#hereticalphysics

[scepticaladventure]

25  Gravity, Time and Light  6Sep18

Introduction In essence, Special Relativity is a systematic attempt to describe the physics of things that move fast, based up on postulates about light, and General Relativity is an attempt to include gravity. Hence a good question at the core of it all is “How does gravity affect the speed of light?” You might think this is a simple question but have a look at the Internet. Confusion reigns!

Sources of Confusion I think a lot of the confusion comes from lack of precision in the question. If Relativity has taught us anything it has taught us to be wary about simple questions about time, distance and speed. We have learnt we must first specify “Who is the observer and what is their situation?” We have learnt that the answers to simple questions about lengths, durations and speeds depend on how they are measured and in what circumstances are they measured - everything is relative.

Hence the speed of light in a strong gravitational field as measured by a local observer who is also embedded in that field might be different from a result obtained by a distant observer well away from the massive object creating the field.

It turns out that the speed of light is affected by a gravitational field, but so to (in fact hence) is local time keeping and so the local speed of light as measured by that local observer is the same as usual. The slowdown is undetectable. But from a more distant perspective the slowdown in the speed of light does become detectable.

Another source of confusion comes from the interrelated complexity between time, distance and speed. In a world where time can run fast or slow, distances can contract and Euclidean geometry may not hold true, the meaning of measurements and hence the quantification of physical properties becomes treacherous.

A third source of confusion comes from confused people teaching confused or confusing messages to innocent student, often with absolute conviction e.g. that the speed of light is a universal invariant that its always and everywhere the same.

What is Time? I was watching a science program the other day and the reporter asked a group of astrophysicists attending a theoretical physics conference in Ontario – what is time? Well they um’d and ah’d and said it was a difficult question and so on. They could not give a ready answer in plain English.

So let me have a go. Firstly the word itself covers two sorts of concepts – a way of tagging a river of events which may or may not be linked causally, and durations between events. Or to take a simple example – If you ask a time keeper at a sports event “What is the time?” she may reply “Do you mean the time of day, or the result of some competitor’s performance in an event?”

The underlying concept is causality. If an event A causes an event B then we say that A occurs before or simultaneously with Event B. No-one has ever witnessed causality running backwards, so we assume that it is a strictly one way affair.

When we come across physical phenomena with a repetitive regularity about them, such as the vibrations of a quartz crystal, we can use it to create a useful clock and hence create a measure of local time durations.

If we standardize such clocks to each other we can start to talk about the time more generally, and we can give an elementary answer to the question “what is the agreed exact time of day?”. But this is a man made convention. We have to be careful not to assume that our concepts can be applied well beyond the scope in which they were created. For example, we cannot assume that the whole Universe is embedded in some sort of all embracing river of time with a Universal standard clock somewhere.

Once we start to consider events on a cosmological scale, or in fast moving situations, we have come to understand that our normal day-to-day concepts of time do not suffice. Different observers can measure different time durations for the interval between the same two events. Time can be observed to run slow, not because clocks are distorted but because the finite speed of light means that the very concept of ‘what happens when’ needs to be reconsidered. Over and above that it turns out that time also runs slow in a gravitational field.

So time is nothing more than mankind’s attempt to quantify intervals between events. It is a manmade construct overlaid on reality, nothing more. It has no independent reality. In fact it can be considered to be a widely shared illusion. And a treacherous one at that.

Definitions and Standards of Measurement Let’s look at the simple equation c = D/T where c is the speed of light, D is a measure of distance travelled and T is a measure of time duration. For this to have any meaning we need an agreed way of measuring D and T and we need agreed units of measurement for both D and T. But where to start?

In the modern world our standards of measurement start with time.

Since the 1970’s there has been an international agreement that a standard second is defined by a set number of oscillations in the electromagnetic radiation (i.e. light) emitted by hyperfine transitions within Caesium 133 atoms held in certain conditions. A standard meter is then defined as being the distance travelled by this light in 1/299,792,458 standard seconds.

It then follows axiomatically that the standard speed of light is 299,792,458 meters per second. If nothing else this helps to pin down some terminology. But it does not mean that the actual speed of light will always be the same as the standard speed of light. A trivial example is if the light is travelling through glass. It’s slower. A more complicated example is if the light is travelling across a spiral galaxy.

Note that this whole approach to the definition of standards could have started in a different way. For example, a standard meter could have been defined as the distance between two scratches on a bar of metal held at a precise temperature in a specified location (e.g. Paris), and a standard second could then have been defined by the time taken for light to travel a set number of meters. Or a standard second could have been defined using an atomic clock and the speed of light could have been left out of it altogether, which is what used to happen before the current system was adopted.

There are three spatial dimensions and only one time dimension, so a democratic approach suggests we should start with defining distance and then move on to define time. Seriously though, length is a lot more observable and tangible than time. We can see and touch and run a ruler over the length of a thing. Time is invisible and intangible.

Timekeeping is always (as far as I can tell) based on motion of some sort, whether this be vibrations in a quartz crystal, the swing of a pendulum or the rotation of a planet. And since motion involves both distance and time, defining time durations based on the motions of things seems a little bit tricky. If time did not exist, how would we know anything was moving? The answer is that we could see things happening – things doing things to other things. Causality at work. But this would offer no guarantees about the nature of time. For example, if everything in the Universe speeded up by 10%, how could we tell?  

Furthermore, we know from experiments that time is affected by motion (Lorentzian time dilation) and by gravity (gravitational time dilation). So time is a rubbery phenomenon and in some situations it is a deceptive illusion.

Length is also affected by motion (Lorentzian contraction). This is a small effect in extreme circumstances, but it is nevertheless quite real. It was realized from experiments on the speed of light and came to become a key feature of the Theory of Special Relativity. But nobody, as far as I know, has been able to demonstrate length contraction in a simple experiment or demonstration. And I have never seen a photo-montage showing a Lorentz contracted object.

It is very difficult to hold up ruler against a physical object travelling at relativistic speeds in a straight line and be  able to record both ends at exactly the same time. The closest experiments I know of come from studies of high speed collisions between atomic nuclei at the Brookhaven Relativistic Heavy Ion Collider. The heavy nuclei have a non-zero radius and the dynamics of the collisions give the results expected if the nuclei are Lorentz contracted into disks. However, the Brookhaven accelerator is not a linear accelerator and this brings into play the theoretical complications of rotating and accelerated systems (see for example the Ehrenfest rotating disc paradox). Determining the effective radii of the ions is also problematical.

