In a previous thread, I suggested that in his Special Theory, Einstein applied the Lorentz effect in a circumstance in which, by Lorentz’s definition, it could not arise. This discrepancy intrigued me, so I've developed a simple thought experiment to describe the behaviour of light in “empty space”, and what its fixed and finite velocity means…

In a region of space far away from other material objects there is a radio transmitter and two girls, Alice and Betty. The transmitter emits time signals at one second intervals. Each girl has a device capable of displaying the time signals as they are received. At 10:00:00am the transmitter sends the time “10:00:00”. Alice is at rest with respect to the transmitter and 4 light seconds distant from it. So at that moment her device displays “09:59:56”. At 10:00:04 her device will display “10:00:00”, and at 10:00:05 it will display “10:00:01”, and so on…

10:00:00_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ <-Betty
Transmitter _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Alice “09:59:56”
0 sec _ _ _ 1 sec _ _ _ 2 sec _ _ _ 3 sec _ _ _ 4 sec _ _ _ 5 sec

Betty is travelling towards Alice and the transmitter at 1/5 of the velocity of light. At 10:00:00am Betty is 5 light seconds distant from the transmitter and thus will receive the time signal “10:00:00” at 10:00:05. However, over the 5 second period she will have moved 1 light second nearer to the transmitter, so at 10:00:05 the girls are adjacent to each other.

10:00:05_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ <-Betty “10:00:00”
Transmitter _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Alice “10:00:01”
0 sec _ _ _ 1 sec _ _ _ 2 sec _ _ _ 3 sec _ _ _ 4 sec _ _ _ 5 sec

At that moment Alice will see her device displaying “10:00:01” whilst Betty will see hers displaying “10:00:00”. Furthermore, Betty, will see Alice’s device displaying “10:00:01”, and Alice will see Betty’s device displaying “10:00:00”. So both girls see Alice’s device displaying “10:00:01” and Betty’s displaying “10:00:00”. Also for both of them, five seconds have passed since the time signal “10:00:00” was transmitted. So there is no discrepancy in how much time has actually passed for Alice and Betty. It is the time signals that are out of sync.

What is the relevance of this to Einstein’s Special Theory? I suggest that by applying the Lorentz effect, Einstein is describing the effect on space-time experienced by the time signals. This is how two different time signals can arrive at adjacent positions at the same moment. However, by attributing these effects to the space-time continuum, he has assumed that the same relationships are experienced by material objects as well. The experiment suggest otherwise. The differences in space-time evident in the behaviour of the time signals do not affect the spatial and temporal relationships between the material entities. They remain resolutely Newtonian.

If this is so, then Special Relativity only affects how observers perceive photons emanating from a distant source. Put crudely, it might be likened to an optical illusion. However, calling it an optical illusion does not make it unimportant. Special and General Relativity has a place, particularly in astronomy. But it would appear to be inappropriate, and potentially quite misleading, to use General Relativity as the basis for a cosmology.

Postscript

There is a further twist to this tale...

Let us now re-run the experiment, but this time, moments before 10:00:05, small transverse velocities are applied to the two girls such that at 10:00:05 they have swapped places.

10:00:05_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Alice “10:00:01”
Transmitter _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ <-Betty “10:00:00”
0 sec _ _ _ 1 sec _ _ _ 2 sec _ _ _ 3 sec _ _ _ 4 sec _ _ _ 5 sec

The small transverse velocities should have no effect on when the girls receive the time signals, so Alice’s device will still show “10:00:01” whilst Betty’s will show “10:00:00”. The girls are at exactly the positions formerly occupied by the other, yet each still receives the time signals according to their own relationship to the transmitter.

This suggests that space does not actually exist as a physical entity (whereas it does in Newtonian physics). If space did exist, it would be impossible for photons to behave in this way. So although the physical and temporal relationships between the material entities seem resolutely Newtonian (i.e. non-relativistic), it would appear that Newtonian physics is not a complete answer either!

I'll now put on a tin hat and duck But if these ideas survive critical review, I would like to present an alternative cosmology...

Heh! This is similar to something I posted
awhile back. If you will allow me to blow my
own trumpet, it was "first glimmerings of
relativity" and it had some kind responces.
Once you accept time dilation for the
traveller, the contraction follows as the
traveller swears he went at such a velocity
but arrived too quickly on his/her clock.
Therefore the distance travelled must be
shorter!

Hi Pete, thanks for your comment. I'm not sure that you have entirely followed my argument. I'm suggesting that the time dilation is apparent, not real. So the actual passage of time, and the distances, are unaffected.

