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GPS and Relativity Misconceptions 2

Posted October 31, 2011 5:00 AM by Jorrie
Pathfinder Tags: GPS Gravity relativity

The anti-relativist fraternity has many a field day, typically misrepresenting Einstein's general theory, apparently in a futile attempt to dethrone it. Here is just one example from a member of that club, with some comments.

Ronald Hatch wrote in his "RELATIVITY AND GPS" page 5, in the section on "Gravitational Effects upon the Clock Rates":

"Now we can see that photons falling in a gravitational field do not increase in energy. Even though they do decrease in wavelength the frequency does not change. The apparent change in frequency is caused by the change in frequency of the local unit of comparison."

Blueshifted photons that are not more energetic than redshifted ones? And wavelength changing without a frequency change? Need one say much more?

Photon energy = hc/λ and λ = c/f, with h and c constants. Hatch tries to get around this by invoking the Shapiro time delay, which says that the effective speed of light is "slower" when passing near a massive body. So, he apparently argues, c gets smaller, hence λ gets smaller without an increase in frequency or energy.

Shapiro time delay is true in the correct context, but it is not applicable for the GPS gravitational time dilation discussed in his document. Wavelength and frequency always change precisely in step, when- and wherever directly measured and hence c remains the same.

In his treatment, Hatch creates the impression that relativity says that the increase in observed frequency and the slower time due to the lower gravitational potential are two different, independent effects. Hence, he argues, relativity requires that both be applied to the same observation, which puts it in conflict with observation. The relativistic view is that they are two faces of the exact same effect and we may use one or the other 'face' to calculate a result, but obviously not both.

There seems to be a common trend among the die-hard absolute frame proponents: incorrectly applying some mix between absolute frame and relativistic concepts. Based on such a misconception, Hatch has built a proverbial 'straw man' (which he claims represents relativity theory) and then shows how he knocks it over - I can hear the anti-relativists cheering.

Interestingly though, he agreed with the final analytical result that every relativist reports. And he got there with the same equations that they use...

-J

I must believe Ron Hatch knows GPS, but his relativistic interpretations seem quite suspect. This is perhaps understandable in the light of his mindset of absolute movement and how "wrong" Einstein's relativity is.

PS: The third and final Blog post of this micro-series will deal with that old favorite of the anti-club, the Sagnac effect.

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#1

Re: GPS and Relativity Misconceptions 2

10/31/2011 9:29 AM

Sadly, the anti-relativistic fraternity is just another chapter in the junk science crowd.

There are two principle members of this club. The first are the ignorant. They lack the basic education on the subject to apply critical thinking to make an informed opinion on the subject. They choose their position based on faith, rather than critical analysis on the subject. They are true believers.

The second type of individual tends to be the leader(s) of the cult. They may be driven by a number of reasons, but find their disciples and followers as useful idiots for their cause.

Such movements tend to be closer to a religion than science. Thanks to the internet these cults have gained much momentum and popularity.

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#2
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Re: GPS and Relativity Misconceptions 2

10/31/2011 4:10 PM

Yea, I guess the troops may be gathering for an attack in defense of one of their leaders.

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#3

Re: GPS and Relativity Misconceptions 2

11/01/2011 5:33 AM

I was led to believe that the GPS system "proved" Einsteins Relativity theory.

If I recall correctly, they had to rejig the satellites algorithms to compensate for relativity after they had previously discounted its effect.

I read it in a book called "Poincares clocks and Einsteins relativity" or something like that, as well as in other places.

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#4
In reply to #3

Re: GPS and Relativity Misconceptions 2

11/01/2011 6:57 AM

"I was led to believe that the GPS system "proved" Einsteins Relativity theory."

I guess the fact that GPS works properly is "proof" of some sorts. The real issue is that relativity was applied to GPS and it works. The funny thing is that the author I quoted in the OP attempts to use GPS to "disprove" relativity and "proof" his own theory.

AFAIK, they built the satellites from the beginning with the relativistic corrections already in, but also left room for adjustment from the ground. Apparently, there was still some uncertainty on the corrections at the time the original design. Today these adjustments are used to correct for satellites in orbits that deviate slightly from the chosen (planned) one at launch.

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#5

Re: GPS and Relativity Misconceptions 2

11/01/2011 7:35 AM

Think twice! 'c' is not constant in a gravity field, otherwise there would not be the bending of starlight passing near the Sun, nor there would be the Shapiro delay difference of radar signals bouncing back from Venus when it is far from the Sun and when it is behind it just at the edge of the Sun's disk.

'c' is constant only in vacuum and within an inertial reference frame, far enough from any gravity fields, rotating bodies, and the like.

The SI definition of 'c' takes into account the local gravity field on Earth.

