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Comment by andrepd | Hacker News Reader

Here's an argument:

If you think about it, "mass" actually means two different things. One one hand, there is mass as the "charge" of gravitational interaction, that is, the gravitational field generated by a body is proportional to its mass. Let's call this concept "gravitational mass". On the other hand, you have mass in the sense of "intertial mass", a body's resistance to change of velocity. Although we kinda take it for granted, it's weird that these two concepts coincide, and not something that would be necessarily true a priori.

Asserting this equivalence as a principle is the starting point for Einstein's theory of General Relativity, which is one of the most beautiful and thoroughly tested theories in modern physics.

On the other hand, you can show that the inertial mass cannot be negative (else the Lagrangian would not be bounded from below and therefore you could not minimise it; the whole of physics then comes crumbling down). Therefore, if that equivalence stands, the gravitational mass also cannot be negative.

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> On the other hand, you can show that the inertial mass cannot be negative (else the Lagrangian would not be bounded from below and therefore you could not minimise it; the whole of physics then comes crumbling down).

Here's a purely thought-experiment argument for inertial mass not being negative:

If you had an object with negative inertial mass, then pushing on that object would cause it to accelerate into your hand. This is a positive feedback loop that immediately results in the object and your hand exerting infinite amounts of force on each other, because applying force just leads to applying more force.

This assumes that the objects of opposite inertial mass are able to interact in the way you describe.

Specifically the interaction is: objects with positive inertia being able to 'push' objects with negative inertia.

This brings up an interesting question, is gravity about exchanging momentum? My mental model of gravity being spacetime curvature would imply no, but that intuition is likely wrong.

That's assuming your hand has negative inertial mass.. which I'm assuming it doesn't.

Your scenario could create a black hole if I'm understanding correctly. Enough 'negative inertial mass' trapped in a feedback loop..

If inertia is resistance to change then negative inertia would be promotion of change? I really dont know, the idea of negative inertia seems wildly counterintuitive.

Inertia isn't "resistance to change". It's defined by Newton's second law, F = ma. Force and acceleration are directional vectors, and mass is scalar.

In the form of the equation favored by my high school physics teacher, a = F/m, we see that when a force is exerted on an object with positive mass, the object will accelerate in the same direction as the force, in inverse proportion to its own mass.

But it's very easy to put a negative number in for the mass, and then you see that such an object would accelerate in response to force just as much as an object of equal positive mass, but in the opposite direction.

Thanks, that's obviously a much better way to think about it. However, you're wrong in at least the typical physics definition of inertia found in dictionaries is in fact, "resistance of change (velocity, acceleration, momentum)."

In that same framework, the maths definition of inertia is also momentum = mv and a google search confirms this. What would negative momentum even look like? Because that's not just movement in the opposite direction.

Velocity, the v in the definition of momentum, is also a vector, so yes negative momentum is just momentum in the opposite direction from positive momentum, whatever direction that may be.

Inertia is generally not defined as being momentum, because an object's momentum in any direction increases along with its velocity in that direction, while we like to think of inertia as being determined solely by mass.

https://en.wikipedia.org/wiki/Inertia begins "Inertia is the resistance, of any physical object, to any change in its velocity". That's specifically resistance to acceleration ("change in velocity"), not resistance to the concept of change in general.

(It does go on: "In common usage, the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified by its mass), or sometimes to its momentum, depending on the context.")

But that's what I just said: resistance to change in v, a, p are the dictionary definitions I found on Google.

You're right about v. I thought a negative velocity was equally absurd, but it looks like it's defined as a vector which makes sense of course. The last time I took a proper physics course was in high school. How embarassing though, as I've read and watched more popular science/physics material than most people, probably. Hah.

Dictionaries are not written by physicists.

Here's a thought experiment that shows that there can't be electrons:

"If you had an object with negative charge, then putting that object near a positive charge would cause it to accelerate towards the positive charge." Getting closer increases the force. "This is a positive feedback loop that immediately results in the object and the positive charge exerting infinite amounts of force on each other, because" getting closer "just leads to applying more force."

Thus, there are no electrons.

So, I don't think the thought experiment rules out negative mass. In fact, the article explicitly says "if a negative mass was pushed, it would accelerate towards you rather than away from you.", and I assume that if that's an obvious contradiction, the author would have caught it.

