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Relativity - Oh dear, here we go again!

The example I like to use is airplanes flying overhead. Because of the finite speed of sound, you hear noise coming from some point noticeably behind where the plane overhead is. But if you know the speed of sound in air and you know how fast the plane is going, you can calculate when the sound was emitted and where the plane was when it was emitted, and you can observe that the sound is indeed coming from the plane and not from behind it.
Sorry to take just part of your post but I’m about ready to go to bed and don’t have much time (where‘s time dilation when you need it? :-).

This makes perfect sense but the same logic doesn’t seem to be being applied in the clock experiment. Unfortunately the clock experiment is designed to prove that the clock runs slower rather than demonstrate it. Let’s say that a clock is travelling away from an observer at half the speed of light. As the light from the clock takes twice the time to reach the observer, it appears to running at half speed. If you know the speed of the clock and the speed of light, you can calculate the delay in receiving the light from the clock (same as the sound in your plane scenario) and that the clock is not running slower. Don‘t both scenarios prove time delay, not time dilation?.
 
Have you studied "The twin paradox"?

The twin who remains on Earth has a clock and he observes his clock to run at the normal rate.
The twin who travels to alpha centauri and back also has a clock and she observes her clock to run at the normal rate.
Yet, when they meet up again, less time has passed for the twin that travelled to Alpha centauri than for the twin who stayed at home.
Which they can both confirm by comparing their clocks.

As I said, this has been proven experimentally to be true on a smaller scale. There is the muon example cited earlier. Also, extremely accurate atomic clocks have been carried on aircraft as confirmation.

These are the facts.

Someone who knew what they were talking about once said:
"You are entitled to your opinion, but not your facts"

Yes I have, and I understand how it would work if Relativity works. I’m just not sure that it does.

"You are entitled to your opinion, but not your facts" - Back at you :D

Really got to go to bed now - Byeee
 
First of all, why have you not addressed the points already put to you?
Why move on to another scenario before you have understood, or acknowledged your misunderstanding, or refuted our understanding of the previous scenario?

An observer is orbiting the ball clock described earlier in a circular motion. The observer is moving in relation to the clock but the clock doesn’t appear to the observer to be moving. The clock is not seen to be moving sideways and the ball is not seen to be moving in a zigzag manner. The clock is observed to be function normally.


This is correct.
Except we are no longer talking about SR.
Circular movement involves acceleration so this is not an inertial reference frames.
This is GR.

Move the clock out from the centre, half way along the same diagonal that the observer is on, and have them both move in a concentric orbit. The observer and clock always remaining on the same diagonal. The observer is moving at a different speed to the clock but the clock doesn’t appear to the observer to be moving. The clock is not seen to be moving sideways and the ball is not seen to be moving in a zigzag manner. The clock is observed to be function normally.


To stay with SR, why not just have these two, A and B, moving in the same direction, at constant speed, in a straight line in reference frame of a third observer, C (because all movement has to be in the reference frame of something else). It doesn't matter what their separation distance is, the clock will run at the same speed in the reference frames of both A and B because they are at rest relative to each other.

Reverse the rotational direction of the clock and have it orbit at it’s previous speed. The observer and clock now pass each other and the clock is seen to be moving sideways and the ball is seen to be moving in a zigzag manner. According to Relativity, the clock now appears to (and actually would) slow down (I can only agree with the appears bit).


(Remember, the clock doesn't slow down, it runs at a slower speed.)
Again, to stay with SR, why not have A and B moving at the same speed, in opposite directions, in a straight line in the refereence frame of C. In this case the clock runs at different speeds for A and B.
 
Regardless of the terminology used, I think that it’s obvious that the closer and more immediate that a thing is observed the more accurately the observation is likely to represent the reality. I believe that every thing only has one reality. I'm not making a claim, I'm asking a question. Why is is an observation that has been distorted by distance and motion claimed to be an accurate representation of the reality of the thing being observed?

All right. Try to imagine two Perfect Clocks(tm) that were manufactured one day by the Perfect Clock Company, Switzerland. They were sitting on the shelf together, clocking away happily and took joy and pride in comparing each other's time and always finding it the same. Why wouldn't they? They were both Perfect Clocks(tm). When they ticked, their sounds perfectly merged together into one single ticking sound.

