Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: hamdani yusuf on 02/06/2020 11:00:58

Here is a picture of two trains moving at + and  0.5c near a station. Train A moves to the right while train B moves to the left. The length of the trains as well as the station is 1 light second.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30746;image)
at t=0, the tail of train A coincides with head of train B and a lamp on the left side of the station, which starts to lit.
at t=0.67s, tail of train B is 0.67 light second away from the lamp, which coincides with the light front.
at t=1s, the light front arrives at right side of the station.
at t=2s, the head of train A is 2 light seconds away from the lamp, which coincides with the light front.

Here is a picture of two trains moving at + and  0.5c near a station. Train A moves to the right while train B moves to the left. The length of the trains as well as the station is 1 light second.
You're drawing the two moving trains the same length as the station. So your trains, if the same length as the station when moving, are actually a proper length of 1.1547 ls, but length contracted to 1 ls in the station frame. This is not immediately relevant to your stationframe observations, but you need to know that if you're to make any observations from the PoV of either train.
at t=0, the tail of train A coincides with head of train B and a lamp on the left side of the station, which starts to lit.
at t=0.67s, tail of train B is 0.67 light second away from the lamp, which coincides with the light front.
at t=1s, the light front arrives at right side of the station.
at t=2s, the head of train A is 2 light seconds away from the lamp, which coincides with the light front.
All correct, and all expressed in the frame of the station, so only true in the frame of the station.
You've not asked any questions, so not sure where to go from here. You've identified no locations of any observers.
The train proper lengths are 1.15 ls each. Each train, relative to the other, is moving at 0.8c and is length contracted to 0.6928 ls.
In either train frame, you can make t=0 coincide with the event of the light flash, in which case it arrives at the other end of the stationary train at t=1.1547s. In either train frame, the station length is 0.866 ls.

The question is in the title. To state it more clearly, how to demonstrate that speed of light is still c when observed by train A as well as train B?

The question is in the title. To state it more clearly, how to demonstrate that speed of light is still c when observed by train A as well as train B?
Well, we can sync clocks at either end of a train and then note that the light emitted at time 0 at one end is detected at time 1.15s at the other end. This assumes that there are clocks that have been thus synced, which is typically accomplished by emitting a pulse from the middle of the train or station and then zeroing the clocks at the endpoints when that pulse is received.
Relativity doesn't demonstrate constant speed of light. It assumes it as one of its postulates. The assumption is made due to the empirical observation that any measurement taken of light speed seems completely independent of the frame in which the experiment is performed.

Relativity doesn't demonstrate constant speed of light. It assumes it as one of its postulates. The assumption is made due to the empirical observation that any measurement taken of light speed seems completely independent of the frame in which the experiment is performed.
Every once in a while we need to check and recheck whether or not our assumptions are justifiable and consistent between one another and compatible with observations.

Every once in a while we need to check and recheck whether or not our assumptions are justifiable and consistent between one another and compatible with observations.
You're not going to do that with a thought experiment. You go out and measure the speed of light using a better method than last time. Last we checked, it hadn't suddenly become frame dependent. This became evident back in the Michelson–Morley days, before Einstein, which is what prompted the need for the theory of relativity in the first place.
Anyway, if you have a specific inconsistency you see in your trains scenario, you need to point it out so your error can be identified. Nobody seemed to be measuring light speed in the scenario you described. I saw no errors in your descriptions of 4 points in time in the OP except for the lack of frame references, which I took to be the station frame.

Here is a picture of two trains moving at + and  0.5c near a station. Train A moves to the right while train B moves to the left. The length of the trains as well as the station is 1 light second.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30746;image)
at t=0, the tail of train A coincides with head of train B and a lamp on the left side of the station, which starts to lit.
at t=0.67s, tail of train B is 0.67 light second away from the lamp, which coincides with the light front.
at t=1s, the light front arrives at right side of the station.
at t=2s, the head of train A is 2 light seconds away from the lamp, which coincides with the light front.
Since the length of the trains are 1 light second in station's frame, their proper length should be 1.1547 light second.
Here is the spacetime diagram in station frame of reference.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30750;image)
How should it be transformed for the trains' frame of references?

here is the same diagram but viewed in train A's frame
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30752;image)
In this frame, velocity of the station is 0.5c. Velocity of train B is 0.8c as per relativistic velocity addition.
In this frame, length of train A is 1.1547 ls. Length of the station is 0.866 ls. Length of train A is 0.693 ls

Looks good. No time or distance labels, but the ratios seem correct.
Light reaches end of station (length .75 of red train) at t'=0.577 s
Light reaches other end of blue train at t'=0.385 s
Note that the station has not cleared the end of either train at the time the light gets all the way to the right of red train.

here is the same diagram but viewed in train B's frame.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30754;image)
The lengths and speeds are similar to train A's frame, but in reverse direction.
The light hit the tail of train B after 1.15 seconds.
The light hit the head of train A after 3.45 seconds.

Here is a picture of two trains moving at + and  0.5c near a station. Train A moves to the right while train B moves to the left. The length of the trains as well as the station is 1 light second.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30746;image)
at t=0, the tail of train A coincides with head of train B and a lamp on the left side of the station, which starts to lit.
at t=0.67s, tail of train B is 0.67 light second away from the lamp, which coincides with the light front.
at t=1s, the light front arrives at right side of the station.
at t=2s, the head of train A is 2 light seconds away from the lamp, which coincides with the light front.
Let's add additional lamps in each trains, they are placed on the tail of train A and head of train B. Those lamps start to lit at t=0. The second postulate of special relativity requires that the light of those lamps propagate at the same speed c. Here is how the sequence would look like from station observer.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30813)

Let's add additional lamps in each trains, they are placed on the tail of train A and head of train B. Those lamps start to lit at t=0. The second postulate of special relativity requires that the light of those lamps propagate at the same speed c. Here is how the sequence would look like from station observer.
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=30813)
From the diagram, we can conclude that station observer measures the speed of light as constant if it is defined as change of distance between light front and the observer per unit time. But if speed of light is defined as change of distance between light front and the lightsource per unit time, it depends on the velocity of the light source relative to the observer.

From the diagram, we can conclude that station observer measures the speed of light as constant if it is defined as change of distance between light front and the observer per unit time.
That definition doesn't work. The speed of anything is the distance it travels in a given amount of time, so it is computed from its location in space at a given time and its location in space at a later time. The observer might be around to take note of this, but his presence or lack of it, or his motion, has no effect on what the light does.
'Location in space' requires a coordinate system, which is one of at least 3 different inertial reference frames (IRF) in your scenario. With each choice, it is the coordinate system that determines the distance traveled and the duration between the emission event and the detection event. The observer again plays no role in that.

