Dave_Oblad » May 5th, 2017, 11:22 am wrote:Hi Jorrie (or Mitch),
In your last diagram, we see Bob has a Blue dashed line at 0.8 that points at Alice's final Destination of Alpha Centauri and Alice also has a Red dashed line at 0.8 that points at Bob's Alpha Centauri.
Can you explain (in simple terms) the significance of these two dashed lines pointing at each others Alpha Centauri(s)?
Regards,
Dave :^)

Dave_Oblad » 05 May 2017, 18:22 wrote:Can you explain (in simple terms) the significance of these two dashed lines pointing at each others Alpha Centauri(s)?
I also happen to know that you still believe that you can detect motion (and speed) through it by comparing clocks that are moving inertially. Well, that idea has been falsified by many an experiment, so why you still cling to it, I don't understand.
Jorrie wrote:I also happen to know that you still believe that you can detect motion (and speed) through it by comparing clocks that are moving inertially. Well, that idea has been falsified by many an experiment, so why you still cling to it, I don't understand.
Mitch wrote:Frankly the whole diagram is simply a way of representing the calculations of lorentz contraction and time dilation as trig functions. It is really nothing but mathematical artifice and the diagrams have no more basis in real physics than this. Accordingly those dashed lines represent those calculations of the the length and time as seen by the other observer in his inertial frame.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:Ok, so on one hand I'm told we can't detect motion or speed by comparing the clocks of two observers and then we are given diagrams that do exactly that. There is an elephant in the room that's pretty hard to miss.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:I understand the concept of being reciprocal, but am I to conclude that at the 0.8 markers both presume the other as having completed the full travel distance? Extra confusing because I thought Bob was essentially not Moving at all.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:By Relativity, I can maybe presume that Alice believes she has no Motion and Bob has the slower clock (reciprocal), which will ultimately be proven incorrect when Alice returns to Bob and finds Bob had aged more than her during her trip. Suddenly.. this reciprocal aspect vanishes and the truth is revealed.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:I'm still confused. I thought the red marker Labeled 0.8 on Alice's distance line to Alpha Centauri meant she had completed 80% of the journey to her destination at a velocity of 60% Light Speed (V/c = 0.6) at the present moment of the diagram.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:
But I still don't understand the relevance of, or significance of, Alice's Red Dashed Line pointing at Bob's Distance coordinate intersecting his Alpha Centauri.
Dave_Oblad » May 6th, 2017, 4:22 am wrote:
Given the full trip span is 4.4 Light Years for the Distance axis of Start to Alpha Centauri:
Dave_Oblad » May 6th, 2017, 4:22 am wrote: Are we saying that at the 80% mark both Alice and Bob believe the other has completed the full distance (4.4 Light Years) between Start and Alpha Centauri?
Dave_Oblad » May 6th, 2017, 4:22 am wrote:
Obviously, Alice knows she still has 20% of her journey remaining (or at least she hasn't arrived at her destination yet), so no way can she perceive that Bob is already 4.4 Light Years behind her.. from her current 0.8 position.
So, obviously I still don't understand.. and need a much clearer English explanation to my Question in Bold just above.
mitchellmckain » 06 May 2017, 21:04 wrote:You are providing an excellent demonstration why I told BurtJordan that introducing Epstein diagrams in a beginner's explanation of relativity is a bad idea.
BurtJordaan » 05 May 2017, 09:55 wrote:Cool! Many thanks Mitchell. This shows that 60% of c is an easy to understand speed in many ways. As you have said, one can do a return trip and have a reserve fuel of 50% x 50% x 50% x 50% = 6.25% of the original fuel. That is if you have a 100% efficient massenergy conversion, which may not be achievable, so practically one may have to settle for much slower trips.
I will continue with the 0.6c deltav's, but just use a higher acceleration to reduce the time for Alice.
hyksos » May 6th, 2017, 11:22 pm wrote:I
Folkmechanics tells us that if motionless Alice sees the laser light at c, Bob "must" see it moving slower than c as he "catches up" to it on his rocket.
(In our universe, comma) Bob's clocks are all running slower, at precisely the rate that causes him to measure the laser light at c. It's a conspiracy of the universe to perfectly time the 'rate of slowdown' of his clocks to match this.
If it helps to ease the medicine down : speed is distance divided by time. The light will travel a farther interval distance per each "Bob second" , which is now longer than a "regular second" because he is in motion.
bangstrom » May 7th, 2017, 2:23 am wrote:hyksos » May 6th, 2017, 11:22 pm wrote:I
Folkmechanics tells us that if motionless Alice sees the laser light at c, Bob "must" see it moving slower than c as he "catches up" to it on his rocket.
(In our universe, comma) Bob's clocks are all running slower, at precisely the rate that causes him to measure the laser light at c. It's a conspiracy of the universe to perfectly time the 'rate of slowdown' of his clocks to match this.
If it helps to ease the medicine down : speed is distance divided by time. The light will travel a farther interval distance per each "Bob second" , which is now longer than a "regular second" because he is in motion.
Folkmechanics also tells us that Bob’s clocks must be moving faster if he is to measure the speed of a light beam moving to the rear of his rocket at the speed of c. This is where motion slowing time becomes counter intuitive.
hyksos » May 6th, 2017, 11:22 pm wrote:If I had to explain special relativity to a high school kid, or explain it to someone in a loud bar, or in a bowling alley. The first thing I would say, to keep it ultrasimple, is to tell the person :
Velocities do not add.
