# Tutorial: Relativity - what is a reference frame?

Discussion in 'Physics & Math' started by James R, Aug 19, 2012.

1. ### OnlyMeValued Senior Member

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No one, but sometimes it seems they are talking about a light sphere as if it were a light horizon. That is why I said the definition of a light sphere was not well defined. This disscussion comes up repeatedly with Motor Daddy, it has just never seemed clear to me that everyone was talking about the same thing.

How does the center or origin of a light sphere move in space?

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3. ### Neddy BateValued Senior Member

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Imagine that a lamp is moving at a constant speed relative to you. The lamp flashes for a very short period of time. The light propagates as an expanding sphere. Where is the center of the sphere? You will say it does not move with the lamp, but instead it remains located where the lamp was at the time the lamp flashed. However, someone at rest with the lamp will say the center of the sphere remains located with the lamp.

I'm not sure if that answers your question, but I don't think it has anything to do with light horizons. Does it?

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5. ### kaduseusmelencolia IRegistered Senior Member

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Only bit I didn't like, it shows a preference of one model over another, also the speed of light is the velocity at which light is propagated in a medium (vacuum, air, water, glass), so it is unclear what you mean by light has a certain speed determined by the reference frame.
(I know what you meant, will others?)
Nice Tut.

@motor daddy, we go to france and have them check whether our sticks are a meter long.

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7. ### Aqueous Idflat Earth skepticValued Senior Member

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Hi James R,

Change that to EM waves and we have the interesting relation

$c\quad =\quad \frac { 1 }{ \sqrt { { \mu }_{ 0 }{ \varepsilon }_{ 0 } } }$

Well, at least I find it interesting. It makes me wonder "what it's all about", as the song goes. Am I lost in some naive notion I invented in my head, am I just to ill prepared to grapple with it, or is this worthy of discussion?

I'm not only addressing you but also the other higher math and science folks posting here.

I suppose the assignment of the intrinsic properties of free space, with respect to E and H wave propagation, can be simply regarded as nothing more than a construct. Maybe I'm tending to think like the person who sees faces in the paint chips on the wall, but I'd like to know if any of you would care to comment.

At the moment I'm thinking about spacetime curving under Lorentz transformation while the intrinsic impedance remains "true". That's just mind boggling to me. I want to ask "why" but it's not exactly the right question.

Another thing that nips at me is that this is the formulation of the geometric mean. I think it might apply to splines, and that's another very weird notion to me. The "melding" of two dissimilar quantities in a common "place"? Something like that. Again, I don't know how to express this exactly, or whether I'm just off in the weeds.

We often see threads where folks are asking "what is time?", "what is space?", "what is -" etc. Everyone must have been there once, questioning some fundamental thing. I think this qualifies as my Rubicon. I'd like to know what intrinsic impedance really is. And to stay on topic, I can cast this entirely within the framework of relativity.

I don't know if it's fair to ask "why the geometric mean?" while most of us are left in the dust by the coordinate rotation that we associate with relative motion, that is, whether it's plausible to try to lump these generalizations together. But I wonder. Here I'm associating the "warping" of the geometric mean with the warping of relativity. Maybe that's irrational. But I'd like to ask the advanced contributors here for some insight, if the question doesn't seem too wacky. Let me try to turn this into a suitable question:

Starting with the formulation that light speed is the geometric mean of the two components of the free space impedance - which are associated with the orthogonal pair of components of the EM wave - we can reword SR by establishing that it is the "impedance" which is held constant while the frequency shifts, and that the contraction might be thought of as the cost of taking in more volume by action of a corkscrew (considering 1D axial rotation). Two questions spring from this (a) what does it mean, or how else might we describe what SR "means" by thinking in terms of the impedance that "operates on" or "reacts to" the E and H components of the wave?; and (b) Why the geometric mean, and what, if any, are the implications of twisting and rolling the moving coordinate system in light of the observation that the geometric mean "means" something akin to a spline?

8. ### OnlyMeValued Senior Member

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That is the problem. The two situations are not equivalent.

When the light flashes it sets off an expanding sphere of photons, which is A light sphere.