How do you determine a location in space without a physical object to refer to?

I don't think space can be defined at all in the absence of physical objects.
Still, there might be a total lack of inertial objects. Suppose we're in a ship under continuous acceleration with nothing else in sight. The only coordinate system you have to work with is an accelerating one, so all the nice little rules about what's true in inertial coordinate systems go away. Speed of light isn't constant. Pairs of clocks on the wall don't stay in sync.

How acceleration affect the speed of light? Let's say an observer is accelerating at 1 m/s^{2} in the same direction as the light propagation. What is the measured speed of light according to the observer?

How acceleration affect the speed of light? Let's say an observer is accelerating at 1 m/s^{2} in the same direction as the light propagation. What is the measured speed of light according to the observer?
The observer doesn't really observe the light after it leaves him, so hard to say.
He can note the time on some remote clock when the pulse gets to it, but lacking that clock being in sync with said observer, not sure what can be concluded from that.
I can say that if the light comes from below (in the same direction as acceleration) from about 10 light year distance, it will never reach the observer at 1 m/s² acceleration.

How acceleration affect the speed of light? Let's say an observer is accelerating at 1 m/s^{2} in the same direction as the light propagation. What is the measured speed of light according to the observer?
It depends on whether he his measuring the local "proper" speed of light or the coordinate speed of light.
Locally, he will measure light moving at c. The coordinate speed for light at points "ahead of him increases, the further ahead, the greater the coordinate speed. "Behind" him, the coordinate speed decreases with distance. At a far enough distance behind him you get a "Rindler horizon", from beyond which, light can never reach him, as Halc alluded to.

An observer is accelerating at 1 m/s^{2}, and a beam of light is travelling in the same direction at c. If the observer measures the speed of the light, would he measure the proper speed, or the coordinate speed?

≈
An observer is accelerating at 1 m/s^{2}, and a beam of light is travelling in the same direction at c. If the observer measures the speed of the light, would he measure the proper speed, or the coordinate speed?
It's not like there's a device that you can just stick into a light beam and it tells you the speed. If there was, it would read 'c', so I guess it doesn't need to be more complex than a bit of cardboard with 'c' written on it.
So how do you propose to go about your measurement? The answer depends on that. Often one measures duration of a round trip using mirrors and such, but you specify that the light goes in one direction, so that doesn't exactly work. So shy of using the bit of cardboard with says 'c' on it (which 'measures' the local proper speed of light), what are you actually going to do?

It's not like there's a device that you can just stick into a light beam and it tells you the speed.
I couldn't think of one, so I was fishing to see if see if there was something among the many things I don't know. :)

Here is another problem:
(https://www.thenakedscientists.com/forum/index.php?action=dlattach;topic=79757.0;attach=31053)
A light source shine a laser beam to the right, λ=300 nm, c=3*10^8 m/s, f=c/λ =10^15 Hz.
Observer O doesn't move relative to the light source.
Observer A move to the left, observer B move to the right, with velocity vA and vB, respectively. Let's say +/ 3000 m/s
What is the frequency and wavelength of the laser beam as measured by each observer?

It's not like there's a device that you can just stick into a light beam and it tells you the speed.
The undergraduate laboratory syllabus used to include diffraction of microwaves of known frequency, then c = f λ, both being easily measurable. Nowadays you can use a LED to produce photons of known energy and measure λ with a diffraction grating made from a DVD in a school laboratory. Or use xray diffraction from crystals at higher energies. In each case you are not measuring speed at a point directly, but if c ≠ fλ there is something wrong with our definition of speed!

The local speed of light in a vacuum is C; if that's what you want to measure then a piece of cardboard with "C" (or 299792458 metres per second if you prefer) written on it is perfectly accurate.
Otherwise, the thing that measures the speed of light is a refractometer.

The undergraduate laboratory syllabus used to include diffraction of microwaves of known frequency, then c = f λ, both being easily measurable.
If the frequency and wavelength are 'known', what's the point of measuring them? If the accelerating ship measures a different frequency than the known one, is the measurement wrong or has he measured the speed of light to be something other than c?
In other words, how is your setup an improvement over my bit of cardboard with 'c' written on it?
An observer is accelerating at 1 m/s^{2}, and a beam of light is travelling in the same direction at c. If the observer measures the speed of the light, would he measure the proper speed, or the coordinate speed?
Light doesn't have a proper speed, so the latter. Proper speed dx'/dt is distance traveled in one frame over time as measured in the frame of the moving thing, but there is no frame in which light is stationary, so the term is meaningless for light.

If the frequency and wavelength are 'known', what's the point of measuring them?
The original question is implicitly querying the constancy of c. We know the frequency and wavelength of the source because it is written on the source or we can measure them directly. The point is that we can carry out exactly the same measurements on the moving train and discover that whilst f and λ are different (thanks to Doppler) the product is the same. So there is indeed a device, or at least an assembly of devices, that can measure c at a point anywhere.
This is quite different from asserting that it is constant.

If the frequency and wavelength are 'known', what's the point of measuring them?
The point is that we can carry out exactly the same measurements on the moving train and discover that whilst f and λ are different (thanks to Doppler) the product is the same.
I understand this point, but on the train, the frequency and wavelength are indeed different, and thus not known.
So there is indeed a device, or at least an assembly of devices, that can measure c at a point anywhere.
I'm pretty sure it can be done, but most of the devices that can do this accurately do so by measuring the wavelength and computing it from that using a known c. That doesn't work if you're trying to measure c.

I'm pretty sure it can be done, but most of the devices that can do this accurately do so by measuring the wavelength and computing it from that using a known c. That doesn't work if you're trying to measure c.
What device do you think can measure the wavelength accurately with high precision?
Radar speed guns measure the frequency instead of wavelength.
https://en.wikipedia.org/wiki/Radar_speed_gun#How_it_works
Speed guns use Doppler radar to perform speed measurements.
Radar speed guns, like other types of radar, consist of a radio transmitter and receiver. They send out a radio signal in a narrow beam, then receive the same signal back after it bounces off the target object. Due to a phenomenon called the Doppler effect, if the object is moving toward or away from the gun, the frequency of the reflected radio waves when they come back is different from the transmitted waves. When the object is approaching the radar, the frequency of the return waves is higher than the transmitted waves; when the object is moving away, the frequency is lower. From that difference, the radar speed gun can calculate the speed of the object from which the waves have been bounced. This speed is given by the following equation:
(https://wikimedia.org/api/rest_v1/media/math/render/svg/fb20af636c9b6a3565b27f6973502bf61d7a8223)
where c is the speed of light, f is the emitted frequency of the radio waves and Δf is the difference in frequency between the radio waves that are emitted and those received back by the gun.
By combining the measurement results from both wavelength and frequency, we can confirm (or refute) the constancy of light speed in vacuum.

