Alternative Twins Paradox

Well, I skimmed through those links, but I think I can present my case without them. All you really need is the Lorentz transform for time.

When the two twins are together in the same place, and one twin accelerates away, he is moving into a different reference frame. The local time in that reference frame would be

t' = γ ( t - vx/c² )

but since x=0, that reduces to

t' = γ ( t )

and since t=0 at the beginning, we have

t = 0
t' = 0

But later on, when the second twin accelerates, the x and t variables are no longer 0. That is why this case is not symmetrical. Let's assume the following

v = .8c
γ = 1/.6
t = 10 years

This means each twin is 10 years old in his own frame, and he considers the distant twin to be only

v = .8c
γ = 1/.6
t = 10 years
x = vt = (.8)(10) = 8 light years

t' = γ ( t - vx/c² )
t' = (1/.6) ( 10 - (.8)(8) )
t' = 6 years

6 years old. Now one of the twins has to accelerate to bring them together into the same frame. When he does this, he will be moving into a different reference frame, just like the first acceleration, but t is no longer 0 in this case. The local time in that reference frame would be

v = .8c
γ = 1/.6
t = 10 years

t' = γ ( t )
t' = (1/.6) ( 10 )
t' = 16.666 years

So whichever 10 year old twin accelerates will still be 10 years old at that instant, but the time throughout the new inertial frame will be 16.666 years. This means that his brother will have to age from 6 years old to 16.666 years old during the second acceleration. So, just as I said, whichever twin accelerates second ends up younger. The accelerations are not symmetrical because t=0 and x=0 are only true for the first acceleration, and not the second.

 

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The accelerations are not symmetrical because t=0 and x=0 are only true for the first acceleration, and not the second.

Does not work.

The acceleration equations depend only on a time interval, which we excused and the relative speed.

Einstein did the same thing in his discussion on time dilation. Essentially, you are refuting his assertions.

If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B
http://www.fourmilab.ch/etexts/einstein/specrel/www/

But, if you insist, we can introduce a burntime interval.

Then you perform the intergral.

Those papers will show you how to do that.


My website will give the exact math calcs given some burntime BT in the accelerating frame with some acceleration a in that same frame.

You may look at that for the integral.

http://www.proofofabsolutemotion.com/srproblems.html

Look for the twins experiment.

 

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Yet another attempt at trolling. Thbe fact I replied with a massively more advanced reply than you can understand makes it obvious to everyone that the one whose understanding falls short is you.

Most people realise as they grow up that often their first assumption about something is not correct or that when something seems incorrect more often than not its their understanding which is at fault. You haven't seemed to learn this, which is all the more strange given you claim you've done plenty of mathematics at university. Your entire attitude smacks of you being a liar.

We've already established that you don't understand what SR says about transformations of light cones. I've had to explain to you many many times that a light cone transforms to a light cone. You have yet to retort anything I've said.

You've had people reply to you on that. It is now clear that we can't discuss something like that physical setup until you have learnt the basics. You whine and whine about someone replying to your first post but people have and now the issue is getting you to be able to apply Lorentz transformations properly. The issue is your lack of understanding. No one is going to be able to explain SR to you if you can't do the simplest bit of workings. And its clear you can't.

I've retorted every single one of your whinings. You haven't replied to any of my retorts, despite me posting them again. The fact you won't and the fact you hasve once again ignored my direct questions about submitting to a journal demonstrates you're making a concious effort to not reply to my questions. As such you don't want to admit you have no plans to submit to a journal, because you know you'd get rejected because you're wrong. Instead you want to just keep posting nonsense in the pseudo science forum and hope to ignore everyone who replies to you with things you don't understand or can't retort.

You know you'll fail peer review, so you're afraid to submit to it. You know you've failed to retort anything I've said so you're ignoring it. You know you've failed to retort anything anyone has said so you go into other threads and lie, saying no one has retorted you. You lie in threads where people have responded to you. All of your actions are simply a combination of lying, deceiving and repeating your own ignorance.

Every single person here who has a qualification in special relativity and has replied to you has corrected you. You keep trying to tell us what SR says but we correct you. Simply ignoring us doesn't mean you're right. If you can't reply to our posts then it demonstrates you know you have no response. This isn't a matter of innocently missing a question, you repeatedly ignore the same questions and you repeatedly tell the same lies. You're obviously aware you're doing it. The laughable thing is you believe no one will notice when you lie again and again or simply make up "SR says..." when its clear you've never studied it at all.

Oh no, you're unable to understand relativity. Emotionally mature people would accept it and move on. You have decided to try to convince others that SR is wrong so you can convince yourself that you don't need to learn it. Classic crank methodology. And all because you can't accept there might be something you don't understand something someone else does. It's pretty pathetic, most 12 year olds are more emotionally developed than that.

 

Yes, the above is LT.

