WIKI and Time Dilation: The Possible Error in Relative Velocity

[JesseM]

The calculations of LT assume you are stationary as an observer and all other objects are moving.

No they don't, using the equations only requires us to assume that you (the person reading the problem, in a textbook or a wiki article) know the coordinates of some event in one frame, then the LT gives you the corresponding coordinates in the other frame. There is no assumption that you are an actual physical observer in the scenario the problem is describing, who has determined the coordinates using rulers and clocks at rest relative to yourself.

I guess that is just one of the reasons Einstein used the term stationary 62 times in his 1905 paper.

Maybe instead of inventing a fantasy version of Einstein who coincidentally thought just the same way you do (but for some reason never explained this thinking explicitly), you should just pay attention to what he actually said and take him at his word that he was using "stationary" purely as a way of verbally distinguishing one frame from others.

 

[Dale]

I am not trying to say the Minkowski metric does not apply to the unprimed frame.

I am trying to say when it does, it is also a Euclidian light sphere for example.

However, when I map that surface of the Euclidian light sphere to the primed frame, the metric is the same 0 but the mapped light beams are different based on direction unlike the light beams in the unprimed frame.

Therefore, for any light beam in the unprimed frame, the metric produces a constant 0 for light, however, the equation x² + y² + z² = c² t²*produces a constant c² t² for all points on the light sphere surface.

When each light beam is mapped, the metric again produces 0 but the equation x'² + y² + z² = c² t'² is such that c² t'² is not constant in all directions.

Consequently, although the metric produces 0 for any light beams in any frame translated or not, the underlying geometry is hidden because of the difference in the fact, c² t² is constant in all directions and c² t'² is not.

Therefore, the originating space is different from the mapped space.

Your conclusions are completely incorrect. Just look at the math:

In the unprimed frame the metric is: ds² = -c²dt² + dx² + dy² + dz²

For ds² = 0 we obtain the equation of a sphere of radius c dt: c²dt² = dx² + dy² + dz²

In the primed frame the metric is: ds² = -c²dt'² + dx'² + dy'² + dz'²

For ds² = 0 we obtain the equation of a sphere of radius c dt': c²dt'² = dx'² + dy'² + dz'²

There is no difference between the frames in any of this. The Minkowski metric produces what you call a light sphere and what everyone else calls a light cone in all reference frames.

 

[Dale]

Isn't a moving clock supposed to be time dilated?

What do you think?

Moving wrt what? Time dilated in which frame? Whenever you are talking about a relative quantity you must specify what the quantity is relative to. How many times do we need to repeat this same point before it sinks in? The idea that velocity is a relative quantity has been around since Galileo in 1632. You are almost 4 centuries out of date when you write about velocity without specifying a reference and you are more than 1 century out of date when you do the same for time dilation.

And yes, a clock is time dilated in any reference frame in which it is moving. Note how easy it is to specify wrt what the relative quantities are measured.

 

[Doc Al]

I am fine with this. But, the article is talking about time dilation.
Under time dilation, it is normal to say the moving clock is time dilation.

But, in the frame of the clock on WIKI, the "moving observer" would not be time dilated. I guess that is why that observer did not have a clock. Isn't a moving clock supposed to be time dilated?

What do you think?

I think you're getting sidetracked by the labels "moving" and "rest", which here refer to the observed speed of the light clock itself. Better to just call them the "unprimed" and "primed" frames. Δt is the time for one cycle of the 'light clock' in a frame in which the light clock is at rest. Δt' is the time for that same cycle as measured from a frame in which that 'light clock' is moving. So, the infamous 'time dilation' maxim that "moving clocks run slow" is exactly what is described by the given equation Δt' = γΔt. All is well.

(As seen in the primed frame, the light clock is a moving clock.)

 

[espen180]

Can observer be moving relative to one another?

Imagine a univarse in which they could not, and imagine what a garbage theory SR would be is it did not allow this. Any physical or nonphysical object can play the role of observer in SR. You and I are both observers of the universe. Does that mean we can't move wrt each other?

