# A New Test of the Equivalence Principle?

1. Sep 1, 2004

### Garth

The Eotvos type experiments test the equivalence principle by comparing the inertial accelerations of bodies of different compositions within a gravitational field.
In short they test whether feathers and cannon balls fall at the same 'rate'.

But has anybody tested whether particles and photons fall at the same rate?

Indeed is anybody aware of the question being posed as a potential experiment before I did?

2. Sep 1, 2004

### Alkatran

The measured how much photons were affected by the sun's gravity. That would count, since they were bent exactly the way they were predicted to be bent.

3. Sep 1, 2004

it is very hard to test gravity effects in qm, since gravity plays such a minute role in particle physics.

4. Sep 1, 2004

### Mike2

Shouldn't the frequency of vibration be affected by how deep it is in a gravity well just as are photons? What particle properties depend on the frequency of string vibrations?

5. Sep 1, 2004

### Garth

A good point but not necessarily true, the deflection of light by a massive body consist of two components,which are equal in GR; a time dilation component and a curvature of space component.

The time dilation component (g oo) is that calculated in SR if you treat photons as a 'massive' particle (their energy being equivalent to a mass) being attracted by the central body such as the Sun. This is the rate at which photons 'fall' according to the theory. It was this value that Einstein first calculated for the deflection of star-light during a total eclipse in 1915 before he corrected it for the 1919 eclipse. (Had he not spotted his mistake history may have been completely different!)

On top of that deflection you add the curvature of space component (g ii)determined by the third (gamma) Robertson parameter.

In Self Creation Cosmology, for example, the first value is 3/2 not 1 as in GR but the second is 1/2 not 1 as in GR, so although photons 'fall' at 3/2 the GR rate, in SCC, the deflection of star-light by the Sun is predicted to be the same as GR. (3/2 + 1/2 = 1 + 1 !)

6. Sep 1, 2004

### pmb_phy

The equivalence principle does not mean that all particles fall at the same rate in GR. It means that the rate the particles fall does not depend on the mass of the particle
A photon will not fall at the same rate as, say a neutron. The rate at which a particle falls depends on the particle's velocity. It follows that since a neutron can never have the same speed as a photon, and hence it can't have the same velocity, then a photon can't fall at the same rate as a neutron.

Pete

7. Sep 1, 2004

### Alkatran

... Particles moving faster aren't affected by gravity for as long. But they still have the same acceleration.

8. Sep 1, 2004

### pmb_phy

That is incorrect. In GR the acceleration of a particle is a function of velocity. This is pretty obvious from

$$\frac{d^2x^{\mu}}{d\tau^2} = -\Gamma^{\mu}_{\alpha \beta} \frac{dx^{\alpha}}{d\tau} {dx^{\beta}}{d\tau}$$

Pete

9. Sep 1, 2004

### Garth

Yes - I was obviously using a simple expression "falls at the same rate", the meaning of which I thought would have been obvious, that is the question is whether "particles of different masses and compositions and photons fall at the same acceleration as each other". The intention is to open up discussion and original thought on the subject, as well as tapping any information about experiments, which I now hope will happen.

Let me now be more precise; the statement by Pete,
is a statement of the weak equivalence principle.
Eotvos and similar experiments test whether different substances, with different relative numbers of neutrons and protons/electrons, typically wood and platinum originally, or gold and aluminium more recently (Dicke) fall at the same acceleration.

These experiments are also testing the strong equivalence principle.

So again, the question I am asking is has anyone tested whether matter and photons fall at the same acceleration.

For example the LIGO gravity wave detectors use two orthogonal 4 km tunnels in which a beam is split and each sent and reflected 8km before recombining in an interferometer back at source. As the Sun 'passes overhead' the the Sun's gravitational field would affect the beam and the Earth differently if photons do not "fall towards the Sun" at the same rate as the solid body of the Earth. Although the experiment can detect a longitudinal motion of 10^-18 m the vertical displacement predicted by SSC (where photons fall at 3/2 the rate of matter - a huge difference) is only 10^-12 m because of the speed of light. As both beams would suffer the same deflection such a deflection probably cannot be detected.
Is there anybody who can confirm this?

However if one of the beams was truncated so that it was immediately reflected back and the interferometer adjusted to look for a daily vertical displacement of the two beams then it certainly could be detected, it the effect is there.

