The burn mark problem

[Jack_]

This is not a coherent sentence, irrespective of whether LT means 'Lorentz transformations' or 'a Lorentz transformation'. A Lorentz transformation is a map from one set of coordinates to another. Each set of coordinates is defined on a tangent space (or rather there's a natural link between the coordinates of M and those of TM), which can sometimes be (and in relativity is) given an inner product in the form of a metric. The Lorentz transformations are defined by the requirement they leave this metric invariant in SR. A Lorentz transformation is representable by a matrix. It doesn't have 'geometry', the underlying metric space (M,g) has a geometry (where M is the space-time manifold and g is the metric). You can represent a Lorentz transformation by the difference in how a particular system is represented in two different coordinate systems but such diagrams are space-time diagrams (of the kind used in this thread) and the Lorentz transformation is deduced from the world lines of each frame. You can talk about the structure (or loosely, the 'geometry') of the group of Lorentz transformations, such as the fact its not simply connected (or even connected) but this is something entirely more abstract and talks about how you embed all matrices which represent Lorentz transformations within a particular matrix set, such as $$SO(n,1) \subset GL(n+1,\mathbb{R})$$.

Your misuse of such terminology, your earlier throwing around of Godel's work and your mention of 'the GR manifold' makes it seem like you don't understand the terminology you're using and you're simply trying to make it appear you grasp more than you actually do.

Good glad to see you.

Let's see, SR models physical reality.

Now, draw the picture and explain LT piece by piece for the problem.

Your misuse of such terminology, your earlier throwing around of Godel's work

If you would like to claim it is false that a theory is consistent iff it has a model, then do that since that is what I said.

Otherwise, you agree I am correct and you can get back to that picture.

 

[Jack_]

Look at the shaded sections more closely. Do you see how they show they represent the scenario according to O at two moments in time?

If you can follow how that diagram represents your scenario in the rest frame of O, then we can move on to figuring out what SR says about the rest frame of O'.

If you still have trouble, we might have to try animations.

Good, now you have the diagram for O stationary. But, this is about the control being the burn mark meeting O' and not time.

Also, show the diagram with O' stationary, since that is the relativity postulate to consider both frames stationary.

Then, if you like, put all that together with animations.

After all this is done, then I say we play with LT.

 

[CptBork]

If you would like to claim it is false that a theory is consistent iff it has a model, then do that since that is what I said.

Otherwise, you agree I am correct and you can get back to that picture.

I know this was addressed to Alphanumeric, and I can't speak on his behalf, but I'd like to know what's wrong about my own personal definition of Godel's Completeness Theorem, and if it's not wrong, then I'd like to know how it relates to your own definition. My personal definition came from http://mathworld.wolfram.com, and I double checked it on Wikipedia as well. The link you gave me was to a book I'd have to purchase and the page you cited wasn't included in the free preview. I also have a book on Model Theory in my personal archives, and I couldn't find any theorem such as what you're claiming.

I'm not terribly well-versed in the deeper formalities of logic theory, but I don't see how your statement makes any sense. What would make sense would be a more trivial statement such as "a theory is self-consistent iff it is self-consistent for every model constructed in that theory". If your own statement were true, that would mean an inconsistent theory couldn't have a model, whereas I don't see why you couldn't construct a model based on contradictory axioms.

 

[Jack_]

This is not a coherent sentence, irrespective of whether LT means 'Lorentz transformations' or 'a Lorentz transformation'. A Lorentz transformation is a map from one set of coordinates to another. Each set of coordinates is defined on a tangent space (or rather there's a natural link between the coordinates of M and those of TM), which can sometimes be (and in relativity is) given an inner product in the form of a metric. The Lorentz transformations are defined by the requirement they leave this metric invariant in SR. A Lorentz transformation is representable by a matrix. It doesn't have 'geometry', the underlying metric space (M,g) has a geometry (where M is the space-time manifold and g is the metric). You can represent a Lorentz transformation by the difference in how a particular system is represented in two different coordinate systems but such diagrams are space-time diagrams (of the kind used in this thread) and the Lorentz transformation is deduced from the world lines of each frame. You can talk about the structure (or loosely, the 'geometry') of the group of Lorentz transformations, such as the fact its not simply connected (or even connected) but this is something entirely more abstract and talks about how you embed all matrices which represent Lorentz transformations within a particular matrix set, such as $$SO(n,1) \subset GL(n+1,\mathbb{R})$$.

