"Light is frame-dependent in PF, but constant in SR"

The reference does not seem to me to be suggesting that bookkeeper coordinates represent any sort of direct measurement. In fact, from the reference cited, "The strength of bookkeeper coordinates is universality; their weakness is isolation of most data entries from direct experience.". That is really the same as saying they cannot be directly measured.

 

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You're making a complete fool of yourself. Behave this way in your daily life and you'll wind up paying for it in a unenviable way.

 

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Really? How and when was such a measurement performed?

If you are referring to Taylor and Wheeler page 2-34, you got it totally backwards. Here is what they tell you:

"For this reason, we often call r, φ, and t bookkeeper coordinates. The strength of bookkeeper coordinates is universality;
their weakness is isolation of most data entries from direct experience." (in other words, you can't measure coordinate speed of light, as I told you).
People can live on a shell and in a free-float frame. In contrast, people can, in principle, live and work in free-float frames and
on spherical shells, taking and analyzing data as if they were in flat spacetime, but unfortunately they can do so only for limited patches of spacetime." (in other words, by contrast, local speed of light is measurable).

 

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No that's 'not really the same' as you suggest. It's a REMOTE measurement from REMOTE coordinates. It's not a DIRECT measurement. A DIRECT measurement is made IN local coordinate and local proper frames [how many times must I explain this?] The example I gave was recorded by the HST. Let's see how much you've learned?

Local coordinate and local proper frame measurement are inv...... [direct measurement]

Measurements made from remote coordinates are frame dep...... [remote measurement]

Another example of a remote coordinate measurement is the Shapiro Delay.

 

Post #64. Another remote measurement of the remote coordinate speed of light is the Shapiro Delay. The Shapiro measurement is over the entire path of the light and is frame dependent.

Darn I just gave part of the answer to OM.

 

"Shapiro delay" , as the name says it, is not a measurement of the coordinate speed of light, it is a measurement made locally of the time taken for an em ray to go to a distant celestial object and to be reflected back, you are getting things backwards.

 

Am I surprised you want to tell me "in other words, you can't measure coordinate speed of light, as I told you". Not really. Try the Shapiro Delay. What are we measuring 'over the entire path of the light'? BTW it's the remote coordinate speed of light. You're saying we can't confirm the prediction from GR.

 

"Shapiro delay" , as the name says it, is not a measurement of the coordinate speed of light, it is a measurement made locally (i.e. with one clock, located at the origin of the em source) of the time taken for an em ray to go to a distant celestial object and to be reflected back, you are getting things backwards, you are contradicting established parts of mainstream science.

Far from me saying that, the Shapiro delay is one of the standard tests of GR. What I am saying is that you have a misconception about what the test measures.

 

If I could get a good laugh at your expense, I would think it would be well worth it. I was actually laughing out loud because of how ignorant you are when I posted that comment. And I still am, lol, I just can't help myself.

 

No, it's a measurement of the entire path. It measures the remote coordinate speed of light. The delay is what's expected when measured from remote coordinates. All remote measurements are made with a clock in the bookkeeper frame. ?. If it was a local measurement there would be NO delay. I have a misconception? Don't think so. Prove I'm getting it backward. Prove that Shapiro didn't measure a delay over the entire path of the experiments. Prove that the HST didn't measure the redshift of the dying pulse train. You're the one getting it backwards.

Think about what you're saying. You're saying measurements of remote natural phenomena and local natural phenomena are all measured in local coordinate frames and local proper frames. You're saying all the measurements are invariant.

 

I don't know why you persist in this misconception. There is no "coordinate speed of light" in the theory of the Shapiro experiment. I can show you the calculations if you are interested.

This is getting worse and worse. If you sent a pulse of light to a distant planet and you waited for the reflection to come back, you wouldn't get it back in zero time. Where are you getting these ideas?

No, this is not what I am saying, what I have been saying is that coordinate speed of light isn't measurable. Taylor and Wheeler, the exact paragraph you cited, tell you the same exact thing. Actually, every mainstream text teaches you the same thing.

