# Nature of Time Dilation and Length Contraction

Discussion in 'Physics & Math' started by Prosoothus, Apr 4, 2006.

1. ### DaleSpamTANSTAAFLRegistered Senior Member

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Allright MacM, I'll bite. I have responded to each of your 3 or 4 repetitions of your question with a repetition of my original answer. You claim my responses are only "negative innuendo". Personally, I don't see it. So, exactly what part of the following quote is "negative innuendo" in your book:
-Dale

3. ### MacMRegistered Senior Member

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Since this does not appear to have been a response to my post please give the link so date and time can be established.

5. ### DaleSpamTANSTAAFLRegistered Senior Member

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Huh? What are you talking about? The date and time is on each post in the upper right hand corner.

-Dale

7. ### MacMRegistered Senior Member

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Certainly but your post does not show when and at what time the comment you are quoting was made. Since it does not address my question it is not in response to it. I am asking that you post when and where you originally made that statement. Then it can be shown that it is not in response to the issue I have raised.

You have also not repeated this resonse each time as you have claimed.

8. ### tsmidRegistered Senior Member

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It would be off by 11,400 meters if you would compare the satellite signal to a ground based clock and let the error accumulate over a whole day. This is not how the the position is determined in practice. A position determination uses differences between the time signals of different satellites. The point is that all satellites have the same height and the same orbital speed, and hence the same clock rate according to Relativity (there may be small differences due to the orbits not being exactly circular, but these would obviously be periodic and not accumulate).
So the only possible effect of the 38 microseconds/day discrepancy with regard to a ground based clock would be that the received time signals would differ by the same relative amount (4.4*10^-10) and thus also the distance derived from this (as shown on my page http://www.physicsmyths.org.uk/gps.htm ). This amounts only to an error of about 1 cm.

Thomas

9. ### DaleSpamTANSTAAFLRegistered Senior Member

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How pathetic

. The information is all in this thread for anyone to read. Since you are either too lazy or too incompetent to look it up for yourself here you go:
(All times EST)

05-09-06, 11:06 PM Your post asserting that v3 is the relative velocity and claiming the "magnitude of correctly posted calculations"

05-10-06, 06:03 PM My post pointing out that you used the wrong formula and also explaining why the SR relative velocity is irrelevant

05-10-06, 06:15 PM Your 1st repetition (this time with correct formula) where you accuse me of dodging the issue

05-10-06, 07:49 PM My 1st repetition of my response why the SR relative velocity is irrelevant

05-10-06, 08:37 PM Your 2nd repetition and second assertion of "dodging"

05-10-06, 09:46 PM My 2nd repetition of my original response why the SR relative velocity is irrelevant

Yesterday, 07:28 PM My 3rd repetition of my original response about why the SR relative velocity is irrelevant and my question about what part you considered to be "negative innuendo"

(Current tangent about dates and times)

Go back through the thread for yourself if you wish. The dates and times are there for anyone and everyone to see (provided you can figure out the procedure

). The record is clear in this case even though you are too lazy to look it up yourself and too addled to remember it without looking it up. This is yet another typical case where you accuse your opponent of doing something that you are the only one doing. So go ahead, we have been over the same ground 4 times now. Tell me how that quote is dodging the issue and how that quote is negative innuendo. Or, more likely for you, respond with your typical dodge* and negative innuendo as you accuse me of doing.

Then after a few rounds of that maybe (probably not, but maybe) you will tire of dodging the issue and making petty accusations and irrelevant tangents, and can actually address the substantive questions I have posed and you are assiduously avoiding:

"However, why would we want to calculate that (V3)?" (05-10-06, 06:03 PM)
"What exactly do you think was the design goal of all of the timing correction factors used in GPS?" (05-10-06, 09:46 PM)

-Dale

*Sorry BillyT, I know the official term is "duck and weave" but "dodge" just fits better in the present conversation.

10. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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Thanks, I understand what you are describing. All the clocks in the satellite constellation would accumilate the same 38 mcrosecond error relative to the ground clocks, so the triangulation signals from each of the four satellite would each be off by the same amount. You are stating that would not affect a triangulation determination because the offsets were of equal value, and the fourth satellite is used to synchronize the ground reciever with the satellite clocks. You do realize that those satellite clocks are also synchronized with UTC time, without having to 'resynchronize' ground clocks to match the constellation tick rate? Some aircraft carriers, for instance, carry their own atomic clock and can accurately determine their location without having to synchronize with the constellation tick rate. If a discrepency of 38 microseconds exist between the timestamp of the broadcast signal and the time recieved on the ground clock, an error in altitude of about 11,400 meters would exist. Such errors are not recorded to my knowledge. The time, as synchronized in the ECI frame, still has to be calculated in the ECEF frame, with WGS84 representing the surface of the Earth in the ECEF frame. I can't see how GPS could possibly work correctly unless the time stamp on the broadcast signals and the timestamp of the recieved signals were both related to synchronized and true time. Again, the accumilation of 38 microseconds offset would arise between the constellation frame and the atomic clock on the ground frame if they weren't synchronized.

