@Vikram, I completely agree with you that lengths of things like meter sticks are determined by particle (de Broglie) wavelengths, and these vary with lightspeed, strangely enough, just as electromagnetic wavelengths.  But actually I believe Pound and Rebka only prove that light travels a local length taking more time at a lower height.  This could be light slowing by Γ (the Schwarzschild time dilation factor) while traveling through a meter of the same length, or slowing by Γ2 while traveling through a meter reduced by Γ, or not slowed at all and traveling through a length increased by Γ.  Or an infinite number of other combinations as long as the ratio is right.

The Shapiro experiments have proved, if I understand them correctly, that for approximately radial distances through a gravitational field, the coordinate velocity of light is slowed by Γ2.  Two interpretations of that are possible.  It is possible that lengths of meter sticks through the field are contracted by Γ so that there are Γ more of them.  But the orthodox interpretation is that space expands on that path to allow the additional meter sticks, not that the meter sticks contract. 

So far as I know, there has not been nor is there planned any experiment to distinguish which of these latter two is the better interpretation.  One could experiment on a massive gravitating cylinder, and I actually ran some numbers on this and it is really impractical without manipulating masses much greater than our sun.  Or if one could produce wormholes or large scale curvature that should settle it.  The length contracted interpretation is bound within the approximately Euclidean background and cannot exhibit an esoteric connectivity like a wormhole.  At least not by a method I know of.  So we can look forward to some suspense over verification of the stranger features of GR for some time to come, I think.

(P.S. I am not the one who voted against your answer.  I thought it was an interesting claim worth responding to.)

It doesn't make sense to compare two vectors on a *curved* manifold, that are not associated to the same point, because the comparison depends on the path taken, when parallel-transporting one vector from the reference frame of one observer to that of the other-that's what *curved* means. This issue doesn't arise on a flat manifold, where Lorentz invariance is a global symmetry.

Thank you Charles and Stam

So I can conclude from your answers that Length contraction measurements in general can't be performed experimentally perfectly from a theoretical point of view. Is the reason may be that the space curvature is ruling out length contraction because each one opposes or contradicts the other

Spacetime curvature doesn't rule out relativistic length contraction (or any other length comparison)-it means that it's not possible to give it an invariant meaning, i.e., independent of the path, if the reference frames don't coincide. It's not a question of some effect canceling  another-it's a property of *curved* spacetime. (And is explained in all courses on general relativity-it's nothing new.) Length contraction measurements make sense in special relativity, i.e. when gravitational effects can be neglected. At any one point the metric can be taken flat, so it's possible to define the contraction at A; similarly at B. What's not possible, in an invariant way, is to compare the two, in the presence of gravity.

I meant Length contraction happened in Gravity but we couldn't observe it due to spatial curvature. 

We can't observe it because it's not possible to relate the two.

I think it's better not to close the door in front of such searching.

The problem is speed of light is it self a variable from the view of GR if we measure it from a non local frame. So assuming time as a variable affected by gravity and treating the length by the same manner while considering light as local variable is a fault in managing such problem.

There is considerable confusion here, so it might be useful to recall the question. If the relative velocity between the spacecraft and each observer is ``negligible'', then the length contraction is negligible, too, for each. End of story. This is a well-defined statement, for *each* observer, because, at *each* observer, it's possible to choose Minkowski coordinates. However, since the observers live in curved spacetime, it's not, in general, possible, to compare the two results in a meaningful way, since it's necessary to perform parallel transport of the length L0 from A to B. That's all.

Dear Stam 

The example that I gave is not the main point of the question is only an introduction to it. 

the question is "I want to know why length contraction in GR is not proven experimentally until now?" by a direct way not indirect one.

The reason is the following: if the relative velocity of the spaceship, in observer's A reference frame, is such that contraction isn't negligible, so the length is gamma_A L0, nevertheless, when parallel-transporting this to observer B's reference frame the result will depend on the path and, thus, it's not *possible* to state whether there was a contraction, or not: there will be paths along which a contraction (of any value) will be found, others along which no contraction will be found. Therefore, there's nothing that can be unambiguously measured here.

(What *can* be measured unambiguously are tidal forces, i.e. the difference in force between head and foot in a gravitational field.)

