One Way Speed of Light a Convention?

Hi Christopher, you asked:

"I think my problem largely stems from this. I thought that acceleration does not alter clock function and that an acceleration field is equivalent to a gravitational one."

If you read chapter 4 of Relativity 4 Engineers carefully, you will find that clock rates depend on the "depth" of the gravitational well and gravitational acceleration on the "slope" of the gravitational well (at least for clocks static in the field). In more technical terms, clock rates depend on the intensity of the field and acceleration on the gradient of the field.

As an example, at Earth's center the gravitational well is "deepest", while there is zero "slope" in the field; hence clocks run the slowest there (compared to distant clocks), but there is no gravitational acceleration there.

"Is the stationary clock of your statement stationary because it has reached the top of its free fall fountain trajectory, or because it is held still without free fall by a table, with legs on the surface of the sun (patent pending) or legs on the floor of a suitably driven rocketship, that it is sitting on?"

It does not matter; for the static formulas to be valid, it must just not move relative to the gravitational field.

"Are the "slower ... 'tick'" and the "slower ... run" of the local clock near the sun intended to refer only to an appearance to a distant observer due to the use of light signals, or is there some sense in which the "slower ... 'tick'" is physically real?"

The "slower ... 'tick'" is real, both from a distant observer's point of view and also from a direct comparison point of view. If two atomic clocks are synchronized on the surface of Earth and one is then slowly taken to the top of a mountain, left there for some time and slowly brought down again, the surface clock will be behind the mountain clock. Such an experiment has been done.

Regards,

Burt Jordaan (www.Relativity-4-Engineers.com)

Burt has proposed ways to measure one-way light speed that might work well for a laboratory in free fall far from heavy objects, because we believe that far from heavy objects space is isotropic and homogeneous and Lorentz invariant.

But what about near heavy objects, such as the sun?

Near heavy objects, simple minded observers see light travel more slowly and in hyperbolic arcs.

Trained physicists know of light defining geodesics, with space-time near the sun being such that things seem to a distant observer to happen more quickly because ideal clocks seem to run slowly, and ideal measuring rods seem to shrink, near the sun. The trained physicist, sciens sub specie aeternitatis, tells us that talk of things happening and light propagating in a frame of cause and effect is nonsense, but simply that in its zero proper time the pulse defines a geodesic, which is eternal.

Simple minded observers may accept that ideal clocks are not affected by acceleration, and so they may infer that they are not affected by gravity.

The effects of gravity on a light pulse can be on its speed, or on its energy content, the latter by way of greater frequency and energy density at the same duration, or by way of longer duration at the same frequency and energy density.

As a light pulse comes from afar to pass near the rim of the sun, it gains kinetic energy at the expense of its gravitational potential energy. Loaded with the extra kinetic energy, the light pulse is heavier and is attracted more by the gravity of the sun.

Supposing it cannot go faster, it has to increase its frequency or its duration (more cycles per pulse) to carry the extra kinetic energy.

Not going faster, and not increasing its duration, it has to delay its leading edge to crimp up the waves to increase the frequency, becoming shorter in length. That makes its midpoint move more slowly on the way towards the sun.

Not going faster, and not increasing its frequency, but increasing its duration, it has to delay its trailing edge to fit in the extra cycles, again making its midpoint move more slowly.

The two are compatible: both the frequency and duration could increase, with the combined effect slowing the motion of the midpoint of the pulse.

The reverse happens on the way out from the sun on the back afar.

Does this make sense for a simple minded observer?

Of course this story is nonsense for a trained physicist, who knows that light defines geodesics and just increases its frequency as apparent to a distant observer, because time and space are different near the sun so that, to the distant observer, ideal clocks, near the sun, seem to run slowly and ideal measuring rods, near the sun, seem shorter.

Please put me right about this.

Christopher

Scruffy notes, in way of explanation:

It could e.g. be that light goes at c+v in the one direction and c-v in the opposite direction and your test will not pick it up.