What device do you think can measure the wavelength accurately with high precision?
A diffraction grating is generally best.

I'm pretty sure it can be done, but most of the devices that can do this accurately do so by measuring the wavelength and computing it from that using a known c. That doesn't work if you're trying to measure c.
If we generalise "light" to "the em Spectrum", then we can use microwaves. There are frequency counters that will let you measure microwave frequencies directly to about 8 digits.
If you choose the right frequency that of a caesium clock you can measure the beat frequency produced by mixing the incoming microwaves with those produced by the Cs atoms
Doing that lets you measure the frequencies to a few parts in 10^10 relatively easily.
Indeed, that's more or less how the radar traps work, but they are only interested in a ratio of frequencies, not an absolute measurement.
What device do you think can measure the wavelength accurately with high precision?
A diffraction grating is generally best.
Yes and no.
Over a relatively large range of wavelengths (say, visible light), a grating is best.
If you are looking to check a change in wavelength over a narrow band you are probably better off with an etalon
https://en.wikipedia.org/wiki/Fabry%E2%80%93P%C3%A9rot_interferometer
It is likely that astronomers have looked at the microwaves from distant stars (which are moving rapidly WRT us) using both frequency and wavelength measurements.
If the measurements didn't agree, they would have noticed.
So this experiment
By combining the measurement results from both wavelength and frequency, we can confirm (or refute) the constancy of light speed in vacuum.
has been done.
Relativity passed the test.

radar traps work, but they are only interested in a ratio of frequencies, not an absolute measurement.
Difference, actually. Much simpler detector, fr  fo generally lies in the audio spectrum, and is directly related to the speed of the target.

What device do you think can measure the wavelength accurately with high precision?
Diffraction grating or inferrometer is common. Michelson, in the 19th century, was able to count wavelengths by hand as a mirror was moved a short distance.
Radar speed guns measure the frequency instead of wavelength.
Radar guns measure a difference in two nearly identical frequencies, not the frequency itself, so you can't use one to just place in an unknown beam of light and get some kind of frequency count from it.
Again, I'm not saying there is no such device, just that I can't readily think of one.

Difference, actually.
No.
Delta f/f is a ratio and that's what's proportional to the speed.
If I tell you that the beat frequency is 1000Hz you can not use that to determine the speed.
If I tell you that the ratio of the beat frequency to the transmitted frequency is 1/10,000,000 then you can tell me the speed.
So, you need both the difference and the base frequency.
Radar guns measure a difference in two nearly identical frequencies, not the frequency itself, so you can't use one to just place in an unknown beam of light and get some kind of frequency count from it.
Again, I'm not saying there is no such device, just that I can't readily think of one.
If one of those frequencies is from a Caesium clock then you can ratio the difference from the standard against the standard and get a measurement. However, current tech doesn't have counters fast enough to do this with visible light (yet).

Difference, actually.
No.
Delta f/f is a ratio and that's what's proportional to the speed.
If I tell you that the beat frequency is 1000Hz you can not use that to determine the speed.
It does addition/subtraction of the two signals to get the beat frequency. If the BF is 1000Hz, I can very much use that to determine the speed since the signal was sent at a known frequency, so the ratio can then be computed.
Key word is that known frequency that the device sends out. When measuring a random beam of light, the frequency is not known since it is what we're supposed to be measuring.
So, you need both the difference and the base frequency.
Which is why a radar gun works, because it has both, and why such a device cannot measure frequency of a light beam because it doesn't have either.
But point taken. I can put a laser on a train, which puts out a known frequency. I have a similar laser on the platform putting out the exact same frequency. I can use radargun technology to subtract the two signals to get a beat frequency which can thus tell me the frequency of the signal coming from the train. That's pretty much a direct measurement of frequency. The we take that same light and measure its wavelength, and poof: we have a measurement of light speed utilizing a beam of light whose exact wavelength is not known ahead of time, but is close to one that is.
Side note: The radar gun does not take relativity into account. It wouldn't give accurate readings for cars moving very fast. They don't need to since their usecase is always very lowspeed difference between the gun and the target and background.

hamdani yusuf " how to demonstrate that speed of light is still c when observed by train A as well as train B? "
Don't think it can be done. This is the way we define it. https://en.wikipedia.org/wiki/Fizeau%E2%80%93Foucault_apparatus and https://www.britannica.com/science/light/TheMichelsonMorleyexperiment
The results are observer dependent as far as I understand it. And that is a weird idea, we use a observer dependent definition as a 'constant', but it is a constant if every observer agree on the result of that experiment no matter how they are defined to move relative something else. https://www.phys.ksu.edu/personal/rprice/SpeedofLight.pdf
Then again, isn't that what we use for all 'repeatable experiments'? It doesn't matter for it what uniform 'relative' motion you are in relative something else, if A and B agree on the outcome then it becomes 'repeatable'. That one you can think of in terms of repeating a equivalent experiment inside differently moving 'black boxes' all in relative motion (different geodesics) relative each other. As far as I get it that relative motion won't matter for if a experiment is 'repeatable' or not.
=
That light change energy, frequency etc, as in the sinks motion versus the source, doesn't change the speed it is found to propagate at.. (All of this presuming relative motion btw.) It also presume your experimental setup to be 'at rest' with the detector. In a 'same frame of reference' as one expression goes. That is also what makes 'c' 'observer dependent' as you collecting your instruments reading also becomes part of that frame of reference. To get it in any other way is to demand a absolute frame of reference, and that frame was what Einstein looked for until his death.
Another way to express it is in terms of 'locality'. It's a 'locally consistent constant'. The thing that is really weird about it is that you can use any light you like to then let it 'bounce' between mirrors. It will always come out as 'c'. The distance of the lights propagation before it, be it a far away star, or that stars motion relative earth doesn't matter for it. So the 'age' of the light doesn't matter (or the lights source if you like). And anyone between you and the source can do the same experiment getting the same results no matter their own 'relative motion'.
Einstein defined gravity as being a equivalence to acceleration. And the way you define a gravity is by using a scale. So, inside a black box you always will be able to define if you're in a 'acceleration' by weighting yourself. You can feel it without a scale too of course. But in that black box you won't know if you are on earth or in a constant, uniform, acceleration. (ignoring spin for this, which is a acceleration we don't want to introduce)
So, it can be defined as a local 'absolute' frame of reference possibly? But if so, so should the absence of weight be able to be defined as a 'absolute' local frame of reference too, shouldn't it? Using this you then find that all geodesics are the same, no weight to them. And that whatever uniform motion you might want to define to this geodesic has no meaning inside that black box.