The three spatial dimensions of an object in spacetime are tangible. You can see and touch and measure lengths, widths and heights. You can put a ruler next to them. Time durations on the other hand are anything but simple, especially if the object is moving. You need to specify the situation of the observer very carefully. You need to carry the same clock from one event to the other or else to use a carefully synchronised set of clocks.

Time is a consequential parameter. It is the consequence of causality. At heart maybe the only thing you can be sure of is that Event A causes Event B, then Event A occurs before Event B. This also creates the Arrow of Time. In other words time is a one way phenomenon. You can never re-measure the exact same time interval, nor can you ever measure a time duration in back to front order.

The usual way to bridge from the world of tangible spatial dimensions to a world that involves time, motion, momentum and energy is to involve the speed of light.

What is an Inertial Reference Frame? After studying the results of experiments by Bradley, Eotvos, Roemer and Fizeau (and presumably Michelson and Morley, which he failed to acknowledge) Einstein simply postulated that that the speed of light in vacuum in an inertial reference frame is always the same (299,792.458 km/sec).

By inertial reference frame he meant one which is not accelerating, rotating or in a gravitational field. A frame in which test particles weigh nothing and stay still or travel in straight lines unless compelled by a force to do otherwise.

I think that an inertial reference frame is a an idealized concepts which is impossible to find in practice. Everything in the Universe is either spinning, accelerating or affected by gravity.  It was and still is common to say that an inertial reference frame is aligned to the “fixed stars”. However, no-one ever clarifies whether such stars are in our galaxy or beyond it, and what such stars can possible have to do with local physics anyway.

I all my reading I cannot find clarity about whether a satellite in orbit constitutes an inertial reference frame or not. The satellite is undoubtedly within a gravitational field or else it could not be orbiting. But the apparent effects of gravity are undone by the fact that the satellite is in free fall. Or you could consider the force of gravity to have been annulled by the effects of centrifugal acceleration. Either way you look at it test particles inside the satellite will be weightless. So are atomic clocks in this situation subject to gravitational time dilation or not?

I think this is a good question. If the answer is that the gravitational potential at which the satellite orbits does slow down the onboard observers’ clocks then they can determine whether they are free falling in gravity field by measuring the frequency of signals received from deep space, a pulsar say, on their local clock. If the signals are coming in too quickly then their clock is running slow. So they can tell that they are in fact free falling in a gravity field. This violates the Einstein Equivalence Principle, even though some authors will try to wriggle out of it by saying that the experiment is not a local one.

If the answer is no then it suggests that gravitational time dilation only occurs when matter has weight. It also suggests that a centrifugal acceleration can undo gravitational time dilation. Both aspects would be worth deep consideration. There would be interesting implications for the Clock Postulate (see an earlier essay).

As far as I can tell the answer is yes, clocks aboard an orbiting satellite are still subject to a degree of gravitational time dilation, quite apart from Special Relativity effects.

Apart from that an orbiting space station is still a potential candidate to be a localized inertial reference frame. But we have to worry about possible rotational effects.

Sagnac interferometers could be used to detect any spinning of the satellite. If the satellite is managed so that there is no spinning detected in any direction then I guess that the satellite is pretty close to being an inertial reference frame. Now let us look out of the windows of the satellite. It is generally accepted that if telescopes were positioned so that they point at very distant galaxies then those telescopes would remain pointed at those distant galaxies.

But then observers on board the satellite would perceive the Earth going round and round the satellite every orbit. And the Sun and nearly stars would all be going around and around too. So is the satellite spinning or not?

You can see that inertial reference frames are not easy to define in practice!

Einstein and the Speed of Light Between 1905 and 1911 Einstein concentrated on generalizing his description of physics and developed an approach/model that has become known as the Theory of General Relativity. By 1911 he had concluded that in the presence of gravity the speed of light is not a fixed invariant. His model of Special Relativity had to be qualified and elaborated upon. The measured speed of light in a gravitational field becomes a variable depending upon the reference frame of the observer.

His logic is contained in his paper On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. This predates the full description of his General Theory of Relativity by four years. The result he came up with was expressed mathematically as c’ = (1 + Φ/c2).c   where Φ is the gravitational potential relative to the point where the speed of light is measured.

In other words, light appears to travel slower in stronger gravitational fields. There is a more complete description in Section 3 of ‘The Meaning of Relativity', A. Einstein, Princeton University Press (1955).

In 1915 Einstein revised this calculation to be c’ = (1 + 2Φ/c2).c  In other words he decided the effect was twice a great as he first thought.

Unlike in the inertial reference frames of Special Relativity, the measured speed of light in gravitational fields depends upon the reference frame of the observer. What one observer sees as true, another observer sees as not true, or at least slightly different.

If you wanted to be mischievous you could say that Einstein’s Theory of Special Relativity is based upon his proposition that the speed of light is invariant, and his Theory of General Relativity is based upon his proposition that the speed of light is not invariant.

Time in a Gravity Well We know from the impressive achievements made in recent decades in developing GPS systems that atomic clocks at rest on the surface of the Earth run slower than identical clocks on orbiting satellites.

For GPS to work, atomic clocks on Earth have to be very well synchronised with identical clocks aboard specially designed satellites. There are a variety of relativistic effects in play but the main one is due to the fact that the earthbound clocks are in stronger gravity than the orbiting satellites. The effect of gravitation is slightly reduced by centrifugal accelerations caused by the spin of the Earth. The overall gravitational effect is about 45 microseconds per day.

The gravitational time dilation effect is then adjusted for smaller relativistic effects, the main one being a Special Relativistic time dilation because the satellites are moving fast relative to the earthbound clocks. This offsets the gravitational effect by about 7 microseconds per day, giving a net relative adjustment of 38 microseconds per day.

When the satellites were first deployed the scientists in charge were not totally confident how much fine tuning would be required to get perfect synchronisation, so they allowed for a large degree of post launch adjustment. Now they make most of the adjustments before launch.

Of course gravity can have a direct physical effect on clocks. For example, a pendulum clock could not work without it. But that it not what we are talking about here. We are talking about an impact on time itself.

The way I prefer to think about all this is to start with the experimental fact that gravity has an effect on the speed of light. Then I remind myself that the measure of time can be thought of as physical lengths divided by the speed of light. Hence time durations are affected by gravity. And then every physical quantity involving time, notably every form of energy, is also affected.

Shapiro Time Delay The Shapiro time delay effect, or gravitational time delay effect, is now regarded as one of the classic tests of General Relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present. The time delay is caused by the slowing passage of light as it moves over a finite distance through a change in gravitational potential.

