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Another way of looking at Special Relativity

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At the risk of wandering into the dreaded realm of Speculation, I wish to offer the following insight into Special Relativity.  To help put you in a proper frame of mind for this offering, imagine standing on the earth and looking UP at the moon. Now imagine standing on the moon and looking DOWN at the earth.  It's just a difference in viewpoint.  

To begin, we will go earth to moon:

Imagine I am standing on a platform next to a train track, and you are on a train speeding past me at 0.8c.  I apply a magnetic field across the track, and a charged object, say a ball, riding with you in your train gets caught up in this field.  What happens?  I will see the ball looping in a vertical plane.  You will see the ball undergoing a serious of weird pogo stick hops and until it hops out the back door of your train.  The Lorentz time and space transformations relate my measurements of the path of motion (t,x,y,z) for the looping ball to your measurements of the path of motion (t',x',y',z') for the hopping ball.

Now let's go moon to earth:

Imagine I set up the following experiment in my laboratory on a Monday - I accelerate the charged ball up to 0.8c, and expose it to the same magnetic field.  I will see the ball undergo the same looping motion that I observed in the train situation.  On Tuesday, I place the ball at rest on a table and apply the combination of electric and magnetic fields that your equipment measured in the train situation (i.e. the image fields produced by applying the Special Relativity field transformations to the magnetic field I applied across the track). In this case, I will see the ball undergo the same hopping motion you observed in the train. 

My observations (t,x,y,z) of the path of motion of the ball in Monday's experiment will map over to my observations (t'x'y'z') of the path of motion of the ball in Tuesday's experiment via the same set of Lorentz transformations, only here the initial velocity of the ball in the Monday experiment is playing the role of the relative velocity between train and platform.

What we have shown here are pairs of object-image observations arising from a pair of object-image "related experiments".  Nothing new here.  Object-Image experiments are useful for illustrating symmetries in natural laws.

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What happens if you simplify all of this and get rid of Earth, moon, trains, and just make them named inertial frames? As described, it makes no difference whether it's set up for an observer on Earth or a test particle in empty space. The Earth frame can be made symmetric to a train frame in experiments like these. Making a moving frame a train gives a concrete example that's easier to think about, but it can also give false impressions of material differences between reference frames. Do your insights remain unchanged if you make all the frames generic, and get rid of the weekdays?

You mention "initial velocity [...] playing the role of relative velocity", but all velocity is relative velocity. Velocities are relative to frames of reference.

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Hi.  Thanks for your post.  You're right - all inertial reference frames are equivalent for illustrating physical laws.  However for a long time, I have believed that the train stories cloud the importance  of Special Relativity for our young high school juniors and seniors and college freshmen struggling to understand how physics challenges their intuitive understanding  of how Nature works.  That's why I have long advocated for the related experiments approach to teaching the subject - one fixed frame of reference and two separate but related experiments, as opposed to a single experiment and two frames of reference in uniform relative velocity (moving at speeds close to the speed of light, no less).

Just a cursory review of questions students ask about slow clocks and shrinking meter sticks illustrate the depth of the confusion.  In the related experiments approach, there are only one set of clocks, one set of meter sticks and, of course, one set of whatever additional laboratory apparatus is needed.  My clocks do not run fast or slow or whatever, my meter sticks do not shrink or grow or whatever, etc.  In my Monday/Tuesday imagery, I only flip a page on the calendar.

Let me give you an example of how confusing things have gotten:

Given a pair of spacetime coordinates (t,x,y,z) and (t’,x’,y’,z’) connected to each other by a Lorentz transformation -

The conventional view:  Two reference frames, Frame O and Frame O’, moving uniformly relative to each other, locate the SAME point in spacetime, where the first set of coordinates are specified by the clocks and meter sticks belonging to observers in Frame O and the second set of coordinates are specified by the clocks and meter sticks belonging to observers in Frame O’.

The related experiments view:  There is a SINGLE frame of reference in which a pair of related experiments are carried out - the first, say, on Monday, and the second on Tuesday - and where the two sets of coordinates identify SEPARATE points in spacetime.  These points appear on the separate world lines produced by the experiments, or, in 3-space, on the separate paths of motion.