 

What is "lights physical change"? Neither 2km/6.66µs nor 10km/33.33µs define the speed of light, only the velocity of the muon as observed from the two different frames. As I told you before, and you vigorously ignored, it is not valid to directly compare the local measurements of two different frames. That is exactly what the Lorentz transform is meant for, which you are not using when making such statements as "the muon frame saw lights physical change ... 1/5 less", whatever you think that is suppose to mean.

You also seem oblivious to the fact that both length contraction and time dilation are reciprocal. This means that an observer in the muon's frame would be equally justified in saying that the ground's time and distance are 1/5 less. Perhaps you have chosen a bad example with the muon, as it has no extent to contract and the ground frame's time has no bearing on the muon's half-life, so you are only seeing the full story.

Or just read this until you reach an epiphany:

The ground observation is also 1/5 that of the muon, as observed from the muon frame.

If you are going to deal with SR, you really should get into the habit of defining in which frame the observation is made.

 

The remote coordinate speed of light is measurable regardless what you think. It's a prediction of GR and confirmed by the Shapiro delay. Where did I say you get it back in zero time.? You mark the bkkpr time when the signal is sent then you mark the bkkpr time when the signal returns. The measurement is over the entire path and the delay is associated with a path through curved spacetime compared to the invariant path over flat spacetime. It's a frame dependent remote coordinate measurement. You're confused about this just like the last time when you argued energy isn't conserved over the path in GR. I already know you don't have respect for text which disagrees with your opinion. I knew this would happen. Kiss off with your grasp for authority.

 

Repeating the same misconception over and over isn't a valid argument. The "coordinate speed of light" never intervenes in the Shapiro delay.
The time taken by an em ray to his a distant body and to come back is (expressed in a system where \(c=1\)):

\(\Delta t= 2(X_1+X_2+ r_s log \frac{X_1 X_2}{R^2})\)

\(X_1\) is the distance from the signal source to the bending celestial body (the Sun).
\(X_2\) is the distance from the bending celestial body (the Sun) to the reflecting body.
\(R\) is the "distance of minimal approach" (see Rindler, "Relativity: Special, General and Cosmological" for details)
\(r_s\) is the Schwarzschild radius of the bending body

Another way of expressing the time delay is:

\(\Delta t=\frac {2}{c}(X_1+X_2+ r_s log \frac{X_1 X_2}{R^2})\)

where \(c\) is the light speed in vacuum, the universal constant.


There is no "coordinate speed of light" anywhere in the derivation or in the final result.
If you still cling to your kooky idea that "the Shapiro delay is a measure of coordinate speed of light" I would like you to demonstrate mathematically how do you get the coordinate speed of light from the formalism of the experiment. Please show the math.

You don't know what you are saying:

Anyway, you have some very serious misconceptions, you need to reflect on the stuff you are claiming because it borders on crackpottery. The fact that you keep copying the same formulas from Taylor and Wheeler without understanding what they mean doesn't make you knowledgeable on the subject.

The very text that you keep citing (Taylor and Wheeler, page 2-34) disproves your kooky claims.
"For this reason, we often call r, φ, and t bookkeeper coordinates. The strength of bookkeeper coordinates is universality;
their weakness is isolation of most data entries from direct experience." (in other words, you can't measure coordinate speed of light, as I told you).
People can live on a shell and in a free-float frame. In contrast, people can, in principle, live and work in free-float frames and
on spherical shells, taking and analyzing data as if they were in flat spacetime, but unfortunately they can do so only for limited patches of spacetime." (in other words, by contrast, local speed of light is measurable).

 

Anyone who spells "dilation" "dialation" isn't in a position to teach anything remotely useful to physicists, scientists or engineers regarding relativistic physics and/or math. By now it should be evident to you that such folks are regularly contributing here.

