Another Way of Looking at Gravitational Time Dilation?

[inflector]

https://www.physicsforums.com/showthread.php?t=433866" that relativistic time dilation does not depend on acceleration, i.e. that there are instances where the acceleration might be zero while there would be significant time dilation. The example in the other thread was gravity and acceleration in the core of a spherical planet where there would be time dilation due to the gravitational potential even though there would be no acceleration due to gravity.

This made me wonder about time dilation itself.

Would it be equivalent to look at gravitational time dilation, not as time slowing down but rather as inertia increasing? Would there be any way of experimentally differentiating between these two perspectives? I.e. how can one tell the difference through experiment between the inertial mass of a system proportionally increasing and time slowing down?

It seems to me that one would only be able to determine inertial mass by looking at the effect of a given force on the acceleration of the mass using the equation F = ma. However, since both time (through the second derivative of position implied by acceleration) and mass are present in the formula, one can't really distinguish between time slowing down and inertial mass increasing.

Does this mean that gravitational time dilation could also really be seen as gravitational inertial mass increase if the two perspectives are mathematically equivalent? Or am I missing something obvious again?

 

[yuiop]

Although you have a sort of point about inertia appearing to increase, there are some time dilation aspects such as biological processes, chemical reactions and characteristic emission spectrums of excited atoms, that are difficult to explain in terms of inertial mass increase.

 

[inflector]

Although you have a sort of point about inertia appearing to increase, there are some time dilation aspects such as biological processes, chemical reactions and characteristic emission spectrums of excited atoms, that are difficult to explain in terms of inertial mass increase.

What is unique to these sorts of biological processes and chemical reactions that couldn't be explained by an increase in inertial mass?

For example, harmonic oscillators change frequencies when the masses involved increase, likewise there are other dynamics involved in biological processes and chemical reactions that seem to me could be explained by increased inertial mass. So I'm not sure that these would be any different than any other dynamics involving time and mass.

I'm not saying that phenomena which can only be explained in terms of time do not exist. That's why I am asking the question here. I don't know the answer.

 

[Ich]

harmonic oscillators change frequencies when the masses involved increase

1. By what factor does the frequency decrease due to SRT?
2. By what factor does the inertial mass increase due to SRT?
3. By what factor does the natural frequency of a harmonic oscillator change when its inertial mass is increased?
4. Is 3 consistent with 1?

 

[DaveC426913]

What is unique to these sorts of biological processes and chemical reactions that couldn't be explained by an increase in inertial mass?

How about electrical currents? EM frequency? Subatomic decay?

There are plenty of phenomena that are not directly a result of mass.

 

[inflector]

1. By what factor does the frequency decrease due to SRT?
2. By what factor does the inertial mass increase due to SRT

NOTE: I am referring to a time dilation due to gravitation under general relativity not SRT.

Under my proposed potential equivalence, this mass adjustment factor would need to correspond to a time dilation for the relationship of:

$$F = ma = m\frac{\mathrm{d}^2x}{\mathrm{d}t^2}$$

3. By what factor does the natural frequency of a harmonic oscillator change when its inertial mass is increased?

The differential equation for a harmonic oscillator extends the above to account for Hooke's Law:

$$F = -k x$$

so we get the differential equation:

$$F = ma = m\frac{\mathrm{d}^2x}{\mathrm{d}t^2} = -k x$$

4. Is 3 consistent with 1?

Since I'm proposing that mass be adjusted according to the same underlying second-derivative-of-x-with respect-to-t equation:

$$F = m\frac{\mathrm{d}^2x}{\mathrm{d}t^2}$$

the change in frequency for the harmonic oscillator would be consistent with that required to satisfy the equation itself almost by definition.

 

[inflector]

How about electrical currents? EM frequency? Subatomic decay?

There are plenty of phenomena that are not directly a result of mass.

Good points, I can see how electrical currents would be related to the mass of the electron, but not EM frequency or subatomic decay.

Have there been measurements of gravitational time dilation that tested these two phenomena? Or have the measurements made so far been restricted to oscillator-based timing?

I don't see how there would be enough precision for measuring time using subatomic decay measurement, so this is probably out.

 

[DaveC426913]

I don't see how there would be enough precision for measuring time using subatomic decay measurement, so this is probably out.

It's ubiquitous in particle accelerators. That's one of the commonest ways they confirm time dilation, by watching particles decay slower exactly in accordance with SR prediction.

 

[inflector]

It's ubiquitous in particle accelerators. That's one of the commonest ways they confirm time dilation, by watching particles decay slower exactly in accordance with SR prediction.

Except that we're talking about stationary objects in gravitational time dilation in this case, not time dilation based on the Lorentz factor.

The time dilations are going to be orders of magnitude smaller in any cases we can measure on Earth as compared with the SR time dilation of a particle close to c.

 

[DaveC426913]

Except that we're talking about stationary objects in gravitational time dilation in this case, not time dilation based on the Lorentz factor.

:blush: GR/SR heh

 

[Ich]

NOTE: I am referring to a time dilation due to gravitation under general relativity not SRT.

:blush: GR/SR heh

Ok, so a black hole has infinite inertial mass?

 

[DaveC426913]

:blush: GR/SR heh

I made a mistake. Answered too hastily.