Time Dilation - Is this a paradox?

[Bjarne]

[PLAIN]http://www.science27.com/forum/rocketL2.jpg


Above the head of observer “A” a mother-ship is moving east 100,000 km/s. and right above the Earth it is launching a small spacecraft moving west with the same speed (100,000 km/s).

REFERENCE FRAME A
Observer “A” would now (from his reference frame) see spacecraft “B” hanging just above his head.
And he would see the mother-ship “C” continues towards East - 100,000 km/s
(We’ll assume the Earth did not have any gravity and will not pull spacecraft “B” down on the Earth).


REFERENCE FRAME C
The Mothership “C” continues moving east 100,000 km/s seen from reference frame “A”
The captain onboard in reference frame “C” agree with observer “A” that his clock (in reference “C”) must tick slower than the clock on Earth (reference frame “A”). .
The captain (“C”) is sure that the spacecraft he had launched right above the Earth was really moving with the speed 100,000 km/s east, relative to his reference frame “C”.
So he certainly expect that the clock on board spacecraft “B” must tick slower as his own.
This mean seen from the reference frame “C” - Captain “B” must have the slowest ticking clock, (and hence both slower than the clock from reference frame B and C) .
After 1 earth-year captain from reference frame “B” then also must have the shortest beard.
But observer “A” (on the Earth) does not agree. Because he have not observed that the spacecraft “B” have moved relative to him-

After 1 year of observation, observer “A” is sure that the beard of the captain in spacecraft “B” must have the same length as his own, - because the clock in spacecraft “B” must tick with the exactly same speed like his own, since from oberser "A's"
reference frame the sapcecraft "B" does not move.

This of course contradict with the way oberserver "C's" must see it, - he is certian that "B" must have the slowes clock and the shortes beard.

Is this a contradiction build into Special Relativity?
Who is wrong , - and why?

 

[Doc Al]

The captain onboard in reference frame “C” agree with observer “A” that his clock (in reference “C”) must tick slower than the clock on Earth (reference frame “A”). .

Why would you think that? Frame C observers measure frame A's clocks to run slow. And vice versa.

 

[DaveC426913]

A sees B moving slowly and C moving slowly.
B sees A moving slowly and C moving very slowly.
C sees A moving slowly and A moving very slowly.

[EDIT] This is wrong. Ignore.

 

[Doc Al]

A sees B moving slowly and C moving slowly.
B sees A moving slowly and C moving very slowly.
C sees A moving slowly and A moving very slowly.

If I read the OP correctly, A and B are at rest with respect to each other, while C moves at 100,000 km/s with respect to A and B. Did you interpret it differently?

 

[DaveC426913]

If I read the OP correctly, A and B are at rest with respect to each other, while C moves at 100,000 km/s with respect to A and B. Did you interpret it differently?

Then I'm completely confused.

Why introduce a rocket seeming to travel 100,000km/s West if that's not what you're demonstrating?

Could we simplify the scenario for the OP?

 

[Doc Al]

Then I'm completely confused.

Why introduce a rocket seeming to travel 100,000km/s West if that's not what you're demonstrating?

Since that rocket traveling west (B) is launched from the mother ship (C), I assume that its speed is given with respect to the mother ship. Making its speed with respect to A exactly zero.

Could we simplify the scenario for the OP?

I have no idea what the OP is trying to demonstrate.

 

[DaveC426913]

One thing that the OP could do to simplify his scenario is ... OK two things ...

1] Label the diagram. What exactly is moving, how fast, and in what direction, and from whose reference frame? (Specifically, the missile's movement).

2] Stop having his participants try to second-guess what everyone else should be seeing. C looks out his porthole and observes X, A looks and observes Y. A should not be guessing what C might experience.

 

[DaveC426913]

The scenario is much simpler than the the OP gets into.

A and B are stationary with respect to each other, as agreed by all observers.

C sees A and B moving slowly.
A sees C moving slowly, B is normal.
B sees C moving slowly, A is normal.

 

[Doc Al]

The scenario is much simpler than the the OP gets into.

