B Relativity of Measures: A vs B Frame & Light Source S

[PeroK]

As I have said before, if the pulse is seen from one frame to hit the mirror, it will be seem from all frames to hit the mirror, if it misses in one frame it will miss in all frames.
That is not a guess, or a hypothesis, or a wish. It is absolutely clear, empirical fact.

Good!

I am not questioning that. I am questioning why that is contradicted in the examples I gave.

Clearly, your examples must have an error in them. There is nothing more profound than that.

The responses have all been something similar to:
“it is not contradicted in your examples if you interpret your examples as we say you should.”
I can accept that if you just explain “why”. Telling me what to “believe” is not teaching me science.

I don't see that's what we've been doing.

Here is another example that I think is detailed enough that any mistake/s I have made should be ealily explained.

Okay, but it looks like another complicated word salad to me.

When I am next to and at rest with the sun, I am at rest with where the light leaves the sun at any instant.

You need to make this more precise.

A minute later I can still be at rest with the sun, but if I am, I am moving roughly 828,000 km/hr away from where the light left the sun a minute ago.

I don't follow this. You need to make this more precise as well.

If I don’t know, or have no way to measure this motion of the sun/me relative to where the light was emitted from it a minute ago, that does not change the path of that light relative to any frame of reference.

That makes no sense to me. You can't do physics in these cryptic terms that might mean many different things.

If that light hits the earth, every frame will see it hit the earth. The motion that determines whether that light hits the earth is not the motion of any frame relative to the earth, or sun. It is the motion of the earth relative to where the light was emitted. The earth is either on a collision path with the light, or not. The light does not change its direction to chase the earth.

This is just a roundabout way to say that the light eventually reaches the Earth.

When A and B see S remain centered between them, you and I will predict the path of the light pulse emitted from S will be symmetric as observed by A and B.

I can't follow what you mean by this.

When E sees A, B and S moving along a common axis (x) they will all be moving relative to where the light is emitted from S at any instant. Unlike me at rest with the sun, E remains where the light was emitted. With this “new” information, you and I will claim the path observed by A and B will NOT be symmetrical.

I don't understand this statement.

Why does what E measures change what you and I predict will be seen by A and B if the relative motion of A, B and S is all that determines the path of the light observed by A and B and that relative motion does not change?

I don't understand anything about your scenario. It's just a jumble of words. Sorry.

 

[PeroK]

@AIMetis here's an important point. Which I also made a few days ago here:

https://www.physicsforums.com/threads/cant-figure-out-this-paradox.1049836/#post-6853546

Whatever scenario you are thinking of has a fixed set of key events. These events can be listed in a suitable IRF (inertial reference frame). E.g. light is emitted from the Sun at $t = 0, x = 0$. Observer $X$ is at $x = 0$ at $t = 0$. Observer $X$ moves with constant velocity $v$ along the $x$ axis. The light reaches the Earth at $t = t_1, x = ct_1$ etc.

That might still get complicated, but in principle everyone will understand your scenario.

Then, you transform those events to a different IRF. You can do this using the Lorentz Transformation or by shortcutting the process in some way.

The critical point is that anyone can check your analysis. If you make a mistake, anyone can do the maths and identify your mistake.

To make any progress, you need to condense your scenario down to a set of specified events in a given IRF. Without that, it's not possible to do physics in any reliable way.

 

[Nugatory]

As I have said before, if the pulse is seen from one frame to hit the mirror, it will be seem from all frames….
I can accept that if you just explain “why”. Telling me what to “believe” is not teaching me science.

A frame is a convention for attaching numerical labels (for example, x,y,z and t coordinates) to events. Therefore, using a different frame can only change the labels attached to the events, not the events themselves. Light hitting the mirror is an event.
That’s why.

However, there are things that we calculate from these labels, and of course these will be different when we use different frames.
Some examples are totally obvious: when using the normal orientation of the coordinate axes “moving left to right” means “the x coordinate is increasing over time”. If I’m facing north and you’re facing south we will totally disagree about whether I was shot by a bullet coming from the right or the left, but not that I‘ve been shot.

Almost all the misunderstanding in this thread comes from a less obvious example: the angles formed by the trajectories of objects or a flash of light are calculated from the coordinates that we attach to the events “it was here at time t” so will be different in different frames.

