Another way of looking at Special Relativity

[studiot]

51 minutes ago, Mordred said:

To provide better clarity. You need the new viriable to distinguish coordinate time from proper time.

 A helpful hint past the oft over complicated distinction between the two. 

 Coordinate time is the time at a specific coordinate event. While proper time is any location along the worldline between any two events. (Emitter,observer). Where  [math]\tau[\math] is the proper time. The further qualification is that proper time is the invariant time where all observers can agree upon. This is set by the Einstein synchronization rules.

Hi Mordred,

My comment was specifically about Minkowski's original 4D World, where he used tau to distinguish as I posted way back on the previous page.
until the introduction of 'proper time' this was the use of tau.

Quote

studiot

Which I grant you is confusing, especially as in the original paper Einstein used tau as time in the second frame.

Quote

Einstein

To any system of values x, y, z, t which completely defines a place and time of an event in the stationary system, there belongs a system of values ξ. η, ζ, τ determining that event relative to the system k, and our task is now to find the system of equations connecting these quantities.

 

Minkowski has always been acknowledged as an alternative simpler route to obtain the same end result.

Edited November 11, 2019 by studiot

[Mordred]

Yes the original SR defined proper time as the at rest frame. GR treats all reference frames as inertial. Good point to keep in mind. +1

Edited November 11, 2019 by Mordred

[swansont]

7 hours ago, RAGORDON2010 said:

-The Fact of Nature that the speed of light is the same in all inertial frames plays NO role in explaining the successful application of Special Relatively to solving physical problems!  It is a Red Herring! There is another Fact of Nature at work here.

It’s the basis for time dilation and length contraction. It does need to be separately applied to solve the problems, true, but that’s true of lots of models. 

 

7 hours ago, RAGORDON2010 said:

 

I would say that accelerating a particle becomes more difficult as particle speed approaches c because the external field responsible for the acceleration loses effectiveness as the particle speed approaches the speed at which the field mechanisms function.

This, of course, offers an explanation for why light speed forms a limiting speed in nature.  An old boot can travel no faster through the water than the maximum speed at which the fisherman can reel in the line.

Whenever I think about this phenomenon, Paul Simon's song comes to mind. The speeding particle slips and slides away from the grasp of the external field.

What if no field is involved?

7 hours ago, RAGORDON2010 said:

 

Thought 3 -

I can’t leave this forum without saying something about time dilation.  It has always puzzled me that while the physics community easily accepts that time dilation effects in General Relativity relate in some way to the interaction between the time-keeping system and the surrounding gravitational field, the analogous time dilation effects in Special Relativity are viewed as “just so”.  Well, I have never cared much for a “just so” story.  But I do hold the view that Nature does not care at all for a “just so” story.  Something is going on out there!

In the most dominant example - the retarded decays of unstable particles moving at speeds close to light speed - I again must fall back on my belief that these effects are in some way a consequence, in ways not at all understood, of the rapid motion of the particles through surrounding electric and magnetic fields.

But it’s not a function of field strength. It’s there for weak fields, and for particles that aren’t unstable.

And they aren’t “just so” as they can be derived from the basic principles.

[md65536]

2 hours ago, Mordred said:

Yes the original SR defined proper time as the at rest frame. GR treats all reference frames as inertial. Good point to keep in mind. +1

Where is that defined? Do you mean that it used tau for something other than proper time? Tau (like other letters) is used to mean different things in different contexts.

Proper time is defined along the world line of a clock traveling along a spacetime interval, ie. only timelike intervals. It shouldn't be used to describe time away from the clock or throughout the frame, because that's not what it is. The proper time of an inertial clock measures the same time as any other clock elsewhere in the inertial frame, but that doesn't mean they're called the same thing. The proper time measured by an accelerating clock doesn't describe time elsewhere, because you can't synchronize with another clock, due to relativity of simultaneity. Even if you have two coordinated accelerating clocks that measure the same in a given inertial frame, they're not "Einstein synchronized" and won't agree with each other in the clocks' respective reference frames because in one clock's accelerated reference frame, the other clock accelerates at different times and has a non-zero relative velocity. Therefore the proper time measured by one accelerated clock can't remain the same all along its world line, as the proper time measured by any otherwise located clock, right?

 

Edit: I think I'm confused as to what I'm replying to, I got the sense from this thread that "proper time" was incorrectly being used to describe time in a reference frame in which a given clock is at rest, but I can't find what gave me that impression.

Edited November 11, 2019 by md65536

[Schmelzer]

On 11/6/2019 at 12:40 AM, studiot said:

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.

