Numbers

[Bomb#20]

Okay, you appear prima facie to be making inconsistent claims. So help me make sense of them. Earlier you asked, "We can look at something like space and ask is it possible to have the smallest amount of space?". Well, you tell me. What is your answer? Is it possible to have the smallest amount of space, or isn't it?

No inconsistency. You simply are calling two things the same thing.

There are two smallest things.

The theoretically smallest volume: Does not exist. A figment of the imagination.

The physically smallest volume: Something real and constrained. The smallest volume that could still be considered space. A quantum of space. To halve it is impossible.

Okay, I see -- you're saying if you have a quantum of space, it would be theoretically possible for there to be a smaller volume of space, but a smaller volume would not be physically possible in the real world. Got it.

The rational case for your claim being wrong is simple: we have a well-tested theory called "relativity" that accounts for all our measurements; and it implies there physically can't possibly be a smallest nonzero volume of real space. This is because distance is relative to motion, and distance is foreshortened in the direction of travel. So if we suppose there is a physically smallest volume, and we have a particular region of actual physical space that has that volume, that same region has a physically smaller volume from the point of view of an observer moving past it quickly than from the point of view of an observer moving past it slowly. No matter how small a physical region is, there is always another physical frame of reference in which it's smaller. You can halve a so-called "quantum of space" by flying past it at 0.866 times the speed of light. Therefore, no physically minimum volume, other than zero, according to the laws of physics as we currently know them. QED. Therefore, if, nonetheless, the universe really does have a minimum volume, it follows that Einstein's theory of relativity must be wrong. Therefore, if in the real world volume is constrained to be greater than or equal to some quantum of space, then there must be an alternative competing theory that's at least as good as relativity at accounting for all our measurements.

Well then, if you insist that real physical space must have a minimum volume, present that alternative competing theory.

 

[untermensche]

Why does the physically smallest volume have to be the same apparent volume for all observers?

They are all measuring the same thing but getting different results.

So what?

 

[Kharakov]

No matter how small a physical region is, there is always another physical frame of reference in which it's smaller. You can halve a so-called "quantum of space" by flying past it at 0.866 times the speed of light.

You're assuming that space, sans matter/energy, has its own reference frame? Is that some QFT I haven't heard of? I haven't read a lot about that- generally what I've read has matter/energy/SE_Tensor associated with the continuum, rather than the continuum being a reference frame in and of itself.

I think that sounds fucking cool though.... it means that Newton was right, which obviously confirms everything that unterbot has said.


Unter- you proved that space was finite, by disproving relativity!

 

[Bomb#20]

No matter how small a physical region is, there is always another physical frame of reference in which it's smaller. You can halve a so-called "quantum of space" by flying past it at 0.866 times the speed of light.

You're assuming that space, sans matter/energy, has its own reference frame? Is that some QFT I haven't heard of?

No, that's me speaking loosely. What I should have said is you can halve a so-called "quantum of space" by flying at 0.866 times the speed of light past the guy who measures it to be the alleged minimum volume, assuming that guy is at rest relative to the objects in space whose observable characteristics he's using to measure that region's volume. Better?

 

[Bomb#20]

Why does the physically smallest volume have to be the same apparent volume for all observers?

They are all measuring the same thing but getting different results.

So what?

This will be easier to explain if we have a specific number to talk about, so for the sake of discussion, let's say there's a quantum of space, and let's assume it's 4.2x10^-99 cubic centimeters. If you claim that's the physically smallest volume -- that nothing can be smaller than 4.2x10^-99 cc -- well, that would be a law of physics, wouldn't it? Some random object doesn't have to have the same apparent volume to all observers; but the laws of physics have to be the same for all observers, because if some statement is true for me and not true for you, what the heck can it mean for the statement to be a physical law? What's the substantive difference between a claim that's "a physical law that isn't true for some people" and a claim that's "wrong"?

Let's suppose there's some region of space, and when you measure it it's 4.2x10^-99 cc, and when I measure it it's 2.1x10^-99 cc. If you're claiming it's "really" 4.2x10^-99 cc, what's the criterion that makes your measurement a "really" measurement and mine a "not really" measurement? If you get to define somebody's measurement as "not really" because it disagrees with what you think the answer should be, what's to stop you from defining the earth as "really" flat and defining all the measurements that show the earth is round as "not really" measurements. What standard does a claim about reality satisfy that can make it qualify as a true claim, if it's some standard other than "agrees with measurement"?

(This is the same reason, in essence, as the reason we're able to know there are no miracles. A miracle is customarily defined as a violation of physical law; and what's the difference between a rule that's "a physical law that the universe doesn't always follow" and a rule that's "not a physical law"?)

 

[Kharakov]

No matter how small a physical region is, there is always another physical frame of reference in which it's smaller. You can halve a so-called "quantum of space" by flying past it at 0.866 times the speed of light.

You're assuming that space, sans matter/energy, has its own reference frame? Is that some QFT I haven't heard of?

No, that's me speaking loosely. What I should have said is you can halve a so-called "quantum of space" by flying at 0.866 times the speed of light past the guy who measures it to be the alleged minimum volume, assuming that guy is at rest relative to the objects in space whose observable characteristics he's using to measure that region's volume. Better?

