I don't see how you can make assumptions like that without some extra stuff. I'm not sure whether thsi is correct, would need definitions of all your terms first. My proof rests only on c is constant.
that is where you are wrong. your proof rests on quite a few more assumptions than c being constant.
Please itemize these, we will check together.
also, i am not making an assumption, i am REMOVING one by introducing F.
i gave the neccessary and sufficient definitions for t_x & t_y above. t_a is a's intrinsic time, t_b is b's. "a" is all available information about a, as "b" is for b. F is undefined. F is the functional that we would try to deduce given empirical data about the other variables. (in SR it turns out to be related to the lorentz transform, but our argument only requires that F(a,b,x) is not necessarily equal to x. which is, as i said, REMOVING the hidden assumption that F(a,b,x) neccessarily equals x, and thus that e.g. a's measurement of b's time is neccesarily the same as b's intrinsic time. )
From your definition of t_a and t_b, I notice:
t_a = t_b
and t_a and t_p are intrinsic (you mean proper) time for A and B.
This statement of equality would of course prove your result immediately. But it is common not to assume the result you want to prove. It is also impossible for you to even state this equality except with reference to some frame. Thus:
t_a = t_b in A frame is different from
t_a = t_b in B frame.
The issue is not that proper time chnages with frame, but that comparing two proper times requires clock synchronisation (twice) which depends on frame.
tomclarke wrote:
...
The problem is asymmetric, because one twin changes velocity and the other does not. This changed velocity alters Doppler. But of course it alters Doppler on the moving twin immediately, and on the stationary twin only after the change has propagated.
see, therein lies your problem: when you say a twin "changes velocity", you don't specify what coordinate system/reference frame it changes velocity with respect to.
Very true. That was deliberate, because I wanted to avoid complication. How about:
"the moving twin changes velocity in all frames before the stationary twin can observe this change in velocity"
You see my proof only depends on one event (pulse frequency changing on A) being strictly after another event (pulse frequency changing on B). since the two events are connected by a light ray this is always true.
If you wish to be more definite you could do the calculation in A frame or B frame.
tomclarke wrote: That is symmetric, but when one twin turns around it affects his counting of other twin's time immediately,
No it affects the counting of the incoming signals for BOTH twins immediately and the effect is the SAME in both reference frames.
[and othr twin is so affected only after some time.
My impeccable derivation by using the Lorentz transformation proves compellingly that this statement of yours IS NOT CORRECT.
the turnaround is a real (asymmetric) physical event.[/quopte] Nonsense! You only have relative speed: According to twin1 it is twin2 who is turning around and according to twin2 it is twin1 who is turning around.
the other twin is turning arou It has consequences for Doppler effect.
The Doppler effect is included in the equations that I have derived and the result is as clear as a bell that both twins observe exactly the SAME number of pulses during the WHOLE trip.
this appears to be a paradox, but the paradox is resolved when one realizes that there is a transform function between between twin B's time and twin A, and vice versa. hence:
I don't see how you can make assumptions like that without some extra stuff. I'm not sure whether thsi is correct, would need definitions of all your terms first. My proof rests only on c is constant.
what it sounds like you have done with you "turn around" thing is accidently created a triplets problem, rather than a twins problem. here, you introduce a third observable at an arbitrary point, who, through his own movements and spins, is able to introduce asymmetry.
Exactly!
No, the movement of one of the twins changes, the movement of the other does not.
The motion is relative so by stating this nonsense you are again displaying collossal ignmorance. I do not enjoy it to point out to you when you are making a fool of yourself. I am sorrty that I hvae to do this because I do think that you have talent if only you will stop kicking at stones.
I'm not sure what is unclear about my diagrams. they illustrate, vividly, how the Doppler frequency change happens assymetrically between the two twins. try having a look?
Not in the case of light waves which are subject to the Lorentz transformation and therefore do not move through a unique medium.
The problem is asymmetric, because one twin changes velocity and the other does not. [/quote[ BOTH twins change their RELATIVE velocity.