Look, Einstein was fully aware of the fact that Maxwell's equations hold their form under a Lorentz transformation.  Had he built on that observation and created a related experiments picture along the lines discussed here, we would stiil have Einstein's Theory of Special Relativity, but without the nonsense.  As things stand today, the conventional view offers a weird, confused, unintuitive and abstract reach for reality.  In contrast, the related experiments view is reality.

 

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27 minutes ago, RAGORDON2010 said:

Look, Einstein was fully aware of the fact that Maxwell's equations hold their form under a Lorentz transformation.  Had he built on that observation and created a related experiments picture along the lines discussed here, we would stiil have Einstein's Theory of Special Relativity, but without the nonsense.  As things stand today, the conventional view offers a weird, confused, unintuitive and abstract reach for reality.  In contrast, the related experiments view is reality

Isn't 20 20 hindsight wonderful ?

Einstein's development is not the one we use today in any case.
Are you aware of the metaphysical reasons for his chosen route?

 

Having defended Einstein, are you aware that 'spacetime' was a later construct?
Changing from separate space and time to integrated spacetime introduces several philosophical issues, best consolidated by Eddington (on page 10 of his book, The Mathematical Theory of Relativity)

In a consolidated spacetime you do not have separate length and time meters, the basic measuring device measures spactime units (the spacetime interval, s),  in any direction in the spacetime continuum.
The Lorenz transformation becomes a (Euclidian) metric for this continuum.
Since all axes are now on an equal footing they fade into the background (where all good frames of reference belong) and what is important is the configuration of events (or points in the continuum if you will)

Edited by studiot

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Still, there's no "nonsense" whether you have separate length and time measurements or not. It all works out consistently. Add a clock, add a train, look at it from a different frame of reference, make a planet an imaginary particle, use different type of coordinates or measuring tools, all you're changing is how complicated is the experiment that you're describing.

RAGORDON2010, since you're saying that using one "fixed" reference frame removes the nonsense, I think that you're missing a lot of special relativity and just avoiding it. Besides, I don't see how "fixed" is meaningful, because to observers with other frames of reference, it's not fixed. Your experiment must make sense from other relatively moving frames of reference. If that leads to nonsense, you've done something wrong.

2 hours ago, RAGORDON2010 said:

As things stand today, the conventional view offers a weird, confused, unintuitive and abstract reach for reality.

That doesn't matter, it can still be used to make accurate predictions that match real measurements. Besides, it needn't be any of those things to someone familiar enough with it.

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9 hours ago, RAGORDON2010 said:

 As things stand today, the conventional view offers a weird, confused, unintuitive and abstract reach for reality.  In contrast, the related experiments view is reality.

I disagree. The theory is normally introduced by a series of simple thought experiments showing how measurements of space and time are affected when viewed from different frames of reference. This can introduce the relevant math at each stage and gradually build up to more complex scenarios (e.g. involving moving charges an magnetic fields).

Personally, I found your approach, leaping straight in to a complex scenario, introducing the Earth and Moon and then saying no more about them, etc. to be confusing and unhelpful. I can't really see it says anything much about special relativity. It seems to say no more than is known from Galilean relativity and the symmetries that make physics independent of spatial or temporal transformation.

Obviously, different approaches work for different people. There may well be a subset who find your approach appealing. And there will be others who find a purely mathematical derivation more helpful.

 

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11 hours ago, RAGORDON2010 said:

Hi.  Thanks for your post.  You're right - all inertial reference frames are equivalent for illustrating physical laws.  However for a long time, I have believed that the train stories cloud the importance  of Special Relativity for our young high school juniors and seniors and college freshmen struggling to understand how physics challenges their intuitive understanding  of how Nature works.  That's why I have long advocated for the related experiments approach to teaching the subject - one fixed frame of reference and two separate but related experiments, as opposed to a single experiment and two frames of reference in uniform relative velocity (moving at speeds close to the speed of light, no less).

One of the things I learned when I was teaching is that there is no explanation or approach that is so wonderful that it will reach 100% of the audience. It's still a subjective experience. Saying an explanation is better isn't correct — it may mean that it's better for you, but you can't necessarily say that it will be better for someone else.

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Thanks to all of you who have taken time to respond to my posts.  The subject of Special Relativity deserves all the attention it gets.  

