SR Issue

[humbleteleskop]

The only way to give light some coordinates is to give emission and absorption events those coordinates, which is what you've done.

In actual experiments emission and absorption events do have actual coordinates. What's the problem?

That's because both frames see the same speed of light; the moving frame sees their own time and space as being the same shape (perpendicular--squares look square) as the frame at rest which sees the moving frame as a different shape (squares look like they are "squeezed" into diamond shapes), both frames 'project' their coordinate systems onto v = c. The curved lines are between the t,t' and d,d' lines in your diagram.

As long as you are not referring to some measurements everyone is free to imagine their own version of what a frame sees or not. Without measurements theories are meaningless.

 

[paddoboy]

As long as you are not referring to some measurements everyone is free to imagine their own version of what a frame sees or not. Without measurements theories are meaningless.

I don't believe that to be true.
Each FoR, will see specifically what length contraction, time dilation and the speed of light dictates.
Imagination does not come into it. Each FoR is as legitimate and valid, as each other FoR.

 

[Neddy Bate]

Notice that the event transforms to x' and t' using straight lines, not the curved lines shown in the diagram you keep posting.

That's because both frames see the same speed of light; the moving frame sees their own time and space as being the same shape (perpendicular--squares look square) as the frame at rest which sees the moving frame as a different shape (squares look like they are "squeezed" into diamond shapes), both frames 'project' their coordinate systems onto v = c. The curved lines are between the t,t' and d,d' lines in your diagram.

On a Minkowski diagram, straight lines are always used to Lorentz transform the (x,t) coordinates of an event to the (x',t') coordinates of that same event:

Above, we see (x,t)=(1.2, 1.4) transforming to (x',t')=(0.45, 0.85) and vice versa. Note the use of straight lines which are parallel to the axes.

The curved lines in your diagram are called hyperbolae of invariance, and they are not used in Lorentz transforming the coordinates of an event. More detailed explanations and diagrams can be found here:

http://lgsims96.hubpages.com/hub/Minkowski-Diagram#

 

[arfa brane]

The curved lines in your diagram are called hyperbolae of invariance, and they are not used in Lorentz transforming the coordinates of an event.

You misunderstood what I said about the hyperbolic curves. They represent the shape the Lorentz transforms must have, whether or not you "use" them, you use straight lines because velocities are straight lines, and because you have a rest frame. This doesn't change the underlying shape of the functions (my point).

This is what it says at your linked page:

If we plot a single coordinate at many different velocities using the inverse Lorentz transformations, it will trace a hyperbola on the diagram. This is the hyperbola of invariance because every point on the curve is the same coordinate for the object at a different relative velocity to the observer.

 

[Neddy Bate]

You misunderstood what I said about the hyperbolic curves. They represent the shape the Lorentz transforms must have, whether or not you "use" them, you use straight lines because velocities are straight lines, and because you have a rest frame. This doesn't change the underlying shape of the functions (my point).

This is what it says at your linked page:

If we plot a single coordinate at many different velocities using the inverse Lorentz transformations, it will trace a hyperbola on the diagram. This is the hyperbola of invariance because every point on the curve is the same coordinate for the object at a different relative velocity to the observer.

Yes the hyperbolic curves arise when "many different velocities" are considered. I think you and I are in general agreement now. I think you agreed earlier that light emission and absorption events can be described by spacetime coordinates. Therefore, we can assign spacetime coordinates to a propagating light ray by placing a series of half-silvered mirrors in its path, and measuring the time and location of that series of absorption events. Thus, light itself can be described with spacetime coordinates. Agreed?

 

[humbleteleskop]

Therefore, we can assign spacetime coordinates to a propagating light ray by placing a series of half-silvered mirrors in its path, and measuring the time and location of that series of absorption events. Thus, light itself can be described with spacetime coordinates. Agreed?

You have my vote. I don't get it how did that even come under question. Too much abstract theory without an anchor in reality, possibly. Hypothetical scenarios need to be set up as if they were real, with emitters and sensors, and clocks and wires, and all that. Otherwise what is supposed to be only hypothetical ends up being untestable and delusional.