A and B are stationary with respect to each other, as agreed by all observers.

C sees A and B moving slowly.
A sees C moving slowly, B is normal.
B sees C moving slowly, A is normal.

When you say 'C sees A and B moving slowly', I think you mean 'C sees A and B clocks running slowly'. Right? (C sees A and B moving quickly--at 100,000 km/s. )

 

[DaveC426913]

When you say 'C sees A and B moving slowly', I think you mean 'C sees A and B clocks running slowly'. Right? (C sees A and B moving quickly--at 100,000 km/s. )

Yeah. Sloppy.

 

[Bjarne]

[PLAIN]http://www.science27.com/forum/rocketL2.jpg

If I read the OP correctly, A and B are at rest with respect to each other

Correct

Since that rocket traveling west (B) is launched from the mother ship (C), I assume that its speed is given with respect to the mother ship. Making its speed with respect to A exactly zero.

Correct

A and B are stationary with respect to each other, as agreed by all observers.

No
“C” is moving in empty space, he have no reference points at all, - everything is completely dark, he even don’t know whether he is moving or not.
He did not see the Earth at the time he was launching the spacecraft “B”, - so he don’t know it exists.
All he know is that he have launched a small space craft; “B” and the speed is 100,000 km/s away from him.
It was a coincidence that he launched right above the Earth.

The small spacecraft “B” is moving away from “C” with 100,000 km/s
Observer “C” have measured that, and used 5 ton to rocket fuel to do it, so it is real, he is sure.

According to SR, “C” now expect that the beard of captain “B” will crow slower (let’s say) 10 times slower as his.
After a certain time; - Observer “C” knows his beard is 10 cm.
According to SR he can easy calculate that then observer “B” must have only 1 cm beard (at the same time) due to the fast speed relative to him.
Now observer “C” send a message to observer “B” just to be sure if he understood Special Relativity correct.
The measure is ; Observer “B” is it correct you beard is only 1 cm ?
But “B” is sleeping and don’t answer. - Anyway “C” expects the beard of “B” to be only 1 cm. (only 10% of his own)

“A” has heard the message from “C” to “B”.
He has also not shaved himself since “C” had launch “B” just above his head.
“A’s” beard is now 1 meter long, - and the spacecraft “B” still just “hanging” above his head.
Seen from “A's” reference frame “B” have not moved at all (1 year) .
Hence observer “B” most also have the same beard length (1 meter long) so like “A” have. .(since "A" is sharing his ref-frame)

So the paradox is now that;
“A” is relative to “B” in rest, - hence A+B must also share the beard grow. (1 meter)
“B“ is relative to “C” is moving 100,000 km/s
(C know that it is really “B” that as moving away from him, - because he have used 5 ton rocket fuel to accelerate “B” op to 100,000 km/s)
Therefore because “C’s” beard is 10 cm. (after a certain time) “B’s” beard must be only 1 cm.

Both “A” and “C” cannot be right.
“B’s” beard cannot at the same time be 1 cm and 100 cm.

It will off course take some time to transmit the communication between difference reference frames, - we assumes that time already is counteracted.

So Either “A” or “C” must be wrong.

So who is the stupid one; - “A” or “C”
We cannot ask “B” to measure, - he is still sleeping (probably drunk) .

 

[nrqed]

Two comments about the very first post (before I read all the posts)

First, in relativity problems, always always always specify with respect to what frame velocities, lengths and times are measured. Otherwise, the questions are ambiguous (and annoying).

Second: People in C do NOT say that their clock (in C) is running slower than the clocks in A! People in C observe the clocks in A to run slow relative to their own clocks!

 

[nrqed]

[PLAIN]http://www.science27.com/forum/rocketL2.jpg

Correct

Correct



No
“C” is moving in empty space, he have no reference points at all, - everything is completely dark, he even don’t know whether he is moving or not.
.

It does not matter if C looks at A and B or not. What the previous poster said was right: according to all frames A and B are at rest relative to one another. That's a fact. I don't know if this has any relevance to the rest of your post but I wanted to point that out.

