Researchers have observed the Lyman-alpha transition in the antihydrogen atom
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An important piece of background info for non-atomic-physicists is that the Hydrogen 1S-2S transition frequency is probably the most accurately measured physical property in the world, thanks to the pioneering work by T. Hansch. Back in 2011 they reported an uncertainty of 4e-12, https://arxiv.org/abs/1107.3101.
Here's a reference: https://physics.nist.gov/cgi-bin/cuu/Value?e
>A conservative estimate of the height difference between clock and experiment contributes a gravitational red shift uncertainty of 7.7 × 10−17.
So, it appears the 4e-15 is not an actual measured value, but a synthetic value based on estimation and measurement.
It's like when you take a caliper and measure the width of an object, you typically neglect the error due to thermal expansion of the caliper since it's hotter/colder than when it was marked with gradations. If you're really anal about uncertainty (like these guys), you'd estimate the effect of this expansion and say "a conservative estimate says this contributes an uncertainty of 0.0003 mm".
They're all listed in table I and the 4.2 * 10^-15 just comes from adding them in quadrature.
It's most typical to describe gravity as dynamical spacetime, not a field existing in that spacetime. The closest people have come to a quantum theory of gravity has been to show that in certain toy universes gravity in a bulk space is the dual of strongly-coupled field interactions existing on the boundary of that space-- that is holography. Information-theoretic approaches have have also suggested that gravity emerges as the 'hydrodynamics of entanglement.' All this suggests gravity is not a fundamental force, but is far from a coherent real-world theory at this point.
The closest to an "antigravity" in general relativity is the cosmological constant, thought to explain dark energy. Its tiny (10^-122) positive value behaves like a constant negative energy attributed to the vacuum itself, driving the exponential expansion of space.
That's not quite correct. The quantum field theory of a massless spin-2 field was developed in the 1960s and 1970s and is perfectly well-defined. The problem with it then was that it is not renormalizable; but today basically all QFTs are viewed as effective field theories anyway, which means not being renormalizable is not a showstopper.
The real issue is that we have no prospect of measuring any quantum aspects of gravity now or in the foreseeable future, so there is no way to test the QFT that has been developed against experiment.
> Gravity has properties such as having its interaction strength grow with the amount of charge (energy), which is very different from the forces described by quantum fields that have constant interaction strength.
This is not correct either. The coupling constant of the massless spin-2 field is just Newton's gravitational constant (modulo some constant factors that depend on your units). The fact that the total interaction in a specific case varies with energy is no different from the fact that the total EM force between two charged objects varies with the charge. Energy is the source for gravity just as charge is the source for EM; the source is not the same as the coupling constant.
> To get antigravity, you need to find a way to have negative energy without it making the vacuum unstable.
Agreed. And as far as we know that is not possible.
> All this suggests gravity is not a fundamental force
This is quite possible, yes, but even if it were true it would not necessarily make the spin-2 massless QFT I referred to above invalid; it would just make it an effective theory that emerges from whatever is the next level down. (Which, as I noted above, is basically how we view all QFTs today anyway, including the Standard Model of particle physics.)
> The closest to an "antigravity" in general relativity is the cosmological constant, thought to explain dark energy. Its tiny (10^-122) positive value behaves like a constant negative energy attributed to the vacuum itself, driving the exponential expansion of space.
No, a positive CC does not have negative energy. It has positive energy and negative pressure. The effective source in the Friedmann equation is the energy density plus three times the pressure, which for a positive CC is negative (because the negative pressure outweighs the positive energy density).
>> To get antigravity, you need to find a way to have negative energy without it making the vacuum unstable.
> Agreed. And as far as we know that is not possible.
Which part are you agreeing to?
Spin-2 essentially means that like charges attract and unlike charges repel. Matter with the opposite gravitational charge from all the matter (incl. antimatter) in the universe we know about could have segregated in the early universe. Opposite-gravitational-charge matter (incl. antimatter) is unobserved, but not in-principle unobservable.
Vacuum instability doesn't arise since m_i stays the same as m_g changes sign under gravitational charge changes.
2) Intuitively if antimatter is regular matter travelling backwards in time, then at the start of time, wouldn't it all go the other way? Kind of like one huge quantum fluctuation.
It isn't. More precisely, while the mathematical trick that this phrase refers to (which also, btw, requires reversing all charges and flipping parity) works as far as making calculations simpler while still getting the right answer, it doesn't correspond to anything physical.
No, that's spin-1. Spin-2 means there is no such thing as "unlike charges"; the interaction is always attractive.
q1q2 > 0 : even integer spin attractive
q1q2 > 0 : odd integer spin repulsive
Jumping up classically, for a vector field like charges repel. For a (symmetric) rank-2 tensor field like charges attract.
The weak equivalence principle only requires m_i = m_g up to the sign of the latter. It's the energy conditions which constrain that, notably the WEC component of the positive energy theorem.
For a spin-2 field all charges attract. There is no such thing as "unlike charges".
> The weak equivalence principle only requires m_i = m_g up to the sign of the latter.
I don't know where you're getting that from. The WEP requires that the trajectory of a body moving solely under gravity depends solely on its initial position and velocity. That means m_i = m_g. It does not allow flipping the sign; that would mean there would be two possible trajectories for a given initial position and velocity, not one.
q1q2 > 0 : even integer spin attractive
q1q2 > 0 : odd integer spin repulsive
Yes, I see I misread your previous post; for spin-1 unlike charges attract and like charges repel. That I agree with.
Antimatter still has regular (i.e. positive) mass, so gravity works in the usual (attracting) way.
> The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5E−8.
I.E. It's the same for all practical purposes, but there may be a extremely tiny difference.
Edit: Comparing the numbers with the results for Hydrogen in an article someone else linked here
Anti-Hydrogen: 2,466,051.7 ± 0.12 GHz
(Normal)-Hydrogen: 2,466,061.413187035(10) GHz
This measurement is the 1S-2P line which has an average frequency of ~2,466,051.625 GHz (there's actually two levels). Which agrees to within 1 sigma - i.e. good agreement.
PS: If someone else wants to know why the 1S-2S and the 1S-2P transition have almost the same energy, but no exactly the same energy, it's an interesting weird story https://en.wikipedia.org/wiki/Lamb_shift
The Mystery Of The Matter Asymmetry
https://www.vanderbilt.edu/AnS/physics/panvini/babar/sakharo...