 

[PeterDonis]

The relativistic Doppler/aberration formula can be derived correctly with both, the classical particle model and classical wave model of light.

There is no classical particle model of light. People like Newton speculated about such a model, but nobody ever actually developed one that accounted for all of the experimental facts. At the classical level, the only experimentally verified theory of light we have is Maxwell electrodynamics.

It should be possible to discuss SR, a classical theory, without invoking QED.

The usual way that is done with light, if you're interested in something that can be treated, if you don't look at it too closely, as a "particle" moving on a null worldline, is to use a "radar pulse" or "light pulse" or something like that: a short burst of radiation emitted over a time scale that is much shorter than any other time scale of interest in the problem.

 

[Sagittarius A-Star]

So stick to classical electrodynamics. It's a pretty simple calculation with a Lorentz transformation of the wave-four-vector.

I think I will first wait until @AlMetis has answered my posting #45 and then do eventually a Lorentz transformation of the momentum-four-vector, because he wrote (wrongly) in #29, that light cannot acquire a momentum.

 

[Sagittarius A-Star]

"radar pulse" or "light pulse"

Yes, I called it already "light-pulse".

 

[PeterDonis]

Yes, I called it already "light-pulse".

Ok, good. But classically, this "light pulse" is not a particle and there is no classical particle theory of light that explains its behavior. It's just a useful approximation to the more complicated behavior that the classical wave theory of light gives.

 

[Dale]

I am not questioning that. I am questioning why that is contradicted in the examples I gave.

Why it is contradicted in the examples? It is contradicted in the examples because the examples you gave all had some mistake in them. That mistake has been pointed out for each example. You have been answered "why". Clearly each time.

The issue is not that you have not been given an answer "why". The issue is that you have not generalized or internalized the physics yet. That takes time and practice, it is not something that we can give to you.

When I am next to and at rest with the sun, I am at rest with where the light leaves the sun at any instant. A minute later I can still be at rest with the sun, but if I am, I am moving roughly 828,000 km/hr away from where the light left the sun a minute ago.

This should read:

"When I am next to and at rest with the sun, I am at rest in the sun's frame with where the light leaves the sun at any instant. A minute later I can still be at rest with the sun, but if I am, I am moving roughly 828,000 km/hr in the milky way's frame away from where the light left the sun a minute ago."

Why does this lead to a contradiction? Because you made a mistake and switched frames silently. To fix this make sure that velocities are always specified with respect to an explicit reference frame.

If I don’t know, or have no way to measure this motion of the sun/me relative to where the light was emitted from it a minute ago, that does not change the path of that light relative to any frame of reference. If that light hits the earth, every frame will see it hit the earth. The motion that determines whether that light hits the earth is not the motion of any frame relative to the earth, or sun. It is the motion of the earth relative to where the light was emitted. The earth is either on a collision path with the light, or not. The light does not change its direction to chase the earth.

No light path was changed relative to any frame. However you mistakenly cited velocities with respect to two different frames without explicitly mentioning which velocities pertained to which frames.

When A and B see S remain centered between them, you and I will predict the path of the light pulse emitted from S will be symmetric as observed by A and B.

This ambiguous and so it would be improved by explicitly stating:

"When A and B see S remain centered between them in their mutual rest frame, you and I will predict the path of the light pulse emitted from S will be symmetric as observed by A and B in the mutual rest frame of S, A, and B."

The phrase "as observed by" is a little ambiguous. It can either refer to the situation as described in some observer's reference frame, or it can refer to signals actually recieved by a specific observer. Either way, the meaning needs to be made clear.

When E sees A, B and S moving along a common axis (x) they will all be moving relative to where the light is emitted from S at any instant. Unlike me at rest with the sun, E remains where the light was emitted. With this “new” information, you and I will claim the path observed by A and B will NOT be symmetrical.

This is also ambiguous and should be written:

"When E sees A, B and S moving along a common axis (x) they will all be moving in E's frame relative to where the light is emitted from S at any instant. Unlike me at rest with the sun, E remains where the light was emitted in E's frame. With this 'new' information, you and I will claim the path observed by A and B will NOT be symmetrical in E's frame."

Why does what E measures change what you and I predict will be seen by A and B if the relative motion of A, B and S is all that determines the path of the light observed by A and B and that relative motion does not change?