 

[nrqed]

“A” has heard the message from “C” to “B”.
He has also not shaved himself since “C” had launch “B” just above his head.
“A’s” beard is now 1 meter long, - and the spacecraft “B” still just “hanging” above his head.
Seen from “A” reference frame “B” have not moved at all (1 year) .
Hence observer “B” most also at the same beard length (1 meter long) so like “A” have. .(since "A" is sharing his ref-frame)

You have to be very precise in relativity about the events you are using. By "now" I assume you mean at the instant B is sending his signal??

Why do you say that A's beard is 1 meter long? It is not 1 meter long at the instant C sends his signal. It is 10 cm long!

 

[Bjarne]

according to all frames A and B are at rest relative to one another.

"C" don't know this
He don't know that "A" exsist, only that "B" exsist and that "B" is moving away from him.
"C" even don't know his own speed.
Hence he must believe that´"B's" bear grow is slower than his own.

What the previous poster said was right: according to all frames A and B are at rest relative to one another

Right
This is how it looks from "A" ref-frame, but not seen from "C" ref-frame.
We must know who have done the wrong observation "A" or "C" ?
Both cannot be right

 

[nrqed]

"C" don't know this
He don't know that "A" exsist, only that "B" exsist and that "B" is moving away from him.
"C" even don't know his own speed.
Hence he must believe that´"B's" bear grow is slower than his own.

Ok, but since we are talking about physics, what matters is what would be observed if it was measured, it does not matter whether the measurement is made or not (as long as we are not discussing quantum physics). When people say that according to all frames B and A are at rest relative to one another, they mean that if one would make the measurement from any frame, they would observe that fact. We don't care if the measurement is made or not so it's a moot point that B does not know about A.

Right
This is how it looks from "A" ref-frame, but not seen from "C" ref-frame.
We must know who have done the wrong observation "A" or "C" ?
Both cannot be right

Yes, this is is how it is from C's frame also! Why do you think it's not the case??
If local observers in C would look at the beard of someone in A at the instant the signal from C is sent, they would observe the beard of the man in A to be 10 cm long.

 

[Doc Al]

No
“C” is moving in empty space, he have no reference points at all, - everything is completely dark, he even don’t know whether he is moving or not.
He did not see the Earth at the time he was launching the spacecraft “B”, - so he don’t know it exists.
All he know is that he have launched a small space craft; “B” and the speed is 100,000 km/s away from him.
It was a coincidence that he launched right above the Earth.

What C knows or doesn't know is irrelevant. Both A and B are moving with the same speed with respect to C.

The small spacecraft “B” is moving away from “C” with 100,000 km/s
Observer “C” have measured that, and used 5 ton to rocket fuel to do it, so it is real, he is sure.

OK.

According to SR, “C” now expect that the beard of captain “B” will crow slower (let’s say) 10 times slower as his.
After a certain time; - Observer “C” knows his beard is 10 cm.
According to SR he can easy calculate that then observer “B” must have only 1 cm beard (at the same time) due to the fast speed relative to him.

Sure, but 'at the same time' is a frame-dependent concept. Observer B will not agree that his beard was only 1 cm long when C's beard was 10 cm long.

Now observer “C” send a message to observer “B” just to be sure if he understood Special Relativity correct.
The measure is ; Observer “B” is it correct you beard is only 1 cm ?
But “B” is sleeping and don’t answer. - Anyway “C” expects the beard of “B” to be only 1 cm. (only 10% of his own)

Messages that are never read don't matter much, right?

“A” has heard the message from “C” to “B”.
He has also not shaved himself since “C” had launch “B” just above his head.
“A’s” beard is now 1 meter long, - and the spacecraft “B” still just “hanging” above his head.
Seen from “A's” reference frame “B” have not moved at all (1 year) .
Hence observer “B” most also have the same beard length (1 meter long) so like “A” have. .(since "A" is sharing his ref-frame)

Both A and B have the same beard length at any given moment according to all observers.

