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The Journal of Things I Don't Understand

Mostly questions that bug me about whats going on and doesn't seem to fit with reality.

Equivalence

From Albert Einstein when talking about the General Theory of Relativity we have:

<2>”This theory arose primarily from the endeavour to understand the equality of inertial and gravitational mass.”

Equivalence being part of this equality indicates it is one of the founding principles of relativity, and very important to its forming. If this is not correct, then the theory of relativity, or at least the gravitational inertial mass part, could well not be valid. But to understand equivalence we must know what the principles behind it are, so let us start with the definition:

As per Albert Einstein

<1>"We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course."

Please note that he says "exact physical equivalence". This then allows the theory to advance to the bending of light by a gravitational field.

He also says:

<2>”...Thus when the gravitational field is included in the framework of the consideration, the inertial system loses its objective significance, assuming that this 'principle of equivalence' can be extended to any relative motion whatsoever of the systems of reference. If it is possible to base a consistent theory on these fundamental ideas, it will satisfy of itself the fact of the equality of inertial and gravitational mass, which is strongly confirmed empirically.”

And from a web interpretation of what is understood to be what he said.

<3>"Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field."

This part of the theory of relativity is generally used to explain the equivalence of gravitational mass and inertial mass of an object.

The experiment I performed was to place a concrete block in my yard for the past ten years. I want to experimentally determine if there is a difference between at rest gravity and speed acceleration. I chose ten years since I knew that in a ten year time frame I would be close enough to the block to experience at least 1 year of any speed/gravitational changes the block may have experienced. Since my clock has shown ten+ years have passed, and I have felt the at rest gravity or speed change for the last ten years, I know that the block has been under the influence of a gravitational field and not a 1 g speed change.

I know this because:

1. The speed of the block after ten years of 1 g speed change in its frame of reference would produce a speed of:

well beyond any speed allowed by relativity. I can say this because when discussing measuring rods and clocks Einstein says <30> "Of course this feature of the velocity c as a limiting velocity also clearly follows from the equations of the Lorentz transformation, for these become meaningless if we choose values of v greater than c." and <31>"Here also the velocity c plays the part of an unattainable limiting velocity." Indicating that it is physically impossible for an object to accelerate at 1G speed change long enough for its speed relative to an external object (or its speed at the start) to even reach c let alone exceed it.

This would be the first logical and provable criticism of equivalence.

2. Since the speed would be in excess of c, <6> <7> <8> <9> <10> <11> <12> <13> <14> <15> <16> the concrete blocks mass, at some time prior to now, would have reached almost infinity and collapsed everything into itself in a crushing gravitational field. Since this did not occur, I know the block is not experiencing a speed change of 1g but rather is in a 1g rest gravitational field.

This is the second logical and physically provable criticism of the equivalence theorem.

3. If the block had been in a craft and accelerating via a speed change, its time supposedly <18> <19> <20> <21> <22> <23> <24> <25> <26> <27> <28> started slowing down (This is how the twins paradox is explained). According to relativistic theory, when its speed reached c its time would stop. This would have occurred after:

had passed in its frame of reference. But since my clock and the clock of the block have gone past 353.82 days, I know for a fact I am not undergoing a speed change but rather am under the influence of a gravitational field. I know the clock of the block has not stopped because when I touch it, its temperature is not anywhere near absolute 0, as a matter of fact it is close to ambient temperature. Along with this, the block is still emitting light. Any object that is traveling at c would have a 0 time, and as such, the electrons would not be able to change orbital positions to emit light. As a second indicator, I can still see the block.

This is the third logical and provable criticism of the equivalence theorem.

In <32> Einstein talks about this equality of Gravitation and Acceleration by giving the example of an observer in empty space outside any gravitational influence in a “chest”. This chest is being pulled by a rope by some entity with a constant force. The constant force seems to have been chosen because it would not allow the occupant to detect the difference in force between at rest gravity and inertial acceleration. (At rest gravity is used because if you would work with free fall gravity, the chest occupant could instantly tell the difference because the occupant in the example is being held against the “floor” of the chest by speed change). Constant force would result in an increasing speed. This change in speed would not be detectable with any force meter such as a scale or such, but it would easily show up, as previously explained.

Since Einstein talked about velocity and gravity one must also consider direction change, so let us use his example of the occupant of the chest but let's modify it for a change in direction only. Let us imagine that the occupant is in a 400ft square chest with a rope attached, and the imagined entity this time is swinging it in a circle. For ease of numbers and such, let us assume that the rope is 100ft long, and the entity is swinging it at 0.57 radians per second. This time, the occupant would experience a 1 g force “pulling him down” ^{Note 1} to the floor (according to his frame of reference).