hamdani;
The parallel blue lines from the origin represent the time interval for 1 em cycle.
The speeds of A and B are exaggerated for clarity.
The vertical blue line is absorbed, in a shorter A timeline (blue shift), and a longer B timeline (red shift).
If t is the original period then,
tA=t*sqrt[(1v)/(1+v)], and
tB=t*sqrt[(1+v)/(1v)].
[ Invalid Attachment ]

When measuring a random beam of light, the frequency is not known since it is what we're supposed to be measuring.
If I wait a while, I may be able to solve this problem.
The current definition of the second involves a microwave frequency; but there are moves afoot to use optical frequencies.
For example, this clock uses 674 nm light
http://resource.npl.co.uk/docs/networks/time/meeting3/klein.pdf
at 444 779 044 095 484.3 Hz
That's enough digits for most of us.
So (in principle) I can put one of these on train and another on the platform.
And I can mix the light signals from them and (for some suitable relative velocity) I will get a beat frequency in the radio frequency bands which I can measure with an offthepeg meter.
That's not terribly practical, but in principle I can do it.
Of course that assumes that we start with the "right" wavelength but that's not much of a problem.
The question posed in reply 23 uses a laser at 300 nM, but I think that's fairly arbitrary.
Hamdani Yusuf,
would you be prepared to accept using a laser at 674 nm instead of 300 nm?
If we do that then we can measure the frequencies to preposterous precision (in principle In practice, I doubt that sort of equipment takes kindly to being put on a train and moved about.)

When measuring a random beam of light, the frequency is not known since it is what we're supposed to be measuring.
Then don't use a random beam. A sodium lamp will give you a nice spectrum with some well defined lines, or you can use mercury vapor around 300 nm. You can calibrate your etalon or grating on the train by using another such lamp. I guess most folk would go for a laser nowadays but I think the line spectrum of a lowpressure lamp is narrower than any UV laser.

I think the line spectrum of a lowpressure lamp is narrower than any UV laser.
In general, it isn't.

Hamdani Yusuf,
would you be prepared to accept using a laser at 674 nm instead of 300 nm?
No problem, I used arbitrarily round number just to make calculation easier.

It is likely that astronomers have looked at the microwaves from distant stars (which are moving rapidly WRT us) using both frequency and wavelength measurements.
If the measurements didn't agree, they would have noticed.
Those experiments assumed that interstellar medium has negligible effects, which may or may not be true. To get more reliable answer, we need a controlled environment.

Hamdani Yusuf,
would you be prepared to accept using a laser at 674 nm instead of 300 nm?
No problem, I used arbitrarily round number just to make calculation easier.
Excellent. And if you are prepared to go to microwave frequencies you can get an easilymeasured Doppler shift on a moving train.

Doppler radar guns have been used by police for decades.
They have been tested in court.
If there was any chance that the outcome was different from what was expected, someone would have challenged it.Those experiments assumed that interstellar medium has negligible effects, which may or may not be true. To get more reliable answer, we need a controlled environment.
The interstellar medium is a much better vacuum that we can achieve in our experiments.

It strikes me that this solves the "one way speed of light" question that turns up here from time to time.
Let A and B have identical apparatus for sending, receiving and analysing an electromagnetic signal. Each measures the frequency and wavelength of a pulse from the other, and calculates c.

It strikes me that this solves the "one way speed of light" question that turns up here from time to time.
Let A and B have identical apparatus for sending, receiving and analysing an electromagnetic signal. Each measures the frequency and wavelength of a pulse from the other, and calculates c.
Due to budget cuts there's only enough money for 1 set of apparatus, and a mirror.
Does that affect the outcome?

According to several correspondents to this forum, it might, and the possibility confirms their belief in the aether, flat earth and fairies.

I can imagine scenarios where it might for example, if you put a black hole there so its event horizon is just behind the mirror.
But most of the discussions are carefully framed to avoid weird things like that.

It strikes me that this solves the "one way speed of light" question that turns up here from time to time.
Let A and B have identical apparatus for sending, receiving and analysing an electromagnetic signal. Each measures the frequency and wavelength of a pulse from the other, and calculates c.
It does calculate c, but it does not measure the oneway speed of a given light pulse. Similarly, Roemer first measured c using a one way method, something I occasionally point out to the absolutists. What he did is entirely valid, but measuring c using a oneway method is very different than measuring the oneway speed of light.
Ditto for the measuring the frequency and wavelength thing, both measurements yielding incorrect results in an absolutist interpretation of the universe. The joke is that they claim this is a simplification, and yet they are forced to use Einstein's relativistic (not abolute) mathematics when computing anything. I've never seen the computations of any complex system done the 'simpler' absolutist way. Fairies indeed.
Due to budget cuts there's only enough money for 1 set of apparatus, and a mirror.
If there's a mirror involved, it isn't a oneway experiment. Roemer used no mirror, but he did use a pair of clocks separated by a very large distance. It was the recent invention of the clock that made this first measurement of c possible. At his time, the most accurate clock for long term (months) measurement was still a sundial.
I can imagine scenarios where it might for example, if you put a black hole there so its event horizon is just behind the mirror.
Again a 2way measurement which will yield exactly c if you use Alan's method.
And a black hole is not necessary. There are reflectors placed on the moon for such purposes, and a light pulse sent there and back again makes the round trip at faster than light. If they did the same on the moon with a reflector on Earth, the round trip would take place at less than light speed. This is a different method of measuring c than Alan's method which doesn't rely on mirrors or round trips. But the method assumes relatively stationary equipment, making it invalid for computing oneway speed under a view that does not assume the postulates of relativity.

And a black hole is not necessary.
It is necessary to make the point.
If there is one set of apparatus and a mirror (with a BH behind it) you get some sort of measurement.
If there are two sets of apparatus, but one of them is within the EH of a BH then there will be no measurement.
So, in those circumstances the budget cut version gives a different outcome.
And that's the point I was making.

Ditto for the measuring the frequency and wavelength thing, both measurements yielding incorrect results in an absolutist interpretation of the universe.
I don't recommend interpreting anything. For a travelling wave, v = fλ by definition of the terms. Nothing to to with relativity as my experiment works when A and B are not moving relative to one another. The theoretical and demonstrable constancy of c is in fact the basis, not the consequence, of relativity.