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#6
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Re: GPS and Relativity Misconceptions 2

11/01/2011 11:00 AM

"Think twice! 'c' is not constant in a gravity field, ..."

The local speed of light is c, even in a gravitational field for any free falling observer.

Hatch's misconception is that frequency remains constant while wavelength decreases when photons fall under gravity. One can only measure frequency and wavelength in your own locality, so Hatch is forced to accept a change in the local speed of light, which is not valid.

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#7
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Re: GPS and Relativity Misconceptions 2

11/01/2011 1:26 PM

Jorry, in the above discussion I didn't notice any mention of a free-falling observer, only observers in orbit and on Earth's surface.

Anyway, I am not against relativity, I am against oversimplified relativity.

BTW, nice book.

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#8
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Re: GPS and Relativity Misconceptions 2

11/01/2011 3:03 PM

I suppose the topic dictated the frames to some extent.

Further, orbiting observers/clocks are free-falling, but I agree that surface observers/clocks are not. The difference between a momentarily stationary free-falling clock at the surface and one on the surface is however quite negligible. The 'paper clock', stationary in the ECI frame at the height of the satellites, is of course truly free-falling.

-J

PS: Thanks. The book is also quite simplified, but I hope not overly so...

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#9
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Re: GPS and Relativity Misconceptions 2

11/01/2011 6:09 PM

"The difference between a momentarily stationary free-falling clock at the surface and one on the surface is however quite negligible."

Well that would depend on the speed of the falling clock, but then the next moment it would stop altogether;o)

Sorry for misspelling your name, I noticed it only when it was too late...

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#12
In reply to #9

Re: GPS and Relativity Misconceptions 2

11/02/2011 1:24 AM

"Well that would depend on the speed of the falling clock, but then the next moment it would stop altogether;o)"

Nope, the clock that I referred to is free-falling, but just reaching its stationary apogee at and relative to the surface of earth. Theoretically, it must be shot out of a hole in the ground at precisely the right velocity- "cunningly", as Clifford Will's succulently wrote. :-)

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#10

Re: GPS and Relativity Misconceptions 2

11/01/2011 10:36 PM

Hi Jorrie,

I have not yet accepted your opinion that Hatch is a crank, but am reading your link to decide for myself. In the first section (before your quote), he suggests some may have misinterpreted how to apply the theory. I think there is a fair chance of that.

Hatch: Now we can see that photons falling in a gravitational field do not increase in energy

You: Blueshifted photons that are not more energetic than redshifted ones?

Why would you expect free-falling photons to increase in energy? Einstein's theory says there is no force in free-fall. Am I right?

Hatch: Even though they do decrease in wavelength the frequency does not change. The apparent change in frequency is caused by the change in frequency of the local unit of comparison."

I understand that frequency and wavelength are reciprocals. However, earlier in the article he says:

Whenever a frame is chosen which does not coincide with the receiver or observer, experiment demands that the speed of light be treated as non-isotropic as far as the receiver or observer is concerned. But this is anathema to the special theory, since it is a direct contradiction of the special-theory teaching that the speed of light is always isotropic relative to the observer

I'm having a little trouble here. Is he saying that the speed of light should change (in a gravitational field), but it can't because it is defined to always be the same by special relativity theory?

Hatch: Several experiments show that clocks run slower the lower they are in the gravitational field... When the satellite is at perigee, it is closer to the earth, the gravitational potential is lower and the satellite speed is higher. The lower gravitational potential causes the satellite clock to run slower per equation (3), and the increased satellite speed also causes the satellite clock to run slower per equation (1). The two effects are exactly equal and add together to give the net change in the frequency of the satellite clock.

I can't agree with the last part. When the satellite is closer to the earth, it's speed is lower if the earth center is the reference, as he said earlier. The two effects (if equal) would cancel, not add together. Do you agree?

-S

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#11
In reply to #10

Re: GPS and Relativity Misconceptions 2

11/02/2011 12:54 AM

Hi S,

"Why would you expect free-falling photons to increase in energy? Einstein's theory says there is no force in free-fall. Am I right?"

No force, yet energy conservation demands it. I have read Hatch's full theory(a) and was astonished to see how he "refutes" both Einstein and Feynman on this issue. What's more, he calls on present day guru Clifford Will (misinterpreted) as an aid in that quest.

"Is he saying that the speed of light should change (in a gravitational field), but it can't because it is defined to always be the same by special relativity theory?"

Hatch (with his absolute frame hat on) misstates the whole relativity theory, either due to lack of understanding it, or by design to further his own theory among the uninitiated. He may be referring to the fact that the speed of light is never isotropic in rotating frames, but I suspect it is the absolute frame that he means. Einstein's stuff is not at odds with any experiment. All GPS clocks are set up in the ECI frame, where the clocks are not-orbiting relative to the stars (in order to keep the speed of light isotropic), but are synchronized to SI time by a simple rate offset.