Hello Terry:

The way this issue is discussed is confusing:

> At 10:00:04 her clock will display "10:00:00"

All I can say is that is silly. At 10:00:04, the clock will display 10:00:04 and receive the first of many signals from the transmitter. I do understand what you meant.

The only people who will ever agree that "transmitter emits time signals at one second intervals" are those observers that happen to be in the same reference frame as the transmitter, namely Alice. Betty, travelling at a speed of .2c relative to the transmitter, will never see a pair of those signals with a spacing of 1 second - ever! Instead it will be:

dt' = gamma dt = 1/(1 - .2²)^1/2

Go to Google:

1 / ((1 - (.2^2))^.5) = 1.02

Betty thinks the signals from the transmitter are separated by 1.02 seconds, not 1.00 seconds as Alice believes. Both beliefs are correct, and depend on the observers relative motion. This is a covariant quantity because we understand how the measurement changes as the observers move.

The covariance of a time interval is not merely a "thought experiment". We get showered every moment of every day by cosmic rays. The collision of the cosmic rays with the upper atmosphere make short lived particles. Thing is, we can see many of those short lived particles in the lower atmosphere because cosmic rays travel at a significant fraction of the speed of light. The cosmic ray data is one of the cooler bits of support for special relativity.

To do this Alice/Betty kind of work, you need to work with Lorentz invariant intervals. For all readers that find that phrase is too full of jargon will need to read a good book, such at "Spacetime Physics" by Taylor and Wheeler. A Lorentz invariant interval is like a 4D Pythagorean theorem.

doug

Hi Terry,
I had written about a page and when I went to post it I saw Doug's reply and scrapped mine. He said it better than I ever could. The SpaceTime Physics book by Taylor and Wheeler that Doug mentions is a great book. I'm a rank amateur and I am able to make sense out of it.

Jim

jedaisoul, there is a long thread, here in the ATM section, which examines a thought-experiment that may have some similarities to the one you propose in the OP. Although it is, notionally, about some other aspect of SR, I think it may cover much the same ground (there's also an earlier thread, by the same BAUT member, that may be relevant too).

I'm interested to know to what extent that thread does not address the Thought Experiment that this thread is about ...

Hi Nereid, thanks for pointing out this previous thread. Yes, there are similarities, but, from a brief view, there would also appear to be significant differences. MacM's post #4 in that thread suggests that he disagrees with the predictions of SR. I do not. I hope I made this clear, but if not I'll gladly repeat it... I do not disagree with the predictions of SR (or GR) so far as they relate to observations of photons from distant sources. For practical purposes, the astronomical predictions of relativity are correct (as far as I'm aware). This is the "how it works" of science, and I have no disagreement with that. See #74 in my first thread "Is there a conceptual flaw...".

I also agree with Ken G's comments (#3 in MacM's thread) except that where he uses the term "pedagogy" I would use "cosmology". This is my point. When used as the basis of a cosmology we move from "how it works" to "what it is". My purpose in raising this point is to "set the scene" for an alternative cosmology. I hope that you (and the other members) will agree that this is a legitimate subject for the ATM section.

Hi Doug, on re-reading the OP, I can see where I have mislead you. The "clocks" carried by the observers are not clocks in the accepted sense. They are merely displays connected to a radio receiver. They are only capable of displaying the time signals received from the transmitter. They are not independent time pieces.

My apologies for this confusion. I've now edited the OP to substitute the word "device" for "clock" as this is more appropriate. If you re-read the OP with the perspective that these are only displays synchronised by electromagnetic means to a remote timepiece, I hope that you will see my logic.

Thanks for pointing this out.

Hi Doug, I entirely agree with you. However, I avoided mentioning this as I think it confuses the issue. If you focus on where Betty is and when she receives the time signals you will see my point. The effect giving rise to the different frequecy of receipt is on the time signals, not on space-time. Space-time is not affected by this. At least, that is the point I'm trying to substantiate.

Thanks for your input.

Hello Terry:

Spacetime is an empty manifold that gets sprinkled with events. Where is Betty on this manifold? The answer could be either invariant or covariant. If you wish to know the time and distance, that is covariant, the numbers like dt and dR depending on who is doing the measurements. If you wish to know the interval to her location, dt² - dR²/c², that is an invariant.

The measurement of the frequency is also a covariant quantity, meaning we know exactly how it changes because folks are moving relative to each other. The classical Doppler shift equation is:

f'/f = 1 + v/c cos A

where f' is the new frequency, f is the frequency in the rest domain of the source, v is the velocity and A is the angle.