Then one day, an astronaut came and purchased one of the clocks, to take it with him on his trip to ISS where he would stay for a year. The clocks were very sad that they had to part ways, but they had no choice. The clock that stayed said to the purchased one, "Don't you worry. One thing we know for sure is that we're both Perfect Clocks(tm). So whenever you get lonely out there, just check your time and think of me with fond thoughts, for you'll know that I'll be showing the same time at that very same moment." That cheered them up (clocks are easily amused) and the astronaut left.

One year later, the astronaut's wife came to the store and purchased the other clock. She came home and put her new purchase on the kitchen table, just next to the clock that her husband brought back from space the previous day. The clocks were of course very happy and the first thing they could think of was, as one might expect, to compare times. (Clocks can sometimes be awfully narrow-minded.) But this time, there wasn't much rejoicing.

"Hey, you're time is wrong!" said the Earth-staying clock. "Did someone adjust you? Or did you just lose track of correct time?"
"Of course not," said the ISS-staying clock, gravely offended at such an insult. "My time is correct, it's yours that's wrong. You should give up your brand and call yourself the Lousiest Clock in the World(tm)."
"Now, now, wait a minute. Maybe this isn't our fault. I remember that I heard something about relativity and time dilation. Couldn't that explain it?"
"No, I don't think so. I heard about that too, but that just speaks about observing something from a different moving frame. Observation can't matter, what matters is what's real. I believe that every thing only has one reality. Look, we're Perfect Clocks(tm) (at least, I know I am) and we are supposed to be perfectly correct in our own local frames."
"But you weren't! As far as I can tell, you were ticking wrong when you were orbiting the Earth."
"No, that was just your illusion, because you were observing me from a distant, moving frame. I was, in fact ticking perfectly correct the whole time. My reality didn't change by your observation of it. Look, from my point of view, it was you who were ticking wrong while I was up there."
"But I wasn't!"
"What I'm trying to say is that a remote observation doesn't matter. What's sure is that a Perfect Clock(tm), manufactured to be that, remains a Perfect Clock(tm) in its own frame, and an observation that has been distorted by distance and motion cannot be claimed to be an accurate representation of the reality of the thing being observed."
The Earth-staying clock had to think about that for a while.
"I guess I understand what you mean. Just... one thing."
"Shoot."
"We are both original Perfect Clocks(tm), carefully manufactured to always remain correct as far as our own reality is concerned. And right now, we're sitting on this same table, and our observation of each other is distorted by neither distance nor motion. And yet... we're showing different times."
"Hmm. Interesting," said the other clock, and while they both thought about that, there was a long silence, disturbed only by two perfect clocks ticking in rapid successive pairs, slightly shifted and out of synchronization.
 
Yes I have, and I understand how it would work if Relativity works. I’m just not sure that it does.


It has been proven empirically.
This means that it is a fact.
Your opinion, therefore, does not count.

"You are entitled to your opinion, but not your facts" - Back at you :D


They are not my facts.
They are empirically established facts.
My opinion did not even come into it.
I have merely related to you the empirically established facts.
 
Let’s say that a clock is travelling away from an observer at half the speed of light. As the light from the clock takes twice the time to reach the observer, it appears to running at half speed. If you know the speed of the clock and the speed of light, you can calculate the delay in receiving the light from the clock (same as the sound in your plane scenario) and that the clock is not running slower.


"The light from the clock takes twice the time to reach the observer"? Twice the time as what?

I think you made a mistake. If relativity were wrong, the clock would appear to run at 2/3 its real rate, not 1/2, if you failed to account for the speed-of-light delay. (Consider a pair of clock ticks, emitted a minute apart. You will see the second one a minute and a half after the first: it was emitted a minute later, plus it had to travel an extra half-minute's distance to reach you because that's how far the clock moved away from you in that minute.)

Anyway, no. In fact, even if you do account for the speed-of-light delay, you will still calculate that the clock is running somewhat slowly. So it's hard to call the slowness just an illusion. How else would you decide how fast the clock is really running, besides watching it tick and taking into account the delay between when it ticks and when you see it tick?
 
This makes perfect sense but the same logic doesn’t seem to be being applied in the clock experiment. Unfortunately the clock experiment is designed to prove that the clock runs slower rather than demonstrate it.

To "prove" it, all you need to do is examine the metric. To demonstrate it, all you need to do is compare two clocks, one of which moves more than the other (and people have done exactly that) and compare that to the metric to see what you should get, and it agrees with the relativistic space-time metric. To make comparison simple, you can even start them off and end them at the same place, and you'll still find that the clock with the straightest world line experiences the most time.

