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Another way of looking at Special Relativity

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Posted (edited)
5 hours ago, RAGORDON2010 said:

To review from Part 1 -

In Part 1, I imagined an experiment consisting of a particle with initial velocity v free to move under the influence of applied external fields E and H, where (t, x, y, z) represents the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

In what way does this answer my question ?

Or if you prefer Ghidion's version which amounts to the same thing.

On 3/20/2020 at 10:37 AM, studiot said:

Introducing v begs the question

As measured by whom ?

If the velocity as measured in the laboratory frame is v then the velocity as measured in the particle frame is zero.

You cannot escape two frames.

 

5 hours ago, RAGORDON2010 said:

I then defined a “Minkowski differential interval” as

\( dS^2  = (cdt)^2 - (vdt)^2 \),

where v is particle velocity as the particle moves over a small time interval dt.

Next, I introduced two key assumptions -

Key Assumption 1 - Assume that the elements dS and cdt can be viewed as minute, spatial intervals in 3-space.

Key Assumption 2 -

Borrowing an idea from Einstein’s 1905 paper on Brownian motion, ”On the Motion of Small Particles Suspended in Liquids at Rest by the Molecular-Kinetic Theory of Heat”, assume the time interval dt is very small compared with observable time intervals but still large enough that the motions performed by a particle during two consecutive time intervals can be considered as mutually independent events.

End of review of Part 1

 

It has been nearly a century and a quarter since the SR paper and clever folk were thinking about this even before that.

Do you not think that in all that time these clever folk and subsequent ones did not give consideration to the issue you are raising ?

 

In fact they thought far more deeply about it than you probably know.
They considered justification for 'key assumptions' such as you are making, and the justification for choosing the specific form of the equations.
Part of this justification is how and why it fits in with known observations and other known deductions about Physics.

Your key assumption is a quadratic.

The general quadratic is


[math]d{s_2} =  + {g_{11}}dx_1^2 + {g_{22}}dx_2^2 + {g_{33}}dx_3^2 + {g_{44}}dx_4^2 + 2{g_{12}}d{x_1}d{x_2} + 2{g_{13}}d{x_1}d{x_3} + 2{g_{14}}d{x_1}dx4 + 2{g_{22}}3d{x_2}d{x_3} + 2{g_{24}}d{x_2}d{x_4} + 2{g_{34}}d{x_3}d{x_4}[/math]


What is your justification for reducing it to four or two terms?

Or indeed why a quadratic at all ?

Why not a modulus or a quintic?

 

 

Edited by studiot

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On 3/21/2020 at 4:48 PM, swansont said:

Why charged and why do the fields have to be present?  None of that shows up in any of your equations. They would seem to be irrelevant.

 

I personally find this annoying, as with the repeated previews of what’s to come. Get on with it already.

I continue to maintain the position that Special Relativity theory is an offshoot of Electromagnetic Theory.  I cannot speak of particles and forces within the context of SR without assuming the particles carry an electric charge and/or a magnetic moment, and without assuming the forces stem from electromagnetic fields.  

I introduced particle/field interactions in Part 2 when I referenced the thinking of Michael Faraday.

My reviews are intended to hold my presentation together so readers will not have to search through my earlier posts each time a post a new one.

Tonight I am posting Part 3. 

On 3/21/2020 at 5:17 PM, studiot said:

In what way does this answer my question ?

Or if you prefer Ghidion's version which amounts to the same thing.

If the velocity as measured in the laboratory frame is v then the velocity as measured in the particle frame is zero.

You cannot escape two frames.

For the present discussion, please assume all measurements are made in the laboratory frame.

 

It has been nearly a century and a quarter since the SR paper and clever folk were thinking about this even before that.

Do you not think that in all that time these clever folk and subsequent ones did not give consideration to the issue you are raising ?

 

In fact they thought far more deeply about it than you probably know.
They considered justification for 'key assumptions' such as you are making, and the justification for choosing the specific form of the equations.
Part of this justification is how and why it fits in with known observations and other known deductions about Physics.

Your key assumption is a quadratic.

The general quadratic is


ds2=+g11dx21+g22dx22+g33dx23+g44dx24+2g12dx1dx2+2g13dx1dx3+2g14dx1dx4+2g223dx2dx3+2g24dx2dx4+2g34dx3dx4


What is your justification for reducing it to four or two terms?

Or indeed why a quadratic at all ?

Why not a modulus or a quintic?

 

 

For the present discussion, please assume all measurements are made in the laboratory frame.