11. ### MacMRegistered Senior Member

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That is correct and is why it is so amazing that you would attempt to do what you are doing.

As any search of this thread will show it is not I that am incompetent or lazy.

My first correction of your negative innuendo claiming I used an incorrect formula inferring the conclusion was therefore incorrect, when NOBODY would use the velocity addition formula when working with the rotational speed of the earth. It is sub, sub, sub, subluminal and you know it.

You hardly can call it a repetition since you posted no actual basis for the claim.

You still did not respond to the issue that your negative innuendo regarding SR and v3 is crap. I demonstrated that the caclulation using the velocity addition formula made no measureable change in the conclusion. Sorry SR doesn't work in GPS.

Still no valid response to the v3 issue nor the fact that you had implied I was incapable of computing the mathematics. I asked several times now if my calculations were valid you have not responded.

Last edited: May 15, 2006
12. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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tsmid, I hope it is OK with you if I cut & paste from your website to illustrate a point. From your website:
http://www.physicsmyths.org.uk/gps.htm
t1 and t2 are the transit times of the two signals broadcast from two satellites. But how do you determine the values of x1/c and x2/c? Those are the times the signals are received by the ground receiver. In order to calculate the transit time of those two signals, the exact time they were received has to be subtracted from the exact time they were transmitted. If the satellite clock is offset in precise time relative to the ground reciever by 38 microseconds, the length of time calculated for the signal to travel from satellite-to-reciever will be skewed.
Let me give a simple example using minutes instead of microseconds to illustrate what I mean.

Suppose the satellite broadcast a signal, according to its onboard clock, at 0100 hrs. Assume the transit time for the signal to receiver is 1 minute. If the satellite clock were 'fast' relative to the receiver clock by 38 minutes, the ground receiver would aquire the signal at 1221 hrs. According to the offset clock in the receiver, the signal was received before it was sent. The satellite applied a timestamp of 0100 hrs as the precise time the signal was broadcast, but the receiver thinks it received the signal at 1221 hrs. The two clocks have to be synchronized in time as well as tick rate or else errors will result, correct?

13. ### tsmidRegistered Senior Member

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Do you have a reference for this? I reckon they only carry their own atomic clock in order to have some back-up in case the GPS system fails. With a number of land/sea-based atomic clocks they would then at least have some basis for accurate navigation. Since the signals could be relayed over a couple of alternative satellites, this would do then pretty much the same as GPS does (although of course the general public would obviously not benefit from this)

Thomas

14. ### tsmidRegistered Senior Member

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But the receiver clock is completey irrelevant. You don't need it at all to determine your position. All you need is to compare the 'time stamps' of the satellite signals.
Going back to the one-dimensional example on my webpage: assume you are located on a line between the two transmitters and you receive a signal from transmitter 1 that says 'Hi, I have been sent out at time t1' and from transmitter 2 you receive at the same time a signal that says 'Hi, I have been sent out at time t2' , then you know for example that if t1=t2, you are located exactly half-way between the two transmitters. If t1>t2, then you know that you are offset from the half-way point towards transmitter 1 by a distance x=c*(t1-t2) (and correspondingly towards transmitter 2 if t2>t1). If you know additionally the absolute positions of the transmitters (which you do because this information is also encoded in the signals), you know therefore also your own absolute position.

Thomas

15. ### DaleSpamTANSTAAFLRegistered Senior Member

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If you weren't incompetent or lazy you could have scrolled through the thread and found the times for yourself.

First, the formula was wrong, that's a simple fact. Second, I never implied that your conclusion was incorrect. And third, you can't blame me for thinking that it was a very amusing joke that you loudly proclaimed the "magnitude of correctly posted calculations" while using the wrong formula. IMO, the fact that the velocities are sub-luminal in no way diminishes the punchline.

You are such a weasel. It doesn't matter if my claim had any basis or not, if I quote myself it is by definition a repetition.

Wow, you are really desperate to have your arithmetic validated. Consider it validated. I have not checked your work, and don't plan to. Since you are now using the right formula I am sure your numbers are correct. And even if they are a little off it is not a substantive error.

The VAF is always appropriate when you are talking about SR, even if c>>v.

This has everything to do with the issue raised, and I note that rather than answer the questions you are trying to dodge them ("Wiggle, wiggle"). The whole point of my thrice-repeated quote is that v3 is indeed the wrong velocity to use here according to SR and that I agree that v3 produces an incorrect time dilation. That is why your whole calculation tirade is irrelevant as I mentioned in the first place. So for the 7th and 3rd times:

"why would we want to calculate that (V3)?"

and

"What exactly do you think was the design goal of all of the timing correction factors used in GPS?"

-Dale

16. ### 2inquisitiveThe Devil is in the detailsRegistered Senior Member

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"you are located exactly half-way between the two transmitters." This I do not agree with. The receiver does not instantaneously receive the signals, his position has changed during the transit times of the signals due to relative motion. The receiver cannot determine how far (the distance) it is from the satellite unless it measures the travel time of the signal. Distance determination requires precise time synchronization. Your method would place the receiver in orbit between the two satellites. A signal recieved from a third satellite would place the receiver in orbit centered between three satellites.
"If you know additionally the absolute positions of the transmitters (which you do because this information is also encoded in the signals), you know therefore also your own absolute position." This I do not agree with. The satellites broadcast their location in their orbital plane at a certain time. They do not broadcast their location or distance relative to the spinning Earth, or any location on Earth.