Let’s say that a clock is travelling away from an observer at half the speed of light. As the light from the clock takes twice the time to reach the observer, it appears to running at half speed.

What you refer to here is Doppler shift (though you messed up the calculation of the shift magnitude). The audio equivalent is the change of tone for approaching versus receeding objects. The Doppler shift is in addition to time dilation, and (unlike time dilation) depends upon the relative direction of movement, not just the magnitude of the relative velocity. A receeding clock will be seen (note I'm not using "observe" here) to go slower because of the Doppler shift, but an approaching closk will be seen (not observed) to go faster.

If you know the speed of the clock and the speed of light, you can calculate the delay in receiving the light from the clock (same as the sound in your plane scenario) and that the clock is not running slower.

That's just the thing: after you do your calculation to account for the Doppler shift (which, BTW, is a purely classical calculation), you will find that the clock really is running slower. And unlike the Doppler shift, your final observed time dilation is independent of direction.
 
I disagree. The clock is only running in it’s own frame. It is only being observed to be running from another frame. It is never actually running in another frame.
This is completely incorrect. No frame is fundamentally different from the others. I will try to explain this better.

At every instant of time in frame A, the clock is a three dimensional object in that frame. Each microscopic part of the clock at a certain time defines an event: it exists at a certain point in space-time, labeled by the coordinates (t,x,y,z).

Let's call the set of events defined by the positions (in frame A) of all the microscopic parts of the clock at time t (also in frame A) "clock(A)_t". The full existence of the clock is not one such "clock(A)_t". It's the set of all of them", let's call it CLOCK(A):

CLOCK(A) = {clock(A)_t | -infinity < t < +infinity}​

Each clock(A)_t is a volume in three dimensional space, but CLOCK(A) is a "four-volume" in four dimensional space. Note that we can think of each clock(A)_t as a three dimensional "slice" of CLOCK(A).

Now consider frame B. At every instant of time in frame B, the clock is a three dimensional object in that frame too. Let's call the corresponding set of events clock(B)_t'. (Each event is labeled by four coordinates, just as in frame A, but in frame B we call them (t',x',y',z') instead of (t,x,y,z)). The full existence of the clock is the set of all the clock(B)_t':

CLOCK(B) = {clock(B)_t | -infinity < t < +infinity}​

The two different observers agree about what events are part of the clock's full existence. They will of course label each event with different coordinates, but they agree about which events are part of the clock's existence. If they didn't, then it would mean that special relativity contradicts itself, and it certainly doesn't. (Special relativity consists of the set of ordered 4-tuples of real numbers and some functions defined on that set, so if relativity contradicts itself, the contradiction would have to come from a fundamental flaw in the real number system. So anyone who claims that relativity is inconsistent is really claiming that real numbers are inconsistent too).

This means that CLOCK(A)=CLOCK(B), so I will just call this set CLOCK from now on.

Each clock(A)_t is a three dimensional slice of CLOCK, and so is each clock(B)_t'. But for any given t, there's no t' that makes clock(A)_t=clock(B)_t'. If space had been two dimensional, clock(A)_t and clock(B)_t' would be two planes that intersect each other at some line, because one of the planes is tilted relative to the other. (The angle is arctan(v/c), where v is the relative velocity of the two frames, and c is the speed of light). Space is three dimensional however, so it's impossible to picture these slices accurately, but it certainly helps my understanding a lot to visualize two dimensional slices instead, so I would recommed that you do the same.

Your confusion comes from the fact that you think of the different clock(A)_t as "reality" and the different clock(B)_t' as either illusions or "different realities". The existence of the clock can be described by talking about different clock(A)_t slices of CLOCK and the changes in t between different slices, OR by talking about different clock(B)_t' slices of CLOCK and the changes of t' between different slices. Both descriptions are equally valid. They are just based on different ways of "slicing" CLOCK into three-dimensional sets of events.

Until I find a good reason to accept that any observation is always an valid, accurate and correct representation of reality, writings on space-time diagrams, math equations, gods, etc isn’t going to help me understand and accept Relativity.
Space-time diagrams aren't going to help you understand relativity?! That's a truly bizarre statement. It's like saying that learning to read isn't going to help a child understand a book.
 
All right. Try to imagine two Perfect Clocks(tm) that were manufactured one day by the Perfect Clock Company, Switzerland. They were sitting on the shelf together, clocking away happily and took joy and pride in comparing each other's time and always finding it the same. Why wouldn't they? They were both Perfect Clocks(tm). When they ticked, their sounds perfectly merged together into one single ticking sound.