Let me make it easier if an observer which is falling due to gravity has in its space shuttle a Young interference experiment will him observe any shifting in the fringes due to length contraction or time dilation or both?

I think its easy to answer this, now if the same observer sending photons from the same ray of the experiment assuming its an entangled photons with the inside ones will the observers outside in points A and B note any difference ? and due to what?

He's in free fall, i.e. following a geodesic, (that's what ``falling due to gravity'' means), so the answer is No. If he's got the engines on, then he's not in free fall and he'll duly find that he can't distinguish this fact from that of the corresponding gravitational field. (This doesn't have anything to do with the discussion up to now.)

I totally agree with you, now if the same observer sending photons from the same ray of the experiment assuming its an entangled photons with the inside ones will the observers outside in points A and B note any difference ? and due to what?

Invariance of Planck length and all kinds of lengths are the basic requirement to retain a flat space-time, and to insure the conservation of energy and momentum associated with the flat space-time. 

Based on functions of the gravitational potential, even though three out of five fundamental constants have turned into functions of the gravitational potential, Planck length, Planck charge and Planck temperature --three out of five base Planck units -- remain invariant in a gravitational field. Detailed discussion is on section 4.1. of my paper.

Article Functions of the Gravitational Potential

Sadeem invited me to comment on this thread.  I have looked at all the answers and made responses [in brackets], then posted my answer to Sadeem's question at the bottom.

Charles Francis said:

• Since the space ship moves from one observer to the other, both observers will measure the same length.

[correct]

• Since the clock on a GPS satellite does not keep time with one on Earth, we know that the circumference of the orbit as measured by the GPS satellite is not equal to 2pi R.

[neglecting SR, we have Tsat_orbit*Vsat=2pi*rsat at the satellite.  Let k be the factor by which Earth's clocks run slower. From earth, then

(Tsat_orbit/k)*(Vsat*k)=2pi*rsat.   So both observers measure C=2piR.  For more information on time and velocity transformations see Shuler 2011]

• Sadeem, either length contraction is a coordinate based manifestation of spacial curvature (and strictly illusory) or it is not an effect at all.

[So C.F. admits there is no spatial curvature???]

Stan Nicolis said (several times):

• It doesn't make sense to compare two vectors on a *curved* manifold, that are not associated to the same point.

[then we can make no reliable comparisons on a curved manifold and should not employ them in physics???]

Sadeem said:

• The problem is speed of light is it self a variable from the view of GR

[correct]

• (original question) I want to know why length contraction in GR is not proven experimentally until now? What' the difficulties (experimental and theoretical) in front of such proving?

My response ...

Refer to figure attached below from Herter's class notes http://rogachev.dyndns-at-home.com:8080/Copy/Physics/Cornell%20A2290_34%20(Schwarzschild%20Metric).pdf

For a constant angular position using c=1 units: dS = dr / (1-2M/r)1/2. So Sadeem asks the question backward.  Length is not contracted, it is extended.  That's how we get the funnel diagram.  But I'll proceed to investigate whether we could measure this.

Let the length of the spaceship be 1 at infinity so that dS2=1.  On Herter's diagram, right side, you see that the local length of the ship dS (Herter uses σ) does not change.  So you can't see any difference with a local measurement. 

If you are at a great distance and blessed with some ability to see the Schwarzschild "coordinate radius" r (the thing Crothers argued so vehemently about), perhaps by using very long calipers, then you would certainly see a difference (provided such calipers could be trusted and the difference were large enough to notice).  But we are not technologically capable of such an experiment.

We ARE capable of remotely measuring dr corresponding to dS using light.  We can use radar to time the light signal as it goes from one end of the ship to the other (dr, assuming the ship is nose down, consistent with our zero angular position assumption). 

In that case, using our clocks, we'll find the time shorter than expected by the expression dτ = (1-2M/r)1/2 dt.  

We may explain that as clocks ticking slower at r than at infinity, or the spaceship being shorter.

So ... you can't see a difference with a local measuring stick, you have to make a remote measurement.  Barring the technologically difficult calipers, using light, one is faced with an arbitrary choice of whether to assume a coordinate velocity of light, or a coordinate shortening which would not produce the correct funnel diagram.

