Twin Paradox: Definitive Proof That It's SR?

[kilopi]

The 1907 paper doesn’t mention “freezing to death”, just as his 1905 paper didn't mention "Bob and Ann".

Figured

The 1907 paper gives a formula that shows how the temperature of the “seen” “moving frame” drops based on relative “v”. You can calculate the temperature inside the “frame” with the formula.

That would be from the point of view of the non-moving frame though. Inside the moving frame, the temperature does not drop. You have it backwards. Just as time appears to slow down, from the point of view of the non-moving frame, it doesn't from the point of view of the moving frame--they don't see their actions taking inordinately longer to perform.

If a spaceship’s ambient temperature is consistently very low inside the cabin, then the humans inside the cabin “freeze to death”.

Just another misapplication of the theory. You can't hold that against Einstein. This is difficult stuff.

But since we are talking about an amateur’s thought experiment with “Bob and Ann”, the consequence of their thermometer drop, based on Einstein’s 1907 formula, would be that they would “freeze to death”.

Not true.

[Sam5]

Shows what happens when you trust the internet. "This guy" has a masters degree in math.

As far as I can tell, the math in the theory is ok, but the basic concept in the theory of clock slow-downs due only to “relative motion” is not ok. The math on the internet website is not ok, since according to SR theory, Bob would not see Ann turn around for 5 years, since Ann is traveling 3 light years at .6c.

Can you tell me how Ann can travel 3 light years at .6c in only 4 years?

The double use of the Lorentz Transformation to calculate what Bob sees of Ann’s clock during the 5 years, is not correct. This is not allowed in the SR theory. So if anyone says that Ann travels 3 light years at .6c in 5 years, but Bob “sees” Ann’s clock tick only 3.2 years, it doesn’t matter how many “math degrees” he has, because he is not using the Lorentz Transformation properly, since it should be used only one time (resulting in 4, not 3.2 years), and he shouldn’t use it twice, based on what Einstein says in his paper. So, if someone uses it twice, that guy is disagreeing with Einstein on that particular math issue, while I'm agreeing with Einstein on that partcular math issue.

[kilopi]

Can you tell me how Ann can travel 3 light years at .6c in only 4 years?

Are you talking about this page?

[Sam5]

Ah, but you said "At turn-around time, Bob has 'seen' 5 years pass, not 4, because he has 'seen' Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock." I've got a copy of Einstein's 1905 paper, and the words "Ann" and "Bob" don't occur anywhere in it.

Doesn't everyone here know that??

Yes, “Bob and Ann” are in the internet website, but NOT in the 1905 SR theory. I thought everyone knew that.

So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.

I’ve also warned you not to trust any of the popular websites about this subject. That’s why I started off discussing the actual clock thought experiment in the SR theory, the A B and K K1 experiment. It was you who brought up the incorrect numbers that are contained in the amateur website. I think you and I should stick strictly to the numbers in the 1905 theory, but you keep insisting on bringing up the incorrect numbers in the amateur website which contains additional mistakes that aren’t even in the original Einstein theory.

[Sam5]

Sean,

It is your reliance on the incorrect numbers contained in the amateur website that causes you to use the double Lorentz Transformation factor to get 3.2 for what Bob “sees” on Ann’s clock. I keep asking you why you use the double Transformaton factor instead of just the single factor, but you never answer my question. Einstein says we are to use a single Transformtion factor only, but you use a double Transformation factor. That’s why you get 3.2 for what Bob “sees” on Ann’s clock while Ann “sees” 5 on her clock.

One use of the Lorentz Transformation factor of .8, based on a velocity of .6c:

5 x .8 = 4

The second use of the Lorentz Transformation factor in the same Bob/Ann frames:

4 x .8 = 3.2

This double use of the LT factor is incorrect, and Einstein never used it twice in one calculation to calculate the amount of “time dilation” on the other frame’s clock. But you incorrectly use it twice, so that’s why you get 3.2 rather than 4 for what Bob “sees” on Ann’s clock during Ann’s 5 (Bob-time) years of Ann’s travel.

