- Oct 10, 2011
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My first question posed to Google AI:
At 50% light speed, what are the individual percentages of both the time dilation effect, and length contraction effects?
Answer from Google AI:
At 50% light speed (\(0.5c\)), the time dilation effect is approximately 15.5%, and the length contraction effect is approximately 13.4%.
My next question posed to ChatGPT now:
Why do they not add up to 50%?
ChatGPT basically told me about a third factor called “Simultaneity”, to which I next asked/said:
I understand time dilation, and length contraction (I think?) but can you describe to me in simplified terms the new to me additional factor of simultaneity, and how this makes 50%, 50% basically?
ChatGPT tried to explain to me the Relativity of Simultaneity, and tilts of axes changing, and angles changing, or something like that, etc, and with all factors, and low speeds, tiny effects, at 50% of c, noticeable effects, and at near c, extreme effects, to which my next question was:
Ok, with any or all effects, low speed: tiny effect, 50% of c: noticeable effect, near c: extreme effect, but with c, straight linear effect on a graph or grid, and not curved exponentially starting out small and only exponentially increasing effect, how is c always the same?
And this was ChatGPT's last response, because I didn't ask it anything else yet, cause I'm still trying to understand it, but here is the whole thing of it's last response if you want to see it, and I was wondering if any of you humans wanted to try and help me understand this a little bit further maybe, because I still don't fully understand it yet?
Here's ChatGPT's whole last response if you want to see it (it left out a lot of the math on purpose, as it kinda figured out that I don't fully understand all of that yet either, etc.
ChatGPT’s whole last response:
This is a really sharp question — you’re noticing an apparent contradiction that almost everyone glosses over:
If relativistic effects grow non-linearly, but light’s behavior looks linear on spacetime diagrams, how can � stay the same for everyone?
The resolution is subtle but beautiful. Let’s walk it carefully.
1. First: what is actually “linear” about light?
On a spacetime diagram (space on the horizontal axis, time on the vertical):
Light always travels at 45°
That line is straight
That slope is the same for every observer
This is not an accident.
The straightness of light’s path defines the geometry of spacetime itself.
Light doesn’t adapt to spacetime — spacetime is built so light looks straight.
2. What isn’t linear: observers, not light
Here’s the key separation:
Light’s worldline → always linear, always the same slope
Observers’ coordinate grids → tilt non-linearly as speed increases
So the nonlinearity you’re worried about is not in light
It’s in how observers rotate their space and time axes
3. Why observer changes are not linear
If velocity added linearly:
0.5c + 0.5c = c ❌
Different observers would disagree on light speed ❌
So nature forbids linear velocity addition.
Instead, relativity uses something called rapidity (you don’t need the math):
Rapidity adds linearly
Velocity does not
As you approach �:
Each “equal push” gives less velocity
But the tilt of your axes keeps changing
This creates:
Small effects at low speed
Noticeable effects at 0.5c
Extreme effects near c
Without ever changing light’s slope.
4. Why this doesn’t require curves or exponentials for light
Think of it this way:
Light defines the edges of the spacetime cone
All observers’ coordinate systems must fit inside that cone
No matter how tilted an observer becomes, the cone doesn’t move
So instead of light curving:
Observers’ grids shear and tilt inside a fixed structure
That’s why light always looks linear.
5. The “graph confusion” resolved
You’re implicitly imagining one fixed grid where:
Effects grow exponentially
Light should curve if effects are nonlinear
But relativity does not use one fixed grid.
Instead:
Every observer has their own grid
Each grid is internally linear
The transformation between grids is hyperbolic, not linear
So:
Light is straight in every grid
The transformation between grids is nonlinear
No contradiction.
6. The deep geometric truth (this is the core)
Relativistic effects are nonlinear because spacetime rotations are hyperbolic — but hyperbolic rotations still map straight lines to straight lines.
That’s the whole answer, distilled.
Just like:
Rotating a graph on paper keeps lines straight
Even though sine/cosine are nonlinear functions
7. Why � could not be constant otherwise
If relativistic effects were linear:
Light would tilt differently for different observers
The light cone would distort
Causality would break
So the only way to keep � constant is:
Nonlinear observer transformations
Linear light paths
Invariant spacetime structure
8. Final intuition (lock this in)
Light is the ruler.
Observers are the ones bending — not the ruler.
That’s why:
Effects grow slowly at first
Explode near �
Yet � itself never changes
If you want, next we can:
Translate this into a purely causal explanation (no geometry)
Connect it to determinism and why “choice” shrinks near light speed
Or explain why acceleration feels different from velocity in this picture
You’re asking the right questions — this is exactly where understanding usually breaks through.
(End of ChatGPT response)
Some human help in trying to understand this will be much appreciated.
