B Do Twins Age Differently in Space?

[Dale]

I cannot see how any convention could change the fact that ...

What you call a fact is simply not a fact. It is a common misunderstanding.

So, ignoring the acceleration phase itself, and looking only post acceleration,

If you want to describe the coordinate system of a non inertial observer, then you cannot ignore the acceleration.

if i am not mistaken, you would also agree that this blue clock being on the simultaneity axis _post acceleration_ is simultaneous to the local clock of the traveling twin according to Einstein's synchronisation convention.

You are mistaken. I would agree that is the usual convention for the momentarily comoving inertial observers, but the non inertial observer cannot simply naively adopt those conventions as his own. See here for a thorough treatment of the math

https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll2.html

Hence it would be absurd to compare "physical" simultaneity to what "one experiences at the same time" who is not local to yourself.

There is no such thing as "physical simultaneity". All simultaneity is a matter of convention, including Einstein's convention.

which suggests the authors understood the very problem i am puzzled about and believe to have resolved it

Yes, the authors understood and resolved the problem, which is the reason I posted the reference. Can you be a little more specific about what you didn't understand?

 

[Dale]

Nevertheless, if the traveling twin at a distance would do non-instantaneous accelerations in opposite directions on repeat, he would measure/calculate the stay at home twin's clock to be moving forward and backwards in time on repeat,

Again, this is referring to the series of frames of the momentarily comoving inertial observers. It cannot represent a single frame because it is not one to one

 

[Dale]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close

This is a philosophical preference that the universe does not seem to share. Nature cares about causality, not simultaneity. Simultaneity is a human-made convention, not a natural fact.

But then where exactly is the "now" of the stay at home twin?

That is the topic of the Dolby and Gulls paper.

 

[Dale]

I was asking how to plot the unique now of the stay at home twin into my simple x-t diagram as described above. That "unique now" would have specific x,t coordinates, not be a worldline. And i need the formula which would allow me to calculate those coordinates.

See figure 3 and the equations immediately above it in Dolby and Gull.

Note that the Dolby and Gull convention is just a convention, so you are free to choose a different convention. But any valid convention must assign a unique coordinate to a given event, as described by Carroll.

 

[Ibix]

Then you misunderstood me. If anything, i am not trying to separate space and time but would go even further to rather talk about 4-space than spacetime.

However, i realize now that this is not a problem i should have brought up in a pure physics forum. Only a philosopher which is also a physicists could possibly solve it.
Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

There is no unique definition of "here" either. For example a passenger on a train and one on the platform will only agree that "here" means "in the station" until the train pulls out. This is not a problem. Why is disagreeing about "now" so different? On a Minkowski diagram, the disagreements even look the same.

 

[robphy]

An important feature of Dolby and Gull's approach is that it is operational (based on a measurement procedure), rather than some mathematical extrapolation of a local situation.

Note that the notion of hyperplanes of simultaneity become less important in general relativity. They are not useful and may not be definable. Other structures (e.g. "spacelike surface") take its place, as needed.

 

[Dale]

Only a philosopher which is also a physicists could possibly solve it.
Pure physicists cannot deal with consciousness and subjective experience.

Philosophers don't know anything more about consciousness and subjective experience than physicists do. The people who know more about consciousness and subjective experience are psychologists.

 

[Herman Trivilino]

I consider this a problem because i want to believe that in spacetime a world exists with things happening while i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where the stay at home twin would exist in the "now" even when i am not close.

How about this instead?

I want to believe that in spacetime a world exists with things happening while and i am not local to those events. And i want to believe that there is an event at an exact x and t position relative to me where and the stay at home twin would exist in the "now" even when i am not close.

Your use of "while" implies that such a thing exists. And that is fine, as long as you understand the conditions under which it does exist. The details of that existence is what the others are trying to explain to you.

And your use of "where" implies, to me, a double meaning. Locating something on a spacetime diagram is not the same thing as locating something in space. Locating something on a spacetime diagram is an assignment of both space and time coordinates. Locating something in space is an assignment of only the space coordinates.

When you say something is located somewhere relative to you, you need specify only the space coordinates. When you say something is located on a spacetime diagram I don't see any sense in adding the phrase "relative to me".

Unfortunately, while i can mark simultaneous events on my diagrams, i am not capable of marking that exact "now" event for the stay at home twin and vice versa if i were to describe the whole scenario from the stay at home twin's perspective.

I don't understand this. Once you mark simultaneous events you have, by definition, marked the exact "now", and vice-versa. The issue, though, is that there is more than one way to do that. In other words, simultaneity is a convention. It's part of the modeling process, it's not part of Nature.

