A spaceship traveling close to the speed of light sending some data....

[Bartolomeo]

If A and B are points (which is another name for the worldlines you say you don't need) then you are using each label to refer to two different things - the worldline through the lightning strike that is at rest in the embankment frame and the worldline through the same strike that is at rest in the train frame. As Orodruin says, this is a very similar mistake to the one Grimble is making.

I agree. It's negligence.

 

[Grimble]

No. If A and B are events they only exist at a particular time. You cannot say that an event is a fixed point in space - it is a point in space at a given point in time.

Yes, Exactly; events occur at a specific locations in each and every frame. - Locations cannot exist just for a moment in time. So the location where an event occurred is fixed, it has coordinates in that frame of reference.

There is no notion of an event "moving" because in order for something to move it must exist at different times.

Exactly, because an event cannot move the location of the event must be a fixed set of coordinates in each and every frame.

You keep repeating the same basic mistake - events cannot be assigned a state of motion and all your reasoning is built on the assumption that it can.

No, my whole reasoning is based on the fact that they have fixed locations. A and B have locations fixed when those events occur irrespective of any movements of the sources of those lights. A and B are fixed locations and cannot move relative to any observer in that observer's rest frame. Therefore the Spacetime Interval between M' and A and between M' and B are fixed and equal in the rest frame of M'.

Why do you have a difficulty with this? It is the fundamental basis of relativity - everything is relative.

 

[Grimble]

And therefore not in the platform frame.

Yes, of course, in the observer's rest frame whether that observer be on the Embankment or the train.

 

[Grimble]

I don’t know, how everyone can be at rest.

Everyone is at rest in their own rest frame - the clue is in the name.

This is at the heart of relativity.
AS A is to B so B is to A.
As A moves in B's frame so B moves in A's frame.

In the Embankment frame M is at rest and A and B are the coordinates relative to frame E where the lightning struck.
The burn marks on the rails are fixed and at rest - in the embankment frame.

The burn marks fixed on the rails are not fixed in the train's frame but are moving, with the embankment, away from the train.

Much of the confusion comes from the fact that A and B are also points on the train that have fixed coordinates in the train's frame.

In the train frame M' is at rest and A and B are the coordinates, relative to frame T, where the lightning struck.

AM = AM' = MB = M'B when the lightning strikes occur; in frame E; A,B (on the track) and M are all fixed and those distance do not change.
AM = AM' = MB = M'B when the lightning strikes occur; in frame T; A,B (on the train) and M' are all fixed and those distance do not change.

 

[Mister T]

Yes, of course, in the observer's rest frame whether that observer be on the Embankment or the train.

No.

In the frame in which the lightning strikes are simultaneous the burn mark from the flash arrivals will be midway between the burn marks from the lightning strikes.

In the frame in which the lightning strikes are not simultaneous the burn mark from the flash arrivals will not be midway between the burn marks from the lightning strikes.

In both the frames the flashes meet. But only in the frame where they meet midway are the strikes simultaneous. That frame can be either the train frame or the platform train, but it can't be both!

 

[Orodruin]

So the location where an event occurred is fixed, it has coordinates in that frame of reference

Obviously. Your fallacy is to go from there to assigning a state of motion to the events themselves.

A and B are fixed locations and cannot move relative to any observer in that observer's rest frame.

Again you fail to see the point: Events do not move. That they have some particular spatial coordinates in some frame is irrelevant. You could then argue that they would be at rest in all frames which would be absurd. Until you get this point you will not understand special or galilean relativity.

Why do you have a difficulty with this? It is the fundamental basis of relativity - everything is relative.

I teach relativity at university level. I am very familiar with the theory and I have seen your fallacy many times in many different people. If you doubt this you can ask any regular here about my understanding of relativity. You have failed to grasp a fundamental concept of relativity and until you dispell this misunderstanding you will struggle to understand relativity.

And no, everything is not relative. In fact, as physicists we try to express as many things as possible in terms of invariants.

 

[Ibix]

In the Embankment frame M is at rest and A and B are the coordinates relative to frame E where the lightning struck.
The burn marks on the rails are fixed and at rest - in the embankment frame.

In which case A and B are points in space, not events.

Much of the confusion comes from the fact that A and B are also points on the train that have fixed coordinates in the train's frame.

In which case A and B are points in a different definition of space, not events.

