Is the brightness of light invariant?

[DaleSpam]

Dale even the abilty to consider the relative velocity of inertial relationship requires historical data. What is velocity after all, but a statement of changes in the distance relationship over a given amount of time. Change can not be determined with out historical data. [ ie. change from what to what]

You cannot ignore historical data because if you did the term velocity is meaningless.

If one was to take a picture, a snapshot of a ship and star at relative v one could not discern that velocity existed. They would appear to be co-moving or at zero relative velocity. It is only the historical data that gives us any meaning to the term velocity. [ This is a part of the reason for generating this thread I might add...to explore aspects of light that do not require time [ change] in the data collected]

Haha! You have me here. This is an excellent point. I really like this, it definitely shows that (regardless of your background) you are clearly putting serious thought into this.

The measure of velocity is very different to a measure of a bars length [ assuming that the bars length is constant and unchanging.]

Different, yes, but not very different. You need two points in space in order to get a length. You need two points in spacetime to get a velocity.

So with the above in mind I find it facinating that acceleration data is able to be ignored yet velocity data is accepted. As both require historical references to make sense.

Well, you need three snapshots to be able to calculate acceleration. You only need two to calculate velocity. With two snapshots you could approximately determine the Doppler shift, but you couldn't even remotely guess at the acceleration.

Have you had any calculus? Mathematically it does make sense to talk about an "instantaneous velocity". In other words, the idea of a velocity at a single point in time is an inherent part of calculus. I tend to think rather mathematically as you may have noticed. But experimentally I don't know of any way to determine velocity from a single point in time, as you pointed out.

BTW I thank you for your patience and yes I will probably do as you suggested regards formal introductions to physcis, classical or other.

I'm glad. I think it would greatly help. Even from well-intentioned people on this forum you will get a hodgepodge of confusing responses. Do be persistent in your studies, I had what I thought were several solid fundamental objections to SR for about 7 years before I worked through each one off and on and determined to my satisfaction that I was wrong in each case.

-Dale

 

[Quantum Quack]

Ahh!! It is nice to make sense some times.....ha

Actually you still need three snapshots to determine that you are not accelerating. Two would only indicate that you have movement three would determine whether that movement was steady or accelerating. [I think]

But even then it is a historical record based on three snapshots taken in the present and looked at with hindsight or after the event.

 

[Quantum Quack]

There is some thoughts about how if we take an infinitely small point in time for an object that is moving and consider this as a two dimensional slice with two sides. One side of this infinitely thin slice is in a different position to the other even though there is virtually no thickness to the slice. [ I think Plank (spls?) would argue against this notion however]

So even a single snap shot of an object that is moving has implied in it the velocity but the velocity may be desribed as a potential for change rather than change itself.....sort of difficult to get the "ole head around I guess.

 

[2inquisitive]

DaleSpan:

I really wish you guys would stop telling me what I claim and don't claim, you are all so inaccurate. Yes, I claim that in any inertial frame the star is moving at different relative velocities wrt multiple rockets. No, I do not claim that it is emitting multiple wavelengths in any frame (assuming only one direction is relevant, otherwise it does emit multiple wavelengths, but I don't think that was the point of your post).

Would you care to clarify what you mean by "moving wrt the emitted wavelength". Let's say that the emitted wavelength in a particular frame is 1m. How do you "move wrt 1m". It doesn't make any sense to me. I am sure you have something else in mind, but I am not a psychic.

OK, an emitted wavelength of 1m is equal to a radiowave frequency of about 280 mHz. If I move toward the distant source of the signal (say 10 lyrs) at .5c, I will measure an increased frequency, to about 560 mHz. I claim the increase in frequency is due to my motion, counting an increase in the wave peaks due to my motion relative to them. I claim the 1m wavelength that was emitted 10 years ago did not decrease to 1/2 meter because the SOURCE increased velocity relative to me, but because I simply count an increase in their frequency because of MY increased relative velocity. Do you claim the source somehow changed the wavelength that was emitted 10 years ago because IT changed velocity?

 

[DaleSpam]

Actually you still need three snapshots to determine that you are not accelerating. Two would only indicate that you have movement three would determine whether that movement was steady or accelerating. [I think]

That is just my point. The movement doesn't have to be steady for the Doppler shift. It is completely independent of acceleration.

