Alternative Twins Paradox

No, it doesn't mean there's a physical inconsistency. You can't use consistent mathematics to declare a physical contradiction as you're trying to use a mathematical model of nature to contradict itself but if the mathematics is consistent then you're model will be to.

If the mathematics is consistent then the only recourse you have is to do an experiment which contradicts the mathematics. The mathematics would still be self consistent but it would be describing a universe which isn't ours.

Yes, people in an actual experiment would point the different centres and say they have measured different times but each point of view it itself consistent and when you do a Lorentz transformation from one to another you go from one consistent point of view to another. It would only be inconsistent if you could Lorentz boost through the light cone and by construction Lorentz transformations cannot do that. Your mathematics is not correct or at least not special relativity. A point is inside the light cone if \(ds^{2} = -dt^{2}+dx^{2} < 0[tex], on it if [tex]ds^{2} = -dt^{2}+dx^{2} = 0[tex] and outside it if [tex]ds^{2} = -dt^{2}+dx^{2} > 0[tex]. By definition and construction a Lorentz transformation from (t,x) to (t',x') has the identity [tex]-dt^{2} + dx^{2} = -dt'^{2} + dx'^{2}\) and so the sign of the space-time interval is unchanged. If you claim you have a particular Lorentz transformation which doesn't do this then its not a Lorentz transformation or you've squiffed your algebra. Try it with the general \(x' = \gamma(x-vt)\) etc transformations, remembering \(\gamma = \left( 1-\frac{v^{2}}{c^{2}} \right)^{-\frac{1}{2}}\) and you'll see that identity explicitly. Nothing else needs be considered and I think you're working yourself into a mistake by trying to convolute the analysis. Working on the level of space-time intervals makes the Lorentz transformation properties simple to work with and explicitly demonstrates you cannot boost through the light cone.

 

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Perfect reasoning.

I must compliment you.

I was hoping you would come here.

Here is my proof that if two light emission points are confessed, and I see you have come to the conclusion that is SR, and my special point is used, then I can use LT measurements to come up with a light path that does not measure c in the coordinates of O.

http://www.proofofabsolutemotion.com/lightpath.pdf

 

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So you made some comments with my post, something about you taught me something.

I assume you can easily prove your case for everyone.

 

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How exactly can you claim absolute simultaneity when dealing with one point?

Further, how exactly are you going to perform LT on the light emission point?

 

You don't.

You say you know how SR works, Jack, and then you ask this?
You start with the x and t coordinates of an event in some inertial reference frame, and transform those coordinates to some other inertial reference frame using the lorentz transform. Look it up.


Jack, if you can't interpret a simple space-time diagram and apply a lorentz transform, you really can't claim to have enough understanding of SR to criticize it.
Do you want to learn how to do those things, or are you happy where you are?

 

Well, it was your post and it confused me as well.

I am a little confused. Perhaps you can help me.

Can you show me how to apply LT to the light emission point in the moving frame?

Silly, me, I use x = vt in the equation t' = (t - vt)γ from which I get t' = t/γ.

Perhaps, you can show me something else.

 

It wasn't that confusing, Jack. The light reaching the spheres happens at many points, not just one.
But I'm really not interested in teaching that brick wall, nor am I interested in continuing a locked thread.

Go away, come back when you can [thread=99581]understand a spacetime diagram and its transformation between reference frames[/thread].

Or when you can [thread=99246]follow a consistent logical argument[/thread].

I spent much time patiently showing you how its done, but you didn't seem to want to understand. Have you changed now, or will future conversations be equally fruitless?

 

Gee thanks.

Anyway, when the clock at the origin of O elapses rγ/c, the clock at the origin of O' must elapse r/c by time dilation. When a clock at the origin of a frame elapses r/c, light must proceed r in every direction in that frame from the light emission point.

This is called consistent logic.

I simply refuse to ignore these facts.

If you are able to use space time diagrams to handle this, let me know. You will find tghe origin of the light spheres diverging by vt after any time t.

But, you cannot refute the facts above I presented.

Now, see if you coul, you would shoot right at it.

Note how my conclusions are crisp and specific. It should be easy to pull a paper and prove me wrong.

But, if I am correct, this logic brings down SR.

 

The problem is that you are ignoring the facts of what statements are true in what reference frames.
Just like in [post=2493759]previous threads[/post].

