Why speed of light is constant?

In summary: So, what did physicists do? They tried to find a theory that could explain the speed of light being the same in all frames of reference. That theory was Maxwell's equations. Maxwell's equations predicted that the speed of light was a constant through the ether. This was a big deal because it meant that the technology we use today--laser--would work. Additionally, Maxwell's equations predicted that the principle of reflection and refraction would work even in a medium with a different speed of light. And lastly, Maxwell's equations predicted that the principle of spectroscopy would work even if the speed of light was not a constant.
  • #1
Ductaper
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How do we know the speed of light is constant?

If the behavior of light can be described by particle theory, and if the perceived speed of a non-light particle is affected by the relative motion of the observer, then it doesn't make sense to me how light is always observed to have the same speed, reguardless of the speed of the emitter or the speed of the observer.

What experiments have been conducted in the past to show the speed of light to be an absolute constant, reguardless to relative motion?
 
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  • #2
The Michelson-Morley Experiment is a historical example. The constancy of the speed of light is also a prediction of Maxwell's Equations.
 
  • #3
And the value of this speed is used in modern technologies such as the global positioning system.
 
  • #4
Ductaper said:
How do we know the speed of light is constant?
It was predicted (derived from Maxwell's equations) and, more importantly, is measured to be constant.
If the behavior of light can be described by particle theory, and if the perceived speed of a non-light particle is affected by the relative motion of the observer, then it doesn't make sense to me how light is always observed to have the same speed, reguardless of the speed of the emitter or the speed of the observer.
The behavior of light can be described by particle theory only in certain cases.
What experiments have been conducted in the past to show the speed of light to be an absolute constant, reguardless to relative motion?
The first to directly address the question of relative motion was the Michelson/Morley experiment in 1890-something. Since then, there have been hundreds of others. Today, not a whole lot of experimentation is being done to confirm its constancy, but there are a number of practical devices (GPS) that wouldn't work if it wasn't constant.
 
  • #5
russ watters said, "It [constant light speed] was predicted (derived from Maxwell's equations)..."

TALewis said, "The constancy of the speed of light is also a prediction of Maxwell's Equations."


Maxwell's equations are consistent with an ether?

Constant light speed is inconsistent with an ether.

So how can Maxwell's equations predict constant light speed?
 
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  • #6
In order for the technology of laser to work, the speed of light must be a constant.

In order for the principle of reflection and refraction to work, the speed of light must be a constant in the medium.

In order for the principle of spectroscopy to work, the speed of light must be a constant.
 
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  • #7
Ductaper said:
How do we know the speed of light is constant?
ductaper said:
If the behavior of light can be described by particle theory, and if the perceived speed of a non-light particle is affected by the relative motion of the observer, then it doesn't make sense to me how light is always observed to have the same speed, reguardless of the speed of the emitter or the speed of the observer.

What experiments have been conducted in the past to show the speed of light to be an absolute constant, reguardless to relative motion?

To remove your ambiguities if you are moving at .9c and you measure the speed of light as c and I am moving at .5c and I measure c as the speed of light, your measuring equipment has slowed more than mine so the one meter or one second you read is much shorter and slower than my meter and second We measure the same at different speeds because our measuring gear is affected proportionately different, so goes the theory that is.
 
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  • #8
jdavel said:
russ watters said, "It [constant light speed] was predicted (derived from Maxwell's equations)..."

TALewis said, "The constancy of the speed of light is also a prediction of Maxwell's Equations."


Maxwell's equations are consistent with an ether?

Constant light speed is inconsistent with an ether.

So how can Maxwell's equations predict constant light speed?
This I'm not sure about. I *think* its because Maxwell's equations predicted a constant speed through the ether and SR just discards the "through the ether" part.

There are, of course, some observations that ether theories can explain identically to SR (mathematically).
 
  • #9
thanks for all the replies, fellas. But tell me something, has GPS or laser technology ever been tested at relativistic speeds?
 
  • #10
What makes you think that the speed of the appartus involved (wrt to which inertial frame?) affects the speed of light?
 
  • #11
On Maxwell's equations...

Maxwell's equations do not predict that the speed of light is the same in every frame of reference.

Before the turn of the 20th century, theoretical physics was in the following state.

1. The laws of mechanics were well-verified.
2. The laws of EM were well-verified.
3. The laws of mechanics were invariant under Galilean relativity.
4. The laws of EM were not invariant under Galilean relativity.