17. ### tsmidRegistered Senior Member

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Yes, obviously, in case of a relative motion, the finite travel time of the light signal means that the distance to the transmitters is not the same anymore when you are receiving the signal, but you should be able to take account of this without having a clock: in my example, assume that the time stamps say t1=t2 i.e. you would be located at the mid-point between the transmitters if you are not moving relatively to them; assume as a first approximation this is the case (this would already be accurate to within a couple of hundred meters considering the speed and distance of the satellites (4 km/sec; 20,000 km)); now the coordinates and velocities of the satellites in its orbit are encoded in the signal, so the receiver can work out by means of a simple coordinate transformation what the correction due to the motion of the satellites relatively to the surface of the earth is. This should usually give you already an accurate position unless you are yourself moving with hypersonic speed relatively to the earth; the latter could be taken easily into account by using a previous determination of the position a fraction of a second or whatever earlier and then comparing this with the difference due to the satellite motion alone.

However, another point is that the signals are not transmitted continuously but only every millisecond or so. Therefore, unless you are by accident at certain points (like the mid-point between the transmitters), you won't receice the signals from the satellites simultaneously, but only separated by anything up to a millisecond depending on your position. Of course, you have to measure this time difference and add the corresponding distance onto your result (which could be anything up to 300 km (the distance light travels in one millisecond)). But this requires basically only a crude timer rather than a synchronized atomic clock (in order to have a 1m accuracy in the position, the timer must only be accurate to about a nanosecond (10^-9 sec) within a millisecond; this amounts to an accuracy of merely 0.1 sec/day (which is about the accuracy of simple quartz wrist watch)). In any case, there is no synchronization needed and the error doesn't accumulate as each measurement is independent from the previous one.

Thomas

Last edited: May 17, 2006
18. ### CANGASRegistered Senior Member

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1,612
Any serious student of Relativistic Length Contraction will have some real fun if they go back to first principles, the assumption of absolute space, and carefully analyze the expected relationship of light to its path in an 1880s Michelson interferometer.

This is similar to a recreation of a derivation of gamma, based on a stylized diagram of the MM. But done THOUGHTFULLY.

After about a half dozen "back of an envelope" grade anasysises(?) I believe I can tell you "we are not in Kansas now, Toto".

Have fun.

19. ### James RJust this guy, you know?Staff Member

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In fact, it's exactly the same as a "recreation of a derivation of gamma". There's only one assumption which is different in the "absolute space" picture, compared to the relativistic derivation - namely, the assumption that the speed of light is the same in the moving frame as it is in the stationary frame. In the "absolute" picture, the speed of light changes between the frames, whereas it does not in the relativistic situation.

It is by comparing the differences between including the relativity postulate and not including it that we arrive at relativity. Then, we go out and test the two scenarios to see which one the universe prefers. It turns out that it prefers relativity.

20. ### CANGASRegistered Senior Member

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JR:

I have done my most recent mathematical activity to examine the conception and derivation of gamma only hours ago.

When, if ever, have you last done the same?

Your preference of relativity might be based upon circumstances other than your own personal investigation of the matter.

Tell us of your own personal mathematical investigation of the conception and derivation of gamma, as obviously based upon MM1880s.

My own admittedly preliminary investigation is showing serious discrepencies, more evident as energy levels increase. Perhaps my preliminary stage of investigation will be upheld as more accurate stages are accomplished. Perhaps my preliminary results will be embarrassingly reversed.

WHEN HAVE YOU PERSONALLY PAINSTAKINGLY EXAMINED THIS ULTRA IMPORTANT ISSUE?

Last edited: May 24, 2006
21. ### PeteIt's not rocket surgeryRegistered Senior Member

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Would you like to share your preliminary results with us, CANGAS?

Examining the MM experiment is pretty basic stuff, unless you're going right back to raw data and full error analysis. Are you?

22. ### James RJust this guy, you know?Staff Member

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CANGAS:

I examined the derivation of special relativity first when I learned the theory for the first time, then later in more detail when I started teaching it to students.

23. ### CANGASRegistered Senior Member

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Pete: You are very good at asking questions but not on record for making substantive statements. My results, pro or con, will be available according to my timing. In the meantime, you could attempt to do an effective analysis yourself. I would really like to see the result of that.

James R.: Your investigations were apparently more frivolous than painstaking. The problems I have uncovered would be immediately obvious to any serious study. Since you have not mentioned and refuted them, it is obvious that you have never discovered them, which means that you have never studied the matter in depth. Anyone seriously investigating the matter could not miss the problems, and if the problems have satisfactory solutions, you would have already jammed the problems and the solutions down my throat without salt or ketchup.

My results, whether in favor or against the legitimacy of Special Relativity, will be made available when I have satisfied myself that I have done the most thorough work I can do. This will happen on my schedule. Not yours.

Last edited: May 27, 2006