When someone moves with the lamp, what they experience as the light sphere moving with them, is not a single light sphere. It is an infinite number of light spheres, the center of each being the next point along the path of the lamp's motion.

If when the lamp is carried, it emitts just one flash as the person and lamp move, that light sphere does not move with them. It expands outward for that single point in space and time.

The center of a light sphere originating from a single flash of a moving lamp, is a single stationary point in space. (Assumming we limit the case to a flat spacetime.)

If the lamp is moving fast enough the light maybe red and blue shifted along the path of its motion, but the velocity of the shell of expanding photons will not be affected and neither will the center or point of origin, or the shape of the sphere.

The expanding light "bubble" from a lamp that is in motion and continously emitting light, from the prespective of the observer holding the lamp, were they able to see it, would not be a sphere. Instead it would be shaped more like a pear or tear drop with a rounded leading edge.

9. ### Motor Daddy☼☼☼☼☼☼☼☼☼☼☼Valued Senior Member

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In order for there to be an infinite amount of observers in space at every point in space at every POINT IN TIME, each observer has to be part of the universal timeline. That is, they all have synchronized clocks that read as one at any point in time. Like in James' sticks example in the reference frame, every clock is in sync, but they are separated by a distance. They tick and read as one!

If we are separated by a distance and have universally sync'd clocks, when I look at my clock I know what your clock reads at that point in time. Sure, if I have to travel for twenty minutes to get to you to verify what your clock reads, your clock will read 20 minutes more than it did when I originally looked at my clock.

The "when" and "where" is not up for debate for any observer, because just like the example I just gave of our clocks, so too did a source emit light in space at a point in time a distance away from other observers. Just because the other observers don't see the light yet due to being separated by a distance from the point of emission doesn't change the fact that it happened at that point and time. It's reality, and reality is in the present. Unfortunately, being separated by a distance means that there is travel time, as motion does not occur instantly. That means everything you observe occurred in the past. You can't see or experience reality, you can only see and experience the past!

10. ### James RJust this guy, you know?Staff Member

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Motor Daddy:

Read my opening post again. I didn't mention anything about the necessity of using a light sphere to define what a reference frame is. If you like, you can mark on any particular reference frame the point at which a flash of light is emitted. Then, make another mark wherever the light has got to after some time has passed. The length of the path light has travelled is simply the number of sticks between the two marks.

I already did that back in post #5. If you have any questions about that, I can elaborate.

Yes.

That's true for a single reference frame, yes. Clocks in a single reference frame can be synchronised.

Yes. That's how the reference frame is set up. The synchronisation of the clocks is part of the definition of what we mean by "reference frame". Every single reference frame has its own set of synchronised clocks.

Yes. That's right.

Yes, that's right too.

At this point you're only talking about one reference frame, and it's all good.

Relativity is all about comparing two different reference frames that move relative to each other, and that is where the complexity starts to creep in.

11. ### BalerionBannedBanned

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The trolling garbage nonsense notwithstanding, this was an excellent tutorial. While I'll probably never have an occasion to put it to any use, it still feels pretty awesome to say I have a basic understanding of reference frames! Thanks, James!

12. ### Neddy BateValued Senior Member

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The lamp does not stay on, it flashes very, very briefly. So briefly that we can neglect the duration of the flash, and just consider it to be an instantaneous flash of light. Because the speed of light is c for all inertial reference frames, the observer moving with the lamp will say the light expands as a sphere that is centered on the lamp. Agreed?

According to relativity theory, the observer moving with the lamp will say the center of the light sphere remains fixed on the lamp. Meanwhile the observer who saw the lamp moving at constant speed will say the center of the light sphere remains fixed on the point where the lamp was located. It sounds like your beliefs are similar to Motor Daddy's. He believes the light sphere is always located at one point in "space" according to all observers. He doesn't believe in relativity, though.

13. ### OnlyMeValued Senior Member

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Centered on the lamp at the time of the flash. Yes.

But inertial does not mean at rest. It just means with a constant velocity. This could include the observer moving with the lamp.

As long as the observer knows and understands any acceleration involved, even an observer in an accelerated frame should say the light sphere has an origin or center that is constant relative to the lamp's rest frame, at the time of the flash.