Then one day, an astronaut came and purchased one of the clocks, to take it with him on his trip to ISS where he would stay for a year. The clocks were very sad that they had to part ways, but they had no choice. The clock that stayed said to the purchased one, "Don't you worry. One thing we know for sure is that we're both Perfect Clocks(tm). So whenever you get lonely out there, just check your time and think of me with fond thoughts, for you'll know that I'll be showing the same time at that very same moment." That cheered them up (clocks are easily amused) and the astronaut left.

One year later, the astronaut's wife came to the store and purchased the other clock. She came home and put her new purchase on the kitchen table, just next to the clock that her husband brought back from space the previous day. The clocks were of course very happy and the first thing they could think of was, as one might expect, to compare times. (Clocks can sometimes be awfully narrow-minded.) But this time, there wasn't much rejoicing.

"Hey, you're time is wrong!" said the Earth-staying clock. "Did someone adjust you? Or did you just lose track of correct time?"
"Of course not," said the ISS-staying clock, gravely offended at such an insult. "My time is correct, it's yours that's wrong. You should give up your brand and call yourself the Lousiest Clock in the World(tm)."
"Now, now, wait a minute. Maybe this isn't our fault. I remember that I heard something about relativity and time dilation. Couldn't that explain it?"
"No, I don't think so. I heard about that too, but that just speaks about observing something from a different moving frame. Observation can't matter, what matters is what's real. I believe that every thing only has one reality. Look, we're Perfect Clocks(tm) (at least, I know I am) and we are supposed to be perfectly correct in our own local frames."
"But you weren't! As far as I can tell, you were ticking wrong when you were orbiting the Earth."
"No, that was just your illusion, because you were observing me from a distant, moving frame. I was, in fact ticking perfectly correct the whole time. My reality didn't change by your observation of it. Look, from my point of view, it was you who were ticking wrong while I was up there."
"But I wasn't!"
"What I'm trying to say is that a remote observation doesn't matter. What's sure is that a Perfect Clock(tm), manufactured to be that, remains a Perfect Clock(tm) in its own frame, and an observation that has been distorted by distance and motion cannot be claimed to be an accurate representation of the reality of the thing being observed."
The Earth-staying clock had to think about that for a while.
"I guess I understand what you mean. Just... one thing."
"Shoot."
"We are both original Perfect Clocks(tm), carefully manufactured to always remain correct as far as our own reality is concerned. And right now, we're sitting on this same table, and our observation of each other is distorted by neither distance nor motion. And yet... we're showing different times."
"Hmm. Interesting," said the other clock, and while they both thought about that, there was a long silence, disturbed only by two perfect clocks ticking in rapid successive pairs, slightly shifted and out of synchronization.
nominated
 
ynot- I'm absolutely mathematically illiterate.
I also do not instinctively accept the "explanations" of relativity you find upsetting.
Lacking your self confidence, I assume I'm wrong.
Try this- forget lateral movement .Consider the limiting case, where the spaceship (it's always a spaceship) is coming straight towards you at as near the speed of light as our special effects budget can manage.
The Klingon in said spaceship now turns on his far Ultraviolet laser.
The question you have to answer- and very, very quickly-is, are you going to get x-rayed, or does it just seem like it?
 
Unfortunately, bad examples are often used to teach the ideas of Special Relativity to children and to general audiences. I've seem them used in science museums and even in some generally very well done science documentaries (including, IIRC, Bronowski's The Ascent of Man). What happens is in order to get the across the basic idea that time and distance are altered in different reference frames, examples are used that get the details completely wrong. While this may be okay for audiences who will never inquire further, those who do later look into the concepts in more detail have to unlearn the examples.

The particular bad example I'm thinking of is the "trolley speeding away from the clock" thought experiment. The way it's described, the clock seems to the observer on the trolley to be moving more slowly the faster the trolley goes, because of the delay of the light from the clock reaching the observer. But this, as has been pointed out, isn't really Relativity at work, it's the ordinary Doppler effect. Using it as an example of SR does indeed create the false impression that it's all just an illusion caused by not taking into account the time light takes to travel. Let's call our observer a "naive observer," because he does no adjusting or calculating to allow for the time light from the clock has taken to reach him; he pays attention only to what meets his eye.

