Why Is Time Dilation Considered a Real Phenomenon?

[mariusmyburg]

Good day. I have read many books, forums, and articles, and watched many youtube videos, all in an effort to understand special relativity and time dilation. Or rather, more precisely, trying to find a valid explanation that does not result in contradictions and paradoxes, and if it does, one that explains why the theory is nevertheless correct, i.e. gives an intellectually acceptable explanation.

I have never found this. So I asked prominent physicists - and never received any reply.

That is why I am here. I would like to ask some questions to anyone who believes that he understands enough of the fundamental theory of time dilation and special relativity. Surely, someone must be able to answer a few questions and finally help me understand how this is not ridiculous and paradoxical. I WANT to learn, I want to understand. But I cannot and will not just accept any claim as if it were gospel, if some serious questions cannot be answered.

And so, I want to please start by asking for a brief explanation of why anyone thinks that time dilation is real. You are welcome to provide either a purely theoretical explanation like a thought experiment, or links to peer-reviewed actual experiments that prove that time dilation is in fact real. Just saying 'otherwise satellites would not work' is not an adequate answer, I would need you to explain exactly why that is the case.

So perhaps it would be easiest if we start with the thought-experiments that Einstein apparently did, to come to his conclusions. Would anyone mind explaining the fundamental thought experiment to me, and explaining the conclusion?

Thank you,
Marius.

 

[PeroK]

If you start with some basic assumptions about space and time (that they are in some sense "the same everywhere"), then you can show that there are two main possibilities:

1) Newtonian space and time.

2) Special Relativity (SR).

There is no way, theoretically, to decide which one applies in our universe. So, you go out and do an experiment to see which one it is.

Note that the crux of SR is the relativistic theory of energy and momentum. A key experiment is to build a particle accelerator (like CERN) and see whether you can accelerate particles beyond the speed of light:

If 1) Newtonian physics were right, then CERN would be able to accelerate particles to many times the speed of light. It can't and the lightspeed limit applies. So, it must be SR.

Time dilation itself is a bit of a sideshow.

 

[Dale]

But I cannot and will not just accept any claim as if it were gospel

So on what specific basis will you accept claims?

 

[phinds]

And so, I want to please start by asking for a brief explanation of why anyone thinks that time dilation is real.

A serious question here is how you define "real". For example, time dilation never happens to you, so is it real? *I* see you as time dilated if I'm moving relative to you. Does that make it "real"?

GPS won't work without taking it into consideration. Does that make it "real"?

 

[mariusmyburg]

So on what specific basis will you accept claims?

Claims that have both experimental evidence and that makes logical sense are best. Claims for which experimental evidence may still be lacking but which makes logical sense comes a close second.

 

[mfb]

Wikipedia has a full article dedicated to experimental tests, all with references of course: https://en.wikipedia.org/wiki/Tests_of_special_relativity
All the predictions it makes have been tested many times, typically with extreme precision.

Special relativity is consistent, there are no contradictions. It's just not very intuitive, so if you try to apply intuition from everyday life then you are going to fail.

 

[phinds]

Claims that have both experimental evidence and that makes logical sense are best.

"Logical sense" is subjective. We humans evolved over an incredible narrow range of experience in terms of speed and gravity. LOTS of stuff in cosmology and quantum mechanics doesn't "make sense" or fit our "intuition" about what should be real.

EDIT: I see mfb beat me to it.

 

[mariusmyburg]

A serious question here is how you define "real". For example, time dilation never happens to you, so is it real? *I* see you as time dilated if I'm moving relative to you. Does that make it "real"?

GPS won't work without taking it into consideration. Does that make it "real"?

Can you please explain exactly why GPS won't work?

 

[phinds]

Can you please explain exactly why GPS won't work?

Because time dilation is real and if you pretend that the clocks on the satellites keep exactly the same time as the clocks on the ground (which is what would happen if there were no time dilation) then you would end up driving into corn fields and the sides of buildings. The synchronization between ground and satellite that figures out the triangulation that says where you are depends on the reality of time dilation, both due to speed and due to gravity.