[SeanF]

Ah, but you said "At turn-around time, Bob has 'seen' 5 years pass, not 4, because he has 'seen' Ann travel 3 light years at .6c for 5 years on his clock, not 4 years on his clock." I've got a copy of Einstein's 1905 paper, and the words "Ann" and "Bob" don't occur anywhere in it.

Doesn't everyone here know that??

Yes, “Bob and Ann” are in the internet website, but NOT in the 1905 SR theory. I thought everyone knew that.

So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.

(emphasis mine)

Where does that website say that Bob sees Ann move 3 light-years at 0.6c?

I’ve also warned you not to trust any of the popular websites about this subject. That’s why I started off discussing the actual clock thought experiment in the SR theory, the A B and K K1 experiment. It was you who brought up the incorrect numbers that are contained in the amateur website. I think you and I should stick strictly to the numbers in the 1905 theory, but you keep insisting on bringing up the incorrect numbers in the amateur website which contains additional mistakes that aren’t even in the original Einstein theory.

All right, I'll make you a deal. I'll be willing to stick strictly to Einstein's 1905 paper for this discussion if you will. So, what exactly is your problem with Einstein's 1905 paper?

[kilopi]

So, if you have Bob see Ann move 3 light years at .6c, then according to the 1905 theory, 5 years, not 4, will lapse on Bob’s clock. But the website that we are discussing has only 4 years lapse on Bob’s clock at turn-around time, so the website does not conform to the 1905 theory. That's what I've been trying to explain to you.

Where does that website say that Bob sees Ann move 3 light-years at 0.6c?

That's apparently derived from your post, where you have Ann perceiving five years have passed. But that's in Ann's reference frame. Sam5 responded a couple of posts later with a calculation that converted the three lightyears into five years as seen by Bob.

[Tensor]

As far as I can tell, the math in the theory is ok, but the basic concept in the theory of clock slow-downs due only to “relative motion” is not ok.

The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why? The slowing of time follows in the math from the second postulate. If you agree with the postulates, and you say the math in the theory is good, then you have to concluded (using the math) that there is no paradox. Celestial Mechanic's post (in the previous thread) using the math demonstrates this. You have never commented on those posts. If you believe there is a paradox, could you show us exactly where Celestial Mechanic is wrong?

[daver]

The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why?

Sam5 before has posted about c-regulators--he seems to think that large bodies regulate the speed of light around them--that they drag the ether somehow. So it would appear that he doesn't believe 2.

Sam5 has also posted about cooler temperatures slowing down biological functions, as if that had something to do with time dilation. I haven't seen this lately, so maybe he's changed his mind about that.

[Celestial Mechanic]

I am going to try to dispel a few more misconceptions by giving coordinates for 6 events that are relevant to our thought experiment involving Anne and Bob. These events are:

A: Anne and Bob are together. Bob sets off at 0.6c in the x-direction.
B: Two years have elapsed for Anne. All signals that she sends to Bob before this time reach him before his turn-around and are redshifted, all signals she sends after this time are blueshifted.
C: Five years have elapsed for Anne.
D: Eight years have elapsed for Anne. All signals that she received from Bob before this time were redshifted. All signals she receives after this time are blueshifted.
E: Ten years have elapsed for Anne. Bob returns from his journey. Eight years have elapsed for Bob.
F: The turnaround point for Bob. Four years have elapsed for him.

In Anne's rest frame, the coordinates of these points are ( (t, x) where time is in years and distance in light-years) :

A: (0, 0)
B: (2, 0)
C: (5, 0)
D: (8, 0)
E: (10, 0)
F: (5, 3)

Notice that C and F are simultaneous in this frame. Notice that the lines BF and FD are null geodesics.

Now we perform a Lorentz transformation to Bob's frame on the outward bound leg of the journey. The transformation is t' = (5/4)*t-(3/4)*x, x' = (-3/4)*t+(5/4)*x .

A: (0, 0)
B: (2.5, -1.5)
C: (6.25, -3.75)
D: (10, -6)
E: (12.5, -7.5)
F: (4, 0)

Notice that F is earlier than C in this frame. Even though a "coordinate time" of 12.5 years separates A and E, the proper time interval between the two events is still 12.5^2 - 7.5^2 = 156.25 - 56.25 = 100 = 10^2, so the proper time is still 10 years.

