If we detect a difference of time dilation between two altitudes on earth, does it mean there is a frame shift between the two altitudes?
If yes, how to explain this frame shift? (Like for example, the impact on our views of the sky)
The question is deep.
There is a bijection between the shorter and the higher time intervals, downstairs and upstairs, mediated by light rays going up and down (the WM diagram).
Dear Amrit,
I agree with you. The shift of time clocks measurement can only be due to changing speed of clocks. Meaning there is no time dilation because there is no frame shift.
Dear Otto,
A bijection works for a given time, meaning for the present. If we consider long period of time (billion years) the bijection should shift the frames, no?
Do you mean there is time dilation with no frame shift? Then, what does time dilation mean if not a shift in space-time?
Sincerely.
Dear No:
I don't know what you mean by frame shift. I just had in mind the bijection across heights of light rays sent up and down via mirrors (which I in 1998 put into a neat mesh of up and down going light rays, the WM (-overlaid) diagram.
Time dilation and Frame shift might exists in relative sense for observer.
Dear Otto,
By frame shift I mean a shift of observer's relative position.
A shift of time (dilation) combined with velocity (rotation of earth for example) should lead to a shift of space (else your velocity contradicts your dilation).
Meaning, two aligned observers (at different altitudes) should be shifted after a long period of time, if time dilation occurs.
Dear Raja,
What do you mean by relative sense? Are the relative positions of the observers shifted or not?
Dear Ni Ge
Thanks, Relative scene of pattern recognition of observers (& events) based on multiple factors like relative positions, relative clock measurements, relative quantum matrix of brain, relative event perceptions etc.
Regards,
All points of the Earth, at any altitude, spend the same time for covering a whole turn of rotation of the Earth with respect to its axis. There is no time dilation. Again mainstream theories with the use of inadequate mathematical models involve wrong conclusions.
NG: By frame shift I mean a shift of observer's relative position.
Well it is inherent in your question:
NG: If we detect a difference of time dilation between two altitudes on earth, does it mean there is a frame shift between the two altitudes?
The origins of the frames are at different altitudes which I suppose you would call a 'shift'. Generally, merely translating the origin has no physical significance.
DS: All points of the Earth, at any altitude, spend the same time for covering a whole turn of rotation of the Earth with respect to its axis.
That is not true, a clock at a higher altitude will count more ticks per rotation than one at lower altitude.
Dear Ni:
You implicitly allude to the gravitational twin paradox, which indeed is surprisingly little known.
No, the axis remains straight but clocks on it tick at different rates when compared to each other. There is no such thing as absolute time.
There's a lot more to the rotation of the Earth than minute relativistic effects, see the link.
https://www.sciencedaily.com/releases/2013/09/130916162005.htm
GD, you write without thinking what you write. You write only as per your uncritical educational knowledges and you don't ask you if those knowledges are still acceptable or are obsolete.
Daniele, I answer as accurately as I can. If the Earth were a solid body, my first answer would be correct, there would be a difference in the rate of the clocks at different altitudes, the body would however be held together by the forces between its atoms so would not get wound round into a spiral as the poster seems to think.
When he asked specifically about the rotation of the Earth, I provided a link to a recent article. It is well known that the core and mantle rotate at different rates but not because of relativistic concerns. That makes it difficult to answer the question as asked.
Dear George, if two physical systems (core and mantle in your case) rotate with different angular velocities,it is manifest that they rotate also at different time rates. If instead we think about the peak and the foot of a mountain we are sure that they rotate with the same angular velocity and at the same time rate, in spite of mainstream theories that claim the exact opposite.
DS: If instead we think about the peak and the foot of a mountain we are sure that they rotate with the same angular velocity
That is a way to rephrase the question that avoids the problem with differential core rotation. As I said before "the body would however be held together by the forces between its atoms". We also know that two identical atomic clocks at the peak and foot will tick at different rates when compared. Those are the facts and I doubt you would disagree.
