Object A 10x Larger Than Object B: Physics Explained

[PhilipF]

In terms of physics (as oppposed to math) can anyone tell me what it means to state that 'object A is 10 times larger than object B'?.Surely this has nothing to do with any property inherent in the object itself such as mass or number of atoms .Nor can it be a property of the space that the object occupies because that would not be a statement about the object but would involve some kind of speculation about what that space would be like if the object were not present (e.g. how long it would take light to cross the region 'occupied'.)

 

[quantumdude]

In terms of physics (as oppposed to math) can anyone tell me what it means to state that 'object A is 10 times larger than object B'?.

It means that the volume of object A is 10 times the volume of object B.

 

[PhilipF]

Isnt that just another way of saying 'bigger' ? i.e. 'volume' is a mathematical description of a hypothetical space , not a physical property of the object itself.

 

[quantumdude]

Isnt that just another way of saying 'bigger' ?

No. It singles out "volume" as opposed to "length" or "width" or "cross sectional area".

i.e. 'volume' is a mathematical description of a hypothetical space , not a physical property of the object itself.

Again: No. Volume is something that can be measured. That measurement is compared against calculations done in a hypothetical space. But the experimental result certainly doesn't hinge on the theory.

 

[PhilipF]

o.k. if I follow your reasoning , we could measure the length width and height of an object ,say a 1 metre steel cube floating in space and multiply these together .(measurements of course are only ever an approximation .If you measured the sides of a real cube with an instrument small enough to register every microscopic indentation in its edges you would arrive at sides and hence a volume far in excess, possibly infinite, of its 'actual' volume) .So I am suggesting that what you are 'measuring' is only a mathematical averaging out ,pretending the sides of the object are really pure straight lines as in a geometry text .
But actually that is not my argument , my main point is that when you multiply the lengths of the sides together , what you are doing is 'true' only in an idealised geometric space not in real space-time ,since you cannot know what is happening to the space inside the cube ,it may be bent crushed or deformed in a way that makes measurement of the outside surface meaningless in calculating real 'volume' of the object .i.e. there is a mathematical volume as you have described but not a measurable 'physical' volume .

 

[quantumdude]

since you cannot know what is happening to the space inside the cube ,

Why can't I know? In principle, I can hollow each cube out and fill them each with water. Then I can compare the capacity of each cube by pouring the water out into a standard container and comparing the water level. There is a measurement of the volume, no?

 

[hitssquad]

In terms of physics (as oppposed to math) can anyone tell me what it means to state that 'object A is 10 times larger than object B'?

It means object A is 11 times as large as object B.

 

[quantumdude]

Whether you interpret his wording as "10 times as large as..." or "11 times as large as..." is immaterial.

 

[loseyourname]

Would a physicist ever state that an object A "is ten times larger than" an object B? Wouldn't the physicist be more specific in which measurement he was referring to, given the ambiguity (it could mean ten times more massive or ten times more voluminous without further data)?

 

[PhilipF]

If you hollow the cube out , how do you measure the volume of the remaining walls ? you are still left with the same problem .

 

[loseyourname]

If you hollow the cube out , how do you measure the volume of the remaining walls ? you are still left with the same problem .

You can measure the volume of the water displaced by the entire cube if that would please you. I and Tom both know that any measuring device has a certain margin of error, so I suppose any physicist that would actually say "object A is ten times larger than object B," though I still don't think any good physicist would ever be that vague, would really have to say "object A is ten times larger +/- x times than object B," x depending on the measuring device he uses. Does that make you happier?

 

[quantumdude]

If you hollow the cube out , how do you measure the volume of the remaining walls ?

With the water. You can dump the contents of both cubes into the same vessel (separately, of course) and compare them against the same standard.

 

[PhilipF]

Thanks Tom and L.Y.N.for your replies. They are helpful and thoughtful .I am sorry I am not able to express my thoughts more clearly . What I had in mind was that I feel common-sense notions of scale that we use in everyday life do not have a fundamental physical basis . We learn the notion of scale as babies finding what we can or cannot pick up or put in our mouths .We now know that mass is something very different from our simplistic everyday notions of things being 'heavy' or 'light' and may involve interaction of forces within matter with the Higgs field and I suspect there is a similar 'blindspot' in our understanding of scale . There is something more fundamental ,more mysterious going on as regards the way in which an object occupies a region of space . Anyway that is the best I can do to express my puzzlement regarding this , in fact I cannot free myself of the notion that somehow it is not so unreasonable to believe that a 'smaller' object or region of space can in some way contain a 'larger' one. Since a cube of empty space is not a geometrical line drawing of volume on a piece of paper but in fact is a fabric with a vast(vacuum) energy content in every tiny region it seems to me that notions of occupation in that realm must somehow involve descriptions of energy ,not just notions of volume that would be familiar to Archimedes .

 

[Nereid]

PhilipF, you may be making things more complicated than they need be.

IF your concerns are to do with meaning within a particular theoretical framework, then I suggest that they can be answered by better understanding that/those theory/those theories.

IF your concerns are to to with how well the best physics we have maps to good results, then please ask away!

IF you wonder how well and how far the best physics we have today can be applied - and what (apparent) inconsistencies arise, wrt some mathematical or philosophical framework - then please try to distill this to its essence.

 

[PhilipF]

Thanks for your reply Nereid ,You suggest I distill this question to its essence . So here goes;
What I am suggesting is that many aspects of the physical universe which were taken for granted as being either well-understood or amenable to commmon-sense explanations such as light ,gravity ,motion , empty space etc have all turned out to be far more complex and counter-intuitive than people thought 100 years ago (ie before Relativity and Quantum theory ).Therefore when you suggest I am trying to make things more complex than necessary I suggest that the history of science shows that it is usually the other way around and we make things too simple.
So as this is a philosophy thread and not a 'how to' discussion I am suggesting an approach such as , "if a fundamental property of our universe such as the notion of scale as we experience it looks simple and obvious we may be wildly mistaken about it and it should be questioned " How it could be tested experimentally is difficult to say .

 

[selfAdjoint]

Thanks for your reply Nereid ,You suggest I distill this question to its essence . So here goes;
What I am suggesting is that many aspects of the physical universe which were taken for granted as being either well-understood or amenable to commmon-sense explanations such as light ,gravity ,motion , empty space etc have all turned out to be far more complex and counter-intuitive than people thought 100 years ago (ie before Relativity and Quantum theory ).Therefore when you suggest I am trying to make things more complex than necessary I suggest that the history of science shows that it is usually the other way around and we make things too simple.
So as this is a philosophy thread and not a 'how to' discussion I am suggesting an approach such as , "if a fundamental property of our universe such as the notion of scale as we experience it looks simple and obvious we may be wildly mistaken about it and it should be questioned " How it could be tested experimentally is difficult to say .

It was Herman Weyl who tried to calculate the results of invariance under changes of scale. In math this is called conformal invariance because the shapes of things don't change if you magnify or shrink the scale. Weyl built a locally conformal theory of spacetime; this was criticised by Einstein, and never became popular, but it foreshadowed gauge theory ("gauge", as in gauge of a railroad, was Weyl's word, referring to the variable scale). For a modern application of Weyl's idea by Heng Chung of MIT, see my post "A "Weyl" theory of dark matter" on the Astronomy forum. String theory finds that the geometry of the string's world sheet is locally conformally invariant.