Understanding The Twin Paradox

[digi99]

The twin paradox seems not to be understand by everybody.

But if you see it like this (see below), everybody would understand it.

Why are we getting older on Earth ? Our (relative) time system is the system we compare time to the axes of the Earth. If we start in 1 point on the surface (see that point in 3D), we come back there after 24 hours. This must be seen as a negative time dilation in some way, you did not loose time, no you did go faster than time and will be older (my opinion, not going back in time).

So time is relative, if you compare it to another point (standing still), this relative time can be used in calculations but not affects age immediately, until you come back in some way to that same point, than you loose/add really extra time to your existence.

In case of a muon, this can also be explained as a calculation with time, not the "age" of a muon.

Could this all be right ?

 

[ghwellsjr]

Einstein introduced the Twin Paradox at the end of section 4 of his famous 1905 paper on Special Relativity. There he said that a person on the equator will experience time dilation and age more slowly than a person at one of the poles would, ignoring all other effects (due to gravity, for example).

So I don't know why you are saying that it is negative time dilation. Both persons are aging, it's just that the person traveling on the equator is experiencing time dilation and aging at a lesser rate than the person at the pole (in the rest frame of the person at the pole).

 

[Dale]

The twin paradox seems not to be understand by everybody.

But if you see it like this (see below), everybody would understand it.

Your idea about what everybody would understand is very strange.

 

[ghwellsjr]

Time dilation (if you ignore the effects of gravity) is very easy to understand. All you have to do is pick one inertial Frame of Reference to describe your scenario. The passage of time for every observer/object/clock is determined by their speed and is the reciprocal of gamma. If they are stationary in that FoR, their clock runs normally. If they are moving, their clock slows down by 1/γ. It's really no more complicated than that. I don't know why you are looking for an easier way to explain or demonstrate it.

 

[digi99]

Your idea about what everybody would understand is very strange.

No DaleSpam, that one sentence was indeed too much, but I asked it in this way to expect a good answer, so I really get answers because I don't have the picture yet (I understand time dilation, it's normal symmetric, so I don't know what is the meaning of it and e.g. related to age).

 

[digi99]

Einstein introduced the Twin Paradox at the end of section 4 of his famous 1905 paper on Special Relativity. There he said that a person on the equator will experience time dilation and age more slowly than a person at one of the poles would, ignoring all other effects (due to gravity, for example).

So I don't know why you are saying that it is negative time dilation. Both persons are aging, it's just that the person traveling on the equator is experiencing time dilation and aging at a lesser rate than the person at the pole (in the rest frame of the person at the pole).

I asked this because I am curious to the answers. I have no feeling yet between age and time. I thought (if V could be greater than C, than time goes faster and in my opinion you will getting older under circumstances, so I thought maybe has our age, going older something to do with faster time, in calculations, because the Earth is round and undergoes forces).

How do you see age ?

 

[digi99]

Time dilation (if you ignore the effects of gravity) is very easy to understand. All you have to do is pick one inertial Frame of Reference to describe your scenario. The passage of time for every observer/object/clock is determined by their speed and is the reciprocal of gamma. If they are stationary in that FoR, their clock runs normally. If they are moving, their clock slows down by 1/γ. It's really no more complicated than that. I don't know why you are looking for an easier way to explain or demonstrate it.

Average people don't undertand it, so it is a topic for a small group in the world, so it looks they are very smart and "we" are not able to understand it. I know it is very simple, but you have to explain it so it is very simple for all the people on earth.

I think time and distance must being educated already when you are young in the way it should be (relative and time dilation), than it will be an ordinary term like distance only ...

I don't have a feeling with time dilation as specified in Lorentz, I know only the speed C has to do something with it. With my light waves topic, now I have the relation how time dilation occurs and understand it exactly (limitation C and to see a light wave just as another object, you know me in the beginning how I was looking to light, totally wrong and that's now different).