This changed velocity alters Doppler
The exact mathematical derivation from the Lorentz transformation proves that, although the Doppler effect on the outward and inward lrgs of thye trip are different, the twins receive the SAME total number of pulses during the whole trip.
But of course it alters Doppler on the moving twin immediately, and on the stationary twin only after the change has propagated.
Both twins are stationary within their respective inertial reference frames and both twins are moving relative to their other brother. There is NO uniquely "stationary" and uniquely "moving" twin. This is the most fundamental truth on which Einstein's special teory of relativity is based; and you keep on violating it!!.
tomclarke wrote: That is symmetric, but when one twin turns around it affects his counting of other twin's time immediately,
No it affects the counting of the incoming signals for BOTH twins immediately and the effect is the SAME in both reference frames.
There is no need for further communication between us Johan. I agree entirely that if this is true you are right and I wrong.
Go back to my pictures.
What you propose would be a clear violation of causality, because only the twin that turns around knows when the turnaround will happen.
I'll let you think about that, but will not answer your further posts until you have changed this statement, since there would be no point in furher debate.
HOW do you determine when the pulse frequency increases for each twin?
As soon as they reverse their relative motion so that they do not move away from one another but towards one another, this frequency changes.
Note that one twin changes direction to mark start of inbound and end of outbound journey.
Both twins move simultaneously away from one another during the oubound motion and simultaneously towards one another during the inbound motion.
Note this could happen at any time
So what!
Note causality requires that the (Doppler) effect of this change cannot propagate to other twin faster than light.
Note that the Lorentz transformation proves that during the outbound leg of the trip both twins receive the same number of pulses and this is also the case during the inbound trip. You might not like this results, but it is the correct result because it is impeccably derived from the Lorentz transformation which is the engine that controls ALL SR effects. If I am wrong, then show me where I have made a mathematical mistake instead of spouting paranormal metaphysics.
Note that (Doppler) effect of this change will immediately alter pulses on the twin that changes velocity.
On both twins as proved by impeccable mathematical derivation from the Lorentz transformation.
tomclarke wrote: That is symmetric, but when one twin turns around it affects his counting of other twin's time immediately,
No it affects the counting of the incoming signals for BOTH twins immediately and the effect is the SAME in both reference frames.
There is no need for further communication between us Johan. I agree entirely that if this is true you are right and I wrong.
Good we are getting somewhere.
Go back to my pictures.
Go back to my impeccable mathematical derivation from the Lorentz transformation.
What you propose would be a clear violation of causality, because only the twin that turns around knows when the turnaround will happen.
How does he know?
I'll let you think about that, but will not answer your further posts until you have changed this statement, since there would be no point in furher debate.
You are welcome to live in further ignorance. I am just sad since you do have possibilities which you are squandering!
tomclarke wrote:
I don't see how you can make assumptions like that without some extra stuff. I'm not sure whether thsi is correct, would need definitions of all your terms first. My proof rests only on c is constant.
that is where you are wrong. your proof rests on quite a few more assumptions than c being constant.
Please itemize these, we will check together.
also, i am not making an assumption, i am REMOVING one by introducing F.
i gave the neccessary and sufficient definitions for t_x & t_y above. t_a is a's intrinsic time, t_b is b's. "a" is all available information about a, as "b" is for b. F is undefined. F is the functional that we would try to deduce given empirical data about the other variables. (in SR it turns out to be related to the lorentz transform, but our argument only requires that F(a,b,x) is not necessarily equal to x. which is, as i said, REMOVING the hidden assumption that F(a,b,x) neccessarily equals x, and thus that e.g. a's measurement of b's time is neccesarily the same as b's intrinsic time. )
From your definition of t_a and t_b, I notice:
t_a = t_b
and t_a and t_p are intrinsic (you mean proper) time for A and B.
This statement of equality would of course prove your result immediately. But it is common not to assume the result you want to prove. It is also impossible for you to even state this equality except with reference to some frame. Thus:
t_a = t_b in A frame is different from
t_a = t_b in B frame.
