock does not remain at rest throughout the journey in any inertial frame.

C. This last condition, along with the idea that there is no location of absolute rest, allows each twin/clock equal entitlement to consider himself to be at rest.

No! Where are you getting that idea? Einstein clearly defines the meaning of an inertial frame in his paper, and a clock moving on a polygonal path is clearly not the sort of clock he was talking about when he imagined constructing an inertial frame using a network of inertial clocks. In particular, if you tried to construct a coordinate system using a network of clocks moving on polygonal paths and then write the equations for the laws of physics in such a coordinate system, it would not be "a system of co-ordinates in which the equations of Newtonian mechanics hold good" as he says at the beginning of section 1.

 

[JM]

To Ich and ZikZak: OK, OK, here's the missing piece. Refer to post 65 and the reference cited there, Relativity 1952 by Einstein. He says that all inertial frames are equal, or in my paraphrase, the carriage and the embankment are both equally entitled to consider themselves at rest and the other to be in motion. The 1905 paper gives results for only one being at rest. Remember the saying ' moving clocks run slow'? If A is at rest he sees B's clock to be slow, and if B is at rest he sees A's clock to be slow. Apply that to each twin (considered to be inertial as described in my recent post ) and you get the same result for each.
To JesseM: I see many points of agreement. But let's focus on the segments. You agree that each segment can be considered to be inertial,and the time dilation calculated using the formula for two inertial clocks, yes? If you do this for each segment and add the results for the total trip, isn't that the same as calculating the time dilation for a single segment of the same length as the round trip? Thats what I'm thinking.

 

[JesseM]

To JesseM: I see many points of agreement. But let's focus on the segments. You agree that each segment can be considered to be inertial,and the time dilation calculated using the formula for two inertial clocks, yes? If you do this for each segment and add the results for the total trip, isn't that the same as calculating the time dilation for a single segment of the same length as the round trip? Thats what I'm thinking.

The answer is the same only if the speed is constant on each segment and the direction is the only thing that changes, from the perspective of whatever frame you're using. If the speed isn't constant, then the time dilation factor is obviously different in different segments.

Even if the speed is constant--if the traveling twin travels away at 0.6c for 10 years and then travels back at 0.6c for another 10 years, from the perspective of the Earth twin--the situation is still fundamentally different from a purely inertial trip at 0.6c for 20 years to a destination 12 light years away (as opposed to the polygonal trip where the traveling twin ends up back at Earth). In the case of a purely inertial trip the Earth twin could calcuate that the traveling twin has only aged 20 years * sqrt(1 - 0.6^2) = 20*0.8 = 16 years when he reaches the destination 12 light years away, but the situation is symmetrical, the traveling twin can also correctly conclude that in his own inertial rest frame, after 16 years he reaches the destination but the Earth twin has only aged 16*0.8 = 12.8 years. This has to do with the relativity of simultaneity and the fact that different inertial frames disagree about whether two events that are separated in space are "simultaneous" or not--in the Earth-twin's inertial rest frame, the event of the traveling twin's clock showing 16 years is simultaneous with the event of the Earth-twin's clock reading 20 years, but in the traveling twin's inertial rest frame, the event of the traveling twin's clock showing 16 years is simultaneous with the event of the Earth-twin's clock reading 12.8 years.

It's because of this relativity of simultaneity that the situation is not symmetric if the traveling twin was taking a polygonal path, so the traveling twin can't calculate how much the Earth twin has aged just by adding the amount the Earth twin ages during the first segment in the traveling twin's inertial rest frame #1 during the first segment + the amount the Earth twin ages during the second segment in the traveling twin's inertial rest frame #2 during the second segment. For example, suppose the traveling twin is observed in the Earth twin's frame to move away at 0.6c for 10 years, aging 8 years during this time while the Earth twin ages 10 years, then return at 0.6c for another 10 years, aging another 8 years while the Earth twin ages another 10 years. In the traveling twin's inertial rest frame #1 where the traveling twin is at rest during the first half of the journey, the event of the traveling twin's clock reading 8 years (when the traveling twin turns around) is simultaneous with the event of the Earth twin's clock reading 6.4 years. But then in the traveling twin's inertial rest frame #2 where the traveling twin is at rest during the second half of the journey, the same event of the traveling twin's clock reading 8 years (and the traveling twin turning around) is simultaneous with a totally different event on the Earth twin's worldline, when the Earth twin's clock reads not 6.4 years but 13.6 years. So, during the 8 years it takes in this frame for the traveling twin to return to Earth, the Earth twin will age an additional 6.4 years, meaning the Earth twin's clock will show 13.6 + 6.4 = 20 years when the traveling twin returns. So the traveling twin cannot just say "well, in my inertial rest frame #1 before I turned around, the Earth twin aged 6.4 years from the moment I left Earth until the moment of the turnaround, and in my inertial rest frame #2 after I turned around, the Earth twin aged another 6.4 years from the moment I turned around to the moment I returned to Earth, therefore the Earth twin should have aged 6.4 + 6.4 = 12.8 years when I return". This calculation would ignore the difference in simultaneity which means the two frames have very different ideas about how old the Earth twin is at the moment the traveling twin turns around, and thus this calculation would fail to take into account the "missing" 7.2 years between the Earth twin's clock reading 6.4 and the Earth twin's clock reading 13.6.

 

[phyti]

Dr Gregg;

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

It requires a force to balance the frictional forces. If the engine stopped delivering power to the wheels, the train would come to a stop.

 

[DrGreg]

Dr Gregg;

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

It requires a force to balance the frictional forces. If the engine stopped delivering power to the wheels, the train would come to a stop.

I agree. I was referring to the total force, what you get when you add all the forces acting on the train; it is zero. And the total of all the forces acting on the embankment is zero too.

By the way, it helps if you use the QUOTE button when quoting what I've said (you can then delete irrelevant parts of the quote); then I can click on the arrow to find the original post in which I said it.

 

[phyti]

I agree. I was referring to the total force, what you get when you add all the forces acting on the train; it is zero. And the total of all the forces acting on the embankment is zero too.

By the way, it helps if you use the QUOTE button when quoting what I've said (you can then delete irrelevant parts of the quote); then I can click on the arrow to find the original post in which I said it.

It was one of those word things!
Normally use the quote button, except for 1 or 2 liners, but you make good point for back tracking.