Finally, we consider Bob's frame on the inward bound leg, using his clock time as the time coordinate.

A: (-4.5, -7.5)
B: (-2, -6)
C: (+1.75, -3.75)
D: (5.5, -1.5)
E: (8, 0)
F: (4, 0)

Notice that here C is earlier than F in this frame.

Some exercises for the student:

1) Show that the proper time from F to E is four years in Bob's outbound frame.
2) Verify that BF and FD are null geodesics in both of Bob's frames.
3) Even though C and F are simultaneous for Anne, C is later than F for outbound Bob and earlier than F for inbound Bob, show that the separation between them is timelike and equal to 3 light-years in all three frames.
Extra Credit) Find the transformation to go from Anne's frame to Bob's inbound frame. Hint: Translate the origin to E, perform the inverse of the transform that got us to Bob's outbound frame, then translate E to (8, 0).

BTW, thank you for reading my posts, Tensor. It's good to know that someone is paying attention.

[kilopi]

So, CM, in your opinion, does my Ann/Bob page describe anything wrongly?

[Sam5]

All right, I'll make you a deal. I'll be willing to stick strictly to Einstein's 1905 paper for this discussion if you will. So, what exactly is your problem with Einstein's 1905 paper?

Ok, let me see if I can explain my point of view about his 1905 paper, without bringing in any amateur websites.

I think the Electrodynamical part of the 1905 paper is mostly ok, because of the way he used the two “frames” in that part. With is moving atoms and electrons, he actually has them “moving through” a medium, which I believe is the earth’s local fields. The “medium” is the “c-regulator” of the other “relatively moving” frame, just as Lorentz had used a “medium” in his 1895 and 1904 electrodynamics papers. This “motion of atoms through the fields” later allowed Einstein to deduce parts of his GR theory and be correct about what he decuced.

Parts of the Kinematical part of the 1905 theory are ok, since he has two relatively moving frames with two relaively moving sets of fields or “c-regulators”.

But, the part of the Kinematical part of the 1905 paper that has “time dilation” due ONLY to “relative motion”, is NOT correct.

Why do some “experiments” tend to seem to “support” all of the Kinematical part of the 1905 theory? These experiments tend to support the whole Kinematical part ONLY when the “relative motion” of the experiments have objects MOVING THROUGH LOCAL FIELDS.

That is why “c” is a “limiting speed” here at the earth (and inside fields), but not when we consider the most distant galaxies. Because objects here at the earth are moving through local fields, but the distant galaxies are apparently not moving through any fields at all.

For example, what I said earlier about the moving magnet and the coil. If you move the magnet AT THE COIL, then the coil FEELS the changing magnetic flux. But, if you move the magnet in Los Angeles, while the coil is in New York, the coil DOES NOT FEEL the changing flux.

This is the crux of the situation. If the two relatively moving frames are CLOSE ENOUGH TO EACH OTHER for their FIELDS TO INTERACT, then there can be a real effect that occurs because of the motion, such as the example I gave about the large magnet being moved NEAR an electric clock. That will cause the coil inside the little electric motor inside the clock to FEEL the changing flux of the large magnet’s magnetic field, and that will alter the motor rpm rate of the electric clock.

BUT if we move the large magnet in Los Angeles while the electric clock is in New York, then the electric clock WILL NOT FEEL the changing flux.

This is a direct analogy to the local “speed limit of c”, as compared to the distant-galaxy non-limit. The distant galaxies are a long way away from our local fields.

Eintein’s slight mistake in the Kinematical part of the 1905 theory was in not recognizing, in 1905, that the thing that caused a real “effect” was the motion of a mass or a clock THROUGH the fields, rather than just the “relative” motion of the two frames, no matter how far apart they were.

This is a fairly minor mistake. It’s no big deal, because later in GR theory he added the FIELDS to the considerataion and he cleared up some of his 1905 errors.

This change in attitude of his is why he said there was “no ether” in 1905, but later in 1920 he said there “was an ether”, and in 1920 he recognized that “ether” to be the “fields”. He actually said so here:

”Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only wonld be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense.”