Then you have to ask "same angular velocity as measured against which clock?" Observers at the top and bottom will agree that the whole planet rotates as one, they will simply disagree on what numerical value to put on that rate.
Where the problem arises is with the apparent suggestion in the questions that the difference in clock rates would mean that the peak of the mountain would move ahead of the base.
I am not rephrasing the question, I am answering to the question on different time rates at different altitudes on the Earth. You introduced the problem relative to core and mantle that isn't connected with the question. We are considering points of the Earth at different altitudes whose relative distance doesn't changes during rotation. It is sure that top and bottom of a mountain spend the same time for covering a whole rotation independently of altitude. If you observe different rates by two equal clocks placed at top and bottom, you have to ask why the two clocks measure two different rates and you don't have to change fundamental situations that say the two time rates are equal. Experimental physics is very important but interpretation of experiments is so much important. Unfortunately we attend always more incautious interpretations of experimental facts in present physics. I would want to observe clocks are real physical systems and aren't ideal systems. Consequently the clock working is based on physical laws and their working can be different in different physical situations. I would want to invite you to think these simple considerations.
Dear George,
"Then you have to ask "same angular velocity as measured against which clock? Observers at the top and bottom will agree that the whole planet rotates as one, they will simply disagree on what numerical value to put on that rate."
Strange statement, see :
http://hpiers.obspm.fr/eop-pc/models/constants.html
Search more informations for "period of earth rotation".
"Mean angular velocity of the Earth" is more directly applicable but they are all related. In the Remarks column it notes "IERS Numerical Standards" which leads to the attached document. Have a look at the bottom of page 17 which leads you to discussions of the time standards used.
https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote36/tn36_015.pdf?__blob=publicationFile&v=1
The problem is not how it is calculated (put aside the tides). The problem is that this mean is a CONSTANT.
You stated that the rates (measured numerical value of the rate of earth rotation at different altitudes) should not be the same. I just show you that the rates are constant at all altitudes, leading to no shift and no time dilation in reality.
If Einstein was true, you were true also: the "mean angular velocity of the Earth" would not be a constant (different rates) and would vary and cumulate (period gap: 22 hours after 4.5 billion years for a difference of 5000m) between altitudes. But this is not the case.
NG: The problem is that this mean is a CONSTANT.
Well the mean is constant simply because because it's a mean. The rate varies, see the chart in the link for example.
NG: You stated that the rates (measured numerical value of the rate of earth rotation at different altitudes) should not be the same.
This is what I said:
GD: Observers at the top and bottom [of a mountain] will agree that the whole planet rotates as one, they will simply disagree on what numerical value to put on that rate.
NG: I just show you that the rates are constant at all altitudes, leading to no shift and no time dilation in reality.
No, the rate is constant when defined against a single internationally agreed timescale (as described in the paper I cited previously). That definition of time corresponds to one particular altitude, observers at other altitudes would assign a different value to the rate if they used a local atomic clock. GR allows you to calculate the difference between those numbers.
http://www.usno.navy.mil/USNO/time/master-clock/systems-of-time
In the link that has been proposed "Systems of time" there are numerous definitions of conventional times. In the paper it is specified differences of time are due to irregularities of the Earth rotation, besides it is specified they are measured in different places of observation, all at the same altitude at the sea level (in fact the paper is by "Naval Oceanography Portal". In no part of the paper it is possible to deduce time differences are due to altitude. That paper proves absolutely nothing about the dependence on altitude of time.
That's right Daniele and it is exactly the point I was making. The published figure for rotation is given using one particular time definition so is not applicable "at all altitudes" as Ni Ge claimed.
It would be like trying to work out the shape of a curve on a graph that only has one data point, and Ni Ge was claiming that it proved that the curve was a horizontal line.
George, I like to discuss with colleagues who reason and they don't take refuge behind expressions like "SR says..", "GR says..", "QM says...", leading to believe those thories represent the absolute verity. At that point discussion ends.