Here's the problem: According to the best theory of the day, absolute motion could not be detected by performing mechanical experiments in an inertial frame, but it could (in principle) be detected by performing electrodynamic experiments in an inertial frame. But this was not corroborated experimentally.

One of the following had to be true:

1. EM theory was wrong.
2. Mechanics was wrong.
3. There are two correct relativitity theories, one that leaves mechanics invariant and one that leaves EM invariant.
4. There is one relativity theory, and Galileo's ain't it.

Since the first two were so well agreed with by experiment that physicists were loathe to consider them (note: I'm not addressing the necessity of quantum theory here). The third one just seemed absurd. Why should one spatiotemporal transformation hold while doing mechanical experiments, and another while doing electrodynamic experiments? How does nature "know" which type of experiment you are doing? And what transformation holds when you do an electro-mechanical experiment (as all EM experiments really are, anyway!)?

#4 is the only choice, and it leads to SR. With a rejection of Galilean relativity, we obtain slight corrections to mechanics (which have been confirmed experimentally), and no change in EM theory, and balance is restored to the universe.
 
  • #12
Are there any experiments that verify the constancy of c. If c were to change by a micron/second over a century, could we detect it?

What would such an experiment entail? Most experiments to find small changes involve the null concept, but I can't think of a way to do that in this situation.

Njorl
 
  • #13
Njori asked, "Are there any experiments that verify the constancy of c. If c were to change by a micron/second over a century, could we detect it?"

Absolutely not. It could be drifting around a LOT more than that, and we couldn't tell.

*********
EDIT: On further thought (suggested by Tom Mattson in post #14) the following statement is obviously wrong.
*********

In fact if the theory of realivity is correct, I'm pretty sure the speed of light could double tomorrow and we'd never know. I'll have to think about that a little, but I'm pretty sure it's right
 
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  • #14
jdavel said:
In fact if the theory of realivity is correct, I'm pretty sure the speed of light could double tomorrow and we'd never know. I'll have to think about that a little, but I'm pretty sure it's right

Sure you could tell: by measuring it.

Remember that the weird effects of SR only become apparent under Lorentz boosts. That means that, if all our measuring apparatus is in the same inertial frame, the doubling of the speed of light isn't going to be hidden by length contraction or time dilation. If you have a light source that is situated 3m from a photodetector and you measure the time between emission and absorption to be 5 nanoseconds, you will calculate a speed of 6E8 m/s, or 2c.
 
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  • #15
Tom Mattson,

Oops, you're right! :redface:

In fact if it slowed down enough, relative simultaneity would be part of our intuititve experience, and all those dizzy posts claiming it can't be right wouldn't exist. The universe would be very different!
 
  • #16
Ductaper said:
thanks for all the replies, fellas. But tell me something, has GPS or laser technology ever been tested at relativistic speeds?
"Relativistic speed" is whatever speed relativistic effects become noticeable for your device. GPS satellites operate at relativistic speed (and gravity effects), meaning if the engineers who designed/built the system hadn't calibrated the clocks in the satellites according to Relativity, the system would lose accuracy by about 2km per day.

The Relativity is so important to the GPS system and the GPS system is so good at measuring its effects, it has actually been used for scientific testing of Relativity.
Are there any experiments that verify the constancy of c. If c were to change by a micron/second over a century, could we detect it?

What would such an experiment entail? Most experiments to find small changes involve the null concept, but I can't think of a way to do that in this situation.
Due to astronomical observations, there are limits on how much/fast it could be changing as the universe ages. The fact that we see stars/galaxies in space that look similar to our own is evidence that the laws of the universe remain constant with changing time and space.
 
  • #17
Ductaper said:
How do we know the speed of light is constant?

If the behavior of light can be described by particle theory, and if the perceived speed of a non-light particle is affected by the relative motion of the observer, then it doesn't make sense to me how light is always observed to have the same speed, reguardless of the speed of the emitter or the speed of the observer.

What experiments have been conducted in the past to show the speed of light to be an absolute constant, reguardless to relative motion?

All the SOL experiments have ignored some crucial physics. If your eye is looking at an oncoming wave stream and you move into the stream the frequency of the light you see will increase. This is the doppler shift. But, ask yourself, "does your eye shorten the wave length of the light you are moving against? Are you applying a pressure, a force on the wave that contracts the wave length?"

