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

[PeroK]

PS it's the speed of light that's invariant. Not its momentum vector.

 

[Ibix]

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

Yes it does. You may be mistaking the (true) statement that the speed of light is independent of its source for the (false) one that the velocity of light is independent of its source. As PeroK has already pointed out, your (mis)conception of how light behaves is internally inconsistent, which is why you are struggling with it.

 

[robphy]

PS it's the speed of light that's invariant. Not its momentum vector.

Indeed, blue light has larger components for its 4-momentum vector compared to red light. But both blue light and red light travel at the same speed.

 

[Sagittarius A-Star]

Whether the pulse strikes the mirror or not is not something determined by an observer’s choice of reference frame

Exactly! Therefore, if you agree, that the light-pulse strikes the mirror in the rest-frame of the light-clock, then you must also agree, that the light-pulse strikes the mirror in the other reference-frame.

 

[Ibix]

In fact, why don't we do some maths? Let's say an object at rest at the origin emits a pulse of light in the $+y$ direction at $t=0$. The coordinates of the light pulse at time $t$ are therefore $x=0, y=ct$. Plug in the Lorentz transforms:$$\begin{eqnarray*}
t'&=&\gamma(t-vx/c^2)\\
&=&\gamma t\\
x'&=&\gamma(x-vt)\\
&=&-\gamma vt\\
&=&-vt'\\
y'&=&y\\
&=&ct\\
&=&ct'/\gamma
\end{eqnarray*}$$So we can see that relativity says that the light pulse's coordinates in a frame where the source is moving are $x'=-vt$ and $y'=ct'/\gamma$. The speed is still $c$: $x'^2+y'^2=(v^2+c^2/\gamma^2)t'^2=c^2t'^2$ so the pulse is distance $ct'$ from the origin at time $t'$. But its velocity has acquired an $x$ component so is not perpendicular to the $x$ axis in this frame.

These are two different descriptions of the same thing.

 

[AlMetis]

Exactly! Therefore, if you agree, that the light-pulse strikes the mirror in the rest-frame of the light-clock, then you must also agree, that the light-pulse strikes the mirror in the other reference-frame.

Yes I do agree. I never said otherwise.

The point of that example was that the choice of frame determines whether the mirror moves or not. That a moving target is struck by the same light pulse that strikes the non-moving target suggest there is a distinction in relative measures that is irrelevant to the physical events.

 

[AlMetis]

This length is a “measurement” not common to both observers, but it is common and a LONGER measure for all observers at rest with the source (platform) and it is common and a SHORTER measure for all observers at rest with the train.

This does not mean the observer on the train is wrong, or the observer on the platform is wrong. It it does mean time is running slower for one of these two observers.

Can anyone explain which it is?

 

[Nugatory]

This does not mean the observer on the train is wrong, or the observer on the platform is wrong. It it does mean time is running slower for one of these two observers.

Can anyone explain which it is?

In the case of uniform inertial movement (which is what we have here, as opposed to the completely different and unrelated twin paradox situations) both observers find that time is running slower for the other observer, both are correct, the situation is completely symmetrical, and there is no meaningful way in which we can say that time is running slower for one or the other.

 

[Sagittarius A-Star]

Yes I do agree. I never said otherwise.

You did say otherwise:

When the emitter at the bottom of the clock is pointing at the mirror at the top of the clock, the light pulse will NOT strike the mirror if the mirror moves after emission. We are talking about a pulse that travels in a straight line in the direction the emitter is pointed.
...
We could say the light pulse scenario is just a tool for discussion and the reality is light is a wave so the light will strike the mirror even when the mirror moves after emission.

SR can treat the particle model and wave model of light equally good.

 

[AlMetis]

the situation is completely symmetrical, and there is no meaningful way in which we can say that time is running slower for one or the other.

Is the symmetry broken if we know which measures a shorter light path?

 

[AlMetis]

You did say otherwise:

You’re taking what I said out of context.
If the light pulse does not hit the mirror, it will not be seen to hit the mirror in any frame of reference.
If it does hit the mirror, it will be seen to hit it in every frame of reference.
It will not hit the mirror if the mirror moves, but whether the mirror moves or not depends on the frame of reference chosen. This is still my original question now posed in three different scenarios.

 

[Ibix]

It will not hit the mirror if the mirror moves, but whether the mirror moves or not depends on the frame of reference chosen. This is still my original question now posed in three different scenarios.

