Relativity of Simultaneity Questions

[Dale]

Ibix thanks Ibex, sorry for being dumb!

As @Ibix said, we have all made that same mistake multiple times on this road.

 

[Ibix]

Ibix thanks Ibex, sorry for being dumb!

It's easy done. I still do it from time to time. To be clear, you correctly calculated $\gamma=1/\sqrt{1-v^2/c^2}$ and correctly calculated $t-vx/c^2$ but then incorrectly combined them as $(t-vx/c^2)/\gamma$ instead of $\gamma(t-vx/c^2)$. As a general policy I'd recommend trying not to mix expressions containing gammas with expressions containing the square root form because if you do it's easy to substitute the wrong value as you did.

 

[mucker]

Yep, so now I've got that out the way and get the math (finally ) let's get back on track to my OP. I am trying to apply it to the train thought experiment. Let's just focus on one lighning bolt for a second.

from observer 1 (green man, stationary) a lighning bolt strikes 2ls away (he knows the distance for this example). He becomes aware of it at t2 obviously. If we were to plot this event on a spacetime diagram from his perspective do we say t=0, x=2ls, or is it actually t=-2, x=2ls? (because the current frame of reference of an observer is always rooted in t=0, so therefore this event lies 2 seconds in his past). I was at first thinking the former but after thinking through it for a while I think you would record it as the latter...

 

[Ibix]

because the current frame of reference of an observer is always rooted in t=0, so therefore this event lies 2 seconds in his past

You're always at t=0? So your watch always reads the same time? That's odd - I might stay in the same place but my watch always advances.

 

[Nugatory]

If we were to plot this event on a spacetime diagram from his perspective do we say t=0, x=2ls, or is it actually t=-2, x=2ls? (because the current frame of reference of an observer is always rooted in t=0, so therefore this event lies 2 seconds in his past). I was at first thinking the former but after thinking through it for a while I think you would record it as the latter...

It is indeed the latter, but not for the reason you say. Negative values of $t$ aren’t necessarily in the past, they’re just before whatever moment we decided to call $t=0$.

 

[Ibix]

It is indeed the latter, but not for the reason you say. Negative values of $t$ aren’t necessarily in the past, they’re just before whatever moment we decided to call $t=0$.

He can record it as either, surely, as long as he records the reception event consistently. The latter might make the maths slightly simpler, but not much. Or am I missing a stated constraint somewhere?

 

[mucker]

You're always at t=0. That's odd - I might stay in the same place but my watch always advances.

What I was getting at is in respect to base observer/inertial frame (as in from what you are going perform your transformations on) - whenever I see spacetime diagrams the worldline of an object always intersects t0 (unless it's been transformed). Another way of looking at it is that say that we plot the wordline of an object at t1x3, t2x4, is that just the same as t0x2, t1x3 if we move the axis's up one second (or wait for one second to pass)? And isn't it essenitally the same thing? What I am saying is that I always see a wordline intercept t=0 so I assumed that is the just the covention we use - as in we can plot a worldline for two events like I just did, and they mean exactly the same thing, but by convention we defer to the t=0 one.

I came to this conclusion based on the assumption that they are the same thing and that all diagrams i see always intercept t=0 at some point, they have to right? cause that is the present moment

EDIT: Maybe another way of me reprasing the question - why would we start drawing a worldline of an object at t1 (in the future) if we can draw it from t0? I can't see a reason to, which is why I proposed that an frame of reference (in the base spacetime diagram) would be rooted in t=0. Am I making sense or not explain myself well?

 

[mucker]

He can record it as either, surely, as long as he records the reception event consistently. The latter might make the maths slightly simpler, but not much. Or am I missing a stated constraint somewhere?

I suppose in a rounabout way, that is what I was asking and actually what I concluded. What I was asking then is if you can plot it both ways, is the norm (convention/standard/whatever) to draw based on the wordline intersecting t0?

EDIT: sorry I misread what you were answering here. Ignore my above comment, willl leave it here so you can see this edit and delete the comment in a bit

 

[Ibix]

You can put your origin anywhere and anywhen you like. However, it's convenient to place it at one event you intend to transform because the Lorentz transform of x=t=0 is really easy. So I would agree that putting the reception event at x=t=0 is sensible, but it's not obligatory.

My point was that you will always pass through t=0 - you cannot avoid it - but you never stay there. Your "because the current frame of reference of an observer is always rooted in t=0" made me think that you thought an observer was stuck at one time in their rest frame, not at one place. Perhaps I misunderstood.