As for the passage of 115 years,  I believe that it's time to go back to basics and re-examine the fundamentals.  I intend to show that much of real importance has been overlooked.

Special Relativity - A Fresh Look, Part 3

To review from Parts 1 & 2

In Part 1, I considered an experiment consisting of a particle with initial velocity \(v_0\) free to move under the influence of applied external fields E and H, where (t, x, y, z) represents the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

I then defined a “Minkowski differential interval” as

\( dS^2  = (cdt)^2 - (vdt)^2 \),

where v is particle velocity as the particle moves over a small time interval dt.

Over the course of Parts 1 and 2, I introduced four key assumptions -

Key Assumption 1 - I assumed that the elements dS and cdt can be viewed as minute, spatial intervals in 3-space.

Key Assumption 2 -

Borrowing an idea from Einstein’s 1905 paper on Brownian motion, ”On the Motion of Small Particles Suspended in Liquids at Rest by the Molecular-Kinetic Theory of Heat”, I assumed that the time interval dt is very small compared with observable time intervals but still large enough that the motions performed by a particle during two consecutive time intervals can be considered as mutually independent events.

Key Assumption 3 - I assumed that the Minkowski differential interval, when written in the form

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \)

may be thought of as an ellipsoid of revolution (“Minkowski ellipsoids”) having elliptic cross-sections with length of major axis cdt, length of minor axis dS, and distance between foci vdt.  A characteristic of these ellipsoids is that the total distance from one focus to a point on the boundary of the ellipsoid and back to the second focus equals the length of the major axis.

Key Assumption 4a - Building on ideas put forth by Michael Faraday, I assumed that electromagnetic fields interact with charged particles and with particles carrying magnetic moments via a stimulus/response interaction.

That is, the presence of the particle in the field initiates a stimulus disturbance that travels outward from the particle at a fixed speed and initiates response disturbances from those elements of the field affected by the stimulus.  These response disturbances, in turn, travel back to the particle at the same fixed speed and, arriving at the particle, exert a force or moment on the particle.

Key Assumption 4b - I assumed that stimulus and response disturbances travel through electromagnetic fields at light speed c.

In this post, I will build on these assumptions and sketch out the rudiments of a new scientific theory within the framework of classical physics - The Einstein, Minkowski, Faraday Theory of Electromagnetic Field, Charged Particle Interaction”, or EMF Theory for short.

To begin, EMF Theory gives form and substance to Michael Faraday's vision.

We can now speak of a distinct field-particle event beginning with the particle positioned at one focus of a Minkowski ellipsoid. Stimulus disturbances travel outward from the particle at light speed c, triggering response disturbances from the affected field elements. These response disturbances return to the particle also at light speed and contribute to a force or moment acting on the particle

This singular event transpires over a time interval dt, during which time interval the particle arrives at the second focus of the ellipsoid after traveling a distance vdt.  All of the field elements, and only those field elements, that could possibly participate in the event are enclosed inside the ellipsoid.  I will refer to these discrete events as “Faraday events”.

Close analogies mirroring the inner workings of a Faraday event are submarine sonar and bat echo-location.  For sonar, the speed of sound in water plays the role of light speed.  For bats, it's the speed of sound in air.

The sequence of Minkowski ellipsoids and associated Faraday events mark off the progress of the particle as it moves along its path of motion under the influence of the applied fields.  Each ellipsoid is positioned with major axis along the tangent line to the curve the particle is tracing out at the specific moment.

What we have arrived at here is a theory that exactly straddles the boundary between Classical Physics and Modern Physics.  In many ways, it is a “missing link”.

Personally, I find it to be quite astonishing that the Theory of Special Relativity, a theory so firmly rooted in Classical Physics, can penetrate so deeply into the secrets of Nature

In my next post, I will begin to develop the close relationships between EMF theory, the Lorentz transformations and object/image experiments

 

Why are my LaTex math expressions enclosed in \( ... \)as in

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \)

not being transcribed properly?  Please advise.

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1 hour ago, RAGORDON2010 said:

I continue to maintain the position that Special Relativity theory is an offshoot of Electromagnetic Theory.  I cannot speak of particles and forces within the context of SR without assuming the particles carry an electric charge and/or a magnetic moment, and without assuming the forces stem from electromagnetic fields.