Read his whole 1920 paper at this link to see what he said about the fields

I realize this might at first be difficult to understand. It took me about 8 years of studying a lot of his papers to figure this out. And after a couple of years I stayed completely away from the error-filled amateur explainaitons of this stuff. He figured some of this out by 1907, more by 1915, and even more by 1920.

What he actually discovered was a “limiting speed of c” for masses moving INSIDE strong fields. But this rule does not apply to the distant galaxies, since they apparently are NOT moving THORUGH strong fields. But he died before he ever learned of galaxy redshift examples that suggest higher than “c” speeds for the distant galaxies.

If he were here today, he would certainly understand all of this and he would probably be the leading cosmologist of our era, and we wouldn’t even need to be arguing about this stuff. One reason I understand some of this stuff is because I have had the advantage of being able to study the past 48 years of experimental and observational data gathered by physicists and cosmologists. He did not have that advantage. If he had known about the high-z galaxies in 1930, 1940, or 1950, he would have worked all this stuff out within a couple of years, and I think he COULD have eventually said something like this: “The Special Relativity principle of relatively-moving frame transformation effects applies on a local level where fields interact between relatively moving frames, but if the frames are so far apart that their fields do not directly interact, then the principle has no actual practical application at such great distances,” just as he DID say in the 1905 paper: “For velocities greater than that of light our deliberations become meaningless;”

By the year 2,000, he could have merely added a couple of extra phrases to that sentence that could have said, “ "superluminal velocities of masses through powerful local fields, on a local level, are apparently impossible, but superluminal relative velocities of masses that are separated by great distances and that are not traveling through any fields, apparently are possible.”

And he could have further said: “The apparent ‘clock paradox’ of Special Relativity only arises if two clocks that are each resting within their own powerful and separate local fields pass each other, relatively, close by one another, and in that case, if the two field strengths are of the same magnitude, then BOTH clocks will exhibit exactly the same clock-rate change, depending on the types of clocks used in the experiment. But if only one of the clocks, which possesses no strong local fields of its own, moves through the other clock’s strong fields, such as the moving clock moving near the surface of the earth, then only the moving clock will experience a rate change.”

Of course he can’t say that now, since he died in 1955, and I think it is incorrect to assume that he never would have amended his 1905 theory to take into account the new physics knowledge that has been gained since his death. And I think it is unfair to try to claim that he would have continued to insist that his 1905 theory should not be amended in any way. Certainly he would have amended it by now, had he survived till now. And it is unfair for anyone to call me a “crackpot” simply because I insist on amending his 1905 paper to include modern physics and astronomical observational data. The crackpots are the ones who won’t allow any amendments to the 1905 papers that are based on modern observational data.

[SeanF]

So, CM, in your opinion, does my Ann/Bob page describe anything wrongly?

I don't know about CM, but I still think your Twin Paradox Redux page explains clock synchronicity wrongly . . .

[SeanF]

Well, Sam5, first of all, you sure made reference to an awful lot of papers other than the 1905 paper. I thought we were just going to talk about that one? At any rate, I realize that my question was too generalized. Let me be more specific.

And he could have further said: “The apparent ‘clock paradox’ of Special Relativity only arises if two clocks . . . "

What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?

[Sam5]

Sean,

I wish I had explained it this way when I first started out arguing about this topic, but frankly, I didn’t think of explaining it this way at that time.

What the amateurs are doing on their “Ann and Bob” websites, is just the same as if some crank read in an old book that said some old Pope, 450 years ago, said, “The sun revolves around the earth”, and then the internet guys would post webpages trying to “prove” the sun revolves around the earth. Whereas in reality, a modern Pope has had the advantage of the past 450 years of scientific observation, and so he wouldn’t say such a thing.

So what these internet guys are doing is taking something Einstein said in 1905, which contained some minor flaws ONLY because he did not have access to the past 98 years of modern observation data. He was basing his 1905 paper on what he had read about the 1886 Michelson-Moreley experiment and some of the attempts to explain the “null” result.

Einstein did NOT base his 1905 theory on year-2003 observational data. He based it on year-1886 observational data.

Had Einstein lived until now, he would have AMENDED his 1905 theory to take into account all the modern observational data, and we wouldn’t be here arguing about this.

