I Relativity of Simultaneity Questions

[PeroK]

Too many words, not enough mathematics!

If you do an Internet search for "Morin relativity", you'll find the first chapter of his book online for free.

I would clear your mind and start again with Morin.

I find the original train and lightning thought experiment is often likely to confuse - it's better avoided until you understand SR.

 

[Ibix]

A general point is that the original experiment as described by Einstein isn't always the best one to learn from. A lot of teaching has happened since and people have learned what seems to confuse students and what seems to get through. Einstein's train has the massive coincidence of a pair of lightning strikes being simultaneous in a particular frame, whereas the variant with a single bulb reflecting provides a less "Act of God" method for picking the grame where things are simultaneous.

I suspect that your problem with light "appearing to go faster" is the Newtonian intuition that if I see you going one way at speed $u$ and someone else going at $v$ in the other direction then you will see them doing $u+v$. Not so in relativity! Look up "relativistic velocity addition".

 

[mucker]

I think I've finally figured it out and where I was going wrong. I'd be grateful if someone can verify that my logic is now sound.I had a feeling I [wrongly] concluded that due to the invariant speed of light, if you are moving at relativist speeds to two events of equal distance apart, you would still see them at the same time. Example - we only need one event here to show where my logic was flawed. Say for Ob A event happens 5ls away at t=0 and takes 5 secs to see it, he concludes it happened t=0. At that exact moment for Ob B, the event is still 5ls away (at least in Ob A frame, let’s not complicate this with length contraction and time dilation yet) and even though he is moving towards it, since light speed is invariant, it won't reach him any sooner. I've realized this logic is flawed - even though light always moves at the same speed in all reference frames, it actually has less distance to travel to reach ObB, so it DOES arrive sooner. I was failing to factor in that by the time the light reaches ObB it never traveled 5ls but was in fact less (if moving towards event). I know this may seem obvious to the rest of you or even dumb on my part but what was throwing me off was 2 facts I kept in mind when processing this:

• That light speed is invariant
• That in an inertial frame you are essentially stationary

So, I rationalised it as so:

• At t=0 ObB is 5ls away from event
• ObB is stationary in his frame over 5 seconds
• At t=5 he sees lightning at the end of the train and he already knows this distance is 5ls

Therefore, he concludes it happened at t=0 just like ObA.

Tbh I just think the train example is a terrible example, I came to the above conclusions because of that diagram. For example, the diagram looks like/implies the light travels 5ls from both ends to mr blue in his frame (for same reasons I say above), when in fact it travels 3ls (approx.) for R ray and 7ls for L ray (I am aware from blue’s perspective this not the case).

 

[PeroK]

I think I've finally figured it out and where I was going wrong. I'd be grateful if someone can verify that my logic is now sound.I had a feeling I [wrongly] concluded that due to the invariant speed of light, if you are moving at relativist speeds to two events of equal distance apart, you would still see them at the same time. Example - we only need one event here to show where my logic was flawed. Say for Ob A event happens 5ls away at t=0 and takes 5 secs to see it, he concludes it happened t=0. At that exact moment for Ob B, the event is still 5ls away (at least in Ob A frame, let’s not complicate this with length contraction and time dilation yet) and even though he is moving towards it, since light speed is invariant, it won't reach him any sooner. I've realized this logic is flawed - even though light always moves at the same speed in all reference frames, it actually has less distance to travel to reach ObB, so it DOES arrive sooner. I was failing to factor in that by the time the light reaches ObB it never traveled 5ls but was in fact less (if moving towards event). I know this may seem obvious to the rest of you or even dumb on my part but what was throwing me off was 2 facts I kept in mind when processing this:

• That light speed is invariant
• That in an inertial frame you are essentially stationary

So, I rationalised it as so:

• At t=0 ObB is 5ls away from event
• ObB is stationary in his frame over 5 seconds
• At t=5 he sees lightning at the end of the train and he already knows this distance is 5ls

Therefore, he concludes it happened at t=0 just like ObA.

Tbh I just think the train example is a terrible example, I came to the above conclusions because of that diagram. For example, the diagram looks like/implies the light travels 5ls from both ends to mr blue in his frame (for same reasons I say above), when in fact it travels 3ls (approx.) for R ray and 7ls for L ray (I am aware from blue’s perspective this not the case).

There are too many issues here to address this early in the morning. All I shall say is to repeat my suggestion to read Morin's book.

That said: you can't "move to an event". And saying "in an inertial frame you are essentially stationary" is meaningless.

 

[mucker]

PeroK I am reading. I know you may think I am not, but I am. I am reading on average 4 hours a day, but sometimes it just raises more questions. I am reading from multiple sources too. I have read up on this one subject from about 4 different sources. The latest one I read, which brought me to above conclusions shows that the light has more distance to cover if you are moving relevant to where the events went off.