Your continuing failure to distinguish between points in space (which are lines in spacetime) and events (which are points in spacetime) is the source of all the confusion, at least in this thread.

AM = AM' = MB = M'B when the lightning strikes occur; in frame E;

Assuming the strikes are simultaneous in E this is true.

AM = AM' = MB = M'B when the lightning strikes occur; in frame T;

Assuming the strikes are simultaneous in T this is true. Note the contradiction to the above. The problem is that in at least one of these frames the strikes are not simultaneous, so "when the lightning strikes occur" is not a single time and the statement for that frame is not coherent.

 

[Ibix]

@Grimble - Perhaps another way to look at this: I am currently sitting in a train waiting to leave a station. Shortly (I hope...) the signal will go green and we will leave.

"The signal goes green" is an event. Five minutes later, where is the signal goes green in the platform frame and the train frame?

You are saying that, five minutes later, in the train frame the signal goes green is at the front of the train, and in the platform frame the signal goes green is at the signal.

We are pointing out that neither the question nor your answers even make sense. "The signal goes green" is a place and a time. You can ask "where did the signal go green" and get a sensible (and frame-dependent) answer because "the place where the signal was when it changed" is a point in space (albeit a different point for different frames). You can't ask where is the signal goes green now, nor say how fast was the signal goes green travelling. They aren't valid concepts.

 

[Mister T]

Everyone is at rest in their own rest frame - the clue is in the name.

This is at the heart of relativity.
AS A is to B so B is to A.
As A moves in B's frame so B moves in A's frame.

In the Embankment frame M is at rest and A and B are the coordinates relative to frame E where the lightning struck.
The burn marks on the rails are fixed and at rest - in the embankment frame.

The burn marks fixed on the rails are not fixed in the train's frame but are moving, with the embankment, away from the train.

Much of the confusion comes from the fact that A and B are also points on the train that have fixed coordinates in the train's frame.

In the train frame M' is at rest and A and B are the coordinates, relative to frame T, where the lightning struck.

AM = AM' = MB = M'B when the lightning strikes occur; in frame E; A,B (on the track) and M are all fixed and those distance do not change.
AM = AM' = MB = M'B when the lightning strikes occur; in frame T; A,B (on the train) and M' are all fixed and those distance do not change.

I am going to restate your details in a more compact form, retaining your notation and defining it in a way that's consistent with the way you are using it:

E is the rest frame of the embankment.
T is the rest frame of the train.

Much of the confusion comes from the fact that A and B are also points on the train that have fixed coordinates in the train's frame.

Okay, then let's say A is one of the burn marks on the train from one of the lightning strikes, and B is the other burn mark on the train from the other lightning strike.

In the train frame M' is at rest [...]

So let's say M' is a burn mark on the train. This burn mark was created there in the following way. When burn mark A was created by a lightning strike, a flash of light was also created. Likewise, when burn mark B was created by a lightning strike, a flash of light was also created. When those two flashes met it set off an explosion that left a burn mark M' on the train. (You might imagine a string of explosive devices laid along either the floor of the train or along the embankment, separated by just a micrometer or so. Each device is set to explode if and only if two flashes of light arrive from opposite directions within a few nanoseconds of each other, so that only one or possibly two adjacent devices will explode, creating a burn mark or two separated by no more than a micrometer or so. this will mark the location of M').

Let's say this same explosion also left a burn mark M on the embankment.

AM = AM' = MB = M'B when the lightning strikes occur; in frame E; A,B (on the track) and M are all fixed and those distance do not change.

Such an arrangement is not possible for several reasons.

First, M and M' are both created after A and B are created.Thus when A is created, M and M' do not yet exist. Likewise, when B is created M and M' do not yet exist.

Second, it's not possible for M and M' to both be midway between A and B. If M' is midway, then M is not, and vice-versa. The reason is because E and T are in relative motion.

 

[PeterDonis]

A and B are fixed locations and cannot move relative to any observer in that observer's rest frame.

Wrong. The spatial locations of A and B are fixed (do not move) in only one frame, the rest frame of M. In any other frame, they move.

Therefore the Spacetime Interval between M' and A and between M' and B are fixed and equal in the rest frame of M'.

Wrong in two ways. First, spacetime intervals are invariants; they aren't frame-dependent. Second, spacetime intervals are between events, not points in space.