 

[arfa brane]

Therefore, we can assign spacetime coordinates to a propagating light ray by placing a series of half-silvered mirrors in its path, and measuring the time and location of that series of absorption events. Thus, light itself can be described with spacetime coordinates. Agreed?

It's a fine point.

You can't give light propagating through space any coordinates, unless you know where and when it was emitted. This is for the fundamental reason that you can't see light propagating; you can propagate it in a rest frame or a frame in motion relative to a rest frame, and you can detect or reflect it back towards the source, or elsewhere, but you can't otherwise assign "events" to light.

What you're really doing by placing mirrors is assigning coordinates to them, then, light being reflected/transmitted at each mirror is an event. Likewise, calculating the distance along v = c that an expanding wavefront has reached is only possible because you know the time and location of the emission event. If you placed a mirror at this distance, you know a reflection event would occur (like, even when there isn't any mirror and so no event).

So you can say, "if a mirror was located at (x,y,z), then light would reach it after time t", if there is no mirror this is still true, but does that mean it's an event, strictly speaking?

 

[humbleteleskop]

So you can say, "if a mirror was located at (x,y,z), then light would reach it after time t", if there is no mirror this is still true, but does that mean it's an event, strictly speaking?

Event implies interaction. No interaction - no event. But you can make it an event in both hypothetical and actual scenarios, only first you should really know what is it you are actually trying to do, and why.

 

[paddoboy]

To arfa and Neddy.
The over riding issue in this thread is that chinglu is claiming his example proves SR invalid.
You both agree that he is in error, and that's what counts.

 

[Neddy Bate]

To arfa and Neddy.
The over riding issue in this thread is that chinglu is claiming his example proves SR invalid.
You both agree that he is in error, and that's what counts.

I'd like to see chinglu make a Minkowski diagram of his claims. If he is trying to prove SR incorrect, then all he has to do is show us a Minkowski diagram which contradicts SR. lol

 

[paddoboy]

I'd like to see chinglu make a Minkowski diagram of his claims. If he is trying to prove SR incorrect, then all he has to do is show us a Minkowski diagram which contradicts SR. lol

Thanks Neddy.
That is the crazy point that chinglu is insidiously trying to make.
It's something he has been pushing since I have been here, and appears to be driven by some Interpretation of creationist's drivel.

I remember a quite lengthy thread with him declaring that time dilation DID NOT HAPPEN.
And no matter how much I and many others gave the many obvious examples, he simply claimed it did not happen, and the world was full of misinformed Idiots.

 

[Neddy Bate]

Assume M and M' are the origins of 2 frames and in the M' frame, there is an observer C' located at $$(\frac{-vd'}{c},0,0)$$ with $$d'>0$$.

When M and M' are co-located, lightning strikes their command location.

Here is the question, when C' and M are co-located, where is the lightning along the positive x-axis for both frame coordinate systems?

Okay, I have chosen v=0.500c and d'=1.000 thus C' is always located at x'=-0.500. The lightning strike has coordinates x=0.000, t=0.000, x'=0.000, t'=0.000.

Here is a Minkowski diagram showing the event when C' is co-located with M:

According to the M frame, the co-location event has a time coordinate of t=0.866, and because c=1.000 that means the light pulse must be located at x=ct=0.866 at that time.

According to the M' frame, the co-location event has a time coordinate of t'=1.000, and because c=1.000 that means the light pulse must be located at x'=ct'=1.000 at that time.

Note that the grey dashed lines represent planes of simultaneity for both frames, and that they do in fact intersect the the worldline of the light pulse at the expected locations and times.

 

[paddoboy]

Okay, I have chosen v=0.500c and d'=1.000 thus C' is always located at x'=-0.500. The lightning strike has coordinates x=0.000, t=0.000, x'=0.000, t'=0.000.

Here is a Minkowski diagram showing the event when C' is co-located with M:

According to the M frame, the co-location event has a time coordinate of t=0.866, and because c=1.000 that means the light pulse must be located at x=ct=0.866 at that time.

According to the M' frame, the co-location event has a time coordinate of t'=1.000, and because c=1.000 that means the light pulse must be located at x'=ct'=1.000 at that time.

Note that the grey dashed lines represent planes of simultaneity for both frames, and that they do in fact intersect the the worldline of the light pulse at the expected locations and times.