By "seen by A and B" do you mean "in the rest frame of A and B" or do you mean "signals recieved by A and B"? Either way, what E measures does not change what you and I predict. But you should get in the habit of writing unambiguous statements.

I mentioned that you need to practice. The first thing to practice is writing clear statements and identifying ambiguities in unclear statements.

 

[AlMetis]

I want to thank everyone for your help, suggestions and criticism. Time doesn’t allow me to respond to every post, but I do read all of them and most more than once. They are all helpful, thank you.
Back shortly

 

[Sagittarius A-Star]

@PeroK, “Objects” acquire momentum from their source (cars), light does not.

Can you provide evidence or a link to evidence for your claim?

It's of course intuitive to assume this, because the momentum of light is usually very small in daily life. If you switch on the light, then you don't feel the push from the momentum of the light.

But experiments were done which prove, that light has a momentum.

Ikaros: First Successful Solar Sail
...
This proved that the Ikaros has generated the biggest acceleration through photon during interplanetary flight in history."

Launched in May 2010, Ikaros demonstrated the effect that individual light photons have when hitting a solar sail. While each photon is small and only generates a small push, over time the accumulated energy from each one of the strikes pushes the solar sail (and anything attached to it) forward.

Source:
https://www.space.com/25800-ikaros-solar-sail.html

 

[AlMetis]

A frame is a convention for attaching numerical labels (for example, x,y,z and t coordinates) to events. Therefore, using a different frame can only change the labels attached to the events, not the events themselves. Light hitting the mirror is an event.
That’s why.

I agree.
I have included another diagram that is (hopefully) less ambiguous than the word salads I’ve been posting.
The diagram plots the Galilean transformation of the same motion of source, mirror and light predicted to be observed by two inertial frames in motion.
The relativistic (Lorentz) transformations which hold the constancy of c in both frames, removes the (apparent) conflict of “different events” observed by each frame predicted by Galilean relativity. To remove the conflict, the slower time of the moving frame (S from E’s frame) allows it to measure a shorter length S-A of longer light path S-c+3v which holds S’s measure of light speed at c.
In other words, the shorter you measure a longer path, the slower your time must run to arrive at the same ratio of d/t = c.

 

[Sagittarius A-Star]

the (apparent) conflict of “different events” observed by each frame predicted by Galilean relativity.
View attachment 322343

Also with Galilean transformation there must be aberration of a vertically emitted light-particle (which was assumed to exist by James Bradley). The light-particle must strike A in the left and in the right diagrams. In the right diagrams, it must have the speed $\sqrt{c^2+v^2}$, according to the Galilean transformation.

 

[AlMetis]

Yes, the illustration is just showing there is a difference between frames, whether speed, aberration, length, time....something has to give to define the same physical event that is not apparent in the initial conditions of both frames.

Attached is a more legible version.

 

[PeroK]

What's the relevance of the Galilean transformation here?

 

[AlMetis]

What's the relevance of the Galilean transformation here?

It’s to help me understand the line of reasoning that gets us from Galilean to Einsteinian.
I understand Galilean fails to describe the empirical evidence of light, the Lorentz transformations give us the conversion from frame to frame that mathematically satisfies the empirical evidence.
I don’t understand how Lorentz transformations represent reality. My examples are pointing to some of what I think are the most difficult physical aspects to understand when we go from Galilean to Einsteinian.

For a point of reference - Poincaré/Lorentz relativity was mathematically as effective as Einstein’s but required the physically absolute interpretation of the transformations. As this is beyond experimental testing, it was dropped in favour of Einstein’s relativity that uses the principle of relativity in place of absolute. It has been successfully tested in every increasing accuracies and physical convolutions - life of particles etc.
I want to understand how it changes our understanding of physical dimension.

 

[PeroK]

It’s to help me understand the line of reasoning that gets us from Galilean to Einsteinian.

There's no logical way, IMO, to get from Galilean to Einsteinian physics. That was the problem. It's the other way round. Once you have SR, you get Newtonian physics as a low speed approximation. SR is not an extension of classical physics. SR didn't evolve from classical physics: not in the critical differences. SR was something new and unimagined within classical physics. Classical physics is a special case of SR.

 

[Ibix]

I want to understand how it changes our understanding of physical dimension.