Hatch seems to be unable to get his head around what it means to measure the speed of light, which by definition has to be a local thing. The speed of light is not different for the transmitters and receivers. You must just do your calculations properly and in the correct frames.

Hatch: "The lower gravitational potential causes the satellite clock to run slower per equation (3), and the increased satellite speed also causes the satellite clock to run slower per equation (1). The two effects are exactly equal and add together to give the net change in the frequency of the satellite clock."

S: "I can't agree with the last part. When the satellite is closer to the earth, it's speed is lower if the earth center is the reference, as he said earlier. The two effects (if equal) would cancel, not add together. Do you agree?"

No, he is correct here, I think. He compares the clocks for the elliptical orbit with the perfectly circular orbit. At perigee, the speed relative to the ECI frame is higher and the gravitational potential lower. But, both translate to slower clocks then the circular orbit's, hence the deviations are added together.

GPS compensates for this, once on-orbit. AFAIK, each GPS satellite is tuned before launch for its expected orbit and then after launch corrected for its particular orbit. Then there are also daily corrections for orbital perturbations.

-J

(a) I think it will require a Blog or more to discuss that monumental work, full of the proverbial straw men. Suffice to say that Hatch's "refutation" of Einstein, Feynman, Will, etc. features centrally in the new theory. As is his "new principle of equivalence", obviously.

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#13
In reply to #11

Re: GPS and Relativity Misconceptions 2

11/02/2011 9:44 PM

S: "I can't agree with the last part. When the satellite is closer to the earth, it's speed is lower if the earth center is the reference, as he said earlier. The two effects (if equal) would cancel, not add together. Do you agree?"

Jorrie: No, he is correct here, I think. He compares the clocks for the elliptical orbit with the perfectly circular orbit. At perigee, the speed relative to the ECI frame is higher and the gravitational potential lower.

I thought sure you would agree. I was forced to do a search, and found from Wiki:

"Orbital speed (how fast the satellite is moving through space) is calculated by multiplying the angular speed by the orbital radius:

"

If we cant agree on that, then I need to know why.

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#14
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Re: GPS and Relativity Misconceptions 2

11/02/2011 11:04 PM

Hi S

The Wiki article is about geostationary (~24 h at 3,963 mi high) orbits, which have only one possible radius and speed, hence the equation you quoted.

For general orbits, you also have to consider this equation:

with μ = GM, giving the usual circular orbital speed.

You can see that this is an inverse type relationship.

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#17
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Re: GPS and Relativity Misconceptions 2

11/03/2011 7:47 PM

OK, I see. So my formula is for the average speed for the (corrected) altitude, and yours is to correct for the elliptical portions? It makes sense that the speed would increase at the lower altitude portions of the orbit if you consider that the satellite is accelerating from the earth's gravity as it comes down and decelerating as it goes up. I was thinking in terms of a ball on a string that you twirl around your head. The longer the string, the faster the ball goes for a constant revolving speed. I will have to read more of Hatch's paper before I can make a judgement.

-S

p.s. I saw NOVA on PBS last night. It was about the fabric of space. It talked about frame dragging, Higgs fields, and much more. Very interesting program.

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#18
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Re: GPS and Relativity Misconceptions 2

11/04/2011 2:51 AM

You might also want to read Prof Ashby in http://relativity.livingreviews.org/Articles/lrr-2003-1/, section 5, near its end, around eq. 38:

"It is not at all necessary, in a navigation satellite system, that the eccentricity correction be applied by the receiver. It appears that the clocks in the GLONASS satellite system do have this correction applied before broadcast. In fact historically, this was dictated in the GPS by the small amount of computing power available in the early GPS satellite vehicles. It would actually make more sense to incorporate this correction into the time broadcast by the satellites; then the broadcast time events would be much closer to coordinate time - that is, GPS system time. It may now be too late to reverse this decision because of the investment that many dozens of receiver manufacturers have in their products. However, it does mean that receivers are supposed to incorporate the relativity correction; therefore, if appropriate data can be obtained in raw form from a receiver one can measure this effect. Such measurements are discussed next."

I see that the eccentricity effect is not applied to the GPS satellite itself, but rather by each receiver. The satellite provides its specific altitude at the time of the transmission to the receiver, which then corrects for it. As the prof says, Glonass does it in the satellite.

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#19
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Re: GPS and Relativity Misconceptions 2

11/04/2011 1:00 PM

So maybe in the neutrino experiment they applied corrections that were already applied by the receiver or transmitter, or didn't apply some that they thought were applied.

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#20
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Re: GPS and Relativity Misconceptions 2

11/04/2011 3:09 PM

Hi S, possible, but unlikely. The fact that they decided on a new test with a better defined pulse train seems to indicate that the clock synchronization passed intensive scrutiny.