 

[PeroK]

PeroK I am reading. I know you may think I am not, but I am. I am reading on average 4 hours a day, but sometimes it just raises more questions. I am reading from multiple sources too. I have read up on this one subject from about 4 different sources. The latest one I read, which brought me to above conclusions shows that the light has more distance to cover if you are moving relevant to where the events went off.

Using multiple sources may be part of the problem.

You can move relative to a source of light, but you can't move relative to where light was emitted. Or, at least, not in your own rest frame.

One of the fundamental issues before you can learn SR is to grasp the concept of a reference frame. And, especially being able to switch from one reference frame to another. A common error is to fix a certain reference frame as absolute in a sense and then only half-heartedly switch to another frame.

In any case, some of your problems are not with SR, as such, but with the concept of events as described in more than one reference frame.

I would focus on that before you dig any deeper.

 

[mucker]

One of the fundamental issues before you can learn SR is to grasp the concept of a reference frame. And, especially being able to switch from one reference frame to another. A common error is to fix a certain reference frame as absolute in a sense and then only half-heartedly switch to another frame.

OK, so can you at least give me some idea of where you think I am not understanding a what a reference frame is?

I paraphasing/summarising with what I say next - I see it like a snapshot in time and space, a perspective if you will from one observer who can map out an event with his own co-ordinate system, I understand that time may be different to another reference frame that is moving relevant to me. Ithink these are ssentially the main points of what a ref frame is. And to move from one reference frame to the other we use the Lorentz Transformation. Is that not correct?

EDIT: GRAMMAR

 

[PeroK]

A reference frame (in this context a global inertial reference frame) is a system of coordinates that label each event in spacetime. It's not a snapshot.

An inertial observer has an associated "rest" frame. But, events may be labelled in that frame without explicit reference to any observer.

In many ways, it's better to imagine a reference frame as an infinite grid of equally spaced observers, all at rest relative to each other and all with pre synchronized clocks. Each observer records any local events, and the information from all observers is collated into the full set of observations.

In classical physics, two reference frames are related by the simple Galilean transformation, which preserves time intervals, lengths and simultaneity.

In SR, two reference frames are related by the Lorentz transformation, which preserves none of these this; but does preserve the length of spacetime intervals.

Read Morin!

 

[PeroK]

PS note the wooliness of your answer compared to the relative precision of mine.

That's not a criticism but it is vital that you learn precision in the use of scientific language.

 

[mucker]

A reference frame (in this context a global inertial reference frame) is a system of coordinates that label each event in spacetime. It's not a snapshot.

An inertial observer has an associated "rest" frame. But, events may be labelled in that frame without explicit reference to any observer.

In many ways, it's better to imagine a reference frame as an infinite grid of equally spaced observers, all at rest relative to each other and all with pre synchronized clocks. Each observer records any local events, and the information from all observers is collated into the full set of observations.

In classical physics, two reference frames are related by the simple Galilean transformation, which preserves time intervals, lengths and simultaneity.

In SR, two reference frames are related by the Lorentz transformation, which preserves none of these this; but does preserve the length of spacetime intervals.

Read Morin!

I've ordered the book!
What you describe above is how I currently understand what a ref frame is - so I don't see how you concluded that I don't understand what one is. Can you please indicate what I have said to make you think this? I am wondering if I am just not explaining myself correctly.

 

[PeroK]

I've ordered the book!
What you describe above is how I currently understand what a ref frame is - so I don't see how you concluded that I don't understand what one is. Can you please indicate what I have said to make you think this? I am wondering if I am just not explaining myself correctly.

In any case, the important thing is to learn and progress. If you already understand something, then that's fine.

 

[vanhees71]

You can move relative to a source of light, but you can't move relative to where light was emitted. Or, at least, not in your own rest frame.

Indeed, and maybe that's also a problem of a lot of confusion of students starting to learn relativity. One should not talk about the "invariance of the speed of light" but rather say the speed of light, as measured by an inertial observer, is independent of the velocity of the light source relative to that observer. Einstein formulated it in this clear and unambigous way already in his 1905 seminal paper. Why textbook writers haven't kept this good tradition, I can't say. The only sin in the 1905 paper is the introduction of "relativistic mass". Einstein rejected this idea however already in 1906/1907 after Planck's less well known paper about the special relativistic mechanics. A nice historical review can be found here (unfortunately there seems to be no freely accessible preprint):

https://doi.org/10.1119/1.3160671

 

[mucker]

Well the funny thing is, I just watched a YouTube video and get it now. Don’t know why i didn’t try it earlier, I think because YouTube is worse for reliability than the internet in general I didn’t trust it. Anyway, I was on the right path with my first question about motion (where I ask if the discrepancy is due to the moving observer not aware he is moving -post 3), but Was told I was wrong so abandoned it. I know that IS wrong btw, but if you look carefully and see the context my point is you should be able to see where I was going with it, and I was close the “getting it”. Ever since then I’ve been on a wild Goose chase and i was never going to figure it out as after I was looking in the wrong area.