In “Fourth Test of General Relativity”, Physics Review Letters, 20 1265-1269, 1968, Irwin Shapiro wrote, “Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2x10−4 sec when the radar pulses pass near the Sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path length to within about 5 to 10% with presently obtainable equipment.”

This test was first confirmed by experiments that ‘bounced’ radar signals off the planet Venus when it was just visible on the far side of the Sun as seen from Earth. It has since been measured using Mercury as well, and also using satellites such as the Cassini probe.

Note that seen from afar the path taken by the photons is a curve in both directions. You might think that this is what makes them take longer, but that is not the best way to think of it. The photons are taking the quickest route possible, but they are still delayed by the presence of the gravity field of the Sun. They do actually slow down in the stronger gravity closer to the Sun.

Light in a Gravity Well If we throw a ball upwards in a gravity field the ball decelerates, comes to a temporary stop at the top of its trajectory, and falls again. If we throw it faster than the Earth’s escape velocity the ball can overcome the overall gravitational attraction of the Earth and fly off into space with a certain amount of residual velocity.

What happens to a photon ejected from the surface of the Sun? Several essays ago we discussed and decided that the photon arrives at its destination detector in a weakened state. By comparison to other photons we can deduce that it has less energy and momentum than when it started and the frequency of its effects upon being absorbed are slower. In other words it reveals that it has become red shifted.

Does this mean that photons must travel slower as they climb higher – just like the ball? No – not at all! In fact the opposite is true (to a tiny extent). In the above section we discussed that the speed of light is faster in a weak field than it is in a strong field, and this is an experimental fact. Therefore the speed of photons (as measured by a distant observer) actually increases as the photons move into a weaker and weaker gravitational field.

This seems paradoxical. The arriving photon is travelling faster when its arrives than when it started, as measured from afar, but it arrives with less energy than when it started.

To understand this I think it is useful to note that the speed of a photon (as observed from afar) has no bearing on its energy level. See my earlier essay about energy remaining the same when photons travel in media with different refractive indices. I think the energy of a photon is embodied in the packet of physical properties it takes with it rather than in the speed of that packet as deduced by an external observer.

So how then does the photon become weaker? And where did the energy that is no longer contained in the photon end up? In the example of the thrown ball, what is going on is that as the ball gains in potential energy it loses kinetic energy until eventually it stops moving for a moment and then starts to fall again. There is a tradeoff between potential energy and kinetic energy. The potential energy can be thought of a being stored in the gravitational interaction between the Earth and the ball.

Much the same thing seems to happen to a photon. As it gains potential energy it loses electro-magnetic energy so that when it arrives it is weaker (i.e. redshifted).

I think this is a partially adequate description of what happens. However, if you want to adopt the Einstein Equivalence Principle as literally true and in some ways a better description of reality, and if you want to replace the greatest force in the Universe with the mathematical trickery of curved spacetime, then you can also explain the result using the language of Doppler shifts related to accelerations in curved spacetime. It also gives the right answer, so it becomes a matter of choice which point of view you want to adopt.

If you do use Einstein’s General Relativity model then note that it is only the perturbation of the time term that is needed in order to come up with the observed results for gravitational redshifts. The full field equations are not needed and there is no need to call upon any warping in the spatial aspects of the spacetime geometry.

Textbook Conventions Textbook explanations of Special Relativity invariably adopt Einstein’s postulate that the speed of light is an invariant constant. Many go further and tidy up all their equations by putting c = 1 and measuring all distances in light-seconds. They then drop c out of all the equations. They also carry over this convention into General Relativity.

However, most of the interesting predictions and effects of General Relativity depend upon the speed of light not being an invariant constant. So (in my opinion) writing c=1 and then omitting it from the equations obscures and confuses the physics of interest. Likewise, defining the speed of light to be exactly 299,792,458 meters per second is confusing unless we call this the standard speed of notional light and allow for the fact that the actual speed of light is slightly different from this in nearly all situations of interest and experience.

Conclusions Light slows down in the presence of gravity and so it is not invariant. But what you measure as its speed depends on how you measure it. A local measurement will not detect any difference. The speed of light is fundamental to the concept, meaning and measurement of time. So unless you can get this sorted out in your own mind, your physics is destined to end up in a muddle. And you would not be alone!

[scepticaladventure]

27  Gravitational Waves  12Sep18

Introduction This essay continues my series of essays discussing tests of Einstein’s Theory of General Relativity. More detailed descriptions of the test themselves can be found online and in the literature. See for example the literature review in May 2017 by Estelle Asmodelle from the University of Central Lancashire Ref:  arXiv:1705.04397 [gr-qc] or arXiv:1705.04397v1 [gr-qc].

I have questioned whether the experimental tests exclude any other explanations for the same phenomenon. So far I have examined gravitational redshifts and gravitational light bending, the Shapiro round-trip light delay and the ‘anomalous’ precession of Mercury. The evidence so far is that while General Relativity provides a satisfying explanation for all of these experimental observations, other ways of describing the outcomes are also viable. Hence there may be more than one way to include all the evidence within a different but still complete and consistent model or theory.

In this essay I will look at the latest of the five so-called tests – gravitational waves.

Gravitational Waves Gravitational waves are generated in certain gravitational interactions and propagate as waves outward from their source at the speed of light. Their possibility was discussed in 1893 by the polymath Oliver Heaviside, using the analogy between the inverse-square laws in both gravitation and electricity.

In 1905, Henri Poincaré suggested that a model of physics using the Lorentz transformations (then being incorporated into Special Relativity) required the possibility of gravitational waves (‘ondes gravifiques’) emanating from a body and propagating at the speed of light.

Some authors claim that gravitational waves disprove Newton’s mechanics since Newton assumed that gravity acted instantaneously at a distance. I think this is unfair to Newton. Whether or not Newton explicitly claimed that gravity acted instantaneously at a distance I do not know, but it would have been a reasonable and pragmatic working assumption to make at the time. Furthermore whether he assumed instantaneous effects or delays at the speed of light makes no practical difference to the validity of Newton’s work for the type of celestial mechanics he was interested in.

In 1916, Einstein suggested that gravitational waves were a firm prediction of General Relativity. He said that that large accelerations of mass/energy would cause disturbances in the spacetime metric around them and that such disturbances would travel outwards at the speed of light. A spherical acceleration of a star would not suffice because the gravity effects would still be felt as coming from the centre of mass. The cause would have to be a large asymmetric mass that was rotating rapidly. Or better still, two very large masses that were rotating around each other.

In general terms, gravitational waves are radiated by objects whose motion involves acceleration and changes in that acceleration, provided that the motion is not spherically symmetric (like an expanding or contracting sphere) or rotationally symmetric (like a spinning disk or sphere).