SR is a model of Minkowski spacetime, i.e. an empty vacuum spacetime devoid of gravitational sources, including electromagnetic fields. It is thus not an “offshoot” of EM.
One can use Minkowski spacetime as a background for field theories, so long as the gravitational effect of those fields is negligible - this leads you to quantum field theory and the Standard Model. This framework is perfectly well capable of describing particles and forces that do not carry electric charge, and are not of EM origin.

1 hour ago, RAGORDON2010 said:

 

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \)

This is not a valid line element, because it isn’t an invariant.

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3 hours ago, RAGORDON2010 said:

“Minkowski differential interval”

 

3 hours ago, RAGORDON2010 said:

Minkowski ellipsoids

When saying "Minkowski" in your definitions, does it imply that the definition of Minkowski spacetime is applicable? Is the spacetime interval between any two events independent of the inertial frame of reference in which they are recorded in your definitions?

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4 hours ago, RAGORDON2010 said:

I cannot speak of particles and forces within the context of SR without assuming the particles carry an electric charge and/or a magnetic moment, and without assuming the forces stem from electromagnetic fields.

SR applies equally to uncharged particles. Charge has nothing to do with SR.

4 hours ago, RAGORDON2010 said:

Key Assumption 4a - Building on ideas put forth by Michael Faraday, I assumed that electromagnetic fields interact with charged particles and with particles carrying magnetic moments via a stimulus/response interaction.

Trying to derive SR from the interaction of magnetic fields with charged particles has a couple of problems:

It is unnecessarily complicated. 

The relationship between electric and magnetic fields can be deduced from SR, so you end up with a circular argument.

Quote

Why are my LaTex math expressions enclosed in \( ... \)as in

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \)

not being transcribed properly?  Please advise.

 

 

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6 hours ago, RAGORDON2010 said:

I continue to maintain the position that Special Relativity theory is an offshoot of Electromagnetic Theory.

Yes. As I have repeatedly pointed out, Einstein based his theory on the invariance of c from electrodynamics, and applied the concept to kinematics. That SR is based on an observation from electrodynamics is not in contention. However, if your contention is that it is an electromagnetic interaction, then you need to present a model of that. Sooner, rather than later.

 

Quote

I cannot speak of particles and forces within the context of SR without assuming the particles carry an electric charge and/or a magnetic moment, and without assuming the forces stem from electromagnetic fields.  

But as we're discussing particles/objects traveling at a constant v, we know the net force on them is zero, per Newton's first law. Further, relativity applies to uncharged systems as well. Which makes this moot.

 

Quote

 To review from Parts 1 & 2

In Part 1

Auuuuugh!

 

We're on page 5 of this discussion. Get to it already.

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6 hours ago, RAGORDON2010 said:

My reviews are intended to hold my presentation together so readers will not have to search through my earlier posts each time a post a new one.

Have you ever come across the concept of a "link" ?

Very useful. I suggest you look into it.

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6 hours ago, RAGORDON2010 said:

1) For the present discussion, please assume all measurements are made in the laboratory frame.

2) As for the passage of 115 years,  I believe that it's time to go back to basics and re-examine the fundamentals.  I intend to show that much of real importance has been overlooked.

1) Thank you.

Sadly this means you are not discussing Special Relativity which is all about transformations between frames and you only have one frame.

Can you not see that if you only have one frame you only one x, one y , one z and one t and therefore one v ?

I suggest you are still trying for an absolute frame.

It is very difficult to abandon this idea.

 

2) Yes the fundamentals. Marcus has put his finger directly on the issue. +1 with a very deep and fundamental point.

5 hours ago, Markus Hanke said:
7 hours ago, RAGORDON2010 said:

 

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \)

This is not a valid line element, because it isn’t an invariant.

Invariants

The whole point about multiple frames is to find an invariant which means it is the same in all frames.

There are many possible candidates as I noted.

S and ds must be invariant as they form the 'stick and ball' model of events which is totally frame free (ie no frames at all).

S and ds stand alone on one side of the equation and the chosen formula stands on the other.

They come from different places. The formula side is determined by the characteristics of the frame system chosen and is intimately bound up in what Marcus and Mordred call 'the metric (tensor)'

But S and ds are there whether there is a coordinate system or not.

Further the choice of the conventional 'four square' formula trickles down from General Relativity to  Special Relativity to Newton depending upon circumstance and therefore meets the requirement of complying with observational evidence and testing.

So I am sorry you have put a deal of hard work into your development but you have made a fundamental mistake right at the beginning.

That is why I am trying to discuss it with you. To save you abortive work.

 

By the way are you any (distant) relative to Robert Gordon (1668 - 1731) of Aberdeen?

