# I The velocity of a moving frame of reference

#### jbriggs444

Homework Helper
a person is on a train heading east. Another person is on a train heading west . Person 1 sees the train whiz by, person 2 sees the other train whiz by

i assume we are expected to conclude neither train is moving ?
Both trains are moving with respect to the other. That is all that can be said from the givens of the scenario.

It could be that the east-facing person is stopped at a station (stopped relative to the tracks) while the west bound train passes by.

It could be that the west-facing person is stopped at a station (stopped relative to the tracks) while the east bound train passes by.

It could be that they are each rolling in their respective directions (relative to the tracks).

It could be that the tracks themselves are moving (relative to the center of the Earth) and that the Earth is moving (relative to the Sun) and that the Sun is moving (relative to the Milky Way) and that the Milky Way is moving (relative to a frame of reference in which the cosmic microwave background is isotropic).

#### RossBlenkinsop

so you say absolute position and movement has no meaning

but then go on to say that a single flash of light from a single light can map back to multiple points where the location of that point is a function of the position of the observer of the event

does

#### RossBlenkinsop

so the outcome of the experiment is a function of the location of where the experiment was conducted !!

#### RossBlenkinsop

that sounds reproducible

#### jbriggs444

Homework Helper
so you say absolute position and movement has no meaning

but then go on to say that a single flash of light from a single light can map back to multiple points where the location of that point is a function of the position of the observer of the event
The flash traces back to a single event. That event has coordinates (x,y,z,t) in each frame of reference that one might choose to use. But if one picks out the event now that that is at the same point (same x,y,z but not necessarily t coordinates) as that event then, the event that is chosen will depend on a standard of rest.

A frame of reference is a standard of rest.

[There is a distinction that can be made between "coordinate system" and "frame of reference". I am running roughshod over that distinction in the name of simplicity].

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#### RossBlenkinsop

so you have multiple people who trace the photons from a single flash of light back to multiple single points

that may be the case but all of those people are stuck with the fact that the particular point they found , as the speed of light is invariant, will not move over time , and if they conducted the same experiment over and over and over over billions of year they would arrive back at the same point

so the points may be in different locations, but all of those points will never move and all of those points will be at rest wrt every other point found

do we now have a matrix of points that appear to hold the same location over any given time frame ?

so if an object is moving wrt those points, is it moving ?

#### PeterDonis

Mentor
so you have multiple people who trace the photons from a single flash of light back to multiple single points
You are really confusing yourself by using this language.

Spacetime has events. Events are points in spacetime, not space. ("Space" is not an invariant concept in relativity; it depends on your choice of reference frame. So there is no such thing as "points in space" in relativity in any invariant sense.) The flash of light is an event. Each of the multiple people observing that flash of light receives it at another event; and those reception events are different for the different people.

If each of the different people uses a different frame (for example, the frame in which they are personally at rest), they will assign different coordinates to the event of the flash of light. But by transforming between frames they will easily be able to show that the flash of light is the same event for all of them.

You need to go back and rethink your entire scenario in the light of the above. Your conceptual grasp of it is fundamentally wrong; until you fix that, nothing will make sense to you, and everyone's efforts to help you understand will be in vain.

#### Janus

Staff Emeritus
Gold Member
so the outcome of the experiment is a function of the location of where the experiment was conducted !!
No.

For example. I we attach measuring sticks to A, B and C in my last example, You would get somethig like this as measured in the rest frame of B.

If A B and C were at rest with respect to each other, they would measure their sticks as being the same length and the each mark being the same distance apart. But Since A and C are in motion as measured from this frame, their sticks are length contracted. B still remains at the center of the light pulse.

From the rest frame of A, this is what is happening.

A's stick is it's normal length and B and C's sticks are contracted, C's more so because it has a greater relative motion. A remains at the center of the expanding light.

Now let's pick an event that takes place after the light pulse is emitted. Well choose when the emitted light flash reaches the right end of C's measuring stick.

According to B, this is how this event looks:
(this image does not show the exact moment, which occurs between frames in the above animation, but the frame just prior to it)

The end of the rod, (14 marks from C), is just past the eighth mark of B's stick and just shy of the 5th mark of A's stick.