Consider this rewording of your statement, quoted at the beginning of this post.

Spacetime is a model of a world that exists. It provides a way of representing things happening even though I am not local to those events. And I want to believe that there is an event with exact x and t coordinates telling me where and when the stay at home twin would exist even when i am not close.

Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

But now is uniquely defined, as long as it's here.

No one here is a pure anything. Each of us is capable of exploring both physics and philosophy. Some better than others.

Richard Feynman often wrote and spoke about a friend of his who was an artist. The friend's claim was that as a physicist Richard's analysis of things prevented him from seeing their beauty. Feynman's response was that the analysis only adds to the beauty, it doesn't subtract from it.

Likewise, the physics of spacetime adds to our understanding of consciousness and subjective experience. The entire point of "here" and "now" is that they do indeed exist in our consciousness as a part of our subjective experience. But our "here" is not the same as their "here" and our "now" is not the same as their "now". Their here and now is part of their consciousness and subjective experience. Physics has taught us a lot about how to connect theirs with ours. The fact that that connection doesn't match our notion of what it ought to be is a lesson to be learned. Anyone with an education in physics has experienced that mismatch so many times that when it happens again we are better able to recognize that it's happening. And we have experience dealing with it. It's a valuable lesson that's applicable in all areas of human knowledge.

 

[PeterDonis]

Pure physicists cannot deal with consciousness and subjective experience.

What does the definition of "now" have to do with consciousness and subjective experience? No matter how consciousness and subjective experience works, it can't violate the laws of physics. And "now" being purely a convention, not a physical thing, is part of the laws of physics.

The only role a better understanding of consciousness and subjective experience might play in helping you (but not for discussion here, since this is a forum about physics, not cognitive science) would be in helping you understand how your brain gives you the illusion that you perceive a universal "now" directly, instead of constructing it from the data in your past light cone. But you don't need to understand consciousness and subjective experience in detail to know that it is in fact an illusion. Physics by itself can tell you that.

 

[m4r35n357]

Pure physicists cannot deal with consciousness and subjective experience. "The entire point is that "now" is not something that is uniquely defined" is quite an indication for that.

FWIW I am not a physicist, I'm just here to learn. I tend to focus on aspects of relativity dealing with what you actually see rather than simultaneity and suchlike. This is a conscious and subjective view, because you cannot be conscious of or subjective about something until you see it objectively.

Look at the moon, you are not seeing it now but about a second ago. OK, so you could say that "now" on the moon is what you see a second later, but by then you have moved on and it is no longer "now" for you. Same for the sun but it's about 8 minutes in the past. And so on . . .

Do you really want to cling to such a useless and unobservable notion of "now" at the expense of learning something useful about the universe?

 

[Jeronimus]

What does the definition of "now" have to do with consciousness and subjective experience? No matter how consciousness and subjective experience works, it can't violate the laws of physics. And "now" being purely a convention, not a physical thing, is part of the laws of physics.

The only role a better understanding of consciousness and subjective experience might play in helping you (but not for discussion here, since this is a forum about physics, not cognitive science) would be in helping you understand how your brain gives you the illusion that you perceive a universal "now" directly, instead of constructing it from the data in your past light cone. But you don't need to understand consciousness and subjective experience in detail to know that it is in fact an illusion. Physics by itself can tell you that.

I will only explain myself briefly as this is truly not the forum to discuss this.
When someone experiences subjectively, the experience he "gathers" is at a specific x,t coordinate a specific instance of his body is located on the worldline his body moves on. Of course the x,t coordinate depends on the frame we use, but nevertheless it is a unique "now" at specific x,t coordinates.

It is also clear that the experience he gathers at that specific instance of his body, the unique now, is a combination from information reaching him from his past lightcone. Nevertheless, the experience itself happens at that specific unique "now" moment.
He does not experience everything at the same time as in experience all of the experience of all the instances of his body on the worldline simultaneously. There is an order.

If we were to use a static block universe, you could think of this unique now or conscious moment as a dvd laser read head moving through the worldline of where the instances of that someone's body reside, on an already prewritten dvd (the block universe).

Similarly, others which have their own dvd laser read head and are moving through this block universe on different worldlines the instances of their bodies reside on, hence on different paths, would also have that unique now as described above.

But most important, whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.
Otherwise one of the two might be conscious at that point, while the other is just a zombie/meat robot.

And this is why this is no problem a pure physicist can solve. As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle.

That will be my last post on this however.