The issue is not that proper time chnages with frame, but that comparing two proper times requires clock synchronisation (twice) which depends on frame.
you are totally making a straw man mess of my argument.
t_a = t_b was a RESULT, not a premise. and i have not even supplied any proof for the result, at that, as it was besides the point. my point was the introduction of F to resolve the apparent contradiction between the two observer's observations.
also, t_a, t_b are in the end CALCULATED quantities, NOT OBSERVED
where a to discover what the functional F() was, they could invert it, and thus then apply the inverse of the functional to their observation and compare it to their clock. same goes for b. if they both deduce F() correctly, their results will be consistent. that is, a would be able to calculate what b calculates a's time to be and vice-versa and so on recursively. but this is a tautoligical because this is how we define a "correct" deduction, is by requiring consistency.
your statement that "It is also impossible for you to even state this equality except with reference to some frame. Thus:
t_a = t_b in A frame is different from
t_a = t_b in B frame.
"
is precisely what I just said. it is the reason de'tre (sp?) for the functional F()! the first parameter of F() is the reference frame of observation, the second parameter is the reference frame being observed, and the final parameter, the (unknown) intrinsic time in the observed reference frame, and the result of the function is the observed time (from the frame of observation; the first parameter) of the observed reference frame (the second parameter).
the goal of the observer then is to discover a function F consistent with all observations available to him, and then use the inverse of that function in order to "transform" his observations into the other twin's observations. if the other twin agrees, then he wins!
Last edited by happyjack27 on Wed Jan 11, 2012 7:25 pm, edited 4 times in total.
tomclarke wrote:
...
The problem is asymmetric, because one twin changes velocity and the other does not. This changed velocity alters Doppler. But of course it alters Doppler on the moving twin immediately, and on the stationary twin only after the change has propagated.
see, therein lies your problem: when you say a twin "changes velocity", you don't specify what coordinate system/reference frame it changes velocity with respect to.
Very true. That was deliberate, because I wanted to avoid complication. How about:
"the moving twin changes velocity in all frames before the stationary twin can observe this change in velocity"
why would you _deliberately_ make such an eggregious error? you assert that you've made irrefutable "proofs", yet you haven't even fully specified the problem! and you think this avoids confusion?!
and then what you offer to fill this gap isn't even sensical!
tomclarke wrote:
You see my proof only depends on one event (pulse frequency changing on A) being strictly after another event (pulse frequency changing on B). since the two events are connected by a light ray this is always true.
If you wish to be more definite you could do the calculation in A frame or B frame.
if you were trying to prove casual consistency, then that would be a fine example of a circular proof. but i see no need to prove such a thing, as we can ALWAYS find a functional which transforms causal inconsistency into causal consistency. and the latter is obviously simpler and more useful, so we would always want to determine such a functional.
if you want to know you have a self-consistent, and thus, valid, theory, you HAVE to do the calculations in both reference frames.
tomclarke wrote:
your statement that "It is also impossible for you to even state this equality except with reference to some frame. Thus:
t_a = t_b in A frame is different from
t_a = t_b in B frame.
"
t_a is always t_a and t_b is always t_b. that is a first principle of mathematics.
so if one observer sees t_a > t_b, and the other sees t_a < t_b, which apparently breaks the rules of mathematics, then how does one resolve this apparent paradox? well, if the rules of mathematics are correct, which they are, and if your observations/measurements are correct, which in this case they are, then it follows that what one observer thinks is t_b is not actually t_b! so to acknowledge this realization, "a" calls his observations instead, t_x(a) and t_y(a), and ponders if there exists a functional F(), that relates the observations of a and b, such that they can accurate predict what the other's observations are. from that we can introduce a new set of variable, t_a and t_b, whose values can be agreed upon by both observer a and observer b. (save a constant linear translation that can be non-dimensionalized out)
so observer a, lets call him einstien, now postulates two things:
1) there is a functional F(), which transforms spatial-temporal observations made in one inertial reference frame, to that of another.
