Understanding Relativity and Its Effects on Lightspeed

[cucumber]

imagine two people in deep space, with no frame of reference but each other. if one of them is speeding along at near lightspeed, he might just as well assume he is stationary and the other guy is moving.

how can we get around this problem, without something like the ether??

secondly, does light speed up when traveling towards a mass, as it slows down when traveling away from it?
or am i just misunderstanding something? i am not too clear about relativity, so please keep explanations simple...

thanksalot.

 

[chroot]

Originally posted by cucumber
imagine two people in deep space, with no frame of reference but each other. if one of them is speeding along at near lightspeed, he might just as well assume he is stationary and the other guy is moving.

how can we get around this problem, without something like the ether??

What problem? What's wrong with each person assuming he is at rest and the other is moving relative to him?

secondly, does light speed up when traveling towards a mass, as it slows down when traveling away from it?

The speed of light, locally, is always c. What this means is that if you arrange for light to travel through some experimental apparatus at rest with respect to you, the apparatus will always indicate light is traveling at c. Only a distant observer will see light slowing down as it moves more deeply into a gravitational field -- but he can't measure that speed directly, only indirectly. To an observer in that field, the same light will appear to be moving at c. This is all caused by what is called "gravitational time dilation."

- Warren

 

[cucumber]

Originally posted by chroot
What problem? What's wrong with each person assuming he is at rest and the other is moving relative to him?

the problem is, that i do not see how time can be slowed down for both at the same time (no pun intended); time dilation should only occur for the one moving at near c, but if there is no reference frame, who experiences time dilation?

do both guys see the other guy moving in slow-motion?
if they do, i need to seriously refine my concept of time...

 

[Janus]

Originally posted by cucumber


do both guys see the other guy moving in slow-motion?

Yes.

if they do, i need to seriously refine my concept of time...

You probably do, but so did everyone when Relativity came to the fore.

 

[chroot]

Originally posted by cucumber
the problem is, that i do not see how time can be slowed down for both at the same time (no pun intended)

You're still hanging onto the Newtonian definition of 'time.' In Newton's day, it was believed that time was independent of space -- it was an absolute quantity. If time were to slow down, then it slowed down from some "normal" rate experienced by the rest of the universe.

This, however, is not correct. It turns out that time is a uniquely local experience -- the time elapsed on your wristwatch does not have to agree with the time elapsed on anyone else's. Furthermore, it is not correct to say that time has slowed down for someone -- all that you can say is that one person, when viewing another person, will measure that other person's time as running slowly.

The key word of the previous sentence is measure. Physics can tell you nothing about reality beyond the measurements that an observer will make on some system. For two people passing one another at high relative velocity (call them Captain A and Captain B), both will measure the others' time as running slowly. Remember that time is a uniquely local phenomenon, and there is absolutely no reason why Captain A's wristwatch on one spaceship should have anything to do with the wristwatch worn by Captain B on another spaceship. It would be very non-symmetrical, and very confusing, for one observer to measure the other's clock running slow, while the other measures the first's as running fast. Instead, both Captains measure the others' time as running slowly, as compared to their own local clocks.

time dilation should only occur for the one moving at near c, but if there is no reference frame, who experiences time dilation?

It is critical to realize that time dilation is not experienced -- it is observed. Captain A can watch Captain B, and measure B's clock as running slow. He will never measure his own clock as running slowly, however -- and this makes complete sense: how could he? At the same time, Captain B thinks his clock is running just fine, and A's clock is running slowly.

do both guys see the other guy moving in slow-motion?

Yes indeed!

- Warren

 

[revesz]

I read on howstuffworks.com that in relativity there is time dilation and another dilation where the object shinks in the direction it is going. is this correct or not(if its not correct it will probably make no sense to you)

 

[cucumber]

so how do you explain length contraction??

i can sort of picture time dilation, due to the constancy (is that a word?) of c, but i can't see how this could influence the size of an object...

oh, and what about the mass increase?? would you "experience" an increase in mass, or is it like time dilation and can only be observed by someone else?

is there any way of explaining mass dilation (other than just quoting E=mc^2, i mean).

this is really doing my head in. it's GREAT!

 

[LURCH]

Originally posted by cucumber


oh, and what about the mass increase?? would you "experience" an increase in mass, or is it like time dilation and can only be observed by someone else?