The relativistic Doppler shift is:

f'/f = gamma (1 + v/c cos A)

where gamma = 1/(1 - v²/²)^.5 = 1.02

Perhaps you were not familiar with the relativistic Doppler equation which would have to be incorporated into the analysis. All things measured are either invariant or covariants, and you must determine which class a particular measurement falls into. Note: not all covariant quantities are just "multiply by gamma": E and B fields are quite confusing because they are part of a second rank tensor, so get two Lorentz boosts working together.

doug

Hi Doug, I'm not sure what to say. I'm questioning the fundamental assumption that the effect exhibited by the time signals affects the underlying space-time continuum. Your reply is predicated upon that assumption. Yes, if that assumption is correct, everything you say follows. But that does not prove (or disprove) the assumption. It is a circular argument.

I have taken the premise that the velocity of light (in vacuo) is fixed and finite and applied that to a thought experiment. Now, I did not mention that because the time signals are affected, the observers' views of the transmitter (if it were visible to them) are likewise affected. I.e. When the observers are adjacent, Alice would see the transmitter as it was four seconds before and four light seconds distant. Betty would see it as it was five seconds before, and five light seconds distant from her. But is this an actual distortion of the space-time continuum, or merely an optical illusion?

The results of the thought experiment suggest that it is an illusion created by the effect of the finite velocity of light on when the time signals reach the respective observers. Can you explain where the logic I have used to arrive at this conclusion is flawed?

Doug, please do not take this as a personal attack, or any disrespect to the enormous amount of work you have obviously put into gaining an advanced knowledge of SR and GR. That is not in question. Within that context you are vastly more knowledgable than I. But this question lies outside that context. It questions that context. It cannot be answered from within that context.

What you should try to do is figure out what happens with George, someone moving in sync with Betty who coordinates clocks with Betty with light pulses and who passes by Alice at the same Betty-time that Betty is far from Alice.

Hi Kwalish, I'm not sure which version of the OP you are commenting on. I initially called the devices "clocks", but Doug/sweetser pointed out the error in that. They are not clocks, they are merely devices capable of receiving and displaying time signals. There is only one time piece in the scenario. Introducing other clocks gets us into deep water with whether you can ever say that clocks which are in motion are synchronous. That's really Doug's sphere, and I'd rather not comment on that.

But you scenario might be useful to Doug. If he can show, without assuming the effects of the fixed velocity of light are acting on the space-time continuum, that he arrives at conclusions which can only arise if they do act on the space-time continuum, then it would be very difficult for me to gainsay that.

Thanks for your input.

Hello Terry:

The relativistic Doppler shift has been measured. The analysis of the moving reference frame, the one for Betty, is not accurate.

doug

Terry,
Try doubling the frequency of the transmitter so it sends out pulses at half second intervals. Now when Betty passes Alice she will be showing 10:00:00.5 instead of 10:00:01. Now change the transmitter to send signals out at one hundredth of a second intervals and when they pass Betty will be showing 10:00:00.01. Betty will always be showing the last signal she gets before they pass.

Jim

How horrible for us all that we must actually use clocks in every aspect of physics!

Actually, you can empirically determine whether or not clocks that are in motion are synchronous. It seems that one really can use the speed of light to synchronize clocks that aren't moving relative to one another, but that are moving relative to some other set of clocks. And this process introduces all of the Lorentz contractions that one expects (plus the time dilation as well).

I think this is one source of trouble, this part of the claimed setup is incorrect. Since Betty is moving, the fact that she starts out at 5 light seconds when the transmitter emits "10:00:00" simply does not mean that it will take 5 seconds to reach her. In fact, it will only take 4 seconds to reach her, and she will receive "10:00:00", just like Alice, when she is next to Alice, but the time at the emitter will be 10:00:04 then, not 10:00:05. How could Betty be receiving something different from Alice, they are next to each other and seeing the exact same light wave. Importantly, the signal here is no different than a sound wave, someone shouting "10:00:00", reaching Alice and Betty just as they are next to each other, at 10:00:04.

But this is not even the largest problem with the scenario-- the largest problem is that there is no relativity in it at all, so it cannot be used to comment on relativity. Exhibited instead are two common misconceptions about relativity, and unlearning these misconceptions I hope will help you understand relativity better.