Dear George (and Daniele),
The way they calculated is very important for altitudes too. Tides are usefull because their rate give the possibility to know time. If the rates of the tides are different, then there is time dilation, if they are the same then no time dilation.
Imagine you have tides (object used for measurement). At 0 meter you will have a rate of nearly 24 hours between two tides (for sideral day only). The mean calculated is nearly 24h.
At 5000 meters you could have a rate of nearly 23+x hours (imagine a sea at another altitude) with time dilation. The mean calculated is less than 24h.
If you were right that rates would be different, an expected tide at 5000 meters would come more than 1 hour earlier than at 0 meter (because tides are coming every 23+x hours. Cumulate that from the creation of the water on earth, you will have hours of delay).
Else you could say that tides have all 24h of rate and that rotational velocity of earth is not constant, but it would contradict all physicists working on it. The period of rotation of earth is T = 86164 s + 98 ms + 903 ns + 69X ps and physicists do not consider that it varies between altitudes. If the period(time) is everywhere the same, where is time dilation counted in this period(time)?
We all use UTC for time on our computers, that doesn't mean atomic clocks don't run at different speeds at different altitudes. Using UTC is just a convention, you cannot draw any conclusions from it.
If you want to look at the physics, the clocks in GPS satellites orbiting at an altitude of 20200km run faster than ground clocks by 38us per day and have to have a correction circuit built in so that the time they broadcast keeps in sync with UTC. If you used a GPS clock that didn't have that circuit, the tides would appear to run slower by that amount than the same tides measured with an identical clock at sea level. The clocks are monitored all the time to maintain their accuracy to a few ns per day, that's a simple experimental verification of the prediction.
I agree with you, we have to correct atomic clocks. But this delay is not due to time dilation but because gravitation impact the clock mecanism.
"If you used a GPS clock that didn't have that circuit, the tides would appear to run slower by that amount than the same tides measured with an identical clock at sea level."
Then you mean that tides are effectively runing slower at high than at low altitude because of a slower earth rotational velocity. [correction]
NG: Then you mean that tides rates are effectively runing slower
No, there is only one set of tides. Numbers like rates and periods are just mathematical labels we apply in order to make physics a quantitative science rather than just qualitative descriptions. Observers at different altitudes would use different rate numbers to describe the same tides. You need to reverse the way you are thinking about the relation between the numbers and the physical phenomena that they describe.
"If you used a GPS clock that didn't have that circuit, the tides would appear to run slower by that amount than the same tides measured with an identical clock at sea level." Here, you say that tides are not the same but are measured the same.
If this is the case, again, add tides after tides and you will have a cumulated delay.
"Observers at different altitudes would use different rate numbers to describe the same tides." Here, you say that tides are the same but are not measured the same.
If this is the case, you are stating that rotational velocity of earth is not the same at all altitudes.
Please, keep one explanation in order that we could agree. I am sorry, but relativity is not relativity of explanations.
"You need to reverse the way you are thinking about the relation between the numbers and the physical phenomena that they describe." Physics is physics and not mathematics, Mathematics helps physics to understand reality but must not replace it. Time and velocity are physical phenomena that once combined give the distance. Experimentations could be wrong interpreted. If the rate of tides is the same at all altitudes with the same velocity, then time is the same.
GD: "If you used a GPS clock that didn't have that circuit, the tides would appear to run slower by that amount than the same tides measured with an identical clock at sea level."
NG: Here, you say that tides are not the same but are measured the same.
No, I siad the same tides would appear to run at different rates when measured by identical clocks at different altitudes.
NG: If this is the case, again, add tides after tides and you will have a cumulated delay.
There can't be a delay between a tide and itself. Our planet only has one set of oceans.
GD: "Observers at different altitudes would use different rate numbers to describe the same tides."
NG: Here, you say that tides are the same but are not measured the same.
Correct, that is what I am saying consistently throughout.
