I think that the reason for the different clock speeds due to different velocities has nothing to with Lorentz factor because measuring "speed of time" with atomic clocks has nothing to with speed of light.

http://toebi.com/documents/AtomModelAndRelativity.pdf

To answer the question, recall first that the speed of light is the same for all observers. If an observer is moving with some velocity with respect to another, this implies the two would not agree on the speed of light unless their clocks were out of sync.

Perhaps an easy way to grasp the idea lies in the fundamentals of electromagnetism; Electric field e has to do with the interactions between stationary charges, whereas magnetic flux b follows from the interactions between charges moving with respect to each other. Consequently, the decomposition of the electromagnetic interaction into e and b depends on the velocity of the observer. However, all observes do agree on a so called Faraday field F. In the language of differential geometry F is given by F = e /\ dt + b, where /\ is the wedge product.

Next, for a thought experiment, think of a GPS satellite circulating around the Earth. Say, one observer is riding with the satellite and another sitting at a fixed position on the Earth. In addition, assume both had a same kind of clock whose pace depends on e and b. Although both observers agreed on F, they do find the same decomposition into the "stationary part" e and "dynamic part" b. Accordingly, their clocks will not run on the same speed. Consequently, it is not a surprise that the GPS system indeed has to take into account the fact that the clocks in the satellites and receivers do not run in sync.

Lauri, why should we assume that there is a "clock whose pace depends on e and b"? What kind of clock is this?

Ivan, counting pulses is enough to come up with a clock. Say one has a charge oscillating back and forth along a line segment, and one counts the pulses by setting a small conducting loop next to the line segment to measure the electromotive force corresponding to the time variation of b.

Now, if the small loop moves along with the charge (that is, the velocity of the charge with respect to the loop is zero) then b vanishes and one finds no pulses. But if the charge oscillates back and forth with respect to the loop, then it also creates a b-field, and one will recognise an alternating electromotive force, i.e., a pulsation, over the loop.

This is a simple example of how the decomposition of the Faraday field into e and b depends on the observer. An observer moving along with the charge will find a electromagnetic interaction in the previous example (no pulses), whereas another one sitting next to the line segment will find it dynamic.

Lauri: Your clock construct is designed with the built-in capability to adapt its running pace to time dilation! Nevertheless it is subject to Dingle's argument which takes into account two equally built clocks in symetric situations, no matter how they are built. I don't see a way out only with one variable representation of “time”. Dingle's argument is logically consistent and leads to question relativity theory if we persist on rejecting absolute time. This is the underlying aspect discussed in detail in the attached paper.

Ivan, yes, agree with you that any attempt trying to describe in simple terms why clocks do not run in sync opens doors to justified criticism. Perhaps the best to take it just as a fact.

Lauri, if you want to be creative in theoretical physics you can not afford to take dogmas just as a fact...

Hello Iván,

I may be wrong but I think two following apply:

First, moving clocks do not run at different "rhythms". If two observers A and B are moving relative to each other, for A his/her clock runs just normal and for B his/her own clock runs just normal. It is just that if A or B measures the rate at which the other persons clock is running at he/she will measure an abnormal rate.

Secondly, I think it is not velocity which causes the twin paradox, it is acceleration. So if A and B are moving relatively fast to each other each will measure different speeds for the other ones clock but you will get the "twin paradox effect" only if one accelerates relative to the other. And in order to have the twin paradox one has to move away from the other and come back to meet again and has to accelerate at some point (to get back).

This is what I understand anyway. I'm not sure if this answers the question (happy to discuss).

It feels counter-intuitive but each moving observers A and B can measure the other's clock to be running slower than his but I think they are in fact travelling at the same speed along time co-ordinate but if they were to meet again and compare their clocks they have to accelerate at some point and that is when they start travelling at different speeds along the time dimension and end up with different times on their clocks upon arrival.

Baris, yes, that's my understanding as well. Accelerations and curvature (of space) are dual views of one and the same thing.

Ivan, all theories involve primitives, that is, undefined terms. What do you consider undefined terms in relativity? What I find tricky in 4D is that in lack of absolute time simultaneity becomes local. Therefore can imagine that an attempt to *describe* relativity is the 3+1d sense relying on classical terms easily lends itself to justified criticism.