There is a more reasoned and newly *discovered dynamic. As you move against the light your eye moves faster over the wave lengths you perceive. If you are moving against a moving train of boxcars that you count as you pass them, do the boxcars get shorter?

Or does your data show only that the frequency of the measured boxcars increases?

*see Grounded's Post# 1 in the Measurement of the SOL Thread. in this forum.
One does not need wave length shortening to explain anything.

All the light measurement answers that are thrown at questions like yours haven't considered the unterpertubed characteistic of wave length subject to moving observers. In fact the squished wave length doctrine is doctrinally implicit and, you get a constant speed of light, no matter what and, SR remains the Wicked ***** of Science, saved!
 
  • #18
geistkiesel said:
As you move against the light your eye moves faster over the wave lengths you perceive. If you are moving against a moving train of boxcars that you count as you pass them, do the boxcars get shorter?

Sorry to interrupt, but you don't measure that train's speed constant either. Isn't light a special case? Speed=frequency x wavelength, so if speed is constant and frequency increases, wavelength must decrease, right?
 
  • #19
wespe said:
Sorry to interrupt, but you don't measure that train's speed constant either. Isn't light a special case? Speed=frequency x wavelength, so if speed is constant and frequency increases, wavelength must decrease, right?

yes you do measure the train speed constant, how could you not? You are measuring the frequency opf box cars passing your eyes as you count. You do see, don't you, that the number of box cars counted passing by you is different depending on whether you are moving with or away from the moving box cars, don't you?

Why do I anticipate that your answer will be steeped in SR dogma, mantras, like your knee jerk interruption in your post? Why do I know that to be the case?

Try to see what the question that is presented to you, not just the question you waqnt to answer. You mesure the number of boxcars per second entering your eye, just like you measure the nomber of wavelengths passing through your eye in a second. The assumption of the SR theorists, at al, is that when you move against the stream of photons that the observer's motion compresses the wavelength, applies a force, a pressure, when all that is occurring is the increase of the number of full wave lengths passing through your eye. The increase in frequency, or decrease, is the observers velocity wrt the photons' wave lengths which may be considered invariant.

The speed relative to the source is fxlambda - C, whee f is the mesured frequency.

Wespe, don't believe or disbelieve this trash, but before you do anything try to understand it.

Hey Wespe it is something new. Do they have somethings new where you come from?
 
  • #20
geistkiesel said:
yes you do measure the train speed constant, how could you not?

So you say no matter how fast you are moving against a train, you measure its speed constant? Surely there must be a misunderstanding.

geistkiesel said:
You are measuring the frequency opf box cars passing your eyes as you count. You do see, don't you, that the number of box cars counted passing by you is different depending on whether you are moving with or away from the moving box cars, don't you?

For trains, the frequency increases, the wavelength (length of a car) remains same, so the measured speed increases. (considering train speed << c)

For light, the frequency increases, the wavelength decreases, so the measured speed remains constant.

Are you ignorant of relativistic doppler formula supported by experiments?
 
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  • #21
wespe said:
So you say no matter how fast you are moving against a train, you measure its speed constant? Surely there must be a misunderstanding.

Velocity wrt a common frame, common to you both. Remember we are talking about the cars counted per sec passing through your eye. There is a misunderstanding. You refuse to understand what some one posed to you to consider. The train is moving 50km/hr, you are moving 25 km/hr wrt the ground. Your relative velocity is what? the train velocity does not change because you are lookingv at it. The frequency of the #cars/sec increases, but the box cars don't shrink. It just doesn't happen that way, unless, of course, you are steeped in SR theory, then the only thing I can suggest is deprogramming, like in deprogramming Moonies, and communists and anti-darwinists.


For trains, the frequency increases, the wavelength (length of a car) remains same, so the measured speed increases. (considering train speed << c)

The frequency of the counted trains increases as ypu mpve against them. The frequency of the counted boxcars increases, i.e. cars/sec that cross you eye. Instead of counting 1 boxcar per sec, when you are stationary, you count 2 boxcars per second when moving. This is the frequency Wespe. Are you trying to be ignorant and pretending you cannot undertstand this?


For light, the frequency increases, the wavelength decreases, so the measured speed remains constant.

