Questions relating to time dilation

[Erland]

Yes, but you said she sees the two flashes at different times, correct? I was wondering what your justification is to conclude that she sees the flashes at different times. I agree with this, I just want to see how you're looking at the situation.

Well, it follows from the original setup of the problem, and is explained in the video, that the passenger sees the front flash before she sees the back flash. If you agree on this, we now see that the assumption that she sees the signals from the detectors at the same time leads to a contradiction. How to resolve that?

 

[salzrah]

But I don't think she sees the signals from the detectors at the same time.
We can agree that the detectors and the light flashes themselves exhibit the same effects, correct?
(Basically, the signal from detectors = flashes of light)
You said she sees the flashes at different times, this means she must see the signals from the detectors at different times as well.

 

[ghwellsjr]

That video is full of errors. Anybody who doesn't already understand Special Relativity is going to be totally confused if they pay attention to what that video shows and says. People who already understand SR are going to be mesmerized by the fantastic production quality of the video and think that its great, but if they would scrutinize it like a beginner does, they would reject it as having no value whatsoever.

I suggest that you do a search on this forum for the youtube code, and read my comments on the video.

 

[Erland]

But I don't think she sees the signals from the detectors at the same time.
We can agree that the detectors and the light flashes themselves exhibit the same effects, correct?
(Basically, the signal from detectors = flashes of light)
You said she sees the flashes at different times, this means she must see the signals from the detectors at different times as well.

I agree completely. She sees the signals from the detectors at different times (the front one first).

Now, wrt the inertial system of the train, the two signals travel equal distances with the same speed, c. Since they arrive to the passenger at different times, they must also have been sent at different times (relative to the train system). Right?

 

[salzrah]

But that's the thing, I don't think they travel equal distances because the train/lady is in motion relative to the reference frame of the flashes, which is like I said before the underlying difference between the way we view the situation.

 

[salzrah]

That video is full of errors. Anybody who doesn't already understand Special Relativity is going to be totally confused if they pay attention to what that video shows and says. People who already understand SR are going to be mesmerized by the fantastic production quality of the video and think that its great, but if they would scrutinize it like a beginner does, they would reject it as having no value whatsoever.

I suggest that you do a search on this forum for the youtube code, and read my comments on the video.

Will do. However, we aren't really using the conclusions of the video and I don't even remember what the video concludes for that matter. But we are using the situation that is described/presented in the video (and others that we created in this thread). Are you saying the train example has a problem in it itself so that it can't prove the relativity of simultaneity?

 

[ghwellsjr]

The video is wrong all the way through, not just any "conclusions". It shouldn't be discussed except as a bad example.

 

[Erland]

But that's the thing, I don't think they travel equal distances because the train/lady is in motion relative to the reference frame of the flashes, which is like I said before the underlying difference between the way we view the situation.

When you talk about "the reference frame of the flashes" I assume that you mean the reference frame in which the light sources of the flashes are at rest. The light sources of the flashes would presumably be points in the air where the flashes originate, and these points will be at rest relative to the platform and in motion relative to the train. Let's agree about that.

But you can't say so about the signals from the detectors (which is the reason that I introduced the detectors and the signals). The detectors, which are the sources of the signals, are at rest relative to the train, let's say they are nailed to the front and back walls of the train. Therefore, you can't deny that the signals travel equal distances relative to the frame of the train.

 

[Nugatory]

Nugatory-
different times as well. He will see flash C, then flash A. When you say -
"a) Platform-guy says A and B happened at the same time, and C happened a bit later.
b) Train-lady says A and C happened at the same time, but a bit after B. "

a) is right, but in b) train-lady should NOT say A and C happened at the same time. Because just as you agreed with me, she can calculate that A and C did not happen at the same time but it was because of her motion she saw it that way. So they are BOTH right.

Why should train-lady not say that A and C happened at the same time? She's at rest so there's no "her motion" to use to calculate any other result. Furthermore, platform-guy agrees with her; he sees his movement towards the back of this at-rest train, and uses his motion to calculate that (using your argument) A and B did not happen at he same time but because of his motion he saw it that way. How is this any more right or wrong than (a) above, where we say that it's the train that's moving forward and the platform is at rest, so train-lady must make be the one who adjust for motion?