 

[mucker]

https://www.physicsforums.com/members/ibix.365269/ Yeah I was asking about what is more convenient I suppose, or what is the standard way to represent it, as from what I've seen, most spacetime diagrams always show a wordline intercepting t0 and not t1 for example, as it's more intuitive to have it intersect t0

 

[Ibix]

By t0, I take it you mean $t=0$ and not some arbitrary time $t_0$? If so then I agree, but very much caution against saving yourself a keystroke by typing t0 instead of t=0. It'll only confuse people.

 

[mucker]

yep that's what I mean Ibex, I still don't the shorthands yet, thought t0 was just easier to write than t=0, I guess they mean different things...

 

[mucker]

So I have done a spreadsheet which does all the calcs based on some events you type in, but I was getting weird results when I played around with it, but the math was correct. I've realized the problem is that the train thought experiment is very unintuitive which is causing problems in me grasping this, but when I use the "train platform” thought experiment (second one by Daniel Frost) it made sense. The issue that makes the Einstein one difficult to visualise is that the lightning bolts disappear straight away so you can’t plot their location over time (they disappear after a second), so I can only list one event (if working with one bolt).

Anyway, see this snippet of the spreadsheet and I think I now “get it”. So the last question (hopefully hehe) is am I correct in my assessment of the following:

Context first – the spreadsheet for Einstein experiment. Ob1 is stood on the ground as the train goes past. Two bolts go hit exactly the same distance apart, each end of the train (like the thought experiment) and take 5 secs to reach him exactly.

Ob2 is a person moving 0.6 and what he concludes (not observes??) happened - that is, bolt 2 (on the right) happens (t=2.5) before bolt1. Is this assessment correct and do the numbers look good?

 

[mucker]

I can't help but feel there is something wrong with this visualisation of simultaneity. At first I thought they were using Lorentz transformations to work out what happens in mr blue frame. But now I don't think it is. In fact I don't see anything in the diagram that makes anything seem unintuitive - in mr greens frame he sees the bolts as expected (hit at the same time) and concludes the exact (and perfect) sequence of events that mr blue will conclude...without any Lorentz transformation. And all of that actually is easily quite intuitive (I mean it's obvious to conclude that R ray will hit mr blue first), so what's the big deal? i feel like how Mr blue's frame plays out might not be correct (as it's identical to what mr green concludes about blue), I feel like a Lorentz transformation is missing. To put it another way, from the diagram it looks like we don't need to use Lorentz transformations for mr green to conclude mr blues events, which would make the Lorentz transformation obsolete - which I know is definitely not the case. Am I missing something or is it a poor diagram? I feel lke it's howing what he observed, but not what he concluded...

 

[vanhees71]

At least the two Minkowski diagrams at the end look correct to me. I've also some Minkowski diagrams in my SRT manuscript (Sect. 1.2):

https://itp.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[Doc Al]

in mr greens frame he sees the bolts as expected (hit at the same time) and concludes the exact (and perfect) sequence of events that mr blue will conclude...without any Lorentz transformation.

The Lorentz transformations are embedded in the fact that each observer sees the same speed of light with respect to themselves. But, as shown in the diagrams, they disagree about whether the lightning flashes were simultaneous. They do agree that Mr. Green receives the light pulses together and Mr. Blue does not, but they draw different conclusions about what that means.

 

[vanhees71]

I find these usual formulations of the 2nd postulate a bit confusing. I think it's better to state that the speed of light for any inertial observer is $c$ independent of the (relative) velocity of the light source. That's also how Einstein stated it in his first paper on relativity (1905).

 

[Dale]

from observer 1 (green man, stationary) a lighning bolt strikes 2ls away (he knows the distance for this example). He becomes aware of it at t2 obviously. If we were to plot this event on a spacetime diagram from his perspective do we say t=0, x=2ls, or is it actually t=-2, x=2ls? (because the current frame of reference of an observer is always rooted in t=0, so therefore this event lies 2 seconds in his past). I was at first thinking the former but after thinking through it for a while I think you would record it as the latter...

You pick whatever origin you like. The origin needn't be at any specific time or place, but once you pick that origin you need to be consistent. So if you choose the origin as the event where the green man receives the light flash then receiving the light flash would be at $(t_r,x_r)=(0,0)$ and emitting the light flash would be at $(t_e,x_e)=(-2,2)$. Of course, if you wanted you could have chosen a different origin, it doesn't matter as long as you are consistent.

I think the usual origin would be chosen such that $(t_r,x_r)=(2,0)$ and $(t_e,x_e)=(0,2)$, but whatever you pick is fine. Just be consistent thereafter.

Is this assessment correct and do the numbers look good?