No, the measured light frequency increases as you move against the photon stream, ie move wrt the source of the photons.The number of photon/sec passing through your eye is the measured frequency. The wavelength remains constant. You do not squeeze the wavelength to a shorter length. The frequency is the (number of whole wave lengths passing through the eye)/sec. The wave length is invariant. Do you see wespe? The wave lengths are not compressed.

wespe said:
Are you ignorant of relativistic doppler formula supported by experiments?

Yes, and so are you. You have never looked at an original paper describing the experimental results of doppler formulae scrutiny. You are completely ignorant of the experimental parameters, assumptions, methods and techniques of measurements used in the experiments you refer. You know, or should know that the experimenters did not consider the frequency mesasurements as discussed by Grounded.

But you are the Wespe man, you don't need any freaking original papers do you?
 
  • #22
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  • #23
geistkiesel said:
Velocity wrt a common frame, common to you both.


There, once again, you start with something like that and expect me to value the rest of your essay. I saw similar misconseptions in that Grounded thread.

Get this: You do not measure speed wrt a common frame, you measure speed wrt yourself. Your speed wrt yourself is zero. The measured constant light speed c is wrt yourself. The measured frequency and wavelength are wrt yourself. And the equation speed=frequency x wavelength holds true for these measured values. Yes, you can calculate other values wrt a third frame. But those values are not your reality. There is no common reality everyone agrees on, there is no way to determine a preferred frame. Everyone is his own preferred frame. Above all, your reality is what you measure, not calculated third frame values. You are a hopeless case..
 
  • #24
Ductaper said:
How do we know the speed of light is constant?

If the behavior of light can be described by particle theory, and if the perceived speed of a non-light particle is affected by the relative motion of the observer, then it doesn't make sense to me how light is always observed to have the same speed, reguardless of the speed of the emitter or the speed of the observer.

What experiments have been conducted in the past to show the speed of light to be an absolute constant, reguardless to relative motion?

Although many assume that the MM experiment is proof that the speed of light is constant, the truth is that the experiment is a two-way light speed test and as such does not prove that the speed of light is constant. The only way to determine if the speed of light is constant is to do one-way tests.
Also contrary to some opinions GPS does not prove that the speed of light is constant.
Your thoughts on the speed of light are logical and seem to suggest that measured speed of light - like a particle - is dependant upon the motion of the observer. I can't find any reason to doubt your logic.
For further info on one-way tests, see
http://www.kevin.harkess.btinternet.co.uk/oneway/oneway.html
 
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  • #25
wisp said:
For further info on one-way tests, see
http://www.kevin.harkess.btinternet.co.uk/oneway/oneway.html

Hi,
That experiment looks interesting to me. But how are you sure that no one bothered to do this test before? I guess you don't have the resources needed to carry out that experiment yourself, since you don't present actual data. So, did you talk to someone who could do this experiment, or did you mention this in other forums, what response did you get?

Also, are you able to calculate relativity prediction of this experiment? If so, could you include that on your page? I'm not sure if the prediction would be null time difference, since Earth is not an inertial frame. Edit: On a second thought, I think it should be null, provided that the clocks are subject to same gravity, but I don't really know much about GR.
 
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  • #26
wespe said:
There, once again, you start with something like that and expect me to value the rest of your essay. I saw similar misconseptions in that Grounded thread.

Get this: You do not measure speed wrt a common frame, you measure speed wrt yourself. Your speed wrt yourself is zero. The measured constant light speed c is wrt yourself. The measured frequency and wavelength are wrt yourself. And the equation speed=frequency x wavelength holds true for these measured values. Yes, you can calculate other values wrt a third frame. But those values are not your reality. There is no common reality everyone agrees on, there is no way to determine a preferred frame. Everyone is his own preferred frame. Above all, your reality is what you measure, not calculated third frame values. You are a hopeless case..

yes, but my speed wrt the undilated waves of the light can be achieved. First I measue the wave length of an incoming photon stream. I want to measure my velocity wrt to the source of the photons coming from a distant star. I know what the speed of light is, I read it in a book. Now as I move against the stream of photons I count the rate at which a complete wave length goes through my counter. I do not disturb the wave length. I do not compress the wave length, nor do I apply a force to the wave length. I count the L/sec (L = wave length) and I get a value of FxL - c for my velocity wrt the source of the photon stream. The mathematical expression FL = C which transforms to L =C/F has the illusory mathematical implication that when I measure the frequency I vary the wave length, which is not physically implicit in the expression and is the fatal flaw in SRT.

