alxm said:
jgm340: You're not talking about science there, IMO you're making a rather confused point about semiotics, not physics.
No, I am making a point about physics.
If I ask you: (i) "What is force?", you might say: (ii) "It is a quantity which measures the relationship between acceleration and mass, described by the equation F = ma."
Then a similar question to that of the OP's is, (iii) "Can we say that force, as defined above, actually exists?"
It's important to note that "F= ma" is conceptual language just in the same way "relationship between" is conceptual language. Sentence 2 is describing a (supposedly) physical object by the abstract properties it is supposed to have. (Here I use object as a general term for object/phenomenon/whatever)
There is an implicit assumption that there is only one physical thing fitting the above definition. For example, "work" also involves acceleration and mass, but doesn't satisfy the equation "Work = ma".
Thus we can rephrase sentence 3 to be less ambiguous: (iv) "Does there exist a physical object/phenomenon that measures the relationship between acceleration and mass, described by the equation F = ma?"
Already we can see a problem in trying to answer this question. What, exactly, are acceleration and mass? Do we even know these exist?
The idea behind a definition, of course, is to provide an unambiguous way of tracing back to a few concepts which are taken as axioms. We like to think that mass, time, and distance as being so fundamental that we do not define them in terms of other concepts. These are basically our axioms.
Because of the way we have defined force, however, it exists by definition, so long as mass, distance, and time exist as quantities! (This step in my argument is crucial to understand).
In other words, what we can make is a conditional statement (which is definitely true) about the existence of force: (v) "If mass, time, and distance exists as quantities, then the quantity force exists". So, using the definition, question 4 actually is equivalent to this question: (vi) "Do there exist quantities mass, time, and distance?"
Here's where things get tricky. How do we know our axioms are true? How do we know mass, time, and distance exist? We have an intuitive notion of mass as being "how heavy something is", and time as being "how long I have to wait", but these are nowhere near suitable for physics. In physics, time, mass, and distance are abstract quantities. They may as well be called mygork, traujdov, and dastyern, as to not be confused with informal notions we may have about them.
(In modern physics, it turns out that time, distance, and mass are NOT fundamental independent quantities. How so? Well, the speed of light is a constant that posits a relationship between them.)
Assuming for the sake of argument that they are fundamental quantities, however, how would we know they exist? As physics is a science, it comes down to empirical evidence. Basically, we make assumptions in how we interpret our sensory information. We assume that when we put two objects on a balance, that it will balance if and only if they are the same mass. We assume that two sets each of two points are the same distance apart if and only if they measure the same on a piece of metal. We assume that if the same number of ticks of a clock happen during the start and end of two events, then they happened in the same amount of time. Basically, we define mass, time, and distance solely in empirical terms. This is the only way in which physics can claim to make statement about reality; any statement physics makes about reality boils down to a statement about what we would experience if we were to do certain things.
What we can conclude, then, is that the axioms of physics are not that "mass exists", "distance exists", and "time exists", but rather statements about the equivalence of certain things. They are statements like "It doesn't matter which balance I use", and "it doesn't matter how fast the object is moving when I use a stick to measure how long something is" and "two clocks ticking the same will tick the same number of ticks during an event no matter what". We just define mass to be a number describing what happens when we put it on a balance with other objects. We just define time to be the number of ticks that happen on the clock. So we are
defining time, distance, and mass in terms of our senses, rather than taking them as axioms.
So the only axioms of physics are statements about our senses. It turns out that some of these statements are wrong! Physicists have chosen the wrong axioms in the past.
But this is precisely what physics is about! Physics is about finding a set of axioms that are actually physically true!
Now we can actually address the issue at hand. How can we say something like "mass" or "force" exists? Well, we say it exists if and only if they are well-defined. In other words, we might define "time" to be "the number of ticks that happen on a clock during the event". In order for time to be a well-defined notion, it must be that it is true regardless of the clock used, regardless of the location of the clock, regardless of the movement of the clock, etc. In other words, there must be a unique number that we can assign to any two points denoting the time between them.
What this boils down to then, is simply the question of "Do all our axioms ALWAYS hold?" If so, then we can claim that "time", "acceleration", etc actually exist as we have defined them! If not, then we cannot.
Does this make sense?
To give a final example, "mass" does not exist in the way most people would define it. Why? Because the usual axioms used to define mass aren't consistent! It is not true that there is conservation of mass!
What is an example of something that we think very strongly does exist? The speed of light. We believe that the speed of lights exists, because is agrees with a set of axioms which people haven't found fault in yet.
If something like "mass" can fail to exist in the way it is defined, then do you see why something like an "atom" could fail to exist in the way it is defined?
I am really real! I call that the reality check.
Oh, continuing onward . . .