I think I’ve stumbled onto some sort of DNA test among followers of SR.  We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments.

I hold the view that both scenarios should be introduced and discussed in high school junior and senior science classes and also at the freshman university level.  Let the students choose their preference according to their natural inclinations.  Obviously I have my own preference but, particularly with the advent of General Relativity, the question of relationships across multiple reference frames becomes significant and must be introduced and discussed.

Which brings me to the subject of scenario equivalence.  Let me give an example.

I pose the following question - 

Without invoking the mathematics of the the Lorentz transformations, is there a way to match an observation by observers in one reference frame with an observation by observers in the other reference frame?

I believe Einstein wrestled with this question because he introduced the notion of the “mutually observed light flash” - a match is struck and the light flash is observed instantly by observers in both frames. 

Beginning with the conventional scenario, let’s not just talk about it - let’s do it, at least in thought.  Let’s go back to the situation where I stand on the platform and you are on the speeding train along with the charged ball.  This time, however, I want to insert a small firecracker inside the ball.  Then, once the ball starts looping as I perceive it, and hopping as you perceive it, I zap the ball with a laser beam and set off the firecracker.  Pow!!! The ball explodes at an object point (t,x,y,z) in my frame and at the corresponding image point (t’,x’,y’,z’) in your frame, where the object-image coordinates satisfy the Lorentz transformations.

Obviously, I cannot reproduce this match-up in the related experiments scenario.  I think what we have here might be what theoretical physicists refer to as a “broken symmetry”.  It certainly looks like a broken symmetry to me.

(Actually after re-reading the above text, I did indeed find a way to match up observations across related experiments, and I’ll describe it in a future post.  In my next post, however, I want to discuss time dilation and “slow clocks”.)

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21 minutes ago, RAGORDON2010 said:

I think I’ve stumbled onto some sort of DNA test among followers of SR.  We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments.

 

You have a really big problem here.

If you only have one frame of reference than you have the difficulty that Fitzgerald (and Lorenz) faced with the results of practical measurements on the propagation of light.

This was that the Lorenz-Fitzgerald contraction was introduced as a mathematical formula which accounted for but did not explain the results of these experiments (in particular the Michelson and Michelson -Morley ones)

Length contraction of the apparatus arms was a pretty heretical explanation.

Einstein on the other hand, deduced the selfsame formulae from purely geometrical considerations of observing the same sequence of events in two frames.

 

Before you press on

28 minutes ago, RAGORDON2010 said:

 

Beginning with the conventional scenario, let’s not just talk about it - let’s do it, at least in thought.  Let’s go back to the situation where I stand on the platform and you are on the speeding train along with the charged ball.  This time, however, I want to insert a small firecracker inside the ball.  Then, once the ball starts looping as I perceive it, and hopping as you perceive it, I zap the ball with a laser beam and set off the firecracker.  Pow!!! The ball explodes at an object point (t,x,y,z) in my frame and at the corresponding image point (t’,x’,y’,z’) in your frame, where the object-image coordinates satisfy the Lorentz transformations.

Obviously, I cannot reproduce this match-up in the related experiments scenario.  I think what we have here might be what theoretical physicists refer to as a “broken symmetry”.  It certainly looks like a broken symmetry to me.

(Actually after re-reading the above text, I did indeed find a way to match up observations across related experiments, and I’ll describe it in a future post.  In my next post, however, I want to discuss time dilation and “slow clocks”.)

 

Before you press on please pause long enough to discuss the points made by various members here about you initial claims.

Otherwise this is just soapboxing.

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56 minutes ago, RAGORDON2010 said:

I think I’ve stumbled onto some sort of DNA test among followers of SR.  We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments.

I don't see how the latter has any relation at all to special relativity. Can you explain, preferably with some math?

 

58 minutes ago, RAGORDON2010 said:

Without invoking the mathematics of the the Lorentz transformations, is there a way to match an observation by observers in one reference frame with an observation by observers in the other reference frame?

I would assume not; that is what the Lorentz transform is for: for relating the observations in different frames of reference.

59 minutes ago, RAGORDON2010 said:

The ball explodes at an object point (t,x,y,z) in my frame and at the corresponding image point (t’,x’,y’,z’) in your frame, where the object-image coordinates satisfy the Lorentz transformations.