Take Care.
At 50% light speed, what are the individual percentages of both the time dilation effect, and length contraction effects?
Answer from Google AI:
At 50% light speed (\(0.5c\)), the time dilation effect is approximately 15.5%, and the length contraction effect is approximately 13.4%.
My next question posed to ChatGPT now:
Why do they not add up to 50%?
ChatGPT basically told me about a third factor called “Simultaneity”, to which I next asked/said:
I understand time dilation, and length contraction (I think?) but can you describe to me in simplified terms the new to me additional factor of simultaneity, and how this makes 50%, 50% basically?
ChatGPT tried to explain to me the Relativity of Simultaneity, and tilts of axes changing, and angles changing, or something like that, etc, and with all factors, and low speeds, tiny effects, at 50% of c, noticeable effects, and at near c, extreme effects, to which my next question was:
Ok, with any or all effects, low speed: tiny effect, 50% of c: noticeable effect, near c: extreme effect, but with c, straight linear effect on a graph or grid, and not curved exponentially starting out small and only exponentially increasing effect, how is c always the same?
And this was ChatGPT's last response, because I didn't ask it anything else yet, cause I'm still trying to understand it, but here is the whole thing of it's last response if you want to see it, and I was wondering if any of you humans wanted to try and help me understand this a little bit further maybe, because I still don't fully understand it yet?
Here's ChatGPT's whole last response if you want to see it (it left out a lot of the math on purpose, as it kinda figured out that I don't fully understand all of that yet either, etc.
ChatGPT’s whole last response:
This is a really sharp question — you’re noticing an apparent contradiction that almost everyone glosses over:
If relativistic effects grow non-linearly, but light’s behavior looks linear on spacetime diagrams, how can � stay the same for everyone?
The resolution is subtle but beautiful. Let’s walk it carefully.
1. First: what is actually “linear” about light?
On a spacetime diagram (space on the horizontal axis, time on the vertical):
Light always travels at 45°
That line is straight
That slope is the same for every observer
This is not an accident.
The straightness of light’s path defines the geometry of spacetime itself.
Light doesn’t adapt to spacetime — spacetime is built so light looks straight.
2. What isn’t linear: observers, not light
Here’s the key separation:
Light’s worldline → always linear, always the same slope
Observers’ coordinate grids → tilt non-linearly as speed increases
So the nonlinearity you’re worried about is not in light
It’s in how observers rotate their space and time axes
3. Why observer changes are not linear
If velocity added linearly:
0.5c + 0.5c = c ❌
Different observers would disagree on light speed ❌
So nature forbids linear velocity addition.
Instead, relativity uses something called rapidity (you don’t need the math):
Rapidity adds linearly
Velocity does not
As you approach �:
Each “equal push” gives less velocity
But the tilt of your axes keeps changing
This creates:
Small effects at low speed
Noticeable effects at 0.5c
Extreme effects near c
Without ever changing light’s slope.
4. Why this doesn’t require curves or exponentials for light
Think of it this way:
Light defines the edges of the spacetime cone
All observers’ coordinate systems must fit inside that cone
No matter how tilted an observer becomes, the cone doesn’t move
So instead of light curving:
Observers’ grids shear and tilt inside a fixed structure
That’s why light always looks linear.
5. The “graph confusion” resolved
You’re implicitly imagining one fixed grid where:
Effects grow exponentially
Light should curve if effects are nonlinear
But relativity does not use one fixed grid.
Instead:
Every observer has their own grid
Each grid is internally linear
The transformation between grids is hyperbolic, not linear
So:
Light is straight in every grid
The transformation between grids is nonlinear
No contradiction.
6. The deep geometric truth (this is the core)
Relativistic effects are nonlinear because spacetime rotations are hyperbolic — but hyperbolic rotations still map straight lines to straight lines.
That’s the whole answer, distilled.
Just like:
Rotating a graph on paper keeps lines straight
Even though sine/cosine are nonlinear functions
7. Why � could not be constant otherwise
If relativistic effects were linear:
Light would tilt differently for different observers
The light cone would distort
Causality would break
So the only way to keep � constant is:
Nonlinear observer transformations
Linear light paths
Invariant spacetime structure
8. Final intuition (lock this in)
Light is the ruler.
Observers are the ones bending — not the ruler.
That’s why:
Effects grow slowly at first
Explode near �
Yet � itself never changes
If you want, next we can:
Translate this into a purely causal explanation (no geometry)
Connect it to determinism and why “choice” shrinks near light speed
Or explain why acceleration feels different from velocity in this picture
You’re asking the right questions — this is exactly where understanding usually breaks through.
(End of ChatGPT response)
Some human help in trying to understand this will be much appreciated.
Take Care.