For a gravitational field without an event horizon, and with a mass M cool enough we could drill through it, perhaps we could put meter sticks end to end from a great distance and see how many it takes.  My prediction is we will find space is flat, time is dilated, and the remote coordinate velocity of light is slowed (locally using slow clocks it still appears as c)

None of our experiments, however, support an stretched meter sticks as the Schwarzschild metric gives.  And if the meter sticks were stretched, and the distance also stretched, we would not be able by putting meter sticks end to end notice any difference from flat space.  Then it would be "a difference which makes no difference."

Dear all,

Robert and Charles thank you for your answers.

Robert

I don't think you need a caliper to make sure length contraction (or extension) is happened because its difficult to achieve experimentally. I suggest an easier one.

Dear all,

lets assume an observer in a space shuttle is falling due to gravity so it's supposed to measure  proper coordinates of the distance between the two slits. Then if s/he is performing a double slit Young experiment by making a ray passes on double slits on the surface of the ship and as the ship is passing near two observers A and B in different gravitational potential then these outside observers note the interference fringes and from that he or she can count the distance between the two double slits which are inside the ship by also knowing the distance between him or her and the ship as it passed close to each A and B. I think there measurements are possible to be done and this experiment is more logical to be performed.

please if its good idea to be published I'm ready to accept participation it's open to be developed...waiting for feedback

Charles when I said "The problem is speed of light is it self a variable from the view of GR if we measure it from a non local frame." 

I meant it will be considered as a coordinate velocity when it's treated from a non local frame.

Thanks

It doesn't make sense to compare two vectors on a curved manifold, that aren't at the same point, because the comparison depends on the path used to parallel-transport one from its point to the point of the other. This is a well-known fact of geometry and presented in all courses of general relativity. It's nothing either new, or controversial; nor does it imply that curved manifolds can't be used in physics. It *does* imply that certain questions don't have a unique answer.

 Dear Stam

I don't want the infinity numbers of answers. That's not the point. The point is there is a proper length that is the distance between the slits from the view of the observer in the ship and two other observers at different gravitational potentials. Each one of them will give a certain value of the measurement of the length between the slits from it's frame. Other words you can make transformation of length between them for a certain path which is tracked by the ship. It's a special case only which is achievable for experimental evidence of length contraction between different gravitational potential observers.

But this length between the slits is *not* invariant under general coordinate transformations-which means that there isn't any way to make the three observers measure the same thing (or a specified result, because there isn't any invariant). Therefore it's not possible to deduce what an agreement-or a disagreement-between their results implies.

But it's change can be concluded from clock delaying. which is precisely can be measured by assuming the space shuttle is emitting a ray at the moment of closure to A and B towards a stationary observer which lies at the trajectory of the space shuttle. the stationary observer can conclude the difference in frequency between the positions and makes his calculations to clock rate.

Clock rate is distinct from  length. They would be related  in this way  in *flat* spacetime. What you're saying works in flat spacetime. 

I'm talking about relating two points A and B not relating the trajectory, so the SR is applied locally at these points. You can think about like quantum mechanics you can't know the path of the particle but you can make measurement at certain point. Here the measurement are assumed to be made at two points, where locally the SR is applicable to each of them. 

This doesn't have *anything* to do with quantum mechanics and *everything* to do with the definition of invariant quantities.   While it *is* possible to give invariant meaning to an appropriate  *area*, or a  *volume*-a standard exercise in general relativity- the corresponding  root, that *does* have the dimensions of a length, can not be identified  as the  distance between any two points that aren't infinitesimally close (since the latter is not invariant under general coordinate transformations)-in the sense of parallel transport. That's why it doesn't make sense to talk about length contraction in GR. Gravitational theories have non-local observables; but not all non-local quantities are observables.

I agree fully with Siam.

THE PARADOX OF A AND B AND THE SUN

A and B are traveling on spaceships, parallel, 2 AU apart.  They determine distance by radar, and navigate (maintain course) by ephemeral stars.  The sun passes between them.  They notice the radar delay between them increases.  The ephemeral stars near line-of-sight to the sun change positions but no others do (so they easily remain on course).  The two observers make different assumptions.