NG: If this is the case, you are stating that rotational velocity of earth is not the same at all altitudes.
I have said before that value for the speed of rotation would be assigned different numbers by observers at different altitudes.
NG: Please, keep one explanation in order that we could agree.
No problem, I'm saying the same thing every time. You seem to want to read something different into it sometimes.
NG: Physics is physics and not mathematics,
It is both. To do quantitative work you need to assign numbers to the physical events and we do that with coordinate systems. Using different coordinate systems results in different numbers being assigned to the same events. It is the combination of the coordinate system and the numbers that describes the physics. Time is a coordinate and is subject to the same effect.
NG: If the rate of tides is the same at all altitudes ...
It isn't. The tides are a physical effect but rate is a coordinate-dependent numerical measurement of those tides.
Dear George,
I am sorry, it wasn't clear for me.
So we agree on everything except the fact:
For you rotational velocity (slower at HIGH altitude) is not measured the same at all altitudes. Coupled with gravitational time dilation, the rate of tides are the same (by rate, I mean time laps between two tides)
For me rotational velocity is measured the same at all altitudes. Coupled with an absolute time, the rate of tides are the same.
For Einstein rotational velocity is measured the same at all altitudes (see relativistic addition of speed). Coupled with time dilation, the RATE (quicker at high altitude) of tides are not the same.
True?
NG: For you rotational velocity is not measured the same at all altitudes. Coupled with time dilation, the rate of tides are the same (by rate, I mean time laps between two tides)
Yes, you've got it.
NG: For me rotational velocity is measured the same at all altitudes. Coupled with an absolute time, the rate of tides are the same.
OK, that is the classical view but it is not compatible with what we see. Real clocks vary with altitude and GR models that accurately.
NG: For Einstein rotational velocity is measured the same at all altitudes (see relativistic addition of speed). Coupled with time dilation, the rate of tides are not the same at all altitudes. True?
No, the last one isn't right, relativistic addition of velocities is for the case where two speeds are combined in the same direction. Here we only have one so we aren't combining, and it is an angular speed, not linear. What you wrote at the top "for you" is in accordance with Einstein's equations, I'm not saying anything original.
I put "see relativistic addition of speed", because a velocity in a not dilated referential is the same or slower FOR a dilated time referential with Einstein theory. (Gravity could be seen as a perpendicular velocity from equivalence principle)
But I agree, "relativistic addition of speed" is not well suited in my example. I am just saying that a faster MEASURED velocity (at LOW altitude) does not happen for a time dilated referential in Einstein theory.
Note: I corrected a previous post where I mix rate with run, but everything is fine.
NG: Gravity could be seen as a perpendicular velocity from equivalence principle
It's equivalent to an acceleration rather than a speed.
NG: I am just saying that a faster MEASURED velocity (at LOW altitude) does not happen for a time dilated referential in Einstein theory.
Because we are talking about measurements of a phenomenon that is limited to the surface, it gets tricky to discuss it unambiguously. Let me go back to the Earth's rotation. Suppose you set up a telescope to look at a distant quasar. You can see it from any altitude and you can time how long it takes the Earth to rotate by when it passes the centre of the telescope. You can do it with two telescopes, one on the top of a mountain and one at the bottom, on the same day to get round natural variations. Doing that, the clock at the top will run faster so measure a shorter time for the rotation than the one at the bottom.
That is what happens, GR gives us a theory that accurately models and explains the effect but there can be any other number of alternative explanations as long as they give the same numerical values
Is that a clear statement?
Your statement is clear, both observers count a different time for the same amount of events.
But what I can't accept is that you consider that an observer at 5000m (fewer time dilation) measures a slower angular velocity than an observer at 0m (time dilation).
With special relativity a twin moving at speed v measures v. But the speed v is also measured v for a "static" observer, not less.
OK, lets take your example of the quasar and imagine it is a light source emitting a light beam every hour:
Beam 1 / stop / beam 2 one hour later / stop / beam 3 / stop / etc.
