Frames vs Lines of Simultaneity

[Mentz114]

Hmmm.
If I have a rotation, my choice of words are rather limited. I can talk of a rotation, or perhaps a revolution. If I am talking about a Lorentz Boost, though, I can call it a Lorentz Transformation, a hyperbolic rotation, an acceleration, a change in velocity, a change in inertial reference frames. Whoever started the habit of calling Lorentz Boost's "rotations" started an unfortunate trend, in my opinion.

Mea culpa. I misused 'rotation', but thought it was obvious it was a Lorentz boost. It just looks like a spatial rotation on the diagram.

As for "here and now" being subjective; that is quite so. In this case "subjective" is not a negative word, but a positive word. Remember, we are talking about relativity, which is essentially the study of subjective measurement. "Here" and "now" are both subjective, and so are "which way is forward; which way is up" and also "how fast and what direction are you going?"

"Here and Now" affects the origin of the diagram
"Which way is forward and which way is up" affects the rotation of the diagram.
"how fast are you going" affects the Lorentz Boost; which determines which world-lines are perpendicular to the lines of simultaneity.

It's all subjective, but it is also all well-defined.

Fine, I have no problem with that.

 

[JDoolin]

You may have seen these before, but there are a couple good graphics showing the visual difference between rotation transformation and Lorentz Transformation on http://casa.colorado.edu/~ajsh/sr/wheel.html" .

And there's the http://commons.wikimedia.org/wiki/File:Animated_Lorentz_Transformation.gif" at Wikipedia, which was inspired, partially, by Andrew Hamilton's work.

And, of course, your demo does it too. Here, I've attached a file called "here and now axes." Load the project into your Minkowski program. There are three events to the left, three events to the right, three events in the future, and three events in the past, and an origin.

Put in a boost by .01 and hit the boost button several times. You should see how the line of simultaneity (horizontal) rotates counterclockwise, in the opposite direction from the world-line (vertical).

 

[Mentz114]

You may have seen these before, but there are a couple good graphics showing the visual difference between rotation transformation and Lorentz transformation on Andrew Hamilton's website.

Please, I may have erred by using 'rotation' to describe the LT in my program, but I do know the difference.

And, of course, your demo does it too. Here, I've attached a file called "here and now axes." Load the project into your Minkowski program. There are three events to the left, three events to the right, three events in the future, and three events in the past, and an origin.

That's interesting. I haven't seen that done. It looks as if the axes are transforming when the events are boosted. I'll have to think about that.

[later]Aha. The events along the x-axis all happen simultaneously in the rest frame of the diagram. When it's boosted, so we're now viewing the events from a moving frame, they are no longer simultaneous. Cool. It illustrates the relativity of simultaneity.

The events on the t-axis all happen in the same place but at different times, in the rest frame of the diagram. Boosted, they now appear to happen in different places, with different intervals. Doppler effect ?

 

[Austin0]

If I understand you correctly I agree 100%

Oh, good. It's a rare thing for anyone to agree with me.

I find that hard to believe

The spacetime diagram shows the past and future of the worldlines. 'Now' is anywhere we choose on a worldline and belongs to that worldline.

Of course ,,,and whatever point you choose on the worldline** has attached a line of simultaneity which graphs the position and times [of the colocated clocks in the other frame] of all the clocks in that** frame that are simultaneously [ a conventional assumption] reading the same proper time.
Would yu agree?

But can I assume you do think lines of simultaneity for inertial frames are useful for telling local clock relationships at different locations?

I can't have an opinion on that because I don't understand 'lines of simultaneity'.

Well as far as I can see they are just the ruler and clocks of the frame itself. Extended in space so if the range exceeds the actual physical bounds of the frame's ruler it is extended by a virtual ruler with clocks and observers. This is exactly the point of the OP

Apparently they connect ( light rays ?) events that are simultaneous according to some rule ? But simultaneity is not very meaningful if events are spatially separated is it ?

Yes we are agreed that simultaneity has no real meaning regarding spatially separated events.
But it does have objective meaning as far as predicting local [colocal] clock relationships between inertial frames. That both frames will always agree regarding these local events. Make sense??

 

[Mentz114]

Make sense??

As I've said I have no quibble with the way you see things, I just have a different POV.

 

[JDoolin]

Please, I may have erred by using 'rotation' to describe the LT in my program, but I do know the difference.



That's interesting. I haven't seen that done. It looks as if the axes are transforming when the events are boosted. I'll have to think about that.

[later]Aha. The events along the x-axis all happen simultaneously in the rest frame of the diagram. When it's boosted, so we're now viewing the events from a moving frame, they are no longer simultaneous. Cool. It illustrates the relativity of simultaneity.

The events on the t-axis all happen in the same place but at different times, in the rest frame of the diagram. Boosted, they now appear to happen in different places, with different intervals. Doppler effect ?

:) Cool

Maybe not the Doppler effect. Maybe the "relativity of simultaneity." I prefer to call it "desynchronization" but that's never caught on.

My perception has been that most of the time I've encountered people who talk about the Relativistic Doppler effect, they are just talking about a more precise means to calculate redshift and blueshift. They may or may not be aware of the relativity of simultaneity.

If your idea of the Doppler effect involves an elongated version of the object coming toward you superluminally, with a high blue-shift, and then a shortened red-shifted version of the object, receding from you by, then yes, it's the Relativistic Doppler effect.

However, this phenomenon is already called by another name; Penrose http://en.wikipedia.org/wiki/Terrell_rotation" .

 

[Austin0]

As I've said I have no quibble with the way you see things, I just have a different POV.

Likewise. I am just not really sure rnough of your POV to even know if there is any disagreement whatsoever. You have said you don't understand lines of simultaneity, but judging by your other posts it appears you are fully knowledgeable in all aspects. So?
But no worries

 

[Austin0]

:) Cool

Maybe not the Doppler effect. Maybe the "relativity of simultaneity." I prefer to call it "desynchronization" but that's never caught on.

My perception has been that most of the time I've encountered people who talk about the Relativistic Doppler effect, they are just talking about a more precise means to calculate redshift and blueshift. They may or may not be aware of the relativity of simultaneity.

If your idea of the Doppler effect involves an elongated version of the object coming toward you superluminally, with a high blue-shift, and then a shortened red-shifted version of the object, receding from you by, then yes, it's the Relativistic Doppler effect.

However, this phenomenon is already called by another name; Penrose http://en.wikipedia.org/wiki/Terrell_rotation" .

Desynchronization is fine with me. But what do you mean by "superluminally"

and I am fairly sure The Penrose-Terrell effect is a purely visual distortion as a consequence of the finite propagation speed of light and different path lengths from various parts of an object to the POV
cheers

 

[JDoolin]

Desynchronization is fine with me. But what do you mean by "superluminally"

and I am fairly sure The Penrose-Terrell effect is a purely visual distortion as a consequence of the finite propagation speed of light and different path lengths from various parts of an object to the POV
cheers

http://en.wikipedia.org/wiki/Superluminal_motion

Superluminal motion, the Penrose Terrell effect and the Relativistic Doppler effect are all three purely visual distortions as a consequence of the finite propagations speed of light.

...and I overgeneralized: The relativistic Doppler effect won't cause superluminal motion for small velocities of course.

Jonathan