You travel 60% of the speed of light on the back of a rocket, and fire a bullet in your direction of your motion at 45% of the speed of light. If velocities add, the bullet should be going 105% the speed of light. But that does not happen, because velocities do not add.
{you educated turtleneck sweaters call this the "Galilean Transformation" i.e. velocities add under that transformation}.
hyksos wrote:Velocities do not add.
BurtJordaan » 07 May 2017, 06:44 wrote:I am working on such a spacepropertime diagram to illustrate the complete situation, but that will have to stand over for the next part.

BurtJordaan » 07 May 2017, 13:22 wrote:Actually the real length of the red curve is identical to the length of the blue arrows. It does not look like it, because I had to squash the diagram from top to bottom to about 1:3 in order not have an absurdly tall diagram. Trust me, the red curve is mathematically of identical length to the blue arrow lengths. IMO, this is really the clincher for this method of diagramming space and time for beginners.
BurtJordaan » May 8th, 2017, 3:54 pm wrote:BurtJordaan » 07 May 2017, 13:22 wrote:Actually the real length of the red curve is identical to the length of the blue arrows. It does not look like it, because I had to squash the diagram from top to bottom to about 1:3 in order not have an absurdly tall diagram. Trust me, the red curve is mathematically of identical length to the blue arrow lengths. IMO, this is really the clincher for this method of diagramming space and time for beginners.
Just to reemphasize this truth about spacepropertime diagrams, it is not solely through the equations that one can test this. Attached is a simple, but rough graphical illustration of why this is so. The curvature of the spacepropertime path, showing the accelerating Alice, is built up from small Epstein diagrams, as shown at an exaggerated scale. The individual blue and red arrows clearly are of equal length, but the curved segments clearly result in less gain in the vertical dimension than is the case for the vertical segments. When a lot of tiny segments are strung together, they form a smooth curve.
mitchellmckain » 09 May 2017, 01:24 wrote:You are making it look like these vector's in Epstein's diagram are displacement vectors  which they are not. These vectors are fixed magnitude with an direction representing the relative velocity between two inertial frames. What can possibly be the meaning of adding such vectors like you have done? I do not see it.
mitch wrote:To get the usual usage of the Epstein diagram you need to drop back to one of these composing diagrams, for I do not see how you are going to use the whole diagram to calculate anything meaningful.
mitch wrote:At first I thought, there are no obstacle to making this continuous and using the tangent vector to drop back to a real Epstein diagram. But then I had to ask myself how you construct such a continuous graph. I guess you would have to do it by taking the limit as you patch more and more of them together at smaller intervals. But then what is the mathematics for doing this, because that is where the real significance will be found.
BurtJordaan » May 8th, 2017, 11:42 pm wrote:mitchellmckain » 09 May 2017, 01:24 wrote:You are making it look like these vector's in Epstein's diagram are displacement vectors  which they are not. These vectors are fixed magnitude with an direction representing the relative velocity between two inertial frames. What can possibly be the meaning of adding such vectors like you have done? I do not see it.
The vectors are indeed displacement vectors in spacepropertime, i.e. and . I see no problem in summing unitvectors like this, provided one realize that you are not going to get the standard displacement in spacetime.
BurtJordaan » May 8th, 2017, 11:42 pm wrote:mitch wrote:To get the usual usage of the Epstein diagram you need to drop back to one of these composing diagrams, for I do not see how you are going to use the whole diagram to calculate anything meaningful.
By vector summing the , displacements, I get the curve which gives me the values that I've shown in complete diagram of this post. They seem to be the correct values. One can check them using Rindler coordinates, which is outside the scope of this thread, for obvious reasons.
mitchellmckain » 09 May 2017, 12:08 wrote:I guess you must be altering Epstein's method a bit by changing the magnitude of the vector from c as he has it to a variable proper time interval. I had this odd image of adding together his fixed length vectors which didn't make a lot of sense.
BurtJordaan » May 9th, 2017, 8:58 am wrote:Thanks for confirming that it checks out, Mitchell,mitchellmckain » 09 May 2017, 12:08 wrote:I guess you must be altering Epstein's method a bit by changing the magnitude of the vector from c as he has it to a variable proper time interval. I had this odd image of adding together his fixed length vectors which didn't make a lot of sense.
I'm not quite sure what you mean here, but I'm only summing identical length spacepropertime path vectors. With the years and light years units, c=1 and doesn't play any other role that I can see. This is the beauty (and perhaps the reason for the distrust in the physics community) of the Epstein diagrams. I will point out some other problems that Physicists may have with the method in the new thread in the physics subforum.
And that is why this explanation talking about clocks going faster or slower is wrong. Time is not slowing down OR speeding up. The real key to what is happening is the relativity of simultaneity.
mitchellmckain » 09 May 2017, 19:21 wrote: My observation that you can make the magnitude of the vector whatever proper time has passed made a lot of what you were saying fall into place.
BurtJordaan » May 9th, 2017, 2:41 pm wrote:Maybe it wasn't such a good idea to mention the Epstein diagram at all in the method that I use. It is really just an application of a spacepropertime coordinate system for 'reallife' scenarios. Maybe the Epstein diagram distracts unnecessarily?
BurtJordaan » May 10th, 2017, 12:44 am wrote:I suppose the next step would be to clearly show how one can go back to the more versatile Minkowski domain.
mitchellmckain » 10 May 2017, 11:50 wrote:Mathematically it must have to with the change of trig functions to hyperbolic trig functions. I would guess that the circle in the Epstein graph becomes a hyperbola in the in the light cone. At least, that is what I have been visualizing all this time.
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