That's exactly right. Your mass increase is related to your velocity, and your velocity is entirely relative. If you travel by at .9c (from my frame of reference), your mass is increased. But to someone traveling alongside you, your velocity is 0, so your mass is the same as it would be if you are at rest ("rest mass" it's called) because to him, you are. Since you are never in motion relative to yourself, you will always measure your own mass to be equall to your rest mass.

Also, if you can grasp time dilation, even vaguely, you are already most of the way to getting length contraction, as they are like two ways of looking at the same thing. The number of seconds it takes light to get from point A to point B changes, but the speed of light doesn't. So we can say the seconds have gotten longer (time dilation) or the distance has gotten shorter (length contraction), whichever is more convenient for the solving the particular equation at hand.

 

[jcsd]

Originally posted by cucumber
so how do you explain length contraction??

i can sort of picture time dilation, due to the constancy (is that a word?) of c, but i can't see how this could influence the size of an object...

oh, and what about the mass increase?? would you "experience" an increase in mass, or is it like time dilation and can only be observed by someone else?

is there any way of explaining mass dilation (other than just quoting E=mc^2, i mean).

this is really doing my head in. it's GREAT!

Think of it this way, imagine your on a spaceship of a certain length traveling past a planet at a speed of 0.9c, you turn on a light at the back of the spaceship and you measure how long (t_spaceship) it takes to travel the length of your spaceship (x_spaceship) because the speed of light is always constant x_spaceship/t_spaceship must equal c . Now imagine someone on the planet making the same measurement and gets x_planet and t_planet. Now we know because of time dialtion that t_planet can't the same as t_spaceship yet x_planet/t_planet must also equal c, so th conclusion is the person on the planet must of measured a different value for the length of the spaceship.

 

[jcsd]

I should add what this shows is that the different contractions/dialtions can be derived from each other (infact historically time dialtion was derived from length contraction)

 

[marcus]

Originally posted by jcsd
[final lines from Wilfred Owen's "Dulce et decorum est"]

here you are talking about space time and almost in the same breath quoting rhymed verse by an outstanding poet. I'm going to try to recall a Jorge Borges sonnet about spacetime (the 4D universe as a crystaline memory containing all the past and future---the world line of each entity that ever has existed or will exist.) Borges did not, IMO, believe in anything like God he just used the idea. The translator is Richard Wilbur, who managed to reproduce the rhymed form of the original in his translation.


One thing does not exist: Oblivion.
God saves the metal and he saves the dross,
and his prophetic memory guards from loss
the moons to come and those of evenings gone.
Everything is: the shadows in the glass,
which, in between the days two twilights, you
have scattered by the thousands, or shall strew
henceforward in the mirrors that you pass.
And everything is part of that diverse
crystalline memory, the Universe.
Whoever through its endless mazes wanders,
hears door-on-door click shut behind his stride,
and only at the sunset's farther side
shall view at last the Archetypes and Splendors.

 

[O Great One]

How can clocks be simultaneously slower than each other?

Originally posted by cucumber
the problem is, that i do not see how time can be slowed down for both at the same time (no pun intended)

Personally, I think it's impossible. The example that's often given is that of two people standing a distance apart from each other. If you have two people that are the exact same size and they are separated by a distance, they both appear smaller to the other person just like each person measures the other persons' time as moving more slowly than their own. But the problem is that they aren't smaller than each other, obviously that's impossible. They only appear smaller than each other. How can I have a clock that moves more slowly than your clock and at the same time your clock moves more slowly than my clock? This is the same problem with the people, the people are still the same size they only appear smaller. This could be illustrated with our clocks: My clock reads 3:00, but when you look at it it reads 2:50. Your clock reads 3:00, but when I look at it it reads 2:50. The clocks only appear to be slower than each other. In reality they are not, that's impossible.

 

[FZ+]

The clocks only appear to be slower than each other. In reality they are not, that's impossible.

And I guess muons only appear to last lthousands of times longer than when they are stationary, and so when we repeatedly measure them when they shouldn't exist we are just having illusions? Really.

Perhaps you should work on WHY the time dilation result was found - it is a logical neccessity of the postulates of SR.

