B What Links High Velocities, Strong Gravitational Fields, and Time Dilation?

[Lutz-F]

TL;DR Summary

Two sets of questions (time and c) – maybe fundamental, but probably naive...

The faster the relative speed or the more intense the gravitational field, the slower time passes. Does it make sense to ask what both have in common that affects time? Or does the question possibly only make sense in the context of certain theories, for example the LQG, where space and time arise through the interactions of gravitational quanta?

Is it a coincidence that both electromagnetic waves and gravitational waves move in a vacuum with the speed c? Is there an underlying cause? Is the reason for this a fundamental property of spacetime or space quanta or gravitational quanta?

 

[PeroK]

The faster the relative speed or the more intense the gravitational field, the slower time passes. Does it make sense to ask what both have in common that affects time?

Both are explained by spacetime geometry. The time dimension is part of four-dimensional spacetime and time dilation is a consequence of that.

Is it a coincidence that both electromagnetic waves and gravitational waves move in a vacuum with the speed c? Is there an underlying cause? Is the reason for this a fundamental property of spacetime or space quanta or gravitational quanta?

The speed of light in vacuum ($c$) is essentially it's a conversion factor between units of length and time. It also represents the speed at which massless radiation propagates in vacuum.

It's not much of a coincidence that gravitational waves also travel at $c$, as it arises from the same mathematical basis.

 

[Lutz-F]

Both are explained by spacetime geometry. The time dimension is part of four-dimensional spacetime and time dilation is a consequence of that.

The two different processes have the same effect due to the structure of our universe. That is very general...

It's not much of a coincidence that gravitational waves also travel at , as it arises from the same mathematical basis.

Does that mean that electromagnetic waves and gravitational waves have at least one common property? Or, in principle, are both waves traveling properties of spacetime? Do they have that in common? Or is the reason for the same mathematical basis the common past as primal force in the Planck epoch?

 

[PeroK]

Does that mean that electromagnetic waves and gravitational waves have at least one common property? Or, in principle, are both waves traveling properties of spacetime? Do they have that in common?

Both EM and gravitational waves are associated with massless wave equations, which imply null paths through spacetime.

 

[Lutz-F]

The faster the relative speed or the more intense the gravitational field, the slower time passes. Does it make sense to ask what both have in common that affects time?

Both are explained by spacetime geometry. The time dimension is part of four-dimensional spacetime and time dilation is a consequence of that.

Is the inertial mass bigger in a more intense gravitational field (for example on earth) than in a less intense gravitational field (for example on the moon)? Is the inertial mass bigger in a system with faster relative speed? Is that what they have in common that affects spacetime in the same way?

 

[PeroK]

Generally we have an invariant mass in GR that is independent of coordinates or the local gravitational field.

 

[Lutz-F]

So the notion of "inertial mass" is out of date? What is the alternative? Faster relative speed effects spacetime in the same way as a more intense gravitational field. - Does faster relative speed cause a kind of bow wave in spacetime that more and more impedes acceleration?

 

[PeroK]

So the notion of "inertial mass" is out of date? What is the alternative? Faster relative speed effects spacetime in the same way as a more intense gravitational field. - Does faster relative speed cause a kind of bow wave in spacetime that more and more impedes acceleration?

There's an equivalence between inertial and gravitational mass. The issue here may be that you are thinking of the concept of "relativistic" mass. This is not relevant to GR and gravitation - so your question is based on a false premise. In general, you are better not using the concept of relativistic mass when looking at modern physics. See, for example:

https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[Lutz-F]

Thank you for your patience and your answers. I think I need to realize that there is no answer for my initial question:

The faster the relative speed or the more intense the gravitational field, the slower time passes. Does it make sense to ask what both have in common that affects time?

Maybe the question really does not make sense. Your answer:

Both are explained by spacetime geometry.

seems to be an answer for many questions. I thought that there are not only the laws and formulas but some knowledge of the processes behind.

 

[jbriggs444]

The faster the relative speed or the more intense the gravitational field, the slower time passes.

Maybe the question really does not make sense.

It does not make sense to speak of time passing slowly. It only makes sense to speak of time passing slowly for one clock compared to another clock.

In the case of relative speed, the discrepancy in clock rates is an artifact of the way you compare the clocks. It is symmetric. Each clock sees the other run slow because each will conventionally use its own synchronization standard when comparing itself with the other. This sort of time dilation is not so much a physical effect as an artifact of coordinate choice.

In the case of a gravitational field it is not the field intensity that matters. It is the gravitational potential -- how deep you are in the gravitational well that comes into play. The local gravitational acceleration does not matter. For clocks hovering in a gravitational field there is little ambiguity about synchronization and there is an asymmetry to the relative clock rates. The lower clock is seen by the higher clock to run slow. The higher clock is seen by the lower clock to run fast. This sort of time dilation might be considered physical rather than merely an artifact of coordinate choice.

 

[Ibix]

Thank you for your patience and your answers. I think I need to realize that there is no answer for my initial question:

Let me ask a different question. If I walk in a straight line on a flat plane then this is shorter route than a zigzag path. If I walk on the surface of a cone I circumnavigate the cone in less distance if I walk near the point than if I walk far from the point. Is this a coincidence?

What answer would you accept to that if "it's just the way the geometry works" isn't acceptable? I can't think of much - it's just that there are longer and shorter routes through space, just as there are through spacetime.

 

[Lutz-F]

@jbriggs444: Now I see the difference - and my lack of knowledge. I just read about the twin paradox and I realized that it is often oversimplified, described without the details.

@Ibix: I acceps the anwers and I'm satisfied.

Thank you all.