So the paradox is now that;
“A” is relative to “B” in rest, - hence A+B must also share the beard grow. (1 meter)
“B“ is relative to “C” is moving 100,000 km/s
(C know that it is really “B” that as moving away from him, - because he have used 5 ton rocket fuel to accelerate “B” op to 100,000 km/s)
Therefore because “C’s” beard is 10 cm. (after a certain time) “B’s” beard must be only 1 cm.

Both “A” and “C” cannot be right.
“B’s” beard cannot at the same time be 1 cm and 100 cm.

No paradox. Simultaneity is relative.

It will off course take some time to transmit the communication between difference reference frames, - we assumes that time already is counteracted.

So Either “A” or “C” must be wrong.

So who is the stupid one; - “A” or “C”

Neither. Whoever thinks that A and C cannot both be correct is the one who is wrong.

To define this scenario more precisely--always a good idea in SR--you'd do something like this: At the instant that C passes A (even if he doesn't know that A exists) he sends out ship B. At that instant all of them are clean shaven. (And since they are all at the same place--let's assume right on top of each other--at the same time, that statement makes sense.) In C's frame, his beard grows normally. He of course observes B's beard to grow slowly. (And B observes C's beard to grow slowly.) C thinks that at any moment his beard is longer than B's; and B thinks that at any moment his beard is longer than C's. They are both right. Simultaneity is relative. So what?

 

[Bjarne]

and B thinks that at any moment his beard is longer than C's.

This is a surprise
Why does B think so ?
And how is it possible that it can contradict that also C thinks that at any moment his beard is longer than B's

 

[Doc Al]

This is a surprise
Why does B think so ?

For the same reason that C thinks his beard is longer. It's symmetric.

And how is it possible that it can contradict that also C thinks that at any moment his beard is longer than B's

No contradiction. After all, they both see the other's clocks as running slowly compared to their own. And they both see the other's ship as being contracted.

There would only be a contradiction if they were to meet up later and then disagree as to whose beard were longer. Of course in that case they would both know who accelerated--and one of them would have to have accelerated--and could figure out whose beard would be longer. And they would agree.

 

[Quinzio]

"C" don't know this
He don't know that "A" exsist, only that "B" exsist and that "B" is moving away from him.
"C" even don't know his own speed.
Hence he must believe that´"B's" bear grow is slower than his own.Right
This is how it looks from "A" ref-frame, but not seen from "C" ref-frame.
We must know who have done the wrong observation "A" or "C" ?
Both cannot be right

Ok, listen. In the relativistic world, there is no more something called "absolute time". Each inertial frame lives in his own world, and comparing A time with C time leads to very odd conclusions.

In our slow human world, we find a natural fact that all the people on Earth share the same time (don't consider fuses). You can call someone in Paris, Bejing, Rome, they will all report you the same exact time and day.
The same thing doesn't happen for distances. We are used to the fact that distance changes when you move. Bob is now in Rome, but he takes an airplane so in 3 hours he'll be in London. No one is surprised.
In our world people never share the same place but we all share the same time.
Ina relativistic world, people don't share neither place nor time.
Each one has it's own time, when they travel.
Two people on the Earth who departs knows they their distance will increase.
The same happens in a relativistic world for time.
When two people travels in opposite direction, they know their time gets difference, just like position gets different. No one is interested who's moving north or who's moving south, they only say they're moving apart.
The same with time: no one cares who's clock runs slower, they know the other clock is slower.
A's clock is slower for C, C's clock is slower for A.
A is moving far away from C, C is moving far away from A.
See how is symmetrical ?
No one says, "you are still, I am moving". Anyone has the impression that the other one is moving away.
Same for clocks.
Everyone has the impression the other's clock is ticking slower.
Everything is symmetrical, everything is fine.

 

[Bjarne]

Everything is symmetrical, everything is fine.

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

 

[pervect]

Well, my general advice is a) draw a space-time diagram and b) remember simultaneity is relative. If you don't know about point b), it's something you need to understand.