This sounds as if you are saying that the observer moving with the lamp will say that the sphere of light created by the flash, will continue to move with the lamp..? Here, the lamp is moving with the observer. The light flash occurred in its, the lamp's past and should be centered on where is was, not on the lamp as it continues to move.

In a flat space/spacetime, the flash should create a light sphere, which remains centered on the location the lamp was at from whatever, frame of reference it is viewed. This is not creating a preferred frame of reference for anything but that single event.., the flash. Which as you stated happens, "So briefly that we can neglect the duration of the flash,..". Any motion of the lamp can have no impact on where that event took place.

For a stationary observer, the relative location of that event should remain constant in their own rest frame coordinate system.

For an observer moving with the lamp or even just relative to the rest frame of the flash, the location of the event should change over time, as defined by their own at rest coordinate system.

In both cases assuming the observers place theirselves at 0,0,0 of their own coordinate sytem.

No problem here. This is an inertial observer.

I cannot say with certainty, because I do not always understand what Motor Daddy is saying, but it sounds to me as if he defines only a Newtonian fixed frame of reference and that all observers are within that frame and that frame alone..?

That is not what I believe... I understand frames of reference, though perhaps I do not always describe them well.

So, to try and sum up what I think is being discussed and how I see it...

A flash of light, is fixed and centered on the point defined by an at rest coordinate sytem defined by the location of the flash. That location within the coordinate systems of observers, in both inertial and accelerated frames relative to the, at rest coordinate system of the flash, will not remain constant. That said all observers with an understanding of relativity should say that the flash occurred at a fixed location in space, which remains at the center of the resulting light sphere.

14. ### TachBannedBanned

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This is certainly false, accelerated observers do not measure light speed as being isotropic, so there is no light "sphere" to talk about.

15. ### OnlyMeValued Senior Member

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Read what I said again! I did not say they will "see" or "measure" a light sphere.., to be a sphere. I said, even an observer in an accelerated frame should say the light sphere has a center relative to the lamp's rest frame. And it was qualified by, as long as the observer knows and understands any acceleration.....

This was not a statement as to what the accelerated observer would see or measure. It was statement as to what they should know.

Maybe I was mistaken in assuming that the observer was a reasonably intelegent person, rather than a dog or a cat or .....

16. ### Neddy BateValued Senior Member

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Yes, but I wouldn't say, "The sphere of light will continue to move with the lamp," because the lamp isn't moving at all in that reference frame. I would put it this way:

According to the lamp's reference frame, the lamp is located at x,y,z=0,0,0 at all times. The flash occurs at x,y,z=0,0,0 in the lamp's reference frame. The light sphere expands outward from x,y,z=0,0,0 at the speed of light in all directions. Therefore the center of the light sphere remains at x,y,z=0,0,0 which is the same location as the lamp.

That is what our intuition tells us, but relativity disagrees. If the reference frame of the lamp were to find the center of the light sphere drifts away from the lamp, then it would not find the speed of light to be c in all directions. There would be a sort of "bias" where light tends to drift in a certain direction. Since the earth is known to revolve around the sun, the Michelson Morley experiment set out to measure such a drift, but it came up with null results.

17. ### OnlyMeValued Senior Member

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This was the quote,

The portion in bold implies that, if the observer is moving with the lamp, the lamp is also moving with the observer... If you did not intend that the lamp and observer were in motion, relative to the point where the flash occurred, I misunderstood your intent.

This is fine where the lamp is not in motion relative to the location where the flash occurred. IOW the frame is the rest frame of both the flash of light and the lamp.

I don't understand your point above. Is the lamp moving or at not?

If the lamp and the flash share a common at rest frame of reference, then the lamp remains at the center of the light sphere.

The problem seems to be that light, or rather the velocity of light, is not affected by the velocity of the object from which it originates. As far as the velocity of light, associated with the expanding light sphere is concerned, even an object with a relativistic velocity, would be at rest as far as the light sphere is concerned at the time of the flash. The motion of the lamp would not cause the light sphere to drift, as you put it.

