## Gravitational mass of an electron?

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lgw
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### Gravitational mass of an electron?

Do electrons have gravitational mass? Of course I assume they do - gravitational mass and inertial mass proportional, if not equivalent, in general - but has an experiment been done? It seems like an impressive experiment.

To be clear, I'm drawing a distinction between inertial mass (F/a, as seen by every instrument that accelerates electrons), and gravitational mass (or: is G uniform). Obviously, the electron inertial mass is well known, and the proton + electron gravitational mass is well known, so if e.g. the electron is less affected by gravity, the proton must be more so.

I guess I'm mostly curious how you'd do the experiment (or how it was done). Measuring G accurately is hard enough, but given the huge ratio between electric and gravitational field strength, I can't imagine how you'd measure accurately enough to know anything about gravity on a charged particle. Just throwing an electron (or a proton) through a mass spectrometer, first curving down, then curving up, would give the answer - if you could measure to 40 sig figs!
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letterX
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### Re: Gravitational mass of an electron?

The first experiment to measure the charge/mass ratio of the electron, the Millikan Oil Drop Experiment, involved measuring the different rate at which drops of oil accelerated (due to gravity) after a single electron ionized off. So, in fact the first experiment measuring the mass of the electron measured the gravitational mass. Though, I'm sure the actual analysis also involves assuming that the inertial and gravitational masses are equal, and the result would change if they were not. Probably, it would be a worthwhile exercise to re-do the analysis not assuming that inertial and gravitational mass are equal, and see how the numbers would change.

Alexius
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### Re: Gravitational mass of an electron?

letterX wrote:The first experiment to measure the charge/mass ratio of the electron, the Millikan Oil Drop Experiment, involved measuring the different rate at which drops of oil accelerated (due to gravity) after a single electron ionized off. So, in fact the first experiment measuring the mass of the electron measured the gravitational mass. Though, I'm sure the actual analysis also involves assuming that the inertial and gravitational masses are equal, and the result would change if they were not. Probably, it would be a worthwhile exercise to re-do the analysis not assuming that inertial and gravitational mass are equal, and see how the numbers would change.

I don't think the Millikan experiment measured any of the masses of the electron. The gravitational mass being measured was that of the oil droplet (minus a few electrons, but the mass of those electrons is negligible).

The mass-to-charge ratio was determined by J.J. Thomson in 1896 (and uses inertial mass).

Tass
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### Re: Gravitational mass of an electron?

Yes. Mass/charge was measured by bending in a magnetic field. Later Millikan measured the charge (compared to the known mass of an oil drop). Since mass/charge was already known, this also determined mass. All these masses are inertial.

Measuring GravMass/InertMass is much harder. Not something you readily do on a microscopic scale.

If this ratio was different for electrons and protons then you would have an imbalance of electrons to protons in an object to measure the difference. But this would make it heavily charged, and since electromagnetism is ~1036 times stronger, electrostatic forces would completely swamp the difference in gravitational mass.

I don't believe this is an experiment will be able to do directly for a very long time. (Of course through indirect means we are pretty damn sure that the ratio is the same.)

p1t1o
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### Re: Gravitational mass of an electron?

If inertial mass and gravitational mass seem to match up wherever we look, why point at electrons and ask "I wonder if their inert/grav ratio is different"?

Is there any indication that electrons might have a disparity between inertial and gravitational mass?

If electrons have a different inertial/gravitational ratio, why not any other particle?
And if any particle can have different iner/grav ratios then their apparent equivalence is a hell of a coincidence.

What stops you measuring this directly by pointing and electron beam upwards and downwards, in a vacuum, and measuring their energy at target? Or some incredibly involved and more accurate variation of that.

lgw
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### Re: Gravitational mass of an electron?

p1t1o wrote:If inertial mass and gravitational mass seem to match up wherever we look, why point at electrons and ask "I wonder if their inert/grav ratio is different"?