I did notice that you used the phrase "In the reference frame of the light flashes themselves" in your post, and this may be contributing to your confusion about how the relativity of simultaneity works. You'll hear people say "In the reference frame of something...", but you have to be aware that this is a just a convenient linguistic shorthand for what they really mean, which is "In a reference frame in which something is at rest...". Thus, there is no "reference frame of the light flashes themselves" because there's no frame in which they are at rest (light always travels at c, right?).
There are two things in this thought experiment that are moving, and can define reference frames: the train and the platform. Thus, we have the train frame, in which the train is at rest and platform is moving backwards; and the platform frame in which the platform is at rest and the train is moving forward. Above, (a) Is the platform-frame description and (b) is the train-frame description. There is absolutely no reason to consider one of them more "right" than the other.

 

[Nugatory]

But that's the thing, I don't think they travel equal distances because the train/lady is in motion relative to the reference frame of the flashes, which is like I said before the underlying difference between the way we view the situation.

Salzrah, you may find this thread to be helpful:
https://www.physicsforums.com/showthread.php?t=594424&highlight=scorch

 

[salzrah]

Erland- Even though the detectors are nailed to the train, as soon as the signals leave the detector the signals become independent of the train. As time passes, the train has MOVED to a new position relative to the origin of where the signal first leaves. It is no longer in the same position that it once was when the signals first leave the detectors, so the back light has to travel more than the front light. Yes, the detectors are nailed to the ends of the train but once it sends the signal, the signal propagates through space from where it was first sent.

 

[Austin0]

That video is full of errors. Anybody who doesn't already understand Special Relativity is going to be totally confused if they pay attention to what that video shows and says. People who already understand SR are going to be mesmerized by the fantastic production quality of the video and think that its great, but if they would scrutinize it like a beginner does, they would reject it as having no value whatsoever.

I suggest that you do a search on this forum for the youtube code, and read my comments on the video.

Hi
I may be a little slow today but I just watched the video and didn't see any immediate errors.
It appeared to be a straight forward if abbreviated visualization of the essential parameters and logic

What did I miss?

BTW i looked for your comments on the tube without success.

 

[Jimmy]

BTW i looked for your comments on the tube without success.

The comments are in this thread:
https://www.physicsforums.com/showthread.php?t=614735&page=9
https://www.physicsforums.com/showthread.php?t=614735&page=11

 

[Erland]

Erland- Even though the detectors are nailed to the train, as soon as the signals leave the detector the signals become independent of the train. As time passes, the train has MOVED to a new position relative to the origin of where the signal first leaves. It is no longer in the same position that it once was when the signals first leave the detectors, so the back light has to travel more than the front light. Yes, the detectors are nailed to the ends of the train but once it sends the signal, the signal propagates through space from where it was first sent.

The train has moved, relative to an observer at the platform, that's true. But the train has NOT moved relative to an observer in the train!

Somehow, you consider the reference system of the platform as more fundamental or correct than the reference system of the train. This means that you actually deny the Special Principle of Relativity, one of the two fundamental postulates of SR. Because by that principle, there is no way to distinguish between inertial systems making one more special than another.

You can of course deny this principle if you want to, but all experimental evidence and observations hitherto are in full agreement with it, and all attempts to find a particular "fundamental" inertial system have failed. The most famous experiment of this kind is the one by Michelson and Morley, who tried to detect the motion of the Earth through an assumed immobile "aether". They couldn't detect such a motion.

 

[Austin0]

The comments are in this thread:
https://www.physicsforums.com/showthread.php?t=614735&page=9
https://www.physicsforums.com/showthread.php?t=614735&page=11

Thanks Jimmy yes i see. it was an unfortunate use of the word "see" that was amiss.
Forgetting propagation time as it related to the perception of the track observer.
Since I naturally assumed, through familiarity, the strikes were simultaneous as observed by proximate track observers with watches this slipped by me completely. Certainly a faux pas on their part and I can see that someone encountering the scenario for the first time, and seriously analyzing it, could be confused if they noticed that the track guy couldn't actually receive the light from the strikes and see the train passenger at the midpoint between them simultaneously .
Ah Well

 

[salzrah]

Nugatory, the lady has motion relative to the origin of the light. And as I said before, this is the underlying thing you and I are disagreeing about. I understand your explanation of inertial reference frames, thanks for that. I will now speak of only ground-frame and train-frame. Let me go through my reasoning one last time leaving out no details.