This can be seen pretty easily by considering exactly your snapshot idea. Let's say that you rig your "camera" so that it is triggered every time that there is a peak in the EM wave. So the time between two peaks is a direct measure of the observed period, and since the period is the inverse of the frequency it is a direct measure of the Doppler-shifted frequency. Three peaks/snapshots will therefore get you two direct measures of the Doppler-shifted frequency. If there is a difference between the two then you can use that to get a single estimate of the relative acceleration, but each measurement of the Doppler effect stands on its own from only the two source snapshots.

There is some thoughts about how if we take an infinitely small point in time for an object that is moving and consider this as a two dimensional slice with two sides. One side of this infinitely thin slice is in a different position to the other even though there is virtually no thickness to the slice. [ I think Plank (spls?) would argue against this notion however]

So even a single snap shot of an object that is moving has implied in it the velocity but the velocity may be desribed as a potential for change rather than change itself.....sort of difficult to get the "ole head around I guess.

What you have described here is actually exactly the calculus idea that makes it reasonable (mathematically) to speak of a velocity at a single instant (even though as you pointed out it is an idealization of experimental reality). If you consider your slices to have some "thickness" in time, dt, then you can look on the front and on the back and measure the distance that it moved, dx. As you get thinner and thinner slices both dx and dt go to zero, but their ratio dx/dt does not. This is what is meant in calculus when we say v = dx/dt. Just that at any point in time the velocity is the ratio of the difference in position (across the two sides) to the thickness of that infinitely thin slice of time.

-Dale

 

[Quantum Quack]

Ahh! I see I am going to have to learn calculus one day....I've been trying to describe this and other similar dimensional reductions in a way that makes sense for ages....calculus....hmmmm..... mind you, how many people can make a lot of sense out of calculus?...I wonder...seems to be an exception rather than a rule....ha

Try to describe the difference between infinitely small and zero thickness...hmmmmm...

 

[DaleSpam]

OK, an emitted wavelength of 1m is equal to a radiowave frequency of about 280 mHz. If I move toward the distant source of the signal (say 10 lyrs) at .5c, I will measure an increased frequency, to about 560 mHz. I claim the increase in frequency is due to my motion, counting an increase in the wave peaks due to my motion relative to them. I claim the 1m wavelength that was emitted 10 years ago did not decrease to 1/2 meter because the SOURCE increased velocity relative to me, but because I simply count an increase in their frequency because of MY increased relative velocity. Do you claim the source somehow changed the wavelength that was emitted 10 years ago because IT changed velocity?

What changed velocity or increased velocity are you talking about? A changing velocity is an acceleration. In your scenario is someone accelerating? If so, which is accelerating?

2inq, I hope you understand. I am not trying to be a pain, but communicating with you can be very difficult when you use such imprecise language to describe precise concepts. You really need to be more careful if you want people to be able to answer your question.

Now, I think that what you are trying to describe is the following situation: a source and a detector start out 10 light-years apart at rest wrt each other, the detector emits a radio wave at a proper frequency of 280 mHz, the detector then rapidly accelerates to .5c moving towards the emitter. Is this the situation you would like me to analyze?

-Dale

 

[Quantum Quack]

Of course I have gotta learn how do algebra first....ha

 

[DaleSpam]

Ahh! I see I am going to have to learn calculus one day....I've been trying to describe this and other similar dimensional reductions in a way that makes sense for ages....calculus....hmmmm..... mind you, how many people can make a lot of sense out of calculus?...I wonder...seems to be an exception rather than a rule....ha

I think you would be surprised. The concepts are not as difficult as most students fear, and the resulting mathematical tools are incredibly powerful. Particularly for physics. Newton was one of the people who really developed calculus. I don't think he was particularly interested in the math for math's sake, but he needed a new tool to describe the physics ideas he had. Personally, I think that you really can't fully understand classical physics without learning calculus, but I am probably a little over-enthusiastic in my pro-math opinions.

Try to describe the difference between infinitely small and zero thickness...hmmmmm...

Yeah, the word they use in calculus for "infinitely small" is "infinitesimal". I like it because it just sounds nice!