If you do this, you'll get something like the attached diagram. The vertical black line is the worldline of a stationary observer, A, the black dots are unit time intervals according to his clock.

The slanted black line is the worldline of a moving observer, B, and the black dots on that world line are unit time intervals according to B's clock. The drawing is to scale with the speed of light represented by a line traveling at 45 degrees.

A's notion of simultaneity is represented by the yellow arrows. You can see that 1 unit on A's clock corresponds to less than 1 unit on B's clock according to A's reckoning of what events are simultaneous.

B's notion of simultaneity is represented by the red arrows. You can see that 1 unit on B's clock corresponds to less than 1 unit on A's clock according to B's reckoning of what events are simultaneous.

Both of these things are true. What makes this possible is the fact that _simultaneity is relative_, the red arrows are not the same as the yellow ones.

 

[Doc Al]

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

And yet you think the same laws would not apply to B. Why is that? The laws of physics are the same in every inertial frame.

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

Now you are changing the scenario. If B does return, he must have accelerated and thus broken the symmetry. Yes, he would be younger when he returns. (For more on this, look up the many, many threads we have on the twin paradox.)

In your original scenario all observers remain in their single inertial frames, so everything is symmetrical.

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

Who cares how they got their initial speed? Once A and B are moving with respect to each other, they will see each other's clocks as running slow. Perfect symmetry.

(Edit: I see that pervect has jumped in while I was dawdling. You would be wise to study his response.)

 

[rede96]

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

I find it helps me to understand all this if I ignore the 'who is observing who' element and the 'what is going on now' element too. After all, for all intents and purposes it is practically impossible to really observe anyone else’s clock when they are traveling at relativistic speeds and distances to you.

So I would look at from the point of view of an experiment. For example, using the case above, whose beard would be longer if A & B were to moving relative to each other and then meet up again.

I make the assumption that A&B start off life in the same frame of reference, otherwise it gets really difficult to solve.


So 'B' accelerates away from 'A' and then is moving at a constant velocity for some time. We now want A & B to meet up again to see whose beard has grown the most.

In order to meet up again, two things can happen. 'B' can turn around and travel back to meet 'A' OR 'A' can travel to meet 'B'

If 'B' turns around and goes back to 'A' then I would say that A's beard would have grown longer because B went through the most acceleration. (This is just may way of looking at it, i.e. who ever goes through the most acceleration would have aged less.)

If 'A' accelerates to catch up with be, then B's beard would be longer because 'A' would have had to accelerate the most to catch up with 'B'. (Again, someone with a better understanding may need to correct me here!)

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

I don't think time dilation happens 'after' acceleration.

For example, if A and B are the same age and at rest with respect to each other, but separated by some distance. If A goes to meet B but does it by constantly accelerating until he meets B, then A will still find that he is younger than B when they meet up.

 

[Quinzio]

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

If you're at discomfort with the relativistic world, you're not alone.
For us time is like a big river that slowly flows, every object that floats in the river will move at the same speed (eg. time will flow equally).

Imagine a phone call between A and C.
A and C are moving in opposite direction.
Each of them knows the speed between them, and their phone has an electronic device that corrects for doppler effect (phone call is carried by radio waves).
They are unaware of relativistic effects.
The speech goes like this:
A- Hi C, how are you ?
C - Fine thank, but how about you, you have a strange voice, are you ok ?
A - Yes, I am really ok. Your voice is strange too, it seems you're talking at a slow speed, as if you recorded your voice on a tape and then you play the tape at a slow speed.
C- That's strange, I have the same perception of your voice, you're talking slowly...
A- But I am talking at a normal speed. My voice is ok. My wife' beside me and she says my voice is ok.
C- But I am talking normally too. Listen I have my CD player next to me. I'll play some Rolling Stones song, so you can be sure I am not joking.
A- The song is slowed down. I'll play the same song on my CD player.
C- I hear it slowed down.
A- But how is it possible ? Let's suppose your time is slowed down. I hear you music slowed down, but you should hear my music at a faster pace !
C- No, I hear you slowed down as well. Each of us hear the other's voice slowly. There's something really strange here. We'll have to investigate.