Jack, you've been proved wrong, repeatedly and patiently.
Go away, come back when you can [thread=99581]understand a spacetime diagram and its transformation between reference frames[/thread].
Or when you can [thread=99246]follow a consistent logical argument[/thread].

I see no point in engaging in a discussion that involves someone repeatedly refusing to even try to understand something. If you can show that you understand what I wrote in those previous threads, then we'll talk.

Otherwise, you're just boring.

 

This is background noise and radio static.

I provided math proofs.

Show me your proofs and the links.

I want to see a proof from you against my stuff. You will not like the results.


OK, so we will now communicate with math proofs only.

 

Jack, I'm not wasting my time with you again. If you review the old threads and see your mistakes, then we can talk.

 

Its comments like this which make it clear that you've never studied mathematics (particularly logic), contrary to what you'd like people to believe. It isn't possible for people with opposing views to provide 'math proofs' because that would mean you can prove two opposite views. Either SR is right or SR is wrong. If you can provide an example where it is inconsistent then you have proven it false and its impossible for someone to provide a proof its consistent. Conversely, if someone can prove it consistent (which is quite difficult as you're proving a negative) then its impossible to provide a proof its inconsistent. You seem to be mistaking 'justification' for 'proof'. If you had given a 'proof' then Pete or I wouldn't be able to provide a proof back. As such it seems like you don't understand basic mathematical terminology.

Its mathematically proven that SR is consistent because its equivalent to geometry or group theory in mathematics. Hence you aren't going to find a mathematical inconsistency. I've explained this to you many times and you've never demonstrated you understand that. All you can hope to do is find an experiment which contradicts special relativity.

Your 'math proofs' always boil down to your inability to understand.

 

If my proofs are wrong, as you claim, then they must be logically inconsistent.

Prove it.

 

That would require me to believe one light sphere is origined at two different points of one space.

 

You keep asking me to do things I've done several times in several threads.

I have already said that I agree that the two frames associated to the rigid spheres will disagree on the question of "Where is the centre of the photon sphere?". Their answers will not be mapped into one another by the Lorentz transformation which related the two rigid sphere frames. You have declared this a contradiction. You haven't proven it is. The onus is on your to prove your claim. You're the one saying that no one in 100 years, in either the maths or the physics communities, has done this problem correctly and you're the first to 'realise it'. Other than you just saying "They disagree, contradiction!" what evidence (and I use the word in a very slap dash way) do you have that its a contradiction? None.

I've already explained to you that despite them disagreeing on the location the causal structure of the space-time is preserved. You don't like the notion of having 2 answers but it follows from the different ways in which null trajectories transform compared to time-like ones. The regions in, on and outside of the light cone are not mixed. All a Lorentz transformation does is 'warp' (in the sense of length contractions etc) the configuration of a system in, on or outside of the light cone. It doesn't introduce discontinuities, the two frames can be smoothly transformed into one another by defining a path through the Lorentz group which starts at the identity and finishes at the element which links the two frames in question.

There's no physical problem with frames disagreeing on the centre of the light sphere. The middle of the sphere doesn't have anything there, there's no mass or energy or whatever which can interact with things. If there were something there, like an emitter, then when you Lorentz boost between various frames you'll find they all agree on the location of that emitter, irrespective of its motion. This is because consistency demands that Lorentz transforms lead to people agreeing on the position of things. But the centre of the photon sphere isn't a thing, its defined by the relative position of other things, ie the light cone. If you pick a photon on the light sphere you'll find every observer in every frame agrees with the location of that photon. If you pick an object moving through space, doesn't just have to be the emitter it could be anything, then you'll find that all observers in all frames agree on its location. All frames agree on all physical objects.

The reason why there's this peculiarity is that you're transforming a photon sphere. Photons transform in a very special way in special relativity, because you can't alter their speed. You can boost to frame after frame after frame and the light sphere doesn't change. But the space-time with the light sphere is changed and is a frame dependent configuration.

Its easily seen via a space-time diagram. Draw a light cone and then a vector \(\partial_{t}\) and sketch its worldline. Then apply a Lorentz transformation. The light cone is unchanged yet the vector is no longer \(\partial_{t}\). Its worldline will be different and thus locations along the worldline change. This is a contradiction according to you. It isn't, its an elementary implication of doing coordinate transformations. The reason why you don't like it is because you struggle to realise that the light cone is special and you can't expect to use it to compute the motion of things within it. Lorentz transform a light cone and its still the same light cone. Lorentz transform any time-like vector and you'll get (in general) a different vector. This isn't surprising at all. Well, maybe it is to you.