2) this functional, F(), is the same in all inertial reference frames.
the problem now is to deduce F() from one's observations and verify that it satisfies these two postulates and remains self-consistent after repeated (iterative/recursive) application. this is SR. (in the case where there is mass (and thus F=ma) but no gravity, at least)
...and now observer b is perpetually flustered, as observer a is always determining his observations correctly, while he can never determine a's. surely observer a must be playing tricks on him!
meanwhile, observer a is having a good laugh! oh, if observer b would only think to introduce a functional! but this is too fun to watch! "10:57.7223534!" he calls out. "blasted, right again! and yours is, err, 5 second fast of that?" "Nope!"
Why is it so hard to accept that the GPS bird clocks run at a different rate?
This is rate difference is real to us and it is a net combination of GR and SR. If the rate difference were not real, we would not need to adjust the rate of the clock before flying it.
This means that without the SR adjustment, and/or without a GR adjustment, over a given period of our time, our ground clock will produce a different number of counts (pulses) than the flying clock. This is known, proven and is happening while we sit here and debate. When you bring it back, it has accrued a different amount of time. This has also been done over and over as I have shown in links to reports. I agree that this has not been done in a gravity free method, but have tried to point out many ways that there are ways to see the SR part occur during a "gravity constant" speed experiment.
The fundamental point is that the clock rate is different. The total number of pulses for a given period of time is different. If I put a pulse counter on the clock (like... a clock!) it will read a different amount when I bring it back and set it next to the ground clock. From that point forward they will be in synch ratewise, and accumulate equally but with the offset incurred during the flight.
If I correct for the GR factor only during the flight, the clock will accrue total counts slower than the ground clock because its rate is slower due to the SR component. This means when it comes back, it will have counted less total pulses than the ground clock(This is the point that is disagreed on by Johan and Happy). But, once together again, they will accrue equal counts, because the rates will be matched again.
I fully disagree with the argued point that the pulse count is the same. The entire point of the dilation is that the rate changes. You can twist the words to misrepresent the math all day long, but at the beginning of the test, one person stays put, the other accellerates to a higher speed, then turns around, and comes back, then slowing down. I think the SR component is a function of the "induced gravity" during accelleration to speed making a rate change. Thus with rate changed, the observation point (the person that stayed put) will see the pulse rate slow, and receive less counts from the higher speed twin.
If he goes straight out, reverses and comes straight back, the slows and stops it should be as follows:
accell to speed (observed rate slows, less pulses received), slows to reverse and momentarily zero difference in speed (observed rate speeds up, and momentarily matches), travelling twin then accells to speed for return trip (rate slows again, less total pulses recieved), he then slows again and stops to see his twin (rate increases until match and synch, total pulses counted are less for the entire trip).
I have left out doppler in the discussion , as all that does is blue shift or redshift the overall rate, but the rate itself remains slower while the traveller is shifting speeds.
In my argument, the rate change only happens during the accelleration and decelleration phases, both on outbound and return. When at speed, the rate remains slowed a consant amount.
The stationary twin, never accellerates nor decellerates, and does not feel this force, thus does not have any change in his own clock, but sees a rate slowing of his travelling twin's clock. He also sees it come back to synch with his own during the turn around maneuver, as well as the final slowing and stopping in the return to home maneuver.
The travelling twin sees the stay behind twin's rate increase, and will count more total counts for him as he accellerates away to speed. During the transit, the rate difference will stabilize and he will see his stationary twin's clock operate at a higher rate. He will then see it slow and match rates during the turn-around, only to speed up again as he accellerates towards home. After he reaches transit speed, he will see his stationary twin's clock signalling at a steady faster rate, accrue more counts, and then during his decell phase, the stationary twin's rate will decline until they match speed and the clocks resynch. The net result is that the travelling twin will see that his stationary twin will have accrued more total counts than he, and he will have seen it during the trip.
