Why do people talk as if the Twin Paradox is problematic?

[yogi]

Janus - thanks for your response. Ok - good - you answered both questions "yes" so each twin has a clock that belongs to a different reference frame, and each can read his own clock at the event where the turnaround post is arrived at. So since the two clocks have recorded different amounts of time in their own reference frames (their own proper times that have nothing to do with how they could or would be viewed by the other twin at this event), why is it necessary to explain why the traveling twin will have a different age upon returning because he has undergone an acceleration, or a change in reference frame - whatever? We already have a reading that confirms actual relative time dilation (or time loss, depending upon how one describes the difference). Don't we already (upon reaching the turn around point) have the necessary asymmetry to conclude that the time loss difference is simply doubled when the traveling twin rebounds off the turn around point and returns home at the same velocity to be reunited. Why does one need to invoke acceleration? ... changing reference frames? ... GR... etc. Have we not already created an inherent asymmetry by specifying the distance traveled in the Earth frame (10 light years proper distance) and the lapsed proper time (11.55 years) vs the 5 light years distance perceived by the traveling twin and 5.75 accumulated clock time?

 

[Janus]

Janus - thanks for your response. Ok - good - you answered both questions "yes" so each twin has a clock that belongs to a different reference frame, and each can read his own clock at the event where the turnaround post is arrived at. So since the two clocks have recorded different amounts of time in their own reference frames (their own proper times that have nothing to do with how they could or would be viewed by the other twin at this event), why is it necessary to explain why the traveling twin will have a different age upon returning because he has undergone an acceleration, or a change in reference frame - whatever? We already have a reading that confirms actual relative time dilation (or time loss, depending upon how one describes the difference). Don't we already (upon reaching the turn around point) have the necessary asymmetry to conclude that the time loss difference is simply doubled when the traveling twin rebounds off the turn around point and returns home at the same velocity to be reunited. Why does one need to invoke acceleration? ... changing reference frames? ... GR... etc. Have we not already created an inherent asymmetry by specifying the distance traveled in the Earth frame (10 light years proper distance) and the lapsed proper time (11.55 years) vs the 5 light years distance perceived by the traveling twin and 5.75 accumulated clock time?

Because you would not be taking all the relevant observations into account. You can't just ignore the fact that from twin 2's frame when he hits the turn around, the Earth clock only reads 2.875 yrs. This reading on Earth's clock is just as real and actual to twin 2 as the reading on the clock he carries with him.

It is not enough for Twin 1 to say 23 yrs passed on his clock, while 11.5 yrs passed on twin 2's clock after the round trip and for twin 2 to agree that 11.5 years passed for him. Twin 2 must also agree that, by his observations, 23 yrs passed on Earth.

And you cannot say that Twin 2's observation of Earth time is less valid than the other observations because it is arrived at by the same rules as the other observations.

 

[yogi]

Janus - your quote:

Because you would not be taking all the relevant observations into account. You can't just ignore the fact that from twin 2's frame when he hits the turn around, the Earth clock only reads 2.875 yrs. This reading on Earth's clock is just as real and actual to twin 2 as the reading on the clock he carries with him."

There is no reading on any Earth clock that says 2.875 years - there is only one Earth clock and it reads 11.55 years.

 

[yogi]

Let me embellish further. Assume a clock is placed at the turn around post and it is sync(ed) with the time when the twin's clocks are set to zero at beginning of the voyage (we can do this with a light signal sent from twin 1's location - it takes 10 years to arrive, so the operator at the remote clock starts it running when he receives the signal from twin 1 and adds 10 years to the dial reading - so when twin 2 arrives, he sees the clock on the turn around post reading 11.55 years. There is no other communication between the frames - twin 2 reads the proper time on the clock which escorts him and twin 1 reads proper time on the Earth clock. Any other times that are calculated are not real - they are apparent - just as is length contraction - a fictitious time calculated from the relative velocity between the two frames.

 

[Janus]

Let me embellish further. Assume a clock is placed at the turn around post and it is sync(ed) with the time when the twin's clocks are set to zero at beginning of the voyage (we can do this with a light signal sent from twin 1's location - it takes 10 years to arrive, so the operator at the remote clock starts it running when he receives the signal from twin 1 and adds 10 years to the dial reading - so when twin 2 arrives, he sees the clock on the turn around post reading 11.55 years.