[kilopi]

Of course he can’t say that now, since he died in 1955, and I think it is incorrect to assume that he never would have amended his 1905 theory to take into account the new physics knowledge that has been gained since his death. And I think it is unfair to try to claim that he would have continued to insist that his 1905 theory should not be amended in any way. Certainly he would have amended it by now, had he survived till now.

He did amend his theory, before he died. It's called general relativity. He made many (self-admitted) false starts.

And it is unfair for anyone to call me a “crackpot” simply because I insist on amending his 1905 paper to include modern physics and astronomical observational data. The crackpots are the ones who won’t allow any amendments to the 1905 papers that are based on modern observational data.

It would be unfair to label me as a crackpot just because I am trying to explain the mathematics and theory behind the 1905 papers. You have asserted that he didn't treat the details of the twin paradox properly in his 1905 paper, that he somehow misapplied his own theory. He did not, you are wrong.

[Sam5]

What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?

The “apparent” clock paradox occurs when we consider the results from the K1 frame-observer’s point of view that the K frame is the one that is “moving” and “time dilating”, while we also consider the K frame-observer’s point of view that the K1 frame is the one that is “moving” and “time dilating”.

But, if we consider that the K clock is moving “through” the K1 frame’s “fields”, or that the K1 clock is moving “through” the K frame’s “fields”, then there would be no paradox; however, we must also accept the real-life observational data that “c” is NOT “always” the speed of light everywhere and relative to every “frame”. We must accept the modern observational data that explains how a light beam passing near the sun “slows down” relative to the earth’s frame and the earth’s atomic clocks, while the photons are at the sun, while the photons are judged to be traveling faster than “c” by sun clocks and observers, when the photons are traveling a long way from the sun. While they are at the sun, they would be seen as traveling at “c” by the sun observers and clocks, but they would be seen as traveling faster than c by those observers and clocks when they are not near the sun.

Einstein includes this basic information in his 1911 theory, and I’ve pointed that out to you many times.

What you want to do is not allow him to ever “update” his theories so they can conform to modern observational data. And I don’t understand why you would not allow Einstein to take modern observational data into consideration. I don’t understand why you insist on keeping his old theories “as is” with “no updates” based on new scientific information learned during the past 98 or 48 years.

Had he lived longer, he would have made more “updates” than he actually did make. If he were alive today, his 1916 book would probably contain 7 or 8 Appendices, or maybe 9 or 10, rather than just 5. You are the guys who are harming his reputation by not allowing him to “update” his theories past the year 1955.

Sooner or later, some of these new physics whiz kids coming along are going to realize that the Kinematical part of the 1905 paper needs to be amended to take into account modern observational data. That kid whose link I posted here already knows it. That’s why he said that the light photons actually DO slow down at the sun, as measured from the earth.

[SeanF]

What "apparent 'clock paradox'"? I do not see any clock paradox in Einstein's 1905 paper. Where do you?

The “apparent” clock paradox occurs when we consider the results from the K1 frame-observer’s point of view that the K frame is the one that is “moving” and “time dilating”, while we also consider the K frame-observer’s point of view that the K1 frame is the one that is “moving” and “time dilating”.

More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

[Sam5]

More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

I’m talking about his original clock paradox thought experiment, the “peculiar consequence” one. The peculiar consequence results when he examines his own theory from the point of view of ONLY the K observer, and he doesn’t report what the K1 observer “sees”. When we realize that the K1 observer would “see” the K frame “moving” and “time dilating”, that results in the paradox. In other words, if we examined what BOTH observers would “see”, then we’ve got TWO conflicting “peculiar consequences”, and that causes the paradox, but just a few years later he began to remove that paradox from his overall relativity theories and various NEW relativity papers.

Since we live in a unified world, and since “the laws of physics are the same everywhere”, then we CAN’T just look at the phenomena from the K “point of view”. We also must look at it from the K1 “point of view”.

He did actually amend part of the 1905 theory with the 1911 theory, and he pointed that out when he said in 1911, (my emphasis in bold):

“The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.”