The first common misconception is that relativity has to do with illusions of time of flight effects-- it does not. Relativity is what you get after correcting for all that. If you doubt this, simply set up the identical thought experiment with sound waves-- let someone be shouting out what their watch reads. You will have exactly the same results as in your setup, but sound waves do not in any way invoke relativity, nor is relativity about setting clocks based on when light signals arrive. It is about just building a clock the normal way clocks work, and letting it do its thing, and comparing to what some other clock is doing. That's the only "structure" of spacetime that needs to be invoked, but that does need to be invoked or it isn't relativity.

So what then is the fundamental difference between sound and light? Here we come to the second common misconception, that you can do relativity experiments in a single frame of reference. That is not correct-- relativity is what happens when you transform to another reference frame. That's where the difference between sound and light appears, and only there-- because sound has a fixed ponderable medium (air), and light does not. That difference shows up when you transform to someone else's frame and ask about their perception of the speed of sound (it'll be different) versus the speed of light (it won't). Simply giving Betty a motion and a receiver does not transform to her reference frame-- that's why it is essential that Betty carry a real clock of her own. Only by measuring Betty's time using Betty's clock can you claim to have transformed to her reference frame.

I realize you addressed this comment before when you claimed this is an assumption about spacetime structure, but it's not an assumption-- it is what relativity is actually for. Relativity is for transforming from what one person's real clock will say, given what some other person's real clock says, not what signals they receive (refer again to the sound-wave substitution, which is not relativity). The whole purpose of relativity is to be able to do physics using either real clock, so if you don't have more than one clock, you just don't have anything that has to do with relativity.

So the bottom line is, the setup is incorrect about what Betty will receive, so perhaps fixing that will by itself clear up the problem. But if you fix that and still see a problem, then consider my comments about the fact that this thought experiment does not access what relativity is designed to do-- it isn't even about relativity until you have two real clocks in it. That's also what Kwalish Kid meant, I believe, about the need for using real clocks when we do physics in different reference frames.

Hi Doug. I do not doubt that the Doppler shift will arise. But we are not dealing with a change of colour. We are dealing with when the time signals will arrive (irrespective of their "colour") and, more importantly, why this is so.

Thanks for your input.

Hi Jim. Thanks for this. I suggested that the time signals are emitted at one second intervals because I could show the effect at this interval with the simplest maths. Yes, if you change the velocity, this simple scenario does not hold. But by all means assume that they are emitted at 1/100, 1/1,000 or 1/1,000,000 of a second intervals. The result is the same, it's just the maths gets more complicated.

I'd like Doug/sweetser to try flexing the scenario this way. I think it could be informative, for all of us...

Nobody remarked on this until post #17?

I saw right away that this assumes absolute time and doesn't
use the Lorentz transforms. I saw even quicker that the two
girls would receive the same signal simultaneously as Betty
passes Alice. And I saw instantly that the assertion that Betty
will receive the time signal "10:00:00" at 10:00:05 was wrong.
That would only be true if she weren't moving. Obviously.

But even after reading your post it took me several minutes
to figure out why it is wrong and what is right.

Assuming there's no such thing as relativity or LTs, as Betty
passes the point in space marked "5 sec" on the diagram, the
signal reaching her from the transmitter says "9:59:55" on her
device. We see her take five seconds to come abreast of Alice,
at which point the signal reaching Alice and Betty makes both
their devices read "10:00:01". During the five seconds that
Betty travels from the "5 sec" mark to the "4 sec" mark (where
Alice is located), she sees her device rapidly speed forward
through six "seconds": 56, 57, 58, 59, 00, 01. Because the
transmitter signal is blueshifted. The blueshift is caused by
her being closer to the transmitter at the reception of each
successive clock tick.

Just plain old Doppler shift! And I was snookered by it!

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

jedaisoul,

Visualize the time signals from the transmitter as water waves:
One wave each second, moving to the right. Alice is hit by one
wave each second. Betty is moving toward the transmitter as the
waves move toward her, so she is hit by six waves every five
seconds, or 1.2 waves each second.

That's Doppler!

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

jedaisoul,

The Doppler shift in your scenario and which I described in
my previous two posts is classical Doppler shift, which ignores
relativistic effects. There is also the relativistic Doppler
formula, as sweetser said, which gives a slightly more
accurate result when Betty is travelling at 1/5 c.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Hi Kwalish.I do not disagree that the effects exist. The thought expeiment is devised to show whether the effect is real (i.e. the space-time continuum is affected ) or apparent (i.e. it is only our view of photons that is affected). It still exists either way. The maths of SR and GR is unaffected.