This time, there will be no more time change or mass change than one would experience with 1g of at rest gravity. But there is a way to tell the difference between rotating or being under the influence of a gravitational acceleration. Simply run around in different directions and it can be determined if the force felt is due to the influence of direction change or at rest gravity. This is because as one travels in whatever direction the entity is rotating the chest one feels heavier. When one runs against the direction the entity is rotating the chest, one first gets lighter and then heavier.

This weight change occurs because running against the direction the entity is rotating the chest one effectively decreases the rate of rotation, reducing the centripetal force, making one feel lighter. This will continue until one would feel weightless, then as ones speed continued to increase one would again have an effective speed relative to the center of rotation, and therefor one would begin to feel a force again.

Mathematically, assuming that our occupant was a normal person and could sprint at 11mph for a short time (worlds record for 100yd dash is almost 22mph). Using

and

We want G's of force so:

And

where theta is the angle of the sprint from the direction of the chests rotation, and Ss is the speed of the sprint.

And we get 1G just standing there rotating at 38.6898mph. When the occupant runs in the direction the entity is rotating the chest (theta = 0 ) the effective speed goes to 49.6898 mph and the force goes to 1.65G's. When the occupant runs in the opposite direction (theta = 180 )the effective speed goes to 27.6898 mph and the force goes to 0.51G's. Both easily detectable.

There are any number of ways here on earth that one can use to verify this. Roulette wheels, carnival rides, etc.

I would also like to address the question of gravitational “free fall” acceleration and speed change acceleration. The chest occupant can tell the difference between them because if the occupant is in a “free fall” condition (consider a free falling elevator) the occupants mass, time and length would change just as in the case of the constant force scenario, but there would be no force holding the occupant to the floor, therefor the occupant would immediately know he/she was under the influence of a gravitational field instead of being under the influence of a speed change.

Conclusion

It is rather obvious to even the most casual of observers that the accelerations are three quite distinct operations which result in quite different results. The one and only thing common to the three is that the resulting force is the same. This is only 1 factor amongst 4 that is the same, and as such means that at rest gravitational acceleration, speed change, and direction change are not equivalent even to the first order.

Also note that one of the teachings is that <5>”There is no experiment done in a small confined space which can tell the difference between a uniform gravitational field and an equivalent acceleration.” This statement in no way limits the time involved. As such, it would not invalidate this experiment even if the statement is proper.

Since the “chest” occupant can experimentally tell the difference between at rest gravitational acceleration and speed change, and we can tell the difference, it is rather obvious that at rest gravity and speed change are not even equivalent to the first order. Equivalence only shows that the force of gravity and speed change are similar, but their end result is not the same.

The only thing common to at rest gravity, speed change, or direction change is that they exert a force. All three are different, and can experimentally be distinguished from each other even with standard test equipment like clocks and our own sense of force. They are not in any way <1>"physically exactly equivalent".

The logic here points to the fact that not only are the three accelerations discussed not the same, the only thing similar between them is the fact that they exert a force. This force is “the same” only because they are acting on “the same” thing, and as such must exert “the same” effort to get “the same” result. Nothing unusual about this. It is the mass that is the “equality”, not necessarily the nature of the accelerations.

And according to Einstein <33> ”If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behavior of the bodies around him on the supposition of a gravitational field, and he would not be justified on the grounds of experience in supposing his reference-body to be 'at rest.'” The experiment performed and the ones described are the actual physical world. They show it is easy to distinguish what is happening to the closed chest without looking outside, and as such one is not justified in equating any of the conditions to a gravitational field. It also means that under all conditions it can be known if the reference frame is at “rest” ^{Note 2} or not based on experimental results. Accuracy of the measuring devices is the only limiting factor. This would effectively mean Equivalence is not proper.

Since equivalence is not a valid concept, it cannot be part of the explanation of the <2>“equality of inertial and gravitational mass” or the General Theory of Relativity.

By studying the works of others, one could easily say that what this ultimately is about is an attempt to determine what causes mass to attract mass (gravity). By assuming equivalence, the constant velocity of light, and incorporated the work of others, such as Lorentz, Einstein derived that gravity was the bending of space. Correct or not about the conclusion of bent space, the idea of equivalence is totally illogical when you look at it critically. This fact alone does not indicate that relativity is incorrect, only that part of the foundation is not proper or may need revision.

Can anyone explain where my logic is wrong?

Thank you for your time

Bruce B Williams

To respond please email bbwilliams_bresnan.net.net and substitute the at symbol for the underscore

Offered Solutions
None so far

Notes

1 – The actual force is centripetal force. And is an acceleration towards the center of rotation.