In that example, note that the presumed travel time over a length d back and forth, d/(c+v) + d/(c-v), is not equal to the measured time, which is presumed to be 2d/c, and which I will call t₀.

In your example
t = 2cd/(c2-v2) = t₀(c2/[c2-v2])
or t₀ times a value that depends on v.

That gets us back to the classic attempts to measure the differences in the speed of light parallel and perpendicular to the Earth's motion, which, as you know, have consistently produced null results.

Adding in the consistency of measured values of c as compared with the expected value based on electromagnetic measurements and I don't understand what you find bothersome about this.

Sorry, SL!

Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)

Burt states:
"I think I understand SL's concern - if interferometry is used, a difference in path length is detected, not a one-way speed."

I'm dredging this up from memory, but the experiment allowed us to vary the mirror rotation rate, and that determined the time. Indeed, as you note, we used the shift in the interference fringes as a measurement of distance, not time.

As I said, this was a long time ago, but it is a classic experiment and still may be part of some school's labs.

I'm talking about a real experiment here, so it would have been impossible with our apparatus to measure the path lengths of two parts of the split beam to within a fraction of a wavelength. However, the shift in fringes was measurable and we could confirm that the rest of the experiment was stable by repeating.

Fred Bortz -- Science and technology books for young readers (www.fredbortz.com) and Science book reviews (www.scienceshelf.com)

Hi SL, you wrote: "...I don't follow how an observer can determine speed relative to the "preferred frame" if he cannot look outside to observe something stationary in that frame."

If you do not use Einstein's method of clock synchronization, you must somehow choose an inertial frame with all clocks set to some "cosmic time" and it is then your preferred frame. For the sake of this argument, say you accelerate a rocket out of this preferred frame until it achieves some large speed and then let it coast inertially, without resynchronizing its nose and tail clocks.

Later, purely inside this rocket, measure the one-way speed of light. You will find that the speed as measured between the nose and tail clocks is different in the 'forward' and 'rearward' directions. Hence, you know that you are moving relative to the preferred frame without looking 'outside'.

No such possibility if you have used Einstein's method to synchronize the rocket's clocks after the acceleration stopped; hence, no preferred frame...

On your final question: I have no idea how you would resynchronize the rocket's clocks, other than Einstein's way. :(

Regards,

Burt Jordaan (www.Relativity-4-Engineers.com)

Here's how I see it.

The famous Michelson-Morley experiment used an interferometer to measure the difference between the speed of light parallel and perpendicular to the Earth's motion. It produced a null result, contrary to what classical physics predicted.

That was not the only experiment to show that the speed of light is independent of the motion of an observer. The statement that the speed of light is always c is thus not an assumption or a mere convention but a result of observations. It has been tested in many ways since, and the result has never been overthrown.

Here's what I write about it in Physics: Decade by Decade (Facts On File, 2007):

Einstein's view of relativity was a natural extension of earlier scientific thought. At first, people viewed the Earth as the unmoving center of everything. Then they realized that Earth was one planet moving in a larger solar system. The natural human reaction was then to place the Sun at the center of the universe. But by Einstein's time, astronomers could tell that the stars were moving with respect to one another. They no longer had reason to think that the Sun -- or any other star -- occupied a special place in the universe. From that perspective, it was easier to give up the idea of an absolute frame of reference.

That led Einstein to state this basic principle of physics: If two observers are moving at constant velocity with respect to one another, neither observer's frame of reference is preferable to the other's. It is impossible to make any observation that determines that one is moving while the other is absolutely at rest in the universe.

That simple principle produces some surprising consequences. As noted in the Introduction, Maxwell's equations predict the existence of electromagnetic waves that travel at a definite speed. That means that two observers, regardless of their relative motion, must measure the same speed for a beam of electromagnetic radiation. (Copyright 2007, Alfred B. Bortz)