Yes, I confirm

 

[mucker]

Wow, so much confusion on my part. I was factoring in how long it takes the light to reach the observers which was over complicating it all (and wrong). I didn't realize when doing all the calcs, spacetime diagrams, Lorentz transformations that in fact you are performing them on exactly when they occurred (in your frame of reference). Once you take out the fact you don't need to account for distance traveled etc it becomes a lot less complex and easier to fathom! The word "observer" and "observed" really should be replaced with more intuitive words, as they just lead to confusion lol - I mean when I read statements that start with "x observes y..." I automatically think that those co-ordinates (on paper) need to be transformed (backtracked so to speak) to factor in the speed of light

If anyone is interested about how/where I went wrong, it was when I inputted ob1 x=5, t=5. I used those numbers because I was inputting in how he would observe it, that is if light was emitted 5ls away it would take 5 ls for him to see it. When in fact I should have just used t=0. I see now.

On a side note I would like to share an amazing spacetime tool I found. Has anyone seen this? Not only does it tell you when events occurred in diff ref frames, it also shows when they would be observed too (click the “show light paths” – the visualisation of it is presented very well - so wish I had access to this last week as it would saved me a week’s worth of headaches!

 

[mucker]

So hey guys, I’ve been ill for a week and been meaning to come back to this. There is one more thing that’s been bugging me since raising the OP; I hoped after doing the maths it would be clearer, but it’s not. I still have problems understanding the Einstein thought experiment. Just to be clear, there is another thought experiment by Daniel Frost” which I understood straight away with no difficulty at all – the exact same thought process I applied to the Einstein experiment which confused me, made perfect sense when applied to the Daniel Frost experiment. This (imo) implies to me that there is something missing in Einstein diagram or I should be applying a different thought process to it.

To get to the root of my confusion I’m going to have to go quite deep and explain my thought process step by step so apologies if the post is overly long and confusing, I am trying to give multiple possibilities of how I could interpret the data. To help in visualising my points I have drawn some spacetime diagrams as below.

Let’s start with the Daniel Frost one, as this to me, is more intuitive and I can completely understand the relatively of simultaneity using this example.

In this thought experiment (call it experiment A) an emitter (call it a bulb) emits light at t=0 from the centre of the train (EventA in diagram). From Observer’s A frame of reference (top right diagram) the light takes 5s to hit the front and back of train (Event B and C) at the same time, then a further 5ls to reach him making a total of 10ls. Since he knows the distance of Event B and C he concludes they happen at the same time. This example is very intuitive and easy to understand. Note the two horizonal lines going vertically are the world lines of the train at rest from his perspective (in case that wasn’t clear).

Now look at it from Observer B (left diagram) who is on the platform. From the diagram you can clearly see that the light emitted from EventA reaches the back of the train first, therefore events B and C do not happen simultaneously. All good so far, and I completely understand this too, again very easy to visualise and intuitive. An important fact I’d like to point out here though, is that it is EventA (from Observer B frame) that causes EventB and C to occur at different times, this is important because when we talk about the Einstein experiment next EventA isn’t present. Let’s now apply the same thought process to Einstein’s train experiment.

In this example (call it Experiment B) we no longer have an emitter at the centre of the train which strikes the front and back at the same time, instead we just have two lightning bolts hitting at the same time. ObserverA (left diagram) is on the platform and everything plays out as expected and he sees them at the same time. Now, it’s here where things start breaking down for me; I realized that the left diagram in this experiment is really just the same as the left diagram in experiment A…minus the emitter. In other words if we remove EventA (the cause of EventB and C) from experiment A you actually have exactly the same setup as experiment B…yet in experiment B OberserverA sees them at the same time whereas in experiment A the exact same observer doesn’t; so, ALL variables exactly the same in both experiments except the emitter at EventA, and we get different results because of it. Therefore, I came to the conclusion that the cause of Event B and C being out of sync is (at least in part) due to the light from the emitter causing the events to happen out of sync and not necessarily the light emitted from EventsB and C. Can someone please explain what I am missing here and tell how to come up with a thought process which will work for both experiments?

The other issue I can’t get my head around is in relation to the original Einstein diagram with mr green and mr blue. Mr greens concludes that R ray will hit blue before L ray because blue is moving to the right. We know that the speed of light is always the same relative to everyone regardless of your relative speed to something else. So when the two events happen “at the same time” the diagram implies/looks like blue is approaching R ray quicker, but since light never speeds up or slows down relative to you then R ray and L ray (moving at the same speed) should still arrive at the same time, even for him, but they don’t, according to the diagram. I could understand this if we said the speed of light was relative, as this would allow R ray to approach blue quicker, but we know this is not the case. Another way I looked at (which could be wrong, so please tell me if so) is to just forget about Observer A, like imagine he isn’t even there and just focus on Observer B. If the bolts hit at the same time, he will see them at the same time too – exactly like EventB and C in experiment A.

Thanks!

 

[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.