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On 3/23/2020 at 3:01 AM, Strange said:

SR applies equally to uncharged particles. Charge has nothing to do with SR.

Trying to derive SR from the interaction of magnetic fields with charged particles has a couple of problems:

It is unnecessarily complicated. 

The relationship between electric and magnetic fields can be deduced from SR, so you end up with a circular argument.

 

 

(1) With reference to my expression - 

\( (dS/2)^2 + (vdt/2)^2  = (cdt/2)^2 \),

aren't \( ... \) proper [math] tags?   I'm missing something here.

(2) In regard to your comment "SR applies equally to uncharged particles. Charge has nothing to do with SR."  

I believe SR is a theory of electromagnetism - in particular, a theory of interactions between electromagnetic fields and particles carrying electric charge and magnetic moments, i.e., spin.  That's where I am mentally at the moment.

On 3/23/2020 at 4:51 AM, swansont said:

Auuuuugh!

 

We're on page 5 of this discussion. Get to it already.

One more post beginning with a review and then no more.  Promise.

On 3/23/2020 at 6:00 AM, studiot said:

1) Thank you.

Sadly this means you are not discussing Special Relativity which is all about transformations between frames and you only have one frame.

Can you not see that if you only have one frame you only one x, one y , one z and one t and therefore one v ?

I suggest you are still trying for an absolute frame.

It is very difficult to abandon this idea.

 

2) Yes the fundamentals. Marcus has put his finger directly on the issue. +1 with a very deep and fundamental point.

Invariants

The whole point about multiple frames is to find an invariant which means it is the same in all frames.

There are many possible candidates as I noted.

S and ds must be invariant as they form the 'stick and ball' model of events which is totally frame free (ie no frames at all).

S and ds stand alone on one side of the equation and the chosen formula stands on the other.

They come from different places. The formula side is determined by the characteristics of the frame system chosen and is intimately bound up in what Marcus and Mordred call 'the metric (tensor)'

But S and ds are there whether there is a coordinate system or not.

Further the choice of the conventional 'four square' formula trickles down from General Relativity to  Special Relativity to Newton depending upon circumstance and therefore meets the requirement of complying with observational evidence and testing.

So I am sorry you have put a deal of hard work into your development but you have made a fundamental mistake right at the beginning.

That is why I am trying to discuss it with you. To save you abortive work.

 

By the way are you any (distant) relative to Robert Gordon (1668 - 1731) of Aberdeen?

(1) I've tried to explain my position as clearly as I can at the end of tonight's post.  I guess the bottom line is that I am simply not interested in a frame-driven physics.

(2) My son living in Cambodia has been tracing our family roots.  I'm unaware that he has found a branch in Aberdeen, but maybe one will turn up.  I would be most pleased, though, to learn that years from now, a university would be named in my honor.  Anyway, back to work.  In these difficult times, it's good to keep the mind active.

 

 

 

Special Relativity - A Fresh Look, Part 4

I want to begin development of the close relationships between EMF theory, the Lorentz transformations and object/image experiments.

But, first, I want to review the differences between Related Experiments as I have defined them in former posts, vs. the conventional Special Relativity viewpoint of a single experiment viewed by observers in a “rest” frame and by observers in a “moving” frame, a frame moving uniformly with respect to the rest frame.

In the related experiments point of view, we have an “object” experiment consisting of a particle with initial velocity \(v_0\)  free to move under the influence of applied external fields E and H, where (t, x, y, z) represent the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

We also have an “image” experiment consisting of an identical  particle initially at rest and free to move under the influence of applied external fields E’ and H’, where E’ and H’ are image fields of E and H transformed under the Special Relativity field transformations with velocity parameter \(v_0\).  In this experiment, (t’, x’, y’, z’) represent the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

The 4-space observations (t, x, y, z) are related to the 4-space observations (t’, x’, y’, z’) by the Lorentz time and space transformations with velocity parameter \(v_0\).  These object and image experiments can be carried out in laboratories widely separated from each other in distance and in time.

In the conventional point of view, the frames move uniformly relative to each other at velocity \(v_0\).  Once the experiment begins, the particle is acted upon by applied fields E and H as determined by observers in the rest frame, and applied fields E’ and H’ as determined by observers in the moving frame, where E, H, E’, H’ are related by the Special Relativity field transformations with velocity parameter \(v_0\).