Lets put two observers on earth radius (one at 0m, the other at 5000m)
They get the first beam synchronized.
39420 billion beams later, you say both observers get the same amount of beams. The clocks are showing "4,5 billion years minus 22 hours" for the observer at 0m and "4,5 billion years" for the observer at 5000m.
What are the source frequencies for both observers?
">1 beam per hour" for the observer at 0m (time dilation).
"1 beam per hour" for the observer at 5000m (fewer time dilation).
Then whatever the exact number of beam emitted, how can a frequency (for a not time dilated frame) be smaller relative to a time dilated frame?
NG: OK, lets take your example of the quasar and imagine it is a light source emitting a light beam every hour:
Once per hour on what clock? Let's assume one in deep space.
NG: What are the source frequencies for both observers?
NG: ">1 beam per hour" for the observer at 0m (time dilation).
Given the definition above, it is >1 per hour for both observers but it will be a higher rate for the lower observer than the observer at 5000m.
NG: how can a frequency (for a not time dilated frame) be smaller relative to a time dilated frame?
Why shouldn't it be? If you walk towards a source, it has a higher frequency due to Doppler. Gravity has a similar effect but without needing you to approach the source.
TDM: .. a fast spinning object at 10 light-minutes from your experiment ..
The two observers will not agree on the spin rate, only that flashes from the distant sources occur the same number of spins apart. Your suggestion doesn't solve the problem, it just moves it to the new object.
OK to resume, so we must assume that earth rotational velocity is not measured the same at all altitudes.
And measured time laps of sidereal day (our tides corrected relative to stars) by atomic clocks is not the same at all altitudes (same rate of events with different time measured as you say).
I think that it is not what we know about sidereal time, but I might be wrong. (Sidereal time calculated by stars and sidereal time measured by atomic clocks are not always the same following you.)
That's correct. You have to realise that published numbers like the sidereal day are basically stated against the time standards we use, like UTC or TAI. The difference between clocks at different ground altitudes is a less than a nanosecond per day but things like the rotation of the Earth aren't even stable to that level anyway.
NG: I think that Einstein would not agree.
What I am saying is nothing more than an application of the formula in his 1911 paper where he also introduced the Equivalence Principle to the questions you are asking. It's all straightforward stuff and well proven by a variety of experiments.
Dear George,
1911 Einstein's paper is about a light beam.
"All bodies of reference K, K', etc., are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion." A. Einstein, Relativity: The Special and the General Theory, 1920
Read §21.,A. Einstein, Uber die Spezielle und allgemeine Relativitätstheorie, 1920 to understand what Einstein understands as the covariance principle.
It means a same phenomenon (as relative velocity of the observers) must be measured/described the same in all gravitational frames.
Einstein would say that phenomena are not happening the same way at all altitudes, but are described the same way: 24 hours of solar day with the same velocity at all altitudes, but in fact 24 hours at 5000m is 23+X hours for the observer at 0m (not for the observer at 5000m).
Then again:
For you rotational velocity (slower at HIGH altitude) is not measured the same at all altitudes. Coupled with time dilation, sidereal events are the same, but sidereal times should not be the same. Furthermore you remain in an euclidean space (where time dilation contradicts the frequency).
For me rotational velocity is measured the same at all altitudes. Coupled with an absolute time, sidereal times are the same.
For Einstein rotational velocity is measured the same at all altitudes. Coupled with time dilation, sidereal times/events (quicker at high altitude) are not the same at all altitudes. Add days after days and you will have (after a while) a gap between two frames (Kerr metric).
True?
Might be process like Quantum Entanglement can be a helpful way out to cause Time Frame Shifts over to human scenes. it can be ?