A simple example is a spinning dumbbell. If the dumbbell spins around its axis of its connecting bar, it will not radiate gravitational waves. If it tumbles end over end, like in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier the dumbbell, or the faster it tumbles, the greater the gravitational radiation. In an extreme case, such as when two massive stars like neutron stars or black holes are orbiting each other very quickly, then significant amounts of gravitational radiation will be given off.

Over the next twenty years the idea developed slowly. Even Einstein had his doubts about whether gravitational waves should exist or not. He said as much to Karl Schwarzschild and later started a collaboration with Nathan Rosen to debunk the whole idea. But instead of debunking the idea Einstein and Rosen further developed it and by 1937 they had published a reasonably complete version of gravitational waves in General Relativity. Note that this is 22 years after the General Theory was first published.  

In 1956, the year after Einstein’s death, Felix Pirani reduced some of the confusion by representing gravitational waves in terms of the manifestly observable Riemann curvature tensor.

In 1957 Richard Feynman argued that gravitational waves should be able to carry energy and so might be able to be detected. Note that gravitational waves are also expected to be able to carry away angular or linear momentum. Feynman’s insight inspired Joseph Weber to try to build the first gravity wave detectors. However his efforts were not successful. The incredible weakness of the effects being sought cannot be over emphasized.

More support came from indirect sources. Theorists predicted that gravity waves would sap energy out of an intensely strong gravitational system. In 1974, Russell Alan Hulse and Joseph Hooton Taylor, Jr. discovered the first binary pulsar (a discovery that would earn them the 1993 Nobel Prize in Physics). In 1979, results were published detailing measurement of the gradual decay of the orbital period of the Hulse-Taylor pulsar, and these measurements fitted precisely with the loss of energy and angular momentum through gravitational radiation as predicted by calculations using General Relativity.

Four types of gravitational waves (GWs) have been predicted. Firstly, there are ‘continuous GWs,’ which have almost constant frequency and relatively small amplitude, and are expected to come from binary systems in rotation, or from a single extended asymmetric mass object rotating about its axis.

Secondly, there are ‘Inspiral GWs,’ which are produced by massive binary systems that are spiralling in towards one another. As their orbital distance lessens, their rotational velocity increases rapidly.

Then there are ‘Burst GWs,’ which are produced by an extreme event such as asymmetric gamma ray bursters or supernovae.

Lastly, there are ‘Stochastic GWs,’ which are predicted to have been created in the very early universe by sonic waves within the primordial soup. These are sometimes called primordial GWs and they are predicted to produce a GW background. Personally I doubt that this last type of GW exists.

On February 11, 2016, the LIGO and Virgo Scientific Collaboration announced they had made the first observation of gravitational waves. The observation itself was made on 14 September 2015, using the Advanced LIGO detectors. The gravity waves originated from a pair of merging black holes millions of years ago that released energy equivalent to a billion trillion stars within seconds. For the first time in human history, mankind could ‘feel and hear’ something happening in deep space and not just ‘see’ it. The black holes were estimated to be 36 and 29 solar masses respectively and circling each other at 250 times per second when the signal was first detected.

By August 2017 half a dozen other detections of gravitational waves were announced. I think all of them have been in-spiral GW’s. These produce a characteristic ‘chirp’ in which the signal becomes quicker and stronger and then stops. This is very useful for finding the signal amongst all the background noise. The flickering light pattern signal in the interferometer detector can be turned directly into a sound wave and actually does sound like a chirp.

In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss, Kip Thorne and Barry Barish for their role in the detection of gravitational waves. (The same Kip Thorne who co-authored the heavyweight textbook on gravity that I have referred to so often in these essays that I gave it its own acronym -  MTW).

As I first drafted this essay in 2017 there was considerable excitement in the world of astronomy because the Large Interferometer Gravity Wave Observatories (LIGO) suggested that a pair of neutron starts were in the process of collapsing. Space based telescopes were then able to look in that direction and they observed an intense burst of gamma rays. This is the first example of the two types of observational instruments working together and the dual result confirms that LIGO had been observing what they thought they were observing. Furthermore it provides evidence that gravitational waves travel at the speed of light.

Detection LIGO is a large-scale long-term physics project that includes the design, construction and operation of observatories designed to detect cosmic gravitational waves and applied theoretical work to develop gravitational-wave observations as an astronomical tool. It has been a struggle lasting many decades. It took many attempts to achieve funding for the observatories and nearly a decade to make the first successful observations. A triumph of persistence, optimism and the begrudging willingness of the USA National Science Foundation to fund a speculative fundamental science project to the tune of US$1.1 billion over the course of 40 years.

To my mind the experimental set up is reminiscent of Michelson Morley experiments 140 years ago. But it is on a much larger scale and is incredibly more sensitive, with all sorts of very clever tricks to increase the sensitivity and to get unwanted noise out of the system. Two large observatories have been built in the United States (in the states of Washington and Louisiana) with the aim of detecting gravitational waves by enhanced laser interferometry. The observatories have mirrors 4 km apart. Each arm contains resonant cavities at the end.

When a gravitational wave passes through the interferometer, the spacetime in the local area is altered. Depending on the source of the wave and its polarization, this results in an effective change in length of one or both of the beams. The effective length change between the beams will cause the light currently in the cavity to become very slightly out of phase (anti-phase) with the incoming light. The cavity will therefore periodically get very slightly out of coherence and the beams, which are tuned to destructively interfere at the detector, will have a very slight periodically varying detuning. This results in a measurable signal.

Or, to put it another way: After approximately 280 trips up and down the 4 km long evaluated tube arms to the far mirrors and back again, the two beams leave the arms and recombine at the beam splitter. The beams returning from two arms are kept out of phase so that when the arms are both in coherence and interference (as when there is no gravitational wave or extraneous disturbance passing through), their light waves subtract, and no light should arrive at the final photodiode. When a gravitational wave passes through the interferometer, the distances along the arms of the interferometer are repeatedly shortened and lengthened, creating a resonance and causing the beams to become slightly less out of phase and thus allowing some of the laser light to arrives at the final photodiode, thus creating a signal.

Light that does not contain a signal is returned to the interferometer using a power recycling mirror, thus increasing the power of the light in the arms. In actual operation, noise sources can cause movement in the optics that produces similar effects to real gravitational wave signals. A great deal of the art and skill in the design of the observatories, and in the complexity of their construction, is associated with the reduction of spurious motions of the mirrors. Observers also compare signals from both sites to reduce the effects of noise.