No, you can live in a quite comfortable way with a single frame, and apply, instead, Lorentz transformations to particular solutions.  This gives you different, Doppler-shifted solutions. 

There was a simple explanation proposed by Lorentz.  Namely, if what holds together condensed matter is the EM force, then condensed matter has to have the same symmetry properties as the EM equations.  Thus, a Lorentz-transformed (Doppler-shifted) solution for some piece of condensed matter will be a solution too.  But the Lorentz-transformed piece of matter is contracted.  

The actual explanation works in the same way, we have a lot more fields in the SM, but they all are wave equations with the same c, so that a Lorentz-transformed solution will be a solution too.  

[Mordred]

38 minutes ago, md65536 said:

Where is that defined? Do you mean that it used tau for something other than proper time? Tau (like other letters) is used to mean different things in different contexts.

Proper time is defined along the world line of a clock traveling along a spacetime interval, ie. only timelike intervals. It shouldn't be used to describe time away from the clock or throughout the frame, because that's not what it is. The proper time of an inertial clock measures the same time as any other clock elsewhere in the inertial frame, but that doesn't mean they're called the same thing. The proper time measured by an accelerating clock doesn't describe time elsewhere, because you can't synchronize with another clock, due to relativity of simultaneity. Even if you have two coordinated accelerating clocks that measure the same in a given inertial frame, they're not "Einstein synchronized" and won't agree with each other in the clocks' respective reference frames because in one clock's accelerated reference frame, the other clock accelerates at different times and has a non-zero relative velocity. Therefore the proper time measured by one accelerated clock can't remain the same all along its world line, as the proper time measured by any otherwise located clock, right?

This quick search pulls up one related paper. When I first was introduced to Relativity WAY back around 1980 I recall being taught the at rest definition. When precisely the change occurred (for the better ) I couldn't tell you. As it largely arose from misconceptions.

https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.humanities.mcmaster.ca/~rarthur/papers/Mptatch.pdf&ved=2ahUKEwinmOX5jeHlAhWQsJ4KHV8PB9IQFjARegQICxAB&usg=AOvVaw2NawrchGmi31GDfvPw4ZoL

 

Edited November 11, 2019 by Mordred

[md65536]

31 minutes ago, Mordred said:

This quick search pulls up one related paper. When I first was introduced to Relativity WAY back around 1980 I recall being taught the at rest definition. When precisely the change occurred (for the better ) I couldn't tell you.

https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.humanities.mcmaster.ca/~rarthur/papers/Mptatch.pdf&ved=2ahUKEwinmOX5jeHlAhWQsJ4KHV8PB9IQFjARegQICxAB&usg=AOvVaw2NawrchGmi31GDfvPw4ZoL

 

Ah thanks, I was worried for a minute there.

If I understand that pdf correctly, there was only ever one definition of "proper time", introduced by Minkowski. Other conflicting (but common) uses are described as stemming from confusion. It sounds like you were first taught the incorrect use.

From the paper:

Quote

The conflation of proper time with co-­‐ordinate time in a system’s own rest frame is also perhaps fostered by the numerical equivalence of the value of the proper time elapsed for a body moving along an inertial path with the value measured by the time-­‐co-­‐ordinate in its rest frame. Thus it is often said that proper time is simply time measured in a body’s “proper frame”, as if a body keeps its own inertial frame while accelerating! There are two confusions here: first, the idea that a body “has” an inertial frame, when a reference frame is just a point of view for representing the body’s motion, and (according to the principle of relativity) one can represent this motion equivalently from any inertial frame; and second, of course, the idea that the body could stay in the same inertial frame even though it is accelerating, and therefore moving non-­‐inertially. At any rate, this is a confused idea of proper time, which is not a time co-­‐ordinate and was not introduced by Einstein, but by Minkowski, in his famous paper of 1908 (Lorentz et al. 1923, 73-­‐91).

Just to add 2 cents, you can have a "momentary inertial frame" at any time, as an accelerating object effectively moves between different inertial frames. But you can't have a standard frame of reference with spatial extent follow the accelerating object, because different locations within the frame must accelerate at different times, and you'd need some additional (non-standard) definition of when those other locations follow the object. Does that make sense? It means that proper time is a measure of time at the location of the clock, but not elsewhere. I'm going off on a tangent to the main topic, other than that it's all related.

