If mass produces gravity, and gravity curves the part of space, then why you say, that electron has no form\scale?

Question

Using Einstein's equation we can calculate the space-time curving(but I'm too stupid to do this). Hence, why everybody say that electron has no form\scale (although has spin at the same time)?

Are you suggesting that the shape of the curvature that the electron creates should be the taken as its actual shape? — user190081, Sep 06 '18 at 19:42
Gravity is weak. Measuring the curvature due to the mass of an electron is way out of our technical capabilities. It can be calculated theoretically of course. — Mozibur Ullah, Sep 06 '18 at 23:03

score 1 · Accepted Answer · answered Sep 07 '18 at 00:33

The basic reason why, is that if you do this, and calculate the Schwarzschild radius of an electron, you discover that it's about $10^{-22}$ Planck lengths, if I'm remembering that right. Now the problem is that we understand that physics must be different at just one Planck length, because any photon with that wavelength has a Schwarzschild radius as big as its wavelength; and we are not 100% sure what happens there. The length scales that you are talking about are much smaller than we know even in principle how to handle. So in practice we tell students not to handle it in the first place. There's no sense even thinking about it, because we have so many other things to think about before we get there.

score 0 · Answer 2 · answered Sep 06 '18 at 22:59

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First, not really mass, but energy and momentum curves spacetime.

Second, we'd have seen in the news if an electron's mass distribution (or charge distribution, for that matter) had revealed anything but point-like properties.

answered Sep 06 '18 at 22:59

stafusa

12,435

score 0 · Answer 3 · answered Sep 07 '18 at 00:11

First, it is stress-energy that bends spacetime, not mass.

An electron has EM charge, and we know that even EM charge bends spacetime.

See this answer:

https://physics.stackexchange.com/a/111762/132371

An electron is an elementary particle, with no spatial extension, it is pointlike. It does have electric dipole moment, and magnetic dipole moment. It does have rest mass and spin.

Yes, a pointlike elementary particle with EM charge can have a spin. This spin is not like an angular momentum of a macro object. Intrinsic spin is a characteristic of a QM object, that is in your case, an electron.

And yes, a pointlike, elementary particle does curve spacetime even if it has no spatial extension. It curves spacetime partly because it has rest mass (stress-energy), and partly because it has EM charge.

If mass produces gravity, and gravity curves the part of space, then why you say, that electron has no form\scale?

3 Answers3