You can try and brain trick yourself into saying "how will they know who left and who stayed?" and then make the follow on leap saying "thus I can do the math from either perspective in the same way..." but that is not true nor correct. Only one twin (the traveller) will experience the accelleration and decelleration cycles for the trip. The other will not. That concept must be tracked in the math for the math to be true and give correct results.
In summary, I say:
Accelleration "induces" gravity. The object accellerating behaves like it is entering a deeper gravity well and "slows". Once accelleration is removed, the object is moving at a velocity that is constant, but higher than pre-accelleration. In this context, once at speed, there is no more rate change. Think of it as imparted momentum. It will keep "moving" as it was pushed and retain the rate imparted for the given level of accelleration. it will coast. Then it will decellerate, in effect "climbing out of the gravity well" and the clock rate will increase with the decelleration.
GPS satellites show this everyday.
The part I am unsure of is thinking through the static speed part. Once the object's accelleration is decreased and zero'd, does the accompanying clock rate shift with this, or "retain momentum" until a decelleration is applied? I am inclined to think the shift is retained given space clock data. But, I also think there may be an impact on this interpretation given the angular momentum involved with orbiting clocks. This is why I am interested in data analysis and comparison of non-orbiting clocks, or those that are operating elsewhere in the solar system, such as Mars. But to date I have not been able to find either analysis or raw data to chew on in this regard. I did find one report discussing life spans of flown atomic batteries, but is was unclear in conclusions. I am interested in the on-going Mars Scince Lab mission, as there should be something meaningful in the life span of the installed nuclear battery to see given a relativistic analysis of the entire mission trip. I have not to date been able to determine if the battery includes only thermal sensors, or has a radiation counting device.
happyjack wrote:
see, therein lies your problem: when you say a twin "changes velocity", you don't specify what coordinate system/reference frame it changes velocity with respect to.
Very true. That was deliberate, because I wanted to avoid complication. How about:
"the moving twin changes velocity in all frames before the stationary twin can observe this change in velocity"
why would you _deliberately_ make such an eggregious error? you assert that you've made irrefutable "proofs", yet you haven't even fully specified the problem! and you think this avoids confusion?!
What I have done is not in error. I have nmerely left out unnecessary details. Can you tell me what is incorrect with it?
and then what you offer to fill this gap isn't even sensical!
tomclarke wrote:
You see my proof only depends on one event (pulse frequency changing on A) being strictly after another event (pulse frequency changing on B). since the two events are connected by a light ray this is always true.
If you wish to be more definite you could do the calculation in A frame or B frame.
if you were trying to prove casual consistency, then that would be a fine example of a circular proof. but i see no need to prove such a thing, as we can ALWAYS find a functional which transforms causal inconsistency into causal consistency. and the latter is obviously simpler and more useful, so we would always want to determine such a functional.
if you want to know you have a self-consistent, and thus, valid, theory, you HAVE to do the calculations in both reference frames.
It is like this - listen carefully:
In SR events in space can be timelike, spacelike, or on light cone (the edge between timelike and spacelike).
causality is about nothing tavelling faster than light. It is not about consistency. Except that we normally reckon causal information travelling faster than light means inconsistent. (technically logical connectivity can be faster than light, because of quantum entanglement, but not causal connectivity).
Although exact lengths and times depend on frame, causality does not. Two events are either timelike (one could cause the other) or spacelike (one could not cause the other) independent of frame.
If your functional can transform coordinates to alter causality then it will itself potentially create paradoxes.
For example Johan's latest statement says that information must travel between two points (the twins) which are spatially separated. (He says "at the same time" - in any frame that means spatial separation). That is impossible without a time machine.
That is why I've stopped replying to him, unless he retract the statement. There is no point.
In this proof all I need to show is that one event happens AFTER another. In general the result is frame-dependent. But in this case the two events are connected by a light ray. Therefore in all frames they will be connected by a light ray. Therefore in all frames the one which emits the light ray happens first.