-Dale

 

[Quantum Quack]

I think you would be surprised. The concepts are not as difficult as most students fear, and the resulting mathematical tools are incredibly powerful. Particularly for physics. Newton was one of the people who really developed calculus. I don't think he was particularly interested in the math for math's sake, but he needed a new tool to describe the physics ideas he had. Personally, I think that you really can't fully understand classical physics without learning calculus, but I am probably a little over-enthusiastic in my pro-math opinions.


Yeah, the word they use in calculus for "infinitely small" is "infinitesimal". I like it because it just sounds nice!

-Dale

I have often heard it said that mathematics is essentially a sophistcated and specialised language. A way of coveying complex visualisation, and communicating such with a degree of accuracy.

I guess it is not unlike most verbal languages, the exeption being that mathematics can afford greater accuracy in the communication of those ideas.

Unfortunately or fortunately I have had a serious learning disability regarding math for most of my life however I can visualise complex structures and models especially dimensional models quite easilly. For some reason I was always held back in the learning process because if I didn't understand the logic of what I was doing I would reject the notion until I did. Thus whilst the class I was in would steam ahead I was sitting there trying to understand the logic of simple functions that most persons simply accepted with out to much of a problem.

Of course most mathematics courses do not include a detailed understanding of the reasoning that exists behind every math function but merely promoted them as a sort of "don't worry about it just accept it" sort of atttude. I quickly lost interest in math, because the teachers themselves could not fully explain what they were teaching...[ high school math was a dead loss]

So when some one quotes for example the Lor. transforms I attempt to see the rational behind it, which puts me in an awkward position because I have difficulty with the symbology in the first place. I can of course compute using the transforms [ a simple spread sheet function - allowing for errors due to the limitations of that spread sheet] with out much of a problem how ever it is the logical premise behind them and how they were derived and why they suggest a physical requirement that interests me.

So in a way I am doing things backwards, Trying to see the mathematics before I can understand it.....sort of.

I am however getting to a point where by I can intuitively grasp mathematics with out the symbology and will endeavour to learn the formalities language in the future.

Just thought I'd mention the above to put my postings in some sort of context and perpsective.

 

[Quantum Quack]

A good example of a complex mathematical problem that I wouldn't even know where to start yet I can visualise it quite easilly is:

If we assume the speed of light to be universally invariant, and that the "flat" space vector and speed of a ray of light is actually determined by the omni curvature of space time. How fast is a ray of light travelling in curved space and not flat space?

And if this can be determined the speed of light can actually be used to determine the size of the universe in flat space terms. As the curved space path of light is but a mere segment of that curve.

There for once the curved speed of a ray of light is determined the circumfurence of the circle can be determined thus giving us the volume that the universe takes up.

Compex imagery, and I would suspect damn complex math as well.

And no doubt it sounds like rubbish as well.

 

[2inquisitive]

OK, DaleSpam, I thought the details weren't difficult to understand.

What changed velocity or increased velocity are you talking about? A changing velocity is an acceleration. In your scenario is someone accelerating? If so, which is accelerating?

In the way I learned English, CHANGED is past tense, i.e. already happened. CHANGING is present tense, i.e. is presently occuring. I capitalized MY motion, i.e. the motion of the spaceship captain this thread is about. I noticed in an earlier post that you implied I did not know the difference between an inertial frame and a non-inertial frame. Do you? The observer in the frame that feels a force is the one accelerating. The captain feels the force, therefore the star is not accelerating. IF the captain measured a continuously CHANGING velocity between his frame of reference and the star's, but felt no force acting on him, THEN the star's frame would be the one accelerating. The captain would never change from his inertial frame while the STAR'S frame accelerated. Again, that was not my scenario.

Now, I think that what you are trying to describe is the following situation: a source and a detector start out 10 light-years apart at rest wrt each other, the detector emits a radio wave at a proper frequency of 280 mHz, the detector then rapidly accelerates to .5c moving towards the emitter. Is this the situation you would like me to analyze?

