Erik says, in his last post that "The idea of stitching together frames makes sense." He italicizes the word "frames" though, as if somehow, stitching together "parts of frames" as I do in the video in Hydra 10, below.
He wants me to define what I mean by "stitching" which is obviously, not only defined, but demonstrated in the video. Of course, I could do that again, but what is the point, if he's intent on not watching it?
Perhaps a video demonstration with Mathematica would help? Perhaps, literally taking out pieces of paper and filming that process?
The other aspect of that Erik is claiming that some proof of pseudogravity at great distances exists... But he cannot show me that proof, and does not seem to see any importance of showing that proof, since supposedly everyone already knows about it from hear-say. Well, I shouldn't have to hear about such a simple proof from hearsay. I should be able to see it, right in front of me.
Here's the wierdest part of Erik's argument: ""You have been arguing that the object's velocity changes over time, due to a phenomenon that you have been calling 'force'"?"
This is ironic, because he's just made my argument much more powerfully than I could have made it. Yet he uses that as his arguement against me, rather than himself. Yes, Erik has been arguing that the Stay-At-Home Twin's velocity changes over time doing a phenomenon he has been calling "pseudogravity" which implies a "force".
The problem is, I don't think it is worth bringing that up right now... It is more important that I figure out how to acknowledge that argument in the context with which he meant it. Was he really thinking it somehow a serious counter-objection to my objection?
=============================
Erik Anson
(Hydra Post 8)
>>While two observers are comoving, their past light cones line upuntil you hit the point where they are no longer comoving. So, if TWIN0 and TWIN1 have been on the same rocket for the past hour, then they assign the same coordinates to the past hour's worth of light-cone, but any farther back than that, all bets are off.
So why were you arguing with me?
>>While two observers are comoving, their past light cones line upuntil you hit the point where they are no longer comoving. So, if TWIN0 and TWIN1 have been on the same rocket for the past hour, then they assign the same coordinates to the past hour's worth of light-cone, but any farther back than that, all bets are off.
So why were you arguing with me?
(Hydra 9)
>>you were extrapolating arbitrarily far back in time
What do you think the domain and range of the Lorentz Transformation equations are?
The domain is the coordinates of all events in space and time. The range is the coordinates of all events in space and time
You seem to be claiming that there are some events that are for some reason, outside this domain and range of the Lorentz Transformation. Let's at least make it clear that this is the case that you are making.
(To claim that I can't go back "arbitrarily far in the past" is to claim that there must be some non-arbitrary boundary in spacetime to the domain and range of the Lorentz Transformation.)
>>you were extrapolating arbitrarily far back in time
What do you think the domain and range of the Lorentz Transformation equations are?
The domain is the coordinates of all events in space and time. The range is the coordinates of all events in space and time
You seem to be claiming that there are some events that are for some reason, outside this domain and range of the Lorentz Transformation. Let's at least make it clear that this is the case that you are making.
(To claim that I can't go back "arbitrarily far in the past" is to claim that there must be some non-arbitrary boundary in spacetime to the domain and range of the Lorentz Transformation.)
1. The LT transforms from one inertial frame to another inertial frame, and
2. The coordinates of events in your non-inertial rest frame only agree with those in the co-moving inertial frame for events that happened while you were co-moving.
You accepted this at the time. Now you're treating it as ridiculous, and asking me to define and explain things that I've already defined, explained, and (I had thought) convinced you of.
Literally just go back a couple posts.
I really don't want to have to go through this entire thing again, so let me know when you've caught back up to where we used to be.
(Hydra 10)
Yes, I accepted your definition, and I spent about 8 hours making a 12 minute video where I explained precisely what was wrong with your idea.
I've agreed that YOUR WAY or (THE STANDARD WAY, if you prefer) of stitching together a noninertial reference frame has exactly the problems that you are describing. But I have never agreed that MY WAY of stitching together the frames to create a noninertial reference frame would have the problems you're describing.
Yes, I accepted your definition, and I spent about 8 hours making a 12 minute video where I explained precisely what was wrong with your idea.
I've agreed that YOUR WAY or (THE STANDARD WAY, if you prefer) of stitching together a noninertial reference frame has exactly the problems that you are describing. But I have never agreed that MY WAY of stitching together the frames to create a noninertial reference frame would have the problems you're describing.