Is there any indication that electrons might have a disparity between inertial and gravitational mass?

If electrons have a different inertial/gravitational ratio, why not any other particle?
And if any particle can have different iner/grav ratios then their apparent equivalence is a hell of a coincidence.

Fundamental assumptions that have never actually been tested bug me - in my day job, such things are a frequent source of trouble. I picked on electrons, because they could have a different gravitational mass without invalidating any measurements, since we only ever really measure the gravity of electron-proton pairs, never either separately, so what we really know is the combined ratio.

Heck, if it weren't for neutrons, we'd have very little basis to claim that any two particles had the same inertial/gravitational mass ratio, because AFAIK the only 2 data points we have are "neutrons" and "electron-proton pairs" (On reflection: I bet we know a bit about dark matter as well, from the CMBR data, since that's just the sort of thing the CMBR data tells us)

p1t1o wrote:What stops you measuring this directly by pointing and electron beam upwards and downwards, in a vacuum, and measuring their energy at target? Or some incredibly involved and more accurate variation of that.

Only the fact that charge is 1039 times as strong as gravity. We should probably distinguish between "active" and "passive" gravitational mass: does an electron gravitationally attract other masses, vs is an electron gravitationally attracted towards other masses (the Wikipedia article on mass actually lists 7 kinds of mass, all assumed to be the same).

Because the Earth is quite a bit more massive than a single electron, we might measure the electrons passive gravitational mass - does it fall towards the floor at the expected rate - but given the whole general relativity model of curved spacetime would break if it didn't, I can't force myself to even be a skeptic on this.

But the electron's active gravitational mass? It's just too small to measure the gravitational attraction caused by 1 electron, and too difficult to get a pound of electrons together in the same place. The only approach I can even imagine is to make a bunch of positronium to hide the charge, but given it's halflife in picoseconds, that seems just as impractical. (I hear the experiment to prove that antimatter falls towards, not away from, matter is just now happening.)

There is one measurement I can think of that would be interesting, however: to see if the neutron I/G mass ratio, and the electron-proton-pair I/G mass ratio, were the same to many significant digits. It's easy to see how an electron and a baryon might have different I/G mass ratios: most of the mass of a baryon comes from the energy of the strong field, not the mass of the individual quarks. Discovering that the "point particle" I/G mass ratio was different from the "potential energy" I/G mass ratio would be quite interesting, but wouldn't actually invalidate anything important in physics.

Hmm, I wonder how many significant digits one could get by comparison of groups of low-metallicity vs high-metallicity stars.
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gmalivuk
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### Re: Gravitational mass of an electron?

lgw wrote:and too difficult to get a pound of electrons together in the same place.
And even if you could, failure to keep them there would be pretty catastrophic.
(Yes, that thread is about a kilogram. Divide numbers by 2.2 as necessary if you really care about a pound of them.)
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mfb
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### Re: Gravitational mass of an electron?

lgw wrote:because AFAIK the only 2 data points we have are "neutrons" and "electron-proton pairs"

Those are very good data points, however. Neutrons and protons are very similar, they both gain most of their energy from QCD binding energy and some small fraction (still larger than the electron mass) from the rest masses of the valence quarks. There is no reason why the proton should be different from a neutron here. If they behave the same, you can measure the gravitational mass of electrons. If they do not, there would be some strange amount of fine-tuning going on to give the same results for both neutrons and [proton+electron pairs].
And there is some work ongoing to measure the gravitational effects with charged particles.

p1t1o
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### Re: Gravitational mass of an electron?

I'm imagine that exactly the same problems arise if you want to do the measurements on a free proton - but wouldn't the thousand-odd-fold larger mass help?

If you could make the measurements on a proton, could you infer the properties of a free electron by comparing to the results from a proton-electron pair?

Tass
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### Re: Gravitational mass of an electron?

p1t1o wrote:I'm imagine that exactly the same problems arise if you want to do the measurements on a free proton - but wouldn't the thousand-odd-fold larger mass help?

