# Experiments about impact of mass in different areas

• Felian
In summary: It would be interesting to know what the theoretical limit might be.Many of these experiments don't really seem like they'd be able to tell that apart.Oh, for any googlers who get here. I found another paper handling 'active' vs 'passive' gravitational mass, though it seems to assume that the laws of conservation would be broken if they were different:https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.57.21

#### Felian

There's important experiments showing the equivalence of inertial mass and gravitational mass ( the Eotvos experiments), but I couldn't really find many that show the equivalence of mass (or the stress-energy tensor) in other contexts.

These are some of the variants of mass I'm interested in:
- Inertial mass
- 'passive' gravitational mass, as in: how much does an object get accelerated due to spacetime curvature?
- 'active' gravitational mass, as in: how much does the object curve spacetime, with important sub-parts such as:
- How much does the object impact gravitational acceleration of other objects
- How much does the object impact gravitational time dillation
- How much does the object impact gravitational lensing
- How much does the object impact gravitational red/blueshift
- How much does the object impact shapiro time delay

Generally, these are assumed to be the same, and of course, everything is much more sensible and works out much neater if they are. We might even run into some issues with conservation laws if they weren't the same.
But neatness aside, I'm wondering if there's any good experiments that show that these effects indeed do all use massenergy, and aren't influenced by some other attribute of the objects that cause them (like say, total particle count or the sum of the particles rest masses).

The only solid experiment I could find that isn't just about inertial mass vs gravitational mass was this one by Kreuzer:
https://journals.aps.org/pr/abstract/10.1103/PhysRev.169.1007
Which is at least something, but it doesn't really cover all the bases

• Eötvös links the inertial mass to the passive gravitational mass.
• Cavendish-like experiments link passive and active gravitational mass for the acceleration (ACC) as the roles are interchangeable. Lunar laser ranging does the same.
• GPS, Hafele–Keating and all the similar experiments link ACC and time dilation.
• Various stellar measurements link ACC and red/blueshift
• Time dilation and red/blueshift are the same thing anyway, just measured in a different way.
• Measurements of galaxies link the Shapiro delay to lensing and they can link lensing to ACC.
• Gaia will add gravitational lensing from planets (with known ACC).
• ... and probably more.

Measurements of the Sun include all types of active and passive gravity you listed. They all agree.

anorlunda and Felian
Thank you! I will explore these!

Cavendish-like experiments link passive and active gravitational mass for the acceleration (ACC) as the roles are interchangeable. Lunar laser ranging does the same
Time dilation and red/blueshift are the same thing anyway, just measured in a different way.

These are of course true, and it'd be extremely weird if it weren't the case that these are the same, but it's still interesting to see whether it has been experimentally shown whether they are. It might be worth some experiments just to remove that tiny bit of doubt.
As far as I'm aware, Cavendish doesn't really test that, though it does test inertial mass vs acceleration.

Various stellar measurements link ACC and red/blueshift

Do you know of any in particular that put bounds on this? I'm guessing you mean something like comparing the rotation behavior of binary stars to the shifts in their emission spectra?Do you know if there's any experiments that have tested whether it's the total massenergy or the rest mass of the particles that matters? Say by testing whether a heated object has a larger effect on spacetime curvature?

I'm curious because I can imagine that in some unified quantum physics + GR/SR, things might work slightly different. Like say, if gravitons exist and are involved in gravitational acceleration but not in time dillation, then whatever creates gravitons may be slightly different from what causes time dillation. Perhaps time dillation is caused by mass energy, but gravitons are created by rest mass, or just by protons, or something like that. Many of these experiments don't really seem like they'd be able to tell that apart.
Oh, for any googlers who get here. I found another paper handling 'active' vs 'passive' gravitational mass, though it seems to assume that the laws of conservation would be broken if they were different:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.57.21

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Felian said:
As far as I'm aware, Cavendish doesn't really test that, though it does test inertial mass vs acceleration.
The Cavendish experiment has been done with a large range of source masses of various materials and size and many of them have been used as test masses as well.
Felian said:
Do you know of any in particular that put bounds on this? I'm guessing you mean something like comparing the rotation behavior of binary stars to the shifts in their emission spectra?
I don't know, check the publications. Gravitational redshift measurements are routine. In binaries you know the average radial velocity of both is the same so you can remove the contribution from the Doppler effect.
Felian said:
Do you know if there's any experiments that have tested whether it's the total massenergy or the rest mass of the particles that matters? Say by testing whether a heated object has a larger effect on spacetime curvature?
We don't have measurements precise enough to detect heat yet (~1-2 orders of magnitude missing), but objects of different composition (=> different contribution from electrons, quarks and binding energies) have been measured, in the lab, for the Earth/Moon system and for stars.
Felian said:
Perhaps time dillation is caused by mass energy, but gravitons are created by rest mass, or just by protons, or something like that.
That is ruled out by a few thousand standard deviations at least. All these measurements are looking for parts per million, parts per billion or sometimes part per trillion effects.

anorlunda

## 1. What is the purpose of conducting experiments on the impact of mass in different areas?

The purpose of these experiments is to understand how mass affects various aspects of our daily lives and the world around us. By manipulating and measuring mass in different areas, scientists can gather data and make observations to better understand physical processes and phenomena.

## 2. How do scientists determine the impact of mass in different areas?

Scientists use various methods such as controlled experiments, mathematical models, and simulations to determine the impact of mass in different areas. These methods allow them to isolate specific variables and measure their effects on the surrounding environment.

## 3. What are some real-world applications of experiments on the impact of mass in different areas?

Experiments on the impact of mass have numerous real-world applications, including in engineering, transportation, and environmental studies. For example, understanding the impact of mass on structures can help engineers design more efficient and safer buildings, while studying the effects of mass on air and water flow can aid in improving transportation systems.

## 4. How does the location of mass affect its impact on the surrounding area?

The location of mass can have a significant impact on its surroundings. For example, a large mass placed on a soft surface will have a greater impact than the same mass placed on a hard surface. Additionally, mass placed in a concentrated area may have a different impact compared to the same mass distributed over a larger area.

## 5. What are some potential limitations of experiments on the impact of mass in different areas?

One limitation of these experiments is that they may not accurately reflect real-world conditions, as they often involve controlled environments and simplified models. Additionally, the results may vary depending on the materials used and the specific conditions of the experiment. Lastly, ethical considerations must also be taken into account when conducting experiments involving mass and its impact on living organisms or the environment.