GPS satellites need to account for -7 microseconds/day due to SR (motion) and +45 microseconds/day due to GR (gravity):

 

[jbriggs444]

help me understand how this is not ridiculous and paradoxical.

Special relativity is self-consistent. It has no paradoxes. Any apparent paradoxes that arise come from some hidden background assumptions that you bring into the argument without thinking about them.

The key assumption that trips almost everyone up is the idea that the universe is split up into three pieces: the certain past, the unknown future and the infinitesimally thin dividing line between them that we call "now".

But if there is no communication beyond the speed of light, then synchronization procedures become interesting. The notion of "now" becomes ambiguous. Clock synchronization can be a function of one's state of motion. In particular, this allows for two relatively moving people to both claim that the other's wristwatch is running slow without any possible experiment being able to prove that either of them is wrong.

 

[mariusmyburg]

"Logical sense" is subjective. We humans evolved over an incredible narrow range of experience in terms of speed and gravity. LOTS of stuff in cosmology and quantum mechanics doesn't "make sense" or fit our "intuition" about what should be real.

EDIT: I see mfb beat me to it.

You actually do perhaps hit the crux of the matter here. "Logical sense" is subjective. Perhaps that is true. But I cannot agree that the possibility of that being true, means that we are impelled in any way to discard our logical sense. In fact, it is forever all we have. If some experimental result shows us that 1 equals 2, then surely, it never ever becomes OK for us to accept that 1 = 2. The best we can ever say, is that we don't know what is going on. But we must always try to make sense of the world, and never be content with "sense not being there" for any of the things we say. Don't you agree?

Can I ask a question? Let's take the thought experiment of the man in the train, traveling near the speed of light. The man in the train is at the middle of the train. As he passes someone standing on the outside, the instant he is exactly aligned with that person, two bolts of lightning strike at the ends of the train.

The man on the outside will see the light from the lightning strikes reach him at the same time. And the man in the train, will first see the light from the front lightning hit, because he has traveled closer to it, and then from the back of the train.

All good so far. But now, here is where things become ridiculous. Because, as far as I can tell, people say that the speed of the light from the front lightning strike, and the speed of the light from the back lightning strike, must be the same for the man in the train, because the speed of light is always constant, no matter the observer's own speed. And because he is in the middle of the train, i.e. equidistant from the two strikes, it means that what actually happened, for him,was that the two lightning strikes did NOT happen simultaneously, that the front lightning hit first.

Now, I do not think logical sense is at all subjective in this case. It is clear that the statement that the speed of light is constant for all observers, is obviously what makes this conclusion of something simultaneous not being simultaneous for another observer, possible.

And I have a serious issue with simply accepting something like 'if there are two observers, the speed of the observed light will simultaneously have two velocities - and both velocities will be c'. It won't have three velocities, because there are not three observers. But it suddenly acquires another velocity when a third observer now looks at the light. Moreover, no matter what the other two velocities are and no matter how fast this third observer travels, he will also measure the speed of light as c. And, because he is traveling possibly at or near the speed of light, the light he is viewing may be well beyond Mars, while for another observer it has barely left Earth.

And they say this is all true, that the light is in reality, both past Mars and not past Mars.

To me, this is a very clear 1 = 2 situation. Why then, is it OK in physics, while in any other field like Mathematics it would be proof that our thinking is flawed?

How it is ever OK for a paradox, a contradiction, to be an accepted theory, touted as being very real?

Or do I misunderstand this thought experiment and the conclusions that have been drawn from it? I would be delighted to learn that that is the case. Because here is my opinion - whether or not logical sense is subjective (which I don't think it is), it is all that we can and must base our understanding on. And for as long as our logical sense makes no sense (pun intended) - there is no understanding whatsoever, and conclusions drawn from such non-understanding are all unlikely to be true.