 

Edited November 11, 2019 by md65536

[Mordred]

Sounds like your describing proper acceleration see

https://en.m.wikipedia.org/wiki/Acceleration_(special_relativity)

Quote

In infinitesimal small durations there is always one inertial frame, which momentarily has the same velocity as the accelerated body, and in which the Lorentz transformation holds

you may notice that link mentions rest acceleration lol. Note the use of Infinitisimal extent. When you accelerate you undergo a type of Lorentz boost called rapidity and this changes worldlines as a worldline is as invariant.

Edited November 11, 2019 by Mordred

[md65536]

23 minutes ago, Mordred said:

Sounds like your describing proper acceleration see

https://en.m.wikipedia.org/wiki/Acceleration_(special_relativity)

you may notice that link mentions rest acceleration lol. Note the use of Infinitisimal extent.

No, there is still confusion here.

From wikipedia: "In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line."

The fact that it is invariant can be paraphrased as: Every observer (every frame of reference) agrees that the clock measured some specific (agreed upon) time at any given event along the path. Eg. everyone agrees that your watch said 12:00 when you were at the base of the mountain and 2:00 when you got to the top. What they won't all agree on is that a clock in town (a non-negligible distance away wrt. speed of light) said 12:00 when you were at the base and 2:00 when you were at the top. (And I add, if you had a drone that followed you at a fixed distance (Born rigid say), and the clock on the drone said 12:00 when you started and 2:00 when you got to the top, not everyone would agree that your watch and the drone were synchronized.)

I think "infinitesimal extent" applies to both for the same reasons.

34 minutes ago, Mordred said:

When you accelerate you undergo a type of Lorentz boost called rapidity and this changes worldlines as a worldline is as invariant.

No, your world line is defined by the path you take through 4d space, including however you accelerate. You never go off your world line, or have to change worldlines.

Say you accelerate by stepping off an inertial train, onto the ground. The world lines of you and the train diverge at that point, but you don't change worldlines.

Your worldline is invariant within its spacetime, and its particular coordinate system. The invariance means that everyone agrees that you pass through a particular set of events and that you do so at the time you measure yourself doing so. Not that the coordinates of those events in different reference frames are the same.

[Mordred]

Quote

A curve M in [spacetime] is called a worldline of a particle if its tangent is future timelike at each point. The arclength parameter is called proper time and usually denoted τ. The length of M is called the proper time of the worldline or particle. If the worldline M is a line segment, then the particle is said to be in free fall.^[

 acceleration isn't freefall. 

https://en.m.wikipedia.org/wiki/World_line

 

 

Edited November 11, 2019 by Mordred

[Eise]

On 11/9/2019 at 1:51 PM, geordief said:

Is it quite easy to research this "tensor reformulation of SR" (googling) or might a few pointers be in order?

I would say 'no'. I would say that in tensor formulation SR becomes wonderfully compact. But understanding tensors in themselves is another matter (I don't). If you are not 'fluent' with vectors and matrices, then the tensor way is definitely not easy. For a layman, sticking to simple algebra is the best way to understand SR. 

19 hours ago, geordief said:

Would you   reccommend "Gravitation" by Misner,Thorne  et al?

I wouldn't. I am sure it is a very good book, but it is a university level text book. 

[Strange]

16 hours ago, RAGORDON2010 said:

In the most dominant example - the retarded decays of unstable particles moving at speeds close to light speed - I again must fall back on my belief that these effects are in some way a consequence, in ways not at all understood, of the rapid motion of the particles through surrounding electric and magnetic fields

Unsupported beliefs have nothing to do with science. In the same way that your "other way" of looking at SR has nothing to do with SR.

[Eise]

20 hours ago, RAGORDON2010 said:

The Fact of Nature that the speed of light is the same in all inertial frames plays NO role in explaining the successful application of Special Relatively to solving physical problems!  It is a Red Herring! There is another Fact of Nature at work here.

<snap>

I would say that accelerating a particle becomes more difficult as particle speed approaches c because the external field responsible for the acceleration loses effectiveness as the particle speed approaches the speed at which the field mechanisms function.

<snip>

I hold (and this is where Special Relativity exhibits its most severe vulnerability as it is commonly described) that no physical effect can occur as a consequence of merely moving at a uniform speed in an inertial frame of reference.

So I was right. You should not teach SR because you do not understand SR, or even worse, you are thinking up wrong explanations. 

You can do two things: 

• learn here what SR really is about
• keep in love with your pet theory, and, as you seem already have chosen to do, leave the forum. 

 

 

Edited November 11, 2019 by Eise

[studiot]

15 hours ago, Schmelzer said:

On 11/5/2019 at 6:10 PM, studiot said:

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.

