Relativity fails with Magnetic Force

This is just flat out wrong and you've been corrected on it several times. No one denies that quantum mechanics was developed after Lagrangian and Hamiltionian methods and after Noether's theorem but that doesn't mean they don't apply to it. That's like saying that calculus predates all physics from 1700 onwards therefore we can't use calculus in any modern physics. No, it is much more general than that.

The mathematical similarities between classical mechanics and quantum mechanics are stricking, anyone whose looked into Hamiltonian mechanics enough will see that. And the claim that no one has checked whether these formalisms apply is just nonsense.

Your website is full of half truths and flat out mistakes. Your bit about the GPS setup has also been high lighted in this thread.

 

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As I indicated before, you are implying that the induction equations are fundamental physical laws (in the form as given in Maxwell's equations). If you don't make that assumption, then the consistency issue you mentioned does not arise. Indeed, you could probably fully explain the induction effects in terms of the Lorentz force if you would consistently model the charged particle dynamics in a conductor on the basis of my proposed electrodynamics (i.e. using only frame independent quantities as defined by the physical configuration).

Well, you can't really cater for everbody's tastes. You accused me of setting a mundane tone in this discussion, and I replied that this is to a great part deliberate, because I think that less fancy mathematical representation of the issues (where possible) will help more people to understand the problems at hand. Obviously, if the problem itself is of a mathematical nature, then that needs to be addressed in the appropriate form, but again 'appropriate' could well be perceived as mundane by those who tend to think and work in terms of more fancy mathematical forms.

Sure, yes. My physics course was indeed very much based on these books, and I have copies of both. But none of these books address in any form the problems we have been discussing here (in fact the relativistic 'wire charging' explanation in Feynman's lectures is exactly the issue I have been discussing here; so is the issue of frame dependent quantities that are used in all books without further justification).

F=dp/dt does not describe a fundamental physical law. It is an operational definition how to measure a force in practice kinematically. There are however other ways to measure forces. For instance you could measure the gravitational force on an object by putting it on a scale (the fundamental law for the gravitational force is F=G*m1*m2/r^2 , so it does not involve any derivatives).

Thomas

 

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If it is experimentally ruled out, then the paper does not derive the Lorentz transformation on its own merit.
And as I said already, at least at the time of Einstein, the only experimental evidence was the invariance of c, and that does not result in the Lorentz transformation if a correct mathematical logic is used. As the Levy-Leblond paper explicitly shows, the Lorentz transformation requires that there is a limiting velocity for material bodies.

At least one of the measuring sticks must be invariable in length, otherwise you are getting a circular definition for the length units. Indeed, the transformation between the markings on the two measuring sticks in Einstein's 1905 paper is given by his equation x'=x-vt, so Einstein himself considers the units as a priori given here.

What I said was that he should given a physical significance to his equation x'=x-vt. Then it would have been evident to him that this is inconsistent with the significance he attached later to his (incorrectly derived ) Lorentz transformation.'

It is not a cop-out. It just says that reality doesn't care whether you think you can predict the 'equation of motion' of a light signal in one coordinate system by measuring it in another and then doing a transformation dependent on the velocity between the two coordinate system. The latter is something we are used to when describing the coordinates of material objects, but light does not behave in the same way as its speed is invariant in coordinate systems moving relatively to each other ( so the usual whole concept velocity dependent transformations can not be applied here).

The equation x = (v + c)*t indeed represent the reaction of the moving row of detectors in the rest frame, but it has no significance as far as the speed of light is concerned. The speed of of light in the rest frame has to be measured by a row of detectors at rest in that frame, which will result in x=ct (as will the measurement by the moving row of detectors).

The Doppler effect as such has nothing to do with the transformation equation. It is simply due to the circumstance that the distance between the source and detector changes (and this applies to all periodic emissions from a source, not just for light waves).

What other options? I am not aware that Einstein considered any options here. He apparently just wanted (for some irrational reason) a transformation formula that describes both the behaviour of material objects and light signals. And as I have said before, not only is this a completely unsubstantiated assumption, but it can in fact not be done consistently.

Thomas

 

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Well, Einstein did differentiate his 'master equation' 1/2*tau2=tau1 in order to determine alpha (that's the whole point of his derivation, otherwise he would be left with an undetermined factor), so you should address your criticism to him, not to me. The fact that he gets a new constraint from this just shows that his differentiation has been mathematically incorrect (as addressed on my page Mathematical Flaws in Einstein's 'On the Electrodynamics of Moving Bodies'). When I differentiate the equation 1/2*tau2=tau1 on this page and find that the derivative is impossible to satisfy (unless v=0), then this shows only that the original equation is impossible to satisfy (unless v=0).