My point was that it was ridiculous for you to continue to accuse me of placing limitations on the domain and range of the Lorentz Transform, because we had already been over that many times.
However, given that you were "finding problems" in some fairly standard Relativity, and given your track record of false claims based on incorrect or incomplete information, I feel rather comfortable saying that the problem is on your end.
(Hydra 13)
>>There are no "problems".
I didn't know, here, what you were referring to. There are no problems with what?
>>My point was that it was ridiculous for you to continue to accuse me of placing limitations on the domain and range of the Lorentz Transform,because we had already been over that many times.
You have not yet acknowledged the existence of two ways of creating a noninertial reffernece frame.
But have instead kept repeating objections based on YOUR way of making the noninertial reference frame.
You have never made a distinction between the two different ways. And are arguing semantically, only allowing your own definition of "noninertial reference frame."
So when you say "There is no problem" you sound to me like you don't know what I am talking about. That's all I'm getting out of this conversation.
I have repeatedly brought up two different methods of making a noninertial reference frame, but all of your objections seem aimed at only one of the two different methods. You have not yet even acknowledged the existence of the other method. Failure to acknowledge the existence of that method convinces me that you do not know what I am talking about.
(Edited for civility)
>>There are no "problems".
I didn't know, here, what you were referring to. There are no problems with what?
>>My point was that it was ridiculous for you to continue to accuse me of placing limitations on the domain and range of the Lorentz Transform,because we had already been over that many times.
You have not yet acknowledged the existence of two ways of creating a noninertial reffernece frame.
But have instead kept repeating objections based on YOUR way of making the noninertial reference frame.
You have never made a distinction between the two different ways. And are arguing semantically, only allowing your own definition of "noninertial reference frame."
So when you say "There is no problem" you sound to me like you don't know what I am talking about. That's all I'm getting out of this conversation.
I have repeatedly brought up two different methods of making a noninertial reference frame, but all of your objections seem aimed at only one of the two different methods. You have not yet even acknowledged the existence of the other method. Failure to acknowledge the existence of that method convinces me that you do not know what I am talking about.
(Edited for civility)
>> I didn't know, here, what you were referring to. There are no problems with what?
In the original context, it was abundantly clear. You were talking about problems you claimed existed, and I was simply contradicting your claim. If something is unclear to you, consider looking back at the comment I was responding to.
>> You have not yet acknowledged the existence of two ways of creating a noninertial reffernece frame.
But have instead kept repeating objections based on YOUR way of making the noninertial reference frame.
I don't know what you're talking about. The translations and rotations of the axes fully define a reference frame. There isn't flexibility here.
>> You have never made a distinction between the two different ways. And are arguing semantically, only allowing your own definition of "noninertial reference frame."
I disagree that there is any such flexibility. Can you show mathematically what you mean by this, i.e., how you assign coordinates to events? Remember, if you use light-cone to define the time of an event, the laws of motion stop working, so you can't do that.
>> So when you say "There is no problem" you sound to me like you don't know what I am talking about. That's all I'm getting out of this conversation.
The fact that there is no problem with the standard formulation (which you're claiming there are) is totally independent of any alternative you may have in mind.
>> I have repeatedly brought up two different methods of making a noninertial reference frame, but all of your objections seem aimed at only one of the two different methods. You have not yet even acknowledged the existence of the other method. Failure to acknowledge the existence of that method convinces me that you do not know what I am talking about.
Are you talking about your "the past light-cone is now" thing? Or something else? It's definitely true that I don't understandsomething about what you're saying, but it's an open question as to whether I'm missing something or whether what you're saying just doesn't make sense.
(Hydra 14)
December 6, 2015
>>Are you talking about your "the past light-cone is now" thing?
If your intention was to accurately represent my claim, then a simple correction and three definitions should help.
"Observations of my past light cone are made here and now."
I was thinking that "past-light-cone" had a standard definition, but it appears I should have defined it more carefully, to get you to understand.