The train-frame has motion relative to the ground-frame. The lights strike at two separate origins which are both in the train-frame and ground-frame. Now, let's say the lightning flashes are simultaneous in the ground-frame. The lightning flashes hit the origins and the lights propagate to the guy on the ground in the same time interval so he concludes they were simultaneous. The ground-frame has no motion relative to the origins and because the ground guy has no relative movement with the origins he can conclude that the lightning flashes did in fact occur at the same time and it is not because he just happened to SEE this. Now, let's assume for this argument's purpose that in the train-frame the strikes are also simultaneous. The train-frame DOES have movement relative to the origins of the light. So in the train-frame the train moves away from one origin and towards the other. So the distance the light has to travel is less from one origin and more for another, therefore the train lady sees the light flashes at different times but can calculate, using her motion relative to the lights origins, that the light strikes were actually simultaneous.
That was my argument-- that, in fact, BOTH reference frames can conclude the two lightning strikes were simultaneous even though the train-frame lady SEES them at different times.
I think the problem that you guys have with my argument, even though you don't explicitly state this, is that you are saying that the train-frame lady can NOT have motion relative to the origin of the light. Is that correct? If that is what you are saying, can you explain why? ... (although I feel like I already know the answer)

 

[Austin0]

Nugatory, the lady has motion relative to the origin of the light.

The train-frame has motion relative to the ground-frame. The lights strike at two separate origins which are both in the train-frame and ground-frame. Now, let's say the lightning flashes are simultaneous in the ground-frame. The lightning flashes hit the origins and the lights propagate to the guy on the ground in the same time interval so he concludes they were simultaneous. The ground-frame has no motion relative to the origins and because the ground guy has no relative movement with the origins he can conclude that the lightning flashes did in fact occur at the same time and it is not because he just happened to SEE this. Now, let's assume for this argument's purpose that in the train-frame the strikes are also simultaneous. The train-frame DOES have movement relative to the origins of the light. So in the train-frame the train moves away from one origin and towards the other. So the distance the light has to travel is less from one origin and more for another, therefore the train lady sees the light flashes at different times but can calculate, using her motion relative to the lights origins, that the light strikes were actually simultaneous.
That was my argument-- that, in fact, BOTH reference frames can conclude the two lightning strikes were simultaneous even though the train-frame lady SEES them at different times.
I think the problem that you guys have with my argument, even though you don't explicitly state this, is that you are saying that the train-frame lady can NOT have motion relative to the origin of the light. Is that correct? If that is what you are saying, can you explain why? ... (although I feel like I already know the answer)

The train lady cannot calculate or consider the strikes as simultaneous for two reasons.

1) Regarding simultaneity any motion relative to the source of light is irrelevant because the speed of propagation is independent of any possible motion.

2) it is simply false because train passengers next to the locations of the light origins will say that by their clocks the lights originated at two different times.

SO in the train frame they are simply NOT simultaneous by any standard.

 

[salzrah]

The basis she uses to consider herself in motion relative to the origins is looking at the origins, which we can say are on the ground/air where the flash occurred, and seeing that those origins are moving away from her.

 

[Erland]

I think the problem that you guys have with my argument, even though you don't explicitly state this, is that you are saying that the train-frame lady can NOT have motion relative to the origin of the light. Is that correct? If that is what you are saying, can you explain why? ... (although I feel like I already know the answer)

What IS this "origin of light"?

You cannot mean the light source(s), for in my example with the detectors and signals, the train-frame lady are at rest relative to the light sources (the detectors). No, you seems to mean that at the moment a signal leaves a detector, it somehow reaches its "origin", which, by some reason, is at rest relative to the ground-frame.

The ground-frame must therefore have the property that all "origins of light" are at rest relative to this frame, a property that no other inertial frame has. This blatantly contradicts the Special Principle of Relativity. So you deny this principle, as I wrote in my previous post.

 

[Austin0]

The basis she uses to consider herself in motion relative to the origins is looking at the origins, which we can say are on the ground/air where the flash occurred, and seeing that those origins are moving away from her.

This is not the right way to look at it. Those locations relative to the track frame are moving away from her but they are not moving relative to her.
For instance ; Even if they did not occur right at the ends of the train but instead happened one foot in front and one foot behind the ends of the train. Those locations do not change in the train frame.
The front origin remains one foot in front of the train no matter how far from the location in the track frame.
Events have a singular location in space and time relative to any frame.
So a flash event. The origin of a light , has a single location t'=?,x'=?,y'=?,z'=? in the train frame whatever the specific coordinates may be, and this is fixed.