If we look at this same event from A's frame, it looks like this.
(this is the first full frame after the event)

Again, the light reached the 14th mark of C's stick, when that end is just past the eighth mark of B's stick and just shy of the fifth mark on A's stick. Even though now A is at the center of the expanding light.

All three frames will agree on any measurable event, though they may disagree on the order some of those events. So for example in the first image, C has reached the fourth mark of B's stick, while in second image, it hasn't even reached the second mark yet. This means that In B's frame of reference, C reaches the Third mark of B before the light has reached the end of C's stick, while in A's frame, C doesn't reach the third mark until after the light has reached the end of C's stick.

This is the "relativity of simultaneity" @Nugatory referred to.

#### Nugatory

Mentor
but then go on to say that a single flash of light from a single light can map back to multiple points where the location of that point is a function of the position of the observer of the event
Yes. One way to see this is to imagine that you and I are in our railcars, moving in opposite directions on parallel tracks. As @jbriggs444 has said above in post #80 it might be that we're both moving relative to the tracks, or I might be stopped at the station as your train passes by, or you might be stopped at the station while my train passes by.... that doesn't matter.... we could even remove the tracks, the station, and the surface of the earth from the thought experiment so that we're moving past one in empty space with no external reference other than the position of the other train.

We're looking out our windows so as we pass one another we're face to face looking at each other from a distance of just a meter or so. At that moment a drone carrying a strobe light zooms between us and the strobe flashes just as it passes between us (the speed of the drone relative to us is irrelevant - all that matters is where it was at the moment that the strobe flashed). For convenience, we both zero our wristwatches at that moment.

Naturally you consider yourself to be at rest while I'm moving. You expect that photdetectors also at rest (relative to you, so they're moving relative to me) and one light-second to your left and right will trigger one second later according to your wristwatch, and indeed they do. You trace the path of the light back from the photodetectors and you come up with the completely unsurprising result that the light was emitted from the point right in front you, where the strobe on the drone flashed. You're not moving, so that point isn't changing.

I can do the same analysis considering myself to be at rest and using photodetectors that are at rest relative to me, and I will come up with a similar conclusion: the light traces back to the point in space right in front of me (in my analysis I am not moving so "right in front of me" is the same point at all times).

But "right in front of me when I'm not moving" is a different point than "right in front of you when you're not moving". That's why there is no absolute position.

However - and this is what we've been teling you even though you don't seem to be listening - an event is a point in spacetime, not a point in space. No matter which of us we consider to be moving, if we trace the path of the light back to where it was emitted, we will agree that it came from:
- right under my nose at the moment that I set my watch to zero
- right under your nose at the moment that you set your watch to zero
- the exact time and place (that's "time and place", as opposed to "place" because we're talking about points in spacetime, not space) that the strobe flashed.

This would be a good time to follow through on my suggestion above about learning about Minkowski diagrams and worldlines.

#### RossBlenkinsop

so you have multiple people who trace the photons from a single flash of light back to multiple single points

Spacetime has events. Events are points in spacetime, not space. ("Space" is not an invariant concept in relativity; it depends on your choice of reference frame. So there is no such thing as "points in space" in relativity in any invariant sense.) The flash of light is an event. Each of the multiple people observing that flash of light receives it at another event; and those reception events are different for the different people.
my understanding from the last series of posts is if multiple people in multiple frames trace a single flash of a single light back to the origin of the flash they will all end up at multiple points in "Space" ?

#### Nugatory

Mentor
my understanding from the last series of posts is if multiple people in multiple frames trace a single flash of a single light back to the origin of the flash they will all end up at multiple points in "Space" ?
Yes. They will each trace it back to the point in space at which the flash was emitted, which will be a different point in space (that is, has different x, y, and z coordinates) in the dfferent frames. However, they will all trace the flash back to the same point in spacetime (that is, an event identified by x, y, z, and t coordinates).