• "A" assumes light slows and bends in gravitational fields.  Reasoning from this A concludes also that time slows, and sending a probe with a clock, confirms this.  With a slow clock on the probe, A realizes it still measures a locally constant speed of light.  Correcting for the slowing and bending of light, A retrieves the same 2 AU distance measurement as previously.
• "B" assumes that space is distorted around the sun.  Space is stretched so that light takes longer.  So the distance to B is greater than 2 AU.  So far so good.  But B wonders what happens to time.

B reasons that if space is stretched, then objects in the space may or may not be stretched a similar amount.  B analyzes these options:

B sends a probe and finds that time is dilated and chooses option 2, that objects are stretched as much as space. 

A and B get together and compare notes.  A points out that if B's assumptions are correct, that objects stretch as much as space, which is required by B's empirical results on time dilation, then the same number of measuring rods would fill the space between A and B as before the sun passed between them.  Therefore the distance would be 2 AU, not stretched at all, contradicting B's assumption.

There is no paradox-this can be completely described by general relativity. 

Then do so.  You would have already if you could!

This is a standard homework exercise in gravitational lensing and solving the geodesic equation of motion (and is off topic of the discussion)-once it's rephrased using what is known from a standard course in general relativity.

After I think in the problem of two observers A and B with an interference experiment carefully I think we can't compare the measured length as Stam and Charles claimed. Nevertheless the cause is as I mentioned previously when discussing this matter with Robert is the metric doesn't describing the space time curvature completely. It just can do it locally. I think this gives enough motivation to develop GR.

Sadeem asks about "length contraction in GR" but that is not the usual way of looking at it and I'm not absolutely sure what is meant.  It could be he means it takes more measuring rods to reach the center of a circle (excess radius), but that is usually spoken of as a stretching of the proper radial coordinate.  But from a relative point of view I guess it's the same thing. 

The question that comes to my mind is why are not the measuring sticks stretched also?  They would match a change in the spatial coordinate in SR, and GR was derived from SR so they should.  But then the same number of (stretched) measuring rods would reach to the center.  This causes a problem as follows.

Taking a general form of the Schwarzschild metric for constant angle dφ=dθ=0:

dτ2 = α dt2 - dr2/α                     (1)

Where τ is proper time for a local observer accumulated on his clock, wherever he has moved, and t is ephemeral (distant) time, and r being defined as C/2π. Units are c=G=1. And α=(1-k/r) where k=2M. Proper distance is S:

dS2 = - αdt2 + dr2/ α                   (2)

Notice that α < 1. If measurement is made along the path at synchronized ephemeral time (dt=0) then:

dS = dr/ α1/2                             (2b)

S = ∫AB (1 / a(r)1/2)dr               (3)

If the distance (r1-r2)

Robert and others

The problem with length concept in GR is it's only defined relative to an infinite distant observers. Also Schwarzschild metric don't give a full description of it.  So may be its a better option to assume time dilation only. Nevertheless there is a best one which is modifying the metric and affine parameter of light and redefine many concepts of GR that's depends on. This may offer new more elastic concepts like a practical definition of length and even may be a global constancy of speed of light.

Only *gauge-invariant* quantities are consistently defined at infinity. This is standard material in a course on general relativity. Given the metric, it's possible to compute trajectories by solving the geodesic equation (care must be taken to properly impose the constraints for massless particles, like photons). The solutions exist and are unique for the metrics discussed here (the flat metric and the Schwarzschild metric, that describes spacetime outside a massive body).

Sadeem, while I agree with you that it may be better to assume time dilation only, which is what we can measure remotely and precisely, GR has this "mechanism" for defining motion of free falling objects involving space and time curvature and geodesics, so to suggest use of time only is to simply suggest doing away with GR.  Unfortunately, there may be no escape from this conclusion.

Length contraction in GR is proven already with Pound and Rebka experiment (1960). In periodic relativity, the basic unit of length is the wavelength of a particle.When particle undergoes gravitational frequency shift, its wavelength also change. To prove this with gross objects or massive particles will require a very strong gravitational field which will break up the object before you can measure anything.

@Vikram, I completely agree with you that lengths of things like meter sticks are determined by particle (de Broglie) wavelengths, and these vary with lightspeed, strangely enough, just as electromagnetic wavelengths.  But actually I believe Pound and Rebka only prove that light travels a local length taking more time at a lower height.  This could be light slowing by Γ (the Schwarzschild time dilation factor) while traveling through a meter of the same length, or slowing by Γ2 while traveling through a meter reduced by Γ, or not slowed at all and traveling through a length increased by Γ.  Or an infinite number of other combinations as long as the ratio is right.