It's whether we can say in a cosmology "the space-time continuum is affected this way..." or "our astronomical view of distant objects has to be corrected for this effect...".

Hi Ken. Firstly, may I thank you for a reply that addresses the experiment on its own terms. However, your comment above is pure Newtonian physics. That is what was expected before the finite velocity of light was discovered. It is an intuitive view, but is wrong. If that was true, the theory of relativity would never have arisen. Also this comment is contradicted by your own comments about light and sound waves. It is precisely because light does not behave like sound waves that we have the theory of relativity.

If someone is five light seconds distant from a transmitter when an electromagnetic signal is emitted, they will receive that signal five seconds later. Irrespective of their subsequent motion. That is what the fixed and finite velocity of light means. If Betty was moving away from the transmitter at the same speed she'd see exactly the same time signal at exactly the same moment. Only the disparity with Alice's view would not be so apparent. I have arranged to have the girls side by side at 10:00:05 precisely because it reveals the disparity in sharp focus.

It is not true that there is no relativity in the example. Special Relativity is an explanation for the disparity in the time signals. SR should not (and does not) change the circumstances. It explains it. If it did change the circumstances, then it's predictions would not match reality.

General Relativity is different. GR changes the view of the universe by invoking gravity. That is why I've used a pure SR example. My argument against GR as the basis of a cosmology (which I did not explain in the OP) is that if SR describes an apparent effect, and GR is SR with gravity, then GR does not describe the space-time continuum experienced by material entities. However, I would reiterate that mathematically GR is fine, so long as you are dealing with electromagnetic phenomena emitted by distant objects.

I agree. I took it for granted that all people involved in the debate understood this. The example is specifically designed to make it unnecessary to deal with the "time of flight" element by placing the observers adjacent to each other when the different time signals arrive.

There are two frames of reference here. Alice's and Betty's. And, as you have said, the speed of light is the same in both.

I'm sorry Ken, this is a statement of belief. You have not substantiated it. I deliberately did not give Betty her own clock because, if you do, it is more difficult to distinguish between real effects on the space-time continuum and apparent effects on electromagnetic phenomena. You get embroiled in questions of simultaneity. I intend to deal with simultaneity when (if?) I present my alternative cosmology.

Anyway, I'm very grateful for your comments and the time you devoted to writing them. I hope you find the thread intriguing, but I don't think that you have demolished my argument just yet...

Hi Jeff, thanks for your input. Please see my detailed reply to Ken G. I think that covers all your points in this post, but please let me know if you think I've missed anything...

Hi Jeff. I agree, up to a point. This is Dopper. However, please see my reply to Ken G re the difference between light and sound (or in this case water waves), and my reply to Doug/sweetser re Doppler. This reply covers posts #21 and #22.

Hi Jim. Please accept my apologies for the delay in replying. My copy of Taylor and Wheeler is on order. I hope it is as good as you and Doug say!

Actually you are quite incorrect on this point, so I think this is all that needs to be clarified. There is actually no physics at all in this scenario, other than the finite speed of the signal from the clock, because we are staying entirely in the same reference frame-- that of the clock. Since you have no other clocks, there are no other reference frames. This is my point, it is neither Newtonian nor Einsteinian, and it matters not whether we use light or sound. Do you not see this? It was your setup that Betty and Alice merely have receivers, not clocks. So if all they have are receivers, why can we not use sound seconds instead of light seconds, and let their "receivers" be ears? You claim this would not work, but on what basis, if they have no clocks to check your assertions? I repeat the key point: relativity is never invoked if you only have a clock in a single reference frame, and that clock is the only generator of a time signal. There is absolutely no need for relativity any time this is the situation, all you are doing is correcting for the finite speed of propagation of something (light, sound, water waves, it matters not). That isn't relativity, trust me.

Ah, this right here is the entire source of your misunderstanding of relativity. You are mixing reference frames. In Betty's frame, the time that elapses does depend on Alice's motion, but at least you can use the clock you have there. In Alice's frame, the time does not depend on Alice's motion, that much is true, but you are using an invalid clock in that frame-- you must use Alice's clock there, or your claim that the time elapsed is independent of her speed will simply be incorrect. What is happening here is that you have a subtle but crucial misunderstanding of how relativity works, so you are making statements about distances and times for Alice but you have not given her a ruler or a clock. That is not how physics works, nor relativity. I can't say this any more clearly: there is never any relativity where all measuring devices are in the same reference frame. Also, your interpretation of how time works would yield inconsistent results even if there were two clocks in the same reference frame (try it if you don't believe me-- put a second clock 1 light second from the first and try to use your understanding of time to get consistent results for Alice). Yours is not Einstein's approach to time, and it's not a useful one either, because it would not yield a consistent definition. It is the time of one clock, exported everywhere using time of flight. It is the tyranny of one clock, when in fact the theory of relativity lies at the opposite extreme-- each clock is its own master, and merely requires synchronization at one moment to be a meaningful standard of time.