The observatories are so sensitive that they can detect a change in the length of their arms equivalent to ten-thousandth the charge diameter of a proton. This is equivalent to measuring the distance to Proxima Centauri with an error smaller than the width of a human hair.

Although the official description of LIGO talks about gravitational waves shortening and lengthening the arms of the interferometers by almost infinitesimal amounts, I think it might also be reasonable to describe what is going on as very slight changes in the speed of the photons being reflected back and forth 280 times in the 4 km long arms, as compared to the reference photons in the resonant cavities.

Some Comments on the Interpretation Commentators continually refer to gravitational waves as being “ripples in the fabric of spacetime”. There seems to be some deep-seated human desire to regard spacetime as being real and tangible, more or less like some sort of four dimensional fluid in in which the Universe is immersed. Computer based animations invariably depict empty space as some sort of rubberized sheet being dimpled by massive ball bearings and this promotes the same sort of mental images, attitudes and beliefs. Which is a pity.

It may be a lost cause but I point out once again that spacetime is a human construct for measuring, modeling and discussing what is going on in the Universe. It has no more reality that the Cartesian coordinate grid of latitude and longitude lines here on Earth.

It was not Einstein who promoted the idea that curved spacetime is an actual physical reality. This only happened after his death and was promoted by authors such as MTW and Stephen Hawking. For example, John Wheeler often made the comment that “mass/energy tells spacetime how to curve, and spacetime curvature tells matter how to move”. The cover of MTW classic textbook shows a little ant wandering around on the surface of an apple and dutifully following its curvature.

I would say to John Wheeler that he has started to confuse mathematical models with reality and that the analogy with the ant is a false one. The ant can feel the curvature of the apple with its little feet. The surface and its curvature is real and tangible. But spacetime is a manmade imagination created for our own convenience. A better analogy is the lines of latitude and longitude we have invented for talking about movement on the surface of our home planet. These lines do not actually exist. They cannot be observed. They are not tangible. I would say to John Wheeler that spacetime does not tell matter how to move any more than the latitude and longitude grid on Earth tells ducks how to migrate.

Which is not to say that I think that spacetime does not correspond to something that it observable. In fact I do. But this is a heretical idea that I will explore in other essays.

I also agree that applying a spacetime metric to this “something” is a good idea. But spacetime is not that something, and that something is not spacetime. In other words, do not get a reference system invented by mankind for convenience of describing physics mentally confused with reality itself.

Another crime in my book is commentators who compare gravitational waves with electromagnetic waves. Unless such commentators can explain how two stars orbiting each other can produce quantized packets of energy and then how these packets can be reflected, polarized, refracted etc. I suggest that they refrain from such analogies. If they must use analogies I suggest that they try acoustic comparisons instead.

Note that Doppler effects are a familiar phenomenon in sound waves and they should also occur for other moving disturbances such as gravitational waves. But where gravitational waves are concerned the effects should not be called red-shifting. The Doppler effect is not called red-shifting when it applies to acoustic waves and I think it should not be called red-shifting for gravitational waves either. It is just a plain old Doppler effect.

Discussion I do not find it surprising that a pair of massive pair of stars rotating about each other might have tiny push-pull effects a long way away. I think this is what you would expect to find even with a basics inverse-square law based on classical physics. For example, if a large asteroid suddenly knocked the moon out of its orbit, I think it reasonable to expect that observers on Earth would notice changes in gravity very soon afterwards.

Nor am I surprised that gravitational disturbances travel at the speed of light. In fact I am surprised that this has not been measured experimentally years ago. For example, the passage of the Moon overhead produces a noticeable gravitational tidal effect on the surface of the Earth. Since the centre of the pattern of this disturbance coincides exactly with where the Moon appears to be then that is evidence for the gravitational effect to be arriving hand in hand with the visible light from the Moon.

I would be surprised if gravitational waves are ever found to consist of discrete quantized packets, analogous to photons. In my currently preferred conceptual model of the Universe, photons are disturbances in something that can be modelled by spacetime constructs, and gravitational waves are disturbances of that something itself.

This is more than a semantic difference. Consider a laser beam that is pointed at the sky and turned on and off again. This sends bunches of well-collimated photons off on a journey into deep space which, in principle, can continue travelling indefinitely. Barring absorption by dust or blocking by some solid barrier, the beam of photons stands a chance of being able to be detected on some distant galaxy at some time in the future. Not so a gravitational wave. The energy from a gravitational wave spreads outwards in all directions and becomes increasingly weak with distance from its source. I think there is almost no chance of being able to detect gravitational waves coming from binary star events and suchlike outside of their local galaxy. Colliding galaxies might be a different story.

Conclusion After initial doubts, Einstein eventually decided that gravitational waves were a necessary feature of his Theory of General Relativity. The recent detection of gravitational waves, apart from being a remarkable achievement, is further confirmation that General Relativity works well as a model. However I think it is not proof that General Relativity is the only viable and useful way of looking at physics in our Universe.

[scepticaladventure]

23  Gravitational Redshift  2Sep18

Introduction Earlier essays in this series of blogs provided a plain English synopsis of the foundations of General Relativity, presented some heretical comments about Einstein’s Equivalence Principle and introduced the Clock Postulate. In this essay I would like to take a closer look at gravitational redshifts. [Note: In this essay I will again be using references from the heavyweight textbook on gravity by Charles Misner, Kip Thorne and John Wheeler  (MTW):   “Gravitation” C W Misner, K S Thorne, J A Wheeler  Freeman Press,  1970  ISBN 0-7167-0344]

Effects of Gravity on the Propagation of Light The effects of gravity on light are not straightforward. Einstein’s ideas evolved over more than a decade and involved discussions with and by other great scientists such as Max Planck, Hermann Minkowski, Max Born, Willem de Sitter, Max von Laue, Hermann Weyl and John L Synge. Einstein wrote on the subject repeatedly, e.g. in 1907, 1908, 1911, 1915 and 1916. His 1915 paper contained significant corrections to his 1911 formulae. His 1915 work opened with the remark “‘I return to this theme because my previous presentation does not satisfy me.”

Einstein came to the conclusion that one of the basic tenets of the Special Theory of Relativity - the constancy of the velocity of light – had to be abandoned when gravity is taken into account. Einstein embraced this consequence and made it the basis of a further prediction – the bending of light passing near a massive body. His 1911 prediction for the light bending was the same as that of classical physicists.