 

[jbriggs444]

The train experiment is intended to force you to discard your background assumption that simultaneity is absolute. If you refuse to discard that assumption but accept the experimental fact that the speed of light is always c regardless of an observer's state of motion, the experiment will seem paradoxical.

 

[phinds]

If you travel towards me at 1/2 c and shine a flashlight at me, I see the light beam blue-shifted but traveling at c. If you are moving away from me, I see the light beam red shifted but traveling at c. You also see the flashlight beam traveling at c regardless of your direction of motion.

If you don't like the way the universe works, then in the words of Richard Feynman, go find some other universe.

 

[mariusmyburg]

Special relativity is self-consistent. It has no paradoxes. Any apparent paradoxes that arise come from some hidden background assumptions that you bring into the argument without thinking about them.

The key assumption that trips almost everyone up is the idea that the universe is split up into three pieces: the certain past, the unknown future and the infinitesimally thin dividing line between them that we call "now".

But if there is no communication beyond the speed of light, then synchronization procedures become interesting. The notion of "now" becomes ambiguous. Clock synchronization can be a function of one's state of motion. In particular, this allows for two relatively moving people to both claim that the other's wristwatch is running slow without any possible experiment being able to prove that either of them is wrong.

Why it is said that "two relatively moving people to both claim that the other's wristwatch is running slow without any possible experiment being able to prove that either of them is wrong"? More importantly, I'd take out the issue of difficulties in measuring something - that is our problems as engineers and has nothing to do with reality - so I'd ask, why is it said that time passes differently for two relatively moving people? Is there a logically consistent thought experiment to show that this is the case?

 

[jbriggs444]

Why it is said that "two relatively moving people to both claim that the other's wristwatch is running slow without any possible experiment being able to prove that either of them is wrong"? More importantly, I'd take out the issue of difficulties in measuring something - that is our problems as engineers and has nothing to do with reality - so I'd ask, why is it said that time passes differently for two relatively moving people? Is there a logically consistent thought experiment to show that this is the case?

Special relativity is a logically consistent thought experiment that shows that this can be the case. You are not going to find a thought experiment to prove that it is in fact the case. For that you need a body of real experiments.

If you have a speed limit on communications, how are you going to synchronize two clocks at a distance from one another?

 

[mariusmyburg]

If you travel towards me at 1/2 c and shine a flashlight at me, I see the light beam blue-shifted but traveling at c. If you are moving away from me, I see the light beam red shifted but traveling at c. You also see the flashlight beam traveling at c regardless of your direction of motion.

Yes, this is the core of the whole relativity theory as far as I understand it. This is the statement that is made. But to me, this statement is paradoxical. Because if you imagine one bean, and two observers, both looking at that beam, one observer traveling at 1/2 c and another traveling at 3/4 c, then, I believe, it is said that they will both see that light traveling at c. And in this journey, let's say to Mars, one observer will reach Mars before the other, and one observer will reach Mars with that one light beam reaching Mars slightly before him. While at the same time, for the other observer, neither he nor the (same) light beam has reached Mars yet.

Can you please explain that to me? How is that not a logical inconsistency?

 

[mariusmyburg]

Special relativity is a logically consistent thought experiment that shows that this can be the case. You are not going to find a thought experiment to prove that it is in fact the case. For that you need a body of real experiments.

If you have a speed limit on communications, how are you going to synchronize two clocks at a distance from one another?

I understand that, and I respect that as an answer. But, because it simply makes no sense, because in fact it results in logical contradictions, is it acceptable? I know what I am asking is "is physical proof more acceptable than logical understanding" and that many may say yes, it absolutely is. But is it really, though? If we cannot for the life of us, understand something, if it is full of logical contradictions and paradoxes - it is OK to just say "Oh well, the experiment shows it is so"?