A more direct answer: Nothing in the maths or philosophy of Einsteinian mechanics (or Newtonian, or Galilean) prevent observers to move wrt each other.

1) If an observer is in a frame and moves in thatr frame, the observer is no longer in that frame.
2) If there is only one observer, how does the observer know he/she is moving?

1) This is nonsense. Look what this logic leads to. Let's sa you and I are on one side of a football field. You start running toward one of the goals. Due this this action on your part, you suddenly ceased to exist in my frame. Notice the absurdity?

On a serious note, I guess the underlying claim on your part is that an observer cannot make measurements in a frame wrt which he/she is moving. Yes, this is in some sense true. On the other hand, the observer can use Lorentz transformations to translate the measurements he/she does in his/her frame to any other frame.

2) How does the observer know he/she is not moving (wrt what)?

 

[chinglu1998]

Imagine a univarse in which they could not, and imagine what a garbage theory SR would be is it did not allow this. Any physical or nonphysical object can play the role of observer in SR. You and I are both observers of the universe. Does that mean we can't move wrt each other?

A more direct answer: Nothing in the maths or philosophy of Einsteinian mechanics (or Newtonian, or Galilean) prevent observers to move wrt each other.



1) This is nonsense. Look what this logic leads to. Let's sa you and I are on one side of a football field. You start running toward one of the goals. Due this this action on your part, you suddenly ceased to exist in my frame. Notice the absurdity?

On a serious note, I guess the underlying claim on your part is that an observer cannot make measurements in a frame wrt which he/she is moving. Yes, this is in some sense true. On the other hand, the observer can use Lorentz transformations to translate the measurements he/she does in his/her frame to any other frame.

2) How does the observer know he/she is not moving (wrt what)?

1) You are the one that claimed if you move in a frame, then you are still in that frame. that is false, you are in another frame.

2) An observer does not know they are moving. They view themselves as at rest and everything else is moving. So, I do not know what you mean.

 

[chinglu1998]

What do you mean "time expanded"? In the frame of the observer, the light clock will take more time to tick forward a given amount (light clock is ticking slower than observer's clock in observer's frame), and in the frame of the light clock, the observer's clock will take more time to tick forward a given amount (observer's clock is ticking slower than light clock in light clock's frame). Do you agree?

How about I ask you. What is your math in the view of the clock frame for the the times of each frame.

Please make sure you use light aberration in tyhe "observer frame" because this is a function of which frame has the light source and the clock frame has the light source. From the view of the clock frame, what do you get?

 

[chinglu1998]

No they don't, using the equations only requires us to assume that you (the person reading the problem, in a textbook or a wiki article) know the coordinates of some event in one frame, then the LT gives you the corresponding coordinates in the other frame. There is no assumption that you are an actual physical observer in the scenario the problem is describing, who has determined the coordinates using rulers and clocks at rest relative to yourself.

I am fine with your typing above. But, now take the next step as I have.

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good.2 In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ``stationary system.''
http://www.fourmilab.ch/etexts/einstein/specrel/www/

In my view, this is cruciel in understanding SR. When you take a frame as stationary, your measurements are Euclidian and your physics is Newtonian. The other frame when mapped with LT is not.

So, this is not a simple verbal distinction, but a logical one.

 

[chinglu1998]

Your conclusions are completely incorrect. Just look at the math:

In the unprimed frame the metric is: ds² = -c²dt² + dx² + dy² + dz²

For ds² = 0 we obtain the equation of a sphere of radius c dt: c²dt² = dx² + dy² + dz²

In the primed frame the metric is: ds² = -c²dt'² + dx'² + dy'² + dz'²

For ds² = 0 we obtain the equation of a sphere of radius c dt': c²dt'² = dx'² + dy'² + dz'²

There is no difference between the frames in any of this. The Minkowski metric produces what you call a light sphere and what everyone else calls a light cone in all reference frames.

Your math is correct but is missing something.

Where in your math have you shown the mapped light sphere by LT is a light sphere?