Your misuse of such terminology, your earlier throwing around of Godel's work and your mention of 'the GR manifold' makes it seem like you don't understand the terminology you're using and you're simply trying to make it appear you grasp more than you actually do.

Now, Pete, LT must have a geometry.

Obviously, I meant the output of LT.

Let's see now, assume O is stationary, since this was the topic.

Are you saying the below is false?

x' = (x - vt)λ

O---vt---O'---------x'/λ-----------x

As we can clearly see,

vt + x'/λ = x

x'/λ = x - vt

x' = ( x - vt )λ

 

[Jack_]

I know this was addressed to Alphanumeric, and I can't speak on his behalf, but I'd like to know what's wrong about my own personal definition of Godel's Completeness Theorem, and if it's not wrong, then I'd like to know how it relates to your own definition. My personal definition came from http://mathworld.wolfram.com, and I double checked it on Wikipedia as well. The link you gave me was to a book I'd have to purchase and the page you cited wasn't included in the free preview. I also have a book on Model Theory in my personal archives, and I couldn't find any theorem such as what you're claiming.

I'm not terribly well-versed in the deeper formalities of logic theory, but I don't see how your statement makes any sense. What would make sense would be a more trivial statement such as "a theory is self-consistent iff it is self-consistent for every model constructed in that theory". If your own statement were true, that would mean an inconsistent theory couldn't have a model, whereas I don't see why you couldn't construct a model based on contradictory axioms.

Yes, I see your issue about this book.

If you go to rpenner's forum, he somehow found the book online or ask him how he found it.

I said your description is correct. I also said I use the extended completeness theorem.

What would make sense would be a more trivial statement such as "a theory is self-consistent iff it is self-consistent for every model constructed in that theory". If your own statement were true, that would mean an inconsistent theory couldn't have a model, whereas I don't see why you couldn't construct a model based on contradictory axioms.

As, I said, a model is a universe of points with functions, relations, and named constants.

From this universe, you assign to formulas in the theory their actual values and evaluate the truth of the statement.

In the case of SR, universal generalization is used for the two postulates such that the postulates must be satisified by all instances of light and frame motion using "reality" as a model.

Now, for "self-consistency" one would have to provide all consequences of the axioms and in fact prove they have all consequences. This way, we know there is not a consequence (A and not A) proved from the theory.

There is no such collection of complete consequences from SR.

Finally, the light postulate says light moves at c regardless of the motion of the light source.

Now, you may want to measure it.

Then SR claims the light path is exactly the distance between the light emission point in the frame and the light receiver.

Question, can you prove this from the two axioms?

You will find you cannot and therefore, it is independent of the two axioms of SR.

Therefore, in fact, it is the third axiom.

 

[Jack_]

This is not a coherent sentence, irrespective of whether LT means 'Lorentz transformations' or 'a Lorentz transformation'. A Lorentz transformation is a map from one set of coordinates to another. Each set of coordinates is defined on a tangent space (or rather there's a natural link between the coordinates of M and those of TM), which can sometimes be (and in relativity is) given an inner product in the form of a metric. The Lorentz transformations are defined by the requirement they leave this metric invariant in SR. A Lorentz transformation is representable by a matrix. It doesn't have 'geometry', the underlying metric space (M,g) has a geometry (where M is the space-time manifold and g is the metric). You can represent a Lorentz transformation by the difference in how a particular system is represented in two different coordinate systems but such diagrams are space-time diagrams (of the kind used in this thread) and the Lorentz transformation is deduced from the world lines of each frame. You can talk about the structure (or loosely, the 'geometry') of the group of Lorentz transformations, such as the fact its not simply connected (or even connected) but this is something entirely more abstract and talks about how you embed all matrices which represent Lorentz transformations within a particular matrix set, such as $$SO(n,1) \subset GL(n+1,\mathbb{R})$$.