Does anybody know of, or has done, this or another similar experiment?
Garth

10. Sep 1, 2004

### pmb_phy

That is incorrect. In GR the acceleration of a particle is a function of velocity. This is pretty obvious from

$$\frac{d^2x^{\mu}}{d\tau^2} = -\Gamma^{\mu}_{\alpha \beta} \frac{dx^{\alpha}}{d\tau} \frac{dx^{\beta}}{d\tau}$$

Pete

11. Sep 1, 2004

### Garth

So Pete in the experiments we are talking about the particles are obviously all travelling at the same velocity, they are stationary in the laboratory frame. But do you think photons should fall at the same acceleration?

12. Sep 1, 2004

### pmb_phy

If they are stationary in the lab frame then since a photon is not stationary then the photon can not accelerate at the same rate. However all photons with the same velocity must fall at the same rate regardless of their mass-energy.

Pete

13. Sep 2, 2004

### Garth

If the light beam is horizontal then their vertical velocity is the same as the stationary masses in the Eotvos experiments. If the EEP postulates that they should 'fall' at the same rate as particles should not this be tested?

To put the question in its most precise and testable format: "Let the laboratory be in free-fall, say the Space Shuttle in orbit, so that it provides the basis of a locally inertial coordinate system. The EEP postulates that, within a sufficiently small region, the laws of nature take the same form as in an unaccelerated Cartesian coordinate system in the absence of gravitation.

So that different masses (the weak EEP) of different compositions (the strong EEP) should all be unaccelerated within that sufficiently small volume.

In fact they would suffer second order tidal forces, and mutual gravitational attraction, so the EEP is questionable from the start; however as far as first order gravitational forces are concerned I am happy to agree that such material bodies suffer no such inertial forces.

The question that is the subject of this thread is, "Do photons travel along a straight line, within a sufficiently small region, in such a laboratory?"

If your answer is yes, because that is the consequence of the postulates of GR, do you think it should be put to the test? Or indeed has it already been tested?

Last edited: Sep 2, 2004
14. Sep 2, 2004

### pervect

Staff Emeritus
Some of the older Eotovos experiments do accomplish part of what you want to do, I think.

There are differences in the amount of elelctrostatic field energy associated with various elements. So the Eotovos experiments do provide evidence that the electrostatic field follows the equivalence principle.

For instance, MTW, pg 1063

"Columb energy, which is proportional to [nuclear charge]^2, amounts in a gold nucleus to .4 percent of the mass, and .1 percent of the mass in an aluminum nucleus."

Given that one accepts that the energy in an electromagnetic wave is the sum of the magnetic and electric field energies, this does test some of what you want to test.

This is probably old news to you, but I thought I'd mention it.

I'm not particularly aware, unfortunately, of what's being done to test the equivalence principle nowadays - the big gravitational experiment in the news today is of course gravity probe B, which is well on its way to providing the first test of frame dragging.

15. Sep 2, 2004

### Garth

Thank you, indeed electromagnetic energy is located within the atom, and its mass equivalent is part of the atom's mass or rest energy. The question is therefore whether free electromagnetic radiation 'falls at the same rate' as matter or not? The significant difference being that when free such photons are relativistic whereas located within an atom it is static (in the system centre of momentum frame)

Gravity Probe B will also test geodetic precession for which SCC predicts a result 5/6 of that of GR. (5.5 rather than 6.6 arcsecs/yr) Hence the theory is testable and soon!

16. Sep 2, 2004

### pervect

Staff Emeritus
I did some googling, and I"m guessing now that SCC is self-creation cosmology. What would be the best introductory reference for this theory?

17. Sep 3, 2004

### Garth

My thread https://www.physicsforums.com/showthread.php?t=32713&highlight=Self+Creation+Cosmology sorry I can't do the "my post" thing! The discussion went off the point a bit in later posts but returned.
The most recent paper is "Self Creation Cosmology - An Alternative Gravitational Theory" http://arxiv.org/abs/gr-qc/0405094 to be published in 'Progress in General Relativity and Quantum Cosmology Research', Nova Science Publishers, Inc. New York.
and if you are into tensor calculus then you may find "The derivation of the coupling constant in the new Self Creation Cosmology", http://arxiv.org/abs/gr-qc/0302088 interesting. I'm afraid I haven't written a introductory article yet, I am waiting to see how GPB pans out - there may be no point!

18. Sep 4, 2004

### Creator

Interesting points you bring up here in this forum, Garth.
Apparently, you are trying to see if a reconfiguration of LIGO could discriminate between GR and SCC. At this point I have my doubts if LIGO will even be able to detect GW's; so why not divert its original intent.

Really? I'm not farmiliar with SCC. However, what are the SCC predictions for the gravitomagnetic precession of GPB?