There is a big difference between the Principle of Relativity and the Principle of Covariance. The PR was masterfully defined by Galileo in 1632, then accepted by Newton in his physics based on absolute space and time and by Einstein with the introduction of the Postulate of the Constancy of the Speed of Light that in actuality changed relativity. The Principle of Relativity claims on experimental basis the invariance of laws of physics for all inertial reference frames with respect to a privileged reference frame that is supposed at rest. The Principle of Covariance, that is at the heart of GR, is instead a principle of equivalence and claims the indisputable possibility to describe any physical phenomenon, but not the invariance, with respect to all reference frames, inertial and non-inertial. It needs to consider adequately that difference independently of the fact that one accepts mathematical models that are used in GR.
George: "The two observers will not agree on the spin rate"
TDM: That is nonsense. Prove that!
It has been proven many times, for example by the clocks on the GPS satellites which run 38us per day faster than those at sea level. Time your distant rotating object using those clocks and the rotation rate will have a lower value.
AE:"All bodies of reference K, K', etc., are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion." A. Einstein, Relativity: The Special and the General Theory, 1920
NG: It means a same phenomenon (as relative velocity of the observers) must be measured/described the same in all gravitational frames.
It means as he said that the behaviour must be described by the same laws. It doesn't mean parameters must have the same numerical values. For example the effects of an electrical charge can be described by Coulomb's Law alone when static but create a magnetic field when it is considered in a different frame (in which the charge is moving). However, the "general laws of nature", in this case Maxwell's Equations, correctly describe the behaviour in any inertial frame.
Dear George,
If you read §21., you understand that Einstein denies any explained difference between K and K' (from poins of view of frames) by the general principle of relativity. Like I say, a difference of earth rotational velocity is not predicted by Einstein equations, nor is it acceptable by the covariance priniple (general priniple of relativity).
Else a fast measured earth rotational velocity would mean that our frame is affected by a strong gravitational field. Einstein says we are unable to know it alone.
(A static charge/rotational velocity in K must behave the same way as a static charge/rotational velocity in K', but static charge of K creates a field for K' and reverse./same measurement for 2 different events)
Sincerely.
The same physical phenomenon cannot be described by the same physical law and by the same mathematical equation similarly in both, an inertial reference frame and a non-inertial accelerated reference frame with respect to the same reference, supposed at rest. The statement " the same phenomenon must be described the same in all gravitational frames" is ambiguous. In fact the only quantity that changes in different gravitational reference frames is the mass M that generates the field. It is manifest that all gravitational fields are equivalent and dependent on the mass M. The real problem is that any physical event is described otherwise in an inertial reference frame and in an accelerated reference frame with respect to a reference frame supposed at rest.
With regard to the synchronization delay of 38microseconds for day in a GPS, it is explained exactly in the Theory of Reference Frames via the tangential graviquantum field. I could give references if there is interest in.
NG: Like I say, a difference of earth rotational velocity is not predicted by Einstein equations,
His equation predicts gravitational time dilation, that is well known, and the observed difference would be in compliance with his formula.
NG: nor is it acceptable by the covariance priniple (general priniple of relativity).
Yes it is. What would not be acceptable would be if observations from the different altitude showed a violation of conservation of angular momentum for example. Our planet spins but there is no law that says how fast it should spin, it depends on past history and environmental effects (e.g. the Moon) so an individual observer measuring the rate cannot use that number in isolation to determine very much.
In actuality in the considered physical situation of GPS, gravitational time dilation in concordance with GR would be 45microseconds for day and not 38. Anyway the problem is that in physical reality there is no time dilation and the effect measured in GPS has another physical explanation. I attach the following link for widenings
Article Quantum Properties of Gravitational Field and Synchronization Delays
The gravitational contribution is 45us/day but that would be for a stationary (non-orbiting) object hovering at constant altitude. There is also a 7us/day reduction due to the orbital speed so the overall result from GR is 38us/day.
The reality is that GPS satellites do show precisely that predicted difference compared to identical ground clocks.