Yes Baris, I agree, moving clocks do not run at different "rhythms". I hope you are aware that this opinion puts us at the side of herecy for orthodox relativists, because this implies that moving clocks run according to absolute time, time dilation becomes an apparent effect due to relativity. I also agree with your solution to the so called twin paradox (different from Dingle's argument), again be aware that we are saying that Einstein was wrong with his calculation of the time difference when both clocks mit again, very bad taste of our claim, to say the least...

Lauri, your direct question to me I can answer in short: x = x(T), where x is the position four-vector in M4, and T is the scalar variable representing absolute time in the Newtonian sense. For more details, please see my publications in this site.

I have just written a critical history of the twins paradox, analyzing several papers and pointing out errors in the acceleration and Minkowski arguments, and coming down on the side of velocity. I have a new method to decide which clock runs slower which I think has not been published before. Also an attempt at explaining why the slow clock runs slow, admittedly at the edges of SR, but still fully relative.

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.108.110801

The link shows that Planck constant may not be a true constant, and its change could be the microscopic cause of time dilation and gravitational redshift. I have a cosmological model shows that an inertial reference frame with a constant speed is equivalent to a reference frame with a constant background gravitational potential.

@Guoliang, interesting link. But the finding is variance in regard to position rather than velocity (implying a gravitational effect? ... the gravitational effect is not ambiguously dependent on the observer the way the velocity effect is)

I have deduced a formula (21) in my paper about a cosmological model, a constant speed is related to a constant gravitational potential by this formula.

Um yeah, I would say most gravitation theories have that prediction.

Dear Mr. Schuler, could you show me the links to those gravitational theories? I have tried but with no luck to find them. Thank you in advance.

@Guoliang, I only meant generally that light speed is related to gravitational potential, not any particular formula. All of the theories, GR, Brans-Dicke, etc. Every modern theory since GR has a variable light speed. It is always "c" locally, but when measured remotely it travels more slowly when near massive objects.

@Guoliang, you can take the time dilation formula of a gravity theory to be the amount by which light is slowed. Otherwise, the local value would be other than 3x10^8 m/s. For example, the Schwarzschild time dilation formula: http://en.wikipedia.org/wiki/Gravitational_time_dilation

@Robert, I understand what you meant now. If you had spent a little bit time to review my paper, then you should be able to understand what I said before.

OK Guoliang, I took a look. But I do not immediately see reference points I can relate to, so I gave up after about 15 minutes. Equation (1) appears out of nowhere, and appears to contradict most of what I know about the relation of potential and mass. Like many authors who have limited publishing success you have too little discussion and referencing of background material to define exactly what you are working on. My own success is so limited I cannot advise you, but I see this problem. Also, generally, papers that are all formulas with no figures do not appeal to me. And just so you won't feel I'm being particularly critical, few people read my most important papers because of some of the same problems, plus they are just very complex.

Thank you Robert anyway. Equation (1) describes the energy of a photon in a gravitational field, which is equal to its kinetic energy plus its gravitational potential energy. If you can not understand this one, then it is better to give up as soon as possible.

I see. Sorry I skimmed too fast and was just expecting an object with rest mass, but you have stated carefully I just didn't read carefully. You may have some luck with it.

That's ok, big fishes seem to be not in the mainstream, we might be able to catch them in a little brook if lucky enough.

1) All physical measures are based on measures of lengths (done at first by surveying) and times (done by clocks). So we need some universal constant c to relate both, and it has the dimension of a speed.

2) Relativity shows that we can relate the "proper time" of two observers with a relative velocity. And the celebrated formulas have been checked with a good accuracy.

3) General relativity shows that gravitation impacts also the proper time, and it has been checked (with the GPS system).

4) From the fact that the ratio betwenn the units of lengths and times has the dimension of a spatial speed, and from the idea that an observer "travels" along its world line at aconstant velocity (even in a curved space time), velocity is generally seen as the source of the discrepancy of the clocks of two observers. But this is less simple.

5) From studies of world lines, trajectories and states of particles I have shown (see my paper on particles and fields) that actually each particle has its own proper time. So this not just a matter of diverging clocks. And the relation between the constant c and the speed of light is not so obvious. There is, to my knowledge, no satisfying formula to state that the force fields (say gravitation and electromagnetic field) propagate at a constant (or variable for that matters) "speed of light" in a curved space time. Propagation of fields is a muddled issue.