Thomas

 

As water is pretty much incompressible, any object falling/rising in it must be accompanied by the same volume of water reversely rising/falling. This is the only way pressure equilibrium (and thus a quasi-static state) can be preserved everywhere.

It is absolutely incorrect to assume a discontinuous distribution function for the particle energies (e.g. a delta-function) and then rectify this unphysical model by adjusting the wave function such that a continuous probability distribution throughout the regions results. This procedure is nothing short of assuming a miracle and it indeed violates the energy conservation law. A particle simply can not penetrate a region with a potential energy difference that is larger than its kinetic energy. If particles are observed on the other side of the potential barrier, then their energy must have been larger than the barrier energy. In reality, each ensemble of a large number of particles will indeed have a continuous distribution function (e.g. a Maxwell-Boltzmann distribution) and there will always be some particles with an energy high enough to penetrate the barrier. This is the only possible explanation for the 'tunnel effect'.

That doesn't answer my question what the motivation and justification is for using Lagrange functions in areas of physics that can evidently not be described in terms of Newton's laws, given the fact that in classical mechanics the Lagrange formalism is exactly equivalent to Newton's laws. Or are you saying that the Lagrange formalism has just been tried on various phenomena and merely found to be accidentally appropriate?

Thomas

 

If you don't make that assumption, you're also stuck in a theoretical context in which you can't explain how radio antennae work.

Well, let's see these explanations then. How do antennae work?

It's not a question of taste. You are investigating the Lorentz invariance of electrodynamics. The Minkowski formalism is a way of expressing theories in a way that's Lorentz invariant by construction. Why are you evading math that's specifically tailored for what you want to investigate?

Both have chapters on the relativistic formulation of electrodynamics. If you'd read (and more importantly understood) the relevant parts of these texts, you'd know that if you take any solution to Maxwell's equations and apply a Lorentz transformation to it, you'll automatically obtain another solution to Maxwell's equations. You'll never find a counter-example. It's a mathematical impossibility.

You're evading the issue. Do you think this (and similar) laws:

\( \frac{\text{d}\bar{p}}{\text{d}t} \,=\, - \, \frac{GmM}{r^2} \, \bar{1}_{\bar{r}} \)​

violate causality?

 

It doesn't matter what you call it. We have observations that we can't explain with Galilean invariant theories. They can either be Lorentz invariant or possess no invariance.

Levy-Leblond's paper was published in the 1970s.

Which is perfectly consistent with observations of material objects, so the requirement of a limiting velocity is relegated to the status of "prediction".

No, it's the axiom you stated we need. We take a metre stick at rest in some particular frame as the definition of the metre in that frame. We similarly take a moving metre stick to define the unit length in the moving frame. The length of the moving stick can, in principle, be measured with respect to the stick at rest. This comparison defines one of the terms (specifically \(\frac{\partial x^{\prime}}{\partial x}\)) in the coordinate transformation between the two frames.

Where does Einstein say that two markings a distance x' apart on a moving stick will also be situated a distance x' apart when the stick is at rest (or in the stick's rest frame)?

We'll that's the problem. You argue that Einstein "should" attribute physical significance to the variable x', and the only "justification" you give for this is that it is inconsistent with the physical significance relativity attributes to the Lorentz transformation. So we're back to the question I asked you earlier: why would Einstein want to formulate a theory that contradicts itself?

Yes it is. The idea of applying the identity transformation to light and the Galilean transformation to everything else breaks down when you consider events involving the interaction of light with matter. Should we apply the identity transformation or the Galilean transformation to such events? It's a fundamental ambiguity that renders your idea completely untenable. Defending your idea by declaring difficult questions are "not allowed" is a cop-out.

Then why don't you present your idea that way? It's a much more sensible statement than "let's apply the identity transformation to light and the Galilean transformation to everything else".

Isn't that more or less what I just said:

?

Well, let's see your derivation of the Doppler effect then. The issue with light signals is that the phase velocity \(c = \frac{\omega}{k} = \lambda \nu\) has to be invariant, so the frequency can't transform unless the wavelength also does.

I was pointing out a fallacy in your argument. You seem to think that if you can find your own explanation for something, then that alone somehow invalidates any other explanation.