 

[Herra Tohtori]

Time slows for an object that accelerates and/or decelerates. This is the answer to, say, the twin paradox. Why does the traveling twin stay young? Becouse he leaves, turns back and stops at home while the other twin stays at Earth all the time.

 

[chroot]

Originally posted by Herra Tohtori
Time slows for an object that accelerates and/or decelerates. This is the answer to, say, the twin paradox. Why does the traveling twin stay young? Becouse he leaves, turns back and stops at home while the other twin stays at Earth all the time.

I'm sorry, but it sounds like you've got some major misconceptions about how relativity works. It sounds to me like you don't exactly know what the twin paradox is either.

- Warren

 

[Janus]

Originally posted by O Great One
Personally, I think it's impossible. The example that's often given is that of two people standing a distance apart from each other. If you have two people that are the exact same size and they are separated by a distance, they both appear smaller to the other person just like each person measures the other persons' time as moving more slowly than their own. But the problem is that they aren't smaller than each other, obviously that's impossible. They only appear smaller than each other. How can I have a clock that moves more slowly than your clock and at the same time your clock moves more slowly than my clock? This is the same problem with the people, the people are still the same size they only appear smaller. This could be illustrated with our clocks: My clock reads 3:00, but when you look at it it reads 2:50. Your clock reads 3:00, but when I look at it it reads 2:50. The clocks only appear to be slower than each other. In reality they are not, that's impossible.

The problem is that you are trying to treat time as an absolute measure, when it isn't.

To use the people example, When you say the one person "appears" smaller, you mean that their angular size is smaller. So in this example, angular size relates to time. Now when you say that they aren't "really" smaller, you are talking linear size, a different type of measurement. This measurement relates to the spacetime interval.

Thus angular size is "distance variant" while linear size is distance "invarient"

And

Time is "Lorentz varient"
While the spacetime interval is "Lorentz invarient".

Time measurement behaves like angular size measurement, not linear measurement.

When you say that it is impossible for the clocks to each be slower than the other, you are trying to treat time like linear measure(As we used to believe it behaved, and how it appears to behave under everyday conditions)

But is not impossible if time behaves like angular measure, and this indeed is how we now know it really behaves.

 

[Netme]

For example if the sun explodes, light would be given off from this explosion. What if you could follow this light that is flying away from the sun at any speed you like. If you were to follow it at slighty below the speed of light you would see the suns light moving slowly through or ahead of you. If you were to follow it at above the speed of light you would see the sun's light that is in front of you appear to flow in reverse since you are catching upto and passing light that is ahead of you. This is where "time travel occurs." But it is not really time travel, it is more like placing yourself into a position in space more quickly than the speed of light creating the illusion of going back into time. Eventually the light will stop and you will have nothing more to view leaving the possibility of traveling into the past or the future impossible. But what happens if you travel with the sun's light at the speed of light? What i believe you would see then is the mechanics of light itself and how it moves and functions in space.

 

[dace]

Can we regard time dilation as a dual phenomenon? Since the speed of light is always the same regardless of your velocity, the faster you go though space, the more slowly you must move in time. Time dilation is not merely the stretching of time but the stretching of a slowed-down time. Thus two things seem to be happening here. Can we decouple the concepts of time dilation and time slowing? Can we conceive of a time that slows down but is not dilated?

Let's say the constancy of the speed of light causes a rocket moving at .5c to slow down in time by one-half. The time is slowed but not dilated. After one year the pilot of the rocket returns to Earth but does not discover that Earth has aged two years. Instead, he's back one year in everyone else's past, on a different time-line.

Of course, this is not what would really happen. In reality, the pilot would return to find that two years had passed on Earth, that he was now one year younger relative to everyone else but very much in their present.

While c causes time to slow down for objects in motion, what is it that causes to time to dilate? It seems the only answer is another constant-- an absolute present which must be maintained regardless of how far time is slowed down. Just as time must vary in order to maintain the constancy of the speed of light, aging must vary in order to maintain the constancy of the present. As you slow down in time, you simply age more slowly as your time is stretched out to keep you in the present.

Does this make sense? Is there some obvious error in my analysis I'm not aware of?

