Overnight everything has doubled in size.

Willowz

Do you know where this 'thought experiment' that cannot be put to test originated from? Was it Bertrand Russell?

Willowz

I'm reading the only other thread that is similar to this one. You might find this interesting.

This is a quote from another thread.
And this is from wiki;
*scratching head*

Willowz

On what basis can physicists suppose that there are dimensionless constants if they can only be calculated by physical measurement?

Hells

Scale is always comparative, it's a definition thing. It's not testable since there is nothing to test.

-Job-

If matter doubled in size and space did not, then the effect would be similar to gravity in a way given that the space between two small objects would decrease slower than the space between two larger objects. More volume, more "gravity". :)

In this model a balloon and a metal sphere with the same volume, would have similar "gravitational" attraction. Curious isn't it? :)

Jimmy Snyder

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:

[tex]F_g = G\frac{m_1m_2}{r^2}[/tex]

where r cannot be the only thing in the equation that changes.

Jamma

Is it actually meaningful to say that all lengths doubled (and everything else to make it all fit in whatever way) if this lead to no observable difference in the world? We are more used to the idea now that everything is relative- in what respect can we say that this is actually a concept which makes sense? What's important is the relations between different things- time and space, for example.

We could, for example, declare tomorrow that all lengths are now doubled. We'd have to half the speed of light and so on, but nothing actually happened except changing our name for things.

Upisoft

Everything doubled in size compared to what? Does your question have meaning?

Twine

John Passmore. [link] Or at least, he discussed it being untestable in 1965.

Jobrag

Imagine a cube (2*2*2) of material density M supported on a 1*1 cross section pillar the force on the pillar is 8M/1.
If all dimensions doubled you would now have 64M/4 or 16M/1 you've doubled the loading on the pillar; that is why elephants have thick legs in relation to their body size and deer have thin ones.

Jamma

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).

My question would be- what is the difference between this and us just renaming all of our lengths? I don't think that it is possible to come up with such a difference.

DaleSpam

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.

Here is a good page on the fundamental dimensionless constants:
http://math.ucr.edu/home/baez/constants.html

And here are a couple of posts explaining the "everything doubled" idea:
http://www.physicsforums.com/showpos...3&postcount=55
http://www.physicsforums.com/showpos...4&postcount=68

Jobrag

[QUOTE=Jamma;3611906]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?

DaleSpam

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.

Jamma

Jobrag, I assumed that everything else was changed to make sure that no difference could be perceived by the inhabitants of the universe in question. We are in the philosophy thread. There are an infinitude of reasons why we'd notice a difference if simply all lengths were doubled in size...

DaleSpam

Not necessarily.

DaveC426913

If everything doubled in size and this could not be measured in principle, the undeniable conclusion is that size is not meaningful in an absolute sense in the first place. It falls out of the equations.