Your misuse of such terminology, your earlier throwing around of Godel's work and your mention of 'the GR manifold' makes it seem like you don't understand the terminology you're using and you're simply trying to make it appear you grasp more than you actually do.

Furthermore, why not have rpenner come here.

He needs to explain why he lifted his hand to me when I used the integral for uniform acceleration in the context of the accelerating frame with proper acceleration and proper burn times. He claimed you integrate within the context of the stationary frame relative to the accelerating frame. He never backed up his logic.

Yet, that frame cannot establish the termination time point for the integral.

My integration is all over the literature.
http://www.ejournal.unam.mx/rmf/no521/RMF52110.pdf
http://arxiv.org/PS_cache/physics/pdf/0411/0411233v1.pdf

 

[James R]

Good, now you have the diagram for O stationary. But, this is about the control being the burn mark meeting O' and not time.

Also, show the diagram with O' stationary, since that is the relativity postulate to consider both frames stationary.

Then, if you like, put all that together with animations.

After all this is done, then I say we play with LT.

Why should Pete do all the work for you? Why don't you do the diagram for O' stationary?

 

[Jack_]

Why should Pete do all the work for you? Why don't you do the diagram for O' stationary?

I already did.

Pete was trying to commit the one frame absolute fallacy.
I called him on it.

My diagram shows both.

 

[James R]

Jack_:

It's called relativity. Doesn't that suggest to you that there are no absolute frames in the theory?

 

[Pete]

Then SR claims the light path is exactly the distance between the light emission point in the frame and the light receiver.

That a definition of distance travelled. It's an axiom of Newton's laws just as much as it is an axiom of SR.

 

[Pete]

Now, Pete, LT must have a geometry.

Obviously, I meant the output of LT.

Well, it's not what you said. But, I'll grant that it could be impliedin the context in which you said it, which was relating to your statement that your diagram is "that of LT". So it seems that you meant that your diagram has the geometry required for a lorentz transform?
Well, that's wrong. A lorentz transform requires both space and time coordinates, while your diagram only included space.
But, let's move on.

x' = (x - vt)λ

O---vt---O'---------x'/λ-----------x

As we can clearly see,

vt + x'/λ = x

x'/λ = x - vt

x' = ( x - vt )λ

This is correct, but not complete, as we shall see...

 

[Pete]

Good, now you have the diagram for O stationary.

Yes, I have the diagram for O stationary. It's the same one as I had way back in post #22. I'm glad you understand it now.

But, this is about the control being the burn mark meeting O' and not time.

Do you think you can pretend that time doesn't exist? Do you want to think about the real world or not?
The burn mark is a marker for a particular location in the rest frame of O.
The burn mark meeting O' is a marker for a particular event. It marks both a time and a location, in both rest frames.
This thread is really about how that marked time and location relates to other events, and how those relationships differ in different frames of reference.

Also, show the diagram with O' stationary, since that is the relativity postulate to consider both frames stationary.

Yes, post 22 also includes the diagram for O' stationary. But just for you, I'll post that diagram again in the same style as the previous one (with the x-axis horizontal, and with the same events shaded):

The first thing you will notice is that the shaded slices have been skewed by the lorentz transform, similarly to the way the the paths of O and O', and the burn mark are skewed.

We expected the paths of O, O', and the burn mark to be skewed, of course, because their velocity is different in the two frames of reference. The burn mark, for example, is stationary according to O so it's path was always on the same value of x. But it is moving according to O, so the x-value of its path changes with time.

But the skewing of the shaded slices will probably come as a surprise if you haven't used the lorentz transform before. What it indicates is that things that happen at the same time but different location in the rest frame of O happen at different times in the rest frame of O'.

In your diagram, your snapshots of the rest frame of O can't be transformed to a snapshots of the rest frame of O'. A simultaneous slice of O does not transform to a simultaneous slice of O'.