That’s because in THIS theory he has only ONE of two clocks actually “slowing down”, so there is no paradox. You can read about it in his dialogue about the two “U” clocks in the 1911 theory. In this theory, the speed of light DOES slow down relative to a DISTANT observer, but NOT relative to a LOCAL observer. This is why the light bends when it passes near the sun, because the gravitational field at the sun, which is strongest nearest the sun, causes the beam of light to act like a plane wave encountering a glass interface. That’s what causes the light to bend at the sun.

So you can’t say his 1905 theory is all “absolutely correct and true and never doesn’t apply to nature under any circumstances”, because he said so himself in 1911 that this new 1911 theory adds some new material to the 1905 theory and so the “ordinary theory of relativity” doesn’t apply here, or it applies “in a different form”, meaning that the sun observer with his local atomic clocks “sees” the light traveling at “c” only when the photons are nearest the sun, while the earth observe “sees” the photons pass near the sun at “less than c” as their speed is measured by the earth clocks.

But you are disagreeing with Einstein’s 1911 statement and you are saying, in effect, that he was wrong in 1911, while I’m saying he was right in 1911. I think you are mad at me because you think that I’m the one who is trying to amend the 1905 paper, but it was actually Einstein himself who did it in 1911.

[Flaney]

Tensor wrote:
The slow down of time is not a concept of SR. There are two postulates of SR(which has been mentioned to you before):

1) The laws of physics are the same in all inertial frames.
2) The speed of light is the same as observed in all inertial frames

Which of the above don't you agree with and why?

2)

How does the reciept of a photon translate into speed? It is an event with no other information (except energy). Subsequent photon receptions build an event history where derived speed can be calculated (based on local clocks). Any event chain variations can be attributed to relative velocity differences.

Photons I emit are not detectble by me any more. As I travel along, I release an additional photon, which I have carried away some distance; it will be farther from the previous photon I emitted by vt. These photons get detected at some point as events that occur in a dilated history: the transmit events no longer coincide with detection events.

Should the reciever think the emitters clock is running slow because the events come less frequently?

To measure a photon's speed, I need to measure it's position at two places and the times it reaches each position. But once I have detected it, it is gone. I have to detect some other photon that was moving near it at the second location, where it subsequenly vanishes. Only if we assume all photons are equal can a specific speed be determined.

When I test a photon's speed in my reference frame, I use a local source and detector. If my reference frame velocity has been added to photon speed, the excess is canceled between the source and detector. That which I added at the emitter gets subtracted at the detector.

This does not need to mean photons are racing around with different speeds. How quickly does the photon speed drop when traversing a non-vacua medium? Space itself might 'force' photons to a local C in a similar manner. Fast photons would not pass up its slower brothers if some depth or maximum transmission transition is exceeded. Beyond such a point, the events would be compressed, but all would be finally zipping along at C.

SR is time series information propagation.

[Sam5]

Sean,

If you let your focus drift away from Einstein’s actual papers, and if you let it drift toward the internet’s self-appointed amateur self-proclaimed “experts”, then you will get completely confused.

The reason I was able to figure some of this stuff out was because I stopped reading the amateur stuff early on, and I persisted in studying the real original Einstein stuff, and I’m sure you know, that’s not “easy” stuff to study.

That stuff about the “U” clocks in the 1911 paper is mind-bending, but I finally worked through it and came out on the other side with a better understanding of the 1911 theory, and THEN I knew EXACTLY what he meant when he said in 1911:

“The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.”

OF COURSE it applies “in a different form”, because the sun observers will measure the photons to travel at “c” ONLY while they are passing through the sun’s gravitational field, while the earth observers will see them “slow down”, at the sun, when observed FROM the earth!

The guy was a GENIUS!

But I think he could have used a good manuscript editor, because the way he worded things is really confusing to the rest of us.

[SeanF]

More specific, please? Einstein doesn't use K1. You're paraphrasing, and that's okay, but I don't know what part of the paper you're referring to.

I’m talking about his original clock paradox thought experiment, the “peculiar consequence” one. The peculiar consequence results when he examines his own theory from the point of view of ONLY the K observer, and he doesn’t report what the K1 observer “sees”. When we realize that the K1 observer would “see” the K frame “moving” and “time dilating”, that results in the paradox. In other words, if we examined what BOTH observers would “see”, then we’ve got TWO conflicting “peculiar consequences”, and that causes the paradox, but just a few years later he began to remove that paradox from his overall relativity theories and various NEW relativity papers.