#### metastable

my understanding from the last series of posts is if multiple people in multiple frames trace a single flash of a single light back to the origin of the flash they will all end up at multiple points in "Space" ?
A thought experient that helped me understand the concept a bit better was this... Suppose I fire a 20gev positron followed immediately after by a 20gev + 1ev electron (both in the same direction from the same gun). If I was traveling alongside the center of mass of the collision at the same velocity, I’d witness 2 photons leave the scene going in opposite directions, likely of equal energy, and to me the photons would appear to only have the rest energy of the electron + positron + a small amount of extra energy

But If I am in the frame of the lab, things look very different. Both photons appear to be traveling in almost the same direction, and one of the photons has much more energy than the other.

#### PeterDonis

Mentor
They will each trace it back to the point in space at which the flash was emitted, which will be a different point in space (that is, has different x, y, and z coordinates) in the dfferent frames.
No, it won't, at least if we suppose that at the instant both observers see the strobe flash, they both mark that point in space (in their respective frames) as the origin, $x = y = z = 0$.

With that understood, both observers will say that the point where the flash was emitted is their spatial origin, $x = y = z = 0$. (And since they both synchronized their clocks to read zero at that instant, they will also say the flash was emitted at the event which is their spacetime origin, $x = y = z = t = 0$.)

The difference between the two observers is that what each one calls "my spatial origin" is moving relative to the other. In other words, what each one calls "a point in space" is not a "point in space" relative to the other, because it's moving.

#### Nugatory

Mentor
No, it won't,
Yes, I need to find a less ambiguous way of wording it. Both will trace the flash back to points to which they assign the coordinates x=y=z=0 when they’re using different coordinate systems. But if we limit ourselves to one set of coordinates (the ones in which I am at rest, for definiteness) to talk about the situation, then no matter how we label the point that the other observer calls x=y=z=0, we’re going to label it something other than x=y=z=0. (And if we do the labeling right, x will be a function of t so in effect we’ve specified a line in the Minkowski x-t plane),

And at this point I’ve recapitulated the reason that @Ibix put scare-quotes around the spatial coordinates in post #47 of this thread. @RossBlenkinsop you should ignore this sidebar conversation, instead work on understanding why both observers trace the light back to the same point in spacetime, not space.

#### Ibix

Here are a couple of spacetime diagrams. These are essentially displacement-versus-time diagrams, except that conventionally time is shown up the page and position horizontally. Also, the scale is picked to be seconds and light seconds, so that the speed of light (one light second per second) gives the paths followed by light a slope of $\pm 1$.

Apologies for the hand-sketching. All lines are meant to be straight. I can draw computer-generated versions at the weekend if it helps.

Here is the first diagram:

In this diagram there is one observer, marked in red, stationary at the origin. A second observer, marked in blue, passes by moving to the right. At the instant they pass, a flash of light is emitted, marked in fine orange lines. Because the slope of these lines is $\pm 1$, the midpoint ("where the flash was emitted") is always where the red observer is. The blue observer is to the right of this at all times after the actual emission event.

Here's the same scenario in the blue observer's rest frame:

Now the blue observer is stationary at the origin and the red observer approaches moving to the left. Again the flashes are emitted when the observers pass, but this time the midpoint of the flashes is where the blue observer is.

So in both cases "where the flash was emitted" is the origin of the spatial coordinates ($x=0$ in one case, $x'=0$ in the other). But it's clear that the two frames mean different things by this - $x=0$ is where the red observer is and $x'=0$ is where the blue observer is. And they are not in the same place.

If, as @Nugatory has suggested a couple of times, you actually mean that "the flash happens when and where the observers pass one another" then everyone will agree. But this is an event (a place and time), not a point. A point in space has multiple different meanings depending on which frame is doing the describing.

#### metastable

A thought experient that helped me understand the concept a bit better was this... Suppose I fire a 20gev positron followed immediately after by a 20gev + 1ev electron (both in the same direction from the same gun). If I was traveling alongside the center of mass of the collision at the same velocity, I’d witness 2 photons leave the scene going in opposite directions, likely of equal energy, and to me the photons would appear to only have the rest energy of the electron + positron + a small amount of extra energy

But If I am in the frame of the lab, things look very different. Both photons appear to be traveling in almost the same direction, and one of the photons has much more energy than the other.
I should add a slight correction to this... the scenario makes a large assumption the lab frame isn't a spacecraft with relatively low mass. If that were the case, the lab derives impulse from each of the firings, accelerating the lab frame between firings, so the collision energy might be a bit different than expected under other circumstances.