This has been answered several times. If the pulse hits the mirror in the mirror rest frame then it will hit in the frame where the mirror is moving. Your argument that the pulse will not hit in a frame where the mirror is moving is not correct.

 

[Sagittarius A-Star]

If the light pulse does not hit the mirror, it will not be seen to hit the mirror in any frame of reference.
If it does hit the mirror, it will be seen to hit it in every frame of reference.

... is correct and contradicts to:

It will not hit the mirror if the mirror moves, but whether the mirror moves or not depends on the frame of reference chosen.

... which is wrong. See:
https://www.einstein-online.info/en/spotlight/light-clocks-time-dilation/

 

[Nugatory]

Is the symmetry broken if we know which measures a shorter light path?

No.
An easy way of seeing this is to provide two light clocks, one at rest relative to each observer. Both observers will consider the path of the light beam in the clock that is at rest relative to them to be "shorter" and the path of the light beam for the other clock to be "longer". Both will consider the path of the light in the clock that is at rest relative to them to be perpendicular to the x-axis and the path of the light in the other clock to be angled relative to the x-axis. Anything either says about one light clock, the other will be able to say about the other light clock, so there is no violation of symmetry anywhere.

It is worth noting that they both agree about the paths through spacetime that both light beams follow - that is, they agree about which points in spacetime the light passes through. They also agree about the lengths of these paths in spacetime. They disagree about what "perpendicular to the x-axis" means, because that notion is inherently frame-dependent.

 

[Sagittarius A-Star]

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

Do you agree, that the light-pulse has in the (primed) rest-frame of the light-clock the following momentum in y-direction?
$p'_y = \frac{E'}{c^2}u'_y = \frac{E'}{c^2} c = \frac{hf'}{c}$

 

[vanhees71]

You did say otherwise:

SR can treat the particle model and wave model of light equally good.

At this level of discussion, please forget anything you think to know about "photons". I don't understand, why we still teach the totally wrong picture of Einstein's conception of 1905. Note that Einstein himself admitted as late as 1954 that he doesn't consider to have understood himself the "nature of radiation". What's for sure is that the naive photon picture of 1905 is completely wrong. Light (i.e., electromagnetic waves) have in no sense the properties of a localizable particle. According to modern QED, and that's what's indeed describet the "nature of radiation", i.e., the electromagnetic interaction, correctly, photons do not even have a proper position observable.

You should think about photons as being quanta of the free electromagnetic field, and their behavior is thus best "visualized" as the minimal portion of electromagnetic field energy and momentum of a given frequency and wave vector that can be emitted and absorbed by matter. In this sense Planck's photon picture was closer to modern QED than Einstein's.

 

[Sagittarius A-Star]

What's for sure is that the naive photon picture of 1905 is completely wrong.

Then you must also admit, that the classical wave picture is completely wrong. It predicts i.e. wrongly the pattern from a double-slit experiment with only a few photons.

But this discussion is not about the double-slit experiment. The relativistic Doppler/aberration formula can be derived correctly with both, the classical particle model and classical wave model of light. It should be possible to discuss SR, a classical theory, without invoking QED.

 

[vanhees71]

Well, that's why we have to quantize the electromagnetic field, i.e., there are phenomena which cannot be described by classical Maxwell theory.

As I said, for the Doppler effect you don't need photons. So stick to classical electrodynamics. It's a pretty simple calculation with a Lorentz transformation of the wave-four-vector.

 

[AlMetis]

This has been answered several times. If the pulse hits the mirror in the mirror rest frame then it will hit in the frame where the mirror is moving. Your argument that the pulse will not hit in a frame where the mirror is moving is not correct.

It has been stated a number of times and the math that repeats those statements has been well documented. But neither explain why.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.
I am not questioning that. I am questioning why that is contradicted in the examples I gave.
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.Here is another example that I think is detailed enough that any mistake/s I have made should be ealily explained.
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.
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. 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. 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.

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?

 

[Ibix]

But neither explain why.

PeroK pointed out the reason on the last page, but you replied:

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

The problem with your reasoning is thinking that light does not acquire momentum from its source. If you accept that it does then all your problems go away (and you don't violate momentum conservation). The self-contradictory mess you are in trying to think otherwise should tell you that you should be considering what we've said.

If conservation of momentum is not enough of an explanation for you, what would be?

 

[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