But that does not represent the present time on Earth from twin 2's frame. There is Relativity of Simultaneity. Simultaneous events in one frame are not simultaneous in a frame moving relative to the first. So while for twin one the events of his clock and the turnaround post's clocks reading 11.55 yrs are simultaneous events, this is not true for Twin 2, for him, when the turnaround clock reads 11.55 yrs, Twin 1's clock will read 2.875 yrs.

There is no other communication between the frames - twin 2 reads the proper time on the clock which escorts him and twin 1 reads proper time on the Earth clock. Any other times that are calculated are not real - they are apparent - just as is length contraction - a fictitious time calculated from the relative velocity between the two frames.

No, all the times are real for each frame discussed. For Twin 2 when he reaches the turn around point the real time on Earth is 2.875 yrs. The length contraction is real also. It is just as real as the fact that for The operator at the turnaround point adding 10 yrs to his clock synchronizes his clock to twin one's clock.

 

[yogi]

Janus - how can different times in the same frame at the same point both be real. The real time on Earth could not be 2,875 years when Twin 2 reaches the turn around point - he would have had to travel faster than the velocity of light in the Earth frame. The real time on Earth is that read by a proper clock in the Earth frame - and the clock at the turn around can be sync(ed) with the Earth clock since they are both in the same frame and not moving with respect thereto.

In the problem posed, there are only two events and two times - you agreed that the 11.55 years measured in the Earth frame was a proper real time and that the 5.77 years in the twin 2 frame is a proper real time (at least I think you agreed to these statements). Event 1, the beginning of the trip all clocks read zero - event 2, the turn around point, the proper time accumulated by the Earth clock and the post clock will both be 11.55 years but the proper time accumulated by the twin 2 clock will be less (5.77 years)

How can length contraction be real in SR - that idea belongs in Lorentz Ether Theory. Eddinton said straight out - length contraction is not real - so have many other authors of relativity texts. Twin 2 cannot make proper distance measurements in the Earth frame because he is moving wrt the Earth frame - any calculation he makes will be fictitious - it may seem that he has traveled less miles because his clock is running slow - but the miscalculation is due to the fact that he uses the clock reading in his own frame to calculate a distance in another frame

 

[Janus]

Janus - how can different times in the same frame at the same point both be real.

Because time is Relative. The time on Earth depends on who you ask. Do not confuse 'real' with 'absolute' or 'universal'.

The real time on Earth could not be 2,875 years when Twin 2 reaches the turn around point - he would have had to travel faster than the velocity of light in the Earth frame.

I'll touch on this later.

The real time on Earth is that read by a proper clock in the Earth frame - and the clock at the turn around can be sync(ed) with the Earth clock since they are both in the same frame and not moving with respect thereto.

again, you are trying to make "real" mean 'absolute', Time is relative. they are only in sync when viewed from the frame they are in

In the problem posed, there are only two events and two times - you agreed that the 11.55 years measured in the Earth frame was a proper real time and that the 5.77 years in the twin 2 frame is a proper real time (at least I think you agreed to these statements). Event 1, the beginning of the trip all clocks read zero - event 2, the turn around point, the proper time accumulated by the Earth clock and the post clock will both be 11.55 years but the proper time accumulated by the twin 2 clock will be less (5.77 years)

The term "proper time" only means "time as measured by a clock that is not moving relative to the frame of reference". This is to distinguish it from time as read by a clock moving with respect to the frame of reference. "proper time is no more "real" than any other time.

How can length contraction be real in SR - that idea belongs in Lorentz Ether Theory. Eddinton said straight out - length contraction is not real - so have many other authors of relativity texts.

Again, confusion of "real" with "absolute".

Twin 2 cannot make proper distance measurements in the Earth frame because he is moving wrt the Earth frame - any calculation he makes will be fictitious - it may seem that he has traveled less miles because his clock is running slow - but the miscalculation is due to the fact that he uses the clock reading in his own frame to calculate a distance in another frame

If twin 2 were to trail a measuring tape behind him, he would note that at the instant he reached the turn around point, the Earth would be exactly opposite the 5 ly mark on his tape. He would also note that if a measuring tape were stretched out from the Earth, that he would be at the 10 ly mark of it when he reaches the turn around point.

Now, the Earth being next to the 5 ly mark of twin 2's tape and twin two being next to the 10 ly mark of the Earth's tape are "space time events".
These space time events provide the markers we need to determine what happens from each frame.

According to twin 2, he reaches the turn around point when his 5 ly mark aligns with the Earth. Now, on Earth, when does the Earth align with the 5 ly mark on twin 2's tape? Well, since from the Earth frame Twin 2's measuring tape undergoes length contraction, this happens when twin 2 is 2.5 ly away. How much time passes on Earth while twin twin moves out to 2.5 ly? 2.875 yrs. So no, twin 2 does not appear to travel faster than c as you implied earlier.


