What exactly is mass?

Factual Questions
61

To add to this, the entire concept that the moon is falling around Earth directly requires the w = mg formula to hold.

Remember that time is absolute and gravity is more than superluminal but instant acting across the entire universe under Newton. Under the Galilean transformations he used you have a R[sup]3[/sup] cover over a R[sup]1[/sup] manifold

Given a 4D space with labeled (ct, x, y, z)

g[sub]1[/sub] =
[1,0,0,0]
[0,0,0,0]
[0,0,0,0]
[0,0,0,0]

g~[sub]2[/sub] =
[0,0,0,0]
[0,1,0,0]
[0,0,1,0]
[0,0,0,1]

Where: Λ[sup]T[/sup]g~Λ = g~

You have non-trivial space, which are non-invertable and are degenerate. Lorentz recognized that the second half of Maxwell’s equations are geometric relations and his “Lorentz transformations” arise from simple trig identities of

g =
[-1,0,0,0]
[0,1,0,0]
[0,0,1,0]
[0,0,0,1]

Where: Λ[sup]T[/sup]gΛ = g

But as simple algebra formulas existed we just modified Newtonian mechanics vs creating newer mechanics (which would still be approximations) which didn’t have the problems of the false concept of absolute time or the math issues related to having a complex bundle.

Newtonian physics is simply satisfactory for most purposes, but as you sitting up in a chair has to be instantaneously felt by not only you but the Andromeda galaxy and the rest of the entire universe we will be stuck with some of these issues.

I don’t want to digress into a discussion on where the concept of “now” is fundamentally wrong, but there is no “now” in Andromeda that maps to your now and technically there is no “now” that relates to you and the ISS.

We could have created a better classical mechanics framework where it didn’t matter, but in the one we have and use avoiding that operational concept of “weight” is a hard requirement. The formulas are simple to use approximations, but they just do not work if you try and move:

W = m/a[sub]gravity[/sub]

To fit the apparent weight model. It simply breaks the math, and the analogies tends to break students forward movement in physics too. We don’t tell people why this is important until well after the classes most students attend and even most Physics teachers and scientists will aggressively assert that the operational implications are related to the fundamental properties, which is purely wrong.

The acceleration observed by an object is what changes, not the weight. And that level of acceleration changes from your toes to your head too, in fact that is what results in you even having a pseudo-force to even call gravity in the first place.

P.S I tried to summarize the math to fit in with what this forum supports and yes there are errors but there is enough for anyone with some linear algebra to see what the issue is with the coverage matrix above.

62

Oxford study on negative mass:

And from Wikipedia:
The Newtonian approximation then provides the following interaction laws:
Positive mass attracts positive mass.
Negative mass attracts negative mass.
Positive mass and negative mass repel each other.
Those laws are different to the laws described by Bondi and Bonnor, and solve the runaway paradox. The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of dark matter, dark energy, cosmic inflation and accelerating universe.[20][21].
How would positive-mass antimatter react to negative mass?

63

They tried to clarify in a later story but the naming and title is a bit click baitish on that article

Trying to describe self-interference and what spin actually is won’t happen with normal language. You have to understand what the math is doing first to grasp most of what is being referenced here. My advice on quantum spin is learn from Pauli don’t try to visualize it. You need to learn the math and then build intuitions based on their results.

The term “spin” is a perfect example of the unfortunate reality that things in physics are typically named before we understand them. This forum doesn’t have the tools to try to even describe the relativistic equations of quantum mechanics.

This is just one of the parts of quantum mechanics goes beyond human intuition.

But this story on “negative mass” doesn’t change the inertial or rest mass of an object, it is simply a problem where someone who was brilliant at physics was awful at language. As I am mediocre at both I can relate. That said we mock and teas the solid state folks who chose one again to overload mass by inventing the phrase Effective mass when they could have used their creativity to create a new name that didn’t cause yet another point of confusion.

Here is the paper that link was based on.
https://arxiv.org/pdf/1612.04055.pdf

Note I have added emphasis the critical term here which indicates it is not a property of inertial or rest mass.

64

Mass is what you heathens should attend on Sundays.
Weight is a measure of time (as in Weight a minute!).
Size doesn’t matter.
Density matters but also applies to anti-matter.
Which leaves the fact that gas is also matter and therefore passing gas is in fact the process of creation and we are all just flatulence in the eyes of the Lord, which you would know had you attended more mass on Sunday.