 

[DaveC426913]

digi99, things such as people aging has nothing to do with the rotation of the Earth. If you lived in a windowless room on the far side of the Moon, you would still live on the order of 2.5 billion seconds (~80 years).

 

[digi99]

Sorry, sorry, this was really a mistake, I was mixing just normal time with time dilation. So a little bit confused.

I was busy too much last days with my topic "light waves" ... (I do it all in a hurry, because busy with work and lost many days income because of the subject, but no problem you have to put time/energy in it, otherwise you never know, so I find it the money worth, it's a one time occasion for me, I get the virus relativity in me for a while).

When I know exact the role of time dilation, I know enough to read relaxed my books without asking myself more than necessary (I don't have to know all, there is a study physics for).

So I know what time dilation is.

But it is symmetric in most cases, so what is his meaning than, just to calculate time from one frame in another frame and vice versa ?

But you should expect when time is going slower, you will be slower older. But it is symmetric. What is the meaning of that time dilation than (if both are not changing in age and in fact time goes normally for your age at the same time) ?

 

[ghwellsjr]

Time dilation (if you ignore the effects of gravity) is very easy to understand. All you have to do is pick one inertial Frame of Reference to describe your scenario. The passage of time for every observer/object/clock is determined by their speed and is the reciprocal of gamma. If they are stationary in that FoR, their clock runs normally. If they are moving, their clock slows down by 1/γ. It's really no more complicated than that. I don't know why you are looking for an easier way to explain or demonstrate it.

Average people don't undertand it, so it is a topic for a small group in the world, so it looks they are very smart and "we" are not able to understand it. I know it is very simple, but you have to explain it so it is very simple for all the people on earth.

I think time and distance must being educated already when you are young in the way it should be (relative and time dilation), than it will be an ordinary term like distance only ...

I don't have a feeling with time dilation as specified in Lorentz, I know only the speed C has to do something with it. With my light waves topic, now I have the relation how time dilation occurs and understand it exactly (limitation C and to see a light wave just as another object, you know me in the beginning how I was looking to light, totally wrong and that's now different).

Digi99, do you think the concept of relative speed is hard to understand? Don't you think everyone, if they stop to think about it, will agree and say that while you are traveling in the car down the highway at 60 miles per hour and you see the cars on the other side of the highway going the same speed in the opposite direction, can easily understand that relative to you those cars are going 120 mph in the opposite direction? And isn't it easy to understand that the people in those cars will also think that relative to them you are going 120 mph in the opposite direction from them? Isn't that a simple concept?

Now neither you nor they would say that it's legitimate to claim that both things are true at the same time, in other words, there's no cars going 240 mph relative to any other cars, correct? So when you're figuring out speeds, you want to select one person (either you or them) or object (like the freeway) as the rest frame from which you will determine the speeds of all other objects or observers.

So now we apply the concept of time dilation which is the factor that a clock runs slow according to the simple formula based on speed as expressed by β, the ratio of the speed of an object or observer to the speed of light, or in other words, the speed as a fraction of the speed of light. The formula is:

√(1-β²)

So if you know the speed, then you know the time dilation factor and if you know that the speed has been constant all the time then you know the aging factor. So we can make a list of the speed vs age:

Speed      Age
0.0        1.000
0.1        0.995
0.2        0.980
0.3        0.954
0.4        0.917
0.5        0.866
0.6        0.800
0.7        0.714
0.8        0.600
0.9        0.436
0.99       0.141
0.999      0.045
0.9999     0.014
0.99999    0.004
0.999999   0.001

Note since you can't go at the speed of light, I made the last few entries be numbers just under 1. If you want to see what you get with other values of speed, I made a graph showing the same information here.

So this means if you see someone traveling at one-half the speed of light, you will know that they are aging at 86.6% of your age. So if you were 20 when they left you and you were 60 when they got back, then they will be 0.866 times 40 (the amount you aged) which equals 34.6 so they will be 54.6 years old. Isn't that simple? Can't anyone understand that?