 

[jbriggs444]

Yes, this is the core of the whole relativity theory as far as I understand it. This is the statement that is made. But to me, this statement is paradoxical. Because if you imagine one bean, and two observers, both looking at that beam, one observer traveling at 1/2 c and another traveling at 3/4 c, then, I believe, it is said that they will both see that light traveling at c. And in this journey, let's say to Mars, one observer will reach Mars before the other, and one observer will reach Mars with that one light beam reaching Mars slightly before him. While at the same time, for the other observer, neither he nor the (same) light beam has reached Mars yet.

Can you please explain that to me? How is that not a logical inconsistency?

What logical inconsistency do you imagine. What experimental result do you see two different predictions for?

Possibly we are talking about different scenarios. If the two astronauts and the light pulse (not a light beam) are launched at the same place and time (as I imagine) then everyone agrees that the light arrives before either astronaut. Please provide the detailed reasoning that shows that the light arrives after one of them.

 

[mariusmyburg]

Because time dilation is real and if you pretend that the clocks on the satellites keep exactly the same time as the clocks on the ground (which is what would happen if there were no time dilation) then you would end up driving into corn fields and the sides of buildings. The synchronization between ground and satellite that figures out the triangulation that says where you are depends on the reality of time dilation, both due to speed and due to gravity.

GPS satellites need to account for -7 microseconds/day due to SR (motion) and +45 microseconds/day due to GR (gravity):

As I replied to jbriggs444, I will reply the same to you.

I understand that, and I respect that as an answer. But, because it simply makes no sense, because in fact it results in logical contradictions, is it acceptable? I know what I am asking is "is physical proof more acceptable than logical understanding" and that many may say yes, it absolutely is. But is it really, though? If we cannot for the life of us, understand something, if it is full of logical contradictions and paradoxes - it is OK to just say "Oh well, the experiment shows it is so"?

I could accept this 'conclusion from measurement'... partially. If we measure something time and time again, then we have to maybe accept it is real.

But still... I don't think I can call myself an intellectual, a thinking person, if I let what I measure completely and utterly override what I think as being logical. Surely we have to understand something, and we have to resolve paradoxes, before we can say that a given theory is true?

I am not qualified to doubt that satellites does show clocks behaving differently than clocks on Earth. Maybe they do. But can we call ourselves logical thinking beings, if we take the knowledge of these differences of the clocks to support ideas that results in logical inconsistencies? Should we let ourselves then conclude that, while it makes no sense, it is proof that a single photon may both be at a certain position and not be at that position yet, simultaneously?

I do not think we can, and that is why I am looking for an explanation that will give me that insight to convince me that special relativity does make sense and that it is not illogical.

 

[mfb]

And because he is in the middle of the train, i.e. equidistant from the two strikes, it means that what actually happened, for him,was that the two lightning strikes did NOT happen simultaneously, that the front lightning hit first.

Correct so far.

And I have a serious issue with simply accepting something like 'if there are two observers, the speed of the observed light will simultaneously have two velocities - and both velocities will be c'. It won't have three velocities, because there are not three observers. But it suddenly acquires another velocity when a third observer now looks at the light. Moreover, no matter what the other two velocities are and no matter how fast this third observer travels, he will also measure the speed of light as c. And, because he is traveling possibly at or near the speed of light, the light he is viewing may be well beyond Mars, while for another observer it has barely left Earth.

Light travels at the speed of light, for all observers. That's a single speed. It doesn't matter how many observers are where.

And they say this is all true, that the light is in reality, both past Mars and not past Mars.

For different observers who are not at Mars? Yes, that can happen. So what? That's just relativity of simultaneity again. Instead of asking where light is you can also ask if the Mars rover landed already or not, or if a lightning bolt has impacted the train already or not. Different observers have a different definition of what's "now".

But, because it simply makes no sense

It makes sense, it's just against intuition from everyday life.

because in fact it results in logical contradictions

It does not. Different observers disagreeing on what is "now" is not a logical contradiction, just like different observers measuring a different speed for a car is not a contradiction either.

 

[phinds]

@mariusmyburg, at this point it really is beginning to seem that you are just trolling us. You have put forth the same argument ("IT'S NOT LOGICAL TO ME !") repeatedly and pointlessly. Yep, we all get that it's not logical to you. Get over it. Try to figure out why it IS logical instead of just repeating over and over that you don't think it's logical.