So, electrons are attracted to protons by the electromagnetic force, but they don't make it all the way there because they are repelled by some other force. You don't have a paradox because our model of the electromagnetic force doesn't specify that it's the only force there is.

But if a negative mass is moving towards you and encounters a repulsive force, that repulsive force will, by definition, move the negative mass further toward you. It would need to encounter an attractive force to reach equilibrium.

Note that, unlike in the electron example, it doesn't matter what kind of force is being applied; the object's negative mass tells us that the response to any repulsive force is acceleration towards the force.

> they don't make it all the way there because they are repelled by some other force

A repulsive force is not the best way to think about it. The potential of the nucleus is the usual -1/r, and goes to (negative) infinity at zero. A repulsive force would be incorporated into the potential and appear as a bump around the nucleus, and would mess up the electron orbital.

A hand-wavy explanation of why the electron doesn't fall in: if you try to push the electrons into the nucleus, you necessarily localize the electron into a smaller volume; this means its wavefunction must get "spikier" and therefore it has more kinetic energy. This kinetic energy rises faster than the potential energy drops, so the state of lowest energy is actually found at an average radius > 0.

Note that it took quantum mechanics to rescue the atom. A classical electron could fall into the nucleus.

I do not see any problem with a negative-mass particle accelerating towards the force. The analogy with opposite charges seems right to me.

A different hand-wavy explanation. The places that an electron can be found are described by a wave pattern. If the electron is staying in place around a nucleus, that wave pattern has to be a standing wave that reinforces itself. To reinforce itself it has to wrap around the nucleus an integer number of times.

This explanation doesn't just explain why it doesn't fall in, it also explains why there are discrete shells that it could be found in, corresponding to how many times it wraps around the nucleus. (It doesn't explain why only a finite number can fit in each shell though. Or why bigger shells can have more electron orbitals. Or...well the actual theory has to be good for something!)

This is the Bohr model of the atom, but was replaced by a proper quantum theory.

Yes. Which is why I called it "a different handwavy theory". And also listed some of the things that it didn't explain.

I'm not really interested (here) in the reality of the interaction between the electron and the nucleus. I don't think the existence of an electromagnetic field is a good argument against its own existence as argued by FabHK further up.

I also don't think FabHK's argument works as an analogy to my problem with negative mass. The electromagnetic field is not self-reinforcing in the same way.

Imagine that you're holding a marble of negative glass in your fist. Negative glass is indistinguishable from ordinary glass except that its mass is negative rather than positive.

As we all know, the first step in solving any physics problem is to draw a free-body diagram. ( http://www.smbc-comics.com/comics/20130616.png ) Let's draw one here. First, we'll do one for an ordinary marble:

1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass.

2. The marble cannot accelerate downward, because it's stuck in your fist. Your fist experiences a downward force equal to the weight of the marble.

3. By Newton's third law, your fist exerts an upward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, but in the opposite direction. The two forces cancel, and the marble is at rest.

Now for the negative marble:

1. The enormous mass of the earth attracts the marble downward proportionately to the marble's mass. Because that mass is negative, the marble attempts to accelerate upward.

2. The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to the weight of the marble.

3. By Newton's third law, your fist exerts an downward force on the marble equal to the force exerted by the marble on your fist. This is exactly equal to the weight of the marble, and in the same direction, effectively doubling the marble's weight. The marble is now trying twice as hard to accelerate upward into your fist.

2. (Again.) The marble can't accelerate upward, because it's stuck in your fist. Your fist experiences an upward force equal to double the weight of the marble. Nothing has moved; we're still just trying to work out the balance of forces within the system at rest.

3. (Again.) You can see where this is going.

What is the conceptual breakthrough that rescues negative mass from this trap? (Note that saying the marble has negative inertial and gravitational mass, as opposed to negative inertial mass and positive gravitational mass, doesn't help: the marble will be trying to accelerate downward instead of upward, but it will still be doing it with infinite force.)

Maybe that's precisely why objects with negative mass do not exist on the Earth? But what stops them to exist in the void of space, between regular matter? And it doesn't need to be actual "objects", but isolated particles or a particle gas. In relativistic physics mass is dependent on the body's energy, so negative mass implies negative energy.

This is an argument that negative mass cannot be contained, not that it does not exist.

(Though it escapes me why you would assume that I believe in theories about negative mass, which actually seem to me to be very speculative and not very likely.)