No, that is not what I described. The SOURCE emitted the radio wave 10 years prior to the event I am describing. Yes, the detector is on the spaceship along with the captain (the observer). No observers are on the distant star. The detector measures the frequency of the radio wave as 280 mHz at the beginning of the exercise. The frames do not have to be co-moving at the beginning of the exercise, only that a signal that is recieved from the distant source is recorded as 280 mHz in frequency and he feels no acceleration forces. The captain then fires his engines, feels an acceleration directed towards the star for a period of time, then shuts his engines off again. He feels no acceleration after shutting off his engines. He checks the frequency of the signal that is being emitted from the distant star again. The frequency has doubled in magnitude, from the first reading of 280 mHz to 560mHz for the current reading.

 

[DaleSpam]

I thought the details weren't difficult to understand.

Of course you didn't, the poster never does or they would include more information the first time. I have done it myself often enough.

In the way I learned English, CHANGED is past tense, i.e. already happened. CHANGING is present tense, i.e. is presently occuring. I capitalized MY motion, i.e. the motion of the spaceship captain this thread is about. I noticed in an earlier post that you implied I did not know the difference between an inertial frame and a non-inertial frame. Do you?

Certainly. No frame was specified in your problem. Neither in your original description nor in this description.

The observer in the frame that feels a force is the one accelerating. The captain feels the force, therefore the star is not accelerating. IF the captain measured a continuously CHANGING velocity between his frame of reference and the star's, but felt no force acting on him, THEN the star's frame would be the one accelerating. The captain would never change from his inertial frame while the STAR'S frame accelerated. Again, that was not my scenario.

Then it is certainly a good thing I asked.

No, that is not what I described. The SOURCE emitted the radio wave 10 years prior to the event I am describing. Yes, the detector is on the spaceship along with the captain (the observer). No observers are on the distant star. The detector measures the frequency of the radio wave as 280 mHz at the beginning of the exercise. The frames do not have to be co-moving at the beginning of the exercise, only that a signal that is recieved from the distant source is recorded as 280 mHz in frequency and he feels no acceleration forces. The captain then fires his engines, feels an acceleration directed towards the star for a period of time, then shuts his engines off again. He feels no acceleration after shutting off his engines. He checks the frequency of the signal that is being emitted from the distant star again. The frequency has doubled in magnitude, from the first reading of 280 mHz to 560mHz for the current reading.

Ah, ok, this is a much clearer description. So in any inertial frame the analysis goes like this: the source and the detector are moving both moving inertially. The source emits some radiation of unspecified and indeterminate proper frequency. In the frame of analysis this radiation travels at c from the source to the detector with a particular coordinate frequency and corresponding coordinate wavelength. The detector, crosses a wave peak every 1/280 us of proper time leading to a Doppler-shifted frequency of 280 mHz in our arbitrary frame. The detector then accelerates towards the emitter, or rather towards where the emitter was 10 years ago. The detector now crosses a peak every 1/560 us of proper time leading to a Doppler-shifted frequency of 560 mHz in that same arbitrary frame. Since the proper time of a clock is a frame-invariant quantity all inertial frames will agree on the results of the experiment.

-Dale

 

[dav57]

Ah, ok, this is a much clearer description. So in any inertial frame the analysis goes like this: the source and the detector are moving both moving inertially. The source emits some radiation of unspecified and indeterminate proper frequency. In the frame of analysis this radiation travels at c from the source to the detector with a particular coordinate frequency and corresponding coordinate wavelength. The detector, crosses a wave peak every 1/280 us of proper time leading to a Doppler-shifted frequency of 280 mHz in our arbitrary frame. The detector then accelerates towards the emitter, or rather towards where the emitter was 10 years ago. The detector now crosses a peak every 1/560 us of proper time leading to a Doppler-shifted frequency of 560 mHz in that same arbitrary frame. Since the proper time of a clock is a frame-invariant quantity all inertial frames will agree on the results of the experiment.

-Dale

Dalespam,

All you have answered here is a “description” of what everybody agrees on anyway. We know what the observer will record and nobody disputes this. I completely understand what is observed and recorded by an observer in the scenario we are discussing and I understand how important it is to defend light invariance on the basis of protecting relativity on the whole. I agree with the maths and I agree that relativity remains intact.