I already calculated the distance with LT. That is one way only.

However, we have not answered the fundamental question. Wehn in the time coordinates of the statioonary frame does the moving frame see the light sphere at its origin a distance r?

I have shown it is rγ/c.

By, time dilation, the clock at the moving frame elapses r/c. Whenever the clock at the light emission point in a frame elapses r/c, light is a distance r in all directions by the SR light sphere.

Hence, light is a distance r from O' which contradicts LT.

You would need to refute time dilation or the light sphere to refute this calculation.

 

It is quite simple, when in the time coordinates of the stationary frame does the moving frame see light a distance r from its light emission point.

You claim this is above me. Well, I have looked through your math and have not seen this answer.

For example, James R calculated LT's answers for the light along the positive x-axis. He did it simply and quickly and I have no problem with that.

But, SR makes the incredible claim that a light sphere emerges from the origin of the stationary frame and one emerges from the origin of the moving frame riding with the frame while the stationary one remains stationary .

So, if SR is a complete theory, it must have an answer for this outlandish claim.

I provided the answer of rγ/c and then used time dilation to prove the answer.

But, of course, that implies the light sphere is in two different positions along the positive x-axis from O' at that one time in O. This contradicts the light cone.

If this time I selected is not correct, I would assume you have a different answer.

Otherwise, mine stands and SR contradicts itself.

 

I am not seeing where you get the c³ and I used t = rγ/c in the stationary frame which implies x = rγ.

I get,

x' = r ( γ² - v γ²/c ).

t' = r/c ( γ² - v γ²/c ).

 

I didn't claim to provide an answer to that question. I said I'd provided you with the explaination of the underlying methodology of special relativity such that the issue you have with different frames saying different things is actually a problem with your understanding. Your issues come down to not liking that light cones are independent of the motion of the emitter, only its location at time of emission. I've explained why this is not a contradiction. You didn't retort it. You claim you read through it but even if you did you obviously didn't understand it since it answers your misunderstanding completely.

You're putting words in the mouth of SR. I've been over this. I even reposted the lengthy posts because you didn't respond to them first time. You didn't respond to them second time. You fail to realise that I know what your 'issue' is. This isn't a matter of me not understanding what point you're trying to get across, its that I know what point you're trying to get across, I know why you're incorrect and I have explained it. Maths and all.

Firstly I don't for a second think you have any grasp of the notions of 'complete' or 'incomplete' logical constructions. Secondly you've made a strawman where you make a claim which you claim is what SR claims but which isn't correct. SR says the light cone maps to the light cone. It says the location of objects within the light cone transform consistently under a Lorentz transform. It says all frames see one and only one light cone and all frames agree on the causal structure of the objects within the light cone.

And what you fail to grasp is that the result is not a contradiction. The issue isn't your very basic algebra, its how your interpretation compared to what SR actually says or what is needed for consistency. You haven't come up with anything new, you've just come up against something which is counter intuitive.

No, it doesn't imple that the light sphere has two different positions. All frames agree on the light cone. All frames agree on the physical distribution of objects within the light cone and their causal structure.

I've already explains that the result you state, that different frames see different points as the light sphere centre, is precisely what you'd require if you were to need the motion of light to be independent of the motion of the emitter, which is an experimentally justified requirement. Nature says you're incorrect to claim a contradiction because that's how Nature works.

Straw man. The issue isn't your algebra its your interpetation. I've already said several times, using equations involving vectors and space-time intervals that its entirely expected that different frames have different centres of the light sphere at times after emission but the light cone is defined by the position in space-TIME of its apex. All frames agree on that location and that is all that matters.

The light spheres are not defined by the location which is their centre at any given moment in time after emission, They are defined only by the location of emission at the time of emission and all frames agree on that and the Lorentz transformations are defined at that point, hence its consistent.

You claim the light sphere is defined by the location of its centre and its radius. 4 bits of information (3 spacial coordinates and a length). This is wrong. The light sphere is defined by the space-time location of the light cone apex. That's 4 different bits of information, the 4 space-time coordinates. The light sphere is a time slice of the light cone and different frames take different slices, all of which are spheres, but they all work with the same light cone. The fact they take different time slices mean that they will disagree on the radius of the light sphere, time dilation and length contradictions come into effect but in such a way as to keep the slice a sphere. Hence its clear to see that its incorrect to consider just the 3 spacial coordinates and a radius. Instead you consider the space-time location of the point of emission.

You have to do this because time and space cannot be separated out in relativity. You are working with only the spacial coordinates and failing to realise how time plays a non-trivial role (compared to how it works for Galilean transformations). In doing this you have failed to understand precisely how the geometry of space-time and Lorentz transformations work.

If you work with the methodology I've outlined everything is perfectly consistent. All frames agree on the space-time location of the light cone apex. For any given time slice of the light cone the one and only one resultant light sphere maps into one and only one light sphere under a Lorentz transformation. All frames agree on causality. All frames agree on physical predictions. All frames agree the motion of light is independent of the emitter's motion.

