Overnight everything has doubled in size.

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

 

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? :)

 

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.

 

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.

 

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

 

John Passmore. [http://test.philpapers.org/rec/PASEHJ" [Broken]] Or at least, he discussed it being untestable in 1965.

 

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.

 

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.

 

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...

 

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.

 

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'.

If I started photographing a light around 6 and a bit feet away, and the light was being spun in a circle 2 feet in diameter and I captured the light from the spinning light in one complete circle the ratio (A) of the time between the rotating source and the observer over the diameter of rotation would be roughly equal to Pi.
In this case the ratio (B) of the actual distance between source and observer over the distance travelled by light in a year would be very small and the ratio (C) of the observation period over the time it takes for the light to be rotated once will equal one. All observations should have a width of field that covers the complete diameter of rotation of the source being observed.

If I halve the exposure period I get half a circle and capture half as much light and when I double the exposure period I get 2 circles over each other and twice as much light in my photograph. If the light is rotated twice as fast I would expect something that looked similar to when I doubled the exposure period but I would also expect to capture the same amount of light from only one rotation despite the doubling of the speed of rotation. If I put two lights together I could halve the exposure time and double the speed of rotation to capture a similar amount of light from 1 light doing 1 complete rotation. If the light moved at an angle to me I would observe an oval instead of a circle but the amount of light captured would remain the same as in a complete circle.

In this simplest base context A = Pi, B = tiny, C = 1 and the observer will capture one complete cycle. On any scale where C >= 1 the observer will capture at least one complete cycle despite the size of B.

On any scale where A = Pi * x, B >= 1 and C < 1 the observer will only capture the light from B * C = x of one rotation during any observation regardless of the speed of rotation of the same object.

On a galactic year scale where A = Pi * x, B = 230 million and C = 1/230 million you would expect to capture the light from B * C = x rotations or roughly one rotation regardless of the speed of rotation.

On a galactic year scale where A = Pi * x, B = 4.2 billion and C = 1/4.2 billion you would expect to capture the light from B * C = x rotations or roughly one rotation.

Only changes in brightness can really make a difference on any scale as the speed of rotation does not change the total amount of light captured from the same source during any similar observation period. I have used figures for convenience, put your own figures in and keep ratio A as Pi * x and you will have a base point to compare observations.

This 'thought experiment' illustrates a common ratio that allows for a perceived mass and size variation from double, as per this threads title, to parity and one half. While it would be impossible to calculate the galactic years of every observed rotating source in the universe it would be logical to say that the difference in the sum of the perceived universal mass calculated from optical observations verses the perceived universal mass calculated from x ray observations is equal to the average of the number of galactic year rotations of each discrete source captured in your visible data sets.