The progress of the particle is tracked with  4-space coordinates (t, x, y, z) by the rest frame observers, and 4-space coordinates (t’, x’, y’, z’) by the moving frame observers, where (t, x, y, z), (t’, x’, y’, z’) are related by the Lorentz time and space transformations with velocity parameter \(v_0\)

(Note, there are some situations where the object/image experiments and rest-frame/moving-frame experiments must be structured differently, e.g., experiments illustrating relativistic Doppler shifts.  I will present examples of these situations in my next two posts.)

Needless to say, I am not a fan of the conventional point of view.  In particular, I cannot “compute" the notion that Frame K observers and Frame k observers move relative to each other at speeds close to light speed.  This idea is so bizarre that I often wonder how it found its way into legitimate scientific discussions.

Secondly, I tend to look at physics through the eyes of an experimental physicist.  What’s the set-up?  What will be measured?  What’s the underlying theory, and how will the data be analyzed?  Conventional SR theory doesn’t offer me much help here.

One Forum member has asked why I am spending so much time critiquing a subject 115 years old.  My first response is that I do not accept a physics where Special Relativity stands apart from modern quantum views of electromagnetic field/particle interactions such as QED and QFT - Nature cannot be that fractured.

My second response is that young students inclined to pursue physics deserve a presentation of the science which doesn’t leave them shaking their heads, rolling their eyes and heading for other fields of study.

But, I suppose my best response is to cite the following from a NYT obituary, October 3, 2014, for the physicist Martin Perl: “In a blog post last year, he wrote: 'The time scale for physics progress is a century, not a decade.' “

Given all of the above, I will continue to discuss EMF theory solely in the context of the Related Experiments point of view.

 

 

 

 

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Posted (edited)

I cannot reproduce the LaTeX problem.

Edited by taeto

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5 hours ago, RAGORDON2010 said:

I believe SR is a theory of electromagnetism - in particular, a theory of interactions between electromagnetic fields and particles carrying electric charge and magnetic moments, i.e., spin.  That's where I am mentally at the moment.

SR is model of Minkowski spacetime, i.e. of the relationships between events in the absence of gravitational sources. It is a special case of General Relativity, for cases where gravitational effects are negligible. The specific form that Maxwell’s equations take is a consequence of relativity, not its cause.

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7 hours ago, RAGORDON2010 said:

I believe SR is a theory of electromagnetism

You also believe you can ignore the syntax required by the forum. 

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7 hours ago, RAGORDON2010 said:

 I guess the bottom line is that I am simply not interested in a frame-driven physics.

Your latest post does not mention Minkowski anymore. Does that affect your definitions in the latest post?

 

8 hours ago, RAGORDON2010 said:

We also have an “image” experiment consisting of an identical  particle initially at rest and free to move under the influence of applied external fields E’ and H’, where E’ and H’ are image fields of E and H transformed under the Special Relativity field transformations with velocity parameter v0 .  In this experiment, (t’, x’, y’, z’) represent the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

You speak of two experiments, possibly separated in time, Lorentz transforms, t and t'. Can you please show the math that you use and how you account for the timing of the experiments? If you neglect time you will have observable differences; your result of the mirror experiment will deviate from what relativity predicts about two experiments in different frame of reference.

 

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14 hours ago, RAGORDON2010 said:

 

One Forum member has asked why I am spending so much time critiquing a subject 115 years old.  My first response is that I do not accept a physics where Special Relativity stands apart from modern quantum views of electromagnetic field/particle interactions such as QED and QFT - Nature cannot be that fractured.

 

 

You obviously do not know the first thing about QFT if you believe this statement. The very first chapters in any QFT textbook deals with how QFT applies the Klein Gordon equation to apply the four momentum etc for Lorentz invariance.

It is a fully SR compatible theory. SR is not limited to just the EM field it affects all qauge groups.

You have been told this numerous times now.

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15 hours ago, RAGORDON2010 said:

(2) In regard to your comment "SR applies equally to uncharged particles. Charge has nothing to do with SR."  

I believe SR is a theory of electromagnetism - in particular, a theory of interactions between electromagnetic fields and particles carrying electric charge and magnetic moments, i.e., spin.  That's where I am mentally at the moment.

So time dilation is an electromagnetic interaction? 
why do neutral atoms and ions experience the same effect?

15 hours ago, RAGORDON2010 said:

  Needless to say, I am not a fan of the conventional point of view.  In particular, I cannot “compute" the notion that Frame K observers and Frame k observers move relative to each other at speeds close to light speed.  This idea is so bizarre that I often wonder how it found its way into legitimate scientific discussions.

what part is troubling - relative motion, or moving at a large fraction of c?