Now I said here that the other person traveled at 1/2 the speed of light and eventually returned to you while you remained stationary. That's to make the calculation really simple. If I had said that the other person traveled at different speeds or if you had also traveled, then we'd have to apply the aging factor in segments, one for each period of time over which the person's speed was constant.

You asked about the symmetry part of it. That is no different than the symmetry part of speed. Just remember to only consider one frame at a time: just like speed is relative to a fixed frame, so is time dilation. You can get different expressions of time dilation (or aging) based on different frames and, in general, they have to remain different. Only in the situation where two observers or clocks start out together at the one location and end up together at the one location (it can be a different location) will their aging be the same in all frames.

So don't be overly concerned about the aging coming out differently in different frames, just remember the same thing happens with speed. In one frame, a given person can experience all the speed and for the exact same situation as viewed from a different frame, a different person experiences all the speed. Just take your understanding of relative speed to apply to relative time dilation and aging.

I hope you will read this carefully and see if you agree it's really very simple.

 

[Dale]

No DaleSpam, that one sentence was indeed too much, but I asked it in this way to expect a good answer, so I really get answers because I don't have the picture yet (I understand time dilation, it's normal symmetric, so I don't know what is the meaning of it and e.g. related to age).

Are you familiar with spacetime diagrams and Minkowski geometry?

 

[digi99]

Are you familiar with spacetime diagrams and Minkowski geometry?

Yes that's what I am going to read in the book of prof. Sander Bais, but you saw already I used spacetime diagrams with the formula 1 - V/C.

He is explaining time dilation in that way, I read later, maybe I can show γ too later in my drawing.

But the question is not anymore time dilation, I know, but it's relation with age without the twin paradox, but I have to read later Ghwellsjr's answer ... first I start my work now ...

 

[Dale]

The reason I asked is that the distinction between age and time is very clear in spacetime diagrams. The age is the "length" of the worldline as calculated using the Minkowski metric. The time is a coordinate, such as the distance up the page.

 

[digi99]

The reason I asked is that the distinction between age and time is very clear in spacetime diagrams. The age is the "length" of the worldline as calculated using the Minkowski metric. The time is a coordinate, such as the distance up the page.

Yes I read that somewhere, do you have a link of such diagram ?

 

[bobc2]

Digi99, do you think the concept of relative speed is hard to understand? Don't you think everyone, if they stop to think about it, will agree and say that while you are traveling in the car down the highway at 60 miles per hour and you see the cars on the other side of the highway going the same speed in the opposite direction, can easily understand that relative to you those cars are going 120 mph in the opposite direction? ...

ghwellsjr,

I am very impressed with your patience and careful explanation for Digi99. Some guys would have just blown it off. Good job. This is what the forum is for... helping out anyone with a burning curiosity about physics. And Digi99, you are to be admired for your curiosity and persistence. Best wishes in your pursuit of this difficult puzzle.

 

[Dale]

Yes I read that somewhere, do you have a link of such diagram ?

This seems to be a good reference.
http://astro.cornell.edu/academics/courses/a290/lectures/A2290_22%20(Spacetime%20Diagrams%20II).pdf

 

[digi99]

This seems to be a good reference.
http://astro.cornell.edu/academics/courses/a290/lectures/A2290_22%20(Spacetime%20Diagrams%20II).pdf

Thanks I am going to read it later while reading my books (at a slow speed) ...

 

[digi99]

I hope you will read this carefully and see if you agree it's really very simple.

Thanks George for the answer.

Later I come back on it while reading my books, I understood it has also to do who has traveled the longest worldline.

So until now I understood that both observers will be slower getting older (because of time dilation, symmetric) even if one observer is not aware of the "moving" of the other observer (e.g. you are reading a book, and somebody else start moving). Difficult to see for all the people in the world. But I come back later on it after reading my books ...