 

[dace]

Indeed. But is "slowing" the same thing as "dilating?" They don't seem to be the same. I can certainly imagine one without the other. What I'm asking is whether Special Relativity conflates two separate concepts under the single heading of "time dilation." The implication is that there are two constants at work, not only the speed of light but the temporal present. The constant speed of light demands a slowing of time, but in calling this effect "time dilation" instead of "time slowing," we obscure the influence of another element, possibly another constant that demands a stretching of the slowed-down time in order to maintain an absolute present.

 

[dace]

And why should that be? After all, "slowing" and "stretching" are obviously different things. Let's say I've developed a limp, so I move more slowly across the room than I usually do. Does this automatically invoke a compensatory stretching of my trajectory that enables me to cross the room at the same speed as usual? No, it does not. So why, when it comes to velocity-induced time-slowing does this "stretching" automatically kick in? This cannot simply be assumed. It has to be explained. That physicists have always understood the concept of "time dilation" to include time-slowing doesn't mean that such slowing necessarily implies dilating or stretching. It may simply be conceptual sloppiness that has become ingrained over time and therefore unquestioned.

 

[LURCH]

Originally posted by dace
And why should that be? After all, "slowing" and "stretching" are obviously different things.

Only in spatial movement. When dealing with time, stretching and slowing are exactly the same thing, since to "stretch" a minute is to make it longer, and a longer minute = slower time. Dilated time simply means that each increment of time is larger, time passes slower because each second is stretched out, they are two diferent ways of saying the exact same thing.

 

[dace]

Thanks for the responses. So, rather than literally dropping back into the past, a clock that undergoes a slowing of time will register the slow-down with an increased interval between ticks, relative to other clocks. The clock might show half an hour ago, but it does so in the present, not half an hour ago.

The source of my confusion on this point is Paul Davies' book, How to Build a Time Machine. Davies claims that if a wormhole can be generated at a large enough size, it could be utlized as a portal into the past (though never to a time prior to the construction of the time machine itself). The way it works is that the entrance to the wormhole remains locked in place while the far end of the wormhole is spun at high speed, say, .9c. This causes the far end to pass through time more slowly, gradually dropping back in time relative to the entrance. Thus, if you enter the wormhole, you will exit at the far end before you entered.

But this is not what would actually happen. Because slowing through time means stretching the interval between events, the far end of the wormhole would simply undergo less aging relative to the entrance while remaining in the same present. Hence no time travel. Davies seems to have gotten it completely wrong.

 

[HallsofIvy]

Not exactly. Because the rotation would be a rotation of all space time in the vicinity, time would be (relatively) slower for all space time in the vicinity of that end of the wormhole. If you go in "slowly rotating" end of the wormhole and out the other you will find that time has progressed more slowly on all planets in that area. You will have gone back in time in that sense.
This is not a very effective system because:
1) You can't go back to a time before the wormhole itself was created.
2) If you start from a planet in the vicinity of the "backward" end of the worm hole, move through "space" to the other end and then through the worm hole you can find that time has progressed more slowly there than during your voyage (even allowing for your own time compression due to your speed) but you cannot go back before you started your journey.
3) Those frightfully different rates of rotation are going to make it extremely difficult to survive the trip through the wormhole!

 

[dace]

Davies notes that muons can be sent through a particle accelerator at such high speed that they decay only one second for every twelve seconds they would ordinarily decay. Thus, in theory, we could place one mouth of a wormhole in an accelerator and spin it for say, ten months, at the end of which it will have dilated in time by ten years (assuming a 12-fold time dilation). The wormhole isn't used as a time machine until the spinning is completed. At that point you enter the wormhole from the end that remained still and exit from the rotated end ten years earlier. He emphasizes that the wormhole couldn't deliver you to a time prior to its own existence. So you'd have to wait ten years before you could use it.

I'm sorry, but this just isn't going to fly.

Let's say we run muons through an accelerator for one minute, causing them to dilate twelve-fold. Okay. Does this mean the particles mysteriously appear out of nowhere in the accelerator twelve minutes prior to the experiment? No. It simply means that at the end of the minute, the muons will have "aged" by only five seconds instead of sixty. Rather than being sent back in time twelve minutes, they are fully present but chemically younger than they should be by 55 seconds.