The Shapiro experiments have proved, if I understand them correctly, that for approximately radial distances through a gravitational field, the coordinate velocity of light is slowed by Γ2.  Two interpretations of that are possible.  It is possible that lengths of meter sticks through the field are contracted by Γ so that there are Γ more of them.  But the orthodox interpretation is that space expands on that path to allow the additional meter sticks, not that the meter sticks contract. 

So far as I know, there has not been nor is there planned any experiment to distinguish which of these latter two is the better interpretation.  One could experiment on a massive gravitating cylinder, and I actually ran some numbers on this and it is really impractical without manipulating masses much greater than our sun.  Or if one could produce wormholes or large scale curvature that should settle it.  The length contracted interpretation is bound within the approximately Euclidean background and cannot exhibit an esoteric connectivity like a wormhole.  At least not by a method I know of.  So we can look forward to some suspense over verification of the stranger features of GR for some time to come, I think.

(P.S. I am not the one who voted against your answer.  I thought it was an interesting claim worth responding to.)

@Robert. Thank you for your response. I think your analysis of the subject is more complete and deserving attention.

Charles, I did not know that the orthodox interpretation was that there was no way to distinguish them.  Thanks.  This could be explained a lot clearer in introductory material.  Even in yours, which is much better than most already.  I wonder if relativists are afraid the public will think they are living in fantasy land and withdraw funding?  The stuff is really not as complex as I had been led to believe and does not need to be hid behind a curtain of math constructs.  Like SR and most other fields, a popularized but still semi-quantitative account should be given.  For sure this could be done for the Schwarzschild metric.  I am beginning to think a "Metrics" class should be taught on applications of Schwarzschild and other metrics before  the field equation is attempted.  Chemistry is certainly taught without first teaching Schrodinger!

@Robert and Charles. In my way of thinking, the notion of space contracting should be ruled out. Space is not physical something that it can contract. That leaves only one option and that is the debroglie wavelengths of the constituent particles of the meter stick contract which will affect the bonds between the particles and atoms of the meter stick and before you can measure such changes, the meter stick will disintegrate. So the breaking of the meter stick itself will be indicative of the length contraction.

@Vikram, that's an old argument and you don't actually realize which side of it I'm on.  Or maybe Charles either but he'll speak for himself.  All such questions should be settled experimentally if they can be.  If they can't be, then sometimes a compelling theory may win the day.  If not there are two very different choices.  Physicists can abandon attempts to formulate the details as they did with ether theory (which was probably good, as there were dozens of theories proliferating and no basis for deciding between them), or then can just indulge in fantasy land as they have with wormholes, branes, and strings.

It takes approximately the same technology to settle the length question as it does to keep a wormhole open and travel to another brane.  Lots of negative energy, which we have never seen, despite predictions that it comprises 75% of the universe.  In fact, what does it do for the universe?  It makes space expand.  Or so we are told.

Here's another puzzler.  Everything is flying away from everything else and there is no edge.  Is that space expanding or objects moving away from each other?  I think now you see the problem.  This is approximately the same question.  The possible answers are at present not distinguishable.  But if we ever see an edge, we'll know.  If we ever see the back of our own heads, we'd know too.  Actually, there were some sky surveys looking for repeating patterns indicating that but none were found.  That was before the 1998-99 discovery of cosmic flatness.  Cosmic large scale flatness together with expansion poses a real puzzle, independent of any theory.  The only explanation I have heard is that the universe is not old enough for us to have seen all of it. 

So that, Sadeem, is why this question is not experimentally settled.  I hope it will be someday.  Not because I can't live without the answer, but because settling it would imply things had gotten rather interesting for the human race.  Assuming it is settled by humans and not robots or something else.

Charles is right about de Broglie wavelengths, per se.  There is some related concept I'm fishing for here.  If it bites I'll report it.