In 1912 Einstein’s approach to modeling the effects of gravity on light using only his principle of equivalence ran into problem after problem. This motivated him to begin studying in earnest the differential calculus of Ricci and Levi-Civita as applied to curved geometrical manifolds (involving tensors, co-variant derivatives, Christoffel symbols and the like.)

Einstein revised his 1911 calculation in his 1915 paper and came up with a prediction twice as large as the original estimate. Sir Arthur Eddington famously claimed to have verified this prediction several years later in 1919. [In spite of World War I, Eddington had received a copy of Einstein’s work on General Relativity and he quickly became an early supporter of its ideas. Eddington came up with the idea of measuring the bending of light during a total eclipse and he obtained support from the Royal Astronomical Society to do so. I think this is a nice example of scientific cooperation transcending national hostilities.]

Einstein’s theory of General Relativity eventually contained three effects of gravity on light: 1. Gravity slows the speed of light, 2. photons climbing out of a gravity well arrive redshifted, and 3. gravity bends the path of light.

The degree to which the second and third effects are were predicted by Einstein’s 2015 theory became important tests for the new theory, along with the calculation of the anomalous precession in the perihelion of Mercury (see latter essays).

As to the redshift, Einstein wrote in a letter to Arnold Sommerfeld in 1912, ”The clock goes more slowly if set up in the neighborhood of ponderable masses. From this it follows that the spectral lines of light reaching us from the surface of large stars must appear displaced towards the red end of the spectrum”.

This makes it clear that Einstein was attributing some or all of the gravitational redshift to the time dilation caused by gravity, which in turn is intimately connected to the speed of light in gravity (for as we discussed earlier, the very meaning of time is intrinsically intertwined with the concepts of distance and the speed of light).

I like these comments by two American writers in 1980 (John Earman and A Glymour): “Einstein’s early derivations of the red shift show his most characteristic style of work - heuristic, allusive, sometimes baffling, but unfailingly fruitful.” They go on to say “Altogether, there may be no other single topic which so vividly illustrates the intellectual ferment, the styles of work, the profundity and the confusion associated with the general theory of relativity.”

We can argue at length about the exact meanings of the language used by Einstein and others to describe the three effects, as many good physicists, mathematicians and philosophers have done for the last century, especially if they are inclined to the modern view that gravity is an illusion created by spacetime curvature.

The more important thing is that the three effects led to new predictions for the size of gravitational redshift and gravitational light bending which became early tests for the new Theory of General Relativity.

The success of Einstein’s new general theory in predicting the size of gravitational redshift and light bending effects has led textbook writers to assert that classical physics has shortcomings that required the genius of Einstein’s curved spacetime theory to correct.

However, I think that the experimental results are what Sir Isaac Newton, Pierre-Simon Laplace and many other great classical physicists scientists over the previous three hundred years had already anticipated to some degree and would not have been surprised at all to see confirmed.

I think that General Relativity is a powerful new approach that brings in a whole new class of mathematical tools and so lends itself to a better description of some small effects in extreme situations. But I also think that if you add Special Relativity and the fact that gravity slows the speed of light to classical physics you can get the same answers. Certainly for the three effects on light (the first result is axiomatic) and possibly also for the anomalous precession in the perihelion of Mercury.  

This is what the next few essays are going to examine. Starting with gravitational redshifts.

Gravitational Redshift - The Long Hollow Rocket Imagine that the very tall elevator shaft in the previous essay has become a long hollow rocket which is in deep space somewhere and that this rocket is accelerating at a high constant rate forwards. Imagine there is a source of photons with a very tightly defined frequency range (a laser for example) situated at the back of the rocket and that this has just fired a burst of photons towards the front of the rocket. When this burst of photons was sent on its way, the back of the rocket was travelling at a certain speed. Due to the rocket’s acceleration, by the time the photons reach the front of the rocket the front of the rocket will have reached a higher speed. In other words there will be a relative speed difference increase from the back to the front of the rocket due to the acceleration that takes place while the photons are in flight.

Detectors at the front of the rocket will find the arriving photons to have lower energy (hence lower frequency and longer (redder) wavelengths) than they had when the photons started. Furthermore, if the arrangement of laser and detectors is reversed, then the detectors when positioned at the back of the rocket will find photons arriving from the laser at the front of the rocket to have acquired extra energy and thus been blue-shifted. It is a straightforward Doppler effect. (There will be infinitesimal Lorentzian effects as well but these can be safely ignored for our purposes).

Einstein’s Equivalence Principle says that the above situation is the same if the rocket is actually a very tall elevator shaft sitting in a uniform gravitational field. Photons fired upwards in the shaft will arrive redshifted and photons fired downwards in the shaft will arrive with a degree of blue shift.

The redshift effect has been confirmed by experiments such as that of Pound and Rebka at Harvard in 1960.

It is possible to persuade ourselves that light must be red shifted in this way using Einstein’s discovery that energy and mass are equivalent to each other, and applying this to a thought experiment (see MTW p187) as follows.

Imagine that a well defined amount of mass falls through gravity and does some work on the way (turning a treadmill for example). It is then entirely converted into photons that are beamed back up to the starting point. Unless these photons lose some energy they could be turned back into the same initial starting mass and the process could be repeated endlessly, performing work on every loop. But this would violate the principle of Conservation of Energy. Hence Einstein reasoned that the photons must lose energy on their way back up to the starting point.

Does Gravitational Redshift Imply Spacetime Curvature? (MTW p 187)  “An argument by Schild (1960, 1962, 1967) yields an important conclusion: the existence of gravitational redshift shows that a consistent theory of gravity cannot be constructed within the framework of special relativity”.

(MTW p189) “Schild’s redshift argument … does say … quite unambiguously, that the flat spacetime of special relativity is inadequate to describe the situation, and it should therefore motivate one to undertake the mathematical analysis of curvature.”

The Schild argument builds on the experimental demonstration of gravitational redshift by Robert Pound and Glen Rebka at Harvard University in 1960.

In 1958 a way had been found to use the Mossbauer resonance effect to emit and absorb gamma rays in a very narrow and precise frequency range using solid samples containing radioactive Fe57. Pound and Rebka made use of this discovery and placed two such samples vertically in a tower at Harvard with a height difference h (and so at a gravitational potential difference of gh in the language of Newton).

General Relativity predicts photons emitted from one sample will no longer be absorbed by the other. But if the absorber is vibrated so that it obtains a range of vertical motions relative to the source, the resulting Doppler effects can restore some absorption.

It is common to see this experimental result described mathematically as ∆t2 = (1 –(Φ2 – Φ1)/c2) ∆t1  where (Φ2 – Φ1) = gh is the difference in gravitational potential.

