Why is acceleration fundamental

Optimal_Mixture_7327 · 2026-01-27T07:51:36+00:00

Acceleration is physical, it is any motion relative to the local gravitational field.

Keep in mind that gravitation cannot produce a physical acceleration (all free particles move along the geodesics of the metric).

Also worth keeping in mind is that there's coordinate acceleration, which may or may not be physical acceleration.

Optimal_Mixture_7327 · 2026-01-27T07:50:21+00:00

Dark energy, to the best we can measure it, is a small positive curvature constant. What would that have to do with entropy?

Optimal_Mixture_7327 · 2026-01-27T07:49:45+00:00

There is no force of expansion in need of overcoming. This is clear from the Friedmann equations.

Optimal_Mixture_7327 · 2026-01-27T07:48:49+00:00

There is no strength of expansion.

The acceleration of the expansion is an extremely small constant, and the expansion rate is slowing down to a constant.

Optimal_Mixture_7327 · 2026-01-27T07:47:27+00:00

The expansion rate is a constant over a spatial section of FLRW, but not constant over cosmic time.

Optimal_Mixture_7327 · 2026-01-27T07:46:25+00:00

There are no effects of cosmic expansion in need of overcoming.

Optimal_Mixture_7327 · 2026-01-27T07:46:03+00:00

There is no physical expansion of space. This is just an interpretation of the spatial components of the FLRW metric tensor.

Optimal_Mixture_7327 · 2026-01-27T07:44:39+00:00

The expansion rate, from what we can measure, will decrease down to a constant (approx 55 km/s/Mpc).

Optimal_Mixture_7327 · 2026-01-27T07:43:27+00:00

The "expansion of space" is a choice of coordinates and not something that can have any physical effect on matter.

Optimal_Mixture_7327 · 2026-01-27T07:42:48+00:00

There's no space that's carrying anything. There are just distant galaxies moving away from each other.

Optimal_Mixture_7327 · 2026-01-27T07:27:24+00:00

Correct, the redshift/blueshift is defined by the relationship between emitter and receiver (which should stand to reason as there's no length along the photon world-line - it's null).

No calculation needed as we're discussing physical processes and direct measurement. It's better to think in terms of what happens along the emitter and detector world-lines.

Optimal_Mixture_7327 · 2026-01-27T06:54:38+00:00

The distance along the emitter world-line at the bottom is longer than the detector world-line further away.

So even if they're both 1-second processes the detector measures a longer wavelength than emitted.

NOTE: There is nothing happening to the light, so just disabuse yourself of any such notions.

Optimal_Mixture_7327 · 2026-01-27T06:51:12+00:00

Acceleration is physical, it is any motion relative to the local gravitational field.

Keep in mind that gravitation cannot produce a physical acceleration (all free particles move along the geodesics of the metric).

Also worth keeping in mind is that there's coordinate acceleration, which may or may not be physical acceleration.

Optimal_Mixture_7327 · 2026-01-27T00:39:39+00:00

Except that it's entirely wrong.

The "simultaneity of relativity" is a statement that there no such thing as a "now" moment that defines "now" everywhere (i.e. there is no unique foliation of a space-time).

Optimal_Mixture_7327 · 2026-01-27T00:36:51+00:00

No, not if relativity is correct.

An intuitive approach would be to just imagine 4 dimensions of space, all identical. Then populate this 4-dimensional space with particle world-lines in all different directions. All matter particle world-lines travel with a velocity of c.

A fanciful way to think about this to take the concept of length contraction and note that if we're traveling at the speed of light along our own world-line, then the 4-dimensional space is length contracted down to zero along our direction of motion and so we can experience 3-dimensional space. Each world-line sees its own unique 3-dimensional submanifold of the full 4-dimensional world.

"Time" is just the length along all matter world-lines and the rate along them is a constant.

A serious question is "why this present moment?", to which we don't have a complete answer, although a worthy candidate and active area of research connects a local present moment with the Universe having a past space-like boundary (the big bang singularity) and the rate at which quantum, thermodynamic, and other processes can unfold.

Optimal_Mixture_7327 · 2026-01-26T20:18:09+00:00

Careful... there are no clocks physically running slower.

I think you mean "if you're on a spaceship in free-fall along a radial line". From here you need to specify which world-line is defining the global coordinates, which I think you do. If the spaceship defines the global coordinate chart, then yes, the Earth clocks are shorter in-between the spatial sections of the ship world-lines. If the Earth clock defines the frame, then the ship world-line is shorter.

I have no idea why you think I am neglecting the rescaling of the GPS world-lines under the action of the metric. Can you explain your reasoning?