A brief aside:

I think that relative simultaneity is really the soul of special relativity. If you start from skewing simultaneous slices in symmetry with skewing stationary paths, you can easily derive everything else - length contraction, time dilation, and a frame-independent speed. I think that people could learn what relativity says much more easily if the started with the relativity of location (ie Galileo's relativity), and then went directly to the relativity of simultaneity (Einstein's relativity).

Galileo: "These things happened in the same place" only means something if you know the context (the reference frame).
In the same place on Earth's surface?
In the same place on the ship?
In the same place in the Solar system?

Einstein: Same goes for "These things happened at the same time"!​

In the next post, we'll look more closely at those diagrams and your diagrams to confirm that your maths for transforming x to x' is correct.

 

[Jack_]

Jack_:

It's called relativity. Doesn't that suggest to you that there are no absolute frames in the theory?

Agreed, that is why I told Pete that he needed to include O' as stationary.
Othewise, we are selecting a preferred frame to solve the problem.

 

[Jack_]

Yes, I have the diagram for O stationary. It's the same one as I had way back in post #22. I'm glad you understand it now.

Do you think you can pretend that time doesn't exist? Do you want to think about the real world or not?
The burn mark is a marker for a particular location in the rest frame of O.
The burn mark meeting O' is a marker for a particular event. It marks both a time and a location, in both rest frames.
This thread is really about how that marked time and location relates to other events, and how those relationships differ in different frames of reference.

Yes, post 22 also includes the diagram for O' stationary. But just for you, I'll post that diagram again in the same style as the previous one (with the x-axis horizontal, and with the same events shaded):

The first thing you will notice is that the shaded slices have been skewed by the lorentz transform, similarly to the way the the paths of O and O', and the burn mark are skewed.

We expected the paths of O, O', and the burn mark to be skewed, of course, because their velocity is different in the two frames of reference. The burn mark, for example, is stationary according to O so it's path was always on the same value of x. But it is moving according to O, so the x-value of its path changes with time.

But the skewing of the shaded slices will probably come as a surprise if you haven't used the lorentz transform before. What it indicates is that things that happen at the same time but different location in the rest frame of O happen at different times in the rest frame of O'.

In your diagram, your snapshots of the rest frame of O can't be transformed to a snapshots of the rest frame of O'. A simultaneous slice of O does not transform to a simultaneous slice of O'.


I think that relative simultaneity is really the soul of special relativity. If you start from skewing simultaneous slices in symmetry with skewing stationary paths, you can easily derive everything else - length contraction, time dilation, and a frame-independent speed. I think that people could learn what relativity says much more easily if the started with the relativity of location (ie Galileo's relativity), and then went directly to the relativity of simultaneity (Einstein's relativity).
Galileo: "These things happened in the same place" only means something if you know the context (the reference frame). In the same place on Earth's surface? In the same place on the ship? In the same place in the Solar system?
Einstein: Same goes for "These things happened at the same time"!

In the next post, we'll look more closely at those diagrams and your diagrams to confirm that your maths for transforming x to x' is correct.

Do you think you can pretend that time doesn't exist? Do you want to think about the real world or not?
The burn mark is a marker for a particular location in the rest frame of O.
The burn mark meeting O' is a marker for a particular event. It marks both a time and a location, in both rest frames.
This thread is really about how that marked time and location relates to other events, and how those relationships differ in different frames of reference

No, the burn mark is a control. It does not need time. The distance to the burn mark determines the outcome of the experiment not the clocks. They are incldental.

Hey, where is the O' frame as stationary?

Well now, I have circumvented space-time and used only space to control an experiment.

What do you think of that?

That implies time is lower than space.

 

[Pete]

No, the burn mark is a control. It does not need time. The distance to the burn mark determines the outcome of the experiment not the clocks. They are incldental.

No, you said (and I quote): ...this is about the control being the burn mark meeting O'
That needs time. The burn mark meets O' at a time.
Jack, remember what we agreed at the start?
We'll never get any smarter if we're not open to learning something.

Hey, where is the O' frame as stationary?

Can't you see it? I can, but perhaps there's some network problem.