 

15 hours ago, RAGORDON2010 said:

Secondly, I tend to look at physics through the eyes of an experimental physicist.  What’s the set-up?  What will be measured?  What’s the underlying theory, and how will the data be analyzed?  Conventional SR theory doesn’t offer me much help here.

Wait - you’re an experimental physicist?

 

15 hours ago, RAGORDON2010 said:

One Forum member has asked why I am spending so much time critiquing a subject 115 years old.  My first response is that I do not accept a physics where Special Relativity stands apart from modern quantum views of electromagnetic field/particle interactions such as QED and QFT - Nature cannot be that fractured.

What modern quantum physics is not Lorentz invariant?

 

 

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Posted (edited)

Great golly gosh, what on Earth do you say to a man who writes this

17 hours ago, RAGORDON2010 said:

I guess the bottom line is that I am simply not interested in a frame-driven physics.

 

Immediately followed by this

 

17 hours ago, RAGORDON2010 said:

The progress of the particle is tracked with  4-space coordinates (t, x, y, z) by the rest frame observers, and 4-space coordinates (t’, x’, y’, z’) by the moving frame observers, where (t, x, y, z), (t’, x’, y’, z’) are related by the Lorentz time and space transformations with velocity parameter v0

 

*************************???????????????????????????????????????????????????*****************************!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

 

Pull the other one, it's got bells on.

 

The following statement is an incorrect attempt at mathematics.

17 hours ago, RAGORDON2010 said:

In this experiment, (t’, x’, y’, z’) represent the 4-space motion of the particle with respect to an origin at (0, 0, 0, 0).

 

Only certain values can represent the locus of a moving particle.

Put as you have done it represents a complete 4D manifold, as you correctly stated earlier.
It cannot represent both the frame and the locus.

Edited by studiot

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3 hours ago, swansont said:

So time dilation is an electromagnetic interaction? 

That is a good question. If I had to make a guess*: 

19 hours ago, RAGORDON2010 said:

In the related experiments point of view

and

19 hours ago, RAGORDON2010 said:

These object and image experiments can be carried out in laboratories widely separated from each other in distance and in time.

My guess is that goal of this "point of view" is to try to get rid of time dilation all together by inventing some set of experiments taking place one after another in one single lab frame. That makes it possible to try to "forget" that observers of events in the lab frame and in the (unused) particle frame would not necessarily assign the same local time coordinate to events. The time dilation may seem to "disappear" when there are consecutive experiments measured in one frame instead of one experiment observed from two frames of reference in relative movement. In a single frame there aren't much of relativistic effects. Then there can be claims that these experiments reproduce some important aspects of SR, without introducing any time dilation or relative movements of frame of reference.

The above is merely my observations from trying to read and really understand the posts in this thread. My conclusion is that OP will not be able to convince me that the "related experiments point of view" is a valid alternative to mainstream SR. That may of course change if there is reliable evidence presented, supported by valid mathematical modelling.

 

*) Disclaimer 1: This is speculation about what's speculated about. Not speculation about mainstream SR.
Disclaimer 2:  I strongly believe Swansont's skills regarding clocks and time are several magnitudes above mine. But I couldn't resist the challenge to try to provide an answer in this case. 

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16 hours ago, Ghideon said:

That is a good question. If I had to make a guess*: 

and

My guess is that goal of this "point of view" is to try to get rid of time dilation all together by inventing some set of experiments taking place one after another in one single lab frame.

The phenomenon has been measured/observed, so you can't get rid of it. What you can attempt is to say it's an interaction, and yet we've seen nothing in the way of detail regarding such a claim.

All we've gotten is seventeen versions of the same introduction. 

16 hours ago, Ghideon said:

That makes it possible to try to "forget" that observers of events in the lab frame and in the (unused) particle frame would not necessarily assign the same local time coordinate to events. The time dilation may seem to "disappear" when there are consecutive experiments measured in one frame instead of one experiment observed from two frames of reference in relative movement. In a single frame there aren't much of relativistic effects. Then there can be claims that these experiments reproduce some important aspects of SR, without introducing any time dilation or relative movements of frame of reference.

In one frame there are zero relativistic effects. So that's moot.

 

 

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32 minutes ago, swansont said:

The phenomenon has been measured/observed, so you can't get rid of it.

I know, and of course I agree!

