Experiment on the variation of weight with temperature

Hello !

According to what I have read on the internet, the weight of a body varies with temperature, its mass remaining unchanged according to the theory of relativity.

My question is what experiment is done to corroborate that the weight of a body increases with the increase in its temperature.

I thank you for your response and I send you my regards.

MartinG said:

the weight of a body varies with temperature, its mass remaining unchanged

Why would you think the weight would change but not the mass?

Doc Al said:

Why would you think the weight would change but not the mass?

Well, I understand that that is what happens

MartinG said:

Well, I understand that that is what happens

Not sure why you think that. Both mass (and thus weight) will increase with temperature -- but the increase will be quite small. (You can calculate it.)

Doc Al said:

Not sure why you think that. Both mass (and thus weight) will increase with temperature -- but the increase will be quite small. (You can calculate it.)

Well, what I am trying to know above all is how experimentally it is obtained that the weight (or also the mass) increases with temperature.

MartinG said:

Well, what I am trying to know above all is how experimentally it is obtained that the weight (or also the mass) increases with temperature.

I'm not aware of any experimental measurements. But it's a direct consequence of Einstein's energy-mass relationship: ##E = mc^2##

Doc Al said:

I'm not aware of any experimental measurements. But it's a direct consequence of Einstein's energy-mass relationship: ##E = mc^2##

Ok, Thank you

@MartinG, be aware that using only Newton's Law of Gravity, a body does not gain weight if its temperature is increased. Einstein's General Relativity (which describes the world we actually live in) is a more comprehensive (and more accurate) description of gravity and it includes energy as part of what affects space time curvature (which we call Gravity).

MartinG said:

According to what I have read on the internet

Where does it say this?

MartinG said:

According to what I have read on the internet

I see you're new, so I assume you're not aware that as far as PF is concerned, that has exactly as much validity as "some guy on the subway told me that ... ".

Better here on PF to just ask your question without trying to back-fill your rationale with a useless "citation".

phinds said:

@MartinG, be aware that using only Newton's Law of Gravity, a body does not gain weight if its temperature is increased. Einstein's General Relativity (which describes the world we actually live in) is a more comprehensive (and more accurate) description of gravity and it includes energy as part of what affects space time curvature (which we call Gravity).

The above distinguishes between how the active gravitational mass of an system changes (or does not change) when the system gains energy under Newtonian mechanics and under General Relativity. As you point out, energy counts under General Relativity but does not count under Newtonian mechanics.

This explanation is slightly unsatisfying because in General Relativity it is not "mass" that gravitates. Instead it is stress and energy (the stress-energy tensor) that gravitates. So let us consider inertial mass instead.

As originally presented and as presented in many introductory physics textbooks and popular science presentations, mass increases with velocity. This is called "relativistic mass increase". Relativistic mass increases with velocity according to ##m_r=m_0 \frac{1}{\sqrt{1-v^2/c^2}}##

However, the notion of relativistic mass has fallen out of favor. Instead, when physicists use the word "mass", they mean "invariant mass". We have an Insights article on this: https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

The invariant mass (or just plain "mass") for a system can be defined in either of two ways. Either as the total energy (divided by ##c^2##) in a frame of reference where the system has zero momentum or as the invariant magnitude of the system's energy-momentum four-vector. The two definitions are equivalent except that the latter still works for objects moving at light speed. We can stick with the former definition since things with temperature cannot move at light speed.

If you increase the energy of a system (e.g. by heating it up) without changing its momentum, you increase the invariant mass of the system.

I have not done the math, but I confidently assert that the inertial mass of a compact, bound system is the same as its invariant mass. Also under general relativity there is no distinction between inertial mass and passive gravitational mass.

MartinG said:

Well, I understand that that is what happens

That does not answer the question "why".

Iron has a heat capacity of around 0.5 J/(gK). Raising its temperature from 300 K to 1800 K (just below the melting point) adds ~750 J/g, increasing its mass by 8*10^-12. You would need a scale that can measure such a small difference reliably, while at the same time getting much warmer. Sublimation of iron might be an issue, too.

I haven't seen a scale that can do it, although it might not be that far away - maybe we'll get such an experiment in the next 20 years.

I think it is pretty far away. You need to be ~1000x better than the best Kibble balance. At this scale, you have a great deal of sensitivity to the surrounding environment, like the gravitational force due to the experimenter. Controlling this is going to be hard.

It's also unclear how useful this is. In terms of PPPN parameters, this experiment lets us measure β to ±1000 or so (today). The proposed improvements would get us to ±1. But we know from other experiments, such as the Nordtvedt Effect to around a part per 10,000.

The Washington group has been working on measuring the weight of magnetic fields with Eotvos-type experiments (as well as the weight of angular momentum) and don't see an effect - this also strongly constrains β.

As there are far more sensitive experiments out there, I don't see a great interest in making this one a million times better, if that is even possible.

It's a bit like the antimatter gravity experiment. There isn't a realistic chance to get a different outcome, but it's still a nice demonstration of a predicted effect.

Superconducting gravimeters can achieve 10^-12 relative precision under ideal conditions, but their test mass needs to be superconducting which reduces the temperature range too much.

mfb said:

a nice demonstration

Sure, but it's hard to get support to improve things by orders of magnitude for a "nice demonstration". Especially when we have other ways of measuring the same thing which are better.

The money goes into more sensitive and more robust scales, which have other applications as well.

If you had the required sensitivity, you could measure G to 11 decimal places. That's a good thing, but a long way from the 5 or maybe 6 we have today. Further, to get to this level of sensitivity, you need to control the environment very well: all kg objects within a meter, all 10 kg objects within 3 meters, etc. This has all sorts of practical problems - where do they park their cars? How to blank the system when a toilet flushes. And so on.

Vanadium 50 said:

If you had the required sensitivity, you could measure G to 11 decimal places.

You couldn't. Measuring G relies on measuring the gravitational forces between masses in the lab as you don't have a direct mass measurement for Earth. What we want to do here is using Earth as source mass for both measurements. It doesn't need a precise value of G or even GM (which is known to 10+ decimal places), it just needs that product to stay the same.

We can do the experiment while no one moves their car within 30 meters, but we don't care that much about horizontal forces anyway. An experiment would mostly worry about things below and above the setup, i.e. masses in your own building.

My point is that if you could measure 10 ppt, you could do a lot more with it.

But I am sick of arguing. If you think measuring this is a good use of your time, go ahead. I'm not going to stop you. To me, the question "Does thermal energy gravitate differently than other forms of internal energy" - essentially what this is asking - is not high on my list of things I would want to spend my time looking into.

Vanadium 50 said:

My point is that if you could measure 10 ppt, you could do a lot more with it.

We can do better than that already. Just not with scales that you can heat up.

I'm not working on these scales. I think it's pretty similar to "antimatter falls down". It's a nice result on its own, and such a project will drive improved gravimeters.