If I make an observation at(t0,x⃗ 0) then the locus of events that are part of that observation are in the cone (t0−|r⃗ |c,x⃗ 0+r⃗ ) . This is what I would call the past light cone of observation at (t0,x⃗ 0)
By contrast, the future light cone represents the locus of events where event(t0,x⃗ 0) can be observed. These events are located in the cone (t0+|r⃗ |c,x⃗ 0+r⃗ )
And the "plane of simultaneity" defined by an observer whose path is tangent to the world-line(t0+t,x⃗ 0) is (t0,x⃗ 0+r⃗ )
With the past and future light cones, though, the locus of events doesn't change for different observers moving through the same point in space at the same point in time. They may observe the events at different locations within their past light cones, but they are all seeing the same events.
However, with the plane of simultaneity, not only do non-comoving observers at the same location and time disagree on the coordinates of simultaneous events, they also disagree on what events are happening at that instant,(t0,x⃗ 0+r⃗ ) .
>>The fact that there is no problem with the standard formulation (which you're claiming there are) is totally independent of any alternative you may have in mind.
You have been arguing that when the traveling twin accelerates toward the earth that the earth ages in his noninertial rest frame, due to a phenomenon that you have been calling "pseudograviy"
Whether this is a "standard" explanation, or distinctly "your own" impression of the standard explanation, it deserves to be acknowledged.
However, you then brought forward this source as a description of the pseudogravitational effect that the stay-at-home twin undergoes:
Page on farmingdale.edu
At this point, it has become clear that you are no longer using a "standard" explanation, but rather, your own distinct and flawed "impression" of the standard explanation.
The document to which you referred describes an approximation which is to be used when the changes in velocity are small, and the distances are small.
In the situation under consideration (i.e the twin paradox), the changes in velocity are large, and the distances are large, and the only reason the final formula works are coincidences of symmetry. Not because of any direct logical reasoning.
You even seem to be aware that your reasoning is not direct... When I asked you "Where does it mention that the earth pops out to its full uncontracted length in that description" you answered "Why should it?"
You seem to be vaguely aware that your "standard" explanation doesn't cover this situation, yet you still maintain that you are espousing a standard explanation.
In conclusion for today
I realize now, there are three different ideas; not two. I thought I could begin with the difference between a plane of simultaneity, and a past-light-cone, and argue my case based on the Lorentz Transformation... I thought this was the main source of confusion.
So Idea 1: My idea, is constructing a noninertial "rest-frame" by stitching together events on the past-light-cone of the traveling observer.
Idea 2: (The idea that I thought you were promoting) Constructing a noninertial "rest-frame" by stitching together events simultaneous with the observations of the traveling observer.
Idea 3: (The idea that I think you are still haven't given up) The idea that the noninertial rest frame of the twin paradox is arrived at via the principle of equivalence.
I think that you are unaware of the Special-Relativistic foundational principles on which Peter Nolan's Chapter 7 derivation was built. This is why when I ask "Do you think there is a limit to the domain and range of the Lorentz Transformations" you seem to regard the question as irrelevant, and so you think you are justified in never answering it. (Edit: After hydra post 9, you answered in regard to ideas 1 and/or 2, but never in regards to idea 3.)
So while you have been saying since the beginning "I know how to use the Lorentz Transformations" it seems to me that you are continuing to reject that their results have any meaning.
>>Can you show mathematically what you mean by this, i.e., how you assign coordinates to events?Remember, if you use light-cone to define the time of an event, the laws of motion stop working, so you can't do that.
I'm sorry, but to explain mathematically what I am doing, I MUST use the idea of light-cones. You could argue that my use of the light-cone is invalid, if you wish, but you cannot understand the idea without acknowledging the light-cone as a conceptual tool. I would be interested to hear how choosing to use the past-light-cone causes the laws of motion to stop working.
December 6, 2015
>>Are you talking about your "the past light-cone is now" thing?
If your intention was to accurately represent my claim, then a simple correction and three definitions should help.
"Observations of my past light cone are made here and now."
I was thinking that "past-light-cone" had a standard definition, but it appears I should have defined it more carefully, to get you to understand.
If I make an observation at
By contrast, the future light cone represents the locus of events where event
And the "plane of simultaneity" defined by an observer whose path is tangent to the world-line
With the past and future light cones, though, the locus of events doesn't change for different observers moving through the same point in space at the same point in time. They may observe the events at different locations within their past light cones, but they are all seeing the same events.