The correct way of reasoning would be: in the rest frame of M', there is a point in space that represents the location of event M'. That point in space is represented by a worldline--a curve in spacetime, whose spatial coordinates in the rest frame of M' are constant. But in the rest frame of M (no prime), that worldline moves--its spatial coordinates are not constant. So even though the spatial locations of A and B are fixed in the rest frame of M, the spatial location of the worldline of M' is not fixed in that frame. Conversely, if we are working in the rest frame of M', the spatial location of event M' is fixed, but the spatial locations of events A and B are not--they move. That is where your reasoning breaks down.

 

[Grimble]

Obviously. Your fallacy is to go from there to assigning a state of motion to the events themselves.

Why oh why do you keep claiming that?
Every event is fixed in every frame at the space coordinates where the event occurred, just as it is fixed at the time coordinate when the event occurred.

Events cannot move. movement is change of location over time.
Events occur at a particular location and exist for a moment of time and therefore cannot move.

So why do you keep insisting that I am assigning a state of motion to events?

Will you please, please, please stop being so enigmatic and explain what you mean?

 

[Orodruin]

Will you please, please, please stop being so enigmatic and explain what you mean?

I have (and so have others) but you have kept refusing to listen. Events are not something that exists for an extended time. They are localised in time as well as in space.

So why do you keep insisting that I am assigning a state of motion to events?

You have claimed that they are at rest. Rest is a state of motion.

Events occur at a particular location and exist for a moment of time and therefore cannot move.

So why do you keep claiming that they do?

 

[Alan McIntire]

With both ships moving away from each other at a fraction of the speed of light v, both ships will see the other moving slow at a rate of
sqrt (1+v/11-v). If approaching each other, they will see the other ship moving fast at a rate of sqrt (1+v/1-v) thanks to Doppler effects.

For example, at 4/5 light speed, the ships will see each other Doppler shifted slow at (1-4/5 divided by 1-4/5)^1/2 = 1/3 speed.

 

[PeterDonis]

Every event is fixed in every frame at the space coordinates where the event occurred, just as it is fixed at the time coordinate when the event occurred.

The word "fixed" implies "does not move". That means you are imputing a state of motion (not moving) to an event.

Will you please, please, please stop being so enigmatic and explain what you mean?

Here is the math. The specification of the scenario is that there are events with the following coordinates in the rest frame of M (coordinates are given as $(x, t)$ pairs, and I have chosen the units of space and time so all the following coordinate values in this frame come out to be nice unit integers):

Event A: a light flash strikes the embankment and the rear end of the train at $(-1, 0)$

Event B: a light flash strikes the embankment and the front end of the train at $(1, 0)$.

Event M: Light from both light flashes reaches the observer on the embankment at $(0, 1)$.

Event O: The observer at the midpoint of the embankment and the observer at the midpoint of the train are co-located (just passing each other) at $(0, 0)$.

Now, assume that the train moves at speed $v < 1$ in the positive $x$ direction relative to the embankment (we are using units in which $c = 1$). Then we can easily compute the events at which the light flashes from event A and event B meet the observer at the midpoint of the train. They will be:

Event MB': Light from the flash at the front of the train reaches the observer at the midpoint of the train at $( \frac{v}{1+v}, \frac{1}{1+v} )$.

Event MA': Light from the flash at the rear of the train reaches the observer at the midpoint of the train at $( \frac{v}{1-v}, \frac{1}{1-v} )$.

It is obvious that these two events are not the same--i.e., they are different points in spacetime. In other words, you have been using the symbol M' under the assumption that it referred to some single event--but it doesn't, because there is no single event where the light flashes reach the observer at the midpoint of the train. In other words: you have been reasoning from a false premise. That is why you have been getting false conclusions.

Using the correct premise, we can see that since MB' obviously occurs before MA', the flash from the front of the train will reach the observer at the midpoint before the flash at the rear of the train, just as Einstein said.

But just to be sure, let's transform everything into the train's rest frame. The Lorentz transformation will be $x' = \gamma \left( x - v t \right)$, $t' = \gamma \left( t - v x \right)$. So the coordinates in the primed frame (the train frame) of all the events above come out to be as follows:

Event A: $(- \gamma, \gamma v)$

Event B: $(\gamma, - \gamma v)$

Event M: $(- \gamma v, \gamma)$

Event O: $(0, 0)$

Event MB': $(0, \sqrt{\frac{1-v}{1+v}})$

Event MA': $(0, \sqrt{\frac{1+v}{1-v}})$

Note that events MB' and MA' both happen at $x' = 0$, i.e., at the midpoint of the train, but at different times.