So to me it seems that the relation between length and time on one hand, and the propagation of a field on the other hand, are different issues. And that the first is probably related to some basic cosmological phenomenon, that is the one which makes all material bodies "travel" along world lines, if we assume, as stated by relativity, that this motion has a physical meaning.

Hi Ivan, the file seems to be corrupted?

Yes, all clocks moving with different speed in the 3D space have different rhythms – the faster the movement, the slower the rhythm. That is because every clock moves of in the 4D Cartesian (“Minkowski spacetime” isn’t adequate to the reality) spacetime with the speed of light only. If a clock is at rest in the space, it moves in the (“coordinate”) time only and so ticks utmost quickly. If it moves also in the space, the speed along t-axes becomes be slower and so the rhythm.

Relating to this topic, the special relativity, which isn’t correct, since is self-controversial theory, gives sometimes non-correct results, an example – if some observer moves with some speed in the spacetime, and lunches to clocks, one – along the movement direction, other - in the reversal direction. Then one of clocks evidently will have slower rhythm, other – the faster one. But the SR predicts that both lunched clocks will be slowed.

More – see:

- “To Measure the Absolute Speed is Possible?” http://vixra.org/abs/1311.0190

- “The Informational Conception and Basic Physics” http://arxiv.org/abs/0707.4657And

- “Space and Time” http://arxiv.org/abs/1110.0003

And the refs, e.g., in the vixra paper.

Cheers

Well of course they do, there are 2 effects, one due to gravity and one due to speed.Considering for instance the GPS satellites, the clocks onboard the GPS satellites experiences relativistic shifts, which have both a constant and time varying components. This constant component is compensated for by introducing a fixed offset, which lowers the frequency of the on-board oscillator.

The fact that there is some orbital eccentricity and the higher order terms (quadropole) of the Earth’s gravity field are primarily responsible for the components that vary with time.

For instance, if two clocks are located on an equipotential surface, the rates of the clocks will be the same. If however one clock is moved to a height of 1 km, their rates would differ by about 1 x10^-13. Earth’s quadrupole’s effect on the potential at the GPS satellite is approximately one part in 10^14 , so in the case of the potential at the height of the GPS satellite, the contribution of the quadrupole can be ignored in most cases (GPS orbits are high enough to be nearly Keplerian); there is also no centrifugal component so that the gravitational potential at the GPS satellite can be easily calculated.The total gravitational frequency shift of the clock onboard the GPS satellite can then be calculated as 45.688 microseconds per day. If you ignored this, you would have a one way navigational error of 13.697 km per day.

Secondly when we consider the speed of a GPS satellite, (~3874 m/s), Einstein's special theory of relativity needs to be applied. The time dilation effect causes the GPS satellite to appear to run slow by about 7 microseconds per day.

The GPS satellite clocks are adjusted for three constant rate corrections before launching them into orbit, the satellite clock has a higher frequency in orbit than on the ground (read geoid, where the clock frequency should be 10.23 MHz) and its proper frequency is therefore reduced to 10.229 999 995 43 Mhz.

So the nett effect is that between the faster clock in the weaker gravity field due to orbital height, and the slower clock due to the clock's in orbit speed, the gravity effect wins.

One can calculate this very accurately, and it works perfectly, otherwise we would not have sub-cm accuracy in positioning using geodetic quality GPS receivers.

I think we are coming to a critical point of physics, where much prudence is necessary.

We see Hawking, after having affirmed the existence of black holes for about 30 years, now he says us events horizon doesn't exist and therefore also black holes don't exist.

I ask me what Hawking is believable. I think, like always, nature must give us the answer through the serious observation. The same thing is valid also for relativistic effects due to motion (SR) and to gravity (GR). Also I have theorized in order of the Theory of Reference Frames those effects exist, but I gave different explanations from Lorentz's Transformations (SR) and from curvature of spacetime (GR). Frequency shifts caused by motion are due to the Doppler Effect and there is no need Lorentz's Transformations. Frequency shifts caused by gravity are due to variation of electrodynamic mass of elementary systems in the gravitational field and there is no need of spacetime curvature.

I think now it is time to look at things of physics with critical mind.

@Daniele, is there one of your papers that explains your conclusions clearly and briefly?

Dear Robert, your request seems simple, but it isn't simple. Nevertheless I feel I must answer your request in order to begin a debate on important questions concerning science and physics. I would want to test indicating this brief and simple paper as attachment.

Good luck.

Article Short History of Relativity