Your insistance on the lack of any preferred frame is SRT. SRT fails under the Grounded scenario. You haven't disturbed that scenario because you haven't studied it. You merely gave an instinctive rejection of any system that violates SR theory. You are correct in evrything you say, that is to those who agree with you and SRT, which means agreeing with the doctriinal assimption that the measured speed of light is invariant in all inertial frames, made true by the silly assumption of time and space dilation.
 
  • #27
russ_watters said:
"Relativistic speed" is whatever speed relativistic effects become noticeable for your device. GPS satellites operate at relativistic speed (and gravity effects), meaning if the engineers who designed/built the system hadn't calibrated the clocks in the satellites according to Relativity, the system would lose accuracy by about 2km per day.

The Relativity is so important to the GPS system and the GPS system is so good at measuring its effects, it has actually been used for scientific testing of Relativity. Due to astronomical observations, there are limits on how much/fast it could be changing as the universe ages. The fact that we see stars/galaxies in space that look similar to our own is evidence that the laws of the universe remain constant with changing time and space.

If the GPS system had been designed using the Grounded system relativistic effects would not exist and corrections would not be necessary.
 
  • #28
geistkiesel said:
If the GPS system had been designed using the Grounded system relativistic effects would not exist and corrections would not be necessary.

That is patently false. "Relativistic effects" can't be done away with just on the basis of a design change.
 
  • #29
Njorl said:
Are there any experiments that verify the constancy of c. If c were to change by a micron/second over a century, could we detect it?

What would such an experiment entail? Most experiments to find small changes involve the null concept, but I can't think of a way to do that in this situation.

Njorl

c shows up in lots of places, not just relativity. Researchers have done studies of changes in the fine structure constant, which includes c (and electric charge and Planck's constant), and find that its maximum change is quite small. Investigation have been done with spectral lines from distant quasars and with the Oklo "natural reactor" in Gabon and get maximum of a few parts per million change over billions of years (IIRC). Measurements have also been done comparing different species of atoms in atomic clocks and find that it's not changing currently any faster than a part in 10^15 per year. More http://www.obspm.fr/actual/nouvelle/may03/varalpha.en.shtml
 
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  • #30
geistkiesel said:
yes, but my speed wrt the undilated waves of the light can be achieved. First I measue the wave length of an incoming photon stream. I want to measure my velocity wrt to the source of the photons coming from a distant star. I know what the speed of light is, I read it in a book. Now as I move against the stream of photons I count the rate at which a complete wave length goes through my counter. I do not disturb the wave length. I do not compress the wave length, nor do I apply a force to the wave length. I count the L/sec (L = wave length) and I get a value of FxL - c for my velocity wrt the source of the photon stream. The mathematical expression FL = C which transforms to L =C/F has the illusory mathematical implication that when I measure the frequency I vary the wave length, which is not physically implicit in the expression and is the fatal flaw in SRT.

It seems you are saying that it is possible to calculate your relative speed to a source of light, by just doing measurements on your side and not knowing the original emitted frequency of the light? I don't think so.

So, first you measure "wave length of an incoming photon stream", that's the wavelength. Then, you "count the rate at which a complete wave length goes through my counter", that's the frequency. OK then, do you agree that:
If you multiply this measured wavelength by measured frequency, you find the speed of the photon stream relative to you? [I assume your answer is yes, otherwise I don't know what to say to you*]

So, if the wavelength was not compressed while frequency increased, the speed you find would be greater than c. But it is not. It experimentally found to be c, not just read in a book. Therefore, the measured wavelength had to be compressed. Not compressed by a force or something, but by length contraction. By the way, with length contraction, you know that the whole universe is contracted from your perspective, don't you?

You don't buy length contraction? Then how do you explain that measured light speed remains constant? You may say that measured constant light speed is two-way. Is this your claim? Then you must find a way to measure one-way light speed and get real data.

By the way, here is a funny article:
http://physics.about.com/cs/opticsexperiments/a/290903_4.htm

*edit: re-reding your post, I noticed your mistake: FxL - c is always 0, not the relative speed to source. So your answer is no to my question above. ...argh... Please try to think why speed of a wave is frequency times wavelengh...
 