Nice Eddy...I have some travelling to do today, so I must be off....but rest assured chinglu will not accept that.
He was unable to ever accept time dilation after many examples were shown to him.

 

[humbleteleskop]

According to the M' frame, the co-location event has a time coordinate of t'=1.000, and because c=1.000 that means the light pulse must be located at x'=ct'=1.000 at that time.

Note that the grey dashed lines represent planes of simultaneity for both frames, and that they do in fact intersect the the worldline of the light pulse at the expected locations and times.

Is there anything I shouldn't be able to explain with classical physics?

 

[arfa brane]

Note how in this diagram, the distance from the origin O to P is given by two other straight lines (like position vectors), these are the timelike and spacelike components of OP as seen by the rest frame.

Contrary to expectations, the coordinate quantity t does not itself describe time as measured by an accurate clock unless it is 'at rest' in our coordinate system ... which means the clock would have a worldline that is vertical ...
Thus, t means "time" only for observers who are 'stationary' (i.e. with vertical worldlines). The correct measure of time for a moving observer ... is provided by the [Minkowski distance].

So the distance OP corresponds to the time experienced by the observer at P, and the at rest observer sees this interval as having a spacelike component.

Or have I slipped up somewhere?

 

[Trippy]

Is there anything I shouldn't be able to explain with classical physics?

The precession of the orbit of mercury.
The measured deviation of starlight passing close to the sun.
The observed orbital decay rate of the Huse-Taylor binary system.
The extended half-lives of muons created by cosmic ray spallation in the earths atmosphere.
Cherenkov radiation.
The colour of gold.
The results of Gravity Probe B.
Gravitational lensing in the bullet cluster.

 

[humbleteleskop]

The precession of the orbit of mercury.
The measured deviation of starlight passing close to the sun.
The observed orbital decay rate of the Huse-Taylor binary system.
The extended half-lives of muons created by cosmic ray spallation in the earths atmosphere.
Cherenkov radiation.
The colour of gold.
The results of Gravity Probe B.
Gravitational lensing in the bullet cluster.

I meant in that particular example given by Neddy Bate in that post I was replying to.

 

[humbleteleskop]

So the distance OP corresponds to the time experienced by the observer at P, and the at rest observer sees this interval as having a spacelike component.

"sees this interval as having a spacelike component." <- what real world type of measurement would that correspond to? What is the practical meaning or consequence of that which you are talking about?

 

[rpenner]

Okay, I have chosen v=0.500c and d'=1.000 thus C' is always located at x'=-0.500. The lightning strike has coordinates x=0.000, t=0.000, x'=0.000, t'=0.000.

Here is a Minkowski diagram showing the event when C' is co-located with M:

[Image]

According to the M frame, the co-location event has a time coordinate of t=0.866, and because c=1.000 that means the light pulse must be located at x=ct=0.866 at that time.

According to the M' frame, the co-location event has a time coordinate of t'=1.000, and because c=1.000 that means the light pulse must be located at x'=ct'=1.000 at that time.

Note that the grey dashed lines represent planes of simultaneity for both frames, and that they do in fact intersect the the worldline of the light pulse at the expected locations and times.

Great work in graphing the OP. Here's Post #2 drawn as an overlay of your image:

 

[Neddy Bate]

According to the M frame, the co-location event has a time coordinate of t=0.866, and because c=1.000 that means the light pulse must be located at x=ct=0.866 at that time.

According to the M' frame, the co-location event has a time coordinate of t'=1.000, and because c=1.000 that means the light pulse must be located at x'=ct'=1.000 at that time.

Note that the grey dashed lines represent planes of simultaneity for both frames, and that they do in fact intersect the the worldline of the light pulse at the expected locations and times.

Is there anything I shouldn't be able to explain with classical physics?

Well, each of the two frames measures the velocity of the light pulse moving along the x & x' axes to be c, as indicated by the two equations given above:

x = ct
x' = ct'

If the M frame measures the velocity of the light pulse to be c, and the velocity of the M' frame to be v, then classical Gallilean physics would say that the M' frame should measure the velocity of the light pulse to be c-v. That was never found to be the case experimentally, and so relativity was born.