## fredag 20 maj 2016

### Gravitational Mass = Inertial Mass by Definition: Hard Thinking

Typical illustration of equivalence principle. Get the point?

In Newtonian mechanics as already observed and understood by Galieo, inertial and gravitational (heavy) mass are equal, because there is only one form of mass and that is inertial mass as a measure of acceleration vs force per unit of volume. Since Newtonian gravitation is a force per unit of volume, gravitational mass is equal to inertial mass, by definition, as expressed by the fact that the dimension of gravitation is $m/s^2$. See also Chap 18 of Many-Minds Relativity.

Let us compare this insight with what modern physics says as told by Nigel Calder in Magic Universe:
• A succession of experiments to check the equivalence principle—the crucial proposition that everything falls at the same rate—began with Lorand Eötvös in Budapest in 1889. After a century of further effort, physicists had improved on his accuracy by a factor of 10,000. The advent of spaceflight held out the possibility of a further improvement by a factor of a million.
• If another theory of gravity is to replace Einstein’s, the equivalence principle cannot be exactly correct. Even though it’s casually implicit for every high-school student in Newton’s mathematics, Einstein himself thought the equivalence principle deeply mysterious. ‘Mass,’ he wrote, ‘is defined by the resistance that a body opposes to its acceleration (inert mass). It is also measured by the weight of the body (heavy mass). That these two radically different definitions lead to the same value for the mass of a body is, in itself, an astonishing fact.’
• Francis Everitt of Stanford put it more forcibly. ‘In truth, the equivalence principle is the weirdest apparent fact in all of physics,’ he said. ‘Have you noticed that when a physicist calls something a principle, he means something he believes with total conviction but doesn’t in the slightest degree understand.’
• Together with Paul Worden of Stanford and Tim Sumner of Imperial College London, Everitt spent decades prodding space agencies to do something about it. Eventually they got the go-ahead for a satellite called STEP to go into orbit around the Earth in 2007. As a joint US–European project, the Satellite Test of the Equivalence Principle (to unpack the acronym) creates, in effect, a tower of Pisa as big as the Earth. Supersensitive equipment will look for very slight differences in the behaviour of eight test masses made of different materials— niobium, platinum-iridium and beryllium—as they repeatedly fall from one side of the Earth to the other, aboard the satellite.
• ‘The intriguing thing,’ Everitt said, ‘is that this advance brings us into new theoretical territory where there are solid reasons for expecting a breakdown of equivalence. A violation would mean the discovery of a new force of Nature. Alternatively, if equivalence still holds at a part in a billion billion, the theorists who are trying to get beyond Einstein will have some more hard thinking to do.’
So Einstein thought to be deeply mysterious, what every high school student directly understands, and was able to imprint his idea into the brains of all modern physicists, who now have some hard thinking to do...

Einstein skillfully jumped between definition as a tautology true by construction and physical principle/law, which may be valid/true or not, thereby creating a total confusion. Another aspect is the constancy of the speed of light, which today is used as definition with the meter defined by distance traveled by light in certain time, yet physicists go around and believe that this works because the speed of light is constant. If you cannot distinguish between a definition without content and statement with content, then you may find yourself in trouble and mislead others...

PS This previous post may be consulted: The Principal Difference between Principles and Laws in Physics. Note in particular the distinction that a law is typically expressed as a formula, while a principle is expressed in words e.g. as equality of inertial and gravitational mass.

#### 14 kommentarer:

1. 'per unit of volume'? Where does the volume come in?

2. This is because mass density is per volume.

3. So when you write inertial mass, you really mean the density of inertial mass, right? More seriously,you seem to mean that inertial mass and heavy mass, *must* be equal. Why? This means that all object accelerate at the same rate when only subject to gravitation and no other forces. Why does it have to be that way? It is certainly not true for other forces.

4. It is true for forces acting per volume, and gravitation is such a force because it does not tear things apart, nor does inertial forces. Another way of thinking is to relate inertial force ultimatelty to gravitational force with the same result of equality of inertial and gravitational mass.

5. forces acting per volume ??

6. That gravity does not tear things apart is kind of a strange argument, right?

What is the relative strength between electronic and gravitational coupling now again...?

7. In any case, since equality seems to hold experimentally to any degree of precision, one should seriously consider the possibilty that it is a matter of definition, a matter of how force is defined and measured, which is not so clear and therefore may very well boil down to definition. What is your evidence that it is not definition?

8. Whether something is a definition or not is not a matter of evidence. Anybody that formulates a theory is free to choose whichever definitions he wants, and the value of the theory then depends on its predictions. I guess it can be said that Einstein took the equivalence of inertial and heavy mass as a definition. It seems you criticized precisely that in a post a few days ago. You called it then an 'empty definition', which made me believe that you thought it was empty because it necessarily has to be that way. But that is not so.

9. Ok, so you agree that the equivalence principle is a definition, but you still believe that a definition true by construction can have physical content, and doing so you follow in the foot steps of Einstein who has confused generations of physicists. But I repeat: A definition does not say anything about the physics of the world, just something about conventions of language.

10. You are contradicting yourself. First you say that since it is an empirical fact we may take it as a definition. Then you say this definition has no physical content. But, yes, the equivalence of heavy and inertial mass says that all bodies subject only to gravitation have the same acceleration. That is as you say an empirical fact and thus has physical content. A lot of content in fact, as Einstein showed.

11. But it is not really true by definition, only within the theory, because you can check it against the physical reality.

If you make a prediction based on the theory that is contradicted by empirical observation, then it is not generally true (Newtonian mechanics is one such example). You kind of illustrates the procedure with your latest post about a falling mass connected with a mass on the table through a string...

The name for this procedure is the scientific method and is the central part of all natural science. If you argue against this procedure you are in quite the trouble and not scientific.

12. The discussion illustrates the sad fact that since Einstein there is no clear distinction between (i) definitions/conventions/agreements, which all are valid/true by construction /language and (ii) statements about physical facts which may be valid/true or not. You can test your standpoint by asking yourself if constancy of speed of light is (i) or (ii)? What is your answer?

13. So now when it is clear that the equivalence principle can be tested (it would show quite spectacular differences in a vacuum free fall experiment) it is time to move the goalpost to the speed of light... nice.

14. ok, you don't have to answer if you can't. What the kitchen experiment shows is that mass does not change with the choice of Euclidean coordinate system, which is not surprising and as such not worth making a big fuss about.