Not compared to the factor duodecillion between the strengths of the electromagnetic and gravitational forces.

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### Re: Gravitational mass of an electron?

Tass wrote:Not compared to the factor duodecillion between the strengths of the electromagnetic and gravitational forces.

Yah. I get that. Is this one of those problems which isn't even hypothetically solvable, even in the foreseeable future? I can't even think of a sci-fi handwavy method of overcoming a 10^30+ factor, it seems to be too fine a margin to be measured in this universe, with the big clumsy particles and charges we have at our disposal. Like trying to find a needle in a haystack with two blue whales ductaped to your hands.

***EDIT***
Actually, if we attempt to insert a 10^39 factor into the metaphor, its closer to looking for a needle in a haystack with 1 billion suns ductaped to each hand...

lgw
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### Re: Gravitational mass of an electron?

To agree with mfb, I think that if we measured the I/G inertia ratio of the neutron, and of the electron-proton pair, to enough significant digits we would likely spot any anomalies. Assuming we're right about the masses of leptons and quarks, and their ratios to the mass of a baryon that comes from the energy of the strong force, then that gives us 2 data points and 2 unknowns. And those should be pretty safe assumptions, since I don't think the gravitational mass of any of that was relevant to deriving the inertial masses.

And it seems pretty straightforward to measure G between 2 masses with high neutron/proton ratio vs two with low neutron/proton ratio, and then in a method unrelated to gravity measure the inertia of each pair. What I don't know is how accurately we can do (or have done) those measurements.

EDIT: After reading up a bit I see that the "current quark mass" (their mass independent of the strong force energy) isn't known yet to even 1 significant digit. So if I put forward a hypothesis that "only the point particles cause gravitational attraction, potential energy doesn't" or it's reverse, I'm back to not seeing a way to falsify that claim.
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### Re: Gravitational mass of an electron?

lgw wrote:I think that if we measured the I/G inertia ratio of the neutron, and of the electron-proton pair, to enough significant digits we would likely spot any anomalies.
Yes. The problem is that "enough significant digits" is about 30, which is about 20 more digits than we currently know of any other physical constants.

lgw wrote:And it seems pretty straightforward to measure G between 2 masses with high neutron/proton ratio vs two with low neutron/proton ratio, and then in a method unrelated to gravity measure the inertia of each pair. What I don't know is how accurately we can do (or have done) those measurements.
We only know G to about 1 part in 10,000, since gravity is so weak already.
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Tass
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### Re: Gravitational mass of an electron?

If there was a significant difference in the mass ratio of electron+proton and neutron, then we could measure it. Organic material (lots of hydrogen) would drift to one side in a space station while heavy elements (lots of neutrons) would drift to the other.

The thing we can't tell is whether the ratio is different for electrons and protons, since any imbalance would be completely swamped by much larger electrostatic effects.

lgw
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### Re: Gravitational mass of an electron?

gmalivuk wrote:
lgw wrote:I think that if we measured the I/G inertia ratio of the neutron, and of the electron-proton pair, to enough significant digits we would likely spot any anomalies.
Yes. The problem is that "enough significant digits" is about 30, which is about 20 more digits than we currently know of any other physical constants.

Why 20 digits?

Consider the claim "only the mass of point particles contributes to active gravitational mass, but you have to add in strong force energy of hadrons to find their inertial mass".

We know the inertial mass of the neutron differs from the inertial mass of proton+electron by about 1 part in 1000.

Under that claim, we'd need to measure gravitational attraction accurately enough to compare (MGUp + MGDown + MGDown) to (MGUp + MGUp + MGDown + MGElectron) where MG is gravitational mass. Those would differ by about 1 part in 10!

So we could falsify that claim by doing the "measure G" experiment with 2 carbon masses and 2 Lithium masses, and we'd only need 2 significant digits, and 4 significant digits might make a more subtle difference in rest mass vs potential energy show up.