That this is not how Relativity works becomes clearer when you consider the opposite case: the trolley is speeding toward the clock. Now, for the same reason that it appeared to be slowing down to the naive observer speeding away, it now appears to be speeding up, due to the same Doppler effect working in the opposite way from before. The Relativistic time dilation effect, by contrast, affects the observed speed of the clock the same way whether the trolley is moving toward it, away from it, or sideways, depending only on the velocity of the trolley relative to the clock.

To be more specific: when the trolley is moving at velocity V toward the clock, the Doppler shift makes the clock appear to be speeding up by a factor of (1 + V/C) disregarding the actual Relativistic effect. That's because in time t, the clock advances by t and the trolley catches up with the light from the clock by an amount t*V/C. So if the trolley is going half the speed of light (V/C = .5), in one second it catches up with the light emitted from the clock half a second earlier, so the observer sees 1.5 seconds counted up on the clock. Since we're disregarding Relativity, we can speed the trolley up to the speed of light, in which case in one second the trolley catches up with the light emitted by the clock 1 second earlier, plus the actual passage of one second, so the naive observer sees two seconds pass on the clock.

The Relativistic time dilation effect, though, slows down the apparent speed of the clock by a factor of the square root of (1 - V^2/C^2). So if the trolley is zooming along at, say, .99 of the speed of light, the Relativistic time dilation makes the clock appear to slow down by a factor of about 0.141. The Doppler shift, as per the formula above, makes it appear to speed up by a factor of 1.99. So in the end, the naive observer sees the clock moving at a rate of 0.281 compared with his own watch -- it's slowed down so much that it even appears slowed down, even though he's moving toward it and catching up with the light from it.

Can others please check my calculations on this? Also, can anyone do the algebra to answer the question: at what speed (other than zero) must the trolley be moving toward the clock to make it appear to the naive observer -- taking into account Relatvity and the normal Doppler effect -- that the clock is running at the normal rate, that is, the same rate as the observer's watch?

Respectfully,
Myriad

ETA: By trial and error, the velocity at which the clock appears normal to the naive observer is between .839 and .840 of the speed o' light. To figure it exactly, it's the solution to v3 + 2v2 - 2 = 0
 
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Thanks for all the posts. Unfortunately I don’t have time to reply right now and will be travelling for most of this week. I will print out the thread and read it while I’m away as I won’t have much, if any, time to access the internet. I don’t know why I’m having so much trouble understanding what seems easy for others. Don’t think I have a mental block, but perhaps I have. Like Soapy Sam “I assume I’m wrong” The point is that I don’t just want to learn the details and accept them. I want to actually know how it works.
 
While staring at the clock, and stopping it, I thought of something, and maybe some really smart person here will explain why it is a true thought, or a dumb thought.

It might be an already thought of thought, in which case it should be easy to explain.

Using the Doppler effect as an example, helps explain how something can seem different, depending on the observer. A note, or tone, seems different depending on your relative motion. Moving towards it, it sounds higher, moving away, it seems lower. Of course the note is what it is, for the observer who isn't moving.

So an event is different depending on the frame of reference, for the observer, or a recording device.

But that isn't the case for time? It isn't the Doppler effect causing time to change? I'm asking here. Because that is what I am understanding.

Also, according to that really cool page about the GPS situation, gravity causes time to change as well. So clocks, (time), runs different depending on gravity. Right?

OK I gotta tell you, that sounds woo. It sounded woo thirty years ago when I first heard about it as well.

In fact, that whole relativity/observer situation sounds woo. More woo than woo.

So, here is the thought, looking at a clock, moving away from it, say a really big clock, so you can still see it, moving away from it, time slows down, according to the clock you are looking at. But this isn't because of the light, but some other effect? Is that right?

The clock on the spaceship is running the same as the other clock, but according to the stationary clock, it is running slower? So the stationary clock, the one you are racing away from, appears to run slower, or faster?

Or is it running faster, but looks like it is slower? Or is it the return journey that causes the change? Or both? Moving away really fast, then moving back really fast, they both cause time changes?

Do they balance out? Or is all movement causing your on board clock to run slower? Does any movement change time, making your clock on the spaceship run slower, relatively speaking?




And then my head explodes...
 
So, here is the thought, looking at a clock, moving away from it, say a really big clock, so you can still see it, moving away from it, time slows down, according to the clock you are looking at. But this isn't because of the light, but some other effect? Is that right?
No. To you while moving away from the big clock the big clock is what appears to slow down. To someone at the big clock your clock appears to slow down. Seems perfectly symmetrical as if an illusion and should cancel each other out. So how do you check to see who is right. You accelerate back to the big clock and see that the big clock was right and your clock was slower. However if the big clock fires its engines and come to you then you will be right and the big clock will have been slower. What breaks the symmetry is acceleration. Observers can disagree on who is moving and who is at rest. However all observers can agree on who is accelerating (just not by how much) and this breaks the symmetry and leads to the clock differences.