In essence Schild invites the reader to consider a Lorentz reference frame aligned to the Earth and containing an electromagnetic wave generator at one level and a suitable detector at a higher level, both at rest with respect to each other. Schild’s argument goes like this: The bottom generator emits a wave of exactly N cycles of well defined frequency √ in time interval T and this is received by the top detector. The observer at the top detector is asked to determine how long this signal lasts. In flat spacetime the answer should be T, since the top and bottom observers are at rest with respect to each other. However, the signal undergoes a gravitational wavelength change, lengthening as it climbs up towards the top observer. N cycles of a longer wavelength should last longer than T. The conflict can only be resolved if spacetime is curved.

I agree that gravitational redshift occurs in reality, and I also accept that gravitational time dilation occurs in reality. And if the time dimension is significantly slowed by the presence of gravity, then the usual Lorentz-Minkowski flat four dimensional spacetime framework becomes suboptimal for describing what is going on in the physics.

However, I do not accept the argument that the Pound-Rebka demonstration of gravitational redshift proves that it is necessary to invoke curvature in all four dimensions of spacetime because I think the Schild argument is inherently flawed and in any case it would only introduce a degree of flexibility in the time dimension.

For a start, the Pound-Rebka experiment example used by Schild does not take place in a Lorentz reference frame at all. Very few experiments do. Inertial setups are so rare and to be almost non-existent. Orbiting space stations come close but even then there is still rotation relative to the so-called “fixed stars”. But my concern is mainly about the misuse of wave concepts.

What is the ‘wave’ talked about by Schild (as described by MTW)? It seems Schild is thinking about the emissions being electromagnetic waves with spatial properties related to their wavelength and temporal properties related to their frequency. He talks as if the wavelength gets ‘stretched’ in transit between the bottom and the top of the tower. He talks as if the signal has a well defined frequency in time T and hence acts as a type of clock.

But Einstein himself was instrumental in demonstrating that electromagnetic radiation takes the form of photons. These are emitted with precise energy level. If they have to climb against a gravitational potential then when they arrive they are detected as having less energy. That is the relatively simple experimental fact.

And as I discussed earlier (and summarise in the box below) I think the whole schizophrenic particle/wave duality concept of light is seriously old fashioned and that it can be resolved simply by following the evidence with a fresh and open mind.

I think of the precise electro-magnetic emissions in the Pound- Rebka experiment as being phots. They have no length, they do not wriggle about as they travel and they are not little clocks. They are just packets of energy with some intrinsic properties that are only revealed upon absorption.

Schild is suggesting that the bottom generator emits a wave that has a well defined frequency in time T and therefore acts as some sort of clock. Now it is perfectly possible to incorporate a beat into an overall emission of lots of phots. Just synchronise their phase at time of emission and change this in a structured manner as time progresses. It is what happens all the time in a radio signal. The signal is encoded in the overall pattern. But not in each individual phot.  

Do not get mixed up between what happens to the pattern of phots and what happens to the phots themselves, which is what I think Schild (and others) have done. And forget about anything with a finite length being “stretched” somehow. Phots have no length.

All the Pound Rebka experiment does is demonstrate that phots emitted in precise circumstances at one point in a gravitational field and absorbed at another point in the gravitational field lose energy consistent with the change in gravitational potential. This shows up upon their absorption/detection/destruction as a decrease in the frequency of their embedded signal. If you insist on using the phots as a way of standardising time in reference frame covering the whole experiment, you are entitled to conclude that time runs more slowly at the bottom of the tower than at the top.

So does a gravitational redshift as demonstrated by a single Pound and Rebka experiment demonstrate that gravity has to be modeled by a fully curved spacetime approach? I do not think so. In fact I think that a gravitational redshift occurring between two specific points in flat spacetime can be understood perfectly well just using classical physics augmented by Special Relativity and the recognition that gravity slows the speed of light (and hence time).

A single gravitational redshift experiment in one particular location is not proof of full spacetime curvature. However, if you consider how to interpret the results of many different redshift experiments spread around a gravitationally perturbed region of the Universe at more or less the same time, then the argument becomes stronger.

Take Earth for instance. If we consider a whole set of Pound-Rebka experiments occurring at different locations around the Earth, then while each experiment might have something to say about its local spacetime environment and local inertial reference frames, the only way to connect all the frames is to admit curvature into the dimensions of spacetime more generally. This is the conventional route to Einstein’s General Relativity.

So I’m saying that while curving all the dimensions of spacetime is not necessary to understand gravity per se, it is still a very useful approach to modeling some subtle effects in physics in gravity fields surrounding massive celestial objects.

How to Interpret Gravitational Redshifting? Pound-Rebka and many others showed that gravitational redshift does occur, and a variety of thought experiments suggest that this is a perfectly reasonable outcome. But how should we interpret the results? It is a debate that went on for decades from about 1911 onwards and it is a question that is still open, although many minds are not.

I will let the photons speak for themselves. Let us turn them into little cartoon characters. On arrival at the top detector the photons could explain what has happened in one of three possible ways: (1) “Hi, we are from bottomland. Time runs slow down there, so please excuse us if we are a bit slow. We are all slow down there. Apart from that we are exactly like you.” (2) “Hi, we are your identical counterparts from bottomland. We have had a tough journey and now we find that we have to give up some of our energy in the form of a tax. So please excuse us for being a bit redder than when we started out.” (3) “Hi, we are your identical counterparts from bottomland. You guys seem to have been accelerating upwards while we were travelling. We can’t climb aboard your detector, even though it is identical to the one that gave us birth, unless you lower the bar a bit and retune it to a lower frequency, or push it towards us to shake off all that extra speed you’ve acquired.”

The first explanation suggests gravity causes time to slow down and any and all processes that involve time to slow down as well. This by itself is enough to distort the time dimension in a four dimensional spacetime reference frame. But it does not say anything about curvature in the three spatial dimensions and hence is not an argument for Einstein’s curved spacetime ‘geometric’ model per se.

The second explanation is akin to a standard Newtonian approach. Newton thought of light as consisting of “corpuscules” and fully expected them to be able to be influenced by gravity. See the following essay about the bending of light by the Sun.

The third explanation of gravitational redshifting uses the Einstein Equivalence Principle to suggest that what is going on is that both the bottom and the top of the tower are being accelerated in curved spacetime. This is what causes the redshift as per our discussion of the long hollow rocket. You could say that this is an explanation in terms of the Doppler effect.

A student of Special Relativity might not be surprised by gravitational redshifting since, if a photon is energy, and energy is equivalent to mass, and mass loses energy when it climbs out of a gravity well, then why would anyone not expect a photon to lose energy also? So such a student might be inclined towards explanation (2).