The same thing will happen with the wormhole. The mouth that's been rotated will be chemically younger than the mouth that hasn't been rotated. But both ends will be in the present. It's not as if the rotated end will literally vanish into the past after it's been spun. It will not be half a wormhole, with the other half occupying the past. You won't see people entering but not exiting, and nobody in the past will see the other half of the wormhole with people exiting it but not entering. The whole thing will exist in the present and will not transport anybody to any time other than the present.

Again, when you send a clock through space at high speed, at the end of the trip, it might read half an hour ago, but it does so in the present, not half an hour ago. This is what Davies seems to be overlooking.

 

[dace]

Originally posted by Ambitwistor:
Imagine someone sitting next to the wormhole mouth, also being spun in the centrifuge. In the lab, if you look through the stationary wormhole mouth, you see time proceeding normally for the spun observer. Thus, after 10 months, you see (through the wormhole) the centrifuge stopping, although looking at it directly, sitting next to you, it's still spinning and will continue to do so for 9 years and 2 months more.

The error here is to imagine that the spun end of the wormhole literally drops back in time 9 years and 2 months. It does not. It undergoes time dilation. Yes, only ten months go by in relation to the ten years than transpire for the stationary end of the wormhole, but those ten months are stretched out to equal the ten years of the stationary end.

Davies mentions that this sort of time machine is based on the twins paradox. Bruce gets in a rocket and travels for ten years before returning to Earth. Ten years for Earth, yes, but for him (at 12-fold dilation) it was only ten months. Does this mean that when he comes back he meets Barry 9 years and 2 months in Barry's past? No. They're both in each other's present, but Bruce is now 9 years and 2 months younger than his twin. The same thing will happen with the wormhole. Both ends will occupy the same timeline, but the spun end will be chemically younger than the stationary end. No time differential and therefore no time machine. Davies, and Thorne before him, got it wrong.

 

[DoG]

What has not yet been mentioned is that Einstein's paper on SR states it is for two way travel, eg back and forth (like a ray thrown back to the source by a mirror). It just doesn't hold for one way travel.

OT: Many physics teachers, including mine, forget to mention that relativistic effects _seem_ to change objects in other inertial frames, but don't actually alter them. It's just a magic trick after all.

very OT:
This is a paradoxical situation I have been thinking about. Suppose you have two rockets facing each other at a certain distance, and halfway in between lys the spot marked with X. The rockets each carry a clock.

Now, you let the rockets fly towards each other with equally high speeds. They will obviously crash over the X, and we assume that the crash stops the clocks, and they will fall on the X together.

From my point of view, standing at the X, the clocks should show less time, but equally for both, than what I measured to be the crash time.

But how would I see this from one of the rockets?

If I am on a rocket, my clock, at the time of the crash, should stop showing a later time than either the time measured by the observer and the other rocket. And considering relativity, since the other rocket was not going twice my speed, we should not even meet at the X. Is that right?

 

[dace]

Ambitwistor,

Let's compare two individuals who are undergoing time dilation. Both are sent through "people accelerators" at such a high speed that they experience only five seconds for every minute that the rest of us experience. The difference is that Fred is lodged in the mouth of a wormhole, while Francine is not. After one minute, Francine leaves the accelerator, and her watch shows that only five seconds went by. She is still in the present but 55 seconds younger than she would have been had she not entered the accelerator. But when Fred's five seconds are up, because he's been in a wormhole, when he pops out of the stationary end, he's able to cash in his five dilated seconds for five normal seconds. He's literally 55 seconds in the past and still has time to wave at himself as he goes by in the accelerator.

Is that what you're saying?

 

[dace]

I don't know what that "cashing in dilated seconds for normal seconds" means, but ... after Fred's five seconds are up, he is just like Francine: five seconds older, standing in the lab when the lab clock reads one minute later. However, if either he or Francine steps through the wormhole mouth that Fred was carrying with him in the accelerator, they will step out of the stationary lab wormhole mouth, at a time that is 5 lab seconds after the accelerator started, 55 seconds before it stopped, while Francine and Fred are still in the accelerator and can wave to themselves.