The whole problem is that you are having trouble coming to terms with the idea of time being Relative.

An analogy:

At one time, a large percentage of the world's population held the world to be flat. As a result they came to the conclusion that "down" was a universal and absolute direction. When confronted with the idea of a spherical world, it made no sense. After all, if they were standing upright, people on the other side must be hanging head down. What kept them from falling off?

Even once the force of gravity, and how it worked towards the center of the Earth was explained, some still refused to give up their idea of universal "down" and would ask, "Then what holds the Earth up?" They might accept that gravity towards the center of the Earth could create a "fictitious down" , but the "real" direction of down was still a universal direction. They refused to accept that the very notion of "down" was defined by gravity.

And you have to learn to accept that the very notion of "time" is defined by observation. And observers moving relative to each other will have different observations.

 

[yogi]

Janus - I have no trouble at all distinquishing between relative and absolute - the times referred to in our story are of course relative - they are not defined with respect to a universal reference frame if there is one - the two times are exactly what is prescribed by the invarience of the interval in SR - the Earth time as measured by a clock at rest in the Earth frame is what determines how fast change is taking place in the Earth frame - and likewise for the twin 2 frame - change occurs slower for twin 2 - RELATIVE TO THE pace at which change is measured in the Earth frame. I fail to see how you could deduce that I am talking absolute(s). There may be an absolute where an observer measures no CBR asymmetry, but it is not part of this query.

What I have tried to do is pin you down as to two simple events in two relatively moving reference frames. You perpetually introduce how the other guy views the other frame and from there you invoke arguments that may be consistent with some interpretations of the LT, but to me they simply obscure the focus.

As most text(s) state - the proper quantities represent "invarient quantities" and that is why I have formulated the problem without using improper lengths and improper times which you claim are as equally real as proper times and proper lengths.

 

[yogi]

janus - again - as to your statement about the reality of length contraction, here is quote I have posted before by Eddinton - and the message is clear:

With regard the actuality of length contraction, Eddington had this to say:

"You receive a balance sheet from a public company ... it is certified by a chartered accountant. But is it really true? Many questions arise; the real values of items are often very different from those that figure in the balance sheet...There is a blessed phrase "hidden reserves" and generally speaking the more respectable the company the more widely does its balance sheet deviate from reality. This is called sound finance ... the main function of the balance sheet is to balance and everything else has to be subordinated to that end. The writing down of lengths for balance sheet purposes is the FitzGerald Contraction. The shortening of the moving rod is true, but it is not really true. It is not a statement about reality (the absolute) but it is a true statement about appearances.

 

[Chronos]

GR explains local relativistic effects nicely. SR gives the illusion that that acceleration is relative to a local reference frame [lorentzian thing]. GR changes the equation using time based topological reference frames.

 

[rtharbaugh1]

The Many Times Interpretation

The desire for an absolute seems to be part of the human condition. We need one thing, just one lousy thing, that doesn't move, isn't broken, and can be relied upon to always be there every time we look.

Children as they grow up have to learn what it is that is reliable about experience, and what it is that changes. A small infant attracted by a shiny toy will reach for it even though it is too far away, not having learned about the limits of arms and fingers. A slightly older child will still say that a tower in the distance is on the right side of the road, and then be astounded and insist that the tower has moved when, on coming closer, the road curves so that the tower passes on the left. How can a tower jump over the road? The child still has to learn about curves, and how they affect our perception.

As recently as Gallileo people didn't understand how a ship in the distance would drop below the horizon. It seemed as if the ship were sinking. Two ships moving apart on the ocean would each see the other sink, and a novice sailor might be surprised to meet up with that same ship again in another port. The other ship always seems to sink over the horizon, shrink in the distance, change sides of the path we are on, yet we learn that there is symetry and these effects are illusions, not "real." Not absolute, but relitive somehow to our own position.

Now in special relativity we learn that there is a curve in time. Things that are moving very fast compared to our own movement seem to change shape, shrink over some horizon. Only this time, it is possible using space-like curves for the shrinking object to remain nearby, as in DW's counter-rotating frames example in another thread in this forum. An object moving very fast seems to shrink, even though it is passing close by us. We are surprised to learn that from the point of view of the object, it is we who have shrunk. This is new. Usually things we know about that seem to shrink are far away, and we have become familiar, as adults, with the idea that things far away only seem smaller. In near space, we have come to assume that the balance sheet requires that if you shrink, I will seem bigger to you, and if you grow, I will seem to become smaller. As growing children and as young adults we are surprised to see our parents get smaller, and our children get large. How many times have you said to a child or heard from an adult, the phrase "My, how you have grown!"

