Proper Acceleration And Time Dilation

[physics2222]

TL;DR

Proper Acceleration And Time Dilation

What causes the time dilation for two observers, one undergoing acceleration and one remaining stationary, in the twin paradox? Assuming both started at point A, one goes to point B and back again. And the clocks were roughly in agreement when they started at point A.
I understand that once an observer has a velocity, their proper time accumulates a larger time discrepancy the longer and faster they travel. However, how does the initial mechanism of proper acceleration induce the time difference?

 

[Dale]

In space the shortest distance between two points is a straight line (geodesic). But in spacetime the longest timelike interval between two events is a straight line. Acceleration is a bend in a path through spacetime.

So the stationary twin has a straight path and the accelerating twin has a bent path, and straight paths are longer than bent paths. The path length is measured by a clock on the path.

 

[Dale]

But on a small scale, what causes the initial acceleration that starts the clock discrepancies?

It doesn’t matter. Any unbalanced force will do.

 

[PeterDonis]

Insights Thread 'When Discussing the Twin Paradox: Read This First'

Jan 2, 2023

This article is intended for anyone who wants to start a thread here at PhysicsForums on the twin paradox. There are already many, many threads here on this topic, and they tend to cover the same ground over and over again, so it seems useful to put a description of that ground into an article that everyone can read before starting yet another thread. If you are in that category, and what is here answers your question, great! But even if it doesn’t, hopefully, this article will help you to frame whatever questions you still have after reading it, in a way that will help you to get...

• PeterDonis
• Paradox Twin paradox
• Replies: 2
• Forum: Special and General Relativity

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[PeroK]

I understand that once an observer has a velocity, their proper time accumulates a larger time discrepancy the longer and faster they travel.

However, how does the initial mechanism of proper acceleration induce the time difference?

You've misunderstood special relativity. There is no concept of absolute velocity. Velocity-based time dilation is reciprocal. Both observers measure the other's clock running slow.

To say an observer "has a velocity" has no meaning in physics. All velocities are relative and reciprocal.

The twin paradox can be presented without acceleration. In that sense, there is no mechanism for acceleration to cause differential ageing.

 

[Matterwave]

The twin paradox can be presented without acceleration. In that sense, there is no mechanism for acceleration to cause differential ageing.

Here's a presentation without acceleration: https://en.wikipedia.org/wiki/Bondi_k-calculus

In the section on twin paradox.

 

[DJDS]

As Dale said, the elapsed time between two events depends on the path between them- it is greater along a straight path than along a curved or crooked path, and that is what accounts for one twin experiencing less elapsed time than the other.

Consider the everyday analogy with a spatial gap. If you walk diagonally across a square to the opposite corner while I walk along two edges to get there, your pedometer will clock up a different distance to mine. What causes one pedometer reading to be different from the other? It is the fact that the routes have different lengths, which is effectively a consequence of the geometry of space. Likewise with the twin paradox, the different temporal path lengths are a consequence of the geometry of spacetime.

Given that, you should now be able to clarify the role of acceleration, which is only that it allows you to follow the non-straight path. In the example of the square, acceleration allows me to walk down one side and turn at the next corner. Of course, you can eliminate acceleration from the set-up by assuming that I walk down one side of the square and hand-off my pedometer reading to someone who happens to be walking along the next edge just as I reach the corner. Likewise with the twin paradox- acceleration is what causes one twin to follow the shorter, crooked path, but you can illustrate the effect by having people moving inertially and handing-off clock readings.

Any disagreements you might see about whether acceleration does or doesn't cause the twin paradox are effectively arguments at cross purposes. The different path lengths are the root cause- acceleration allows the shorter path to be followed.