I don't recommend interpreting anything. For a travelling wave, v = fλ by definition of the terms.
Yes, but your measurement of both depend on some postulates made by the relativistic view, postulates not proven true.
Those postulates are assumptions, and yes, are the basis of relativity. But being assumptions, they're not necessarily true in a theory which doesn't assume them.
The theoretical and demonstrable constancy of c is in fact the basis, not the consequence, of relativity.
Agree. Nobody is suggesting that c is a different figure. But in the case under discussion, we're not measuring the constancy of c, but rather attempting to measure the oneway speed of light, something which cannot be measured.

Yes, but your measurement of both depend on some postulates made by the relativistic view, postulates not proven true.
Really? I'm using two identical stationary clocks and two diffraction gratings, none of whose properties depend on relativistic postulates, and since their relative velocity is zero, even if you insisted on introducing relativity, you'd find that the measurements are exactly as predicted by classical nonrelativistic postulates because v_{rel}/c = 0 in all the relativistic equations.
Indeed the first test of relativity is that its predictions must degenerate to classical mechanics if v_{rel} = 0.
v_{wave} = f λ is an obvious definition that does not depend on the constancy of c or the value of v, however it is measured. λ is the distance between wave peaks and f is the number of peaks passing a point per second.
Now using my technique I measure the speed of light transmitted from A, as received at B. I can move B to any distance and find that c_{B} is invariant, so that must be the speed c_{A→B}  the oneway speed of light.

Yes, but your measurement of both depend on some postulates made by the relativistic view, postulates not proven true.
Really? I'm using two identical stationary clocks and two diffraction gratings, none of whose properties depend on relativistic postulates
You apparently used one of those postulates when you declared your clocks and gratings to be stationary, something that cannot be demonstrated. How can you measure the 1WSoL with a moving device?
While I'm on your case, what's the second clock for? I thought this was a local test to determine c. Seems only one clock is necessary to do it that way. Are we changing the test now?
even if you insisted on introducing relativity
That's my point. I'm deliberately not invoking relativity.
you'd find that the measurements are exactly as predicted by classical nonrelativistic postulates.
No argument there, but neither of the views claims they can measure the 1WSoL nor can a device that measures the absolute time be produced. For instance I notice that the absolutists do not posit an actual age of the universe corrected for all the relativistic dilations that act on an Earth clock.
Indeed the first test of relativity is that its predictions must degenerate to classical mechanics if v_{rel} = 0.
That doesn't change even if the 1WSoL is frame dependent. If you disagree, then you have the test nobody seems to be able to come up with.
Now using my technique I measure the speed of light transmitted from A, as received at B. I can move B to any distance and find that c_{B} is invariant, so that must be the speed c_{A→B}  the oneway speed of light.
That's pretty much what Roemer did. Now why doesn't that constitute a valid measurement of the 1WSoL? Assume A and B are on the same path moving at 0.8c. How would that change my results given an absolute interpretation? Light would go from A to B in a 9th the time it takes it to go from B to A. How would you go about demonstrating that? If you can, you'd have a falsification test for one theory or the other.

You apparently used one of those postulates when you declared your clocks and gratings to be stationary, something that cannot be demonstrated.
Stationary relative to each other. Like joined together with a stick  or more likely an optical bench.
what's the second clock for?
So that the frequency I measure at B does not depend on the clock at A.
nor can a device that measures the absolute time be produced.
Irrelevant. All I need to do is count the number of waves that reach B in a second as measured at B with a clock like the one at A. Any second will do!
Light would go from A to B in a 9th the time it takes it to go from B to A.
I'm not measuring the transit time from A to B, but the speed of the travelling wave as it passes B

One of the experiments that is often quoted a proof of special relativity is called the photon clock experiment. The photon clock consists of a coach in a train whose interior is equipped with mirrors on the floor and the roof. A beam of light shines from the mirror on the floor to the mirror on the roof and is reflected back. One whole reflection, from the floor to the roof and back again is taken as one tick of the clock. Alice is sitting in the coach with the photon clock.
(https://www.mediafire.com/convkey/a609/d7c1yieut8dfsk34g.jpg) (http://www.mediafire.com/view/d7c1yieut8dfsk3/photon_clock.jpg/file)
To her the beam of light appears to go straight up and down. To Bob, assume the coach has glass walls, standing on the platform and watching the train go by, the beam of light appears to travel a longer distance than it does for Alice sitting in the coach with the clock. How can one account for this discrepancy in measurement. Alice is measuring one length that the beam in the photon clock travels while Bob on the platform watching the photon clock perform the same up and down journey in the same identical time frame, measures a much longer length over which the beam travels. What is happening here? The answer is simple, light travels the same distance in both instances, but to Alice who is moving with the same momentum as the train the light appears to go straight up and down, while to Bob it appears to be moving a greater distance. In actual fact Alice would see the light travel up and down (in reality it travels a triangular route)and arrive a fraction behind her own position. If the roof of the carriage is 3m above the floor of the carriage then in 1 tick of the photon clock, light would travel 6m (3m up and 3m down), and it would take 6 ÷ 3 x 10^{8} or 2 x 10^{8} s for 1 tick of the photon clock. If the train is travelling at 60 kmh (16.666m/s) then in 2 x 10^{8} s the train would travel 3.33 x 10^{7} m in one second. So the difference in distance that either Alice or Bob would see would be too tiny to differentiate. But Bob and Alice would both measure the correct distance that the light travels. Since light does not acquire the velocity of the moving train. The light travels the same distance for both of them. The above assumption, often quoted in explanation of this thought experiment, that the light would assume the velocity of the train, is false. For instance if you had a ball and you bounced it up and down in a coach in a moving train, then the ball would acquire the momentum of the train, in other words it would behave as if it were part of the train and moving with the same speed. This is a pure Galilean transformation. The same does not hold good for a wave like light or sound. The speed of light will always be independent of any vehicle it is travelling on. It is important to note that in both instances, the boy bouncing a ball up and down in a train moving at constant speed and light bouncing between two mirrors, both observers, the stationary observer (Bob) and the moving observer (Alice) measure the correct distance. There is no question of time dilation or length contraction.
There are some strange facts associated with this problem. First of all special relativity admits that the speed of waves in a medium behaves exactly like light does, meaning that its speed remains constant irrespective of the frame of reference from which it is being viewed. The difference, special relativity claims arises when waves like sound are travelling with (inside a vehicle) or not. If the source of the sound is merely fixed to the outside of a car, the sound from that siren will travel at a constant speed depending on the properties of the medium it is travelling through. If, however, the source of the sound is inside the cabin of the vehicle, the sound will acquire the speed of the vehicle. Special relativity claims that this is the reason that light is different from a wave travelling in a medium. Even if the light were in the cabin of the vehicle its speed would remain constant unlike the speed of a wave which would vary because the medium it travels through take air, acquires the speed of the vehicle it is travelling in. Surely a spurious excuse, when viewed from the point of Newton, Rutherford or any sane scientist. What about dark matter for instance, what if light travels through dark matter and dark matter is the medium that light travels through. Because of the low interaction of dark matter with matter, if light were travelling through it, the light would not acquire the speed of the vehicle it is travelling in.