No, you can live in a quite comfortable way with a single frame, and apply, instead, Lorentz transformations to particular solutions.  This gives you different, Doppler-shifted solutions. 

There was a simple explanation proposed by Lorentz.  Namely, if what holds together condensed matter is the EM force, then condensed matter has to have the same symmetry properties as the EM equations.  Thus, a Lorentz-transformed (Doppler-shifted) solution for some piece of condensed matter will be a solution too.  But the Lorentz-transformed piece of matter is contracted.  

The actual explanation works in the same way, we have a lot more fields in the SM, but they all are wave equations with the same c, so that a Lorentz-transformed solution will be a solution too. 

Why do you say no ?

Although your English is very good, perhaps you didn't catch my meaning.
Yes it is true that if you are only working in one frame you can apply the Fitzgerald contraction to bodies in motion relative to that frame.
(Note You cannot apply the Lorenz transformation, since by definition, that transforms values measured in one frame to those measured in a different frame.)

But all you are then doing is finding a formula that curve fits experimental results.
There is no way, that I am aware of, of deriving that formula from fundamental theoretical principles, in a single frame.

However I am quite open to someone who knows more showing me how.

[Celeritas]

On 11/10/2019 at 6:23 PM, studiot said:

Studiot ... Did you mean ... s = √( ∆x² + ∆y² + ∆z² + ∆t²) ?

Studiot reply ... 

It is conventional to introduce the new variable tau to distinguish it from time.
tau has the units of length as do the three spatial coordinates.
This is the necessary and sufficient for treating them all equally.
It is necessary to introduce 'i' to make the coefficient of the square negative.

τ = ict

Does this help ?

Sorry this took so long. I've been down for awhile.  I also am having a little problem with the formatting of my response here.  But anyway ...

OK, I see what you mean.  I'm good with ict. It’s just that I always took “time” to be represented by the variable t (as associated with x,y,z), and tau to be time as associated with the other system (usually x’,y’,z’,t').  So t' = Tau, Tau being time in the moving system per the stationary.  ict is t represented as space.  s is units of spaceTime, and icTau = s.  So Tau is numerically equal to s, but has units of time. OEMB uses Tau for time in moving system per itself, which is not units of space.  That's what confused me.

Best regards,

Celeritas

 

No I meant substitute a new variable tau.

[RAGORDON2010]

I want to apologize to the Forum for the abrupt way in which I exited from this thread several months ago.  Time has passed, whatever was troubling me has been resolved, and I would like to continue to offer my thoughts on Special Relativity.

In particular, I would like to focus the attention of the Forum on the following question:

What is the underlying physical foundation upon which SR rests?

Or simply - Why does Special Relativity work so well?

This will require a new thread, which I hope to begin sometime in the future.

 

 

 

 

 

 

 

 

 

Edited February 15, 2020 by RAGORDON2010
I created this post with the Pages app in my Mac iOS with LaTex. I found that the LaTex Greek letters are not carried over into my post.

[swansont]

7 minutes ago, RAGORDON2010 said:

I want to apologize to the Forum for the abrupt way in which I exited from this thread several months ago.  Time has passed, whatever was troubling me has been resolved, and I would like to continue to offer my thoughts on Special Relativity.

In particular, I would like to focus the attention of the Forum on the following question:

What is the underlying physical foundation upon which SR rests?

Or simply - Why does Special Relativity work so well?

What is the shortcoming of saying it’s based on the two postulates?

 

 

[Markus Hanke]

On 2/14/2020 at 11:58 PM, RAGORDON2010 said:

What is the underlying physical foundation upon which SR rests?

On a purely non-technical, common sense level it all boils down to this - everyone experiences the same laws of physics, regardless of their state of relative motion. Whether you turn on your laptop in your living room, or while coasting along in a rocket at nearly the speed of light wrt Earth, it is going to function in the exact same manner (I use this example, because laptops are complex machines, and make use of most of physics in some way). Any experiment you perform locally in either environment will yield the exact same results, so “being in motion” is not a local, intrinsic property of something, and has no bearing on the form of the laws of physics.

When you look at this simple fact in more detail, and ask yourself what premises must hold for this to be true, you’ll eventually arrive at SR, or at least at something very close to it.

[Strange]

On 2/15/2020 at 12:58 AM, RAGORDON2010 said:

What is the underlying physical foundation upon which SR rests?

The fact that physics, and in particular the speed of light, is the same for all observers independent of their state of relative motion.

On 2/15/2020 at 12:58 AM, RAGORDON2010 said:

Or simply - Why does Special Relativity work so well?