> But if a negative mass is moving towards you and encounters a repulsive force, that repulsive force will, by definition, move the negative mass further toward you

I am not sure you understand what "repulse" means..

Joking aside, it's easy enough to imagine negative gravity. Do you mean that such counter intuitive behavior would be the natural consequence of negative inertial mass?

> that repulsive force will, by definition, move the negative mass further toward you.

only if the repulsive force is negative gravity.

If a positive-mass electron attracts a negative-mass electron, the repulsive electromagnetic force will still keep them from making it all the way there.

>> that repulsive force will, by definition, move the negative mass further toward you.

> only if the repulsive force is negative gravity

We're talking about negative inertial mass, not negative gravitational mass. Negative inertial mass means accelerating against the direction of any force applied to you, including but not limited to gravity.

The problem with these papers is there is no compilers to perfectly test the logic except peer review so no one knows if its horse shit or not until someone comes along and comes up with some way to prove it wrong, so I would not be so quick to say “if that’s an obvious contradiction, the author would have caught it”

Physics is highly mathematical and as such, can indeed be "tested" (i.e. proven) to be consistent with mathematical laws. This is fairly straightforward (for suitably mathematically literate people). The real issues are:

1. can the theory make testable predictions that can be verified by observation? e.g. string theory has had issues with this.

2. what does <wierd-mathematical-construct> "mean"? e.g. negative mass, spooky action at a distance, spacetime singularity.

In practice, only 1 really matters. However, 2 tends to bug a lot of people (consider the arguments around what the quantum world really represents). I'm one for whom 2 is important. "But what does it really mean?"

Back to your original point, looking at the paper [0], it doesn't seem too ridiculously hard to validate the math for someone familiar with this space (see what I did there?), unlike me who has forgotten everything I was taught [1].

[0] https://arxiv.org/pdf/1712.07962.pdf

[1] I have a physics degree but that was 33 years ago and I've been doing nothing but IT since.

1. OpenGL makes good predictions. Why not to switch to OpenGL terms when talking about physics?

Because physicists would find it totally unsuitable for their requirements?

Why match is better for that? To compute prediction, you will need to use computer and compiler, so it better to talk directly in these terms because of (1) (see above).

You should go back to 1910 and tell Einstein he can't start for another 50 years.

Einstein used the best tool he had at hands - math. Now we have mach better tools: computer models, knowledge databases, AI. Math is good because math formulas are very compact, so they are easy to play with, but computer models are much better, because computer can visualize them directly, calculate values correctly, and verify result automatically. Think about Computer Aided Science.

I'm confused - are you trolling us? You do realise that computer science is based on math right? All the calculations that that OpenGL does are mathematical calculations. Even databases are based on relational algebra. AI - linear algebra, probability, multivariate calculus, optimization etc. There would be no computer science without math.

No, I'm not trolling. English language just have no word for that thing. How would you name something in middle of OpenGL, Kerbal, Wikipedia, Recursive Text, Alpha Go, etc? Something where you can setup your experiment, start it emulation, and then zoom from macro level to quantum level, with description of every effect at each level, with formulas at hand, with links to experiments, papers, reviews, confirmations? Something that can actually answer your questions, teach you actual physics. Something where you can plug your own theory to see is it fits real world better that someone else theory. I have no idea how to name it. Universal Programmable Augmented Disсoverable Science Model?

> If you had an object with negative inertial mass, then pushing on that object would cause it to accelerate into your hand. This is a positive feedback loop that immediately results in the object and your hand exerting infinite amounts of force on each other

No, it doesn't; since this turns the repulsion of normal objects (which is what makes them resist interpenetration) into attraction by switching the orientation of the resulting acceleration, what it results in isn't more force at the boundary (the boundary is a repulsive effect), but interpenetration, which results in force declining to zero as the masses centers are at the same place. (And then switching directions as they cross.)

What makes us think the objects would actually interact at all?

I'm assuming that you can push in the classical sense but for what negative mass does to the equations, but sure, if you can't then the whole question is moot.

How do you think Thor’s hammer works when it’s sitting on the toilet seat?

Obviously, toilets are capable of exerting more upward force than any mere mortal.

Positive mass has a speed limit though, so I think there would be an upper limit on the amount of force returned?

What happens if the gravitational mass is the exact negative of the inertial mass for some fraction of matter, though? Does that break GR?