Ordinarily, when someone undergoes velocity-induced time dilation, they will not find themselves in the past but only younger in the present (twins paradox). So why does the wormhole negate the usual effect? One mouth of the wormhole is spun such that only five seconds transpire for the minute that otherwise goes by. Fred passes through the wormhole and drops back in time by 55 seconds. Why? The mouth of the wormhole itself is still fully present, its five seconds dilated twelve-fold into a full minute. The only thing that's happened to the mouth is that it's 55 seconds "younger" than it should be. Why would it be any different for Fred? Why wouldn't he simply come out of the wormhole 55 seconds younger than he should be? In fact, why would anything happen to him at all? It was the mouth of the wormhole that got spun and dilated in time, not Fred. Of course, if the wormhole mouth did drop back into the past, Fred could not enter it anyway because he's presumably still in the present, like everyone else.

What is so special about a wormhole? Why would it transfer its dilated time to someone passing through it? And more importantly, why does it enable you to exchange your five slowed-down seconds for five "normal" seconds when you come out? Ordinarily (because slowed-down time equals dilated time) your five slowed-down seconds are dilated into a full minute, and you're in the present but 55 seconds younger. But for some reason when a wormhole is involved, your five slowed-down seconds are applied directly to "real" time, and you literally drop back by 55 seconds. The wormhole seems to short-circuit the otherwise automatic link between slowed-down time and dilated interval between events.

I suspect that the wormhole to physics is much like the philosopher's stone to alchemy. It's the magic spell that transforms lead into gold, or in this case present time progression into backwards time travel.

 

[dace]

Because the wormhole mouth is connected to another wormhole mouth at a different time.

This is really the core of our disagreement. Both mouths of the wormhole occupy the same time. That one mouth is spun at high velocity doesn't mean it drops back to another time. It merely dilates, aging less than it should while remaining present.

It's the same thing with muons or other particles sent through a collider. Do the muons actually drop back in time or merely decay less than normal?

The spun wormhole mouth doesn't "drop into the past"; it's simply connected to another wormhole mouth (in the lab) that is in the past.

This doesn't make sense. Certainly the wormhole mouth that hasn't been spun is not in the past. That's not the issue. The issue is whether the mouth that has been spun is in the past. I'm saying that it would not be in the past either, according to the principles of time dilation.

According to him in the centrifuge, he stops after five seconds and let's go of my hand. But of course he's only been holding my hand for five seconds according to me, too, and we've only had time for five seconds of conversation through the wormhole. The centrifuge next to me with him and his wormhole mouth in it are still spinning, of course, and will continue to do so for 55 more seconds on my watch. Do you disagree with that?

His five seconds will equal one minute for you, since you are not in the centrifuge. When you pull him out through the wormhole, five seconds will have passed for him and one minute for you and the lab. He has never left the present but only aged 55 seconds less than normal.

 

[dace]

Originally posted by Ambitwistor
I didn't say that the spun wormhole mouth travels into the past. I said that it's connected to the unspun wormhole mouth in the past.

Nor did I claim that it travels to the past. Davies claims that it progresses through time more slowly and therefore falls back into the past as the rest of the world proceeds into the future. But it does not progress through time more slowly and does not remain in the past. It stays present while aging more slowly. This is because time-slowing equals time-stretching. Davies appears to be decoupling the concepts, which was the source of my original confusion. I appreciate that you cleared up my confusion on this point. However, in the process you've helped me understand why Davies' model is invalid.

What does it mean for the wormhole mouths to "occupy the same time"? If I spin one wormhole mouth and take it out of the centrifuge, both mouths are still there at the same time, but they're not connected to each other at the same time: one mouth at one time is connected to the other mouth at a different time.

So the mouths of the wormhole are in the same time and are not in the same time. I assume you mean that they're in the same time externally but at different times internally. But it doesn't matter how you slice it; they're still in the same time. The mouth that gets spun in the centrifuge does not recede into a different time but merely ages more slowly while remaining present.

If so, sorry, but that's how wormholes work: no matter how the other end of the wormhole is moving with respect to you, there is no time dilation through the wormhole.

I understand that there's no dilation from one end of the wormhole to the other. It doesn't matter as long as both mouths of the wormhole occupy the same timeline.

 

[Janus]

Mentor note: I split off the discussion between David and Ambitwistor to a new thread of the same name to be found in the theory development forum

 

[dace]

There is nothing preventing the spun observer from immediately stepping through the wormhole and meeting the unspun observer, when both of their watches still read 5 seconds.