 

[jbriggs444]

you could think of this unique now or conscious moment as a dvd laser read head moving through the worldline

If it's unique, there is only one. It cannot move.

are the unique now instances for both individuals meeting at that point

The point at the intersection of two worldlines is guaranteed to be a "now" for both worldlines for the simple reason that every point on a worldline is a "now" on that worldline. None of the points are unique.

 

[Dale]

Nevertheless, the experience itself happens at that specific unique "now" moment.

Since you are not going to respond to the thread, you should think about how that specific unique "now" moment can be defined experimentally. (This is where philosophers get lazy)

most important, whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.

Since the laws of physics are Lorentz invariant, any experimental measurement is guaranteed to be frame invariant. This includes any experiment to detect the specific unique "now" moment of a given individual: so this is guaranteed.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle

Again, I think a philosopher is worse than useless for this question. What would be far more useful is a psychologist. They have developed many tools for measuring many aspects of consciousness. Philosophers have not.

 

[PeterDonis]

it is a unique "now" at specific x,t coordinates.

Yes, but this is not the usual meaning of the word "now". What you are describing is "here and now"--a single event, a single point in spacetime. Defining "now" in this sense does not require any assumptions at all about simultaneity--about which different events, different points in spacetime, can be said to happen "at the same time". The latter is only a convention; but consciousness and subjectivity have nothing to do with that.

He does not experience everything at the same time as in experience all of the experience of all the instances of his body on the worldline simultaneously. There is an order.

Of course, and this is modeled in relativity as proper time along the observer's worldline. Each event on his worldline--each "here and now", each individual experience--has a unique proper time associated with it. Again, this does not require any simultaneity convention at all, and it is all that is required to model consciousness and subjectivity.

whenever two worldlines cross, hence where two instances of different bodies "meet", one would have to ensure that those instances of the bodies are the unique now instances for both individuals meeting at that point.

This is already ensured by the above--the event where the two worldlines cross has a unique proper time for each worldline. Nothing else is required.

Otherwise one of the two might be conscious at that point, while the other is just a zombie/meat robot.

Um, what? What does that have to do with assigning a unique "now" to each event?

As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This claim, I agree, is out of bounds for discussion here, but that's not because consciousness can't be captured by physics. It's because you are using an unscientific definition of "consciousness".

 

[Ibix]

And this is why this is no problem a pure physicist can solve. As far as physicists are concerned, we are nothing more than complex meat and bones machines. Consciousness as i described it above, moving through the worldline does not really exist or is not of concern.

This is a problem only a "meta-physicists" who also has a strong background in physics could tackle.

You are manufacturing problems for yourself by jumping far outside the bounds of what is understood and then trying to find a way back to those bounds. The solution is to be a scientist: wait until we have a detailed understanding of our brain function (and/or manage to produce an artificial intelligence in a machine whose function we do understand in detail) before worrying about whether or not "we are nothing more than complex meat and bones machines".

 

[ljagerman]

Twins leave Earth in opposite directions, accelerate at the same rate until their relative v = ~c, hold this v for 20 years (or however long), then decelerate at the same rate to v=0, and accelerate at the same rate back towards Earth until their relative v again =~c, hold for same amount of time, then decelerate at the same rate until they reunite where they started. For the entire journey, wouldn't each have seen the other as aging much more slowly? Are they the same age now? How much time has passed on earth?

The situation you pose can be simplified, in which case the answer is more obvious: The two travelers need not be twins, and they need not travels in opposite directions. In fact invoking "twins" and the idea of motion in "opposite directions" confuses the issue with irrelevant information. Think of each traveler, a human being, going on a trip from a site on the Earth and back in any direction; let's call them traveler A and traveler B. The only essential peculiarity is that each happens to move in the same manner; maybe each was given a copy of the same instructions about how much and how long to speed up, how long to coast, and how to slow down. From the vantage of an observer on Earth called C, traveler A will return having aged less than C. As a separate event, traveler B will return having aged less than C. Since the motion-parameters happen to be the same, A and B each will have aged the same with respect to C. The two trips do even need to be exactly synchronous; as long as they do not collide, A and B can even use the same launch pad at different times.

As for how much time has passed on earth, this kind of calculation of fairly intricate (because motion in this case is not uniform) but I showed the equations in a previous post, and they usually appear in any thorough publication on special relativity. From the algebraic point of view, you will simply apply the same equations to A and B.