Minkowski noticed that the Lorentz transforms were an analogue of Euclidean rotation in a non-Euclidean space now known as Minkowski spacetime, so he proposed that Einstein's maths could be interpreted as implying the existence of a 4d spacetime. That turned out to be useful in understanding gravity, since Newtonian gravity is incompatible with relativity. It was basically a matter of recognising the mathematical theory of (pseudo-)Riemannian manifolds in the maths coming out of physics.

A more abstract approach is to start with the principle of relativity and show that there are only two coordinate transforms consistent with this - Galileo and Lorentz. There's no need to impose the invariance of light speed. Then you simply check by experiment which kind of universe we're in.

 

[Sagittarius A-Star]

I understand Galilean fails to describe the empirical evidence of light, the Lorentz transformations give us the conversion from frame to frame that mathematically satisfies the empirical evidence.

Yes. As @Ibix mentioned: Either there exists a finite invariant speed or not.

• If not, the assumed invariance of causality implies t'=t, that means the Galilei transformation must be valid.
• If yes, the only possible transformation between inertial frames is the Lorentz transformation.

The role of the 2nd postulate of SR - which is not really needed - is to separate between these two possibilities. Experiments showed, that light moves in vacuum with this invariant speed.

Einsteins new idea was to distinguish between $t$ and $t'$ in combination with defining time as that, what a standardized clock shows. He dropped Newtons assumption, that an absolute time exists.

 

[AlMetis]

There's no logical way, IMO, to get from Galilean to Einsteinian physics. That was the problem. It's the other way round. Once you have SR, you get Newtonian physics as a low speed approximation. SR is not an extension of classical physics. SR didn't evolve from classical physics: not in the critical differences. SR was something new and unimagined within classical physics. Classical physics is a special case of SR.

Yes, I didn’t mean to suggest there is a one to one evolutionary correspondence from Galilean to Einsteinian relativity.If I take SR at face value, of course it works perfectly. But I’m not a “shut up and calculate” person.

My diagrams show a distinction that is not made clear in most explanations of SR I’ve read.
When we are given the information on the left of my diagram, we have no reason to expect, or predict an asymmetry in the observations via Galilean or Einsteinian relativity.
When the same motion is observed relative to the light,(right side of diagram) Galilean relativity fails. It predicts what is not consistent with empirical evidence.
When we apply the Lorentz transformation from the left to the right, Einstein’s relativity works on the right (pulse strikes A) predicted observation equals evidence once more.
But we don’t regain the symmetry.
The symmetry is not exclusive to Galilean relativity, it is also predicted by Einsteinian relativity on the left and lost on the right.

Why did it disappear?

 

[PeterDonis]

I don’t understand how Lorentz transformations represent reality.

They give you the proper way to transform your view of reality in one inertial frame, to the correct view of reality in another inertial frame.

But we don’t regain the symmetry.

What symmetry are you talking about?

 

[Dale]

A more abstract approach is to start with the principle of relativity and show that there are only two coordinate transforms consistent with this - Galileo and Lorentz. There's no need to impose the invariance of light speed. Then you simply check by experiment which kind of universe we're in

Well, you do still need more than the first postulate. You can either use the second postulate or you can use experiment. But you need something more.

I do like postulating the invariance of the spacetime interval. That is one single postulate that actually does get you all the way. Of course, it isn’t so intuitive, but then again this is relativity we are talking about.

 

[Dale]

But we don’t regain the symmetry.
The symmetry is not exclusive to Galilean relativity, it is also predicted by Einsteinian relativity on the left and lost on the right.

Why did it disappear?

What symmetry? You must be misunderstanding something because all of the predicted symmetries of SR have been experimentally confirmed. So either you think some symmetry is predicted and it isn’t, or you are not actually looking at the symmetry that you think you are.

 

[AlMetis]

They give you the proper way to transform your view of reality in one inertial frame, to the correct view of reality in another inertial frame.

Yes, they do this by translating numerical values of a measure in one frame, to the numerical values of the same measure in another frame. Why do our measures of dimension change with our motion relative to another frame? Einstein explained “what” happens, time slows, length contracts, mass increases and when all of these are calculated via the Lorentz transformation they accurately predict the “amounts” that each change. The Lorentz transformation explains how to get there, it does not explain why we have to go there. What aspect of reality is defined in the need for the Lorentz equations? If they didn’t work and light was still a constant, reality would be different a very different thing.

 

[AlMetis]

What symmetry are you talking about?

