[Origin]

A time dilation calculator shows that objects with relative velocity of 100,000 km/s would supposedly show time dilation of 1.060752 seconds from one observer's point of view, and objects with relative velocity of 200,000 km/s would show 1.342385

OK.

So if two objects are moving in the same straight axis in opposite directions from a third object, all of equal mass, at velocity of 100,000 km/s each from that middle object, would the two outer objects show the same times or different times on their clocks?

First there is no need to specify the mass, it is irrelevant to the problem.
There is not enough information in your question to give a valid answer.  You need to specify which frame you are talking about.
When thinking about SR you should consider yourself at rest compared to all other inertial frames.  The clocks in all the other frames are moving slower and the amount they are slower depends on their velocity relative to you.

I guess you have a problem.

The problem is trying to get you to understand physics.

[Bored chemist]

So why do you hold at least one of them out to be the authority on the characteristics of light in relative frames?

I didn't.
This is what I said was the authority.
https://en.wikipedia.org/wiki/Tests_of_general_relativity
https://en.wikipedia.org/wiki/Tests_of_special_relativity

It's called experimental evidence.

Oh right, Wikipedia knows all. Where do you think they got General Relativity from, pulled it out of a hat?

Did you deliberately miss the point?
The authority is the experiments themselves.

[Bored chemist]

It appears that I may have identified a flaw in Einstein's equations for time dilation.

It only appears that way to you.

And those with a high enough level of comprehension.

Name two.

[Centra (OP)]

There is not enough information in your question to give a valid answer.  You need to specify which frame you are talking about.
When thinking about SR you should consider yourself at rest compared to all other inertial frames.  The clocks in all the other frames are moving slower and the amount they are slower depends on their velocity relative to you.

But do the clocks really show different times when all three objects go back together or not? I assume you don't mean they just look different from the frame you're viewing them from. If they really change time then the problem is that you can consider either of the three objects to be the stationary one, there is no true stationary. How can the times showing on the clocks depend on which object you arbitrarily choose to consider the stationary one? The view that one of the outer objects is stationary, the middle one is moving away from it at a certain speed, and the third object is moving away from the middle one at that same speed is as valid as choosing to consider the middle object stationary and both outer objects moving away from it in opposite directions at equal speeds, but relativity would predict different times showing on the clocks depending on which of those scenarios we arbitrarily chose to view the situation as. Thereon lies the paradox, nothing really changed, we just chose to view things from a different perspective, but each perspective would suggest a different time dilation outcome.

[Origin]

So if two objects are moving in the same straight axis in opposite directions from a third object, all of equal mass, at velocity of 100,000 km/s each from that middle object, would the two outer objects show the same times or different times on their clocks?

Here is how it would work.  Assume there is a planet point A and both ships fly in opposite directions at 100,000 km/sec from the planet.  The one going to the left is B and the one to the right is C.
After one second the point A would see that only 0.943 sec had elapsed on B and C.  From point B frame after 1 sec they would see that only 0.943 sec had elapsed on A and only 0.745 sec had elapsed for C.   From point C frame after 1 sec they would see that only 0.943 sec had elapsed on A and only 0.745 sec had elapsed for B.

[Centra (OP)]

Here is how it would work.  Assume there is a planet point A and both ships fly in opposite directions at 100,000 km/hr from the planet.  The one going to the left is B and the one to the right is C.
After one second the point A would see that only 0.943 sec had elapsed on B and C.  From point B frame after 1 sec they would see that only 0.943 sec had elapsed on A and only 0.745 sec had elapsed for C.   From point C frame after 1 sec they would see that only 0.943 sec had elapsed on A and only 0.745 sec had elapsed for B.

Do you mean they only looked like they showed those times due to the time it took for the light from the clocks to reach each person's eyes or do you mean they literally had their times altered such that if the clock times were written down when B and C got 100,000 km away from A and then they went back to A that A would see those times written down? Because A wouldn't be able to see 0.943 on both papers and B and C also see 0.745 on each other's papers. My understanding is that Einstein meant the times literally changed and time to observers' eyes was not considered. I could accept that it might LOOK like those times but obviously the times couldn't actually  change by different amounts at once. If we're just talking about how it LOOKED then it can LOOK like light is moving faster than it really is, the illusion of velocity just like the illusion of times on clocks.

[Halc]

Assume there is a planet point A and both ships fly in opposite directions at 100,000 km/sec from the planet.  The one going to the left is B and the one to the right is C.
After one second the point A would see that only 0.943 sec had elapsed on B and C.

