# Special Relativity III

#### topsquark

Forum Staff
This is a post by
GatheringKnowledge

3. Let's consider a simple scenario: There are 3 objects - A (red sphere), B (blue sphere) and C (yellow sphere). A and B are moving towards eachother at 0,25c. At t=0 distance between A and B is equal to 2su (space units), while object C is located right in the middle of that distance and remains stationary - so, from the perspective of C, all 3 objects will cross the same point in 1D space at t=4. The point is to begin from the perspective of stationary C and use the rules of SRT, to change the perspective to A, only to use this result as a base, while switching the perspective once more to B...

Here's a spacetime diagram for the inertial frame of object C (yellow sphere).

Here's an animation of the same scenario in 2D space and with time dimension expressed in frame numbers - 10 frames is here equal to 1tu (time unit)
(you can ignore for now everything except the spheres)

And here's the result, which we'll get by using the rules of classic Galilean relativity, to see this scenario from the perspective of red sphere A. Of course, since after the Galilean transformation of coordinates, symmetry of motion will be maintained in all frames, there's no sense to show you the diagram for blue sphere B, as it will be the same, as the results below - only in reverse...

There was already one person, who tried to deal with my challenge and gave me the results, which he got after using Lorentz transformation, to switch between the perspectives. Problem is, that he started from the result, which I've got after using the Galilean transformation to show the perspective of stationary A (the ones above) and used it as base, to show other 2 perspectives - and since he used as well the formula of Einstein's velocity addition, there was no symmetry of motion for the inertial frame of C (yellow sphere), on which I based this entire scenario... Here are the results with his commentary:

"Blue (A), Green (B) moving 0.25c, and Red (C) moving at 0.5c"

"It's probably not super apparent at these relative velocities, but I think you can see here that the slopes of the red and blue lines are not purely mirror images of each other. Red's slope (C) is just a little bit steeper than Blue's (A), representing its slightly greater speed in this frame (0.286c vs 0.25c)"

"I included a frame with C stationary just for completeness. This one makes it really clear how the starts and ends of the objects' paths are not simultaneous in every frame. It should also be clear that at any given moment in their paths, Blue (A) is not quite twice as far from Red (C) as Green (B) is, owing to the fact that the relative velocity of Green (0.286c) is more than half that of Blue (0.5c) here."

It's funny, how he considered those results as valid ones, while the entire scenario got completely broken. I won't discuss here, how wrong those diagrams are, as there's a limit of post lenght - but anyone, who knows, how to read those diagrams, should be able to make his own conclusions. Anyway, it might be possible, that if he would begin from the frame of stationary yellow sphere, the symmetry of motion would be maintained, while changing perspective between red and blue spheres - because now, this symmetry is completely gone. In relation to yellow sphere, objects A and B are moving at the same speed (0,25c), so for them velocities of moving objects have to be the same, just as the distances, which they pass in a given time...

If there's no way to get a valid result for such simple scenario, then Einstein obviously fooled everybody. But I want to give everyone a second chance in dealing with my scenario. If there's someone, who wants to defend the Special Relativity, all he needs to do, is to show me some spacetime diagrams, where after using the Lorentz transformation, we will get reversed results, while switching between the perspectives of red and blue spheres - so the symmetry of relative motion will be maintained in all frames. Using frame of stationary C as base for other 2 diagrams, will be considered, as cheating...

#### topsquark

Forum Staff
Your proposal is based on what you would get without SR. Applying SR, as your responder did, you will see that there is no obvious symmetry to your problem.

If there's no way to get a valid result for such simple scenario, then Einstein obviously fooled everybody.
It would seem that Einstein also fooled the Universe itself as all of the evidence points toward a validation of SR.

-Dan

#### GatheringKnowledge

Your proposal is based on what you would get without SR. Applying SR, as your responder did, you will see that there is no obvious symmetry to your problem.

-Dan
Problem is, that my responder began from a result, which I've got after the Galilean transformation of the "original" situation, where 2 objects are moving at the same speed in relation to a 3'rd stationary observer. However you are probably right - the symmetry of motion would be most likely lost, even if he would start from the perspective of yellow sphere - only the differences in results would be smaller.

Besides, I've tried to find a possible solution by myself - and couldn't find any... Sadly, this leaves us with a serious problem: if for a stationary observer 2 objects are moving in opposing directions at the same speed, it's logically inconsistent to tell, that one of moving objects will experience a different timeline, than the other

What we get here, is completely against the idea of relativity in motion - red sphere experiences a different timeline, than blue sphere, what leads to a conclusion, that in the case of one those objects, motion is definitive and it is against the main postulates of relativity. Besides, we would get an opposite situation, just by changing the order of transformations (start from red sphere and change to blue one). And keep in mind, that my scenario is quite simplistic. Imagine, what would happen, if red and blue spheres would emit a light pulse at t=0... I will probably discuss such scenario in the near future.