I'll admit, its something which isn't particularly easy to get across in text, its something which is more apparent as you do more vector calculus and geometry. Perhaps you're just out of practice?

No, it wouldn't. A Lorentz boost will alter time-like vectors but not null vectors. You're applying a boost to a time-like vector and then complaining that its not associated to a different light cone.

This is a conceptual problem, as its going to be something you only get your head around once you've had a bit of experience with relativity. Its easy to see if you know how to do worldline diagrams. I suggest you learn how to do them.

 

You have never disproven any of my proof.s You only say you did, repeat it and then claim you did 10 times. Either that, or you simply do not understand math proof. You need to run me into a contradiction to refute my proofs.

Let's get down to basics. I am ready to show you the problem with SR.

Here is Einstein's "proof" of logical consistency.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

OK, he claimed this is the proof. He made the statement, "The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system."

Here is what he did.

He started with a point (x, y, z) that was struck by the spherical light in stationary K.

He performed LT on that point.

He then claimed in moving k, ξ² + η² + ς² = c² τ² . This is true for ONE light beam only.

Thus, he claimed he proved the spherical wave in K is also spherical in moving k, based on this single light beam translated by LT.

He then universally generalized this one beam to all beams. But, for the spherical light wave in K to be spherical in k, c² τ² would need to be constant for all (x, y, z ) attained by the stationary light sphere and then translated by LT.

This is clearly false.

Hence, he committed the logical fallacy, dicto simpliciter.

Therefore, the light sphere in K is not spherical in k when translated by LT.

Hence, the light postulate and the relativity postulate are inconsistent.

 

You continue to struggle to use the word 'proof' correctly.

Firstly, this level of mathematics is very very simple, just because you're stretched past the point of understanding doesn't mean other people are. Secondly the burden of proof is on you. You haven't demonstrated any contradiction. You basically don't like the fact that under a Lorentz transformation the light cone is invariant yet time-like vectors are not. It demonstrate you lack of grasp of the fundamentals in Minkowski geometry.

The light cone defined at a point, call it p, is invariant under a Lorentz transformation. A vector at p in the light cone is not. This follows from the action of the rotational subgroup of SO(3,1). Likewise a time-like vector at p is not invariant under all Lorentz transformations. The centre of the photon sphere in a given frame is associated to a choice of this vector. If you need me to explain this I will.

Now when you come to consider the effects of a transformation you are comparing apples and pairs. You say "The light cone hasn't changed but the location of the centre has" and you claim this is a contradiction. But the light cone has changed in that points on the light cone have moved around. It is only because you're comparing the surface of null points that you have an invariance. You then compare this to the fact a vector is not a Lorentz scalar. This is obvious, its practically a tautology.

If instead of considering the entire photon sphere you considered a single point on it you'd find that when you apply a Lorentz transformation it is not invariant (generally) but it will still be null. In your considerations you're ignoring that the Lorentz transformation image of the points on a light cone is a different configuration.

Here's a picture to illustrate it :

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It's a circular slice out of the usual light cone, looking down towards the apex. The crosses are three vectors coming out of the paper and denote 3 different vectors. The red one is in the centre and so it represents the vector which just points straight up the time axis of this picture. The other two are vectors which have some angle deflection. The dots around the edges are the locations of some generic points. For the red ones they are evenly spaced and this is the stationary frame. If you boost such that the red vector head goes to one of the other vector heads the Lorentz transformation of the points is seen. They move around the circle (but always remain on the circle as Lorentz transformations map null to null) and bunch up closer to one another or spread out more, depending on where they are and what transformation they are associated to.