To be precise, B and C would age 0.943 sec relative to A's frame. The observer at A wouldn't actually see that since the objects are receding and Doppler effect would reduce that to around 0.63 seconds, what observer B actually sees.

From point B frame after 1 sec they would see that only 0.943 sec had elapsed on A and only 0.745 sec had elapsed for C.

Only 0.804 for C. It's only moving at 178432 km/sec relative to B, not 200000.  Don't forget relativistic velocity addition.

To Centra:
There is no 'paradox' since there is no absolute time that you are assuming.
Relative to any object, time runs slower for the other objects. This is not the same as saying that time runs faster for one object than another, a statement which lacks a frame reference and is thus meaningless.

You seem to have no desire to actually understand anything, so I don't expect you to, but you have no grounds to declare the inconsistency of a theory which you admit yourself you lack even the most basic understanding.

[Centra (OP)]

To Centra:
There is no 'paradox' since there is no absolute time that you are assuming.
Relative to any object, time runs slower for the other objects. This is not the same as saying that time runs faster for one object than another, a statement which lacks a frame reference and is thus meaningless.

You seem to have no desire to actually understand anything, so I don't expect you to, but you have no grounds to declare the inconsistency of a theory which you admit yourself you lack even the most basic understanding.

I said it was seen as inconsistent with the results of experiments in 1942. What's wrong with declaring an observable fact, unless you want to suggest that those scientists were lying, which nobody else ever suggested at the time. You still haven't explained those results not matching up with the predictions of SR, by the way, you just completely ignored it, like Einstein himself did. If you can't explain something, act like it never happened, is that the strategy? "You seem to have no desire to actually understand" that experiment, what's that about, Halc?

[Bored chemist]

To Centra:
There is no 'paradox' since there is no absolute time that you are assuming.
Relative to any object, time runs slower for the other objects. This is not the same as saying that time runs faster for one object than another, a statement which lacks a frame reference and is thus meaningless.

You seem to have no desire to actually understand anything, so I don't expect you to, but you have no grounds to declare the inconsistency of a theory which you admit yourself you lack even the most basic understanding.

I said it was seen as inconsistent with the results of experiments in 1942. What's wrong with declaring an observable fact, unless you want to suggest that those scientists were lying, which nobody else ever suggested at the time. You still haven't explained those results not matching up with the predictions of SR, by the way, you just completely ignored it, like Einstein himself did. If you can't explain something, act like it never happened, is that the strategy? "You seem to have no desire to actually understand" that experiment, what's that about, Halc?

Why don't you stop messing about, repeat the experiment they did, show that relativity is wrong, and collect your Nobel prize?

[Centra (OP)]

To be precise, B and C would age 0.943 sec relative to A's frame. The observer at A wouldn't actually see that since the objects are receding and Doppler effect would reduce that to around 0.63 seconds, what observer B actually sees...

...Only 0.804 for C. It's only moving at 178432 km/sec relative to B, not 200000.  Don't forget relativistic velocity addition.

Sounds complicated, Ill have t think about it some more.

[Centra (OP)]

Why don't you stop messing about, repeat the experiment they did, show that relativity is wrong, and collect your Nobel prize?

Pretty sure they don't give out prizes for repeating experiments.

[Origin]

The observer at A wouldn't actually see that since the objects are receding and Doppler effect would reduce that to around 0.63 seconds, what observer B actually sees.

I didn't include the doppler effect because I was talking about relative times on the clocks, but my sloppy language didn't make that clear.

Only 0.804 for C. It's only moving at 178432 km/sec relative to B, not 200000.  Don't forget relativistic velocity addition.

Right-o, thanks for pointing that out, I was clearly incorrect on that [GD it!]

[Bored chemist]

Why don't you stop messing about, repeat the experiment they did, show that relativity is wrong, and collect your Nobel prize?

Pretty sure they don't give out prizes for repeating experiments.

If you overturned Einstein, you would get a prize.
Why don't you hurry up- before anyone else does it?

[Origin]

What would B and C write down on paper as being the time on their clocks when they reached 100,000 km from A?

You do realize that when A and  B say they have traveled 100,000 km that point A will say they have traveled about 106,000 km.

I could accept that it might LOOK like those times but obviously the times couldn't actually  change by different amounts at once.