 

[salzrah]

The origin of light is the POSITION where the light comes out from. The detector source is at rest with respect to the train-frame BUT that is not the origin of the light. The origin of the light is a position, like x=4. The train-frame lady can see the lightning strike at x=4 and see that this position is moving away from her as her position in the x-axis increases. The train-frame lady is moving relative to this position of the origin at x=4.

 

[salzrah]

This is not the right way to look at it. Those locations relative to the track frame are moving away from her but they are not moving relative to her.
.

The positions ARE moving away from her because she is moving away from those positions. If there is a stationary ball at x=4, the train-frame lady will see this ball move away from her as the train moves in the positive x-direction.

 

[Erland]

The origin of light is the POSITION where the light comes out from. The detector source is at rest with respect to the train-frame BUT that is not the origin of the light. The origin of the light is a position, like x=4. The train-frame lady can see the lightning strike at x=4 and see that this position is moving away from her as her position in the x-axis increases. The train-frame lady is moving relative to this position of the origin at x=4.

But if we put an x-axis inside the train, which is at rest relative to the train, then the x-coordinate on that axis of the point where the light comes out from the detector does NOT move relative to train-lady.

We all the time come back to the fact that you consider the ground-frame as privileged compared to the the train-frame, and this contradicts the Special Principle of Relativity.

 

[Austin0]

The origin of light is the POSITION where the light comes out from. The detector source is at rest with respect to the train-frame BUT that is not the origin of the light. The origin of the light is a position, like x=4. The train-frame lady can see the lightning strike at x=4 and see that this position is moving away from her as her position in the x-axis increases. The train-frame lady is moving relative to this position of the origin at x=4.

The positions ARE moving away from her because she is moving away from those positions. If there is a stationary ball at x=4, the train-frame lady will see this ball move away from her as the train moves in the positive x-direction.

you are confused regarding coordinate systems.

Forget detectors. Someone sets of a flashbulb on the platform at x= 4 (track frame)as the lady is right next to it.
She is then moving away from the burnt out flash bulb at x=4 but the event of the flash itself remains right next to her at whatever coordinates she assigns relative to the train car.
This is the location of the flash event (origin of the expanding light sphere) in her frame.
Remember this is not the location of anything physical like your ball at x=4. Once the light begins propagating there is nothing there but an abstract coordinate location.

 

[salzrah]

But if we put an x-axis inside the train, which is at rest relative to the train, then the x-coordinate on that axis of the point where the light comes out from the detector does NOT move relative to train-lady.

We all the time come back to the fact that you consider the ground-frame as privileged compared to the the train-frame, and this contradicts the Special Principle of Relativity.

Yes, that is true. But the point of the light origin IS NOT MOVING with the train. It stays at the position where it was. So while the train moves relative to the point, even though the x-axis is at rest wrt the train, the x-axis is not at rest with respect to the point. Okay, can you tell me if you can represent the point of where the light originates as a ball? Or any object? It will help me in making an example if you agree with that...

 

[salzrah]

you are confused regarding coordinate systems.

Forget detectors. Someone sets of a flashbulb on the platform at x= 4 (track frame)as the lady is right next to it.
She is then moving away from the burnt out flash bulb at x=4 but the event of the flash itself remains right next to her at whatever coordinates she assigns relative to the train car.
This is the location of the flash event (origin of the expanding light sphere) in her frame.
Remember this is not the location of anything physical like your ball at x=4. Once the light begins propagating there is nothing there but an abstract coordinate location.

Why in the world does the point at which the flash occurs stay next to her? That is entirely false. The point remains where it was. The point IS PHYSICAL LIKE A BALL. It is a position that can be occupied by the place where the light comes out from initially. The lady can move away from this point.
It's baffling that people can't understand you can move away from where the light originates.

 

[salzrah]

Erland, can you please explain to me why you keep saying I "consider the ground-frame as privileged"?

 

[ghwellsjr]

That video is full of errors. Anybody who doesn't already understand Special Relativity is going to be totally confused if they pay attention to what that video shows and says. People who already understand SR are going to be mesmerized by the fantastic production quality of the video and think that its great, but if they would scrutinize it like a beginner does, they would reject it as having no value whatsoever.

I suggest that you do a search on this forum for the youtube code, and read my comments on the video.

Hi
I may be a little slow today but I just watched the video and didn't see any immediate errors.
It appeared to be a straight forward if abbreviated visualization of the essential parameters and logic

What did I miss?

