I feel that Aurino tagged out and now you are stepping in the ring.
***The central issue here is that he has defined acceleration in a specific way. He claimed "you could not possibly run any experiment to prove that the definition of acceleration does not describe the motion of bodies in space". Clearly "motion of bodies in space" is intended to be a reference to position as a function of time (at this point, position and time are nothing but numeric specification). The definition he gives is that acceleration is *defined* to be the second derivative of position with respect to time which is totally equivalent to telling you that the position obtained by integrating twice (a mathematical relationship).***
Agreed. I have no problem with the definition of acceleration as he presented it. I'm saying that the application of this definition is not clear cut.
***Let us suppose you could prove his statement false. In order to run an experiment to disprove that statement, you would have to accomplish a number of things. First and foremost, you would have to be able to specify x as a function of t (otherwise the derivative is undefined).***
Okay, let's take the photon example. The x position is x=0 (approximately where the electon emits the photon), and t=0 (approximately when the electron emits the photon). We can specify t=1 nanosecond, t=2 nanosecond, etc. We can also specify x=1 meter, x=2 meters, etc. So far nothing is wrong with our definition of acceleration, right?
***All of your complaints went to this issue, essentially pointing out that you could not accomplish that facet of the problem (which essentially is a proof that you cannot prove the equation wrong in any of the situations you describe). If you can not calculate a value, how can you prove the result of the calculation is wrong?***
Where couldn't I establish x in terms of t?
***The second step (presuming you can specify x as a function of t for some experiment you are going to perform) just exactly how do you prove the equation is wrong if the equation *defines* acceleration?***
Here is where I dispute this whole notion of the equation defining acceleration. This is not how the history of acceleration entered into the conscious of science. The first person from what I can tell to describe acceleration as a rate of change in velocity is Galileo in his book 'Two New Sciences'. You can read the section yourself it's on-line (I know I shouldn't be giving references, forgive me):
For an overview of the history of acceleration see this webpage by Michael Fowler:
So, what I dispute is this notion that the equation defined acceleration. The concept was eventually defined by the equation (just like Einstein's E=mc^2 eventually defined energy), but it didn't start out that way. If you read that chapter by Galileo he states in his own words his feeling about this subject:
"The properties belonging to uniform motion have been discussed in the preceding section; but accelerated motion remains to be considered... And first of all it seems desirable to find and explain a definition best fitting natural phenomena. For anyone may invent an arbitrary type of motion and discuss its properties; thus, for instance, some have imagined helices and conchoids as described by certain motions which are not met with in nature, and have very commendably established the properties which these curves possess in virtue of their definitions; but we have decided to consider the phenomena of bodies falling with an acceleration such as actually occurs in nature and to make this definition of accelerated motion exhibit the essential features of observed accelerated motions. And this, at last, after repeated efforts we trust we have succeeded in doing. In this belief we are confirmed mainly by the consideration that experimental results are seen to agree with and exactly correspond with those properties which have been, one after another, demonstrated by us. Finally, in the investigation of naturally accelerated motion we were led, by hand as it were, in following the habit and custom of nature herself, in all her various other processes, to employ only those means which are most common, simple and easy." (my emphasis)
More to the point, Galileo even says the following:
"And thus, it seems, we shall not be far wrong if we put the increment of speed as proportional to the increment of time; hence the definition of motion which we are about to discuss may be stated as follows: A motion is said to be uniformly accelerated, when starting from rest, it acquires, during equal time-intervals, equal increments of speed."
So, you see that acceleration was introduced by a guy who was following experimental outcomes. If the term didn't follow experiment then Galileo surely would have rejected the concept.
***just exactly how do you prove the equation is wrong if the equation *defines* acceleration***
If the assumptions of classical acceleration are violated, then the definition is meaningless. For example, the photon in a vacuum does not accelerate. Had Galileo been able to measure photons and known about quantum mechanics he certainly would have restricted his definition to those attributes which the concept is useful.
***Aurino did not say that the result would agree with some other definition you might dream up; he stated it as the definition! I think your problem is that you have some other concept of "acceleration" which is confusing your thoughts.***
No, I don't. I think it is a mistake to think that acceleration is not an aquired concept through experimentation (as if science defined it out of the blue) when in fact that is how it was acquired by science based on good theoretical insight and thorough experimental results. In addition, I get these queasy feelings anytime someone treats a phenomena that has been identified with an equation as true by definition. It is not true by definition, it is true by a definition that fit the experimental data (as Galileo said in his own words)! The derivative equation that came later was only a restatement of Galileo's definition. Had Aristotle been right, the equation of acceleration would include mass. But, Aristotle was wrong which Galileo established in his experiments.
***In fact I think you have difficulty comprehending the rigor necessary to work with exact definition particularly if what you have in your head is askew of what is being talked about.***
There you go again... Particle physicists don't talk in terms of acceleration when talking about quantum tunneling (etc). This concept doesn't apply even if the classical components (time, space, change of time, change of space) are all present to apply the definition to quantum phenomena (or other non-classical phenomena). Of course, acceleration is still a useful concept even in particle physics, but the use needs to be specific to the needs of the physicist.
***Communication is very strongly dependent on understanding the meaning intended by parties trying to communicate. No matter how sure you are that you "know" the meaning of any word, it is always an assumption to believe that others are attaching the same meaning you intended.***
Exactly. The definition is dependent on meaning and meaning is dependent on circumstances. If the circumstances change such as we switch from classical phenomena to quantum phenomena, then we have to be very careful. The term acceleration is very useful, but it was not elected as definition so that it would be true by definition, it was selected because it was found true in experiments. How many times does this happen in physics? Very often.
Let's all be nice to each other. This is all that I've asked in debating others. I don't like unfriendly debates. Take care.
Warm regards, Harv