Now, lets get to the point. For relativity and light invariance to survive we must always place the reason for the Doppler shift as being attributed to the movement of the source, right?. Ok, I can live with that, if you wanted to continue along the lines of relativity.

But before I just simply accept this notion, please help me rule out the other possibilities.

As 2inquisitive is trying to say, the ACCELERATING observer KNOWS he is the one who moved through an ALREADY emitted light beam and he measured a larger frequency and reduced wavelength.

Why does science forbid the idea of the observer travelling relative to the light at c-v ?

Why can’t the reason for the reduced wavelength be the result of the observer having moved whilst “pinning down” each approaching wave peak?

Does this idea require an aether?

 

[DaleSpam]

All you have answered here is a “description” of what everybody agrees on anyway. We know what the observer will record and nobody disputes this. I completely understand what is observed and recorded by an observer in the scenario we are discussing and I understand how important it is to defend light invariance on the basis of protecting relativity on the whole. I agree with the maths and I agree that relativity remains intact.

If everyone agrees then why are we arguing?

Now, lets get to the point. For relativity and light invariance to survive we must always place the reason for the Doppler shift as being attributed to the movement of the source, right?. Ok, I can live with that, if you wanted to continue along the lines of relativity.

No. I disagree with that entirely. What justification can you possibly offer for that assertion? That is certainly not what SR claims, and it is not how I did the above analysis.

The First Postulate of SR is that "The laws of physics (including electrodynamics) are the same in all inertial frames of reference." So the SR position (and my position) is that you can carry out the analysis in any inertial frame. That includes the rest frame of the emitter, the rest frame of the detector prior to acceleration, the rest frame of the detector after acceleration, or any other inertial frame regardless of what objects may or may not be at rest.

But before I just simply accept this notion, please help me rule out the other possibilities.

As 2inquisitive is trying to say, the ACCELERATING observer KNOWS he is the one who moved through an ALREADY emitted light beam and he measured a larger frequency and reduced wavelength.

Be careful here. He knows that he accelerated. He can't know that he has anything other than a relative velocity to any given object or reference frame. As long as you aren't trying to imply some sort of absolute velocity with the "he is the one who moved" comment then we agree.

Why does science forbid the idea of the observer travelling relative to the light at c-v ?

The question should be "why does nature forbid it"? Science has no good answer for "why", it just recognizes the fact and builds a theory based on it. In general religion is much better at answering "why" questions, science is much better at "what" and "how".

One subtle point that may be a source of confusion and contention here is that light travels at c in all inertial reference frames. This does not imply that the relative velocity between an observer and a photon is c in all reference frames. If, in a particular inertial frame, an inertial observer is moving at v towards a stationary emitter then, since a photon moves at c, we will measure the relative velocity between the photon and the observer to be c+v. In the observer's proper frame he will measure his own velocity to be 0 and the same photon's velocity to be c so he will determine their relative velocity to be c. He will also measure the emitter's velocity to be v and therefore will measure the photon-emitter relative velocity to be c-v.

I am concerned that you and others may be misunderstanding the invariance of c and thinking that it implies that all relative velocities between any photon and any object must be c in all frames. That would be mathematically inconsistent. The point is that nature, not science, forbids light traveling at any speed other than c in any inertial frame. So, in the observer's proper frame, the light cannot travel towards him at a relative velocity of c-v, but there certainly are frames where the light does travel at c-v relative to the observer.

Why can’t the reason for the reduced wavelength be the result of the observer having moved whilst “pinning down” each approaching wave peak?

Well, you can't pin down the wave peak. Each wave peak is traveling at c in any inertial frame. But, as I demonstrated above, you can certainly perform the analysis in a frame where the observer is moving.

Does this idea require an aether?

No.

-Dale

 

[DaleSpam]

I have often heard it said that mathematics is essentially a sophistcated and specialised language. A way of coveying complex visualisation, and communicating such with a degree of accuracy.

I guess it is not unlike most verbal languages, the exeption being that mathematics can afford greater accuracy in the communication of those ideas.

I always think of it as the language of logic. It is a language where no illogical statement is gramattically correct. Of course, being logical doesn't mean that you are right, but being illogical is a sure sign that you are wrong. SR has a rigorous mathematical framework, so it is logical (aka self-consistent), but some future experiment may eventually prove SR to be wrong.