BTW i looked for your comments on the tube without success.

I didn't put my comments on the youtube website, they're on this forum. You have to first search for a thread with the youtube code and then find my posts that have a lot of screen shots from the video.

 

[salzrah]

Sorry to spam posts but can whoever answer this question.
Let's say I am standing between two light bulbs and they both turn on at the same time. At that instant, I begin to run towards the light bulb on the right at a speed .5c. Will I see the light from the right bulb before the light from the left bulb?

Can everyone please please please read this explanation about the relativity of simultaneity by HowStuffWorks.
http://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity13.htm

Now, just because Garett (the guy on the skateboard) SEES the light at different times does not mean they actually occurred at different times in his frame of reference. He can use his relative velocity with respect to Meagan OR with respect to the origin of the light source, which is a point in space that is at rest in Meagan's frame, and calculate how much extra distance the light on the left had to travel. He will then determine that the two light bulbs in fact turned on at the same time.

 

[Nugatory]

The basis she uses to consider herself in motion relative to the origins is looking at the origins, which we can say are on the ground/air where the flash occurred, and seeing that those origins are moving away from her.

OK, let's say that when a bolt of lightning strikes, it leaves a scorch mark on the train and on the rails where it hits. Platform guy is moving relative to one of these scorch marks (the one on the train) and at rest relative to the other (the one on the platform). Train lady is at rest relative to one (the one on the train) and moving relative to the other (the one on the platform).

How, in this completely symmetrical situation, can we say that train-lady must consider herself to be in motion? There's no argument you can make that's she's moving that I can't just as easily make about the platform guy.

Before you respond to this, take a moment to read the questions and answers below. If you disagree with any of the answers, find your mistake before you proceed - this is fundamental to understanding relativity. In the answers, c is the invariant speed of light and v is the relative speed between the train and the platform. Train-lady and platform-guy are exactly even with each other at the moment that a bolt of lightning strikes and leaves a scorch mark on both train and platform.
1: How long does it take for the light to travel from the scorch mark on the train to train-lady's eyes, according to the people on the train? Answer: P/c, where P is the distance from the scorch mark on the train to train-lady, according to the people on the train.
2: How long does it take the light to travel from the scorch mark on the train to train-lady, according to the people on the platform? Answer: Q/(c-v), where Q is the distance between platform guy and the scorch mark on the platform, according to the people on the platform.
3: Would the answer to #1 be different if we were asking about the scorch mark on the platform instead of the train? Answer: No, and this may be where you've been getting hung up.
4: Would the answer to #2 be different if we were asking about the scorch mark on the platform instead of the train? Answer: No.
5: How long does it take for the light to travel from the two scorch marks to platform-guy, according to the people on the platform? Answer: Q/c, for both scorch marks.
6: How long does it take for the light to travel from the two scorch marks to platform-guy, according to the people on the train? Answer: P/(c+v), for both scorch marks.

(we have enough eyes on this thread that if I fat-fingered one of the answers, someone will point it out)

 

[salzrah]

Okay, while I am reading and deciphering your post Nugatory, can you look at the last post I put up?
And in the beginning when you say "Platform guy is moving relative to one of these scorch marks (the one on the platform)" do you actually mean the one on the train?

 

[Nugatory]

Okay, while I am reading and deciphering your post Nugatory, can you look at the last post I put up?
And in the beginning when you say "Platform guy is moving relative to one of these scorch marks (the one on the platform)" do you actually mean the one on the train?

I'm working on that reply now, and you're rightbabout the typo... Fixing it now

 

[levytate]

Sorry to spam posts but can whoever answer this question.
Let's say I am standing between two light bulbs and they both turn on at the same time. At that instant, I begin to run towards the light bulb on the right at a speed .5c. Will I see the light from the right bulb before the light from the left bulb?

Can everyone please please please read this explanation about the relativity of simultaneity by HowStuffWorks.
http://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity13.htm

Now, just because Garett (the guy on the skateboard) SEES the light at different times does not mean they actually occurred at different times in his frame of reference. He can use his relative velocity with respect to Meagan OR with respect to the origin of the light source, which is a point in space that is at rest in Meagan's frame, and calculate how much extra distance the light on the left had to travel. He will then determine that the two light bulbs in fact turned on at the same time.

Hi salzrah, this can be a tough one to get your head around, because we have to challenge our common sense understanding. I had similar troubles understanding it, but I think I have better understanding now. Someone will have to confirm whether what I say is accurate or not, but hopefully I can help to explain my understanding of it.

