I The velocity of a moving frame of reference

[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]

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]

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]

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

 

[RossBlenkinsop]

also anyone who is aware of the basics of time dilation would never claim that the source of light was under their nose as it is apparently impossible to tell if your frame is moving or not and therefore no reasonable minded person would conclude their frame was not moving or was ...at best they can conclude "maybe it is, maybe it isn't ...i really have no clue"

Now if it is moving then the light source is back there somewhere where my frame came from

further this is confirmed in the explanations given by the so called experts

In fact I think it is even confirmed by experiment where a very accurate "moving" clock apparently lost time ,,,,,despite that being apparently impossible as there is no such thing as a moving clock

 

[Ibix]

my question has still not been answered

It has been answered repeatedly in many different ways. You just aren't grasping it.

a point in space or in space time (you choose)

Your failure to distinguish between these two things is the basis of your issue here.

If you mean a point in space then this is a frame-dependent notion because "space" is a frame-dependent notion.

If you mean a point in spacetime (usually called an event, and it will help immensely if you use standard words) then it is not anywhere at all except at the time when the flash was emitted.

also anyone who is aware of the basics of time dilation would never claim that the source of light was under their nose as it is apparently impossible to tell if your frame is moving or not and therefore no reasonable minded person would conclude their frame was not moving or was ...at best they can conclude "maybe it is, maybe it isn't ...i really have no clue"

Um. I'm not sure where to begin correcting this. The choice of a frame includes (among other things) the definition of "not moving" that is in use. That other people use other definitions doesn't invalidate your choice. And "the basics of time dilation" require a frame, so that implies a definition of not moving.

I rather suspect you need an actual textbook - I recommend Taylor and Wheeler's Spacetime Physics.

 

[weirdoguy]

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

There is no such point since movement is relative, even in Newtonian mechanics.

 

[jbriggs444]

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

You still need to work on your terminology.

The light traces back to an event in space-time. Events in space-time are neither moving nor unmoving. The notion is simply irrelevant since an event has no duration.

If you try to walk over to the place where that event occurred, the place you walk to will depend on your standard of rest. It is not that the place moves. It is that the place is ambiguous until you specify what standard of rest you are using.

 

[Nugatory]

also anyone who is aware of the basics of time dilation would never claim that the source of light was under their nose as it is apparently impossible to tell if your frame is moving or not

Many posts back in this thread we cautioned you about using the phrase "a frame is moving" - it is easily misunderstood and you have misunderstood it here. A frame is a mathematical convention for assigning coordinates to points in space and events in spacetime, and mathematical conventions don't move.

and therefore no reasonable minded person would conclude their frame was not moving or was ...at best they can conclude "maybe it is, maybe it isn't ...i really have no clue"

If the spatial coordinates of an object, as assigned by a particular frame do not change with time then it is correct to say that the object is "at rest using coordinates assigned by that frame" (usually shortened to "at rest in that frame"). There's no question about whether an object is at rest or moving using any given frame nor that the point at the tip of my nose is not moving if we use a frame in which I and my nose are at rest.

So no reasonable-minded person would conclude that "their frame was not moving or was", because that would be like concluding that quadratic formula is moving south or that the Pythagorean theorem is purple and weighs 20 kilograms - it's a nonsensical conflation of words that don't go together.

However, a reasonable-minded person can choose to use any frame they want to assign coordinates to coordinates to an object (we often choose the frame in which we are at rest); that choice will determine whether the object is moving and if so, how fast.

 

[Nugatory]

In fact I think it is even confirmed by experiment where a very accurate "moving" clock apparently lost time

Presumably you mean the Hafele-Keating experiment, and if so you have misunderstood the result. It is demonstrating the twin paradox in which two clocks are synchronized, one of them flies somewhere else, and then when they are brought back together less time has passed on the traveling clock. It's tempting (but wrong) to explain this as time dilation and "time slows down for the moving clock"; but this leads to a paradox because we could just as well say that the on-the-ground clock is the moving one and therefore it's the one that should have lost time. The resolution of the "paradox" is that time dilation isn't what's going in this experiment.

However, you probably don't want to take on the problem of understanding the twin paradox until you have corrected your basic misunderstandings about what a frame is and the distinction between points in spacetime and points in space. For that, I will second @Ibix's recommendation of Taylor and Wheeler - their presentation gets to these issues early and thoroughly.

 

[RossBlenkinsop]

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

it could be a single point, according to multiple people in multiple frames or multiple points according to multiple people in multiple frames , it is immaterial. What is of interest is the points appear to be in the same point in space or the same point in space time, over time, over all time. Ie if the same experiment of tracing light back to its source is conducted over and over and over , over a time period , by the same person in the same frame, they should get the same result if the speed of light in in fact invariant.

if they get a different result then the speed of light is variant ?

 

[RossBlenkinsop]

Many posts back in this thread we cautioned you about using the phrase "a frame is moving" - it is easily misunderstood and you have misunderstood it here. A frame is a mathematical convention for assigning coordinates to points in space and events in spacetime, and mathematical conventions don't move.

this "convention" is based on the premise that a person within a frame cannot determine the absolute velocity of that frame, should it have an absolute velocity or only a relative velocity

as no one can determine if the frame which they are in has an absolute velocity or not no one can say it definitely does not have a velocity or it definitely does

I believe a frame is a mathematical convention that is based on a real world phenomena. It seems somewhat pointless to have a mathematical representation of something that simply cannot exist for example a mathematical model of the physiology of a unicorn or a mathematical model of the pressure differentials in the feet of Yetis

 

[RossBlenkinsop]

one of them flies somewhere else, and then when they are brought back together less time has passed on the traveling clock.

which clock was traveling ? what does "travelling" mean ?

the experiment as I understood it is they synchronized some very accurate clocks, had one clock in a frame, put another clock in another frame and another clock in another frame again, the frames moved relative to each other. Later they all met back at a point where all clocks were in the same frame and compared the clocks. The results were time passed at a different rate in the frame that the experimenters deemed was moving !

 

[PAllen]

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

Since both of your statements are trivially false, there is no logical answer. You might as well ask:

Since 1+1 is 3, how can you say there are no pink flying pigs?

 

[PAllen]

one of them flies somewhere else, and then when they are brought back together less time has passed on the traveling clock.

which clock was traveling ? what does "travelling" mean ?

the experiment as I understood it is they synchronized some very accurate clocks, had one clock in a frame, put another clock in another frame and another clock in another frame again, the frames moved relative to each other. Later they all met back at a point where all clocks were in the same frame and compared the clocks. The results were time passed at a different rate in the frame that the experimenters deemed was moving !

No, as has been explained many times. If between two points on a plane, you draw two different length lines, each will be at an angle to the other along various comparison lines you may choose to draw between them. However the difference in length is simply a fact of the difference in curves you draw. Similarly, between two spacetime paths between separation and meeting events, each path is in motion relative to the other (different spacetime angles), but one path is simply longer in time than the other. In plane geometry, the shortest possible line is a geodesic. In special relativity, the longest possible time is a geodesic, which means an inertial path.

The result of comparison on meeting again has absolutely nothing to do with with the experimenter rest frame, or any frame at all. It is a frame independent fact.

 

[PeterDonis]

a point in space or in space time (you choose)

This is nonsense. A point in space is not the same as a point in spacetime.

You have received repeated correct explanations. Enough is enough. Thread closed.