I've marked the symmetry break in this copy.

 

[PeterDonis]

they do this by translating numerical values of a measure in one frame, to the numerical values of the same measure in another frame.

Lorentz transformations don't transform "measures", they transform coordinates.

What aspect of reality is defined in the need for the Lorentz equations?

The geometry of spacetime.

If they didn’t work and light was still a constant, reality would be different a very different thing.

You have no basis for this claim unless you have some alternate theory in which the transformations are different from the Lorentz transformations but the speed of light is still the same in all frames. And we already now such a theory is impossible if we accept the principle of relativity, because the POR only allows two possibilities, Galilean transformations (infinite invariant speed) and Lorentz transformations (finite invariant speed). In the former case, the speed of light is not the same in all frames. So your claim is assuming an impossibility.

I've marked the symmetry break in this copy.

Your diagram on the right is not correct for the SR case, so all you are showing is that Galilean relativity makes a wrong prediction.

 

[Dale]

I've marked the symmetry break in this copy.

I don’t get it. I don’t know what you are calling asymmetry there

 

[strangerep]

What aspect of reality is defined in the need for the Lorentz equations?

The principle that all inertial (i.e., non-accelerating) observers perceive the same laws of physics.

That, plus a couple of technical points about Lie groups implies a group of transformations among inertial reference frames that, in general, involve 2 universal constants: one has dimensions of inverse velocity squared (usually identified with $1/c^2$) and another with either dimensions of inverse time or else inverse length squared (the latter corresponding to the de Sitter group). The 2nd constant is usually ignored, leaving us with the Poincare group, of which the Lorentz transformations are a subgroup.

The value of the $1/c^2$ must then be determined from experiment.

 

[Ibix]

Why do our measures of dimension change with our motion relative to another frame?

On a Euclidean plane, why do the x and y separations between things change when you rotate coordinate axes? Because you've changed which directions in space you call the x axis and the y axis.

On a Minkowski plane, why do the x and t separations between things change when you boost coordinate axes? Because you've changed which directions in spacetime you call the x axis and the t axis.

That's really all that's going on here. Relativity allows you some freedom to choose which direction in spacetime to call "only moving in time" and "only moving in space". That choice affects how you choose to describe things in much the same way a Euclidean rotation might change a long narrow thing into a short wide one.

 

[AlMetis]

Lorentz transformations don't transform "measures", they transform coordinates.

How far apart are these coordinates?

 

[AlMetis]

The geometry of spacetime.

That’s true, I should have said the geometry of spacetime represented by the need to employ the Lorentz transformations between inertial frames expresses a continuum of fundamental dimension we don’t, but I would like to, understand.

 

[AlMetis]

You have no basis for this claim

The basis I have is they “do” work , light “is” a constant and reality “is” what it is.

 

[AlMetis]

Your diagram on the right is not correct for the SR case, so all you are showing is that Galilean relativity makes a wrong prediction.

Both sides are Galilean representations. The red line labeled ‘c_3v” on right side at t=1 represents the time dilated position of A relative to E (in principle, not to scale). If this is not correct, please explain why.

 

[jbriggs444]

How far apart are these coordinates?

What are you talking about?

There is a formula that we can use to determine "how far apart" two coordinate four-tuples are from one another. Let us identify two events $E_1$ and $E_2$ with coordinates $(x_1, y_1, z_1, t_1)$ and $(x_2, y_2, z_2, t_2)$ respectively. The "how far apart", $s$ between the two events is given by:$$s^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2 - (t_1 - t_2)^2$$If we shift to an a new reference frame where the same two events $E_1$ and $E_2$ are identified with coordinates $({x'}_1, {y'}_1, {z'}_1, {t'}_1)$ and $({x'}_2, {y'}_2, {z'}_2, {t'}_2)$ then the same formula applies:$${s'}^2 = ({x'}_1 - {x'}_2)^2 + ({y'}_1 - {y'}_2)^2 + ({z'}_1 - {z'}_2)^2 - ({t'}_1 - {t'}_2)^2$$Further, it will turn out to be the case that $s^2 = s'^2$.

So "how far apart" is an invariant measure. It looks like it is a function of coordinates, but that is just because we specified our events with coordinates. It is actually a function that takes two events as input and spits out a [squared] separation as the output.