One of things that intriques me about gravitational redshifting is this. If the photons arrive at the top of the experiment with less energy than they started out with – where did that energy go? If the photon were a little rocket then it would end up in the heat and kinetic energy of the exhaust gases. If the photon was a solid projectile the lost energy is apparent in the gradual loss of kinetic energy. If the photon was pulled upwards by a string it would clearly come from whatever was winding up the string. But in the case of a photon it starts off with one amount of energy and arrives with an amount that is lower than that of photons being created in exactly the same way but at the ‘higher altitude’. Where did the difference go?

I think that the question goes to the heart of understanding gravity and hence is a quite profound. But most lecturers will just say “It has ended up as a reduction in negative potential energy” and leave it at that. Personally I think that this ‘papers over’ a gap in a better understanding of the situation. The same thing happens is you ask questions like – what gives matter its mass? or what gives mass its inertia? or why does a moving object want to travel in a straight line? Just giving physical phenomena names instead of explanations tends to block our minds to deeper understandings.

The first and third of the explanations require a non-flat spacetime reference frame due to distortion in the time duration dimension.

If one of the answers is correct it does not necessarily mean that the others are incorrect. In principle the correct answer might depend upon what point of view you are using. Then the best answer is then the one that is consistent with the point of view you are using. And the best point of view is generally the one that is the most convenient for your purposes at hand.

Furthermore, it is also possible in principle that the best answer requires a combination of the various explanations. In fact I think it does, as I will explain later.

So what about explanation (3) that interprets the redshift as a Doppler effect? My take on this is that if you want to adopt the Einstein Equivalence Principle, and if you want to replace the greatest force in the Universe with the mathematical trickery of curved spacetime, then this is the explanation you should use. It also gives the right answer, so it becomes a matter of choice.

But the fact that you could prefer Explanation (2) shows that the curved spacetime approach is not the only way to understand the Pound Rebka experiment. And even if you do want to use Explanation (3) you should note that this does not require you to use Einstein’s full model. If you do use Einstein’s General Relativity model then it is only the perturbation of the time term that is needed in order to come up with the observed results for gravitational redshifts. The full field equations are not needed and there is no need to call upon any warping in the spatial aspects of the spacetime geometry.

Gravitational Redshift in the Solar Spectrum Light reaching Earth from the Sun’s surface has climbed a long distance up the Sun’s considerable gravity well, and has fallen into the Earth’s smaller gravity well. The light itself comes from a large number of sources with known spectral frequencies, but these spectral lines are complicated by the extreme thermal motion of the sources, the Sun’s rotation and the Earth’s own motion. All of this creates a blur of Doppler shifts. Nevertheless it is possible to screen and correct for the blurring effects and the resultant redshifts are consistent with the expected result.

Early attempts to measure the gravitational redshift of light reaching Earth from the Sun were plagued by practical difficulties. The earliest results tended to disprove Einstein’s predictions. When Einstein’s fame and reputation soared towards the end of the second decade of the 20th century, the trend reversed and it became more fashionable to produce results corresponding to Einstein’s predictions. Modern results do confirm Einstein’s predictions.

It is interesting that the earlier attempts to explain the spectral shifts in light from the Sun did not use General Relativity. This shows that while on one level Einstein’s general theory won wide acceptance, on another level there was a reluctance to fully adopt the curved spacetime approach. General Relativity was thought of as being impressive and interesting, but also a bit too weird and not to be taken literally.

The Best Way to Interpret Gravitational Redshifts? General Relativity has now become the orthodox paradigm but even today arguments continue about how best way to tie in the experimental evidence about gravitational redshifts. Some authors/teachers prefer one type of explanation, others prefer another.

I’m pretty sure many students find this confusing. But I also think that there may be more than one way to look at it. I do not think that one view corresponds to “reality” and the others are fallacies. They are all just mental models created for our own convenience of understanding.

Here is an analogy. A cone can be seen as a triangle from one perspective and a circle from another. The real nature of a cone transcends both views.

In this spirit I object to those who insist that spacetime curvature is real and gravity is not real. I say that you can use a curved spacetime model if you like, but it is only a model. Likewise you can hold the view that gravity is a real force of nature, but you still also have to recognize the lessons revealed to us by Einstein.

My preferred way of explaining gravitational redshift is as follows. When a photon reaches a zone of space where everything has a higher gravitational potential than things did where the photon came from, it arrives in a new environment. It may have been created in outer shell of a certain type of atom, but it now finds itself unable to join similar situations in similar atoms in the new environment. It has to pay a tax to be allowed to join in. Its energy wallet now longer buys what it used to. The photon can now longer afford the sort of home it came from. It has to settle for a lower energy type of accommodation. One with lower energy levels. For example, a photon than came from a green home might have to settle for a new home in the red light district.

So if we go back a couple of sections and eavesdrop on our animated photon’s conversation when they arrive, what they are saying is (2) “Hi, we are your identical counterparts from bottomland. We have had a tough journey and now we find that we have to give up some of our energy in the form of a tax. So please excuse us for being a bit redder than when we started out.” And their newfound friends say “Don’t worry about it. It happens to everyone. And you haven’t lost any value – it is just that some of your energy is now embedded into your relationship with your new environment all around. You can have it back again should you return home.”

Conclusion Gravitational redshifts can be described in Einstein’s General Relativity model but it is not necessary to invoke the full field equations and curvature in all of the dimensions in order to do so. The basics effect was predicted well before Einstein using nothing more than Newtonian gravity and Galileo’s Weak Equivalence Principle.

Once Special Relativity is taken into account the phenomenon can still be understood in terms of differences in gravitational potential.

The mystery is why this phenomenon is considered to be one of the proofs that General Relativity is the only valid way to look at gravity. I think that what happens to photons encountering changes in gravitational potential can be described without reference to Einstein’s General Relativity field equations at all.

Here is a bit of basic logic. “If General Relativity is to be a useful model then it must not contradict the evidence of gravitational redshifts.” Let us agree that this is true. Then we also have to accept the contra-positive argument that goes as follows. “If General Relativity contradicts the evidence of gravitational redshifts, then it is not a useful model.” What we do not have to agree is the argument that “If General Relativity is consistent with the evidence of gravitational redshifts, then it is a useful model”. This statement may or may not be true. And we certainly do not have to agree without question the insistence by many modern physicists that because General Relativity is a useful model then its method of approach is the only interpretation of Nature that we should agree to be “reality”.

On this I am pretty sure that Einstein would agree.