2 - Rest in this case indicates being in a steady state gravitational field. It does not imply some sort of absolute 0 velocity.

<2>Albert Einstein, Relativity The Special and General Theory, Robert W. Lawson translator, 1961, p 172. ISBN 0-517-88441-0

<3>http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/grel.html#c1 . July 29, 2007

<4>Michael Fowler, General Relativity, http://galileo.phys.virginia.edu/classes/252/general_relativity.html, © 2000, Sept. 23, 2007.

<5>D. Acosta, Relativity5, http://www.phys.ufl.edu/~acosta/phy3101/lectures/relativity5.pdf, Sept. 23, 2007

<6>W. Kaufmann, "Uber die Konstitution des Elektrons" Ann. Physik 19 ,495 (1906) ( first historical experiment)

<7>W. Kaufmann, "Uber die Konstitution des Elektrons", Sitzungsberichte der preussichen Akademie der Wissenschaften, 1915, Part 2.

<8>M. Planck, "Die Kaufmannschen Messungen der Ablenkbarkeit der beta-Strahlen in ihrer Bedeutung fur die Dynamik der Electron", Verhandlungen der Deutschen Physikalischen Gesellschaft, 8, 1906.

<9>M. Planck, "Nachtrag zu der Besprechung der Kaufmannschen Ablenkungsmessungen", Verhandlungen der Deutschen Physikalischen Gesellschaft, 9, 1907.

<10>A.H. Bucherer, Phyz. Zeitschr. 9 (1908), p. 755; Ber. d. deutschen Phys. Ges. 6 (1908), p. 688.

<11>A. Bucherer, "Die experimentelle Bestatigung des Relativitatsprinzips", Annalen der Physik, 28, 1909.

<12>E. Hupka, Ann. Phys. 31 (1910), p. 169.

<13>Cl. Schaefer and G. Neumann, Phys. Zeitschr. 14 (1913), p. 1117.

<14> Ch.E. Guye and Ch. Lavanchy, Comptes rendus 161 (1915), p. 52.

<15>Rogers et al. Physical Review 57, p. 379

<16>Meyer et al. Helv. Physica Acta 36 , p. 981 (1963)

<17>W. Bertozzi in Am. J. Phys. 32, 551 (1964)

<18>Rossi and Hoag, Physical Review 57, p. 461 (1940)

<19>Rossi and Hall, Physical Review 59, p. 223 (1941)

<20>Rasetti, Physical Review 60, p. 198 (1941)

<21>Durbin, Loar and Havens, Physical Review 88, p. 179 (1952)

<22>D. Frisch and J. Smith, Measurement of the Relativistic Time Dilation Using Mesons Am. J. Phys. 31 (1963) 342.

<23>Farley et al., Nuovo Cimento Vol 45, p. 281 (1966)

<24>Farley et al., Nature 217, p. 17 (1968),

<25>Farley et al., Nuovo Cimento 9A, p. 369 (1972)

<26>Bailey et al., "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit," Nature 268 (July 28, 1977) p. 301.

<27>Meyer et al., Physical Review 132, p. 2693

<28>Balandin et al. JETP 40, p. 811 (1974)

<29>Bardin et al. Physics Letters 137B, p. 135 (1984)

<30>Albert Einstein, Relativity The Special and General Theory, Robert W. Lawson translator, 1961, p 41. ISBN 0-517-88441-0

<31>Albert Einstein, Relativity The Special and General Theory, Robert W. Lawson translator, 1961, p 42. ISBN 0-517-88441-0

<32>Albert Einstein, Relativity The Special and General Theory, Robert W. Lawson translator, 1961, pp 75-76. ISBN 0-517-88441-0

<33>Albert Einstein, Relativity The Special and General Theory, Robert W. Lawson translator, 1961, p 77. ISBN 0-517-88441-0

Writing Notes

1. Original Writing Date Sept 05, 2007

2. © 2007 Bruce B Williams

3. No independent math checks as of publish date. If errors they will be corrected at a later date if they do not solve the problem. If this is a math problem then the errors will be noted as the cause of the illogical conditions.

4. Major Revision Sept 25, 2007

5. Proofread and references updated Sept 26, 2007

6. Direction change initial entry Oct 02, 2007. No math checks yet.

7. Direction change math check Oct 03, 2007.

8. Proof read Direction change and removed MM type device reference. Oct 18, 2007

9. Major rewrite Oct 22, 2007.

10. Final Nov 03, 2007.

11. Changed email address Aug 13, 2012