Yes, it is actually different.  If 2 different space ships left earth at different speeds and then retuned, the earth clock and the 2 ships clocks would all show different times.

[Bored chemist]

I could accept that it might LOOK like those times but obviously the times couldn't actually  change by different amounts at once.

The experiment was done.
https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
Relativity won.

[Kryptid]

I have split the posts that Puppypower made off into a new thread. As such, I expect Puppypower to keep any such discussion about energy differences between reference frames in that one thread. Any posts about it made elsewhere will be considered spam and I will act accordingly.

[Centra (OP)]

This may be shocking to some sensitive viewers, but Einstein did not originate E=mc2, just thought you should know in case you were under any illusions to that effect.

E = mc2: Who Got There First? The equation E = mc2 is synonymous with the name Einstein. However, it may come as a surprise to many to find out that Einstein was not in fact the first to derive the famous equation. In 1903, the Italian Olinto De Pretto, who was an engineer/industrialist with experience in materials and their properties, gave the precise formula E = mc2. It was first published in June 1903. De Pretto delivered a second paper on November 29th 1903 in Venice, and this paper was published in the proceedings of the Venetian Royal Institute of Science, Literature and Art in February 1904. This is a translation of what De Pretto concluded in that paper: Given then E = mc2, in = 1 kg and c = 3 x 106 km/s. anyone can see that the quantity of calories obtained is represented by 10794 followed by 9 zeros, that is more than ten thousand billions. To what terrible result has our reasoning brought us? Nobody will easily admit that an amount of energy equal to the quantity that can be derived from millions and millions of kilograms of coal is concealed and stored at a latent state in one kilogram of matter of any kind; this idea will be undoubtedly considered foolish. However, even if the result of our calculations be reduced somewhat, it should be nevertheless admitted that inside matter there must be stored so much energy as to strike anyone's imagination. What is in comparison to it, the energy that can be derived from the richest combustible or from the most powerful chemical reaction?

Challenging Modern Physics: Questioning Einstein's Relativity Theories
By Al Kelly (page 15)

[Centra (OP)]

I could accept that it might LOOK like those times but obviously the times couldn't actually  change by different amounts at once.

The experiment was done.
https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
Relativity won.

That was a very shoddily executed experiment, and the facts that the atmosphere travels with the earth's rotating surface and that airplanes travel relative to air rendered it pointless. The earth did not rotate beneath the planes as if they were in space, it pulled/pushed them with it in the atmosphere. For the experiment to be valid, there would need to be wind at the altitude of the planes blowing from East to West at a velocity of about 1000 mph relative to the surface of the earth, which there wasn't.

You could also cite the experiment with the highly sensitive atomic clock in recent times where they found that raising the clock 33 cm caused a difference in the time rate due to gravity difference and also claimed to have confirmed that motion also affected time. The problem there is that their "motion" was in fact making the cesium atoms vibrate, which is not the same as simply moving the clock around. We don't know how vibrating atoms effects a cesium clock's operation.

I accept that gravity seems to slow clocks, another experiment was done by others involving taking a cesium clock 1000 feet or meters up a mountain, which also showed the expected difference. Gravity and motion are two different things though, and I don't know of an experiment that proved conclusively that motion really has that effect. There may be some, I just don't know of them. We don't know why gravity affects time though, we don't know that it's due to curvature of spacetime, just that it does.

[Centra (OP)]

I must clarify what I said about the Sagnac effect being inconsistent with Special Relativity. It's actually the experiment by Dufour and Prunier in which part of the apparatus was in rotation and part was stationary in the lab frame. That was the experiment I quoted earlier a couple times. Here's what they said about the regular Sagnac experiments.

1 The optical circuit, closed, is in its entirety fixed to the revolving disc. --
This is the well-known case of experiments of Sagnac. The two theories are here in agreement between them and in agreement with the experiment, with regard to the total shift of the 8 fringes recorded on the disc turning. However, the traditional theorist and the relativistic theorist are not in agreement between them on the distribution that they make, of the cause of the phenomenon, between the various components of the total course. But so that the physicist operator who makes the experiment has the possibility of choosing between these two theoretical interpretations, it would be necessary to take an experimental measurement directly of the speed of light on the platform in rotation, an operation which is obviously impossible to realize with the precision necessary, in the current state of the art.

[Bored chemist]

This may be shocking to some sensitive viewers, but Einstein did not originate E=mc2, just thought you should know in case you were under any illusions to that effect.

As I already said, it's the experiments that matter.