The only think you can show is each mapped light beam measures c.

So, you have to look inside the problem to find the distinction.

Hence, for all light beams in the stationary frame, each measures ct in all directions for some t.

This same set of light beams mapped by LT do not measure a constant distance from the light emission point in the moving frame.

These are mathematical facts.

 

[JesseM]

How about I ask you. What is your math in the view of the clock frame for the the times of each frame.

What does "times of each frame" mean? You can only compare the times between a specific pair of events, comparing "time" without specifying events is totally meaningless. What events do you want to look at? If we look at two events on the worldline of an object at rest in the unprimed frame, then the time between them in each frame is given by t' = t γ. If we pick two events on the worldline of an object at rest in the primed frame, the time between them in each frame is given by t = t' γ. If that doesn't answer your question you'll have to be more specific about what you're asking. But please don't avoid my own question, which was asking what you meant by "time expanded" in this comment:

What does this do to time dilation given the observer could have a clock.
that means the clock at rest with the light source will view the moving observer and clock as time expanded.

Please make sure you use light aberration in tyhe "observer frame"

Obviously light that is sent by a light source moving relative to the observer will be aberrated in the observer frame, but beyond this I have no idea what you mean by "use" light aberration. Again, you'll have to be more specific.

From the view of the clock frame, what do you get?

"Get" for what specific quantity? Again, are you asking about the time between some events in the clock frame?

 

[chinglu1998]

Moving wrt what? Time dilated in which frame? Whenever you are talking about a relative quantity you must specify what the quantity is relative to. How many times do we need to repeat this same point before it sinks in? The idea that velocity is a relative quantity has been around since Galileo in 1632. You are almost 4 centuries out of date when you write about velocity without specifying a reference and you are more than 1 century out of date when you do the same for time dilation.

And yes, a clock is time dilated in any reference frame in which it is moving. Note how easy it is to specify wrt what the relative quantities are measured.

Well, maybe you are correct. Can you provide the math using the clock frame and prove the observer frame is time dilated compared to the clock frame?

We are using light by the way as the test as is for WIKI.

 

[chinglu1998]

I think you're getting sidetracked by the labels "moving" and "rest", which here refer to the observed speed of the light clock itself. Better to just call them the "unprimed" and "primed" frames. Δt is the time for one cycle of the 'light clock' in a frame in which the light clock is at rest. Δt' is the time for that same cycle as measured from a frame in which that 'light clock' is moving. So, the infamous 'time dilation' maxim that "moving clocks run slow" is exactly what is described by the given equation Δt' = γΔt. All is well.

(As seen in the primed frame, the light clock is a moving clock.)

Alright. Primed and unprimed is fine with me.

What if the unprimed frame is taken as stationary? What results do you get?

Or, maybe say, the unprimed frame is the context.

 

[chinglu1998]

What does "times of each frame" mean? You can only compare the times between a specific pair of events, comparing "time" without specifying events is totally meaningless. What events do you want to look at? If we look at two events on the worldline of an object at rest in the unprimed frame, then the time between them in each frame is given by t' = t γ. If we pick two events on the worldline of an object at rest in the primed frame, the time between them in each frame is given by t = t' γ. If that doesn't answer your question you'll have to be more specific about what you're asking. But please don't avoid my own question, which was asking what you meant by "time expanded" in this comment:


Obviously light that is sent by a light source moving relative to the observer will be aberrated in the observer frame, but beyond this I have no idea what you mean by "use" light aberration. Again, you'll have to be more specific.

"Get" for what specific quantity? Again, are you asking about the time between some events in the clock frame?

Let us assume you take the context of the frame with the clock. The start event is the light emission and the end event is the light reaching y=L.

Please calculate t' and t.

 

[Doc Al]

What if the unprimed frame is taken as stationary? What results do you get?

Not sure what you mean, since the light clock is at rest in the unprimed frame. But if there were another clock at rest in the primed frame, then observers in the unprimed frame would see it as running slow. In that case, the 'time dilation' formula would be Δt = γΔt'. (As seen from the unprimed frame, that second light clock is a moving clock.)