Now we have to get our minds around the idea that time is curved, and objects still very close to us in space can seem to shrink in a way that has to do with their being "far away" in some time sense. Usually things far away in time are in the past or the future, and we do not expect to see them sharing our bit of space, but we have to adjust our idea again. THere is a far-away sense in time that is not far away in the past or future or far away in space. This new direction in time is orthagonal, at right angles, to everything we think we know. There is not just one direction in time, there are at least two. There is not just past and future, there is also fast and slow. There may even be other orthagonalities in time, more time dimensions, and we have trouble fitting more ninety degree angles into three dimensional space, so we find this difficult to model in our mind's eye. Yet the evidence is impossible to deny. Time is multidimensional. It curves. There is not just a single straight path from the past through the present into the future.

We deal with the effect of time curvature every day in our ordinary experience. We move. If time were not curved, it could not be so, and the universe would be unitary indeed, not allowing for time or change. There is no great mystery here. We are growing up as a species, and have to get around this new curve. There are more directions than three in space and one in time. We access other directions in time by making choices, that is, by changing our velocities. If we had made the other choice, gone the other way or gone there faster or slower, we would be in a different universe.

We have to accept then that there is not just one universe, which is difficult because the very word "universe" seems to insist that there is just one. That at least seems absolute, unchangeing, reliable. Every time we look, there is only one. But it seems to me now that we must give up even this idea of constancy.

Some have a problem with multiple universes because it seems to them untidy, and anyway, if there are so many universes, what does that say about the total sum of energy? Isn't energy additive and so if there are many universes doesn't this mean that the total sum of energies explodes into unwieldy and embarrassing infinities? I think these arguments are shown to be specious, and it is time to grow up. The Universe, meaning the total sum of everything that is, was, and ever can be, is much bigger than we can imagine.

Let us cease arguing about what is real and what is not real. Your god or my God, and if there is only one God, which of the two should be capitalized? It is a schoolyard fight that will never be settled by bullies. Instead, we need to think about how to accept our own greatness without insisting that others must be diminished.

Thanks for Being,

rth

 

[yogi]

rthar - the issue is not nitpicking - it is fundamental to explaining the nature of the universe - if the classical paradox can be resolved w/o resort to ancilliary accelerations - then the time differential between two moving systems is "real" ..it must be consequent to a physical cause.

Janus - here is quote from Robert Resnick's book - introduction of SR at page 93:

At page 93 of his book “Introduction to Special Relativity, Resnick analogous length contraction to Doppler shift: “ Is the frequency, or wavelength, shift in the Doppler effect real or apparent. ...When the source and observer are in relative motion, the observer definitely measures a frequency (or wavelength) shift. Likewise the moving rod is definitely measured to be contracted. The effects are real in the same sense that the measurements are real. We do not claim that the proper frequency has changed because of our measurement shift. Nor do we claim that the proper length has changed because of our measurement contraction. The effects are apparent (i.e., caused by the motion) in the same sense that proper quantities have not changed."

 

[SuperKamiokande]

I couldn't really be bothered reading everything everyone had to say but i got the gist of it from the beginning. It is possible to solve the twins paradox in terms of SR. Instead of taking a laser light, take pulses of laser light released from each twin.

Now consider the twin on Earth, he will be receiving a pulses of laser light at a lower frequency than he is sending them due to the absolute velocity of light and the near light speed at which the other twin travelling. However, the traveling twin will be receiving signals at a slower rate than that twin on Earth because his spaceship is moving at near light speed away from the earth. This is where the age difference occurs because one twin receives more signals than the other.

Now because we are in SR we just turn the spaceship around and head to earth. Suddenly the traveling twin is receiving much more frequent signals while the twin on Earth receives none until he/she gets a whole bunch of signals at once. But the number of signals sent and received during this part of the travel should be the same.

So overall we have one twin who has received fewer signals than the other twin despite both signals having sent (relative to themselves) the same number of signals. Job done I feel.

 

[yogi]

Signaling gets the right answer (ostensibly) because each twin assumes that the received frequency of transmission is altered from the proper frequency measured in the transmitting frame (by the Doppler effect). So one twin ages more than the other, but we all agree on that (I guess), so that is not the issue. SR predicts that each observer will see the other clock running slow consequent to relative motion.