 

[vela]

Can you please explain that to me? How is that not a logical inconsistency?

@jbriggs444 pointed out the problem in posts #10 and #12.

You don't use logic in a vacuum. You always start with assumptions and see where they lead. Paradoxes often arise in SR when you reach a logically valid conclusion but refuse to accept it because it doesn't square with your intuition.

When you say some result of SR doesn't make logical sense, what you mean is some conclusion doesn't fit in with your intuition, but your intuition is based on many assumptions that you've incorporated over the years based on everyday experiences. Some of these assumptions, however, are no longer valid in the regime of special relativity. It takes practice to unlearn these hidden assumptions.

 

[PeroK]

I do not think we can, and that is why I am looking for an explanation that will give me that insight to convince me that special relativity does make sense and that it is not illogical.

There's no such explanation. Only hard graft on your part. That's the deal when it comes to anything really: you either trust those who have studied something or roll your sleeves up and learn the subject for yourself.

There's nothing to be gained from arguing whether SR is "logical" or not. To flat-Earthers the spherical Earth is absurd and illogical. Maybe it is "illogical". But, the Earth is a sphere nevertheless.

 

[mariusmyburg]

@mariusmyburg, at this point it really is beginning to seem that you are just trolling us. You have put forth the same argument ("IT'S NOT LOGICAL TO ME !") repeatedly and pointlessly. Yep, we all get that it's not logical to you. Get over it. Try to figure out why it IS logical instead of just repeating over and over that you don't think it's logical.

@phinds OK I am stupified by why you feel compelled to start being rude to me. This will be my last communication to you, as I am not at all interested in this kind of behavior, and I value kindness and good manners. I don't see why it is so bloody wrong for someone to express that a theory and even an observation that seems to contradict logic, is probably not a valid theory. How you equate this to me trolling anyone, and how you think you have the bloody right to start being rude to me, is beyond me. I was hoping for friendly, open-minded discussion. Life is so damn hard, the least we can do it try to be friendly towards one another. It is not even about being friendly, just having basic decency. Of all places, I would have expected an intellectual gathering place like this to be free from people like you. Work on your manners, rude little man.

Thank you to those who tried to help. I will be closing my account now, since I was hoping for intellectual engagement, not personal attacks.

Goodbye.

 

[weirdoguy]

I don't see why it is so bloody wrong for someone to express that a theory and even an observation that seems to contradict logic, is probably not a valid theory.

Because you have no basis to claim such things. You don't go to the doctor and say he's doing something wrong, or there is something wrong with medical science, do you? So why you say such things to physicists? If you don't understand something, ask about it, don't say it's wrong or not valid.

 

[jbriggs444]

Thank you to those who tried to help. I will be closing my account now, since I was hoping for intellectual engagement, not personal attacks.

Disappointing, but not unexpected. I think we were all trying to assist with an understanding. But some express more bluntly than others the truth:

"It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so."

 

[PeterDonis]

Claims that have both experimental evidence and that makes logical sense are best. Claims for which experimental evidence may still be lacking but which makes logical sense comes a close second.

What about claims which have mountains of experimental evidence confirming them but which don't make logical sense to you? That appears to be the category into which relativity falls. Your apparent strategy is to either ignore or disbelieve the mountains of experimental evidence if no explanation can be given that seems logical to you. I think you will find that this is not a good strategy.

I don't see why it is so bloody wrong for someone to express that a theory and even an observation that seems to contradict logic, is probably not a valid theory.

That's not what you're expressing. You're expressing that a theory which has mountains of observations and controlled experiments extending over many decades that confirm it (not just "an observation") that seems to contradict logic, is probably not a valid theory. And, as I said above, I think you will find that that is not a good strategy.

