A program is described which measures the gravitational acceleration of antiprotons. This idea was approached from a particle physics point of view. That point of view is examined starting with some history of physics over the last 200 years

Goldman, T.

Hughes, Richard J.

Nieto, Michael Martin

English

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THEINVERSE-SQUARELAW ANDQUANTUMGRAVITY
MICHAELMARTINNIETO,T.GOLDMAN,
ANDRICHARDJ.HUGHES
Theoretical Division, Los Alamos National Laboratory,
University of California, Los Alamos, New Mexico 87545
Ngo- 19949
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I'm going to describe a program which Terry Goldman, Richard Hughes, and I
are involved in at Los Alamos. As a matter of fact, it started 7 years ago when Terry
and I proposed measuring the gravitational acceleration of antiprotons. We came to
this idea from a particle physics point of view. I'm going to explain what I consider
to be that point of view, starting with some history of physics over the last 200 years.
At the beginning of the 1800's, there were understood to be three forces:
electricity, magnetism, and gravity. Through the work of Faraday, Orsted, and
Maxwell, we realized that electricity and magnetism are two aspects of the same force.
So, there were two forces: electromagnetism and gravity. Around 1900,
manifestations began to appear of what ultimately became known as the strong and
the weak forces.
In the same period, Einstein put relativity into gravity in the form we discuss
it today, general relativity. If you apply general relativity to Mercury in a power
series expansion you get a 1# 3 force. But you do not say that this is a new,
nongravitational force. You say that this is a new aspect of gravity which becomes
manifest when you put in relativity.
Similarly, when quantum mechanics was applied to electromagnetism, we
found that there were new aspects which appeared. This was not because we
changed Maxwell's equations but because we put quantum mechanics into them. To
me, the prime example is the Lamb Shift. In the 1930's, this was parametrized by
something that was called the Uehling potential. Nobody said that the Uehling
potential manifested a new force. It was a new aspect of electromagnetism which
appeared when you brought quantum mechanics into it.
In this spirit, it is the prime goal of modern particle theory to try to unify all
the forces of nature in a relativistic, quantum field theory. The work of Weinberg,
Salam, and Glashow, in the 1960's and 1970's, resulted in the unification of the weak
and the electomagnetic forces into what we now call the electroweak force. This
theory was verified in the discovery of the W and Z particles at CERN. In this
unification the Z particle and the photon are two aspects of the same object: one has
a mass and one doesn't.
Independently, a model of the strong force was invented. It is called QCD, for
Quantum Chromo Dynamics. It is still by itself. The hope was that we could unify QCD
and the electroweak theory using the group SO(5). But one of the predictions of the
theory was that the proton would decay with a lifetime <1032 years. To test this idea,
people, instead of taking one proton and waiting for 1032 years, decided to take 1032
protons and wait for 1 year. Unfortunately, they waited for more than 1 year and the
protons still didn't decay. So, as it stands now, even though we wish we had a
successful unified theory of the strong and the electroweak forces, we don't.
However, we particle physicists are undaunted. Even though we have not
unified the strong and electroweak interactions, we already are trying to unify them
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https://ntrs.nasa.gov/search.jsp?R=19900010633 2020-03-19T23:00:13+00:00Z
with gravity. Such theories are called theories of quantum gravity. One of the
manifestations of these theories is that, as with electromagnetism,new gravitational
effects arise simply becausequantummechanics is brought into gravity.
But how could things be different with these new quantum gravity theories?
Before I answer that I must emphasizethat none of these theories produce anything
like the particle spectrumwhich you see. In fact, every time a new acceleratorgoes
on, people first search for the expectednew particles and then say, "Wait till the next
accelerator." So, all of these conceptsremain theories of theories. I'm pushing them,
but I have to be honest. However, they all have tantalizing phenomenological
features.
In general, in these theories, the spin-2 graviton has spin-0 and spin-1
partners. The partners may couple to fermions (and therefore violate the weak
equivalence principle), and they may have a finite rest mass (and so violate the
inverse-squarelaw). There are many people who have put in a lot of work: Joel
Scherk,CosmosZachos,and I could go on and on. But let me tell you what it all boils
down to. One can parametrizethe static potential as
V = -Gmlm2[ 1 + (-/+) a e-v/r + b e-sIr ]/r. (1)
The first term is normal gravity. The second term is from the spin-1 graviphoton. It
has the (-) sign for matter-matter interactions (overall repulsion) and the (+) sign
(overall attraction) for antimatter-matter interactions. The graviscalar term is
always attractive. For matter-matter interactions these two new forces could
approximately cancel and yield a small effect. For matter-antimatter interactions the
two new terms add, and so could produce a relatively large effect.
But, people often wonder, does a different gravitational acceleration for
antimatter violate CPT? You might think so, that if you drop antimatter it has to fall
the same as if you drop matter. But actually, CPT only tells you that if you drop an
apple to the earth it will fall exactly as if you drop an antiapple to an antiearth. CPT
doesn't tell you what happens if you drop an antiapple to the earth.