Of course most mathematics courses do not include a detailed understanding of the reasoning that exists behind every math function but merely promoted them as a sort of "don't worry about it just accept it" sort of atttude. I quickly lost interest in math, because the teachers themselves could not fully explain what they were teaching...[ high school math was a dead loss]

Unfortunately most math teachers in high school were education majors. They typically have a fairly weak grasp on the math and could not have answered your questions even if they were so inclined. Also unfortunately, most math teachers in college were math majors. They often have fairly weak teaching skills and may not be able to answer your questions either, although for a different reason. The people who understand both the material and the communication are quite rare.

-Dale

 

[2inquisitive]

all quoted text by DaleSpam:

So in any inertial frame the analysis goes like this: the source and the detector are moving both moving inertially. The source emits some radiation of unspecified and indeterminate proper frequency.

Correct, until the frequency is measured, it is indeterminate.

In the frame of analysis

There actually is not only one frame of analysis....(1) The comoving frames in which the first measurements were taken, i.e. 280mHz. (2) The accelerating phase in which the detector's frame is non-inertial and the source's (star's) frame is inertial. (3) The inertial frames, which are not comoving, within which the detector makes the second measurement in its inertial frame, i.e. 560mHz.

The detector, crosses a wave peak every 1/280 us of proper time leading to a Doppler-shifted frequency of 280 mHz in our arbitrary frame.

This measurement is not Doppler-shifted. It was stated at the beginning that the two frames were comoving when this measurement was taken.

The detector then accelerates towards the emitter, or rather towards where the emitter was 10 years ago. The detector now crosses a peak every 1/560 us of proper time leading to a Doppler-shifted frequency of 560 mHz in that same arbitrary frame.

You are mixing frames, DaleSpam! The detector is in a non-inertial frame while accelerating. The detector is in an inertial, but not comoving, frame after the acceleration frame. Yes, the frequency is then Doppler-shifted.

Since the proper time of a clock is a frame-invariant quantity all inertial frames will agree on the results of the experiment.

This will take some explanation on your part. Are you stating the clocks tick at the same rate during the comoving phase at the beginning? Agreed. The two frames are not comoving at the end of the exercise, there is a relative velocity difference indicated by the Doppler shift in the final phase. Are you stating the proper time (?...proper tick rate?) of clocks located at the source and the detector are identical when there is a relative velocity difference in the two frames? If, according to STR, the 'tick rate' of a clock located at the star is beating slower than the detector's clock, shouldn't the frequency emitted by the source be of a LONGER wavelength at the end, i.e. 140mHz? Now if the detector's clock was the one beating slower, it would register more wave peaks arriving per its increased interval between seconds. Correct?

 

[DaleSpam]

Correct, until the frequency is measured, it is indeterminate.

Sorry, I wasn't clear here. I meant that there was not sufficient information in the description to be able to determine the frequency.

There actually is not only one frame of analysis....(1) The comoving frames in which the first measurements were taken, i.e. 280mHz. (2) The accelerating phase in which the detector's frame is non-inertial and the source's (star's) frame is inertial. (3) The inertial frames, which are not comoving, within which the detector makes the second measurement in its inertial frame, i.e. 560mHz.

There is only one reference frame in my analysis. This comment seems to indicate that you don't understand what a reference frame is. A reference frame is simply a set of coordinates. If I draw only a single set of coordinates in my analysis then there is only a single reference frame, regardless of how many objects with different velocities there may be. I can, if I wish, choose my frame so that any given object is at rest within it, or I can draw my coordinates so that nothing is stationary.

If you wish to introduce multiple frames in your analysis then feel free to do so, but you are putting yourself through a lot of extra work. You will have to do coordinate transforms between the various frames in order to determine everything. It is much simpler, IMO, to pick any single frame for the analysis and that is the approach I took here. The nice thing about SR is that you can use any inertial frame you choose.

This measurement is not Doppler-shifted. It was stated at the beginning that the two frames were comoving when this measurement was taken.

Huh? How did you expect me to get that from:

The frames do not have to be co-moving at the beginning of the exercise

I can work the analysis either way, just please pick a scenario and describe it precisely and completely. I am not a mind-reader.