65

Mass is “frozen” energy. (just a quip). I think I read once that the Little Boy atomic device used at Hiroshima involved the “thawing” of something in the range of less than 1 gram of matter.

Weight- I’m a master horologist as a serious hobby. The Shortt–Synchronome (Inventor’s name) Free Pendulum Clock housed at the Naval Observatory is a mechanical clock housed in a case with as good a vacuum as they could produce back in the day (1921). Unlike all other pendulum clocks, the master pendulum swings “freely” until its arc lessens to a degree requiring an additional impulse, at which point the astonishingly complex mechanical /electo (i.e., 99% mechanical) mechanism imparts a tiny impulse to the pendulum each 30 swings. Time is actually kept on a second clock with a more standard pendulum, synchronized to the free swinging master pendulum. Not going to write out the formula for the period of the pendulum. But it includes the mass of the pendulum and the gravitational force (usually assumed to be a constant).Thing is, it has been shown this clock is so fundamentally accurate that it has the ability to discern the change in weight of the pendulum in response to the tidal force exerted by the rotation of the moon- which changes the gravity “constant”, therefore changing the weight (but not the mass) of the pendulum bob over time, causing the clock to gain and loose fractions of a second over the period of the tides. So gravity is not only different at different places on the Earth’s surface (partially due to Earth not being a perfect sphere, and partially due to differences in sub-strata density (i.e., local mass), it also changes in response to the earth being part of a gravitational system. Using modern super clocks, it is also possible to show variation in the gravitational force over the Earth’s rotation around the sun, since the orbit is not a perfect circle.
The closest analogy to mass for the concrete thinker is, I think, the concept of inertia. Hang 1 oz and a 1 ton ball of lead from cables. Their weight is held by the cables. Push the 1 oz ball 1/100th of an inch- you could blow on it to do it. TRY and push the 1 ton weight the same tiny distance. Will take some effort- that (ignoring change in height from the arc of the circle center on the suspension points created by movement, which includes overcoming a tiny gravitational force) and you are feeling the impact of MASS. Weight changes according to local gravity; mass is constant everywhere, excluding fission, fusion, or nuclear decay events.
See:

Quote: In 1984 Pierre Boucheron studied the accuracy of a Shortt clock preserved at the US Naval Observatory. Using modern optical sensors which detected the precise time of passage of the pendulum without disturbing it, he compared its rate to an atomic clock for a month. He found that it was stable to 200 microseconds per day (2.31 ppb), equivalent to an error rate of one second in 12 years, far more accurate than the 1 second per year that was previously measured. His data revealed the clock was so sensitive it was detecting the slight changes in gravity due to tidal distortions in the solid Earth caused by the gravity of the Sun and Moon.

66

I hate to do this, but no mass is not consistent across fission and fusion, the binding energy is typically just too small for us to care about but we can measure it.

Even the mass of a compressed spring is greater than that of an uncompressed spring, this is what Einstein’s mass-energy equivalence formula shows.

Most of your post was spot on but it still has the problem of using pre-civil war scientific assumptions. The majority of the effects of the tidal force are due to the tractive force and not the change in “weight”. This is a very common misconception among even most scientists. But it is because in spacetime the time dimension is so much larger than the spacial dimensions that our “weight” is almost exclusively due to that change in dimension. The force vectors on the spacial dimensions are mostly a “squeeze” and only their sum ends up being a vertical component.

While those experiments can be quite acculturate, especially with the limited ability to measure, they are not demonstrating what we have known for a century about time.

There simply isn’t one universal clock, even at one location, as a moving clock will have a different proper time than a stationary clock at the same location. There simply isn’t a universal time at all.

Note If this thread wasn’t about the fundamentals behind mass I wouldn’t have responded. But the “gravity” doesn’t change the actual geometry of spacetime seems to change under our best known theory today.

Note you are using the operational definition of weight, the gravitational version does not change, it is just a formula calculated on sub elements and the sub element of gravitational acceleration is what changes.

Unfortunately unless we encourage more people to learn more modern physics I am tilting against windmills here though. Or entire education system tends to paint Newton’s laws as the absolute truth instead of being a more convenient but less accurate model compared to the GR model which is still currently more accurate than our ability to measure.

67

Sure, you can put a balance in a vacuum. But most people don’t care about true mass. They care about conventional mass.