All this is bog standard SR, and this is what we mean when we say you are incorrect.

 

[Ibix]

Every event is fixed in every frame at the space coordinates where the event occurred, just as it is fixed at the time coordinate when the event occurred.

...which means that it does not exist except at one place and time. So it neither moves nor is stationary.

An event is a point in spacetime. Things neither move nor do not move in spacetime. Motion (or not) is something you can only get by taking two non-intersecting slices of spacetime, calling them "space at two different times" and asking "has this thing changed location?" An event only exists in at most one of the slices, so you cannot meaningfully answer the question.

You can certainly assosciate (x,y,z,t) coordinates with an event and refer to (x,y,z) as "the point at which the event happened/will happen". But (x,y,z) is a worldline, and is different for every frame. You keep referring to events and worldlines interchangeably. It's extremely confusing. It's referring to "the traffic lights" and "the traffic lights changed to green" as if they were the same thing.

 

[Ibix]

And therefore not in the platform frame.

Point taken. However, I think we were both confused - the original setup has simultaneity in the platform frame:

observers at rest upon the embankment will observe the lights meeting at midpoint M proving that events A & B were simultaneous in their frame of reference.

I'm not disagreeing with any of your argument, @Mister T, but I think you might have the setup backwards (and I managed to have both his and yours backwards...).

 

[Grimble]

Ah! now I do see what you are all saying and why we seem to be using the same words yet speaking different languages!
You say I am giving motion to events when I say their locations are at rest in the rest-frame of an observer - because that 'rest frame' is only 'at rest' measured from itself! From any other frame it is moving - and because 'at rest' has to be relative to something and that something has a state of motion relative to everything else.

Because I have tried to explain how I understand relativity using your framework it doesn't work (for explaining my understanding); because I immediately place myself within the constraints of your views using anthropomorphised frames of reference (well not exactly given human form but at least given physical form - embankments and trains); because that immediately gives rise to 'preferred frames' - usually the embankment - e.g. when we say that the lightning flashes were simultaneous in that frame.
I believe there is a fundamental error in that very phrase for events A and B are not simultaneous in the Embankment frame but are measured to be simultaneous in that frame.

I do not believe that Spacetime has any rest state. That everything moves relative to everything else. That every observer measures Spacetime from their own rest frame. That is not stating that any frame is truly at rest for the very concept does not exist for there is no way to assign a state of rest in Spacetime.
A frame of reference is no more than a map of Spacetime based upon a particular event - a point in space at a point in time and therefore every frame of reference is at rest relative to that initial event.
I am sorry if I do not use the correct phrases for I am not a professional scientist, but I am trying to explain what my understanding is.

Let me ask you all a question that is at the very heart of my understanding of relativity. If A and B are two events in Spacetime and light emitted at those events meets at point M midway between A and B, were A and B simultaneous? Note, this is without defining any frames of reference and without defining any observer, let us say it is an objective view that could be measured from anywhere.

 

[Bartolomeo]

My additions in square brackets.

If A and B are points (which is another name for the worldlines you say you don't need) then you are using each label to refer to two different things - the worldline through the lightning strike that is at rest in the embankment frame and the worldline through the same strike that is at rest in the train frame. As Orodruin says, this is a very similar mistake to the one Grimble is making.

You do seem to me to consistently have trouble separating things that are frame dependent and things that are not. At least, your writing is extremely confused about it.

I think in this case we did not understand each other. I thought that you found fault with the notation and agreed with you. Indeed, it is not entirely correct labeling event by point’s index.

I thought it was a formality, but yes, it is significant in certain sense.

So, your addition in the brackets is unnecessary. It is clear that E is on the Embankment and T1 is in the train.

Sure, it is senseless to look for fallacy in train experiment. I think I misinterpreted Grimble. I am not sure I understand what he wanted to say. Does he unwittingly assigns simultaneity of events to the train and admits that rays of light will meet in the centre of the train, if they were simultaneous in embankment frame?

 

[Battlemage!]

Let me ask you all a question that is at the very heart of my understanding of relativity. If A and B are two events in Spacetime and light emitted at those events meets at point M midway between A and B, were A and B simultaneous? Note, this is without defining any frames of reference and without defining any observer, let us say it is an objective view that could be measured from anywhere.