You are mixing frames, DaleSpam! The detector is in a non-inertial frame while accelerating. The detector is in an inertial, but not comoving, frame after the acceleration frame. Yes, the frequency is then Doppler-shifted.

No, I am not mixing frames. I use a single frame throughout so I can't possibly get frames mixed. Don't you understand that an object can accelerate in an inertial frame?

This will take some explanation on your part. Are you stating the clocks tick at the same rate during the comoving phase at the beginning? Agreed. The two frames are not comoving at the end of the exercise, there is a relative velocity difference indicated by the Doppler shift in the final phase. Are you stating the proper time (?...proper tick rate?) of clocks located at the source and the detector are identical when there is a relative velocity difference in the two frames? If, according to STR, the 'tick rate' of a clock located at the star is beating slower than the detector's clock, shouldn't the frequency emitted by the source be of a LONGER wavelength at the end, i.e. 140mHz? Now if the detector's clock was the one beating slower, it would register more wave peaks arriving per its increased interval between seconds. Correct?

Again, there is only one frame in my approach. The arrival of any two successive wavefronts at the detector represents two events in spacetime. The spacetime interval between the two events is a frame-invariant quantity, and the spacetime interval is equal to the proper time between the two events. The proper time is the inverse of the proper frequency and therefore the proper frequency recorded by the detector is a frame invariant quantity. All frames therefore agree what Doppler-shifted frequency the detector records.

-Dale

 

[2inquisitive]

There is only one reference frame in my analysis. This comment seems to indicate that you don't understand what a reference frame is. A reference frame is simply a set of coordinates. If I draw only a single set of coordinates in my analysis then there is only a single reference frame, regardless of how many objects with different velocities there may be. I can, if I wish, choose my frame so that any given object is at rest within it, or I can draw my coordinates so that nothing is stationary.

Yes, in YOUR analysis, you only used one set of coordinates, an 'at rest' set of coordinates centered on the detector. That does not analyize the scenario I presented, though. I stated the captain of the ship, within which the detector is located, turned on his engines, felt the force of acceleration directed at the source of the signal, and then shut his engines off. This felt force of acceleration REQUIRES a change from an initial inertial frame, to a non-inertial frame, and ending in an inertial frame once again. Your analysis was inadequate to illustrate the scenario.

Huh? How did you expect me to get that from:
“ Originally Posted by 2inquisitive
The frames do not have to be co-moving at the beginning of the exercise ”

I can work the analysis either way, just please pick a scenario and describe it precisely and completely. I am not a mind-reader.

Sorry, I began the scenario BEFORE any measurements were taken. How do you know if the frames are comoving, i.e. no Doppler shift, at the beginning? How do you know if the frames are comoving (at rest wrt each other) even after the initial frequency is measured? You don't until after a Doppler analysis is taken because it was stated that the signal frequency was unknown when it was emitted from the source. No measurements were taken at the source. But since the source was a STAR, the Doppler shift could be determined by analysizing other parts of the spectrum for identifiable elements. It has not been determined WHAT was emitting the 280mHz radio signal we are focusing on, only that it was emitted. How could that be known with no observer located at the star, the source of the 280mHz signal?

I can work the analysis either way, just please pick a scenario and describe it precisely and completely. I am not a mind-reader.

from my post

....(1) The comoving frames in which the first measurements were taken, i.e. 280mHz. (2) The accelerating phase in which the detector's frame is non-inertial and the source's (star's) frame is inertial. (3) The inertial frames, which are not comoving, within which the detector makes the second measurement in its inertial frame, i.e. 560mHz.

The initial MEASUREMENTS (plural) indicated the beginning inertial frames were comoving. The measurements are what determined this.

No, I am not mixing frames. I use a single frame throughout so I can't possibly get frames mixed. Don't you understand that an object can accelerate in an inertial frame?

You are mixing a comoving inertial frame, a non-inertial frame and an inertial frame where there is relative velocity difference together into ONE inertial frame in which the coordinates of the detector do not move. That does not describe my scenario. Yes, I understand an object, THE STAR, can accelerate in the detector's inertial frame. The detector CANNOT accelerate in an inertial frame, which I specifically stated did happen. Your analysis applys to a different scenario than I described, one in which the star, THE EMITTER, is the one that accelerates. I would think you know this without question, Dale, so why change my scenario?

