# Can you help me refute this SOB?

1. Jan 22, 2004

### Julian Solos

One morning, this SOB showed up and told me that every dimension of everything had shrunk to half of its original size overnight. He's been bugging me with the same statement ever since.

I think this SOB has been lying, but I haven't been able to come up with rigorous proof to refute him.

Would you help me refute this SOB and shut the **** him up for good?

2. Jan 22, 2004

### Jimmy

I think I know what you are suggesting but I'll play along. First, tell me exactly what you mean by dimensions?

3. Jan 22, 2004

### chroot

Staff Emeritus
There is no way to prove your friend wrong. However, such a transformation is not really meaningful. Constants with dimensions are not fundamental; they are a result of our choice of units, and that is all. You could not detect any sort of change to a dimensionful constant in any way at all. The statement "everything is half as big today as it was yesterday" is exactly equivalent to "we are now using units which are twice as big as yesterday." It's not a real change.

On the other hand, changes to dimensionless constants (like the fine structure constant) would be very noticeable.

- Warren

4. Jan 22, 2004

### Jimmy

Earlier I was considering the change in cross-sectional area as it is related to strength versus a changing volume. I hadn't considered any fundamental change in mass yet.

Actually I think I'm probably missing something and am curious as to what that might be. Anyway,

If you take an object, say a plank or board, and reduce all if it's dimensions by one half, the cross-sectional area of the board is reduced by one fourth, and the volume is reduced by one eighth. In this case mass would also be reduced by one eighth. The strength of the board is reduced by one fourth since strength is directly proportional to cross-sectional area. So we have a board which is supporting one eighth the mass but is only reduced in strength by one quarter. Proportionally, the board is twice as strong as the one twice the volume.

If mass were to change by one half per unit volume as well, this means that when the original board shrunk to half it's original dimensions. The mass would be again, half as much (1/16th the original mass) and the proportional strength of the object would be double that of the original case; four times as much. Conversely, if an object were to increase in size and mass in this manner, wouldn't a change be noticeable?

Last edited: Jan 23, 2004
5. Jan 23, 2004

### Julian Solos

size.

6. Jan 23, 2004

### NateTG

Well, there are square-cube relationship issues that need to be resolved. Scaled down humans would be much stronger per weight since strenght is proportional to size squared, and weight is proportional to size cubed.

If you halve my size (linearly), I weigh $$\frac{1}{8}$$ but my capacity for lifting is only $$\frac{1}{4}$$. That means that I can lift twice as much, relative to my body weight.

Of course, if the physical constants of the universe also change accordingly, then there is no problem.

This type of question is really more philosophical than physical in nature unless it makes predicitions that differ from the typical physical ones. If this theory does not make new predictions, then it falls only to Occam's Razor - which is a pragmatic argument.

7. Jan 23, 2004

### yanniru

Why not just ask the SOB how he or she knows all dimensions are half size.

8. Jan 23, 2004

### Integral

Staff Emeritus
Heres where you nail him. First pin him down to exactly what has changed, if he sticks to his changing length . You can show him that if the sides of a cube are reduced by .5, its volume is reduced by by a factor of .125. Since only the lengths changed its mass must remain the same, therefore its density has to change.

Of course there has been no change in the density of any material, therefore he is wrong.

9. Jan 23, 2004

### Julian Solos

Size as used in every day language.

"Everything" seems to suggest things at sub-atomic level changed too. (I don't know if that makes any difference.)

10. Jan 23, 2004

### Jimmy

If just size has changed (length, width, height), then you would definitely notice a change.

http://www.faqs.org/docs/Newtonian/Newtonian_37.htm

I'm not really sure about changes at the sub-atomic level. How would changes in the size of electron orbits affect atoms? Would electrons have to be more massive to orbit closer to the nucleus? How would the other constants have to be scaled to make unnoticeable changes?

Last edited: Jan 23, 2004
11. Jan 23, 2004

### Nereid

Staff Emeritus
Now a really sneaky SOB might have said "all the fundamental constants got shrunk overnight, to half the values they had yesterday". Of course, you could immediately tell, as Warren says, he (SOB, right? not DOB) was lying.

But what if he said "half the fundamental constants got changed"? Could you still tell?

12. Jan 23, 2004

### ophecleide

Not only will the mass-density change as integral suggested, but the charge density would change as well, and I'm pretty sure that would change things on the sub-atomic level.

Like people have been saying, if ALL the physical constants changed overnight, (the relative mass of an electron as well as th universal gravity constant, etc.), there would be no way to detect it, but if it is only the size of things, it would become quite obvious.

13. Jan 23, 2004

### pallidin

I suppose this might explain why my paycheck was cut in half

Seriously, though, I find this somewhat interesting, as it seems to imply that it is theorectically possible(though obviously improbable) for certain types of catastrophic universal change to occur without being detectable.
Wow. Now that deserves another beer.

14. Jan 23, 2004

### Arcon

That is a meaningless statement since size only has a meaning when one is comparing the dimension of one thing to that of another. So if all things change size its not only unverifiable but it's meaningless.

Tell him that he's right but that this morning tiny angels stretched everthing back to its normal size.

15. Jan 23, 2004

### Nereid

Staff Emeritus
Prosecco, mio amico, prosecco (not beer).

Change any one of the 26 by 50% and you'd cease to exist, and the SOB couldn't have told you anything (he'd have been blown out of existence within a nanosecond of making the change). That's obvious for some (e.g. mass of the electron), somewhat less obvious for others (e.g. which one of "the U(1) coupling constant, the SU(2) coupling constant, the strong coupling constant" hides the fine structure constant?), and I really don't know for several (e.g. "the mass of the tau neutrino, 4 numbers for the Maki-Nakagawa-Sakata matrix, the cosmological constant").

Change all 26 by 50%? You wouldn't be around to know. Why?

16. Jan 23, 2004

### yanniru

26

It's great to see that someone learned believes in 26

17. Jan 24, 2004

### Julian Solos

I originally thought only "size" (including the distance between objects) changed. Does the shrinkage of everything in "size" change time (the rate of flow, etc.)?

18. Jan 24, 2004

### Nereid

Staff Emeritus
Re: Re: Can you help me refute this SOB?

Back to what chroot said, if all your friend has done is changed the definition of 'second', nothing physical has changed. Of course, you could read in yesterday's astronomy textbook that the Earth rotates on its axis in ~24 hours, and your new watch says it's ~12 hours (or 48), then you would know what the SOB had done.

Back to the 26 - where is 'time' among these?

19. Jan 24, 2004

### ophecleide

If the three physical spatial dimensions were all cut in half, you most certainly would notice. For starters, you'd way four times as much as you did before...

20. Jan 24, 2004

### yanniru

Back to the 26 - where is 'time' among these?

It states in the Green, Schwarz and Witten book, vol.I that there are two timelike dimensions in the 26. But do not ask me anything more about that!