Here’s the deal: when you put a specimen on a scale or balance, the balance makes two assumptions:

  1. The balance assumes the specimen is made of solid, stainless steel.

  2. The balance assumes the air density is 1.2 kg/m[sup]3[/sup].

After placing the specimen on the pan, the balance makes these two assumptions and displays a value in kg (or mg) on the screen. The value it displays - e.g. 10.3659 mg - is the conventional mass of the specimen, not the true mass of the specimen. The true mass of the specimen can be easily calculated, but in practice this is rarely done; most people simply report the conventional mass value.

Now if your specimen is constructed of stainless steel and the air density is 1.2 kg/m[sup]3[/sup], then the conventional mass value reported by the balance will be accurate (± some uncertainty). However, if the specimen is not constructed of stainless steel, and/or the air density is not 1.2 kg/m[sup]3[/sup], then the value displayed by the balance will have error. These two, systematic errors can be easily taken into account if you know the density of your specimen and you know the density of the air. After you take these into account, you will have an accurate value for the conventional mass of the specimen.

68

While I am horrified by running into yet another qualified definition of the way too overloaded term of mass I always wondered how metrology accounted for the changes in (true|inertial|rest) mass and temperature.

Is appears that conventional mass is corrected for buoyancy, temperature and density…Here is a link to a definition for those who are trying to keep track of “yet another type of mass”

http://www.npl.co.uk/reference/faqs/what-are-the-differences-between-mass,-true-mass-and-conventional-mass-values-(faq-mass-and-density)

69

What’s interesting is that almost all the mass values you encounter in your day-to-day life - and even mass values used by scientists in the lab - are not true mass values. Most people don’t know this. Of course, most the time the difference between the (reported) conventional mass value and its true mass is so small that it doesn’t matter, and many balances don’t even have the accuracy or resolution for it to matter. But it’s something to keep in mind…

A more serious concern is when someone weighs something that has a density much different (and usually much lower) than stainless steel. They plop the specimen on the pan, take a mass reading, write it down, and then assume the value is correct because the instrument is a fancy, NIST-traceable Mettler balance that costs $20K. Unbeknownst to them, the value reported by the balance has some systematic error; the reading is too low. This is because the balance was calibrated & adjusted with stainless steel weights, which means the balance assumes everything placed on the pan is also stainless steel. (Or more precisely, it assumes everything placed on the pan has a density of 8000 kg/m[sup]3[/sup].)

A number of years ago a pharmaceutical company was having a problem: their drugs were too potent. During the investigation they discovered they were not performing a density correction when taking mass measurements of the drug, and errors were compounding. The balance assumed everything placed on the pan was stainless steel, and so the actual conventional mass values of the drugs were higher than the conventional mass values reported by the balance. Oops.

70

Bullshit.
A helium filled balloon has a negative WEIGHT, but a positive MASS.
And Buoyancy is the correct and only reason for this difference.

71

The helium balloon has both a weight force pulling downwards, and a buoyant force pushing it upwards. There is no more reason to call the force of the air pushing up on the balloon part of its “weight” than there is to call the force of the floor pushing up on my feet part of “weight”.

72

Ask an English speaker pre-Newton if a rock has less weight in water, and they would say yes, off course. Ask a layperson today the same question, and many if not most would say the same thing.
Physicists are free to define what weight means to other physicists, but cannot redefine it for everyone else unless **norma loquendi **goes along. Perhaps physicists should have used another word to avoid confusion, such as the Latin word pondus. Then we could all agree that a rock has less weight in water, but the same pondus.

73

I would disagree with this, every time I push the accelerator on my car I interact with mass all the time.

The fact that other forces impact the total effective force and that inertial mass is impacted by energy content is closer to the “true” meaning of mass.

If you want to talk about “true mass” in an intrinsic, physical fashion, it is not the form produced by metrology. Metrology created these tools to work around a model of mechanics which was based on closed systems in an inertial frame when we are not living in a closed model nor in an inertial frame.

If you are talking about the actual physical properties of a body that relates to it’s resistance to changes in momentum, one doesn’t need to correct for temperature etc… Those corrections are only required once the precision required exceeds the implications of our daily world not being in an inertial frame.

74

Outside of taxation and trade, which is why metrology was invented or even weight came up were based in the “sciences”.

The units of weight or mass were created at a time when precision wasn’t high enough to even worry about buoyancy. But they also didn’t have calibrated spring scales and would have used balance scales which compare mass.