The clock on the spaceship is running the same as the other clock, but according to the stationary clock, it is running slower? So the stationary clock, the one you are racing away from, appears to run slower, or faster?
The thing to remember here is that to you you are stationary and the clock is moving away from you. To the clock it is stationary and you are moving away from it. As long as neither is accelerating you can both be at rest even though the distance between you is increasing. You both say the other is doing the moving.

Or is it running faster, but looks like it is slower? Or is it the return journey that causes the change? Or both? Moving away really fast, then moving back really fast, they both cause time changes?
Yes it is the return journey or more specifically the acceleration required for the return journey. It doesn't matter if it's a little acceleration for a long time or a lot for a little time it comes out the same.

Do they balance out? Or is all movement causing your on board clock to run slower? Does any movement change time, making your clock on the spaceship run slower, relatively speaking?
Yes they do balance out until acceleration enters the picture. Yes all relative movement leads to changes is clock rates. Note also that any change in the direction of motion is also an acceleration. Slowing down is the same thing as going faster in the other direction.
 
Thanks for all the posts. Unfortunately I don’t have time to reply right now and will be travelling for most of this week. I will print out the thread and read it while I’m away as I won’t have much, if any, time to access the internet. I don’t know why I’m having so much trouble understanding what seems easy for others. Don’t think I have a mental block, but perhaps I have. Like Soapy Sam “I assume I’m wrong” The point is that I don’t just want to learn the details and accept them. I want to actually know how it works.


Laudable aim. When you're happy you do, please explain it to me.:)
 
No. To you while moving away from the big clock the big clock is what appears to slow down. To someone at the big clock your clock appears to slow down. Seems perfectly symmetrical as if an illusion and should cancel each other out. So how do you check to see who is right. You accelerate back to the big clock and see that the big clock was right and your clock was slower. However if the big clock fires its engines and come to you then you will be right and the big clock will have been slower. What breaks the symmetry is acceleration.
I just want to add that this stuff is very difficult to understand, maybe even impossible to understand, without the aid of space-time diagrams. This thing with two clocks that are moved away from each other and then brought together again is called "the twin paradox". There are of course no real paradoxes in special relativity. They only seem to be paradoxes to people who don't understand them. And of all the so called "paradoxes" that I've heard about, the twin paradox is probably the most difficult one to understand.

I can't imagine any other way to understand it than to learn how to draw space-time diagrams, and see how in this case, the lines of simultaneity gets tilted one way as the clock/twin moves away and then the other way as it/he/she comes back.

One more thing (this one for my_wan): You started your reply with the word "no", but robinson didn't say anything wrong in the text you quoted before the reply. In particular, he was quite right when he said: "But this isn't because of the light, but some other effect? Is that right?". (The rest of your post was fine).

Robinson, you were right about that. The "other effect" is that different observers disagree about which events are simultaneous, and that's caused by the existence of a universal speed, one that is the same in all frames. We call it the "speed of light" because light just happens to be traveling at that speed.
 
Yes I have, and I understand how it would work if Relativity works. I’m just not sure that it does.
"You are entitled to your opinion, but not your facts" - Back at you :D

Really got to go to bed now - Byeee
Ah, but it DOES work that way.

There have been experiments done in which a clock (extremely accurate atomic clock) is taken on an airplane trip while an identical (as identical as humanly possible) clock stays home.

There are basically two effects that were accounted for in doing those experiments:
1. Time speeds up closer to a large mass (the higher above the earth's surface, the slower your clock.)
2. Time slow down at higher speeds. (Travel fast and your clock slows down.)

The experimenters calculated both effects according to relativity and the recorded flight data (altitude and speed.) The sum of the two matched to within the accuracy of the actual change measured. That is, when the traveling clock returned home, less time had passed for it than for its twin. That difference was (as closely as could be measured) identical with the difference predicted by relativity.

They've also done the obvious: Just altitude and just speed. Both work out as realtivity says.

I watched a documentary on these experiments on TV a few months ago. The altitude experiment was done by carting an atomic clock to the top of the highest mountain in Germany. (German experiment, shown on German public TV, though the experiment was not carried out for TV.)
 

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