If you did some special relativity you'd have seen all of this before and be comfortable with it. You'd also have found out about experiments which are very much like this and in which SR is used and tested. Two things coming along on a head on collision, passing through one another and emitting radiation is pretty much exactly what a particle accelerator measures. Lorentz transformations are used in the quantum field theory which describes such processes (A textbook I'm sure you won't understand but which goes into beautiful and clear discussions of this is 'An Introduction to Quantum Field Theory' by Peskin and Schroder) and the predictions match experimental results. If this lead to a contradiction you'd be unable to apply the Lorentz transformations which go from the rest frame of one particle, to the centre of mass frame and then through to the rest frame of the particle coming the other way. Doing the calculations in any of those frames gives the same predictions. If there were a contradiction in doing such things (as you claim for your rigid spheres setup) then prediction wouldn't match experiment. It matches experiment. It matches experiment to the limit of our ability to test. It matches experiment to the limit of our ability to test, which is to parts per trillion and makes for the most accurate and deeply tested physics model ever.

So you can argue all you like that we're too stupid to understand you or we're too 'primitive' or we're not on your level or we're afraid to accept we might be wrong but you also have to argue with the universe itself. I originally explained to you (and did so again when discussing fibre bundles) that your claim would imply that Euclidean geometry is wrong. That's pretty bad. Now I've explained to you that your claim implies the universe is wrong. I'd say its pretty hard for you to explain that one away as 'too primitive' or not on your level. If you believe in God then you're basically saying he screwed up.

 

Yes, but I do not see how you get the c³ term.

OK, t = rγ/c and x = rγ.

x' = ( x - vt) γ

Substitute the above

x' = ( rγ - v(rγ/c)) γ = r ( γ² - vγ²/c)

To get t', always take x'/c.

Then we cannot have a c³ term.

Yes, SR claims the moving frame will see a light sphere emerging from its light emission point.

Hence, the question to ask is when in the time of the stationary frame does the moving frame conclude light is a distance r in all directions.

If SR contends it happens, there must be a time that it does. Otherwise, it does not happen.

It is a single emission event, but after any time t, the light emission point diverges by vt in the tim of either frame.

This is a problem.

 

I provided the math to prove this is so.

You will need to provide math to refute it.

Typing is not proof.

 

Jack is starting from the moving frame, at t' = r/c when the light reaches x'=r and x='-r.

He wants to know when this occurs in the stationary frame. He seems to expect an answer of a single value of t (ie he hasn't grasped relative simultaneity).

He's calculated t = rγc by transforming (x',t')=(0,r/c)
I'm not sure where x = rγ came from - possibly by naive length contraction?

You've confused him a bit by starting from the stationary frame - he's going the other way.

 

The scenario is clear, but the question that he asked and you answered is awfully ambiguous. I think that maybe you've read it differently to what Jack intended:

 

It is a convenience tool. The object was to put the gamma factor in there such that time dilation would resilbe to r/c. There is no other reason.

Yes, this is my intention.



This is wrong due to the extra gamma factors, but otherwise ok.

No, as I said, t=rγ/c and x=rγ.

Once you plug these in, you will find my answer is correct.

I am allowed to terminate the experiment as I see fit. I chose to terminate it when t = rγ/c hence x=rγ.

First, we calculate time dilation.

If these calculations are false, then SR immediately fails.

Given time dilation, the clock in the moving frame elapses r/c at the origin.

When the lcok at the origin elapses r/c, then by the logic of the light sphere, it must be the case that light is r in all directions. Otherwise, the clock at the origin O' elapsed r/c but light did not reach r in all directions in the moving frame and hence the light sphere is false.





You seem to be asking about the motion of a coordinate location in space rather than an event in spacetime.

Let's see if we can clarify things a bit. Suppose by some magic, at the exact instant that light is emitted from the origin at time t=t'=0, somebody plants a flag at the location on the ground where the light was emitted. Now, the light pulse moves outwards from the origin (in both reference frames), and the flag stays where it is on the ground.

Of course, in the "stationary" frame, the flag never moves from its original location in space. In the "moving" frame it appears to move in the negative direction at speed v. This motion of the flag is independent of the motion of the light pulse.

You seem to being trying to somehow connect what the flag is doing to what the light is doing after it has been emitted.

Perhaps you can explain in more detail what you think the problem is using this picture of the light and the flag.[/QUOTE]

 

Nope.

I am starting in the stationary frame, with some elapsed time at the origin.

Then I apply time dilation to get the time at the origin of the moving frame.

Then I apply the logic of the light sphere for the moving frame.

Then I compare these conclusions to LT and they are different.

 

I think James has it correct but we are trying to get the original setup of time and distance the same.