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  • #31
geistkiesel said:
All the SOL experiments have ignored some crucial physics. If your eye is looking at an oncoming wave stream and you move into the stream the frequency of the light you see will increase. This is the doppler shift. But, ask yourself, "does your eye shorten the wave length of the light you are moving against? Are you applying a pressure, a force on the wave that contracts the wave length?"

No. Relativity makes no claim of such a force or pressure.
 
  • #32
pelastration said:
The speed of Light, being 299,792.458 km/sec, is a constant by convention.
But measurements showed small variations: http://www.sigma-engineering.co.uk/light/series.htm
History: http://www.sigma-engineering.co.uk/light/lightindex.shtml
Has any information about the latest (more exact) measurements?
Not quite. The speed of light has been fixed by derivation and the more accurate our measurement capabilities get (obviously, methods are better today than 100 years ago), the closer the measurements get to that value.
If the GPS system had been designed using the Grounded system relativistic effects would not exist and corrections would not be necessary.
Could you explain what you mean by "the Grounded system" and how it could change the fact that a clock in orbit does not keep time at the same rate as a clock on earth? You can't just decide not to use a theory and expect reality to conform to your wishes.
 
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  • #33
wespe said:
Hi,
That experiment looks interesting to me. But how are you sure that no one bothered to do this test before? I guess you don't have the resources needed to carry out that experiment yourself, since you don't present actual data. So, did you talk to someone who could do this experiment, or did you mention this in other forums, what response did you get?

Also, are you able to calculate relativity prediction of this experiment? If so, could you include that on your page? I'm not sure if the prediction would be null time difference, since Earth is not an inertial frame. Edit: On a second thought, I think it should be null, provided that the clocks are subject to same gravity, but I don't really know much about GR.

I can say with certainty that the closest anyone has come to doing this test is DeWitte. His results produce a similar changes in electrical signals caused by the motion of the Earth through the ether. His results suggest that the one-way speed of electrical signals is not constant, but changes as the Earth's speed changes through the ether.
In the one-way light speed experiment the effects of GR, time dilation and synchronisation errors are unimportant, and the predicted result is large enough to detect using modern equipment.
This type of experiment has been discusses several times on forums and always gets ignored because of GPS, etc, etc. But it will be quite embarrassing if the results of what is a simple test proves Einstein claim - that the speed of light is constant – to be wrong.
 
  • #34
committing heresy anyway.

swansont said:
No. Relativity makes no claim of such a force or pressure.

Does SR in any manner restrict the mode of frequency determination? I mean, is a measured frequency of counting the rate of (whole wave length segments)/sec passing through one's eye in determining frequency prohibited?

Grounded offers a number of expressions I will stipulate are heretical, such the following:
  1. Delta F = (Distance traveled wrt source)/Lambda
    where Lambda is he wave length.
  2. Speed wrt source FxL - C
  3. Measured frequency (c + v)/L where v is velocity wrt source of the photons.
  4. Lambda wrt universe = v/F

Do any of these expressions offer any technological challenges for data acquisition?

What are the physical implications of using these measured values ?

It appears that the postulate regarding the measure of a constant SOL is targeted for overt violation, doesn't it?
 
  • #35
Does SR in any manner restrict the mode of frequency determination?
Absolutely - every theory has very specific meanings for the terms. You can't just plug in random numbers pulled out of the air. Put quite simply, SR requires that the "frequency" you use fit the definition of "frequency."
Do any of these expressions offer any technological challenges for data acquisition?
Only #4, which can't be measured because it doesn't exist.
What are the physical implications of using these measured values ?
Using them where? In an existing theory? You can't arbitrarily change the definition of the variables in an equation to suit your wishes. You can't mix and match values from different reference frames.
geistkiesel said:
It appears that the postulate regarding the measure of a constant SOL is targeted for overt violation, doesn't it?
Huh? Once again, you can't change reality simply by assuming its different from what is actually observed.

You keep ignoring this, but I'll say it again for the benefit of others: If you send an accurate clock into orbit, leaving its synchronized twin on the ground, and then bring them back together, they will no longer be synchronized. This has been verified experimentally. It is real, whether you want it to be or not.

Similarly, the speed of light has been measured thousands(millions?) of times and every time, the value measured is the same to within the limits of the accuracy of the measurement.
 
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