My non-professional take: asking if events are simultaneous without specifying which frame you are speaking about is like asking if an object is big or small. Compared to what? It's a meaningless concept.

 

[Ibix]

Let me ask you all a question that is at the very heart of my understanding of relativity. If A and B are two events in Spacetime and light emitted at those events meets at point M midway between A and B, were A and B simultaneous? Note, this is without defining any frames of reference and without defining any observer, let us say it is an objective view that could be measured from anywhere.

That question does not make sense. You need to pick a simultaneity criterion to be able to discuss simultaneity.

You certainly can express relativity without reference to frames - "coordinate free representations". But simultaneity is not a concept in such views.

 

[PeroK]

Let me ask you all a question that is at the very heart of my understanding of relativity. If A and B are two events in Spacetime and light emitted at those events meets at point M midway between A and B, were A and B simultaneous? Note, this is without defining any frames of reference and without defining any observer, let us say it is an objective view that could be measured from anywhere.

Sadly, your question takes as a premise that simultaneity of two events is absolute. If you assume this, then you are bound to run into a contradiction at some point, given that SR shows that simultaneity is relative.

 

[Ibix]

I think I misinterpreted Grimble. I am not sure I understand what he wanted to say. Does he unwittingly assigns simultaneity of events to the train and admits that rays of light will meet in the centre of the train, if they were simultaneous in embankment frame?

I'm not sure. From his last post, I suspect he's figured out the block universe model but has not quite worked through the idea that there is no preferred direction in which to view it. I could be wrong...

 

[jbriggs444]

A frame of reference is no more than a map of Spacetime based upon a particular event - a point in space at a point in time and therefore every frame of reference is at rest relative to that initial event.

An event has no definable state of motion. You cannot be "at rest" relative to something for which no state of motion is defined.

 

[PAllen]

Ah! now I do see what you are all saying and why we seem to be using the same words yet speaking different languages!
You say I am giving motion to events when I say their locations are at rest in the rest-frame of an observer - because that 'rest frame' is only 'at rest' measured from itself! From any other frame it is moving - and because 'at rest' has to be relative to something and that something has a state of motion relative to everything else.

Because I have tried to explain how I understand relativity using your framework it doesn't work (for explaining my understanding); because I immediately place myself within the constraints of your views using anthropomorphised frames of reference (well not exactly given human form but at least given physical form - embankments and trains); because that immediately gives rise to 'preferred frames' - usually the embankment - e.g. when we say that the lightning flashes were simultaneous in that frame.
I believe there is a fundamental error in that very phrase for events A and B are not simultaneous in the Embankment frame but are measured to be simultaneous in that frame.

I do not believe that Spacetime has any rest state. That everything moves relative to everything else. That every observer measures Spacetime from their own rest frame. That is not stating that any frame is truly at rest for the very concept does not exist for there is no way to assign a state of rest in Spacetime.
A frame of reference is no more than a map of Spacetime based upon a particular event - a point in space at a point in time and therefore every frame of reference is at rest relative to that initial event.
I am sorry if I do not use the correct phrases for I am not a professional scientist, but I am trying to explain what my understanding is.

Let me ask you all a question that is at the very heart of my understanding of relativity. If A and B are two events in Spacetime and light emitted at those events meets at point M midway between A and B, were A and B simultaneous? Note, this is without defining any frames of reference and without defining any observer, let us say it is an objective view that could be measured from anywhere.

To answer your last question, it again shows a very basic misunderstanding. Midpoint between A and B in spacetime is an event with space like separation between A and B, therefore no signals from A and B could possibly reach it. So, to define a reachable event you have to posit a world line through M, and there are an infinity of such choices, thus your question has no meaning without a frame of reference - which picks which world line through M is considered to be stationary. Given a choice such that signals from A and B arrive at the same event on this world line, you can say that in the frame where this particular world line is stationary, events A and B are simultaneous. In every other frame, which pick different world lines through M as the stationary one, they are not simultaneous.

 

[PeterDonis]

were A and B simultaneous? Note, this is without defining any frames of reference

Then your question makes no sense, because "simultaneous" has no meaning unless you define a frame of reference. This has been said many times in many ways in response to your posts. Enough is enough. Thread closed.