 

[JesseM]

Let's take a timeout here.

Each slice of the light cone is a certain time. So, yes, you must consider all mapped light beams at a particular time in the "chosen" frame. See how you need to specifiy this?

No, because the LT doesn't say anything about being restricted to events which are all on the same "slice" of a light cone, you can transform a set of events that all happened at different times in your frame.

In the stationary frame, the light sphere is a sphere.

If you pick events on the light cone that all happened at the same time in the frame you label "stationary", then their positions form a sphere. If you pick a bunch of events that happened at different times in this frame (and I'm not talking about doing a LT, I'm saying you're free to pick as your initial data a set of events which are non-simultaneous in whatever frame you start out with) then their positions may form some other shape like an ellipsoid. If you pick all events on the worldlines of the light beams at all possible times in this frame, they form a 4D cone.

Similarly, if your initial set of events was such that when you transform into the "moving frame", you get a bunch of events that are simultaneous in the moving frame, then their positions form a sphere. If your events in the moving frame are non-simultaneous, then they may form some other shape like an ellipsoid. And if you are looking at all events on the worldlines of the light beam in the moving frame, they form a 4D cone. So, I still can't make any sense of your distinction between "Euclidean space" in the stationary frame and "Minkowski space" in the moving one, still seems like a totally incoherent distinction.

OK, but, for each time t in a frame, there exists the surface of the sphere and for some reason, they map a sphere surface to a circle and then use time to make the cone.

If a light sphere is not a sphere, then just say that. But, by the relativity postulate, each frame sees a sphere and hence the geometry should present the facts.

I have no idea what you mean by "sees a sphere". If you think of yourself as an actual physical observer at rest in some frame (as opposed to adopting the omniscient perspective of someone reading a problem in a textbook), then you understand that you can't actually visually "see" a set of simultaneous events in your frame at a single moment, right? Since you are at different distances from different points in space, what you see visually at a single moment will be light from a bunch of events at different times in your frame. Statements about what was happening at a single t-coordinate can only be made in retrospect, like if in 2010 I receive a signal from an event E1 10 light-years away in my frame, and in 2020 I receive a signal from an event E2 20 light-years away in my frame, and I conclude retroactively that they both happened simultaneously at the t-coordinate of 2000 in my frame. So the "light sphere" is every bit as much of a retroactive reconstruction as the "light cone", both involve charting the coordinates of a bunch of events that I didn't become aware of until various later times.

But it's clear they are talking about an observer "moving" relative to the clock frame.

They never said the observer was moving at speed v in his own frame, it's clear from the context they mean the observer is moving at speed v in the clock frame.

You can justify all you want. Under SR, when you refer to a single observer, that observer is stationary.

"Stationary" is meaningless unless understood to mean "stationary relative to" some object or frame. Certainly an observer (or any other object) is stationary relative to their own frame, but moving relative to other objects and frames.

That observer does not move and thinks all other objects move.

In their own frame yes, but the observer is perfectly capable of understanding that they would be seen as "moving" in other frames, unless they are an idiot who doesn't understand the LT.

Just look at LT and that will help you udnerstand this fact.

What fact? What aspect of the LT will "help me understand"? It would certainly be helpful if you would give some actual math rather than these endless incoherent verbal arguments.

 

[Dale]

What if the unprimed frame is taken as stationary? What results do you get?

Do you have some sort of diagnosed learning deficit? Stationary wrt what?

 

[chinglu1998]

Not sure what you mean, since the light clock is at rest in the unprimed frame. But if there were another clock at rest in the primed frame, then observers in the unprimed frame would see it as running slow. In that case, the 'time dilation' formula would be Δt = γΔt'. (As seen from the unprimed frame, that second light clock is a moving clock.)

Δt = γΔt'.

Can you please show this by including light aberration just like WIKI did and following the same style argument? Thanks.

 

[chinglu1998]

Do you have some sort of diagnosed learning deficit? Stationary wrt what?

