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Do you know where this 'thought experiment' that cannot be put to test originated from? Was it Bertrand Russell?
And this is from wiki;If all of the universal lengths changed in such a way that none of the dimensionless constants were changed, then the change would not be measurable.
*scratching head*At the present time, the values of the dimensionless physical constants cannot be calculated; they are determined only by physical measurement. This is one of the unsolved problems of physics.
A dimensionless constant would be a ratio of dimensionfull constants that are measureable. Lengths can't be doubled without any other change occuring concurently and those other changes would be noticable. For instance, gravitational force is given by:On what basis can physicists suppose that there are dimensionless constants if they can only be calculated by physical measurement?
John Passmore. [http://test.philpapers.org/rec/PASEHJ" [Broken]] Or at least, he discussed it being untestable in 1965.Do you know where this 'thought experiment' that cannot be put to test originated from? Was it Bertrand Russell?
You can always make a dimensionless constant by taking some dimensionful constants and combining them so that the units cancel. So the existence of dimensionless constants is not in doubt. Dimensionless constants are important because their value does not depend on your choice of units.On what basis can physicists suppose that there are dimensionless constants if they can only be calculated by physical measurement?
Yes, but we are assuming that all the other constants change accordingly. Obviously if this was not the case then things would be noticeably different (just think about the orbits of planets).
The original question just asked if everything doubled in size whether we could observe a difference, I think that the answer to that is yes we could by structures falling down as their mass cubed but supporting framework only squared. Even if you push a bit further and alter the density and strength of materials so that everything stays upright I think that things like the way waves break on a shore and ripples propagate would change (if you look at films with scale models of nautical disasters the sea always looks a bit wrong), all down to Reynolds number. If you want to push things to the limit and modify the laws of physics so that everything acts the way it did before you doubled it's size, I suppose that then you couldn't see a difference but what would be the point of the question?
The point is that that question, as stated, is incompletely specified. There are multiple ways that everything could double in size, some would be observable and some would not. The way to determine if a difference is observable or not is to determine if there is a change in any of the dimensionless fundamental constants.The original question just asked if everything doubled in size whether we could observe a difference
Not necessarily.There are an infinitude of reasons why we'd notice a difference if simply all lengths were doubled in size...
This 'thought experiment' shows one. All of the constants on the 3 ratios below can be regarded as time or distance (based on the distance travelled by light in the time). Mass is not part of any ratio used in this 'thought experiment'.On what basis can physicists suppose that there are dimensionless constants if they can only be calculated by physical measurement?