There's a huge fallacy, when it comes to time dilation due to relative velocity. How can anyone tell, that the faster someone is moving, the less time he's experiencing, if velocity of his motion depends on motion of others? If someone is moving towards me at 99% c, then from his perspective I'm moving towards him at 99% c. If for both of us time would flow at different rate, then we would be able to learn about motion of the one, who's aging slower - and this completely violates the main rules of relativity

#### GatheringKnowledge

It would seem that Einstein also fooled the Universe itself as all of the evidence points toward a validation of SR.

-Dan
From what I know, SR is validated just in some 50%. Big part of the model (lke relativity of simultaneity) exist only as a theory, while some of Einstein's claims are theoretically impossible to validate (like time not flowing at c). And there's also that part, where SRT is against experimentally proven scientific facts, like quantum entanglement or wave-function collapse in QM. Not to mention, that there's absolutely nothing, what would allow us to tell, that time is determined in any moment, other than the one which is observed and directly measured - time as a linear axis of determined physical dimension is a total "what if...", while physicists treat it, like a experimentally proven fact...

And when it comes to those parts of SRT, which are in fact scientifically proven: why should we assume, that someone is in 100% correct, because he was right in half of the things he said? How can we decide about things, which we can't in any way observe, just because it turned out, that speed of light is constant for every observer? Besides, one possible explanation doesn't exclude other possible explanations - I can for example explain the velocity time dilation with nothing more, than the doppler's effect

While for example the results of Hafele-Keating experiment can be explained with the fact, that both planes are passing different distances in relation to the rotational motion of Earth - which in the difference to velocity in a constant & linear motion, is definitive in relation to cycles of rotational motion of other celestial bodies. In shortcut, we measure time, using the distance, which Earth's surface is passing during one rotation (which can be identified, using Sun as relation) and the planes were in fact moving in opposite directions relative to distance, which defines our mesurement of time... It's slightly more sophisticated, than the rule: "the faster you move, the longer you live", but instead it doesn't violate the main postulates of relativity...

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#### GatheringKnowledge

Ok, it seems that I have to be the one, who will actually try to defend SRT against my own accusations. I was searching for a proper tool, to deal with the spacetime diagrams from my scenario, for quite some time - and finally, I've found one:

After playing a bit with the interactive diagram, I can now tell, that indeed, symmetry of motion in my scenario will be more or less maintained for the frames, which are incoming at each other at 0,25c after using the Lorentz transformation - so, science got lucky for now...

But better don't celebrate your victory just yet, as I still didn't finish dealing with this scenario. Now let's go a step further and shine some light on the whole situation. As you might notice, now the timeline for stationary object C (green line) begins at t=-1 with emission of light pulse which at t=0 reaches simultaneusly both incoming objects, as at this moment they are 1su (space unit) away from the stationary source of light C. Now lets assume, that objects incoming at 0,25c are actually mirrors and at t=0 the light emitted by C at t=-1 is being reflected back to it's source. In the rest frame of C, distance to each of incoming mirrors is equal 1su, so it should be pretty obvious, that from the perspective of stationary object C, light which was emitted at t=-1 and reflected back at t=0, should come back to it's source at t=1 - and this is exactly what can be seen on the diagram above this text (stationary green axis). Of course, just like before all 3 objects will cross a single point in 1D space at t=4. Those smarter ones should be able to see already, where it leads and that there's no way around. But just to clarify:

a) at t=0 distance between the light source C and incoming mirrors A&B is equal (1su), so the reflection of light has to be simultaneus. However, since the simultaneity has to be reserved for the event at t=4, from the perspective of mirrors A&B, moment of reflection (which marks also t=0 in their own respective rest frames) is different for each object. However, if we would force the simultaneity of events at t=0, time axes of objects A&B wouldn't cross the green axis at the same moment

b) if at t=0 distance from A&B to C is equal 1su, then distance from A to B is equal 2su. Since c is constant in every frame, light emitted/reflected 2su away, will ALWAYS need 2tu to travel that distance. We see however, that since the moment of reflection at t=0 is different for A and B, while distance between the mirrors is at the same smaller, than 2su (around 1,8su), moment at which light reflected at t=0 reaches the opposite mirror, is at around t=1,6 - and this leaves us with situation, where for the light source C, which is placed exactly between the mirrors, light as it is recorded in the frames A&B will pass the distance of 2su just in 1.6tu - while in the frame in stationary frame of C, light is passing half of that distance in 1tu. It means, that objects A&B will experience less time, than C and their relative motion will become 100% definitive - so, in the end, we will end up with incorrect results anyway

HAPPY NEW YEAR!!!

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