Because that fact appears to be true of the universe we live in.

[geordief]

2 hours ago, Strange said:

The fact that physics, and in particular the speed of light, is the same for all observers independent of their state of relative motion

Can it be said that the speed of light  is an example  of the maximum speed of propagation of information and as such is measured by all observers as the same value? (I am fairly sure though that this maximum speed  is observed/posited rather than proved logically)

 

Can it also be said that all inertial observers will measure the rate of relative motion between 2  other bodies when account is taken of the spacetime interval : ie when apparent relative movement is adjusted for "real" relative movement  ?(it is a question, I am not sure of this)

[Carrock]

15 minutes ago, geordief said:

Can it be said that the speed of light  is an example  of the maximum speed of propagation of information and as such is measured by all observers as the same value? (I am fairly sure though that this maximum speed  is observed/posited rather than proved logically)

I thought the answer was 'yes' until you asked the question.

On reflection I think the speed of light is the (unachievable) upper speed limit for propagation of information.

Semi classically, infinite bandwidth (i.e. no fuzziness) would be required for light speed propagation of information.

(Alternatively, Heisenberg UP could be invoked.)

[geordief]

1 hour ago, Carrock said:

I thought the answer was 'yes' until you asked the question.

On reflection I think the speed of light is the (unachievable) upper speed limit for propagation of information.

Semi classically, infinite bandwidth (i.e. no fuzziness) would be required for light speed propagation of information.

(Alternatively, Heisenberg UP could be invoked.)

Have to admit ,I am out of my depth....

[studiot]

On 2/14/2020 at 11:58 PM, RAGORDON2010 said:

I want to apologize to the Forum for the abrupt way in which I exited from this thread several months ago.  Time has passed, whatever was troubling me has been resolved, and I would like to continue to offer my thoughts on Special Relativity.

In particular, I would like to focus the attention of the Forum on the following question:

What is the underlying physical foundation upon which SR rests?

Or simply - Why does Special Relativity work so well?

This will require a new thread, which I hope to begin sometime in the future.

 

Since you have decided to return, perhaps you would like to revisit this question of yours from earlier in the thread.

 

On 11/5/2019 at 5:40 PM, 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?

 

The answer to this is yes, but not in the way you might expect.

There are (simple) graphical ways of comparing by direct measurement on the same piece of paper both frames at once.

What is done is to compare the length of the same line as drafted (not sketched) in two different ways.

In fact more than this can be achieved.

In his book "Einstein's Theory of Relativity",   Max Born shows exactly how to do this with no more than simple high school maths.

Furthermore he derives Lorenz from this diagram in three different ways showing that each time the formula arrived at is identical.
One of these is directly from Maxwell.

 

I would thoroughly recomment this book to anyone looking for simple but correct insights.

 

 

Another good source (more easily obtainable in the US) is the treatment by Wangness in his

Introductory Topics in Modern Physics.

This is a bit more mathematical, but the author is very chatty (but still compact) and his justifications are physical, rather than mathematical.

[RAGORDON2010]

Studiot, thank you for your reply to my 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?"

To review, I used this question as a lead-in to my story about a charged ball on a speeding train exposed to an external magnetic field, and how the "at rest" observer sees that the ball begins to vertically loop, while the "moving" observer, riding on the train, sees that the ball begins to hop toward the rear of the train. I then wrote about how one could imagine inserting a firecracker in the ball and striking it with a laser beam to set off the firecracker.  Both observers would then have a fixed point in spacetime about which they could compare notes.  I had taken the idea from Einstein's light flash in his original paper.

My story was part of a presentation I had developed some time back as a way of introducing high school students to Special Relativity.  I worked around the idea of bringing the students into the story by having one group imagine that they were the research team in the "rest" frame that applied the magnetic field while the other group imagined that they were on the train with the ball.

It turned out to be useful imagery, and I found myself falling back on it from time to time.   in fact, I just referenced it again in a post I submitted last week to a thread discussing the SR twin story. 

 

[RAGORDON2010]

Strange, I appreciate the Latin - The burden of the proof lies upon him who affirms not he who denies. (Google translation)

Here's the problem as I see it.  Einstein's attempt to demonstrate that the Lorentz transformations correctly associate his "at rest" observer observations with those of his "moving" observer observations, which I discussed in an earlier post regarding his use of a stripped down Michelson interferometer, is fundamentally flawed.  The fact that he immediately jumps from there into successfully applying the Lorentz transformations to many physical problems raises real doubts in my mind about the foundations of SR.    

I hope to develop these thoughts in future posts.