I do not agree that both of their watches read 5 seconds. After Fred returns from his ride in the centrifuge, his watch reads five seconds. But Frank, who merely watched the ride, shows 1 minute on his watch. The reason Fred's watch shows only 5 seconds is that the high speed at which he traveled dilated him in time twelve-fold, so that his 5 seconds are stretched out to equal one minute of "normal" time. He has not dropped into the past but simply aged 55 seconds less than normal.

The wormhole is neither here nor there (so to speak). It doesn't matter whether a wormhole mouth has been sent through the centrifuge along with Fred. It doesn't matter whether Fred steps through this wormhole to get back to the lab or just walks through a door. The wormhole cannot transmute Fred's 5 dilated seconds into 5 normal seconds. Regardless of how Fred returns to the lab, his 5 seconds will equal the 1 minute that passed outside the centrifuge, and he will not be back in time.

The mind can play tricks on us. A seemingly magical element comes along, in this case the wormhole, and all judgment is suspended. Surely the fabulous wormhole will not let us down! Like Dorothy, who disovers that the power to get back to Kansas is within her, we cannot travel back to the past except in our minds.

By the way, Davies credits Thorne for the model, with the only change being that Thorne attaches a mouth of the wormhole to a rocket while Davies attaches it to a centrifuge. Davies also points out that gravity will have the same effect, with one end of the wormhole placed near a neutron star.

 

[dace]

Fred's 5 seconds in the centrifuge equal Frank's 60 seconds in the lab. If Fred pulls Frank's arm into the wormhole, then Frank's watch will also be dilated 12-fold and will show only 5 seconds passing. However, unbeknownst to Fred, Frank is wearing a second watch on his other arm, and when he pulls his dilated arm from the wormhole, he compares watches and finds that the dilated watch reads 5 seconds while the one on his other arm reads 60 seconds. This does not mean that his dilated arm is now 55 seconds behind the other arm in time. Both his arms are fully present at his sides, but one of them is now 55 seconds younger than the other.

That's fine, but 55 seconds earlier on Frank's watch, when Frank's watch read 5 seconds, Fred's watch also read 5 seconds, through the wormhole, and Fred can step through the wormhole at that time.

...and cash in his 5 dilated seconds for 5 normal seconds. That's what you're saying. Somehow, through the magic of wormholtronics, Fred's 5 slowed-down seconds in the wormhole are translated into 5 normal seconds when he leaves the wormhole through the stationary end. What this means, in effect, is that the slowing down of time is decoupled from the stretching out of time. If time is slowed down, then by logical necessity, the interval between events is stretched out. As Lurch stated, when it comes to time, slowing down and stretching out are two different ways of saying the exact same thing. Ordinarily, as with the twins paradox, we recognize this. But when a wormhole shows up, it's like we're hypnotized, and all of a sudden we imagine that when time slows down, instead of stretching out and remaining present while aging less, it literally recedes into the past.

Fred, Frank, or anybody else can drop into the past, regardless of whether they were centrifuged or time dilated with respect to anyone, if they step through the spun wormhole mouth.

Wormholes are no different from anything else. You can spin one end of it as long as you want, but all it does is to dilate in time, to stretch out the intervals so that it's still at the same time as the other end. Yes, wormholes have a special property of internally connecting one place to another, but both places are always going to be in the same timeline. The difference we see from one end of the wormhole to the other is not a difference in time but a difference in age. The spun end is younger. That's it. No magic show.

Nobody's dilated seconds are being "transmuted", traded or anything else. Why do you keep repeating yourself after being corrected several times?

Because you keep demonstrating that you're not following.

Your statement is has nothing to do with the predictions of general relativity, or even logic.

Logic? Time travel to the past opens up insoluble paradoxes. Not exactly logical.

When something vanishes into the past, the matter-energy comprising it is gone. Meanwhile, back in the past, it's now doubled up, a copy having been produced out of seemingly nothing. If Fred is waving at himself 55 seconds in the past, he's been destroyed in the present and copied in the past.

Now take a look at the following syllogism:

1. No energy can be created or destroyed
2. Time travel entails both the creation and destruction of energy.
3. Therefore, time travel is impossible.

Now that's logic.