It is likely that there is no situation where the lamp and the flash can in fact share an at rest frame of reference. I would go as far as to say that if the problem is expanded to include GR, there can be no situation where the lamp and flash can share an at rest frame of reference. If such were possible Relitivity would be in the crapper, as it would create a preferred and perhaps absolute frame of reference.

Since I reject that idea, only in a hypothetical where it is understood that the conditions do not represent reality, can we entertain the idea that the lamp and the flash can share a common at rest frame.

EDIT: it is likely that the lamp and flash cannot share any frame of reference, except for that brief moment when the flash occurs.

In ALL realistic frames and constructions of the lamp, flash and light sphere, no matter what the expanding sphere of light might look like to an observer, were they actually able to observe it, the lamp could only be at the center of the light sphere for moment in time.

18. ### OnlyMeValued Senior Member

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As an after thought, I do see how it might be interpreted that what I am saying about a light sphere, creates a preferred frame of reference.

I don't believe that is true. It may be a special frame of reference, in that the light sphere can be thought of as creating a fixed frame of reference in spacetime, centered on the flash. The reason it is not a preferred frame is because space/spacetime is not flat. It is curved and dynamic. So no two light spheres would create identical frames of reference.

Gravity or the curvature of space/spacetime changes the game completely. The curvature and dynamic nature could even introduce some drift associated with space/spacetime. Even that drift would be proportion to the changing curvature of space/spacetime.

In an idealized hypothetical, in flat space/spacetime, while the light sphere would represent an at rest frame of reference, it must be qualified by the understanding that is relatively at rest, not to be confused with absolutely at rest.

Even so, I do not believe that in anything but the idealized hypothetical the lamp could share the light sphere's frame of reference over time.

19. ### TachBannedBanned

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There is no "the light sphere" for accelerated observers. Do you understand that?

There is no point in becoming insulting when it is obvious that you don't know what you are talking about.

20. ### TachBannedBanned

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Light spheres cannot "create frames of reference". There is no such thing as a frame of reference associated with light. It would be good if you stopped rubishing the good thread started by JamesR with your musings.

In mainstream SR, one cannot associate frames of reference with light.

Would you please stop repeating this kind of nonsense? Let JamesR continue the thread without your "additions".

21. ### OnlyMeValued Senior Member

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Do you understand that I did not start the discussion?

A little touchy there, no? The comment what's not directed at you. If it had been I would have used your name. You should know I generally try to avoid, personalizing discussions.

Again, I did not begin the discussion. On the other hand, it is a discussion constructed entirely in the realm of the hypothetical. There is nothing wrong in attaching a frame of reference to an event, like a flash of light that results in a light sphere, in an attempt to explore a hypothetical or reach any consensus, in a discussion.

Following is a quote from my second post in this thread,

From the above you should be able to see that I also thought (think) that this discussion was not adding to the OPs initial intent.

You know as well as anyone that discussions take on a life of their own. The discussion of light spheres began before I entered the conversation. And if James wanted me to stop posting he has many tools with which to see it through himself, including just asking.

Nothing you have posted here is in any way constructive.

22. ### Neddy BateValued Senior Member

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Sorry for the confusion. There is a lamp moving relative to you, and there is also an observer at rest with the lamp. According to you, the lamp is moving, but according to the other fellow it is not.

That's right, so the fellow on the lamp would say the light sphere is expanding away from the lamp at constant speed, c, in all directions. That puts the lamp at the center of the light sphere, and it stays there (for him) as long as the lamp does not accelerate. You and he do not agree where the center of the light sphere is located at any time, except for the instant it flashed.

Yes, it does sound that way to me. I thought we were talking about flat spacetime. In that case, SR agrees with what I've been saying. I'm not sure to what extent GR might change that.

23. ### OnlyMeValued Senior Member

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Neddy Bate, I think we hashed out the confussion. I have had some trouble with the definitions in this light sphere discussion, in many of its incarnations.

I would still add that, even in completely flat space time, I am unsure that any observer or lamp could remain at the center or point of origin of any expanding light sphere. In a hypothetical it is a usefull concept, but it still seems that no observer can assume they are at rest, in space and the flash of light takes place, in an instant as if they were at rest.