Perhaps gravitational mass is indeed polarised and inertial mass corresponds to the absolute value of the gravitational mass?

Actually the lagrangian is not minimized, it is merely stationary. An example of this is the harmonic oscillator, the lagrangian is clearly not bounded from below.

Yes, I realised that but I couldn't edit the post anymore :) I mean the action, not the Lagrangian, must have a minimum.

The action of a trajectory is not minimized either, it is usually at a saddle point, maximal relative to some trajectories and minimal to others. The linked paper has a detailed discussion of this.

http://www.eftaylor.com/pub/Gray&TaylorAJP.pdf

Another framing of the issue with negative inertial+gravitational mass is that it would result in perpetual acceleration.

E.g. assume two bodies, one with mass M, the other with mass -M. The standard gravitational model describes a "repulsive" force on each of these objects, in the direction opposite each other. However, since the object of mass -M has negative inertial mass, this force would cause it to accelerate toward the object of mass M.

This results in these objects not accelerating relative to each other, and perpetually accelerating relative to an independent observer. One might attempt to explain this by saying that the negative mass has a growing negative kinetic energy level, but (it seems as a layman) this would violate the second law of thermodynamics.

Edit: Actually just negative inertial mass does this all by itself; it is just in the opposite direction if the gravitational mass is positive.

Well, even the possibility of inertial mass not exactly equaling gravitational mass on interstellar scale open a big can of worms for physics

I’m not sure this stands true when you think about fields.

Think of charged particles in a magnetic field and how polarity and and strength of the charge impacts their interaction the strength would do the same thing for both particles while the polarity would mirror their interaction.

I need to read the paper a few more times tho.

I was thinking, what if body's resistance is actually the norm, even when there is no change of velocity ? But the negative mass would provide the energy to let the body's in movement ? From our point of view it seems that body's can move by theirselves and it seems also that we have to provide energy to change their velocities. But if we think the universe as a fluid, body's should be constantly slowed. It's very strange to have two distinct behavior, except if we have a negative mass in the universe.

Don't you have two things that can generate gravitational fields though? As distortions in spacetime can be caused by either mass or the momentum of massless particles, such as photons. Or do I have that wrong and photons merely follow the distortions and not cause any of their own? As presumably, you could have a negative gravitational field from a photon traveling backward in time, without having any issues with changes in inertial mass.

> Or do I have that wrong and photons merely follow the distortions and not cause any of their own?

You have that wrong in the momentum of massless particle has mass, independently of its carrier. Massless particles do not actually exist, what exist are particles with zero "mass at rest" and that are never at rest.

Ahh, I was getting a bit confused from photons distorting spacetime off their wavelength and plank's constant, given they also apparently have no mass. Thanks for that. I have to go and re-read a lot of stuff now though. ;)

You may like to make a quick read of this:

https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati...

Besides it being a basic relation for relativity, there's also an entire "parallel" quantum mechanics for particles that have too much energy at the momentum component based on it.

You're talking about relativistic mass, but that isn't a commonly used concept anymore. Today it is indeed the norm to think of "mass" as being the mass at rest. Massless particles are really massless and have momentum without having mass.

In which case, we seem back to having two things distorting spacetime. Could mass just be the momentum of massless particles going in really small circles such that you can pack them together and call them matter?

Space is distorted by the stress-energy tensor field. Mass is only a component of that.

If you use "mass" to mean the rest mass of something. If you use it meaning the relativistic mass, it's the entire value, not a component.

Yes, using it as the relativistic mass leads to confusing papers and equations, so it's better avoided. Yet, the press does that, what makes everything very confusing for lay people. I should have clarified that the OP usage of the term wasn't optimal (although common on the media he sees), but this following discussion about word definitions seems to be completely missing the point.

What you described sounds like a geon.

https://en.wikipedia.org/wiki/Geon_(physics)

Oh, cool, yep. I didn't know that's what they are. I have basically been wondering if all matter is variations of those.

Energy distorts spacetime. Mass only distorts spacetime because it is a form of energy. Light is also a form of energy.

I think this might be dumb, but, what if negative mass was just positive mass in some alternative dimension? If mass could be negative with respect to our observable space time, does that actually mean it is a binary kind of thing, or could there be lots of mass in lots of others semi-or-non-interacting dimensions? Maybe even the mass we can observe is only part of anything’s actual substance...

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