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2(tv^2/c^2) (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.

That the one? Okay let's see. Einstein gives the equations for converting coordinates from one reference frame to another at the end of Section 3. These are, as he points out, simplified in that they assume that the origins of both reference frames are at the same point and that motion is restricted to the x-axis. This "peculiar consequence" can be dealt with under those restrictions, though, so we can use the equations as-is.

So. We'll start out with the A clock having (x,t) coordinates of (0,0) in the initial reference frame. The B clock is located 3 light-years away at coordinates (3,0) in the initial reference frame. He says "the clock at A is moved with the velocity v along the line AB to B." We'll use our standard velocity of 0.6c. So, B's going to stay where its at (spatially speaking) and end up at (3,5) [t=d/v=3/.6=5]. A's going to end up in the same place - (3,5)

So, let's use his equations and transform those coordinates into the other reference frame. The two equations are:

t' = (t - vx/c^2)/(1-v^2/c^2)^0.5
x' = (x - vt)/(1-v^2/c^2)^0.5

so the three coordinate points become:

A's starting point = (0,0) = (0,0)
B's starting point = (3,0) = (3.75,-2.25)
A&B's ending point = (3,5) = (0,4)

The first reference frame has B remaining stationary at x=3 and A moving from x=0 to x=3. In that reference frame, B's time coordinates go from 0 to 5, a total of 5. A's time coordinates also go from 0 to 5, but since we expect A's clock to be dilated to 80%, we expect to see A only show a duration of 4 (5*.80).

The second reference frame has A remaining stationary at x=0 and B moving from x=3.75 to x=0. In that reference frame, A's time coordinates go from 0 to 4, a total of 4. B's time coordinates go from -2.25 to 4, a total of 6.25, but since we expect B's clock to be dilated to 80%, we expect to see B only show a duration of 5 (6.25*.80).

So, regardless of whether A or B is considered to be stationary, they both expect to see A show a duration of 4 and B show a duration of 5.

Where's the paradox?

[SeanF]

Uh, Sam5? You still there?

[Starbuck]

Everybody's gotta eat dinner sometime...

[kilopi]

But you are disagreeing with Einstein’s 1911 statement and you are saying, in effect, that he was wrong in 1911, while I’m saying he was right in 1911. I think you are mad at me because you think that I’m the one who is trying to amend the 1905 paper, but it was actually Einstein himself who did it in 1911.

In effect, I am saying that certain parts of the 1905 paper, that you say are wrong, are not wrong. And we're just trying to explain the math.

[Sam5]

Uh, Sam5? You still there?

Yeah, yeah, I’m back. Look, I’ve been sitting in this chair so much during the past couple of weeks, bent over my keyboard so much, my feet have been swelling up. I think the circulation has been cut off to them. So, to keep me from having to have my feet amputated, I’ve had to get out some and walk around. I’ll study your last stuff a little later.

In the meantime, while I was out, I thought of this. We are not that far apart, if we totally leave out the amateur internet Bob and Ann type stuff.

And think of this, the speed of light is apparently fixed at “c”, relative to an observer who has an atomic clock sitting on his desk, if he and the clock are resting somewhere on the surface of an astronomical body, and if they are measuring the speed of the local photons that are passing by them at the moment they measure the local speed of light. So, the local speed of light is apparently tied directly to the tick rates of local atomic clocks, if those clocks are resting inside a gravitational field when the local photons pass close by the clocks.

But, if the observer and the clocks measure the speed of photons that are traveling somewhere else, such as they are just passing by the sun, close to the sun, while the observer and the clocks are on the earth, then that speed they would measure would be more or less than “c”. In the case of the sun photons and the earth observer, the sun photons would be measured by the earth observer as traveling less than c, while they are passing near the sun.

But, a sun observer, using a sun-based atomic clock, would measure “c” for the speed of the photons as they pass near to the sun, while he would measure the photons moving faster than c when they are well away from the sun, such as when they are passing by the earth when the sun observer measures their speed.