 

You're either lying or, at best, haven't bothered to read Einstein's paper very carefully. The solution he obtains after his diffentiation is:

He doesn't pretend he's determined \(\alpha\). He explicity states otherwise:

He only determines \(\alpha\) later in the same section of his paper, starting at:

What follows basically boils down to an imposition of reciprocity. No differentiation is involved whatsoever. I've already corrected you on this issue several times now, including twice (in anticipation) in my previous post, so you really have no excuse for continuing to misrepresent Einstein's paper this way.

I've disproved this already. For any multiple of the Lorentz transformation, differentiation of both sides of the constraint equation should produce:

\(\frac{\alpha}{c} \,=\, \frac{\alpha}{c}\)​

which isn't a contradiction. You can only arrive at a contradiction if you apply an operation at some point that effectively substitutes \(\frac{\alpha}{c}\) for something that is not equal to \(\frac{\alpha}{c}\). Any such operation is mathematically invalid basically by definition, so the contradiction on your webpage is most definitely an error. I've even identified the offending operation and explained why it's an error. There's really nowhere meaningful you can go from here.

 

Counter-example. All I've done is change the shape of the container. What's (for example) preventing a similar current in an open tank, or something even more complicated?

Where are you getting this from? It's the Schrodinger equation that requires the wavefunction to be continuous. The simplest way of seeing this is to integrate the equation:

\( - \, \frac{\hbar^{2}}{2m} \, \frac{\text{d}\psi}{\text{d}x}(x) \,+\, \int^{\text{ }x} \text{d}x^{\prime} \, V\psi \,=\, \int^{\text{ }x} \text{d}x^{\prime} \, E \psi \)​

Even if V and/or \(\psi\) are discontinuous, the integral terms will be continuous, so \(\frac{\text{d}\psi}{\text{d}x}\) has to be continuous in order to satisfy the equation. Integrate once more, and the same argument applies to \(\psi\).

A classical particle, described by Newton's laws, can't penetrate such a barrier. A quantum particle, described by completely different physics, can. You're reasoning classically about a non-classical phenomenon.

Can you explain why the flux of particles through the potential barrier depends on the thickness of the barrier? With the dependence predicted by quantum tunneling? If not, your explanation is useless to people who build scanning tunneling microscopes.

Something like that. Except:

• The "various phenomena" cover more or less all of contemporary physics. The standard model alone, for example, is a (Lagrange-based) quantum field theory that successfully describes almost everything we know about the strong, weak, and electromagnetic interactions. Its only experimental shortcoming as far as I know is that it doesn't explicitly include massive neutrinos (though there are a few proposed mechanisms for introducing neutrino mass terms).
  
• As you pointed out, most Lagrangians in real theories tend to be quite similar: they generally consist of "kinetic" terms (which depend on the first derivatives of the dynamical variables), "interaction" terms, and "potential" terms (in QFTs these describe particle masses and self-interactions). We're nowhere near exhausting the full range of theories that Lagrange formulations can describe.
  
• Quantum theories require a Lagrange/Hamiltonian formulation.

Whether you want to call all that "accidental" or not, I'll leave up to you.

 

przyk made me notice this bit of your post. Wow, didn't you ever do a quantum mechanics course? Never heard of tunnelling? Comes up in atomic physics (alpha particle tunnel out of the nucleus) and astrophysics (vacuum state tunnelling to another vacuum state). Working out the probabilities of tunnelling through various potential profiles is literally homework for a 1st QM course. The 1 dimensional problem is nothing more than solving some very very simple second order ODEs and then using continuity to match solutions on various boundaries.

Excellent example of you putting your own foot in your mouth.

 

That's nothing. Take a look toward the end of this page. Specifically, look at how he derives equation 11 from equation 10:

Just where do you start with someone who won't admit an outright mathematical error like that?