Robert,

The essence of the De Broglie matter wave has been discussed in section 7 of my paper. The electron zitterbewegung energy or De Broglie matter wave energy is in fact the energy carried by the gravitomagnetic field of an electron, since the gravitational field along with the associated intrinsic magnetic field of an electron are actually two sides of one coin. 

Article Functions of the Gravitational Potential

Robert,

don't get close to a wormhole, you might end up as the worm.

Thanks Matts, and Guoliang.  : )

What I was trying to get at with the wavelength comment is just that atomic and molecular bond dimensions are determined by waves.  Maybe "wavelength" is too simple, but if something affects wavelength and affects everything globally in the same way, it should change the lengths of those bonds.  de Broglie frequency is the clock that drives quantum waves (though Schrodinger uses a different zero energy reference point, the wavelengths don't change).  If the relation of de Broglie frequency to the speed of light changes, then lengths change.  In "natural" coordinates these always change together.  But in extensions of observer coordinates, the de Broglie frequency of particles (their energy) changes as 1/Γ, but the coordinate velocity of light is c/Γ2.  I will look at Guoliang's paper to see how he explains this.

@Robert. You are right about experiments. For experimental purpose, it will be much easier to crack an electron rather than a meter stick. Following experiment seems feasible. If a spectroscope containing hydrogen atom is launched for outer space in a rocket, it will experience very high g forces during launch. At this time the wavelength of electon in the hydrogen atom will contract and it will jump the orbit and absorb a photon from its surrounding. As the rocket ascends and stabilizes in its orbit, the electron wavelength will increase again and it will jump the orbit and emit a photon which can be detected. This same experiment can also be conducted as a free fall experiment or in NASA centrifuge for training astronauts. Whether change in the gravitational potential on surface of the earth is sufficient or not, that needs to be calculated.

Regarding the accelerated expansion of the universe -- space expanding or objects flying away -- I have discussed this in the following article. Space does not expand. It is there through eternity and will remain so. It does not have any boundary. Space is the fundamental substance of the universe which is perfectly motionless and does not interact with all that is in motion. When fraction of this fundamental substance begins to move, it becomes detectable and becomes part of our universe. This theory is based experiences of some one who has really seen the back of his head. Regarding the experiments in physics I like to point out that there are certain truths in the universe that you can never demonstrate experimentally to others but each individual can experience it for himself and verify. For example, how can you experimentally prove that sugar is sweet. You can write volumes on what sweetness is and it would mean nothing. But every individual can put sugar in his mouth and find out for himself what sweetness is.

Article Periodic quantum gravity and cosmology

I can see where that would explain a lot of things.  But I have trouble mixing theories of consciousness with physics.  von Neumann did something similar with QM and no one has recovered from it since.  ; )

@Robert If the skull (protons) and the mind can be mixed then why not QM and consciousness? I guess it is a matter of taste.

You are in good company with von Neumann, et. al.!

Interesting comment from Charles.  I have always viewed information printed on paper or encoded on a computer disk as knowledge.  I spent the early part of my career doing data acquisition and control.  The computer would measure data from spacecraft or lab experiments, and control them.  Rocket science some people call it.  Balancing a pencil on its end while accelerating it rapidly, that sort of thing.  :D  I got the impression from what other authors said about von Neumann that he considered these systems still in superposition, like Schrodinger's cat, and the matter not settled until a "conscious" entity, i.e. a human, looked at the measurements.  So I infer that the father of computing disagreed with others such as Turing who argued for specific conditions under which a machine would be considered intelligent.  There being of course a shift in word usage from conscious to intelligent.  

Computability theory has trouble with "consciousness."  As do philosophers.  This is not because it is inherently difficult, but because it is something humans experience including the sensory impressions of images, memories, emotions, etc.  Humans can function quite well when not conscious.  It is not usual.  We usually think of unconscious humans as "out cold" or "asleep."  But people sleepwalk, or talk in their sleep.  To sleepwalk one must be aware of obstacles, doors, etc.  I have done quite complex things in my sleep and awakened in the middle of doing them.  Consciousness is related to accessible memory.  Most people claim to have been unconscious if they simply do not remember doing something.  So there is a tremendous spectrum of gray areas. 

I can simulate all of this in a computer.  Not at high fidelity, but I can.  I can include a model of the computer itself in the computer's model of the environment, meeting the self-awareness requirement.  Obviously I can have the computer remember some things and not others.  I can have a switch on the side of the computer to select whether it is "conscious" or not.  None of this will convince any of you that the computer is conscious, but none of you can give any better definition.