This conversation has branched into multiple points of contention at multiple layers of complexity and detail. This is what I imagine the old one-room schoolhouses had to contend with, when students at all stages of advancement were relegated to taking their lessons simultaneously. No doubt many layers of insight were crisscrossing the room as here in this thread.

Education requires that one has to submit to the doctors who wrote the texts, designed the experiments, researched the data, cranked out the numbers, verified the axioms, demonstrated the proofs, and published innovations under scrutiny of their mentors. There simply is no better, more practical method for debugging every eureka moment that anyone might come up with. Each of us starts at the baseline, rarely moves beyond it, and almost never advances it. Those who do are generally proficient in math as the primary language and tool of science, often at quite a young age. They have surpassed the fear and suspicion of strange symbols and relationships they don't understand, and have learned to wield formulas and the principles they represent as a means of expressing the laws of nature, whether evident to the casual student or whether more esoteric and specific to some detail or specialization. Along the way the best of them will occasionally need to invent new math to express new discoveries and ideas. Don't forget that Latin used to be the international language until math broke the language barrier.

Quite a few experts are chiming in here, finding themselves in teaching moments for anyone who is attentive, curious and/or capable of understanding the basis for their remarks. Alpha, for example, quite clearly pointed out that velocity is a time rate of change of position. That's a high school or freshman concept. He went on to give the very concise definition of world lines as geodesics, from which we recognize the norms of their tangents in three classes, positive (space), negative (time) or zero (free space propagation). If I'm not mistaken Alpha, Tach, BruceP, and especially James R and rpenner -- and at least a several other regular contributors, all of whom are a great asset to this site, plus perhaps half a dozen others who I haven't exactly understood yet -- have at one time or another expanded on this. I'm quite certain I never believed I ever needed to lay down the law for them, as I would defer to anyone who actually reads and at least halfway understands technical journals -- and/or have established themselves academically -- I would defer to these folks or any other expert or reasonably informed person in a heartbeat.

Why is that? Why do I recognize folks who have either paid their dues or demonstrated wisdom and honesty? And why do you stand so far afield harping on these fine (some even excellent) minds with cynical objections over trivia?

Why don't you merely turn a leaf, see the error of your ways, surrender to your betters, accept advice when generously given? I'm not saying this merely to pick on you; it's a rhetorical question for all of the fringe "self-made" experts out there. Why aspire to be a legend only in your mind? Isn't that a very delusional place to be? This is a good site for learning science from folks who are are generous with their contributions. I certainly recognize, and I'm quite certain that they do - and I would argue strenuously with anyone opposed to this -- that each of us, at some time or another, find ourselves deluded, misled, confused and (at best, in moments of personal honesty) just plain WRONG. Add to that the denial that comes from persistently misleading oneself (often accompanied by suspicion, fear and doubt about how science works), and you get some of the more extreme cases of folks who are perpetual trolls, even if in their minds they are sitting on some great chunk of wisdom that the world simply won't accept because they believe they are so brilliant that no one can understand them. Most of this category of person is stuck on high school and freshman concepts (such as perpetual motion folks who simply don't want to accept the laws of thermodynamics). These kinds of doubts about the limits of human knowledge are wrung out in the entrance exams and remedial courses that precede a formal education, so that's why folks who actually got somewhere with their science education all generally on the same page about this. It's not about mimicry. It's about wisdom.

Give in. Take the high road. Celebrate the hard work, advantage and intellect of everyone who has ever crossed through the portals you scoff at (rhetorically addressing all the cynics out there, too). Give it a go. Accept that you are not really the genius you imagine yourself to be, that knowledge is truly free, not manipulated or spoonfed to programmed robots -- but the fractional gain of dogged work, endless late nights cracking the books, and poring over problems, equations, and axioms of science and math, and slaving at the lab bench grappling with materials, equipment and measurement issues. Accept this, recognizing that effort alone can truly liberate you from quirky, superstitious, delusional or JUST PLAIN WRONG beliefs.