In each of those three cases the points all lie on the same circle and yet each one believes their vector to be 'the centre'. Overall the circular null surface is mapped to itself but the 'centres' represented by the crosses are different each time. This is the situation you've been dancing around with convoluted physical setups and it is not a contradiction. Its immaterial that the frames don't agree on the locations because their physics is entirely equivalent. Relativity says the speed of light is frame invariant, which means the circles of dots map to circles of dots. It also says physics is frame invariant. You can see how this follows from the diagram by considering what would the diagram look like if I'd included points within the light cone. Notice how in each case the cross is roughly in the average place of all the points. Points which are close to the red cross would be mapped to be close to the green cross if I applied the appropriate Lorentz transformations. Different frames agree on what is near what and the order in which events happen, ie no causal violations. This is all you need for consistency. You have come up with your own criteria because you don't understand the underlying principles. But rather than realising it might be a good idea to at least have some sort of grasp of geometry and calculus you've jumped in head first proclaiming you've killed relativity. All you've done is smash your head on the floor of the pool.

 

Yea, I posted a simple proof above that debunks SR.

Stop me in the simple context I provided.

You are supplying deductions of SR and then claiming SR is consistent. That is vacuous implication.

Let's get back to the Einstein proof.

If you are intellectual, you can do this.

Otherwise, bring your so called Cambridge folks to help you.

In this way, instead of defeating one, I will defeat many.

Stay on task and stop my clear refutation of SR. If you cannot address my proof, I will assume you are simply not up to the task.

Note how I provide math proofs here and all you do is talk.

 

No, Jack. Look at the threads. Read the arguments. Don't waste any more of your time working from the wrong foundation.

 

No, you've done nothing which supports your claim and you've just demonstrated you don't understand coordinate geometry.

You've failed to respond to anything I said, all you're doing now is just going into 'denial mode'. I type lengthy responses which explain various aspects of geometry to you and you make it abundantly clear you don't understand and you fail to respond.

Like I said, you've convinced yourself that you're a lot better at maths and physics than you actually are and when you're faced with people who can actually do it you have to go into this "I'm amazing, I've destroyed all of maths and science" delusion mode within which you fail to respond to any point raised. Instead you just bluster about telling people how great you are but failing to back that up.

Oh I can play that game of flawed logic too. If you can't tell me the number I'm thinking of I will assume you're a murderer.

Non-sequitors are easy to make, shame they don't validate your claims in any way. I've addressed your misunderstandings. The problem is not that you're coming to some incorrect algebraic expression, its that you're failing to understand the context of the results because you're unfamiliar with things like coordinate transformations and the non-Euclidean nature of special relativity. As I said in my previous post, there are some things which cannot be conveyed in a short snappy sound bite, something in order to understand something you have to gain experience with it. This is something you haven't done, either because you're unwilling to put in the time and effort or because its simply beyond your ability to understand.

Its a common trait with cranks. They come up against something which they don't understand and they are either unwilling or incapable of understanding it due to time and effort being something they will not invest. Thus they try to come up with excuses about why they won't learn it. Ironically it generally turns out they'll put in more effort avoiding learning something than it would take to learn. The bests of special relativity I learnt in a short summer course, 8 1 hour lectures. You've spent more time whining about SR than that, you could have actually learn the basics by now.

You haven't provided any maths proofs. You haven't reached an algebraic expression which proves your claims. I've already explained that I agree different frames will give different answers for the centre of the photon sphere. Special relativity says that. Your entire argument is that this makes it inconsistent. But it doesn't. You haven't given a maths proof that its inconsistent, you point at a result and declare it inconsistent. You have failed to provide the justification for that leap in logic.

Your entire argument is "I say this is inconsistent", despite the fact it has absolutely no bearing on any physical predictions since the centre of the photon sphere has no physical properties. If you think I'm 'too primitive' and that you can take down all my Cambridge buddies then why are you still on this forum? If you're so sure you're right and you're so sure I'm a thicko why are you stuck arguing your point in the pseudoscience section? Why aren't you sending your work to a journal? It'd take less than an afternoon to type up a 5 page paper outlining your idea, so why haven't you? Every one who talks with you on this forum disagrees with you. I am 100% positive that the problem is you don't understand and your repetition of your misunderstandings is not going to convince me. So why don't you take your work to a journal and prove me wrong for all to see?

I want you to submit your work to a journal because I am certain you'll be rejected for the same reasons I've given. Go on, submit your work. If you think I'm all talk and you're able to 'defeat' many a Cambridge graduate fucking prove it. The fact you're sticking to this forum and not daring to venture into the big wide world of journal reviews shows you know you're all talk with nothing to say. If you really believed you'd have submitted it to a journal before you posted it here.

Your actions speak much louder then you realise.