-J

P.S. I think we will only see NOVA a little later here in my valley. I'll keep my eyes open for it.

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#15
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Re: GPS and Relativity Misconceptions 2

11/03/2011 11:08 AM

Please forgive me for jumping in. I thought a Geosynchronous orbit was approx 22,000 SM (36,000 Km). I also thought the higher the orbit, the slower the speed. LEO's being much higher velocity than geostationary.

Interesting thread.

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#16
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Re: GPS and Relativity Misconceptions 2

11/03/2011 12:54 PM

Hi JWT, Oops, I've made an error copying the altitude in there; you are right, it's ~22,236 mi above the surface.

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#21

Re: GPS and Relativity Misconceptions 2

11/05/2011 12:29 AM

Jorrie, you hammered Ron Hatch for his misinterpretation of Ashby. On the Shapiro time delay you said "Shapiro time delay is true in the correct context, but it is not applicable for the GPS gravitational time dilation discussed in his document."

Yet I noted in the Ashby article on Living Reviews (section 10) Ashby acknowledged that this time delay is present as a secondary effect. He says "The net effect for a satellite to earth link is less than 2 cm and for most purposes can be neglected".

Granted, that is only 15 picoseconds of light time, but in principle, why cant Hatch utilize the "slowing" of light in his argument?

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#22
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Re: GPS and Relativity Misconceptions 2

11/05/2011 2:28 AM

True, but it does not feature in the redshift or gravitational time delay under discussion.

Shapiro time delay is observed when a signal is timed on a round trip through lower potential, e.g. a signal is from a satellite to the surface of earth and back again. When a signal is timed (say) from the ground to a GPS satellite and back (i.e. trough a higher potential), it gives a negative time delay, i.e., the signal arrives back too early for the geometric distance. It cannot be used to deduce the speed of light anywhere, except perhaps stating that the average round-trip was smaller or larger than c, depending on the potential along the path relative to the receiver-transmitter.

-J

PS - 2 cm gives around 66 picoseconds for light, not so?

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#23
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Re: GPS and Relativity Misconceptions 2

11/06/2011 12:30 AM

Yea, but doesn't this mean that the speed of light from satellite to receiver must start out faster than the average and must finish slower than the average? If this is so, then by using relativity one should be able to calculate these deviations. I recall something that the speed of light can only be measured over a round trip and that Einstein just declared the one-way speed to be half of that, without proof.

OK, I agree with your 66 picoseconds deviation. Made a silly calculation error from: light moves about one foot per nanosecond.

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#24
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Re: GPS and Relativity Misconceptions 2

11/06/2011 1:44 AM

"I recall something that the speed of light can only be measured over a round trip and that Einstein just declared the one-way speed to be half of that, without proof."

I guess you meant that Einstein took the one-way time to be half of the round-trip time? This is true for light in inertial frames and as such, it is just an 'Einstein convention', leading to the Einstein clock synchronization method. It is not the only way to synchronize clocks, but AFAIK, Einstein's is the only simple method that always works. The GPS is a good example of where it has been applied.

-J

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#25
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Re: GPS and Relativity Misconceptions 2

11/06/2011 2:12 AM

Now onto your first question: "but doesn't this mean that the speed of light from satellite to receiver must start out faster than the average and must finish slower than the average?"

There is no real way of knowing. If you set up experiments (locally) inside the satellite to measure the speed of light and do the same locally on the ground, you will get c in both cases. When you measure the round trip average speed sat-ground-sat, you get a figure less than c. If you repeat that for ground-sat-ground, you get a figure higher than c. You see the dilemma? All you have achieved is verifying the Shapiro time delay. There are also some issues with determining the orbit altitude from the satellite vs. ground P.O.V.

-J

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#26
In reply to #25

Re: GPS and Relativity Misconceptions 2

11/06/2011 8:42 AM

Jorrie, thanks for the explanation, but I do not understand this: you said that there are also some issues with determining the orbit altitude from the satellite vs. ground point of view. I thought distances were well defined in relativity. Can you please say more?

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#27
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Re: GPS and Relativity Misconceptions 2

11/06/2011 11:09 PM

Yes, distances are well defined, but the observed distance between two points depends on the coordinate system you choose. In a gravitational field, even observers separated radially, but stationary relative to each other, are strictly speaking in different frames of reference.

The radar distance directly measured from a satellite to the ground is larger than the radar distance measured from the ground to the satellite, if measured simultaneously (which in itself is a problem :-). The difference for the usual LEO satellites is however of order millimeters and can be predicted, because we know the frame of reference of each radar.

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#28
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Re: GPS and Relativity Misconceptions 2

11/07/2011 1:22 PM

OK, so it is much more complicated than what I thought. I will have to read up a bit more. Tx anyway.

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