This "how far apart" formula is the "metric" for the flat space-time of special relativity. When you get to the curved space-times that general relativity can contemplate, the metric will not have this exact form. Though in the limit of increasingly nearby events, it will approximate this form ever more closely.

If you are evaluating the separation between the two ends of a physical rod, then you are asking for the separation between the world-line corresponding to the one end and the world-line corresponding to the other end. That is not the separation between two events -- it is the separation between two trajectories.

In order to apply the "how far apart" formula, you need to identify two events. We conventionally pick out two events that are "at the same time" according to some agreed-upon simultaneity convention.

Each frame has its own simultaneity convention. So each frame will be comparing different pairs of events when they measure the separation between two trajectories.

The two frames are not measuring the same thing. They are measuring different frame-specific hings. This is the same way that the measured width of a strip of paper depends on the angle at which you hold the ruler.

 

[AlMetis]

I don’t get it. I don’t know what you are calling asymmetry there

You and a number of people have said I have unknowingly switched frames of reference resulting in me mistaking the aberration observed in a “different” frame as a change in the observations in the same frame.
From everything posted, this seems to be the most consistent advice.
I need to understand at what point in time, I have switched frames of reference in context of what I think is being observed, in order to see/understand what would be observed.
So please indulge me one step at a time.

In the rest frame of the light source S and a mirror M at rest with S a fixed distance on +y, the path of the light pulse is observed perpendicular to x between emission at t=0 and reflection t=1, while S is in motion along x in the +x direction relative to the frame E.
Then
1. E will see the aberration of the light pulse from t=0 to t=1 as a path at an angle from x toward -x.
(when increasing x is in the right hand direction relative to you, the reader)Yes, no?

 

[Dale]

1. E will see the aberration of the light pulse from t=0 to t=1 as a path at an angle from x toward -x.
(when increasing x is in the right hand direction relative to you, the reader)Yes, no?

Yes. The worldline of the light in $S$ is $$r^\mu=(t,x,y,z)=(t,0,t,0)$$ and in $E$ is $$r^{\mu'}=(t',x',y',z')=(t',-t' v, t' \sqrt{1-v^2},0)$$ using units where $c=1$.

 

[PeroK]

In the rest frame of the light source S and a mirror M at rest with S a fixed distance on +y, the path of the light pulse is observed perpendicular to x between emission at t=0 and reflection t=1, while S is in motion along x in the +x direction relative to the frame E.
Then
1. E will see the aberration of the light pulse from t=0 to t=1 as a path at an angle from x toward -x.
(when increasing x is in the right hand direction relative to you, the reader)Yes, no?

Probably yes. I would have said simply:

In a frame where the source and mirror are at rest, the light path is along the positive y axis.

In a frame, E, where the source and mirror are moving to the right (along the positive x axis), then the light path is at an angle to the x axis.

In terms of aberration, this means that when the light is observed in frame E, the source is further to the right than it appears when the light is received.

 

[AlMetis]

Yes.

Thank you.
@ PeroK, yes, I will likely say more than necessary. It's a symptom of doubt.

2. The principle of relativity requires the laws do not discern one "inertial frame" from another when the Lorentz transformations hold the laws valid in all.Yes, no?

 

[Dale]

2. The principle of relativity requires the laws do not discern one "inertial frame" from another when the Lorentz transformations hold the laws valid in all.Yes, no?

Yes. Another way of stating this is that the laws of physics, both the differential equations and any associated constants, are the same in all inertial frames.

 

[PeterDonis]

How far apart are these coordinates?

The question makes no sense. You can ask what the spacetime interval is between two events (points in spacetime), but that's all.

I should have said the geometry of spacetime represented by the need to employ the Lorentz transformations between inertial frames expresses a continuum of fundamental dimension we don’t, but I would like to, understand.

Why do you think we don't understand it? You should not generalize from your own experience, because you evidently don't have a good grasp of SR, but that doesn't mean nobody does.

The basis I have is they “do” work , light “is” a constant and reality “is” what it is.

None of this justifies the claim I responded to. I gave you reasons why your claim was not justified. You haven't responded to those reasons at all.

Both sides are Galilean representations.

Which means, as I said, that they tell us nothing about SR. But you said your claim about some symmetry not being there after switching frames applies to SR. What are you basing that on?

 

[AlMetis]

Yes.