Stationary with respect to the observer in WIKI. Does WIKI have something else in the problem?

 

[JesseM]

Let us assume you take the context of the frame with the clock. The start event is the light emission and the end event is the light reaching y=L.

Please calculate t' and t.

I already told you that "If we look at two events on the worldline of an object at rest in the unprimed frame, then the time between them in each frame is given by t' = t γ." I suppose since one event is on the worldline of the bottom mirror and the other event is on the worldline of the top mirror this doesn't precisely fit the sentence I wrote, but since both events are at the same position on the x-axis, and the x-axis is the axis of relative motion between the two frames, it still works out the same. If you need a derivation for this I could give you one, but please first do me the courtesy of answering the question about what you meant by "time expanded" in this comment, as I have asked twice now:

What does this do to time dilation given the observer could have a clock.
that means the clock at rest with the light source will view the moving observer and clock as time expanded.

 

[JesseM]

I am fine with your typing above. But, now take the next step as I have.

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good.2 In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ``stationary system.''
http://www.fourmilab.ch/etexts/einstein/specrel/www/

In my view, this is cruciel in understanding SR. When you take a frame as stationary, your measurements are Euclidian and your physics is Newtonian. The other frame when mapped with LT is not.

Any Newtonian equation that holds in one frame holds in all of them. As usual, you base your statements on some weird notion of "Minkowski space" that no actual physicists use (as opposed to Minkowski spacetime, which we all understand), but none of your attempts to justify the notion that one frame involves "Euclidean space" and the others involve "Minkowski space" make the slightest bit of sense to me--see my recent comments in post #195.

So, this is not a simple verbal distinction, but a logical one.

You may have the confused belief that it's more than simply a verbal distinction, but please stop using Einstein's use of the word "stationary" to support your belief, since he never introduces any nonsensical notion that Newtonian/Euclidean laws only work in the "stationary" system (this would contradict the first postulate of relativity in section 2, which says 'The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion'), and he explicitly says that his purpose in introducing the word "stationary" is "to distinguish this system of co-ordinates verbally from others".

 

[chinglu1998]

No, because the LT doesn't say anything about being restricted to events which are all on the same "slice" of a light cone, you can transform a set of events that all happened at different times in your frame.

Sure you are correct. Except, we were considering the light sphere, remember?

If you pick events on the light cone that all happened at the same time in the frame you label "stationary", then their positions form a sphere. If you pick a bunch of events that happened at different times in this frame (and I'm not talking about doing a LT, I'm saying you're free to pick as your initial data a set of events which are non-simultaneous in whatever frame you start out with) then their positions may form some other shape like an ellipsoid. If you pick all events on the worldlines of the light beams at all possible times in this frame, they form a 4D cone.

I agree.

Similarly, if your initial set of events was such that when you transform into the "moving frame", you get a bunch of events that are simultaneous in the moving frame, then their positions form a sphere. If your events in the moving frame are non-simultaneous, then they may form some other shape like an ellipsoid. And if you are looking at all events on the worldlines of the light beam in the moving frame, they form a 4D cone. So, I still can't make any sense of your distinction between "Euclidean space" in the stationary frame and "Minkowski space" in the moving one, still seems like a totally incoherent distinction.

No, I have an equation from the context of the "stationary frame" frame such that for all light beams that strike this object in the stationary frame, the LT calculates the same t'. It is not a sphere BTW. Do you have this math?

I have no idea what you mean by "sees a sphere". If you think of yourself as an actual physical observer at rest in some frame (as opposed to adopting the omniscient perspective of someone reading a problem in a textbook), then you understand that you can't actually visually "see" a set of simultaneous events in your frame at a single moment, right? Since you are at different distances from different points in space, what you see visually at a single moment will be light from a bunch of events at different times in your frame. Statements about what was happening at a single t-coordinate can only be made in retrospect, like if in 2010 I receive a signal from an event E1 10 light-years away in my frame, and in 2020 I receive a signal from an event E2 20 light-years away in my frame, and I conclude retroactively that they both happened simultaneously at the t-coordinate of 2000 in my frame. So the "light sphere" is every bit as much of a retroactive reconstruction as the "light cone", both involve charting the coordinates of a bunch of events that I didn't become aware of until various later times.