 

[jeremyfiennes]

Is Chris Miller's original question not resumed in this diagram?:

https://fbcdn-sphotos-c-a.akamaihd.net/hphotos-ak-xft1/v/t1.0-9/15094864_10208324911981049_8498090670732290477_n.jpg?oh=98c817ae6121041ee66a5b4bb6f40cb7&oe=58C283CA&__gda__=1489513784_f6eaeff47d1cd034eadd542b819e5fb4

 

[Ibix]

I think that diagram is supposed to be a pair of light clocks in relative motion, so no. That's an illustration of the reciprocal nature of the Lorentz transforms, not differential aging as seen in the Twin Paradox.

As a general rule, it will help discussion if you say why you think a diagram is relevant, rather than just posting a picture.

 

[jeremyfiennes]

Ok, sorry. I thought that in the context it would be self-explanatory. It is the two twins in inertial motion in spaceships, each seeing the other's photon clock running slower than his own.

 

[robphy]

The OP's twins are both "traveling twins", non-inertial though piecewise-inertial observers. I think my diagram in #24 is closer to the situation, and further tries to diagram what one would "see" by signaling with light rays. If one is interested in what one measures as "simultaneous" along each leg, use the spacelike diagonals of the clock diamonds rather than light rays.

 

[Ibix]

Ok, sorry. I thought that in the context it would be self-explanatory. It is the two twins in inertial motion in spaceships, each seeing the other's photon clock running slower than his own.

If you want to explain the Twin Paradox in terms of time dilation then you also need to take into account the relativity of simultaneity and the problems that causes at turnover for the traveling twin's accounting. That's a big part of what the OP was missing. It is also missing in your diagram, presumably because that isn't what it set out to show. Hence me wondering why you were posting it.

 

[Tommyboyblitz]

If both are traveling at the same velocity in any direction then time will be slowed down the same for both, so they would see each others clocks staying the same. time has slowed equally for both.

 

[Ibix]

If both are traveling at the same velocity in any direction then time will be slowed down the same for both, so they would see each others clocks staying the same. time has slowed equally for both.

This is incorrect, as has been pointed out several times on this thread. Both twins always see the other twin and the Earth in motion relative to them. Once they correct for the changing light travel time, they will always calculate both the Earth's clocks and the other twin's clock to be running slow.

The underlying error here is the assumption of an absolute rest frame with regard to which the twins are in motion. There is no such frame. The twins may always regard themselves to be at rest.

 

[Herman Trivilino]

Ok, sorry. I thought that in the context it would be self-explanatory. It is the two twins in inertial motion in spaceships, each seeing the other's photon clock running slower than his own.

When I look at the original posts I see the OP's variant of the twin paradox as an attempt to eliminate the conflating issue of simultaneity, hoping to come up with a variant that could explain the effect using only time dilation. Of course, that cannot be done.

One way of looking at this issue is to understand that time dilation involves comparing a proper time to a dilated time, and that's the only type of comparison shown in your drawing. The twin paradox, on the other hand, involves a comparison of two proper times. (Each twin ages an amount of proper time, so any difference in their ages is a difference in proper times.)

Why is this important? Because to measure a dilated time you need two events separated along the line of relative motion. And to measure the time that elapses between those spatially separated events you need to know what the two different clocks at those locations read. And those clocks of course have to be synchronized for that process to be in any way meaningful. When measuring the amount of elapsed proper time you need only one clock because you are measuring the time that elapses between two events that occur in the same place.

 

[Herman Trivilino]

The underlying error here is the assumption of an absolute rest frame with regard to which the twins are in motion. There is no such frame. The twins may always regard themselves to be at rest.

Which of course implies the erroneous notion of an absolute velocity.

It just seems natural to think that for me to travel at a very high speed I must first accelerate. Thus changing my speed. Deeply seated in there is the misconception that I'm now at rest.

 

[Battlemage!]

That's why I quoted it in my question.
This, and your entire explanation was extremely helpful/interesting (even the cartoon!). Although I still don't understand how, if each (after discounting light travel time) sees the other's clock running slow for the entire journey (as SR would predict) how their (discounted) sums match at the end.

I think this response from Dale, especially the bold part, may be relevant:

No, this is not at all what SR predicts. Not only is it not what they visually observe, there is also no reference frame where that is what they calculate to be true.

What they would observe is the other twins clock being redshifted during the first part, normal in the middle, then blueshifted during the last part. They end with the same elapsed time.

In the Earth's frame they are always equal. They end with the same elapsed time.

In an inertial frame where one twin is initially at rest then the other will start slow, but the first will end slow. They end with the same elapsed time.

In a non inertial frame the math is complicated. They end with the same elapsed time.

No matter what frame you pick, if you actually do the math... They end with the same time.

No, it is nothing like that at all.