 

[Jack_]

No, you said (and I quote): ...this is about the control being the burn mark meeting O'
That needs time. The burn mark meets O' at a time.
Jack, remember what we agreed at the start?
We'll never get any smarter if we're not open to learning something.


Can't you see it? I can, but perhaps there's some network problem.

See, time may occur, whatever that means.

But, I have figured out a way to eliminate the clock based on the relative motion and light.

I am comparing motion directly to light.

I am wondering why you force yourself to inject clocks when this experiment does not need them.

Please explain.

When you have learned enough, you will find you can compare any motion to the motion of light and clocks are a sideshow.

See, light always travels through space at one speed. That is sure dependable.

 

[James R]

Jack_:

Agreed, that is why I told Pete that he needed to include O' as stationary.

O' is stationary in post #152. Did you follow Pete's explanation in that post?

No, the burn mark is a control. It does not need time. The distance to the burn mark determines the outcome of the experiment not the clocks. They are incldental.

Your experiment involves a travelling light beam and an observer O' who moves relative to O. Things can only move if there is time, so your experiment necessarily involves time.

Hey, where is the O' frame as stationary?

See Pete's diagram and explanation in post #152.

You can see that the x' coordinate of O' is zero at all times. The location of O' is indicated by the red line on the graph, which is always located at the same x' location, so it is stationary.

Do you understand this?

I am wondering why you force yourself to inject clocks when this experiment does not need them.

Clocks are not needed, but time is unavoidable.

Now, Pete has taken quite a lot of time and effort in this thread in an attempt to educate you about your own scenario, which you do not appear to fully grasp.

You are not giving any signs of even being able to comprehend the spacetime diagrams that Pete has posted.

Have you even tried to understand them, or is it that they are beyond your ability to comprehend?

I'm seeing a lot of nervous "LOL"s from you, but not much substantive discussion of the points put to you.

Why don't you address the points that Pete has put to you, instead of pretending you are superior to people who have actually studied relativity formally?

 

[Pete]

See, time may occur, whatever that means.

But, I have figured out a way to eliminate the clock based on the relative motion and light.

Yay, you have no clock!
When you figure out a way to eliminate time, come back and we'll talk.

I am wondering why you force yourself to inject clocks when this experiment does not need them.

What clock? I have never mentioned a clock. I have only pointed out that things in this scenario happen at different times.

Are you really maintaining that everything in your experiment happens at the same time, or are you just being obstinate?

 

[Pete]

Now, Pete has taken quite a lot of time and effort in this thread in an attempt to educate you about your own scenario, which you do not appear to fully grasp.

Well, It's also about educating myself. I learn something new every time I work a scenario through, and dissecting it in this way is good.
I'm also learning some diagramming techniques, and coming up with ways of making them better.

 

[Jack_]

Jack_:



O' is stationary in post #152. Did you follow Pete's explanation in that post?

Yea, he did not show it the way he showed O as stationary and he knows better.

Your experiment involves a travelling light beam and an observer O' who moves relative to O. Things can only move if there is time, so your experiment necessarily involves time.

No, it involves a preprogrammed burn mark that controls the logic.
I do not need clocks. Are you going to say if humans did not have clocks then the earth would not move around the sun? How silly.

Do you understand this?

Nope, Pete provided a linear drawing for O stationary and refuses to provide one with O' stationary so we can compare them.

Clocks are not needed, but time is unavoidable.

Now, Pete has taken quite a lot of time and effort in this thread in an attempt to educate you about your own scenario, which you do not appear to fully grasp.

You are not giving any signs of even being able to comprehend the spacetime diagrams that Pete has posted.

Have you even tried to understand them, or is it that they are beyond your ability to comprehend?

I'm seeing a lot of nervous "LOL"s from you, but not much substantive discussion of the points put to you.

Why don't you address the points that Pete has put to you, instead of pretending you are superior to people who have actually studied relativity formally?

Oh, I can break relotovity many ways.

This is one sample.

I provided the drawing and you all continue to use worldlines that do not consider the diverging origins.

For me to use those, that would imply I must leave off scientific evidence.

Doi you want to do this?