Calculates a sphere.

"Stationary" is meaningless unless understood to mean "stationary relative to" some object or frame. Certainly an observer (or any other object) is stationary relative to their own frame, but moving relative to other objects and frames.

I do not know how to answer this. Let's ask you a question. Assume you are in a rocket in space without acceleration. You want to use SR from your view. What are you stationary wrt?

In their own frame yes, but the observer is perfectly capable of understanding that they would be seen as "moving" in other frames, unless they are an idiot who doesn't understand the LT.

Where can I find this in the axioms of SR? This is a math theorynot a human theory.

 

[chinglu1998]

I already told you that "If we look at two events on the worldline of an object at rest in the unprimed frame, then the time between them in each frame is given by t' = t γ." I suppose since one event is on the worldline of the bottom mirror and the other event is on the worldline of the top mirror this doesn't precisely fit the sentence I wrote, but since both events are at the same position on the x-axis, and the x-axis is the axis of relative motion between the two frames, it still works out the same. If you need a derivation for this I could give you one, but please first do me the courtesy of answering the question about what you meant by "time expanded" in this comment, as I have asked twice now:

I am having trouble calculating t' = t γ using the light aberration argument of WIKI and the clock frame as stationary wrt to the universe. Can you help me?

 

[Doc Al]

Δt = γΔt'.

Can you please show this by including light aberration just like WIKI did and following the same style argument? Thanks.

Huh? The argument would be identical to that which lead to the time dilation formula shown in WIKI. The only difference would be that primed and unprimed frames would be reversed. Obviously the physics doesn't change.

 

[chinglu1998]

Any Newtonian equation that holds in one frame holds in all of them. As usual, you base your statements on some weird notion of "Minkowski space" that no actual physicists use (as opposed to Minkowski spacetime, which we all understand), but none of your attempts to justify the notion that one frame involves "Euclidean space" and the others involve "Minkowski space" make the slightest bit of sense to me--see my recent comments in post #195.

Wrong. You use Newtonian and Euclidian in your "rest" frame. LT does not translate to Newtonian physics and Euclidian genometry since it is hyperbolic.

You may have the confused belief that it's more than simply a verbal distinction, but please stop using Einstein's use of the word "stationary" to support your belief, since he never introduces any nonsensical notion that Newtonian/Euclidean laws only work in the "stationary" system (this would contradict the first postulate of relativity in section 2, which says 'The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion'), and he explicitly says that his purpose in introducing the word "stationary" is "to distinguish this system of co-ordinates verbally from others".

Wrong again. All I need do is take another frame as stationary and the Newtonian/Euclidean laws work there. I never said only in one frame.

 

[chinglu1998]

Huh? The argument would be identical to that which lead to the time dilation formula shown in WIKI. The only difference would be that primed and unprimed frames would be reversed. Obviously the physics doesn't change.

Can I see it with light aberration?

You do realize light aberration as used with WIKI is absolute correct? The frame with the light source is the only one in the inverse that does not see light aberration. If you disagree with this then you disagree with SR section 7.

 

[JesseM]

Wrong. You use Newtonian and Euclidian in your "rest" frame. LT does not translate to Newtonian physics and Euclidian genometry since it is hyperbolic.

If you pick any specific example of a Newtonian/Euclidean equation that works in the coordinates of one frame in SR, it works in the coordinates of every other frame in SR. As I recall you have already admitted this is true, but retreated into nonsense about things not working in "Minkowski space" which is not a concept that any physicist uses and which does not seem to make any sense (see post #195).

You may have the confused belief that it's more than simply a verbal distinction, but please stop using Einstein's use of the word "stationary" to support your belief, since he never introduces any nonsensical notion that Newtonian/Euclidean laws only work in the "stationary" system (this would contradict the first postulate of relativity in section 2, which says 'The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion'), and he explicitly says that his purpose in introducing the word "stationary" is "to distinguish this system of co-ordinates verbally from others".