To get physics mixed up in this pointless debate about consciousness is ridiculous.  I suppose I should add "in my opinion," but to me it is an absolute fact as clear as Newton's law of gravity.  If you step off a tall building, you are going to hit the pavement.  If you take physics into the realm of the mysticism of consciousness, you may as well be running ESP experiments.  I have no objection to ESP experiments either, by the way.  It just simply isn't physics until you can perform the experiments repeatably.  People have looked at "randomness" and confused this with mysticism, but it is unrelated.  QM experiments are extremely repeatable. 

I am not picking on Charles with my next objection, he just used the words "everyone" uses in connection with QM... "QM is a theory of what an observer knows about nature."  There is a lot wrong with that statement.  Some of it is discussed in the literature, for example the observer is necessarily a part of nature.  Some of it is not, for example once you have the observer as a physical system (anything with a state memory, from an atomic orbit to the largest computer) then "know" is an ill-defined English verb that is associated both with "consciousness" in its most mystical quality, and with the most mundane memory devices.  We should talk only of states and avoid the word "know."  Then we would be forced to quantify waveform collapse.

Some people have speculated God intervenes in the world through the window of randomness, by which the future of the universe is not completely determined (i.e. it is undetermined whether Schrodinger's cat is dead or alive).  I once toyed with this idea before I actually studied QM.  While it is not impossible, it rules out most of the "miracles" described in the Bible, since they involved massive changes in energy levels and tampering with entropy, e.g. parting the Red Sea.  No QM process can part the Red Sea just by selecting a different random outcome of some measurement.  No measurement process results in violation of conservation of energy or momentum.

Robert,

" No measurement process results in violation of conservation of energy or momentum."

I agree with you, because this is equivalent to no curved space-time in violation of conservation of energy or momentum, and that's why the length contraction in GR has not been proven experimentally until now.

Vikram

If a spectroscope containing hydrogen atom is launched for outer space in a rocket, it will experience very high g forces during launch. 

No Vikram, not very high. 

First of all there should be some assessment of how much gravitational potential difference is required. then the next thing is to find out where to get it. If it is beyond the reach, then the experiment would not be possible.

There is another experiment possible in principle. Practical feasibility is not clear. This will require much lower potential difference than the spectroscope experiment. In hydrogen atom, electron wavelength change by integer multiples. It can change by 100% or 66% or 33% etc. But if we experiment with a free electron and prove only 1% change in wavelength, that would prove the length contraction. If you fire an electron through a vacuum tube parallel to the surface of the earth and measure its momentum at departure and after travelling distance d, then de Broglie wavelength = Planck constant / momentum. Radial gravitational acceleration will be uniform through out distance d. Change in the wavelength can be found. Next we rotate this apparatus by 90 deg. and fire the electron vertically upwards and again find the change in the wavelength. This time electron will experience the gravitational potential difference. If you can detect even 1% difference between the two computed change in wavelengths, you would have proved length contraction. One can clearly see that the momentum is bound to be affected by the variation in gravitational potential and if it doesn't, then that would mean violation of Newton's inverse square law of gravitation.

But Newton's inverse square law of gravitation.is anyway violated n GR because it is not covariant.

Just a little 2 cents worth response to Matts comment above.  : )  Einstein stacked the deck on this one by defining the laws of physics in such a way that an inverse square law does not appear to be covariant.  Think about it for a minute.  No one ever tried to state the laws of physics without using Riemannian spacetime, other than me, that I know of.  If you take into account the logical impact of time dilation on force and energy (a la Planck relation for example) then you have a transform under which an inverse square law can hold.  The particular transform Einstein picked was curvature.  But as with all things mathematical, when you have a large number of parameters and some of them are changing, there are many transforms you can select for the others to make any given subset appear not to change.

@Matts. I like to add following to Robert's comment. Newton's inverse square law of gravitation (modified) is not violated in PR which has a revised equivalence principle which states that the gravitational mass is equal to relativistic mass. So the mass of the orbiting body in Newton's law is changed to relativistic mass. The mass in the momentum used in de Broglie formula is also relativistic mass. So the arguments  presented here by pass the GR.