34 minutes ago, swansont said:

In one frame there are zero relativistic effects. So that's moot.

Yes, I agree. 

 

Trying to clarify, I interpreted OP's material and ideas as a doomed attempt to get rid of time dilation. The posted ideas seems incompatible with current mainstream theories that are supported by huge amounts of observations. Sorry if my way of presenting the arguments caused confusion. 

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On 3/25/2020 at 7:02 PM, taeto said:

I cannot reproduce the LaTeX problem.

Must be my browser.  

Regarding the comments, I ask the Forum to be patient.  I think most concerns being raised will self-resolve eventually.

A little more background on Related Experiments, and then I will focus on the question of invariance.

(Most of us are home-bound anyway because of this damn virus, so it's probably healthy to have some anonymous person on the outside to argue with.)

Note to all who view this thread -

The count of views to this thread surpasses 60,000.  I take this view count very seriously.  It is my intention that every one of my posts be an accurate and clear reflection of my thinking.  To this end, if I draft a post on, say, Monday, the draft is read/edited and read/edited  until, say, Thursday or Friday when I finally submit it to the Forum

Unfortunately, this discipline does not hold for my responses to individual comments from Forum members.  Those responses tend to be “off the cuff” and ill thought out.  In particular, my disrespectful comment on a frame-driven physics in the context of the expression:

\( (dS/2)^2 + (vdt/2)^2 = (cdt/2)^2 \).

I interprete this expression as pointing to the formation of “Minkowski ellipsoids” that mark off the progress of a particle as it moves along its path of motion under the influence of applied fields.  Instead of commenting the way I did, what I should have said, upon reflection, is that neither these ellipsoids nor their defining expressions are intended to be viewed as transformation invariants across a pair of related experiments, or in the conventional sense, across the associated “rest” and “moving” frames of reference.

I hope all of this will become clearer to the Forum in my future posts.

Special Relativity - A Fresh Look, Part 5

This post begins with the Related Experiments treatment of the “In-Line” Relativistic Doppler Effect and follows with the Related Experiments treatment of the “Transverse” Relativistic Doppler Effect.

In his 1905 paper, Einstein* begins his analysis by imagining a monochromatic source placed at rest at a point some distance from the origin of his “rest” frame, Frame K.  If we only wish to focus on the in-line Doppler effect, we may limit the positioning of the source to somewhere along the Frame K negative x-axis.

*(ref. “Einstein’s Miraculous Year - Five Papers That Changed the Face of Physics", Edited by John Stachel and Published by Princeton University Press, 1998, pgs. 146-149.)

Following Einstein’s approach, we write the wave function argument for a  light wave emanating from the source and traversing in the positive x direction with frequency f, period T = 1/f, and wavelength w = c/f = cT as it would be recorded by a stationary detector positioned at the origin: \( 2(\pi)(f)(t - x/c) \).

For our Related Experiments analysis, we assign the above set-up to our image experiment.  We place a monochromatic source with frequency f’, period T’ = 1/f’, and wavelength w’ = c/f’ = cT’ at rest at a distant point somewhere along the negative x’-axis and we place a stationary detector at the origin.  We expect that the detector will record a wave function argument equal to \( 2(\pi)(f’)(t’ - x’/c) \).

Moving over to our object experiment, we use the a similar set-up, but here we place the source in motion with velocity v in the direction of the stationary detector.

We now determine what the detector would record in the object experiment as follows:

We substitute for t’ and x’ in the argument \( 2(\pi)(f’)(t’ - x’/c) \) using the Lorentz transformations in the form:

\( t’ = (\gamma)(t - vx/c^2) \), and \( x’ = (\gamma)(x - vt) \), with \(\gamma\) defined in the usual way.

After some simplification, we will find that the stationary detector records a wave with argument:

\( 2(\pi)(\gamma)(f’)(1 + v/c)(t - x/c) \), giving a frequency of \( (\gamma)(f)’(1 + v/c) \).

This represents the relativistic Doppler shift for a source moving toward a fixed observer (or equivalently, for an observer moving toward a fixed source.)

To determine the frequency transformation for the case where the source moves away from a fixed observer (or equivalently, where the observer moves away from the fixed source), we need only replace v in the above with -v.

 

For the case of the Transverse Relativistic Doppler Effect (TDE), we follow Einstein’s general analysis, but, for Frame K, we position the source at the origin and place the detector at rest at an arbitrary point, point P, on the positive z-axis some distance from the origin.