#### Janus

Staff Emeritus
Gold Member
Here are a couple of spacetime diagrams. These are essentially displacement-versus-time diagrams, except that conventionally time is shown up the page and position horizontally. Also, the scale is picked to be seconds and light seconds, so that the speed of light (one light second per second) gives the paths followed by light a slope of $\pm 1$.

Apologies for the hand-sketching. All lines are meant to be straight. I can draw computer-generated versions at the weekend if it helps.

Here is the first diagram:View attachment 244704
In this diagram there is one observer, marked in red, stationary at the origin. A second observer, marked in blue, passes by moving to the right. At the instant they pass, a flash of light is emitted, marked in fine orange lines. Because the slope of these lines is $\pm 1$, the midpoint ("where the flash was emitted") is always where the red observer is. The blue observer is to the right of this at all times after the actual emission event.

Here's the same scenario in the blue observer's rest frame:
View attachment 244703
Now the blue observer is stationary at the origin and the red observer approaches moving to the left. Again the flashes are emitted when the observers pass, but this time the midpoint of the flashes is where the blue observer is.

So in both cases "where the flash was emitted" is the origin of the spatial coordinates ($x=0$ in one case, $x'=0$ in the other). But it's clear that the two frames mean different things by this - $x=0$ is where the red observer is and $x'=0$ is where the blue observer is. And they are not in the same place.

If, as @Nugatory has suggested a couple of times, you actually mean that "the flash happens when and where the observers pass one another" then everyone will agree. But this is an event (a place and time), not a point. A point in space has multiple different meanings depending on which frame is doing the describing.
Here, I took the liberty of knocking them out for you. It just took a couple of minutes, as I have a program that is designed just for plotting space-time diagrams.

It's a nice little piece of software that allow you to create world-lines, light beams, and events. Then you can either click on any world-line to "match speeds" with it, or assign your own boost to choose the frame from which you want to plot from.

#### Ibix

It just took a couple of minutes, as I have a program that is designed just for plotting space-time diagrams.
Thanks. I have something similar, but it doesn't work on my phone. I should do something about that one day, given the amount of PFing I do on my phone.

#### metastable

if multiple people in multiple frames trace a single flash of a single light
How do you propose multiple people observe the same photon?

#### jbriggs444

Homework Helper
How do you propose multiple people observe the same photon?
No need to invoke quantum mechanics. A single flash of light, such as a flashbulb going off can be seen by many people.

#### Ibix

How do you propose multiple people observe the same photon?
Why do you assume "flash of light" means one photon?

#### metastable

I was thinking a flash of light meant many photons, but each photon can only been seen by one observer.

#### Ibix

That really doesn't matter to this scenario. Nothing in this has anything to do with individual photons. The basic idea is to emit an arbitrarily short but very bright pulse and have the observers use a beam splitter to detect the pulse while passing most of it for other observers to detect.

All of the issues that @RossBlenkinsop is struggling with arise without complicating the situation with quantum field theory. Which neither you, Mr Blenkinsop, nor I is qualified to analyse.

#### PeterDonis

Mentor
I was thinking a flash of light meant many photons, but each photon can only been seen by one observer.
If we're talking about classical relativity, the term "photon" should really not be used at all. If it is used, it should be taken to mean "a really short pulse of light in a specific direction", without making any claims whatever about its quantum nature, since at the level of classical relativity we ignore all quantum effects. Basically it's just a pulse of light that travels on a null worldline.

#### RossBlenkinsop

my question has still not been answered

if the speed of light is invariant, then according to all frames light will always trace back to a point in space or in space time (you choose) that does not move over time , over all time

on what basis do any of you assert that absolute movement, or lack of absolute movement aka absolute stillness, is not possible ? or is somehow a freakish outcome

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