I'm not measuring the transit time from A to B, but the speed of the travelling wave as it passes B
But you're not measuring that, or if you are, you're assuming that the one way speed of light is c in all directions, which would be begging your conclusion. To demonstrate the speed of the travelling wave as it passes B, you need to not start with the assumption that it is travelling at c.
That's why I picked the absolute interpretation which suggests that the absolute speed of light is constant, and thus the relative speed of light is not, and thus the eastbound light measured by an observer moving (absolutely to the west) at 0.8c passes him at a vastly different relative speed (1.8c) than the westbound light (0.2c), despite its identical appearance from our observer. He measures the same wavelength and frequency for both, and thus does not measure the speed at which it is passing him by. The actual frequency and wavelengths of the two beams are significantly different, but our observer happens to be in the exact frame where their appearance is identical, which is no surprise since both identical emitters are moving with him. In an absolute interpretation, the frequency of the light emitted by a moving laser is very dependent on the direction you point it, just like in regular SR where its frequency is frame dependent.
My point is that both theories acknowledge that there is no way for our observer to measure what you're suggesting above.

To demonstrate the speed of the travelling wave as it passes B, you need to not start with the assumption that it is travelling at c.
I haven't. I merely state that v = fλ, which is the definition of v for all travelling waves in any medium, then measure f and λ at B by independent means.

To her the beam of light appears to go straight up and down.
That's an unjustified assumption!

To demonstrate the speed of the travelling wave as it passes B, you need to not start with the assumption that it is travelling at c.
I haven't. I merely state that v = fλ, which is the definition of v for all travelling waves in any medium, then measure f and λ at B by independent means.
The weird thing about this is that it's not a 2 way measurement (in any way I can spot)
and it's not even a one way measurement you aren't timing a flash of light over a distance.
So what is it?
You can easily imagine splitting the incoming light into two paths and measuring the wavelength of one beam, and the frequency of the other; so the two measurements are independent.
Practically speaking, getting a precise measurement is going to be tricky you would need large equipment but that's just a human technology problem It will get easier as we learn how to do mm wave stuff better

So what is it?
It is a measurement of the speed of a wave travelling in one direction.
The joy of a continuous travelling wave is that you don't have to time a pulse over a distance because the speed at any point defines two independently measurable quantities: how many peaks pass that point in a second, and what angle the beam is deflected by if you place a grating at that point.
I didn't subscribe to your earlier etalon suggestion because that requires multiple reflections, so could be argued to be a twoway measurement. The angle at which a beam is diffracted from a simple transmission grating depends only on the wavelength of the incoming radiation and the periodicity of the grating. Or you can use a zone plate and just measure the focal distance, which is an inverse function of wavelength.
As we both pointed out earlier, these measurements (particularly of f) are difficult at optical frequencies but very easy with microwaves.
The fun bit is that the measured value of c turns out to be exactly that calculated by Maxwell from independent electrostatic and electromagnetic measurements.

I didn't subscribe to your earlier etalon suggestion because that requires multiple reflections, so could be argued to be a twoway measurement. The angle at which a beam is diffracted from a simple transmission grating depends only on the wavelength of the incoming radiation and the periodicity of the grating.
Afaik, there is no guarantee that the reflected wave would behave exactly the same way as the icoming wave, in terms of speed, frequency, and wavelength, especially when the reflectors move relative to the medium or light source.

Alan Calverd That's an unjustified assumption!
The explanation [afaik] is as follows. Substitute the beam of light with a boy bouncing a ball. Suppose that the ball is constituted such that when dropped it returns to the boys hand. If the boy is on a train running at 60 kmh and he drops the ball from a height of 1m . Then according to t^{2} = 2/0.5a it should take 0.63 seconds for the ball to return to the boys hand. During this time the train would have travelled approx. 10.5 m. Total distance travelled by ball equals 1^{2} + 5.25^{2} = 6.25^{2 }= sqrt 28.625 = 5.34 m x (2) = 10.68 m. So the ball travels a distance of 10.68 m approx. To the boy in the train it appears as if the ball has bounced and come back up in a straight line. If there were no windows the boy would not be able to tell if he were moving or not and he would assume that the ball is bouncing up and down in a straight line. This is made possible because both the boy and the ball acquire the same velocity as the train.
For the observer on the platform it is quite obvious that the ball is travelling in a diagonal zigzag pattern from the boys hand to the floor and back again to his hand.
The situation with a beam of light travelling in the carriage is different because the speed of light remains constant. Assuming that the distance between the mirror on the floor and the mirror on the roof of the railway carriage is 3m, then the total distance for one click of the clock is 6m. The time taken for one click of the clock is 0.00000002 s approx. During this time the train would have travelled 0.0000003 m. Now reverse the situation, have the light clock situated on the platform with the train moving past. One tick of the clock would still take 0.00000002 s and the train would still have travelled 0.0000003 m . The speed of the light clock would be independent of the speed of the train.
No time dilation and no length contraction needed to explain what is happening here. Yet, this is one the favourite thought experiments quoted by famous physicists such as Brian Cox and Brian Greene to justify special relativity. As calculators become better and more accessible special relativity is slowly but surely unravelling.
This might be interesting, and relevant for the first 45 seconds: https://www.youtube.com/watch?v=kpuGjzdHqgI (https://www.youtube.com/watch?v=kpuGjzdHqgI)

So the ball travels a distance of 10.68 m approx.
Or not, depending on whether you are measuring the distance travelled within the train (2m), or over the ground (10.5 m) or through the earth's atmosphere (10.68 m). But those who believe in an aether think differently about light, and would claim that you have arbitrarily defined 20 nanoseconds as the time it takes the clock to tick