Obviously, I cannot reproduce this match-up in the related experiments scenario.  I think what we have here might be what theoretical physicists refer to as a “broken symmetry”.  It certainly looks like a broken symmetry to me.

No, what we have is a demonstration of the fact that your "related experiment" concept says nothing about special relativity.

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1 hour ago, RAGORDON2010 said:

Without invoking the mathematics of the the Lorentz transformations, is there a way to match an observation by observers in one reference frame with an observation by observers in the other reference frame?

There are a number of examples of this. many point out issues of simultaneity being relative. Trains and flashes of light as the train and platform observers are adjacent, for example.

In general, in these examples one tries to simplify the scenario, so that only one behavior is being investigated and tested. Every added caveat is an opportunity to misunderstand what's going on.

 

 

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On 11/3/2019 at 1:14 PM, md65536 said:

What happens if you simplify all of this and get rid of Earth, moon, trains, and just make them named inertial frames? As described, it makes no difference whether it's set up for an observer on Earth or a test particle in empty space. The Earth frame can be made symmetric to a train frame in experiments like these. Making a moving frame a train gives a concrete example that's easier to think about, but it can also give false impressions of material differences between reference frames. Do your insights remain unchanged if you make all the frames generic, and get rid of the weekdays?

You mention "initial velocity [...] playing the role of relative velocity", but all velocity is relative velocity. Velocities are relative to frames of reference.

I apologize for confusing you with my initial remarks.  I hope you will see that I've tried to be more specific in my later posts.  The Earth to Moon imagery was just a way of letting the readers know that I was going to present a change of viewpoint.

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6 minutes ago, RAGORDON2010 said:

I apologize for confusing you with my initial remarks.  I hope you will see that I've tried to be more specific in my later posts.  The Earth to Moon imagery was just a way of letting the readers know that I was going to present a change of viewpoint.

What does a "change in viewpoint" have to do with special relativity? Unless you are going to quantify the relative velocity of the Earth and Moon?

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On 11/3/2019 at 5:42 PM, studiot said:

Isn't 20 20 hindsight wonderful ?

Einstein's development is not the one we use today in any case.
Are you aware of the metaphysical reasons for his chosen route?

 

Having defended Einstein, are you aware that 'spacetime' was a later construct?
Changing from separate space and time to integrated spacetime introduces several philosophical issues, best consolidated by Eddington (on page 10 of his book, The Mathematical Theory of Relativity)

In a consolidated spacetime you do not have separate length and time meters, the basic measuring device measures spactime units (the spacetime interval, s),  in any direction in the spacetime continuum.
The Lorenz transformation becomes a (Euclidian) metric for this continuum.
Since all axes are now on an equal footing they fade into the background (where all good frames of reference belong) and what is important is the configuration of events (or points in the continuum if you will)

Studiot, you are becoming one of my favorite responders because you seem to have a knack for leading me into areas I very much want to address.  I am aware that Hermann Minkowski first dealt with the problems of the 4-space of t,x,y,z, i.e. "spacetime", circa 1908.  His concern was how to specify a "distance" or separation between two spacetime events by building on Einstein's special relativity theory.  This separation we now refer to as "proper time".  I will have much more to say on Minkowski's contribution in later posts.  It is worth noting here that, as the story goes, when Einstein first became of aware of Minkowski's paper, he mumbled something about mathematics muddling up good physics.  (Hmm.)

14 minutes ago, Strange said:

What does a "change in viewpoint" have to do with special relativity? Unless you are going to quantify the relative velocity of the Earth and Moon?

By "change of viewpoint" in the context of Special Relativity, I am working at a higher level of abstraction than simply relative velocities as seen by moving observers.  This is what I am talking about -

"We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments".

(And, please, forget I ever mentioned the Earth and the Moon.)

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24 minutes ago, RAGORDON2010 said:

This is what I am talking about -

"We have, on one hand, the conventional scenario consisting of a single experiment and two inertial frames of reference in uniform relative motion and, on the other hand, an alternative scenario consisting of a single frame of reference and two separate but related experiments".

As far as I can see that has nothing to do with special relativity. And, as you have failed to provide any explanation, I can only assume it doesn't.