There are two schools of thought on all of the above arguments. The loyal
opposition believes that there actually may be a new force of nature. They can argue
that this is just like in the days when Einstein was trying to unify electricity and
gravity. He couldn't do it because he didn't know about the weak and the strong
forces, so he missed the boat. So too, this school would argue, the reason why we're
having trouble unifying things is because there is a "fifth force" out there and we
just haven't realized it before.
Of course, the school to which I belong says that if there are new forces of
approximately gravitational strength, then they are new manifestations of gravity
which arise because we're bringing quantum mechanics into it: if it's approximately
of gravitational strength it's gravity. That's where I'm coming from. But you know,
God didn't talk to me when he built this place. So, it could indeed turn out that there
is a "fifth force" of nature. This is something which experiment and theory will
have to settle.
So, what are the experimental indications? As to possible Principle of
Equivalence violations, Jim Failer will be talking about this tomorrow. Let us just
note that the recent tests of the Principle of Equivalence have all found, with one
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notable exception, a null or very small signal. Contrariwise, there have been three
recent tests of the inverse-squarelaw, on scalesof the order of hundredsof meters to
perhaps as much as hundreds of kilometers. All of them have found an anomaly.
This includes the Australian mine results, the Air Force tower experiment, and
geophysical well-logging results. So, could it possibly be that there is a lack of
violation of the Principle of Equivalence and not a violation of the inverse-square
law? This entire question is very exciting right now.
I want to mention two ongoing Los Alamos experiments. One is the proposalto
measure the gravitational acceleration of antiprotons at LEAR, the low energy
antiproton ring at CERN. This is a "Galileo" experiment which measures the
antiproton's time of flight (at 4° K) up a drift tube. The experimentis approved,is
underfunded and undermanned,but is going along. Equipment is being built and
hopefully we're on the floor in 1991. (A complementary experiment to measure
gravity on positrons is being pushed by Bill Fairbank.) An experiment to test the
inverse-squarelaw was performed last summer in the Greenland Ice Sheet. A thin
bore-hole gravity meter was lowered down the DYE-3 bore-hole, which is 2
kilometers deep. This experiment is now being analyzed and the results should come
out August 1.
There are many related experimentswhich can be done in space. Most obvious
are tests of Newton's Law. For scaleson the order of 10's to 100's of kilometers one
could do a precise orbit analysis of a lunar positional satellite, or even analyze
LAGEOS or Starlette data to higher precision. Smaller-scaletests could be done in
earth orbit.
But in any event, these are exciting times for gravity.
collaborators are excited.
Certainly I and my
REFERENCES
Forreferencesby themanypeoplewhohavecontributedto thisfield,seeourarticles:
Ander,M.E.,Goldman,T. Hughes, R. J., and Nieto, M. M. 1988, Phys. Rev. Lett., 60, 1225.
Goldman,T, Hughes, R. J., and Nieto, M. M. 1986, Phys. Left. B, 171, 217.
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DISCUSSION
SCHUTZ: In theories where antiparticles couple to gravity differently from particles,
what happens to photons, which are their own antiparticles?
NIETO: The genesisof your questionwas raised by the old "anti-gravity" ideas studied
in the 1950's. This one asked if one could have normal tensor gravity for matter, but
exactly opposite gravity for "anti-matter", then you would have "likes attract" not
"opposites attract".
Such a system would violate conservationof energy. In Morrison's gedanken
experiment, you could create an antiproton-protonpair in the earth's field, raise it at
no cost in energy, annihilate to photons, which gain energy following, and then
create a new pair with added kinetic energy. In fact, this is a variation of Wigner's
perpetual motion machine if change is not conserved.
For the quantum-gravity ideas, the tensor forces are normal, and you have no
changein photon dynamics. The new vector piece has 'like repel' and no coupling to
photons,so this is no problem. The scalar piece could or could not couple to photons
and/or not violate the principle of equivalence,depending on the particular model.
Therefore, although the models are mathematically consistent on this point,
different models will have restrictions imposed upon them on the size of the effects
allowed by experiment.
SHAPIRO: Can you particularize the limit on the ability to "maneuver" within grand
unified theories as far as the lowest "acceptable"proton decay rate is concerned?
NEITO: The simplest,most obvious, and specifically predictive "Grand Unified Theory"
was SU(5), which was to break down into SU(3)-color (the strong interactions) cross
the SU(2) x SU(I), the electroweaktheory. This is now ruled out by the lack of proton
decay. The decay rate goes as X-4, where X is the massivevector boson that converts
quarks into leptons. The existence of a unified coupling constant then determines
rather precisely what X must be since it is the scale where all the various interaction
coupling constants become the unified coupling constant. The end result is that,
even with optimistic theoretical "fudges", the proton lifetime must be less than 1032
years. The experimental limits are now significantly greater than this number. See,
e.g.,T. Goldman,Ad. Nucl. Phys.18, 315 (1987), Sec. 7.
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The inverse-square law and quantum gravity

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