 

[DaleSpam]

Yes, in YOUR analysis, you only used one set of coordinates, an 'at rest' set of coordinates centered on the detector.

Actually, I explicitly specified that the frame could be moving wrt the detector and the source. I said "the source and the detector are moving". I specifically mentioned this so that you could see that the analysis could be done in any inertial frame. It is not necessary to consider a reference frame where anything is at rest. That is the whole point of the first postulate of SR. I can pick any random frame with absolutely no justification whatsoever and still be confident that the analysis will work.

I do not understand why you are so stuck on the detector's rest frame, particularly considering that it is a non-inertial frame. Several of you have now mentioned words to the effect that I must use the detector's rest frame to do the analysis. I have disagreed with such comments and continue to disagree. If you think there is some reason that the detector's rest frame is the only frame you can use to do the problem then you need to justify it. If you can't justify it then why should I abandon SR? Why shouldn't I use the first postulate to allow me to pick a convenient reference frame?

Either justify your claim that the analysis must be in the detector's rest frame or stop telling me that I have to do it that way.

That does not analyize the scenario I presented, though. I stated the captain of the ship, within which the detector is located, turned on his engines, felt the force of acceleration directed at the source of the signal, and then shut his engines off. This felt force of acceleration REQUIRES a change from an initial inertial frame, to a non-inertial frame, and ending in an inertial frame once again. Your analysis was inadequate to illustrate the scenario.

It is perfectly adequate. Do you want me to put numbers on it to show that it is adequate? The force experienced by the captain implies that his rest frame is a non-inertial frame. So why would I want to use it in the analysis? You are really mixed up about reference frames.

Sorry, I began the scenario BEFORE any measurements were taken. How do you know if the frames are comoving, i.e. no Doppler shift, at the beginning? How do you know if the frames are comoving (at rest wrt each other) even after the initial frequency is measured? You don't until after a Doppler analysis is taken because it was stated that the signal frequency was unknown when it was emitted from the source. No measurements were taken at the source. But since the source was a STAR, the Doppler shift could be determined by analysizing other parts of the spectrum for identifiable elements. It has not been determined WHAT was emitting the 280mHz radio signal we are focusing on, only that it was emitted. How could that be known with no observer located at the star, the source of the 280mHz signal?

OK, I understand the comment now. I misunderstood it previously. My analysis still stands except for the indeterminate comment. Now the proper frequency of the emitter can be calculated as well as the frequency and wavelength in any inertial frame used as a frame of reference.

The initial MEASUREMENTS (plural) indicated the beginning inertial frames were comoving. The measurements are what determined this.

Got it now. Sorry about my confusion.

You are mixing a comoving inertial frame, a non-inertial frame and an inertial frame where there is relative velocity difference together into ONE inertial frame in which the coordinates of the detector do not move.

There is no such thing as "an inertial frame in which the coordinates of the detector do not move". How many times do I have to say this? I am using a single inertial frame so I can't possibly mix frames. In that frame both the source and the detector are moving.

That does not describe my scenario. Yes, I understand an object, THE STAR, can accelerate in the detector's inertial frame. The detector CANNOT accelerate in an inertial frame, which I specifically stated did happen.

What do you mean by "the detector's inertial frame"? There is no such thing. The detector's rest frame is a non-inertial frame. Why would you say that the detector can't accelerate in an inertial frame? You are way off here, the opposite is true.

The detector must accelerate in all inertial frames. In any inertial frame there are no frame forces, by the definition of an inertial frame. The rocket's engines are the only real force in the scenario. If there is a single real force and there are no frame forces then that single real force is not balanced by an opposing force. An unbalanced force leads to an acceleration. Therefore the rocket accelerates in any and all inertial frames.

Your analysis applys to a different scenario than I described, one in which the star, THE EMITTER, is the one that accelerates. I would think you know this without question, Dale, so why change my scenario?

I didn't change your scenario one bit. You are stuck on several completely mistaken notions about reference frames which you need to consider.

-Dale