# How big is an object in empty space?

1. Aug 15, 2015

### =SJ=

Hello,

I'd like to share with you a core idea of simple thought experiment which I have had on my mind for a while.
I'll be happy if you tell me your opinion and what I am missing.
Please note, as English is not my first language, the text below may not be written in the best way (I hope you'll be able to figure out what I had in mind).

2. Aug 15, 2015

### =SJ=

If you imagine an object in empty space, could you tell how big it is?
It is 1m tall and 3m wide or 3m tall and 1m wide? Does it occupy the size of pea or the size of an apple?
If you added another object, you could say that, for example, the second is greater than the first.
It make sense to speak of the size related to something else.
If were not, you could inquire about how big these objects are and keep adding new objects forever with no answer.
If you employed a series of diverse objects, you might want to establish your own unit to compare their's size base on, for example, average size of all objects around you. But there would be a limit given by the smallest object and the biggest one.

If we come back to the 2-objects world, how you would change the size of one of these objects?
If you were allowed to magnify the 1st object to 1.5 times of its size, you would need to take 1 smallest element which exist in your system and added one half of it. If so, the 1st object would not be no longer the smallest element which exist and at the same time it would be again and still the smallest element in your system. You were not able to distinquishe whether its size differe or not (from 1) and therefore wheter has been any operation done. Futhermore, since you are allowed to change the size by limitless possibilities (number), the increment could be every time infinity small. Again, the object would be before and after the same size and no change would come to be.

If you would agreed that, the the smallest element which exist is the element number 1 and the biggest element is number 2, you could increment the smallest object just by the smallest element (itself).
The biggest object on the other hand could be of the size of the maximal number which exist - 2. Since the smallest size is already occupied, the only possibility that remain is twice the size of the smallest object.
In this case of 2-os world its meaningfull to speak about the size as long as it is different and can be relate to something. If you would imagine plenty of diverse objects, they would differ one from each other by finite small amount (the smallest element), which you would hardly notice on the large scale.
It seems that it makes sence to follow certain rules (limits) given by a world around.

3. Aug 15, 2015

### davenn

your distance from it would help estimate its size. The closer you are to the object the easier to estimate
this is no different to looking up into the sky and estimating the size and distance to an aircraft passing overhead

either ... you would normally relate that to your own orientation

if it's 1m x 3m obviously it isn't .... I haven't seen too many peas or apples of that size

yes of course ( larger or smaller)

it helps but isn't completely necessary

no, see previous comment
additionally ... most people can visualise a metre length ( a yard for our non-metric American friends) and from that, do a good estimate of an object's size without any reference to any other object nearby

Am not even going to respond to the rest of your post ... seems very jumbled and doesn't make too much sense

Regards
Dave

4. Aug 15, 2015

### Alec Dacyczyn

If you need some sort of natural measuring stick, something intrinsic to nature, to could describe objects as multiples of the Plank Length. And there are various ways to define units based on the sizes of atoms, wavelengths of photon emissions (how we define the second and, via the speed on light, the meter), etc.

You may find this interesting.

5. Aug 15, 2015

### phinds

You have just SAID what the size is. Why do you then question what the size is? If you are questioning what the size APPEARS to be then that's entirely based on the point of reference and is not a meaningful question.

6. Aug 15, 2015

### =SJ=

Thank you for all your posts, I aprreciate them! I'll try to reply to each one of you.

davenn: You approache the idea with the common sense but if add an observer (you) in the system, there would not be no longer 1 object but 2. If take to your help a ruler, you would put in relation these two objects. But would you know if the scale on the ruler would be in meters instead of centimeters? Or if everything in the system would be 100x bigger (the ruler, the scale, the object)?

Alec Dacyczyn: Thank you for the video. Actually, the "thought experiment" aims this area. Of course, everything is made of atoms and empty space is not entirely "empty" but it the "though experiment" begins by another end, from sketch. If you were a designer and you could place your very first, an indivisible object into an existence, how big would this one be? There do not exist nothing more as yet. Could you define its size?