That is simply false, any experiment would show that. There isn't even any need for relativity to demonstrate this, the error is there even at highly nonrelativistic speeds (i.e., to order v/c not (v/c)^2). It is not even necessary that it be a "time" signal, it could be a showing of a movie for all the difference it would make. Alice's time is measured on Alice's clock, and it would read something different in those two situations. That's how time is defined, not your way. This is not even relativity yet, it's all mistaking the illusions of time-of-flight effects for what time is actually doing.

It's not really your fault that you think this, it's often poorly explained. But now it's time for you to know: a reference frame is a set of tools for measuring distance and time. If you aren't using those tools, you are not in that reference frame, in the physics sense. Just having a sentient mind that can detect signals is not a reference frame, pure and simple-- it's just someone watching TV, for all the physics that's in it. If you doubt this, then instead of Alice let it just be a box that displays whatever signal it detects. That's a TV, not a reference frame. I realize that you are intelligent, but you have not had explained what physics actually is.
It is not belief, it is physics. If you doubt that, then your issue is not just with relativity, but with the entire field of physics. Physics is the science of predicting the results of measurements, along with the mental pictures in support of those predictions, which afford us a sense of understanding. That's just what physics is, look it up anywhere. There is zero "opinion" in this remark. But because of the reliance on measurements, Alice needs a clock and a ruler or she does not have a reference frame there. Sentience is insufficient. On the contrary (and this is the whole point), by not giving her a clock you assured that you would confuse "apparent" effects from "real" ones-- your entire scenario is all about apparent effects, except your mistaken claims about what "time is doing". You can say nothing about what time is doing in a given reference frame until you put a clock in that frame, and this is not my opinion-- it is the means of demonstrating the truth of my remark. I am not trying to be hard on you, I actually want you to see where you have made an error in physics.

You see, time does what clocks do-- that is very simply the definition of time. All you need light signals for is to synchronize the clocks with each other, to set the "zero" time. You are doing more than that when you claim "how much time will elapse", and Alice's clock will simply not follow your claims. Hence, your claims are just not physics, and that is the core of the problem here. The core of the problem is that you assert the time it takes the signal to reach Alice does not depend on her motion, but that claim is only true in Alice's reference frame, not Betty's. Thus it is only a true claim when referenced to Alice's sense of time, which in turn must be measured on Alice's clock. You mistakenly take that statement and use it to say something about when Alice will receive the signal as measured on the clock in Betty's frame, and that will not be supported by experiment. If you don't believe me, just put a second clock 1 light second from the first, not moving, sending out signals just like the first-- and test your concept of time for self-consistency. You'll find that Alice will be very confused indeed-- your concept of time will be unsavable. Try it.

Except for Doug (Sweetser), you folks are spinning your wheels.

It is not an assumption. It is not an affect that time has on the properties of the underlying space-time continuum. It is the nature of our universe. All of special relativity consists of demonstrated properties of our universe, and it is known to be correct to one part in 10 to 20th (see Wiki article). It's been 100 years since Einstein published, and the theory has withstood every test - including some it was expected to fail (see recent frame dragging research). There is nothing, repeat, nothing wrong with the fundamental postulates. Objects shorten in the direction of motion, time slows down for moving objects, mass grows exponentially for moving objects, all relative to the non-co-moving external observer. Personally, if I were Fraser, I would treat these threads that beat misunderstandings about relativity to death like the electic universe threads - if you don't have anything new to say, and are instead weak in the math and physics, then get thee to a library.

Oh dont be too hard on newcomers who want to
clarify this spacetime buisness. I have liked
to stand at the farm gate comfortable in my
cosy three dimensional space thinking the
mathematicians overeach themselves. But a few
decades of reading and thinking here and there
has given some insight. I was amazed how I had
never understood sound doppler till recently.
A sound source at a frequency coming towards
you has a higher frequency than if it were
stationary and you were moving towards it at
the same speed! This is not allowed for light
waves otherwise double stars would look
smeared in their orbit. A moving body exhibits
time dilation and light behaves for all
observers who see the same redshift or
blueshift whether they are the traveller or
the stationary. Simple really!