However, with the plane of simultaneity, not only do non-comoving observers at the same location and time disagree on the coordinates of simultaneous events, they also disagree on what events are happening at that instant,
>>The fact that there is no problem with the standard formulation (which you're claiming there are) is totally independent of any alternative you may have in mind.
You have been arguing that when the traveling twin accelerates toward the earth that the earth ages in his noninertial rest frame, due to a phenomenon that you have been calling "pseudograviy"
Whether this is a "standard" explanation, or distinctly "your own" impression of the standard explanation, it deserves to be acknowledged.
However, you then brought forward this source as a description of the pseudogravitational effect that the stay-at-home twin undergoes:
Page on farmingdale.edu
At this point, it has become clear that you are no longer using a "standard" explanation, but rather, your own distinct and flawed "impression" of the standard explanation.
The document to which you referred describes an approximation which is to be used when the changes in velocity are small, and the distances are small.
In the situation under consideration (i.e the twin paradox), the changes in velocity are large, and the distances are large, and the only reason the final formula works are coincidences of symmetry. Not because of any direct logical reasoning.
You even seem to be aware that your reasoning is not direct... When I asked you "Where does it mention that the earth pops out to its full uncontracted length in that description" you answered "Why should it?"
You seem to be vaguely aware that your "standard" explanation doesn't cover this situation, yet you still maintain that you are espousing a standard explanation.
In conclusion for today
I realize now, there are three different ideas; not two. I thought I could begin with the difference between a plane of simultaneity, and a past-light-cone, and argue my case based on the Lorentz Transformation... I thought this was the main source of confusion.
So Idea 1: My idea, is constructing a noninertial "rest-frame" by stitching together events on the past-light-cone of the traveling observer.
Idea 2: (The idea that I thought you were promoting) Constructing a noninertial "rest-frame" by stitching together events simultaneous with the observations of the traveling observer.
Idea 3: (The idea that I think you are still haven't given up) The idea that the noninertial rest frame of the twin paradox is arrived at via the principle of equivalence.
I think that you are unaware of the Special-Relativistic foundational principles on which Peter Nolan's Chapter 7 derivation was built. This is why when I ask "Do you think there is a limit to the domain and range of the Lorentz Transformations" you seem to regard the question as irrelevant, and so you think you are justified in never answering it. (Edit: After hydra post 9, you answered in regard to ideas 1 and/or 2, but never in regards to idea 3.)
So while you have been saying since the beginning "I know how to use the Lorentz Transformations" it seems to me that you are continuing to reject that their results have any meaning.
>>Can you show mathematically what you mean by this, i.e., how you assign coordinates to events?Remember, if you use light-cone to define the time of an event, the laws of motion stop working, so you can't do that.
I'm sorry, but to explain mathematically what I am doing, I MUST use the idea of light-cones. You could argue that my use of the light-cone is invalid, if you wish, but you cannot understand the idea without acknowledging the light-cone as a conceptual tool. I would be interested to hear how choosing to use the past-light-cone causes the laws of motion to stop working.
The observations, yes. But not the events you're observing.
>> I was thinking that "past-light-cone" had a standard definition, but it appears I should have defined it more carefully, to get you to understand.
It does have a standard definition, although the concept is usually used in the context of an inertial frame, because otherwise it's not actually a "cone".
>> If I make an observation at
That is accurate if and only if the frame is inertial; specifically, an observer at rest in that frame must not have accelerated between
>> With the past and future light cones, though, the locus of events doesn't change for different observers moving through the same point in space at the same point in time. They may observe the events at different locations within their past light cones, but they are all seeing the same events.
This is true. This is the part I was agreeing with. However, you then tried to make claims based on your definition of "light cone" above, which doesn't recognize the conditional nature of that definition.
>> However, with the plane of simultaneity, not only do non-comoving observers at the same location and time disagree on the coordinates of simultaneous events, they also disagree on what events are happening at that instant, (t0,x⃗ 0+r⃗ ).
Yes. So?
>> You have been arguing that when the traveling twin accelerates toward the earth that the earth ages in his noninertial rest frame, due to a phenomenon that you have been calling "pseudograviy"
Why do you keep phrasing it like that? Would you say, "You have been arguing that the object's velocity changes over time, due to a phenomenon that you have been calling 'force'"? It's an entirely inappropriate way to describe physics that has been standard for almost a century.