For source frequency f, period T = 1/f, and wavelength w = c/f = cT, we would expect that this detector will record a plane wave emanating from the source with argument

\( 2(\pi)(f)(t - z/c) \).

For our Related Experiments analysis, we assign Einstein’s Frame K set-up to our image experiment.  We place a monochromatic source with frequency f’, period T’ = 1/f’, and wavelength w’ = c/f’ = cT’ at rest at the origin, and we place the detector at rest on the positive z’-axis at a  point P some distance from the origin.  As in the Einstein model, we expect that this detector will record a plane wave emanating from the source with argument \( 2(\pi)(f’)(t’ - z’/c) \).

Moving over to our object experiment, we use the a similar set-up, but here we locate the source somewhere along the negative x-axis and set it in motion with velocity v in the positive x direction.

We now ask how the wave emitted by the moving source as it passes the origin would appear to the detector at point P.

We substitute for t’ and z’ in the argument \( 2(\pi)(f’)(t’ - z’/c) \) using the Lorentz transformations in the form:

\( t’ = (\gamma)(t - vx/c^2) \) and z’ = z, with \(\gamma\) defined in the usual way.

After some simplification, we find that the detector records a plane wave with argument

\( 2(\pi)(f’)(\gamma)(t - (vx/c + z/(\gamma))/c) \).

This represents a plane wave with frequency \( f = f’(\gamma) \) and direction cosines, (l, m, n), with l = v/c, m = 0, and n = \(1/(\gamma)\).

We see that the light detected by the receiver is blue-shifted by a factor of gamma.  Also, we see that the light beam will appear to be emanating from a displaced source, an example of “aberration”.

Let \( \theta \) = angle between the light beam and the x-axis.

Let \( \phi \) = angle between the light beam and the z-axes.

Then \( cos (\theta) \) = l = v/c, and \( cos \(phi) = n = 1/(\gamma) \).

Since \( \theta \) and \( \phi \) are complementary angles,

\( cos (\phi) = sin (\theta) \), and we would expect \( (l)^2 + (n)^2 = 1 \), which is true here.

 

 

 

 

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24 minutes ago, RAGORDON2010 said:

The count of views to this thread surpasses 60,000.  I take this view count very seriously. 

You shouldn't. It is pretty meaningless. You should ignore it.

What you shouldn't ignore is all the people asking you questions and to clarify what you mean.

Treating this forum as your blog is against the rules.

25 minutes ago, RAGORDON2010 said:

It is my intention that every one of my posts be an accurate and clear reflection of my thinking. 

You are failing dismally.

 

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Where’s the part where you explain how this is an electromagnetic phenomenon?

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Why does it feel like I'm back in school attending a lecture each time I open this thread ?
This is supposed to be a discussion forum.

RAGORDON2010    should state his case, allow for discussion, and answer questions posed to him.
Or, this thread should be shut down.

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11 hours ago, RAGORDON2010 said:

Regarding the comments, I ask the Forum to be patient.  I think most concerns being raised will self-resolve eventually.

Don't worry,  patience is not an issue, at least not in my case. But I think the forum rules still apply, you can't keep blogging and hope for questions to self-resolve in some distant future. 

I have reread the posts so far and I can't find that my questions are adressed. The addition of doppler in the last revision does not add clarification regarding issues raised earlier. 

Basic question:
Can you please post the complete set of postulates used in your "related experiments"-idea? There is no need to repeat the whole "fresh look" stuff, just tell the postulates and, if necessary, how they deviate from the postulates used in SR.
 

What you have posted so far does seem to match SR predictions, it is not a "fresh look" of SR and it is not an alternative point of view of SR. In my opinion clearly stating the postulates you use and how your postulates differ from SR may help bring the discussion forward. Since you state that SR is an offshoot of Electromagnetic Theory I guess that your postulates must differ from SR in some way; when deriving certain relativistic effects from your postulates we see how electromagnetism comes into play in some way that deviates from the mainstream SR.

 

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14 hours ago, RAGORDON2010 said:

Regarding the comments, I ask the Forum to be patient.  I think most concerns being raised will self-resolve eventually.

!

Moderator Note

Discussion has that advantage, certainly, but only when one listens rather than lectures. Unfortunately, you aren't discussing this, so nobody is learning anything they really need to. Discussion would mean you actually incorporate comments from others in your replies. Instead we see an outlined lecture series you obviously don't want any critique on.

Please go elsewhere to do this kind of blogging. Nobody is interested in that format here. This is a science discussion forum. Thread closed.

 

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