You affirm as per the mainstream theory the total delay for an orbital station at the average speed v=14000km/h and at the average distance d=26500km from the Earth is 38us/day. You specify that number (38) in part is due to the gravitational contribution (45us/day) and in part to the orbital speed (-7us/day). That calculation doesn' t consider the rotation speed of the Earth is different from the revolution speed of the orbital station. That calculation is uncorrected if one considers correctly physics of the event. But in manstream physics every event is explained always through one or more of following concepts: the curvature of spacetime, the Lorentz Transformations and the Indetermination Principle. There aren't other possible explanations.
In the Theory of Reference Frames for a clock that is placed into an orbital station with those physical parameters the synchronization delay instead is due to the sum of two effects: a delay (7.27us/day) due to the orbital speed of the station and a delay (30.29us/day) due to the difference between the rotation speed of the Earth and the revolution speed of the station. The total delay is therefore 7.27+30.29=37.56us/day. Calculations are into the paper that has been cited before.
DS: You affirm as per the mainstream theory ...
No, I affirm the empirically confirmed value which coincides with current theory.
DS: That calculation doesn' t consider the rotation speed of the Earth ...
The surface moves at 464m/s at the equator giving a slowing of 0.1us per day, but the numbers above are rounded to the nearest microsecond.
The only two questions that matter are (a) how much does your prediction differ from that of GR and (b) is that difference larger than the accuracy of the orbiting clocks? If (b) is "yes", then you can propose a test.
The empirically confirmed value is 38us/day. Current theories give two values -7us/day (SR) and 45us/day (GR): 45-7=38us/day. In my paper I have specified and justified the result of the calculation: 7.27+30.29=37.56us/day.
You don't have to consider the absolute rotation of the Earth but you have to consider the difference of angular speed between the Earth and the orbital station. With regard to the first part of delay SR predicts -7us/day while TR predicts +7.27us/day. The difference is smallest but there is a problem of sign. For the second part of the delay GR predicts 45us/day while TR predicts 30.29us/day. The difference is great.
Certainly I am able to propose a test: the measurement of the delay in a geostationary orbital station at the average distance, for instance d=26500Km, from the Earth.
DS: Current theories give two values -7us/day (SR) and 45us/day (GR): 45-7=38us/day.
Well actually, the theory will give those numbers to several decimal places, as I say the popular sources are rounded. Your value of 37.56 would round to 38, the same as the GR value, so there may be no difference if you look up the exact value.
DS: For the second part of the delay GR predicts 45us/day while TR predicts 30.29us/day.
We know speed alone gives a reduction, your figure of +7.27 is in conflict with experiments like Ives and Stilwell which is done in the lab.
In the considered physical situation, i.e. orbital station, the Ives-Stilwell experiment measures a transversal Doppler effect that generates blueshift and not redshift. It justifies the positive sign in my calculation.
The result from Ives-Stilwell is that there is a greater redshift than can be explained by classical theory, not a blue shift. The excess red shift is sometimes called "time dilation" or sometimes "transverse Doppler" but they are the same thing.
The transverse Doppler effect generates always blueshift in any theory of relativity. In the physical sistuation that we are considering the Doppler effect is transverse and non longitudinal.
See the link Daniele, it reduces the frequency by the Lorentz factor.
- "As Einstein put it in 1907: according to special relativity the moving object's emitted frequency is reduced by the Lorentz factor, so that the received frequency is reduced by the same factor."
https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Transverse_Doppler_effect
Let you persist in proposing obsolete formulas and mathematical models. Our discussion could go on only if you could read my papers in which I propose new and alternative solutions based on the criticism of old and obsolete solutions. Let you persist to propose solutions that are in mainstream texts or in encyclopedic sites that not always are credible and that anyway aren't updated about recent researches.
With regard to the transverse Doppler effect I inform you also in Einstein' s equations of SR (paper of 1905) the transverse Doppler effect generates always blueshift, being f'=(gamma)f>f in spite of your references thar are wrong.
The reference is accurate Daniele, in SR time dilation always slows a clock, it never speeds it up.
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