>> Whether this is a "standard" explanation, or distinctly "your own" impression of the standard explanation, it deserves to be acknowledged.
How is this even a question? I have sent you sources. This is not some thing I'm putting forward, it is standard physics.
>> At this point, it has become clear that you are no longer using a "standard" explanation, but rather, your own distinct and flawed "impression" of the standard explanation.
Not really, no.
>> The document to which you referred describes an approximation which is to be used when the changes in velocity are small, and the distances are small.
Yes. That is the simplest context in which to derive the effect. That doesn't mean that the effect ceases to exist in other regimes.
>> In the situation under consideration (i.e the twin paradox), the changes in velocity are large, and the distances are large, and the only reason the final formula works are coincidences of symmetry. Not because of any direct logical reasoning.
Yes, doing it out fully and properly would be more mathematically complex. There exists a shortcut that works, so I used it. What's your point?
>> You even seem to be aware that your reasoning is not direct... When I asked you "Where does it mention that the earth pops out to its full uncontracted length in that description" you answered "Why should it?"
As I have said before: I was explaining what pseudo-gravitational time dilation was, and showing you a source to prove that I wasn't just batty. I was not presenting that source as a direct application of gravitational time dilation to the Twin Paradox.
>> You seem to be vaguely aware that your "standard" explanation doesn't cover this situation, yet you still maintain that you are espousing a standard explanation.
You seem to be missing the point entirely.
>> In conclusion for today
I realize now, there are three different ideas; not two. I thought I could begin with the difference between a plane of simultaneity, and a past-light-cone, and argue my case based on the Lorentz Transformation... I thought this was the main source of confusion.
I'm not sure anymore where your main source of confusion is.
>> So Idea 1: My idea, is constructing a noninertial "rest-frame" by stitching together events on the past-light-cone of the traveling observer.
Define "stitching together" in this context? The idea of "stitching together" frames makes sense, but I'm not sure what you'd mean by "stitching together events on the past light-cone". If you mean treating those events as somehow simultaneous, then that's not going to work very well. If you mean something else, define what that is.
>> Idea 2: (The idea that I thought you were promoting) Constructing a noninertial "rest-frame" by stitching together events simultaneous with the observations of the traveling observer.
Still not sure what kind of "stitching" you have in mind, but equal time coordinates had better correspond to simultaneous events.
>> Idea 3: (The idea that I think you are still haven't given up) The idea that the noninertial rest frame of the twin paradox is arrived at via the principle of equivalence.
This is a way to do it, yes. Although, it depends on your starting point; you could think of it as accelerating frames producing time dilation, which then implies gravitational time dilation by the equivalence principle.
>> This is why when I ask "Do you think there is a limit to the domain and range of the Lorentz Transformations" you seem to regard the question as irrelevant, and so you think you are justified in never answering it. (Edit: After hydra post 9, you answered in regard to ideas 1 and/or 2, but never in regards to idea 3.)
I have answered this repeatedly. I have no idea what you're talking about, "justified in never answering it". If you keep forgetting that I've answered it, over and over, that's hardly my fault.
>> So while you have been saying since the beginning "I know how to use the Lorentz Transformations" it seems to me that you are continuing to reject that their results have any meaning.
This is nonsense. Lorentz transforms are great for getting from one inertial frame to another. You're trying to apply them to a non-inertial frame, which is fine within limits, but there are additional restrictions on when it is valid that I have gone over many times now and that you seem to be ignoring.
>>>>Can you show mathematically what you mean by this, i.e., how you assign coordinates to events?Remember, if you use light-cone to define the time of an event, the laws of motion stop working, so you can't do that.
>> I'm sorry, but to explain mathematically what I am doing, I MUST use the idea of light-cones. You could argue that my use of the light-cone is invalid, if you wish, but you cannot understand the idea without acknowledging the light-cone as a conceptual tool. I would be interested to hear how choosing to use the past-light-cone causes the laws of motion to stop working.
Light-cones are perfectly good conceptual tools, but they do not define simultaneity, as you seem to want to. If you define your time coordinates that way (such that everything on a light cone is simultaneous) then everything breaks. It no longer sounds like that's what you're trying to do, but for a while, it very much did.
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