I have discovered recently that the correct explanation can depend on the reference frame chosen.  In the curved coordinates chosen by Einstein (who also said it doesn't matter what the choice is), geodesics explain motion.  Locally time dilation and velocity of light changes don't exist.  In Euclidean coordinates, Huygens bending using the coordinate velocity of light explains light paths, and Euclidean geodesics do not correspond to free fall generally.

Vikram brings up the point of relativistic mass increase, which locally is always taken in Minkowski coordinates and not as easily dismissed as a coordinate effect.  However, in a hypothetical uniform gravitational field, where one can translate indefinitely without changing height, it againbecomes a coordinate choice, because we can always find a rest frame of any object, and the falling pattern in that rest frame must Lorentz transform into any other laterally translating frame.  From that and symmetry (I think you do not even need the equivalence principle, but you can use it to easily prove the point) you can infer that there is de facto a Lorentz transform of gravitational acceleration which is different than normal acceleration, i.e. not time dilated.  I.e. gravity ignores Lorentz effects.  I commented on this in a 2011 paper available on my profile page. 

Length contraction is proven in at least one "experimental" way: cosmic-particle rains. When a cosmic ray hit the upper layers of the atmosphere, a rain of "child" particles are created. Those are for some of them very-short-lifetime particles, such that we should detected very few of them on the ground. However, we detect much more particles than expected assuming "classical physics". It actually means that, in their own referential, the travel of the particles from the top of the atmosphere down to the ground lasted a shorter time than what an observer "at rest" would measure from the ground. The speed of those particles can be considered as being fixed (few interactions) and is quite close to the speed of light, hence this relativistic effect. Then, a shorter travel in time also mean a short travel in terms of length: from the point of view of these particles, the distance between the top of atmosphere and the ground was contracted relative to what an observer "at rest" would measure from the ground.

To be specific, Adrian's comment on a well known effect concerns primarily the lifetime of muons produced in the decay of pions..The pions have been produced by cosmic ray collisions in the upper atmosphere.

Thanks Matts for this precision.

Adrien, how is this well known SR length contraction related to GR?

Even this well know SR length contraction can be explained only by the time dilation to retain the absolute space and the associated conservation laws. 

An interesting statement Guoliang.  I have difficulty relating to the details of your papers, and I have difficulty with the term "absolute space" because it is hard to absolutely know anything.  But if I read between the lines at what you probably really mean, and judge also by your reaction to my ideas, there may be some common ground. 

The way I would put it, though, is that of the two possible interpretations of curved spacetime, one is that space expands so more objects fit in it.  The other is that objects contract so that more of them fit in the space.  And the orthodox view (according to Charles) is that in principle one cannot tell the difference so there is no use talking about it.  Preliminary investigations of how one might test this lead me to agree with the orthodox view, at least until we become an advanced civilization able to open wormholes, or equivalent.

But from a theoretical point of view, there is a difference.  It is not too hard to explain the contraction of objects using an electromagnetic theory of matter such as Asif's.  It is quite hard to explain (constructively account for) the expansion of space.  I'm sure this will generate howls of protest from those who just love space expansion, but loving it is the only justification for it.  Expansion is not the simplest explanation.

I believe this is not a replay of the situation with the ether and SR.  There were many ether theories and no way to choose between them.  SR was in at least some sense the simplest choice.  With gravitation, I believe we have enough constraints there would only emerge a narrow range of constructive theories.

The work I'm doing on deriving curvature from equivalence may shed some light.  Would you like to look at it?  I could use a critical eye before submitting it somewhere.

Robert,

The absolute space is a perfect vacuum full of pure Higgs field. It has property defined by fundamental constants, but I don't think its property can be defined just by the so-called curvature. 

@Robert Shuler

It is quite hard to explain (constructively account for) the expansion of space. I'm sure this will generate howls of protest from those who just love space expansion, but loving it is the only justification for it.

Maybe there is another justification for it within a different conceptual framework such as my paper Quantum Euclidian Geometry which I have just posted on my profile. I would welcome your comments.

Well, the constructive explanation is the simplest.  Try looking at Asif's recent work, I think you will find it simple and compelling.  (M. Asif, he is on RG)