Creator

19. Sep 4, 2004

### Garth

Creator - Thank you for your interest SCC predicts a geodetic precession of 5.5120 arcsec/yr and a "frame-dragging" or gravitomagnetic precession equal to GR of 0.0409 arcsec/yr.

If it is thought these predictions are inconsistent, they are for a metric theory. SCC is a non-metric or "semi-metric" theory. There is a metric as in GR and photons obey the equivalence principle but particles do not. There is an extra "scalar-field force" that acts on particles but not relativistic trace-free forms of energy such as photons.

20. Sep 4, 2004

### Creator

Thanks for the clarification. So let me address again this issue:

So why worry about using laser interferometry, where the accuracy is severely limited by c and the path length, when the above statement implies SCC should reveal a measureable divergence from GR in time dilation alone? Why not simply use gravitational time dilation measurements directly and have the advantage of long time periods to accumulate any differential in time dilation? In fact, if SCC is correct, such a large descrepancy should already exist & be detectable in existing data.

Creator

21. Sep 4, 2004

### Garth

The discrepancy is only detected when the behaviour of photons is locally compared with that of particles.
If Brans Dicke theory(BD) is "GR + Mach's Principle" then SCC is "BD + the local conservation of energy". The BD scalar field perturbs space-time, however the SCC local conservation of energy produces a scalar-field force which exactly compensates for this perturbation. Consequently the trajectories of free-falling particles in SCC are the same as their geodesics in GR. That is why the predictions of the two theories have been identical to date.
Time dilation is normally thought to be measured by gravitational red shift, however if you assume the local conservation of energy you find that the time dilation would apply to both the photon and the atoms it interacts with at the bottom and top of the gravitational well. Gravitational red shift is re-interpreted in the theory as the apparatus gaining (potential) energy, rather than the photon losing it. See "The derivation of the coupling constant in the new Self Creation Cosmology", http://arxiv.org/abs/gr-qc/0302088 (Section 3.2 "The Gravitational Red Shift of Light" page 20).

22. Sep 4, 2004

### Creator

You still seem to be missing my point.
You are referring to the 'discrepancy' in the trajectories which is a result of both time component and the geodetic component. My comment was referring to the fact that if SCC is correct a measurement of clock dilation ALONE would be sufficient to reveal the
3/2 discrepancy (SCC vs GR) IN theTIME DILATION factor, ex. from atomic clocks for example. Don't you agree?

Forget red shift for a moment, Garth, and how your Scc theory explains it. Answer one question:
Using only atomic clocks in a constant gravitational potential, don't you think SCC predicts an accumulated gravitational time dilation different from GR????? YES or no?

Creator

Last edited: Sep 4, 2004
23. Sep 5, 2004

### Garth

First, what do you mean by "using only atomic clocks"? To ask what rate a clock 'ticks' only makes sense when we compare it with another clock.

If that clock is higher/lower in a gravitational well to the first then how do you make the comparison? The experiments that have been carried out make the comparison by sending an electro-magnetic signal from one to the other, which reduces the experiment to the gravitational red shift scenario.

So I assume your question is asking what would happen if two clocks are synchronised next to each other and then one lowered slowly (to avoid SR effects) down a deep gravitational potential well and left at the bottom for some time before being brought up again to be compared a second time with the control clock. In this case what do you think happens in the GR case?

We note that an accelerating clock tells the same time and 'ticks' at the same rate as an unaccelerating one that is "moving momentarily along with" the first. (MTW pg 164 Box 6.2)

By the Equivalence Principle the accelerated frame of reference is equivalent with one in a gravitational field - within a small enough region. Therefore in a gravitational field the clock sitting on the bench tells the same time and 'ticks' at the same rate as the one that has just ("moving momentarily along with" the first) fallen off the bench and is in free-fall. So a clock even in a gravitational field does not lose time! That is, it doesn't "on its own"; the time dilation is only observed when its rate is compared with another "higher up the slope".

The time dilation is caused by the electro-magnetic time signals' null-geodesics diverging as they traverse the curved space-time between the clocks. Which brings us back to the red-shift scenario.

Therefore the answer to your question is the same (if I have understood the question correctly) as with gravitational red shift: SCC predicts the same observed gravitational time dilation as GR.

In SCC time dilation is experienced both by the photon and the apparatus it interacts with and the 3/2 increase is thus not observed, what is observed is an increase in the mass of the apparatus by the Newtonian potential. Such red shift is interpreted not as a loss of energy by the photon but by a gain of (gravitational potential) energy by the apparatus measuring it.

Last edited: Sep 5, 2004