Similarly, if the proton and neutron had the same I/G mass ratio, but the electron had no active gravitational mass, we might find materials that would show that with 5 significant digits of measurement, though I guess we're not quite there yet.

Or am I missing something important here?
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Tass
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### Re: Gravitational mass of an electron?

lgw wrote:
gmalivuk wrote:
lgw wrote:I think that if we measured the I/G inertia ratio of the neutron, and of the electron-proton pair, to enough significant digits we would likely spot any anomalies.
Yes. The problem is that "enough significant digits" is about 30, which is about 20 more digits than we currently know of any other physical constants.

Why 20 digits?

Consider the claim "only the mass of point particles contributes to active gravitational mass, but you have to add in strong force energy of hadrons to find their inertial mass".

We know the inertial mass of the neutron differs from the inertial mass of proton+electron by about 1 part in 1000.

Under that claim, we'd need to measure gravitational attraction accurately enough to compare (MGUp + MGDown + MGDown) to (MGUp + MGUp + MGDown + MGElectron) where MG is gravitational mass. Those would differ by about 1 part in 10!

So we could falsify that claim by doing the "measure G" experiment with 2 carbon masses and 2 Lithium masses, and we'd only need 2 significant digits, and 4 significant digits might make a more subtle difference in rest mass vs potential energy show up.

[snip]

Or am I missing something important here?

No, you are not. We could indeed measure that. We have done so, and the result is negative. Gravitational mass and inertial mass is equivalent to about ten digits.

lgw wrote:Similarly, if the proton and neutron had the same I/G mass ratio, but the electron had no active gravitational mass, we might find materials that would show that with 5 significant digits of measurement, though I guess we're not quite there yet.

Here we have a problem. If a material had an imbalance of protons and electrons then it would also be heavily charged which would preclude any fine measurement. (Well actually the neutron would have to have the same I/G ratio as a proton electron pair, which it does.

Edit: Forgot to close my parenthesis. Rather than fix it I'll just link to this.

lgw
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### Re: Gravitational mass of an electron?

Tass wrote:
lgw wrote:So we could falsify that claim by doing the "measure G" experiment with 2 carbon masses and 2 Lithium masses, and we'd only need 2 significant digits, and 4 significant digits might make a more subtle difference in rest mass vs potential energy show up.

[snip]

Or am I missing something important here?

No, you are not. We could indeed measure that. We have done so, and the result is negative. Gravitational mass and inertial mass is equivalent to about ten digits.

Could you explain more? It's easy enough to measure the inertial mass of anything you can put a charge on and fling through a magnetic field, but how could you get 10 significant digits on gravitational mass (of an object small enough to know its composition well)? I'd expect we have several significant digits on the mass of the large bodies in the solar system (but surely not 10?), but we don't know their composition that well.
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Meteoric
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### Re: Gravitational mass of an electron?

Put it on a scale and weigh it?

Technically that would just tell you its "passive" gravitational mass, but unless you're seriously concerned about the validity of conservation of momentum, that doesn't strike me as too serious a limitation.
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lgw
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### Re: Gravitational mass of an electron?

Meteoric wrote:Put it on a scale and weigh it?

Technically that would just tell you its "passive" gravitational mass, but unless you're seriously concerned about the validity of conservation of momentum, that doesn't strike me as too serious a limitation.

I don't understand the claim about conservation of momentum. Surely inertial mass is what's important there.

"Passive" gravitational mass must be proportional to inertial mass, or there's a fundamental flaw in general relativity: all objects in freefall must follow the same path.

"Active" gravitational mass it the uncertain bit. It's hard to measure the active gravitational mass of a controlled sample (it's basically the same experiment as measuring G), but it's measurable to a few significant digits. You'd have to do that separately for high-neutron-ratio and low-neutron-ratio materials, however, and I wonder if that's been done.
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Meteoric
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### Re: Gravitational mass of an electron?