Wrong again. All I need do is take another frame as stationary and the Newtonian/Euclidean laws work there. I never said only in one frame.

You seem incapable of giving a mathematical definition of what it means to "take a frame as stationary". If "stationary" is simply a verbal label (as Einstein asserts) then it can have no effect on the derivation of any mathematical equation, so Newtonian/Euclidean laws still work in other frames even if you don't label them as "stationary". If you disagree, give me an actual example of a mathematical law for which you think this doesn't work, don't just resort to more evasive verbal nonsense.

 

[Doc Al]

Can I see it with light aberration?

See what? The derivation of time dilation 'using aberration' (the slanting of the light as seen in another frame) is what is given in WIKI. Just exchange primed with unprimed quantities.

You do realize light aberration as used with WIKI is absolute correct? The frame with the light source is the only one in the inverse that does not see light aberration.

Why do you think it's 'absolute'? The frames are in relative motion. You could just as well say that the frame with the light clock is the only frame that doesn't see that clock's time as dilated. True, but trivial.

If you disagree with this then you disagree with SR section 7.

Now what are you talking about?

 

[chinglu1998]

If you pick any specific example of a Newtonian/Euclidean equation that works in the coordinates of one frame in SR, it works in the coordinates of every other frame in SR. As I recall you have already admitted this is true, but retreated into nonsense about things not working in "Minkowski space" which is not a concept that any physicist uses and which does not seem to make any sense (see post #195).

Sure you can pick any Newtonian/Euclidean equation that works in one frame, it works in any frame. This is true by the relativity postulate. Everyone knows that.

But, if you take the Euclidean light sphere in a frame, LT does not translate it to a Euclidean light sphere. Again, everyone knows that, do you?

You seem incapable of giving a mathematical definition of what it means to "take a frame as stationary". If "stationary" is simply a verbal label (as Einstein asserts) then it can have no effect on the derivation of any mathematical equation, so Newtonian/Euclidean laws still work in other frames even if you don't label them as "stationary". If you disagree, give me an actual example of a mathematical law for which you think this doesn't work, don't just resort to more evasive verbal nonsense.

I posted over and over Einstein's distinction for the "stationary" system. I do not know what else to do. It is obvious to me.

 

[Dale]

Your conclusions are completely incorrect. Just look at the math:

In the unprimed frame the metric is: ds² = -c²dt² + dx² + dy² + dz²

For ds² = 0 we obtain the equation of a sphere of radius c dt: c²dt² = dx² + dy² + dz²

In the primed frame the metric is: ds² = -c²dt'² + dx'² + dy'² + dz'²

For ds² = 0 we obtain the equation of a sphere of radius c dt': c²dt'² = dx'² + dy'² + dz'²

There is no difference between the frames in any of this. The Minkowski metric produces what you call a light sphere and what everyone else calls a light cone in all reference frames.

Where in your math have you shown the mapped light sphere by LT is a light sphere?

Right here:

we obtain the equation of a sphere of radius c dt': c²dt'² = dx'² + dy'² + dz'²

This same set of light beams mapped by LT do not measure a constant distance from the light emission point in the moving frame.

These are mathematical facts.

No, I already disproved this, and it is contrary to the second postulate. If you believe otherwise then post your derivation.

 

[chinglu1998]

See what? The derivation of time dilation 'using aberration' (the slanting of the light as seen in another frame) is what is given in WIKI. Just exchange primed with unprimed quantities.


Why do you think it's 'absolute'? The frames are in relative motion. You could just as well say that the frame with the light clock is the only frame that doesn't see that clock's time as dilated. True, but trivial.


Now what are you talking about?

Light aberration is absolute I was very specific.

Are you going to calculate how the time dilation works for this WIKI example?

I am curious how you will convert absolute light aberration to reciprocal time dilation.

I was hoping you would calculate this.