 

Przyk:
I think your mathematical treatment on Physics is very respectable and that's why I comment about something you posted although it goes out of the discussion you are having with tsmid:

Have you realized that nobody has ever determined a solution to a real and practical case of an antenna starting from Maxwell's equations? If you know one I would like you to show me.
I mean all what is said is that the electromagnetic waves are possible solutions of Maxwell's equations but looking a little deeper we find that only infinite constant and planar solutions are possible for the Electric and Magnetic Fields and those are not solutions for any real antenna because there's no possible source of Electric and Magnetic Fields that could produce such kind of fields.
Someones have argued that the real cases could be obtained considering the composition of infinite series of those "planar waves" to obtain any possible solution required but, as I said, nobody ever have really found such kind of solution for even ONE case.
That's why I mantain my position that "electromagnetic waves" actually do not exist in: http://geocities.ws/anewlightinphysics/sections/Section7-1_Electromagnetic_waves_do_not_exist.htm and give a complete description about how antennaes work emitting and absorbing photons as "electromagnetic particles" (http://geocities.ws/anewlightinphysics/sections/Section7-2_Hertz_experiments.htm and http://geocities.ws/anewlightinphysics/sections/Section7-3_Communicating_with_photons.htm).
The structure of those electromagnetic prticles is well presented through Chapters Three and Four of the manuscript of: http://www.geocities.ws/anewlightinphysics.

 

Done. http://farside.ph.utexas.edu/teaching/jk1/lectures/node82.html

 

I will look at your link.
I would like also a comment from przyk.

 

Have you not ever heard of a Fourier decomposition? It and the fact the equations are linear means non-trivial solutions to the equations exist.

If you have n planar solutions \(f_{n}(\mathbf{x},t) = e^{i(\mathbf{k}_{n}\cdot \mathbf{x} - \omega_{n}t)}\) then their linear combinations \(F = \sum_{n}a_{n} f_{n}\) are also solutions if \(\nabla a_{n} = 0\), ie have constant coefficients. What precisely don't you like about that?

 

Well, the first problem is that I have never seen one developed solution of an electromagnetic wave for some real practical case of a real antenna based on such Fourier decomposition. Is a managed argument with no practical example to show.
The other and may be bigger problem is that there are no possible real sources of Electric and Magnetic Fields capable to generate the constant-planar waves solutions to the Maxwell's equations and so I don't see how a Fourier composition of them would have a real source.

 

Well you already got the answer to your question in a [THREAD=81518]thread[/THREAD] you started nearly two years ago. Basically, Maxwell's equations (in the Lorentz gauge) are just a set of wave equations, and the wave equation with source is a well-studied problem with a well-known general solution. In particular, the solution in terms of the scalar and vector electromagnetic potentials is given by the retarded potential formulae. The general solution in terms of the electric and magnetic fields themselves is given by Jefimenko's equations. There's really not much I can add to this.

By the way, you really shouldn't treat me as any sort of authority on physics. There are several regular posters here - and this includes rpenner and Alphanumeric - who are much more capable and much better informed physicists than I am. The only reason I've got much to say in this thread is because I'm debating someone even less informed than I am.

 

I don't see you as an "authority in the subject" but you discuss the way I think everything should be discussed: showing where someone could be wrong in his reasoning or belief with rational arguments (Logic, Math, etc) and not with disregarding comments as most in forums use to behave in front of someone with an idea or viewpoint different from the mainstream Physics.

Well, then is not about some kind of Fourier compositon as argued by alphanumeric here and others in that old thread.

 

They're not arguing that you need a Fourier decomposition to find the electromagnetic field produced by an antenna. They're just pointing out that the field can be expressed as a superposition of plane waves. That doesn't mean the decomposition will be particularly interesting or helpful in solving the problem in the first place.

 

I think they do. If not why they brought "Fourier decomposition" into the discussion? I didn't do it.

Anyway, seems I could have been wrong when I said no one had developed a solution to the electromagnetic waves for a real antenna starting from Maxwell's equation. The link presented by rpenner seems to show that.
I admit that math goes beyond my expertisse and at this moment I have no time (may be it would be needed a lot to me) to learn about in deep.
What I know is that my argument stands for the simple commonly known "planar electromagnetic waves" solutions of Maxwell's equations presented in basic Physics textbooks: there's no possible source capable to produce such kind of Electric and Magnetic Fields and then those solutions actually don't exist in nature.
I will leave a possible analogue proposition for the solutions found through the methods you mention (and "cptbork" in that old thread) even for the case presented by rpenner for someone with more expertisse in the subject. I believe something could not work well in those cases for "electromagnetic waves"... Just to mention some justification I don't understand the following: if the general solution of an "electromagnetic wave" within Maxwell's equations, which turns into a differential equation of second order, are two kind of planar waves how some other kind of solutions would be possible? My little knowledge in mathematics tells me that a linear second order equation can have only two linear independent solutions and any other solution can be expressed as a linear combination of them what leaves to some other solution but of the same kind: "planar wave"...


Thanks for your comments.