The reason there is this confusion is not because that relationship changed, but because our needs for precision increased and because the definition you are using for weight changed.

The confusion is an artifact of how we teach the concept of weight, specifically Newton’s third law: For every action, there is an equal and opposite reaction

Newton couldn’t identify the equal and opposite reaction for gravity, and due to limitations of the math related to relative effects he was using, which was based on the ideas of Galileo he didn’t have the tools to find them. Thus he took this “fictional force” and developed other formula to describe what he observed.

A fictitious force is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference. As gravity accelerates an elephant and a feather at the same rate but you can’t identify more “energy” Newton’s third law doesn’t hold. But the same thing is true with the backward force when you accelerate in your car. And in this case the helium balloon will also go forward.

This is due to Archimedes’ principle, where the weight of the displaced fluid is directly proportional to the volume of the displaced fluid. Air is a fluid and this has been known for a long time, and in fact Archimedes of Syracuse died before 200 BC.

Newton discussed centrifugal force, which is another fictitious force when he wrote his Principia. He knew that this was unsolved but he anticipated what was later found in Mach’s Principle and General Relativity.

The reason that this is confusing for you and most people is because our education system took these approximations and concerns of Newton and changed them into a curriculum that teaches complicated, incorrect concepts in an attempt to treat the works of Newton as absolute law.

After these deficiencies in the amazing advances Newton were addressed by later scientists the education system decided to basically stick to a model where they teach pre-civil war classical physics and ignoring almost all modern advances until higher levels of education.

The now common operational definition of weight that you view as the normal or non-physics version is this corrupted version.

This artificial, and counter-productive, conflicting definitions of weight are so ingrained due to our choices on how to teach the subject that Sciences has completely abandoned it. In fact if you look at a modern periodic table compared to one just a few decades old you will see that “molecular weight” is now called “molecular mass”.

The common one-upmanship of “mass is invariant but weight changes” is a myth. But even professional scientists and almost all K-12 science teachers and even many undergrad physics teachers will loudly and forcefully claim it is true, as will the general public.

The term weight is just so encumbered by conflicting definitions and misunderstandings that most sciences have abandoned it totally when possible.

But if you asked an English speaker pre-Newton if a rock has less weight in water, they would say no, it has an upward buoyant force. Pre-Newton English speakers simply didn’t have spring scales, or space travel or the operational definition of weight to confuse the issue.

75

So an aircraft carrier has no weight, either? I know of nobody who would say that an aircraft carrier is weightless.

76

I don’t disagree. I was simply pointing out that, when we weigh something, conventional mass is what’s displayed on the digital readout, not true mass. Of course,

  1. This only applies to analytical balances that have enough resolution, and a low enough uncertainty, that the difference can be quantified.

  2. If the mass is (for example) being horizontally accelerated, you will want to compute the true mass value based on the conventional mass value.

77

Oh, and Crafter_Man, I alluded to that issue in post 46, though I didn’t know all of the practical details, like that the standard calibration masses were made out of stainless steel, or that one often leaves the value uncorrected and just gives it a label indicating that. As you might guess, I haven’t done much laboratory work where enough accuracy was needed to make the distinction relevant.

78

That depends on how you weigh it. If you take my friend’s old bathroom scale with you to the moon and weigh that kilogram on it, the scale will tell you it weighs 2.205 pounds, because the sliding weights on the scale also weigh proportionally less. In essence, a regular balance scale measures mass, not weight.

We were in the Norfolk area, taking the Hampton Road bridge-tunnel across the mouth of the James River estuary when a question related to this occurred to me. If your aircraft carrier sails through this passage, over the tunnel, since it floats by displacing less mass than that of the water, is the tunnel subjected to reduced pressure while the ship is passing over it?

79

It floats by displacing the same mass of water as its own mass. The tunnel couldn’t tell the difference.

80

Mass is, essentially, a measure of how much matter is in an object. When you move from Newtonian to Relativistic Physics, then you have to make a distinction between rest mass and relativistic mass, which I’m sure the science channel will do a much better job of describing than I can (my degree is in engineering, not physics). But when you are talking about an object at rest, it’s the same thing. The resistance to a force, you are, essentially, talking about inertia, which ALMOST is the same as Mass, but a better man than I will have to explain the distinction (it’s been far too many years since I’ve been in college).