I have chosen my notation and statements so that everything is frame-independent. Thus when I count received pulses all I care about is the relative frequency (1+v/c)/(1-v/c). The value of f, which would be affected by gamma, drops out of the equation. We know that anything which affects f must be equal for both twins by symmetry, so even though I have not included gamma scaling f everywhere, I have shown that any scale factor is equal for both twins and therefore the result holds.
Technically you are right I should specify a whole load of frames, saying I was counting received pulses in the current rest frame of each twin. Would that help?
The clear asymmetry in Doppler effect is real and including the relativistic correction (gamma scaling all the received pulse frequencies) does not change it.
I could simply include the full LT in the calculations, but that would be putting the cart before the horse, and making things more complex. All you need to prove this is that c is constant.
happyjack27 wrote: the problem now is to deduce F() from one's observations and verify that it satisfies these two postulates and remains self-consistent after repeated (iterative/recursive) application. this is SR. (in the case where there is mass (and thus F=ma) but no gravity, at least)
happyjack, you are wasting your time on Tom. A person who thinks that there can be an asymmetry in the Lorentz transformation does not know what Special Relativity is all about.
He just cannot imagine that in SR relative motion between the two twins is (well yes) RELATIVE. SR and the Lorentz transformation does NOT give an asymmetry when an outbound motion flips around to inbound motion: Both twins experience themselves in SR as being stationary and that his brother is moving RELATIVE to him (outbound and inbound). This is the whole essence of Special Relativity which Tom just throws out of te window to suit his dogmatic, and physically indefensible reasoning.
We must, however, forgive him since, incredibly, famous physicists have been making this same GROSS mistake for 100 years. This is one of the reasons why modern physics is not interpreted in terms of reality as classical physics has been and as it should be, but in terms of paranormal Voodoo!
Last edited by johanfprins on Wed Jan 11, 2012 8:43 pm, edited 4 times in total.
tomclarke wrote:
What I have done is not in error. I have nmerely left out unnecessary details. Can you tell me what is incorrect with it?
firstly, the presumption that they are "unnecessary details". that, alone, is sufficient.
Well, I will agree that the proof could be made more precise by specifying the frame in which the pulses received by each twin are counted: although since this is the twin rest frame that is normally assumed.
I agree that technically I should have two scaling factors scaling the frequencies. They are the same for the two twins (by symmetry argument), but could in principle be different for the two different frequencies, although in reality they are the same since gamma(-v) = gamma(+v). But in order not to prove this they could be allowed to be different.
That would only be a small extra complexity in the equations, and make no change of course to the result, even with different scaling factors for the two frequencies.
Last edited by tomclarke on Wed Jan 11, 2012 8:57 pm, edited 1 time in total.
happyjack27 wrote: the problem now is to deduce F() from one's observations and verify that it satisfies these two postulates and remains self-consistent after repeated (iterative/recursive) application. this is SR. (in the case where there is mass (and thus F=ma) but no gravity, at least)
happyjack, you are wasting your time on Tom. A person who thinks that there can be an asymmetry in the Lorentz transformation does not know what Special Relativity is all about.
He just cannot immagine thatin SR relative motion between the two twins is (well yes) RELATIVE. SR and the Lorentz transformation does NOT give an asymmetry when an outbound motion flips around to inbound motion: Both twins experience themselves in SR as being stationary and that his brother is moving RELATIVE to him. This is the whole essence of Special Relativity which Tom just throws out of te window to suit his dogmatic, and physically indefensible reasoning.
We must, however, forgive him since, incredibly, famous physicists have been nmaking this same GROSS mistake for 100 years. This is one of the reasons why modern physics is not interpreted in terms of reality as classical physics has been and as it should be, but in terms of paranormal Voodoo!
yeah, it just frustrates me. i give up. i recall in reading "surely you're joking, mr. feymann" feymann's remarks that he found even doctoral physicists failed to grasp basic concepts to the extent of not being able to answer questions that should be trivially easy. though clearly upsetting, perhaps it is we who are in error when we find this also surprising.
i have said all i need to say. to continue would just be to repeat myself... more. what i have said is there to be read. some people will understand, and some people won't. so be it.