I haven't read the full example in the link, but I presume it's similar to many of the other examples used to explain relativity of simultaneity. Are you taking length contraction into account?

In Garett's frame of reference, the distance between the two lights won't be the same as it is in Meagan's frame of reference, because Garett is moving relative to the light bulbs while Meagan is at rest relative to them. This is because lengths are contracted in the direction of motion.

In Meagan's frame of reference the distance between the two lightbulbs is some distance we label 'D'. The midpoint between the lightbulbs is given as half that distance, or D/2. This is because Meagan is at rest relative to the lightbulbs.Garret, however, is moving relative to the lightbulbs and so the distance in his reference frame is contracted. The distance that the light has to travel from each light bulb to the midpoint isn't the same D/2 as in Meagan's reference frame. Instead, the distance to the midpoint between the lightbulbs in Garret's reference frame is γD/2.

γ is known as the Lorentz factor - which can be seen here: http://en.wikipedia.org/wiki/Lorentz_factor

It would be too messy for me to try and type out.
So, given the same speed of light, but the different distances that the light has to travel, both observers will calculate different times for the events. Garret will calculate that one light flashed before the other, while Meagan will calculate that both lights flashed simultaneosuly.Someone will need to confirm if that is accurate, but that is [the short version of] how it was explained to me.

EDIT: Something that might cause confusion in the "how stuff works" explanation is the use of the use of the cannon example before using the lightbulb example. It gets us thinking in our everyday "common sense" manner, before trying to change it. I'm not sure this is helpful.

 

[salzrah]

OK, let's say that when a bolt of lightning strikes, it leaves a scorch mark on the train and on the rails where it hits. Platform guy is moving relative to one of these scorch marks (the one on the train) and at rest relative to the other (the one on the platform). Train lady is at rest relative to one (the one on the train) and moving relative to the other (the one on the platform).

How, in this completely symmetrical situation, can we say that train-lady must consider herself to be in motion? There's no argument you can make that's she's moving that I can't just as easily make about the platform guy.

You're completely right - the motion is relative so we can say either one of the people is moving. However, in this situation the train-lady in the train frame is moving with respect to the origins of the light, whereas in the ground-frame the origins of the light are at rest with respect to the guy on the ground. Therefore, we can say the lady is moving wrt the light origins while the guy on the ground is not.

1: How long does it take for the light to travel from the scorch mark on the train to train-lady's eyes, according to the people on the train? Answer: P/c, where P is the distance from the scorch mark on the train to train-lady, according to the people on the train.

That answer is incorrect. Let me explain. After the lightning flash, the lady moves relative to the point where that lightning flash occurs. The scorch mark does not. You are confusing these two to mean the same thing. Yes, the scorch mark stays the same distance away from the lady, but the origin of the light source does not remain the same distance away because the train-lady moves away from it. It'll be easier to visualize if you imagine the lightning strike to happen in the air on the sides of the train and understand that the lady moves away/towards these points in the air.

 

[Nugatory]

Sorry to spam posts but can whoever answer this question.
Let's say I am standing between two light bulbs and they both turn on at the same time. At that instant, I begin to run towards the light bulb on the right at a speed .5c. Will I see the light from the right bulb before the light from the left bulb?

Yes. (But the only reason you can get away with saying that both light bulbs turned on "at the same time" and "at that instant" is that you started at rest relative to the two bulbs)

Now, just because Garett (the guy on the skateboard) SEES the light at different times does not mean they actually occurred at different times in his frame of reference. He can use his relative velocity with respect to Meagan OR with respect to the origin of the light source, which is a point in space that is at rest in Meagan's frame, and calculate how much extra distance the light on the left had to travel. He will then determine that the two light bulbs in fact turned on at the same time.

You used the same line of thinking in post #53... And it's not right, but I can fix it with just three little words:

He will then determine that the two light bulbs in fact turned on at the same time in Meagan's frame.

That is, you have just described the way in which events that are not simultaneous in one frame can be simultaneous in another. And that's what relativity of simultaneity is all about.

Where you've been going wrong is in thinking that the simultaneity in Meagan's frame is "right" while the non-simultaneity in Garett's frame is an illusion of his motion. But as far as Garett is concerned, Meagan is the one moving, not him... So as far as Garett is concerned, the non-simultaneity in his frame is real while Meagan is the one experiencing an illusion of motion.