Alan Calverd: Or not, depending on whether you are measuring the distance travelled within the train (2m), or over the ground (10.5 m) or through the earth's atmosphere (10.68 m). But those who believe in an aether think differently about light, and would claim that you have arbitrarily defined 20 nanoseconds as the time it takes the clock to tick.
The answer I had given is supposed to take both factors into consideration, since 10.68 m is the path travelled by the ball in a zigzag diagonal pattern , from the boys hand to the moving floor of the train and back to the moving boys hand. Leaving that aside for the moment; there are far more critical problems to do with the special relativity.
The crucial problem with relativity is that most people cannot come to terms with the fact that in special relativity lengths do actually contract and time does dilate for different observers. Look at the twin paradox, where one twin goes off into space travelling near the speed of light and the other twin stays at home. If the twins are living on a planet and twin A travels on a spaceship to a star 10 light years away at a speed of 0.8 c while twin B remains at home then the journey to the star and back again will take 20/0.8 = 25 years as observed from earth. According to Einstein both of these twins will age differently and it is possible to calculate the age difference between the twins by using the time dilation equation:
v is the speed of the space ship;
c is the speed of light; and
γ is called the gamma or Lorentz factor.
Δt' is the time as measured by the traveling observer;
Δt is the time as measured by a stationary observer;
Using the time dilation equation it is possible to see that :
t’ = = 56.8 years
Therefore, according to special relativity the twin who remains behind on earth while his twin travels to a planet 10 light years away and back, will be 31.8 years older than the twin who went into space. Thus, if both twins were twenty years old when they parted, the twin on earth will be 20 + 56.8 years = 76.8 years old while the twin who went into space will be only 20 + 25 = 45 years old.
Imagine not one set of twins but a million or more people out in space travelling at near light speed, each will measure a different distance and a different time. Therefore, what results is an n! (n factorial) number of possible speeds and times depending on the number of travellers. This yields impossibly huge numbers such as 1000! (one thousand factorial) for 1000 travellers all travelling at varying near light speeds which is an absolutely unacceptable result. Like it or not it is an impossible situation. It is much more probable that the speed of light is constant because it is travelling through a medium even though such a medium has not as yet been identified than to suppose that length contracts and time dilates in order to keep the speed of light constant.
It might be profitable to continue arguing with these conclusions, or not.

Imagine not one set of twins but a million or more people out in space travelling at near light speed, each will measure a different distance and a different time. Therefore, what results is an n! (n factorial) number of possible speeds and times depending on the number of travellers. This yields impossibly huge numbers such as 1000! (one thousand factorial) for 1000 travellers all travelling at varying near light speeds which is an absolutely unacceptable result.
Why is that unacceptable?
Imagine you consider groups of 3 people and the motion of the centroid of the triangle they form.
How many velocities are there?
Did you know that the results of statistical thermodynamics are derived using quantities of the order of Avogadro's number factorial?
3X 10^6 !
is really big.
It's still the same number.
Why is one set of velocities acceptable, but the other isn't?

Bored Chemist: Why is one set of velocities acceptable, but the other isn't?
It isn’t acceptable because people are involved. It is actual space and time which is being chopped into these impossible numbers. This is illustrated by the differences in Age in the twin paradox. Would it be acceptable to you if you could not synchronise your life with events happening around you. Even if you state that it would be acceptable, let me tell you that from a practical point of view, it isn’t. In fact such a situation precludes the existence of sentient life.

Would it be acceptable to you if you could not synchronise your life with events happening around you.
If people are travelling at relativistic velocities, they are not "around" each other.
I don't have a problem with the gravitational shift of GPS satellite clocks  it's a simple computation built into the firmware. Aiming a gun at moving target is a bit of an art, but you can learn to synchronise the arrival of the shot with the predicted position of a bird. Though squirrels are more difficult because they run in random spurts.

It is actual space and time which is being chopped into these impossible numbers.
No it isn't.
Space isn't getting "chopped"; what would be in the gap between the two bits os separated space?Would it be acceptable to you if you could not synchronise your life with events happening around you.
Yes.
I accept that, if I want to synchronise a clock in the the GPS system, I have to set it to run at the wrong rate while it is here on Earth.
Even if you state that it would be acceptable, let me tell you that from a practical point of view, it isn’t.
We are doing it; we always have. Up until fairly recently, we didn't even know we needed to.

Alan Calverd: I don't have a problem with the gravitational shift of GPS satellite clocks  it's a simple computation built into the firmware. Aiming a gun at moving target is a bit of an art, but you can learn to synchronise the arrival of the shot with the predicted position of a bird. Though squirrels are more difficult because they run in random spurts.
This is how the GPS system works:
“Each GPS satellite continuously transmits a radio signal containing the current time and data about its position. Since the speed of radio waves is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the receiver receives it is proportional to the distance from the satellite to the receiver. A GPS receiver monitors multiple satellites and solves equations to determine the precise position of the receiver and its deviation from true time. At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).”
Nothing in that passage as far as I can see about special relativity. Gravity does play a part in speeding up clocks, therefore regardless of whether it is a digital clock or a mechanical one, if gravity pulls on the components with less force, the clocks will speed up. This is exactly what happens when clocks are placed in satellites many hundreds of kilometres above the earth’s surface where the force of gravity is weaker. The fact that clocks speed up does not mean that gravity effects time itself! Further common sense tells us that if General Relativity makes a difference then special relativity should also make a difference with 4 satellites up in space, surely each would be measuring time in a different way from the others, since each is viewing the others through its own frame of reference? How would the software adjust for that? As I said special relativity is untenable by any standard.

Bored Chemist: Space isn't getting "chopped"; what would be in the gap between the two bits of separated space?
Why don't you tell me. You are the one supporting the twin paradox where the twins really do have different ages after one goes off into space travelling at some fraction of the speed of light while the other remains at home. You might as well ask, what happened to the years that the twin in space lost or the twin on the ground gained? You are using a ridiculous etymology...

Nothing in that passage as far as I can see about special relativity.
Then don't pretend it is relevant.
Find a better passage, like this one.
https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Special_and_general_relativity
. You might as well ask, what happened to the years that the twin in space lost or the twin on the ground gained?
Time passed at different rates for the two people. So what?
Why is that difficult?How would the software adjust for that?
I don't know and I don't care.
But my GPS works, so I know that the software does the job.
Of course it helps that you are wrong about this.
if General Relativity makes a difference then special relativity should also make a difference with 4 satellites up in space, surely each would be measuring time in a different way from the others, since each is viewing the others through its own frame of reference?
They are all in free fall. So they all experience exactly the same gravitational effects/
So they all keep time WRT each other.
There's nothing for the software to correct on that score.
Gravity does play a part in speeding up clocks, therefore regardless of whether it is a digital clock or a mechanical one, if gravity pulls on the components with less force, the clocks will speed up.
Why?
And why is the extent of the change exactly that which is calculated by GR?