And if you are already stumped by apparent logical issues with relativity, you won't even want to try quantum mechanics. But technology that relies on QM being correct is much more ubiquitous than technology that relies on relativity being correct. GPS, which has been mentioned already in this thread, is the only common technology I can think of whose workings rely on significant relativistic effects. But, for example, everything to do with computers, which are in practically everything these days, relies on QM being correct. In fact, the very existence of atoms relies on QM being correct.

 

[phinds]

@phinds OK I am stupified by why you feel compelled to start being rude to me.

No rudeness was intended, just being factual. You'll get that a lot here of PF. We don't attack people, we attack ideas and you KEEP putting forth an incorrect idea regardless of how much help people try to give you.

 

[Janus]

Yes, this is the core of the whole relativity theory as far as I understand it. This is the statement that is made. But to me, this statement is paradoxical. Because if you imagine one bean, and two observers, both looking at that beam, one observer traveling at 1/2 c and another traveling at 3/4 c, then, I believe, it is said that they will both see that light traveling at c. And in this journey, let's say to Mars, one observer will reach Mars before the other, and one observer will reach Mars with that one light beam reaching Mars slightly before him. While at the same time, for the other observer, neither he nor the (same) light beam has reached Mars yet.

Can you please explain that to me? How is that not a logical inconsistency?

Let's clarify this a bit:
Observer A travels at 0.5 c relative to the Earth.
Observer B travels at 0.75 c relative to the Earth.
both observers and the light beam leave Earth together.
We will assume that Mar's, at this time is 10 light min from the Earth ( as measured from the Earth.)
We also assume that there is a clock on Mars synchronized to the Earth clock in the Earth-Mars rest frame.

Both observers and beam leave Earth when the Earth clock read 12:00

According to someone that remains at rest with respect to Earth and Mars:
The beam arrives at Mars in ten minutes, when the Clock on Mars reads 12:10:00
Observer B arrives at Mars in 13 min 20 sec, when Mars clock reads 12:13:20
Obeserver A arrives at Mars in 20 min, when the Mars clock reads 12:20:00

According to Observer A:
The Earth Mars distance undergoes length contraction and is 8.66 light minutes
The Mars clock, due to Relativity of simultaneity already reads 12:05:00 when A leaves Earth.
The light beam travels at c towards Mars, while Mars travels at 0.5 c towards A.
Thus it takes 8.66/(1.5) = ~05.77 minutes for the light and Mars to meet.
During which time, the Mars clock is time dilated and ticks off 0.866*~.577 = 5 min and reads 12:05:00 + 00:05:00 = 12:10 when the light arrives.
Observer B has a speed of (0.75c- 0.5c)/(1-0.75c(0.5c)/c^2)* = 0.4 c relative to observer A
Thus Observer B takes 8.66/(1.4) = ~9.62 min to meet up with Mars. During which time the time dilated Mars clock ticks off 8.33 min and reads 12:05:00 + 00:08:20 = 12:13:20 when B arrives.
Observer A takes 17.32 minutes to meet up with Mars, during which time the Time dilated Mars clock ticks off 15 mins to read 12:20:00 on arrival.

According to observer B:
The Earth - Mars distance is contracted to ~6.614 light min.
The Mars clock already reads 12:07:30 as he leaves Earth
The light beam takes (6.614/(1.75) = ~3.78 min to meet up with Mars, during which time the time dilated Mars clock ticks off 0.6614*3.78 = 2.5 min to read 12:07:30 + 00:02:30 = 12:10 when the light arrives.
B himself takes ~8.82 mins to arrive at Mars, and the Mars clock ticks off 5.83 mins during this time to read 12:07:30 + 00:05:50 = 12:13:20 when B arrives.
As far as A is concerned, we have to assume that Observer B continues past Mars in order to avoid any acceleration issues complicating things.
A has a speed of 0.4c relative to B, in the same direction as Mars' velocity with respect to B.
Thus A will take 6.614/(0.75-0.4) = ~ 18.9 min to reach Mars (after B itself has passed by Mars)
The Mars clock will tick off 0.6614* 18.9 = 12.5 min to read 12:07:30 + 00:12:30 = 12:20:00 upon A's arrival.