Exactly, thank you for that! It is not meaningful until there's something to relate with - a reference. Since you measure not a position but size, you may want to use somenthing like a ruler as davenn proposed. Only if you compare it with something else, then it makes sence. You can define the size base on somenthing different. It is the same as you would imagine 2 object in empty space and ask how fast they are moving. But would be able to recognize if the size of both object is in meters or kilometer? The idea is trying to show that what matters is only the ralationship between objects.

Sorry for the English :-)

7. Aug 15, 2015

### phinds

But that's true everywhere. You don't have to be in space. When I say my son is 6' 3" tall, I am comparing his height to a one-foot standard stick. I also say he's too damned tall, but that's another story.

8. Aug 15, 2015

### =SJ=

Yes and what happens if we applied this logic on things like colours, taste, weight, speed, position, ... Take the last one for example.
The position of an "object" could be everywhere as long as there's nothing to compare with. I'll borrow the qoute of Brian Green "Is the moon on the sky if we don't look at it?"

9. Aug 15, 2015

### phinds

I have no idea what you are really asking and what your point is.

Yes, the moon is there whether anyone is looking at it or not.

10. Aug 15, 2015

### =SJ=

Last edited: Aug 15, 2015
11. Aug 15, 2015

### Staff: Mentor

Yes, the moon is there. The Uncertainty Principle is applicable at the quantum mechanics level, not for much larger scale objects such as the earth's moon.

12. Aug 15, 2015

### =SJ=

Thank you Mark44 for posting in this thread. As far as I can understand the quantum mechanics its laws apply everywhere but due to small value of Planck's constant it is barely noticable on the large scale and the effect is futher reduced by the complexity of big-world objects as the Moon is. It is the same case as you would trying to go through a wall. Due to complexity of your body and large width of wall it would take an immense time before all electrons and other particles would tunneling through. The probability you success at the first time is negligibly small but laws of nature makes it possible. And that's what going on in our 2-objects world. The object would be everywhere because its position is not defined as yet.

Last edited: Aug 15, 2015
13. Aug 15, 2015

### phinds

No, nothing is everywhere at once. It can be in an undefined position, or it can have NO position until you measure it, but it cannot simultaneously have more than one position.

14. Aug 15, 2015

### =SJ=

Yes, this is what I had had in my mind. But I think this is becoming a bit playing with the words and I'd be happy if we can focus at the key ideas and find out whether there's something on it or what I have missed in my logical chain.

Last edited: Aug 15, 2015
15. Aug 16, 2015

### davenn

the person is there by default, be they just imagining the scenario or actually there physically

so either way they can use there own physical size as a yardstick

16. Aug 16, 2015

### =SJ=

I think you have actually on mind what we have agreeded upon with phinds.
May I reformulate that to this sentance: "It is meanunfull to ask as long as there is a reference (as phinds said) in the system to compare with."?

If not, could please answer this question: "If you were 2x bigger, how would you find it out?"

Last edited: Aug 16, 2015
17. Aug 16, 2015

### Staff: Mentor

I believe that what you are asking is if there were some omniscient outside observer that could see "the way things really are" and if everything doubled in size, then would we notice from our physical perspective? I would now be twice as tall as I am now, but our meter sticks would be twice as long so it would still take the same number of them to match my size.

If this is what you are asking, then this is closely related to the idea of dimensionless vs. dimensionful fundamental constants. An object's size is a dimensionful measurement, as are things like the speed of light, the gravitational constant, and Planck's constant. It turns out that those numbers tell you about your system of units, not about physics. If you want numbers that tell you about physics then you need to look at dimensionless numbers. See:

https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://www.physicsforums.com/showpost.php?p=2015734&postcount=68

18. Aug 17, 2015

### =SJ=

Thank you for the links. I'll be study and think about it.

Leave the observer and it is excatly what I am asking.

19. Aug 17, 2015

### jbriggs444

A standard meter stick is constructed to have a length that is a particular multiple of the distance light travels in one second. The second is defined as a particular multiple of the frequency of a particular type of electromagnetic radiation. So making all of the meter sticks longer will be detectable.

If you dot all the i's and cross all the t's so that increasing the size of all the meter sticks is indectable then you no longer have anything to test.

20. Aug 17, 2015

### =SJ=

That's a very good point. Except for the fact that to measure the speed of light, you would need a photon - another object :-)

Last edited: Aug 17, 2015