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

This is the twin paradox.
It's something even more subtle, because it implies who accelerates and who stays at rest.

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do

Time, (and length) dilation happens at instantaneous speed.
During acceleration the situation becomes even more garbled. The simultaneity line will rotate... will begin to tilt.
If you look at the time-space Minkowski diagram, you would see the x' and t' axis that rotate and narrow their separation angle.
During acceleration it's even possible that you "see" two sequential events K and J in the reverse order, first J than K. But again it's only a sort of illusion, as a movie which is played in the reverse direction for a certain interval.

 

[ZealScience]

[PLAIN]http://www.science27.com/forum/rocketL2.jpg


Above the head of observer “A” a mother-ship is moving east 100,000 km/s. and right above the Earth it is launching a small spacecraft moving west with the same speed (100,000 km/s).

REFERENCE FRAME A
Observer “A” would now (from his reference frame) see spacecraft “B” hanging just above his head.
And he would see the mother-ship “C” continues towards East - 100,000 km/s
(We’ll assume the Earth did not have any gravity and will not pull spacecraft “B” down on the Earth).


REFERENCE FRAME C
The Mothership “C” continues moving east 100,000 km/s seen from reference frame “A”
The captain onboard in reference frame “C” agree with observer “A” that his clock (in reference “C”) must tick slower than the clock on Earth (reference frame “A”). .
The captain (“C”) is sure that the spacecraft he had launched right above the Earth was really moving with the speed 100,000 km/s east, relative to his reference frame “C”.
So he certainly expect that the clock on board spacecraft “B” must tick slower as his own.
This mean seen from the reference frame “C” - Captain “B” must have the slowest ticking clock, (and hence both slower than the clock from reference frame B and C) .
After 1 earth-year captain from reference frame “B” then also must have the shortest beard.
But observer “A” (on the Earth) does not agree. Because he have not observed that the spacecraft “B” have moved relative to him-

After 1 year of observation, observer “A” is sure that the beard of the captain in spacecraft “B” must have the same length as his own, - because the clock in spacecraft “B” must tick with the exactly same speed like his own, since from oberser "A's"
reference frame the sapcecraft "B" does not move.

This of course contradict with the way oberserver "C's" must see it, - he is certian that "B" must have the slowes clock and the shortes beard.

Is this a contradiction build into Special Relativity?
Who is wrong , - and why?

I think you brought some ideas of simultaneity. Because you cannot say somebody is certain about length of beard, it's somebody is observing the length of the beard. Because in different reference frames, observations would be different, unless they return to earth. In this case, time dilation is relative, but not absolute. THe absolute dilation is by gravity where space-time is curved. But in that case clock of B would be faster than A because he is at the outer place of the curvature. So your assumptions are not completely correct in first place, how can you get a correct answer?

 

[ZealScience]

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

When B returns it is not inertial any more to reference frame A, if B is moving inertial frame it is a different story! Time dilation is derived from that light travels at constant speed. On Earth A observes photon travels on B covers more distance than what it is observed by B, so B seems to be moving slower as time is dilated for photon to travel less distance. But it is exactly the same for B observing photon traveling on earth! But when B return to Earth there would be dramatic change that makes his beard shorter.

 

[Mike_Fontenot]

I am confused.
Because if someone (let’s say B) moving faster than me "A" (in any direction) he should ageing slower
B's clock would then tick slower than mine

If B really believes the same happen for him in the case as for me, - it’s can't be true, - because when B return I would be older. And my clock has counted more time.

Furthermore I also thought that someone should accelerate to higher speed , -before the time dilation could take place.
So how can “symmetrical” have anything with that to do.

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

 

[DaveC426913]

https://www.physicsforums.com/showpost.php?p=2934906&postcount=7

https://www.physicsforums.com/shsowpost.php?p=2923277&postcount=1

Please, don't post unannotated links. Describe why the reader should follow the links and what they'll find.