At present, in your remarks above, as in Maxilla's posts, you are merely limited by your lack of exposure to derivatives (differential calculus). It's freshman material. It's in the high school curriculum. Yet you're addressing folks (congrats, Alpha -- good luck, Tach) recently earning their PhDs, or pursuing them, or (James R, rpenner, plus others) demonstrating their acumen of this highest academic achievement. And you are telling them they're wrong.

How and why that doesn't bother you speaks to to the question of intellectual honesty (again I'm addressing naysayers and cranks in general). If there is one thing that makes a conversation intelligent (the stated goal of this site) it's the ability to let your hair down and confess your lack of experience and your desire to learn from folks who've been there, done that.

If you were to simply admit "I don't understand the time derivative of position" we (or plenty of folks) could go off in a corner and wring that out. You would certainly need to get past this to even begin to understand what Alpha meant by "the norm of the tangent of the geodesic". Personally I really like that phrase. It's says a huge amount of stuff in so few words. It's just the language of science. It ought to spur you on to learn more, not feel bruised and wanting to bite the hand that feeds you.

That's my advice. Rewind, reset, calibrate, and disengage all the artifices of cynical response to superior knowledge. Pretty soon you'll be on the same course as any purist, reaching for the understanding. (You and countless cynics.) Take my advice -- take the next turnoff, and go for the high road. There simply is no better way to realize your own sense of engagement with reality.

Call it morbid, but I am curious about the psychological aspect of such a reaction (assuming, of course it's not just trolling), that people actually think they can walk up to strangers who made a career pursuit of science (and related academia), and throw the gauntlet down, and say "screw you, you are are an idiot; you are deluded; you are a robot". Just look at such a reaction objectively (or at least try to imagine an objective appraisal). Is this not the quintessential character of pathological thinking? In my mind, science -- as it manifests in the intellect of modern people -- is the ultimate cure for the devious mind. Thinking errors of every kind can be purged merely by a strenuous application of the axioms of geometry. We can go back to Plato (or a dozen others of the Golden Age of Greece) and find such good formulas for resetting, re-centering our biased opinions and striving for truth. In such a state of mind, basic principles of freedom and humanity can be reasoned out using syllogisms and rules of logic. Does doing that make a person a robot? No. It's the best application of human intellect for the highest of all purposes.

Why is it that we (so many of us) never seem to learn? It's one thing to be deprived of opportunity. But it's quite another to slap the spoon away when it's been pre-digested and served up as pap for the undeveloped palate.

 

If we apply special relativity to a mass traveling near C, it space-time reference contracts. If we extrapolate this toward the speed of light the contraction approaches a point-instant. The question is how can light show larger than point-instant expressions of space and time (wavelength and frequency) like radio waves? Also how can light show a range of output affects from gamma rays to radio waves even with one velocity?

 

Brucep, it seems the main difficulty is an understanding of the definition of bookkeeper coordinates/time. I have been looking for some clear description or definition and it has a not been an easy task. Following are a couple of quotes from 2003 MIT course notes, which at least indirectly address the intent and use of the term "Bookkeeper" in reference to coordinates and or time. They are not intended to represent physical distances or time and thus cannot be used in the measurement of any real distances, times or velocities. In fact in most presentations of the metrics involved \(c = 1\), which already defines the speed of light as, assumed constant.


Gravity, Metrics and Coordinates, MIT course notes (2003)

Page 4

Note that all of the coordinates in the metric are bookkeeper coordinates —they have no meaning independent of the metric. The metric tells us how to measure distances and times – the coordinates do not! If you never confuse r or t with physical distance and time, you will save yourself a lot of grief! The authors of EBH are careful to put subscripts like shell on physical distances and times measured by shell observers. Bookkeeper coordinates have no subscripts.​

Though the above quote does mention, "The metric tells us how to measure distances and times", it goes on to clarify and limit that measurement to the metric used to represent space-time, by continuing, "If you never confuse r or t with physical distance and time, you will save yourself a lot of grief!", and a reference to how the authors of EBH attempted to handle the issue...