39 minutes ago, RAGORDON2010 said:

I am aware that Hermann Minkowski first dealt with the problems of the 4-space of t,x,y,z, i.e. "spacetime", circa 1908.  His concern was how to specify a "distance" or separation between two spacetime events by building on Einstein's special relativity theory.  This separation we now refer to as "proper time".

That is not proper time; it is a spacetime interval, which is invariant unlike either the spatial or temporal separation. (Proper time is the time measured in a given frame of reference.)

44 minutes ago, RAGORDON2010 said:

 It is worth noting here that, as the story goes, when Einstein first became of aware of Minkowski's paper, he mumbled something about mathematics muddling up good physics.

Do you have a citation for this "story"?

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53 minutes ago, Strange said:

That is not proper time; it is a spacetime interval, which is invariant unlike either the spatial or temporal separation. (Proper time is the time measured in a given frame of reference.)

Yes indeed the spactime interval (which is what I did indeed mean)  is invariant but is not a time.

 'proper time' is also a Lorenz invariant, and is the time measured in the rest frame of the moving object, not any old frame.

https://en.wikipedia.org/wiki/Proper_time

 

As a footnote Minkowski died in 1909.

Edited by studiot
improve the English.

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59 minutes ago, Strange said:

As far as I can see that has nothing to do with special relativity. And, as you have failed to provide any explanation, I can only assume it doesn't.

That is not proper time; it is a spacetime interval, which is invariant unlike either the spatial or temporal separation. (Proper time is the time measured in a given frame of reference.)

Do you have a citation for this "story"?

Lately, I’ve been using “Special Relativity and Classical Field Theory”, Leonard Susskind and Art Friedman, Basic Books, 2017, as a desk reference.  They  state on p.57 that “proper time” and “spacetime interval” are negatives of each other, each referencing spacetime distance.

I have no citation I can give you regarding the Einstein-Minkowski story.  It may be apocryphal.

 

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1 minute ago, RAGORDON2010 said:

They  state on p.57 that “proper time” and “spacetime interval” are negatives of each other, each referencing spacetime distance.

I would like to see the context for that because it obviously isn't true in general.

19 minutes ago, studiot said:

'proper time' is also a Lorenz invariant, and is the time measured in the rest frame of the moving object, not any old frame.

Yes, that is a much better (more accurate) way of putting it.

3 minutes ago, RAGORDON2010 said:

Lately, I’ve been using “Special Relativity and Classical Field Theory”, Leonard Susskind and Art Friedman, Basic Books, 2017, as a desk reference.  They  state on p.57 that “proper time” and “spacetime interval” are negatives of each other, each referencing spacetime distance.

I have no citation I can give you regarding the Einstein-Minkowski story.  It may be apocryphal.

 

You still haven't explained how doing the same experiment in two different locations (or at two different times) relates to special relativity. Maybe this is because it doesn't?

(Now doing the same experiment at two different velocities would be a different matter...)

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On 11/4/2019 at 5:03 AM, swansont said:

One of the things I learned when I was teaching is that there is no explanation or approach that is so wonderful that it will reach 100% of the audience. It's still a subjective experience. Saying an explanation is better isn't correct — it may mean that it's better for you, but you can't necessarily say that it will be better for someone else.

I too have been a teacher at various points in my life and, if on any given day, I found that I had held the attention of my students, prodded their curiosity, and possibly stimulated their imagination, I went home that night feeling that I had a very good day.  I would imagine you have had days like that also.

Teaching is not easy, particularly as the ideas become more abstract and removed from the students' day-to-day experiences.  That's one reason I feel there is value in giving students alternative ways to view a problem. and the conceptual problems posed by Special Relativity definitely could use an alternative viewpoint.  

And if this viewpoint is grounded in their sense of two separate experiments conducted in the same laboratory, I believe a that good number of students would benefit from this viewpoint and find that they would be more open to arguments drawn from the conventional viewpoint of one experiment and two laboratories moving uniformly relative to each other at near-light speeds.

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34 minutes ago, RAGORDON2010 said:

Lately, I’ve been using “Special Relativity and Classical Field Theory”, Leonard Susskind and Art Friedman, Basic Books, 2017, as a desk reference.  They  state on p.57 that “proper time” and “spacetime interval” are negatives of each other, each referencing spacetime distance.