If "passive" and "active" gravitational mass are not the same, then suppose we have two objects A and B, with different ratios of "passive" and "active". The force on A from B will not have the same magnitude as the force on B from A. Integrate that over some time period to calculate impulse, and the unequal-but-opposite forces will produce a nonzero net change in momentum. Which is to say, momentum will not be conserved.

That's a Newtonian perspective, and I suspect relativity may have something more to say about it, but I have no idea what (other than "the Equivalence Principle forbids any of this").
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thoughtfully
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### Re: Gravitational mass of an electron?

I'm shocked it hasn't been brought up yet:
http://en.wikipedia.org/wiki/E%C3%B6tv% ... experiment
Spoiler:
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elasto
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### Re: Gravitational mass of an electron?

thoughtfully wrote:I'm shocked it hasn't been brought up yet:
http://en.wikipedia.org/wiki/E%C3%B6tv% ... experiment
Spoiler:
9+ sig figs, for the equivalency of inertial/gravitational mass

Good link, but people have already acknowledged it's been demonstrated to a high degree of accuracy for neutrons and proton-electron pairs. They want to know if it's been demonstrated for electrons/protons individually; It doesn't look like it has.

Obviously the former strongly implies the latter, but the thread is all about if there's any wiggle room for a discrepancy.

lgw
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### Re: Gravitational mass of an electron?

Meteoric wrote:If "passive" and "active" gravitational mass are not the same, then suppose we have two objects A and B, with different ratios of "passive" and "active". The force on A from B will not have the same magnitude as the force on B from A. Integrate that over some time period to calculate impulse, and the unequal-but-opposite forces will produce a nonzero net change in momentum. Which is to say, momentum will not be conserved.

That's a Newtonian perspective, and I suspect relativity may have something more to say about it, but I have no idea what (other than "the Equivalence Principle forbids any of this").

That's quite insightful, actually - IMO that's conclusive:
* If passive gravitational mass and active gravitational mass are different, momentum is not conserved
* If inertial and gravitational mass are different (other than by sign), objects would follow differing paths in freefall

While it's still good to do experiments to confirm things you don't doubt (if those experiments haven't been done before), it looks like any variance in I/G mass ratios would be a fundamental problem for our current understanding of physics (and thus quite unlikely to have gone unnoticed).

Also, these forums rock.
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itaibn
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### Re: Gravitational mass of an electron?

First of all, the binding energy of a nucleus can take away as much as 0.9% of its mass (in the case of Fe-56). However, these tests of the equivalence principle have been done with a precision of about 10^10. This makes any conspiracy where electrons and protons have gravitational masses deviating from their inertial mass which cancel out much more unlikely.

Second, if the electrons and nuclei had different gravitional masses, then an atom in freefall or in orbit would naturally become polarized from the differing gravitational pulls. While I don't know of any experiment testing this, I would expect scientists to notice such an effect, even if it's very small. In particular, atomic clocks use a resonant frequency of an atom in freefall, and those are some of the most precise instruments in existence.
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### Re: Gravitational mass of an electron?

I had a similar question a while back: Does the gravitational attraction on a particle increase if it is accelerated to near light speed?

Relativity tells us that‚ near light speed, momentum increases to more than just rest mass times velocity. We can interpret this two ways: Either the mass increases, or momentum is more than m*v. As far as momentum is concerned, it doesn't matter, but what people seem to have missed is that if you talk about gravity, the formulations are not equivalent.

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### Re: Gravitational mass of an electron?

They are equivalent, since what gravity actually couples to is the stress tensor.
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lgw
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### Re: Gravitational mass of an electron?

DrZiro wrote:I had a similar question a while back: Does the gravitational attraction on a particle increase if it is accelerated to near light speed?

Relativity tells us that‚ near light speed, momentum increases to more than just rest mass times velocity. We can interpret this two ways: Either the mass increases, or momentum is more than m*v. As far as momentum is concerned, it doesn't matter, but what people seem to have missed is that if you talk about gravity, the formulations are not equivalent.