Page 7

We will not say more about the Schwarzschild metric now, because that will be the main business for the next few weeks. However, we do wish to emphasize again that the coordinates (t, r, θ, φ) are simply bookkeeper coordinates with no physical significance by themselves. In General Relativity, the metric gives the coordinates meaning.​

In this last reference the significance is expressly laid at the foot of GR and thus any measurements remain confined to the metric rather than any physical distance, time or velocity.., and as noted earlier most of the time the metric begins with a definition of \(c = 1\)... No measurement.

 

You made a few mistakes by missing some details in the posts. This link http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html from the Georgia University physics department where I got the data for my original post showed the Lorentz transformations for the ground frame to the muon frame, at the muons relative velocity of .98c to the ground. This relationship was 10km/34µs to 2km/6.8µs, the example you are refereeing to showed the relationship for the observation of a photon 10km/33.33µs to 2km/6.66µs (1/5 less also). To demonstrate, where c=.3km/µs, (.3km/us)*6.66µs=1.9998km (round to 2km, and (.3km/µs)*33.33µs=9.999km (round to 10km).

That comparison is just as physically valid as the muon’s travel difference observed between the ground frame and muon frame, because it is what SR predicts each frame will observe for the travel of a photon relative to the other frame (note the ratio value of c is still .3km/µs).

Quite the contrary, it is obvious and my post was clear that both frames see the reciprocal of length and time, except you made a mistake above as the muon would claim the ground observe's the muon's distance and travel time as 5 times the muon's own observations, and the ground wound say the reciprocal 1/5 (this includes how they observe light travel distance and time). Did you know that's what reciprocal meant in mathematics, as opposed to the word definition of reciprocate?

I recognize it is easy to make mistakes like the one you made above, when pointed out to me, I will acknowledge and correct them; none of us are perfect.
Maxila

 

I would be sarcastic about this, but honestly, it would be a wasted effort.

 

You're post is clueless. You think measurements can't be made from remote coordinates. Clueless. Joseph Dolan said the spacetime event 'dying pulse train' observed and recorded by the HST lasted .2 second measured by a clock in the remote coordinate frame of the HST. The Shapiro Delay is derived from the remote coordinate speed of light and the confirmation of the predicted delay, for all his experiments, can be translated as a confirmation of the GR prediction of the remote coordinate speed of light.

The Shapiro Delay is DERIVED from the GR prediction for the radial remote coordinate speed of light

This is a simple example

The light leaves our sun and is received on our planet.

The remote radial coordinate speed of light

dr/dt = (1-2M/r)

You can integrate this over the path and build a formula for predicting the Shapiro delay.

dr/dt = 1-2M/r

dt = Int(rdr/r-2M)

dt = (r-2M) + 2M ln(r-2M)

For this example experiment

dt = [r_earth orbit - r_sun] + 2M_sun ln[r_earth orbit/r_sun]

The 1st component is the distance between where the light is emitted and received and the 2nd component is the predicted Shapiro delay due to a path through curved spacetime.

I'll solve it for this example experiment

r_earth orbit = 1 AU = 1.495978E11 m

r_sun = 6.9598E8 m

M_sun = 1477 m [using geometric units]

dt_bkkp = [ 1.495978E11m - 6.9598E8m] + 2954m ln[1.495978E11m/6.9598E8m]

= 1.4890182E11m + 15854.11645m = 1.489018359E11m

15854.11645m is the delay time in geometric units. dt_meter.

To convert this to seconds divide by c.

dt_second = 15854.11645m/2.99792458E8m/s

= .00005288367752 second

~ 53 microsecond

That is the extra time due to the path through curved spacetime.

What do you think MOST DATA ENTRIES means? ALL DATA ENTRIES? It turns out the data entries that are recorded from remote coordinates is enough to do the science. The spacetime curvature [effects of gravity] over the entire path of each Shapiro experiment is accounted for in the result. You should read that book. I've explained it to you more than once. If you want to believe the GR prediction of the remote coordinate speed of light hasn't been empirically verified 'have at it'.