No contradictions: All three, Earth, A and B agree as to what time the Mars clock reads when either A or B arrives.
You could even go further to show that all three agree as to what times shows on A and B's clocks when they arrive at Mars.

And is what the clocks respectively read as they pass each other that counts as to whether or not there is a "paradox". It doesn't matter that, according to the Earth, A's clock reads 12:06:40 when B reaches Mars, But A claims that his clock reads 12:09:37 when B reaches Mars.

*Velocity addition theorem

 

[Nugatory]

It is clear that the statement that the speed of light is constant for all observers, is obviously what makes this conclusion of something simultaneous not being simultaneous for another observer, possible.

Yes, so we must turn to the question of why we say that the speed of light is constant for all observers. The answer is that we have better than a century of experiments and measurements that support that claim.

 

[russ_watters]

And so, I want to please start by asking for a brief explanation of why anyone thinks that time dilation is real.

I see a lot of long answers and some irritation, but I haven't read them all, so I don't see if anyone tried the simple answer:

We know time dilation is real because it is observed to happen. It's really that simple.

That's a very different question from asking how or why it happens.

 

[robphy]

What about claims which have mountains of experimental evidence confirming them but which don't make logical sense to you? That appears to be the category into which relativity falls.

Speaking of mountains... Mt. Washington...

Time Dilation : An Experiment With Mu - Mesons (1962)
(D. Frisch and J. Smith)


http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muonex.html
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html#c1(Related and possibly enlightening, but probably not at the appropriate level for the OP,
my calculation and spacetime diagram of the muon experiment
https://physics.stackexchange.com/a/325582/148184 )

This might be more appropriate for the OP:
Bondi's Relativity and Common Sense
https://archive.org/details/relativitycommon0000bond

 

[Sagittarius A-Star]

Can you please explain exactly why GPS won't work?

Please see chapter "2.4.2. Relativistic Corrections" on page 22 and the related appendix F "Brief Derivation of Relativistic Corrections" on page 127 in:
https://www.ptb.de/cms/fileadmin/in...d_frequenz/pdf/Feldmann_2011_Dissertation.pdf

 

[robphy]

This may be useful:
Neil Ashby - Relativity in the Global Positioning System
https://www.aapt.org/doorway/TGRUTalks/Ashby/AshbyTalk1of6.htm
from
AAPT Topical Workshop:
Teaching General Relativity to Undergraduates
Syracuse University, July 20-21, 2006
https://www.aapt.org/doorway/TGRU/

 

[Dale]

Claims that have both experimental evidence and that makes logical sense are best. Claims for which experimental evidence may still be lacking but which makes logical sense comes a close second.

Looks like I missed a bunch of posts somehow.

SR makes logical sense. That is guaranteed by using a coherent mathematical framework. All of relativity boils down to the geometry of spacetime which can be written (globally for SR and locally for GR) as $ds^2=-c^2 dt^2 + dx^2 + dy^2 + dz^2$. Everything about SR can be derived from this one equation, and this equation is just as logical as the Pythagorean theorem. It simply describes the geometry of spacetime.

For your question specifically, time dilation can easily be derived from the above formula. The proper time is given by $c^2 d\tau^2=-ds^2$ and time dilation is $\gamma=\frac{dt}{d\tau}$. A few lines of algebra can derive the usual expression for $\gamma$

SR is also supported by a mountain of experimental evidence. My favorite resource for that is

https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

In particular, see section 4 regarding your specific question on time dilation.

So SR in general and time dilation in specific is both logical and well supported by evidence, thus meeting your stated criteria.

By the way, I completely disagree that logical sense is subjective. If something is logical then it can be mathematically proven. The existence of a mathematical proof is not subjective. This is precisely why the mathematical framework is so important. It avoids the issue that happened here where you confused “makes intuitive sense” with “makes logical sense”. The math guarantees it is logical. The intuition has to be developed.