What Doogly said, plus: relativistic mass doesn't work. It's all time dilation.

If mass were increasing, you'd expect proportional increases in momentum and energy from relativistic effects. But you don't see that. Energy diverges from Newtonian prediction at the square of the rate momentum does. It's not mass, it's velocity, or more specifically, time. So, sure you could interpret that as "momentum is more than m*v", because it's mass times velocity adjusted for time dilation. Momentum is "m * v * Lorentz factor" and energy is "0.5 m * v2 * Lorentz factor2" just as you'd expect from time dilation.

[Can I get a gamma in this forum without slowing the page way down with TeX math rendering? U+0263, dangit, U+0263]
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### Re: Gravitational mass of an electron?

Looking for ɣ? I just have a character picker on my bookmark bar. (Granted, mine's for IPA, but that's one of them, so it works out fine in this case.)

lgw wrote:Momentum is "m * v * Lorentz factor" and energy is "0.5 m * v2 * Lorentz factor2" just as you'd expect from time dilation.
I'm not sure where you're getting that from.

E2 = p2c2 + m2c4 and p=ɣmv, so
E2 = ɣ2m2v2c2 + m2c4, with ɣ dwarfing everything else when v is close to c, so
E2 ≈ ɣ2m2v2c2 or E ≈ ɣmvc ≈ ɣmc2 (because v≈c by assumption).

Of course, when I got to the end of this I remembered that I could as easily have used the exact Ek = (ɣ-1)mc2
Conveniently, when v << c, ɣ ≈ 1+(v2/c2)/2, so we can approximate Ek ≈ mv2/2
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### Re: Gravitational mass of an electron?

lgw wrote:[Can I get a gamma in this forum without slowing the page way down with TeX math rendering? U+0263, dangit, U+0263]

I copy 'n paste from a page of Unicode, rather than attemping to enter some magic ketstroke combination. Might depend on your browser settings/capabilities, but I haven't run into any trouble with Firefox on Linux/Windoze.

http://en.wikipedia.org/wiki/Mathematic ... in_Unicode
http://en.wikipedia.org/wiki/Mathematic ... ic_Symbols Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.
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Schrollini
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### Re: Gravitational mass of an electron?

lgw wrote:[Can I get a gamma in this forum without slowing the page way down with TeX math rendering? U+0263, dangit, U+0263]

Take a look at my signature. You only have to remember "\gamma", not some arcane key combination.
For your convenience: a LaTeX to BBCode converter

fff
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### Re: Gravitational mass of an electron?

There's an article about measuring the gravitational field of an electron [I was surprised as well.]
"Gravitational force between two electrons in superconductors" by Clovis Jacinto de Matos (ESA-HQ, European Space Agency, 2007)
(on 5th page pf googling electron gravitational mass)

waltmck
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### Re: Gravitational mass of an electron?

I believe (Please correct me if I'm wrong) that electrons have zero rest mass. This means that, if the electron is not moving relative to the object with which you are calculating the gravitational force, it would have a gravitational mass of zero. However, if it is moving relative to the aforementioned object, if would have a gravitational mass that varies with the difference in speed. I believe that this is also what explains how photons can be attracted to centers of mass such as black holes (hence the name, "black hole") while having zero mass.

I got this information mostly from http://en.wikipedia.org/wiki/Invariant_mass.

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### Re: Gravitational mass of an electron?

No, they definitely have a rest mass.
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waltmck
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### Re: Gravitational mass of an electron?

doogly wrote:No, they definitely have a rest mass.

Then how is it possible for them to move at the speed of light without an infinite amount of energy?

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### Re: Gravitational mass of an electron?

They don't move at the speed of light.
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waltmck
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### Re: Gravitational mass of an electron?

gmalivuk wrote:They don't move at the speed of light.

Right, sorry, stupid moment. I was thinking of an electromagnetic wave.