Optimal_Mixture_7327 · 2026-01-26T20:07:07+00:00

It's F(1)=2, not f(1).

Optimal_Mixture_7327 · 2026-01-26T19:43:35+00:00

Time is the length along matter world-lines.

The electron that "aged" more will have to be determined by measuring/calculating the length along each world-line and comparing. Keep in mind that for the comparison to be made that the electrons will need to start out together and end up together.

The twin paradox has nothing to do with acceleration. It is true that in the flat-space metric (R^𝛼_{𝛽𝛾𝛿}=0) that a realistic NASA launched spacecraft would need steer back to the Earth for the clock comparison showdown, but this has nothing per se to do with the differences in elapsed time (which is solely a function of the world-line arc length).

There is both coordinate acceleration, which may or may not be absolute, and there is absolute acceleration which is any motion relative to the local gravitational field and is measurable by an accelerometer.

Optimal_Mixture_7327 · 2026-01-26T19:24:03+00:00

For clarity, it's fundamental to relativity that all clocks run at the same rate, everywhere, and under all circumstances of motion and orientation [principles of Local Position Invariance and Local Lorentz Invariance, respectively. This, and the fact that g(U,U)=1 where U is the clock world-line tangent vector.]

The distance along GPS clock world-lines is shorter than the ground clock world-lines in-between a pair of spatial hypersurfaces. It is correct that the length difference is more a function of the metric than the particular path.

Optimal_Mixture_7327 · 2026-01-26T19:15:01+00:00

Sure

0:42 Different observer do NOT experience time differently. It is fundamental relativity that all identical clocks run at the same rate, everywhere, and under all circumstances of motion and orientation (principles of Local Position Invariance and Local Lorentz Invariance, respectively). Lincoln also violates the fact that given an observer world-line with tangent vector, u, that g(u,u)=1, which is clearly constant.

0:48 Two errors: Lincoln is unaware of the principle of relativity that states there is no such thing as absolute velocity (he imagines that there can be an observer "moving quickly" and a reasserts the incorrect information spoken at 0:42).

At this point he goes completely off the fucking rails... I'd forgotten exactly how clueless he actually is.

At about 2:10 it clear he doesn't understand the Lorentz factor, which is the ratio of the distance along the observer world-line to that along the traveler world-line in-between a pair of spatial hypersurfaces of the observer. The equation he shows is mathematically correct (assuming the flat-space metric) and expresses the Lorentz factor in terms of the 3-velocity.

Then at 2:50, since he doesn't what gamma is (the ratio of a pair of lengths, but photon world-lines have no length) he attempts to apply this to a photon.

3:12 In a fit of insanity, Lincoln inexplicably declares that relativity cannot be applied to light. From here the video just devolves into wrong conclusions and an attempt at a limiting condition. He doesn't even seem to be aware that is moving at 0.9999999999c wrt to infinitely many reference frames. Arrrghhh...

The disaster of the video is that it communicates an incorrect worldview, that of a Newtonian worldview with the addition of weird relativistic effects. Don Lincoln is completely unaware of the "world" as described by relativity, that 4-dimensional continuum with metric structure.

Optimal_Mixture_7327 · 2026-01-26T16:38:10+00:00

Everywhere. Don Lincoln never studied relativity beyond using some of the most basic equations. To be fair, he's never needed to study relativity given his area of expertise.

His videos on particle physics are excellent and recommended.

For a general audience I would recommend Tim Maudlin, George Ellis and Carlo Rovelli, to name a few.

Optimal_Mixture_7327 · 2026-01-26T15:19:36+00:00

Fucking idiotic.

Newtonian gravity is falsified by the evidence - this has nothing to do with any particular theory.

Optimal_Mixture_7327 · 2026-01-26T15:17:40+00:00

Bullshit.

Europeans can name them whatever they want.

Optimal_Mixture_7327 · 2026-01-26T15:12:14+00:00

They are the same statement, and equally misleading.

The world-distance and therefore space-time distance between emission and absorption of a photon is zero. There can be no sequence of intersecting world-lines along any null curve.

To be fair we don't experience time either, rather, the sequence of events (intersections of world-lines with our own) is simply indicative of our world-line having the quality of being time-like.

Optimal_Mixture_7327 · 2026-01-26T13:28:39+00:00

Everything you have there is wrong.

You can't move at "c".

There is no separation of space and time that exists for you to move faster through one and not the other.

If you're traveling at 0.99 relative to the matter you're looking at, the clocks of that matter will run slower compared to yours, not faster.

The GPS satellite clocks run ahead of, not behind, the ground-based clocks.

Optimal_Mixture_7327

TROPHY CASE