Thank you.
3. Then by virtue of 2, the motion of S is relative to the rest frame of E and the motion of E is relative to the rest frame of S, in that neither hold the equations 'More" valid in terms of the laws.

Yes, no?

 

[PeterDonis]

Thank you.
3. Then by virtue of 2, the motion of S is relative to the rest frame of E and the motion of E is relative to the rest frame of S, in that neither hold the equations 'More" valid in terms of the laws.

Yes, no?

Not as you state it. There is no such thing as "the" motion of anything. The correct statement is that S and E are moving relative to each other, so that in the rest frame of E, S is moving, and in the rest frame of S, E is moving. Both frames are equally valid.

 

[PeroK]

Thank you.
@ PeroK, yes, I will likely say more than necessary. It's a symptom of doubt.

2. The principle of relativity requires the laws do not discern one "inertial frame" from another when the Lorentz transformations hold the laws valid in all.Yes, no?

Yes. It means that the laws of physics must be Lorentz invariant. Newton's laws of motion, Hooke's law, Coulomb's law are all special case approximations of the "real" Lorentz invariant laws.

Note that Maxwell's equations are Lorentz invariant. That makes them incompatible with Galilean relativity, which was Einstein's starting point for his discovery of SR.

 

[Dale]

3. Then by virtue of 2, the motion of S is relative to the rest frame of E and the motion of E is relative to the rest frame of S, in that neither hold the equations 'More" valid in terms of the laws.

Yes, no?

That is oddly written, but I think you are saying that S is moving relative to E and E is moving relative to S, and that both are valid inertial frames so the laws of physics will be the same in both. If that is what you intended then, yes.

 

[AlMetis]

That is oddly written, but I think you are saying that S is moving relative to E and E is moving relative to S, and that both are valid inertial frames so the laws of physics will be the same in both. If that is what you intended then, yes.

Thank you, that is what I mean.

4. When the light pulse is emitted from S (t=0) the position of S and E coincide on x.
Does this corresponding time of emission with position of S and E change the path of the light pulse observed from the rest frame of either S, or E from the path agreed in #1?
Yes, no?

 

[Dale]

4. When the light pulse is emitted from S (t=0) the position of S and E coincide on x.
Does this corresponding time of emission with position of S and E change the path of the light pulse observed from the rest frame of either S, or E from the path agreed in #1?
Yes, no?

This is problematic. The event $(t,x)=(0,0)$ is the same event as $(t',x')=(0,0)$ but "coincide on x" seems to mean that you think that all events $(t,x)=(0,\chi)$ are the same events as $(t',x')=(0,\chi)$, which is not the case for any $\chi \ne 0$.

I also do not understand what you mean by "Does this corresponding time of emission with position of S and E change the path of the light pulse observed from the rest frame of either S, or E from the path agreed in #1?" The light pulse does not exist prior to emission, so I am not clear how it would make sense to speak of its path changing at emission.

 

[PeroK]

4. When the light pulse is emitted from S (t=0) the position of S and E coincide on x.
Does this corresponding time of emission with position of S and E change the path of the light pulse observed from the rest frame of either S, or E from the path agreed in #1?
Yes, no?

This may be the root of your confusion. The emission event has a single coordinate (in any frame). For convenience, we may take that event as the origin of the two inertial reference frames. There is no common path at that point. There is only the single emission event.

As coordinate time passes in each frame, the path of the light becomes a trajectory, or locus or worldline (depending on your terminology). This worldline is the same physical path, but is described by different coordinates in each frame. This idea that the same physical path can be described by two different sets of coordinates seems to be the problem.

This is tied up with your misunderstanding of the invariance of the speed of light, and your desire to make the direction of light invariant. You want the path of light in all frames to be determined by the orientation of the source at the time of emission. In this case, the source may be a laser pointing in the positive y-axis in both frames. But, if the laser is moving in one frame, then the velocity of the light it emits will not be in the positive y direction. This seems to be your stumbling block.

This goes back to an early post where I said that light inherits velocity and momentum from the motion of the source and you contradicted this. This is where you are going wrong.

Just to make this absolutely clear. The second postulate is:

The speed of light is independent of the motion of the source.

The following are not true:

[Wrong] The (vector) velocity of light is independent of the velocity of the source. (This would be physically absurd.)

[Wrong] The momentum of the light is independent of the source. (In fact, even the magnitude of the momentum is dependent on the motion of the source: this is the (relativistic) Doppler shift.