I would beware of that book, although I generally like the series.

Susskind spends a whole chapter obfuscating and beating around the bush as to what he means by t and t' which he 'corrects' in the next chapter intriducing 4-vectors.

Here is a much more compact and succint (and correct) version of Minkowski. (Wilson)

Note1 to use Minkowski to the fullest extenrt you need to get into 4-vectors. The presentation below gets you started here.

Note2 Wilson introduces the same comments about the role of events in the 4D 'Minklowski World' that I mentioned in my first reply to which you have yet to respond.

Quote

If a number of events are represebted by points in this space, the configuration of these points wil be fixed by the intervals,s, between evey pair of them and so will be the same whatever rectangular axes like x, y, z, τ are used.

mink1.jpg.c00d5f66425e8b5530979db6746b1511.jpg

mink2.thumb.jpg.7949ad68227fc7a554b2201117ee53bc.jpg

mink3.thumb.jpg.dc70164b750ab4c656737602ddc965d4.jpg

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36 minutes ago, RAGORDON2010 said:

And if this viewpoint is grounded in their sense of two separate experiments conducted in the same laboratory, I believe a that good number of students would benefit from this viewpoint

You haven't yet explained how this has any connection with special relativity.

Maybe I am being dense, but I can't see it.

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22 hours ago, studiot said:

I would beware of that book, although I generally like the series.

Susskind spends a whole chapter obfuscating and beating around the bush as to what he means by t and t' which he 'corrects' in the next chapter intriducing 4-vectors.

Here is a much more compact and succint (and correct) version of Minkowski. (Wilson)

Note1 to use Minkowski to the fullest extenrt you need to get into 4-vectors. The presentation below gets you started here.

Note2 Wilson introduces the same comments about the role of events in the 4D 'Minklowski World' that I mentioned in my first reply to which you have yet to respond.

mink1.jpg.c00d5f66425e8b5530979db6746b1511.jpg

mink2.thumb.jpg.7949ad68227fc7a554b2201117ee53bc.jpg

mink3.thumb.jpg.dc70164b750ab4c656737602ddc965d4.jpg

Studiot, I appreciate your attempt to educate me on the history of Special Relativity.  We all need occasionally to fill in gaps in our knowledge.  However, I have been delving among the ins and outs of SR for maybe 5 decades now, and I'm afraid me ideas are pretty well set.  There is a comment of yours, though, that I do wish to expand upon, to wit:

[If you only have one frame of reference than you have the difficulty that Fitzgerald (and Lorenz) faced with the results of practical measurements on the propagation of light.

This was that the Lorenz-Fitzgerald contraction was introduced as a mathematical formula which accounted for but did not explain the results of these experiments (in particular the Michelson and Michelson -Morley ones)

Length contraction of the apparatus arms was a pretty heretical explanation.

Einstein on the other hand, deduced the selfsame formulae from purely geometrical considerations of observing the same sequence of events in two frames.]

Studiot, I have been "looking over Einstein's shoulder", in a manner of speaking, for some time now, and I want to call your attention to the manner in which he introduces the Lorentz transformations in his1905 original paper.  (I have found the English translations of his 1905 papers in the book "Einstein's Miraculous Year - Five Papers That Changed the Face of Physics", Edited by John Stachel and Published by Princeton University Press, 1998, to be particularly helpful.)

One almost has to read between the lines, but it soon becomes clear that Einstein is working with a central device consisting of two sticks joined at the ends to form a right angle, one vertical and the other horizontal, with a mirror at the free end of each stick.  He also needs a source of light, say, a match.  (Please note that there is more than a passing similarity here to Michelson's interferometer.)  

Einstein imagines that the device is placed in a "moving" frame labeled Frame k with the horizontal stick pointing in the direction of motion.  The device is accelerated up to a speed v on the order of light speed and allowed to pass an observer in a "rest" frame, Frame K.  When the vertex of the device comes up even with the Frame K observer, the match is struck.