So, it depends on where the observer is and where his atomic clock is, and whether or not he’s resting inside a gravitational field, and where the photons are that he is measuring. I think Einstein did not know that in 1905, since he didn’t mention the role the gravitational field plays in all of this, but I think he figured it out by 1911.

I’ll get back to you later.

[kilopi]

In the meantime, while I was out, I thought of this. We are not that far apart, if we totally leave out the amateur internet Bob and Ann type stuff.

If you left off the amateur internet stuff, you'd be out of business yesterday.

I think Einstein did not know that in 1905, since he didn’t mention the role the gravitational field plays in all of this, but I think he figured it out by 1911.

By his own admission, not until 1915 and after. It doesn't excuse your errors in math in trying to discredit his early work, and, having admitted that Einstein was a genius, and that he eventually got his complete theory in order, I'm not sure what your purpose is.

[Tensor]

BTW, thank you for reading my posts, Tensor. It's good to know that someone is paying attention.

To your posts, always. You belong to a group, (the BA, Kilopi, Tim, Eta, JSPrinceton before his banning, and a few others) that I learn something from almost all the time.

[Sam5]

Sean,

You:
”The first reference frame has B remaining stationary at x=3 and A moving from x=0 to x=3

The second reference frame has A remaining stationary at x=0 and B moving from x=3.75 to x=0.’

Me:
This is incorrect.

A the beginning of the thought experiment, points A and B are stationary in K and K1. Since no one is moving, K and K1 overlap along their x axes.

Distance AB = BA

So, you can’t change the distance from B=x3 to B=x3.75 in the middle of the thought experiment.

That’s like saying the distance from Los Angeles to New York is 3,000 miles, but the distance from New York to Los Angeles is 3,750 miles. You can’t do that because you’ve already set the distance at B=x3.

You’ve got to tell what B “sees” when A moves from x=0 to x=3, and then you have to tell what A “sees” when B moves from x=3 to x=0.

You’ve got to tell what a Los Angeles resident “sees” when a New Yorker flies to Los Angeles and you’ve got to tell what a New Yorker “sees” when a Los Angeles resident flies to New York.

You can’t have the New Yorker leaving from Nova Scotia on the way to Los Angeles, while the Los Angeles resident leaves from Los Angeles on the way to New York.

Einstein said in the paper: “It is clear that the same results hold good of bodies at rest in the “stationary'' system, viewed from a system in uniform motion.”

He also said:

“whence it follows that the time marked by the clock (viewed in the stationary system) is slow by seconds per second”

From B’s point of view, B is in “the stationary system”. From A’s point of view, A is in “the stationary system”.

You:
”So, regardless of whether A or B is considered to be stationary, they both expect to see A show a duration of 4 and B show a duration of 5.”

Me:
No. You’ve been misled by the Ann and Bob example. You’ve got to put it completely out of your mind.

[Sam5]

SeanF,


One of Einstein’s errors in the paper is that he says this:

“If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by

(up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B.”

And then he stopped that particular thought experiment.

Had he gone on to say what the A observer “saw”, it would be like this:

“If at the points A and B of K1 there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at B is moved with the velocity v along the line AB to A, then on its arrival at A the two clocks no longer synchronize, but the clock moved from B to A lags behind the other which has remained at A by


(up to magnitudes of fourth and higher order), t being the time occupied in the journey from B to A.”

When people, including legitimate physics professors who I’ve discussed this with, follow Einstein’s symmetry rule that says: “It is clear that the same results hold good of bodies at rest in the “stationary” system, viewed from a system in uniform motion,” then that’s when they see the paradox, since the A system is “stationary” to the A observer, and the A observer “sees” the B clock as the one that “moves”.

This is one of the hazards of purely “theoretical” physics, ie leaving something out or forgetting something or not following one of your own rules, and this often comes from working on a theory and a thought experiment completely by yourself without much feedback from other physicists. This is why he had to backtrack in 1907 and admit that none of the frames actually “shrivel up”, since “relative motion” alone can’t cause any frame to really shrink. Lorentz’s frames could “shrunk” in his theory because they were moving through an “ether”, and he thought that one arm of the Michelson Morley apparatus might have really shrunk because of its motion through the ether as the earth moved around the sun at 18.6 mps.