[Wrong] The direction of the light relative to three coordniate axes that coincide at emission is independent of the motion of source. (This again would be physically absurd.)

It seems to me that you've spent a lot of time ploughing your own furrow on this one. From my experience, it will now take considerable intellectual courage on your part to admit this is wrong and abandon these ideas and start with a clean slate using the correct second postulate.

 

[AlMetis]

This is problematic.

I am not thinking two events that occur in the same place and time are the same event.

In my #1 question we had not discussed the relative position of E and S.
This question is confirming that the aberration will remain as observed in #1 when the position of S and E coincide on x at the time of emission.
It’s purpose is to make clear the position of emission relative to E and S. We will call it 0x in E’s frame and for convenience we will call it 0x in S’s frame.
Unless this is the point of my mistake, we now have a symmetry of relative motion on x across y for both frames. E will observe exactly the same motion of S as S does of E with opposite sign of x.
(We will assume observers in E and S are NOT facing each other so the x direction will be common to both.)

Yes, no?

 

[Dale]

I am not thinking two events that occur in the same place and time are the same event.

Two events that occur at the same time and space coordinates with respect to a single frame are the same event. Also, any event and its Lorentz transform are the same event just with that one event’s coordinates expressed in two different frames.

In my #1 question we had not discussed the relative position of E and S.

E and S are reference frames, so I don’t know what you mean by their relative position. A reference frame extends throughout spacetime. Its position is everywhere.

Perhaps you are asking about the relative position of the spatial origin of the frames?

This question is confirming that the aberration will remain as observed in #1 when the position of S and E coincide on x at the time of emission.

Yes, the equations I wrote apply for all $0\le t$ and $0\le t’$. That does include the time of emission, $t=t’=0$.

But I still don’t understand what you mean by the path changing at the time of emission. The path didn’t exist before the time of emission and after emission the path went in a straight line. There is no change in direction. There was no direction before emission, and after emission it goes in a straight line.

Aberration is not a change in direction, it is a disagreement about direction.

It’s purpose is to make clear the position of emission relative to E and S.

Ok, I thought that was already clear $\left. r^\mu \right|_{t=0}=(0,0,0,0)$ and $\left. r^{\mu’} \right|_{t’=0}=(0,0,0,0)$

Unless this is the point of my mistake, we now have a symmetry of relative motion on x across y for both frames. E will observe exactly the same motion of S as S does of E with opposite sign of x.

Yes, although that was part of your problem setup from the beginning and is not something that we just “now have” as a result of some analysis.

 

[AlMetis]

But I still don’t understand what you mean by the path changing at the time of emission.

When I make reference to an inertial frame by its label alone (E, S, A, B etc), I’m refering to its spatial origin x0, y0, z0.
I didn’t think I ask if the path changes at time of emission. I asked if the observed path, or aberration would change from #1 when E and S coincide at the time of emission.
You answered it as I meant it.
I should have set the relative positions of E and S from the beginning. I didn’t think it would matter, but then I didn’t think I was mistaken, so I am being more careful to avoid assumptions.

5. When the light pulse is emitted from E not S, does this change the aberration observed in the rest frame of S or E from that agreed in #1?

 

[AlMetis]

The speed of light is independent of the motion of the source.

The following are not true:

[Wrong] The (vector) velocity of light is independent of the velocity of the source. (This would be physically absurd.)

[Wrong] The momentum of the light is independent of the source. (In fact, even the magnitude of the momentum is dependent on the motion of the source: this is the (relativistic) Doppler shift.

[Wrong] The direction of the light relative to three coordniate axes that coincide at emission is independent of the motion of source. (This again would be physically absurd.)

I am not suggesting any of these.
Just to make it absolutely clear, my earlier reference to the momentum of light was in reference to the example in your post I responded to which was an analogy of a ball tossed from a moving car. I thought the analogy was understood in my response. I did not expect the pedantic attack that followed.
All the physical characteristics of light emitted from a source in motion would not happen if light did not have momentum.
My point was unlike balls and cars, light does not move with speed c+v, or c-v its speed is always c.

If I am mistaken, which everyone posting says I am, I will be as gracious and grateful as possible in acknowledging and thanking everyone for their help.
But as a scientist you will understand I cannot believe what I don’t understand. That is superstition, not science.