The observers in Frame k and Frame K, let's label them Observer k and Observer K,  must then measure the times for the light rays emanating from the match to reach the two mirrors and the times for the reflected beams to return to the vertex of the device.  As Einstein describes events, it appears that Observer k has the easier task. It is as if she struck the match.  In fact, it's as if she is not moving at all.  As she perceives the rays, one travels straight up to the vertical mirror and the reflected ray returns straight down to the vertex, the other ray travels in a straight line to the horizontal mirror and the reflected ray exactly retraces the path and returns to the vertex.

Observer K has the more difficult task.  It is as if he struck the match.  As he perceives the rays, they must catch up to the moving mirrors, and the reflected rays must then meet up with the moving vertex.

Einstein now sets out to demonstrate that the data obtained by the two observers satisfies the Lorentz transformations.  In other writings, I have described Einstein's analysis as "unnecessarily and uncharacteristically opaque".  After plunging into the depths of an argument that I have never been able to parse, he finally breaks through the surface of the water proudly holding in his hand a Lorentz-Fitzgerald contracted horizontal stick as perceived only by Observer K.  I have often wondered why the editors of the journal where this work was published didn't insist that he take a clearer approach in his analysis.  I do intend to suggest one possibility in a future post, but there is no avoiding his conclusion that the horizontal stick as perceived by Observer K is Lorentz-Fitzgerald contracted.

This is Michelson-Morley all over again!  Nothing new here!  That Einstein was able to proceed from this point and create his magnificent Special Relativity Theory is a tribute to his genius. 

 

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6 minutes ago, RAGORDON2010 said:

This is Michelson-Morley all over again!  Nothing new here!  That Einstein was able to proceed from this point and create his magnificent Special Relativity Theory is a tribute to his genius. 

The difference is that he derived the length contraction from first principles, whereas before it had been purely based on experimental results. And, not surprisingly, the theoretical derivation matched that produced from experimentation.

Why do you refuse to explain how your "related experiments in a single frame of reference" has any connection to SR? 

Perhaps because it doesn't? So why pretend it does? I can't see the point of this. (Maybe I should ask for the thread to be closed...)

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1 hour ago, Strange said:

The difference is that he derived the length contraction from first principles, whereas before it had been purely based on experimental results. And, not surprisingly, the theoretical derivation matched that produced from experimentation.

 

Exactly the point I was trying to make although it seems it fell on deaf ears. +1

 

1 hour ago, RAGORDON2010 said:

Observer K has the more difficult task.  It is as if he struck the match.  As he perceives the rays, they must catch up to the moving mirrors, and the reflected rays must then meet up with the moving vertex.

Can you refer me to the page and line where Einstein discusses the striking of a match?

Can you also explain the the appearance of the function φ(v) on page 7 at the end of  paragraph 3, which, as Strange says, derives the Lorenz transformation from first principles plus his additional postulates.

He says

Quote

Einsteim
Where φ is an as yet unknown function of v

This is one of the situations where Einstein was demonstrating his extreme care in formulating his approach as I was discussing earlier and you have chosen to ignore.

When you do the maths properly it is necessary to introduce φ(v) and it appears in the list of transformations for all four coordinates.

 

Oh and by the way, my last post was stated to be about Minkowski, not Einstein.
Did you miss line 3

Quote

Studiot
Here is a much more compact and succint (and correct) version of Minkowski. (Wilson)

 

 

Edited by studiot

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On 11/6/2019 at 9:01 PM, Strange said:

Do you have a citation for this "story"?

I have: Abraham Pais, Subtle is the Lord, page 152. Einstein called Minkowski's 4-dimensional spacetime 'superfluous learnedness' (I just googled and only found a citation. I can look it up at home). Which of course is not exactly the same as:

On 11/6/2019 at 8:35 PM, RAGORDON2010 said:

... he mumbled something about mathematics muddling up good physics.

But it is close enough.

9 hours ago, RAGORDON2010 said:

One almost has to read between the lines, but it soon becomes clear that Einstein is working with a central device consisting of two sticks joined at the ends to form a right angle, one vertical and the other horizontal, with a mirror at the free end of each stick.

I nowhere found something about 2 perpendicular sticks in Einstein's original article. I think you read more between the lines then there is room between them. 

I really doubt if you should teach others about relativity. As I see it you yourself miss basic understanding of SR. But I will postpone my judgement until I see how you answer Strange's question.

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