This is how the GPS system works:
“Each GPS satellite continuously transmits a radio signal containing the current time and data about its position. Since the speed of radio waves is constant and independent of the satellite speed, the time delay between when the satellite transmits a signal and the receiver receives it is proportional to the distance from the satellite to the receiver. A GPS receiver monitors multiple satellites and solves equations to determine the precise position of the receiver and its deviation from true time. At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).”
Nothing in that passage as far as I can see about special relativity.
Nothing in that passage concerning gravity or other relativistic adjustments they decide to put into its design either. You've simply not chosen a passage that gets into those details since it is fairly irrelevant to how it works, but very relevant if you're actually engineering the system.
Gravity does play a part in speeding up clocks, therefore regardless of whether it is a digital clock or a mechanical one, if gravity pulls on the components with less force, the clocks will speed up.
It is not a function of gravitational force, but rather gravitational potential. A clock at the center of Earth will be more dilated than one at the surface despite no gravitational force there. The potential is lower there, and that's what counts.
The fact that clocks speed up does not mean that gravity effects time itself!
Technically, it is the geometry of spacetime (which is distorted by the presence of mass) that effects time itself.
Further common sense tells us that if General Relativity makes a difference then special relativity should also make a difference with 4 satellites up in space, surely each would be measuring time in a different way from the others, since each is viewing the others through its own frame of reference?
SR very much needs to be taken into consideration by said engineers, else the system will not work. Yes, each satellite is moving relative to any of the others, so none of their clocks are in sync in any satellite's momentary inertial reference frame. So what? They're not 'viewing' each other. We on Earth listen to them all, and we must track how far out of sync they grow over time.
Look at the ISS clocks, which run slower, not faster, despite being in orbit just like the GPS satellites. SR explains it, despite your seeming denial of its effects.
How would the software adjust for that? As I said special relativity is untenable by any standard.
All these fancy posts about how it works, but always twisted, typical of a denier. .
The GPS satellites move at a fairly constant speed relative to Earth, so the clocks are adjusted to compensate accordingly. The software only need deal with deviations from perfect orbits, and these deviations are significant, especially with the moon up there yanking everything this way and that.

As I said special relativity is untenable by any standard.
And yet I navigate hundreds of miles above the clouds and end up in the right place (within 5 degrees of the runway), at the correct height (within 50 ft) entirely due to everyone else's understanding of relativity.
How sad that my life depends on something you don't believe in.  it's like religion in reverse!

Perhaps McQueen should enrol in a university physics classand pester then to do this
That way, he can see relativity in action with his own eyes.
https://arxiv.org/abs/1108.5977
It's probably just about in the realms of what an amateur could do as a DIY set up.
That way you don't need to worry about conspiracy from "Big Science"

Ah, progress! In my day we (or at least I) didn't have a magnetic spectrometer or even a reliable surfacebarrier detector to hand. We measured kinetic energy with a calorimeter and wavelength with a sodium chloride crystal and dental xray film. But undergraduates were mostly stoned and ready to believe anything in the Sixties.

The problem as I see it is that many of the contributors and ‘experts’ on this forum desperately believe in Newton’s notion of absolute time and space and at the same time swear blind that Einstein’s special relativity is what works. Yet the two points of view are incompatible. In special relativity lengths do really contract and time really does dilate. One cannot claim to believe in special relativity and still harbour the hope that everything will work out and that the distance from London to New York will remain the same, whether you travel by turbojet or by prop plane. It doesn’t. For instance :
“Everything is relative; it depends on your frame of reference. Different observers see different things if they are in different reference frames (i.e., they are moving relative to each other).”
Would most of you be in agreement with this statement, that different observers, moving relative to each other at constant speeds see different things, because they are in different frames of reference?
Here is another statement which is a little more clear:
Different observers (i.e., observers moving relative to each other) measure different times, lengths, and masses. Only spacetime is observer independent.
What is the difference? The difference is that Newton believed in absolute space and time, whereas Einstein created the notion of spacetime, where time and space were no longer immutable but changed according to the frame of reference (i.e., if the objects were moving relative to each other) Note that this need not include relativistic speeds. Einstein frequently used trains in his examples.
Before 1905, scientists considered space and time as completely independent objects. Time could not affect space and space could not affect time. After 1905, however, the Special Theory of Relativity destroyed this old, but intuitive, view. Specifically, Special Relativity showed us that space and time are not independent of one another but can be mixed into each other and therefore must be considered as the same object, which we shall denote as spacetime. The consequences of space/time mixing are:
• time dilation
• and length contraction.
From the above it is obvious that if there are 4 GPS satellites and one ground station, they are all moving with respect to one another and would measure different times. To claim that they are all falling through space at the same speed is wrong. Each satellite is at a slightly different altitude and hence all have different speeds. Which means that they are in different frames of reference with regard to each other and therefore measure different times. Wikipedia not withstanding.

They don't measure time. They transmit time signals. The GPS receiver does the measuring.

They don't measure time. They transmit time signals. The GPS receiver does the measuring.
Congratulations like Alice in the Caucus race, we are back at the beginning and who knows that may very well be the best place to be. :D :D

They don't measure time. They transmit time signals. The GPS receiver does the measuring.
Congratulations like Alice in the Caucus race, we are back at the beginning and who knows that may very well be the best place to be. :D :D
Are you aware that, before launch, the clocks on the GPS satellites were carefully set to run at the wrong rate?

And resynchronisation is (theoretically) easy because all the ground stations know where they are. Or at least they think they do. There's nothing quite as upsetting to GPS as a tectonic plate shift, though rebuilding a runway can add a lastminute frisson for the user. Like the man said, New York ain't always where it used to be.

Time dilation from STR and GTR have opposing effects to orbiting satellites.
(https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Time_Dilation_vs_Orbital_Height.png/360pxTime_Dilation_vs_Orbital_Height.png)
https://en.wikipedia.org/wiki/Time_dilation#Combined_effect_of_velocity_and_gravitational_time_dilation

The graph shows gravity potential due to a solid sphere. It should somehow be related to blue curve in previous graph.
(https://conceptstories.s3.apsouth1.amazonaws.com/test/Stories%20%20Images_story_16865/image_20190319%2005%3A49%3A59.522818%2B00%3A00)