No. I wanted space to get squished.

So you have an object, vibrating back and forth the plank length at sqrt(.99c^2). The object is 10 cm in length.


You're looking at it, and you have a device that can emit vibrations designed to nullify the object's vibrations. What happens when you use the device?

 

[untermensche]

....let's assume it's 4.2x10-99 cubic centimeters. If you claim that's the physically smallest volume...

You missed my point entirely.

While they may be measuring the physically smallest volume it is a relative measurement, like all measurements. Somebody else could possibly measure the same exact thing differently.

I am not saying one number, even 4.2x10-99 cubic centimeters, could represent the physically smallest volume. Because it is real and needs an observer to measure it.

 

[Kharakov]

Energy to vibrate the object is generated using quantum tunneling and a black hole, if you're curious.

 

[Bomb#20]

No. I wanted space to get squished.

So you have an object, vibrating back and forth the plank length at sqrt(.99c^2). The object is 10 cm in length.


You're looking at it, and you have a device that can emit vibrations designed to nullify the object's vibrations. What happens when you use the device?

I don't know, it nullifies the object's vibrations? It shorts out, because the laws its design is based on are outranked by Murphy's? The universe vanishes in a puff of logic? It nullifies the front of the object's vibrations, but since it takes 1/3 ns for the device's vibrations to get from the front to the back, by the time they nullify the back of the object's vibrations, the front of the object has started vibrating again?

 

[Speakpigeon]

Me, I give up.

Je donne ma langue au chat.
EB

 

[Bomb#20]

....let's assume it's 4.2x10-99 cubic centimeters. If you claim that's the physically smallest volume...

You missed my point entirely.

While they may be measuring the physically smallest volume it is a relative measurement, like all measurements. Somebody else could possibly measure the same exact thing differently.

I am not saying one number, even 4.2x10^-99 cubic centimeters, could represent the physically smallest volume. Because it is real and needs an observer to measure it.

Okay, let me try to understand this. Let's say you measure region A to be 4.2x10^-99 cc, and you measure region B to be 8.4x10^-99 cc, whereas I in a different frame of reference measure region A to be 2.1x10^-99 cc. What am I going to get when I measure region B? Do you mean I'll find region B is 4.2x10^-99 cc, because it's two quanta of space for me, the same as it is for you, but a single quantum is 2.1x10^-99 cc for me? Or do you mean I might measure region B to be 2.1x10^-99 cc as well, or perhaps even 1.05x10^-99 cc, because in my frame of reference it might be region B that's one quantum of space and region A that's two quanta?

 

[untermensche]

....let's assume it's 4.2x10-99 cubic centimeters. If you claim that's the physically smallest volume...

You missed my point entirely.

While they may be measuring the physically smallest volume it is a relative measurement, like all measurements. Somebody else could possibly measure the same exact thing differently.

I am not saying one number, even 4.2x10^-99 cubic centimeters, could represent the physically smallest volume. Because it is real and needs an observer to measure it.

Okay, let me try to understand this. Let's say you measure region A to be 4.2x10^-99 cc, and you measure region B to be 8.4x10^-99 cc, whereas I in a different frame of reference measure region A to be 2.1x10^-99 cc. What am I going to get when I measure region B? Do you mean I'll find region B is 4.2x10^-99 cc, because it's two quanta of space for me, the same as it is for you, but a single quantum is 2.1x10^-99 cc for me? Or do you mean I might measure region B to be 2.1x10^-99 cc as well, or perhaps even 1.05x10^-99 cc, because in my frame of reference it might be region B that's one quantum of space and region A that's two quanta?

Why do you have to measure two things?

In my frame of reference I will get some value for the smallest possible volume of space. If physical limits allow such a measurement by creatures on our scale.

And in your frame of reference you could possibly get a different value.

So what?

It is the same volume.

Space has structure. Something with structure can only be broken apart so many times until the structure is destroyed. You can only divide matter so far before you destroy the structure of the matter and it is no longer matter you are talking about.

 

[Kharakov]

I'm going to randomly murder people who deny the continuum. Unter, you don't have to worry, you're not a person.

 

[Bomb#20]

Okay, let me try to understand this. Let's say you measure region A to be 4.2x10^-99 cc, and you measure region B to be 8.4x10^-99 cc, whereas I in a different frame of reference measure region A to be 2.1x10^-99 cc. What am I going to get when I measure region B? Do you mean I'll find region B is 4.2x10^-99 cc, because it's two quanta of space for me, the same as it is for you, but a single quantum is 2.1x10^-99 cc for me? Or do you mean I might measure region B to be 2.1x10^-99 cc as well, or perhaps even 1.05x10^-99 cc, because in my frame of reference it might be region B that's one quantum of space and region A that's two quanta?

Why do you have to measure two things?

Because you wrote "The physically smallest volume: Something real and constrained. The smallest volume that could still be considered space.". An "-est" word like "smallest" is a comparison. When you claim volume A is the "smallest", that means whatever number of cc's A is, any other volume B is an equal or greater number of cc's. I'm trying to examine the implications of this.

In my bedroom I have a hairy black and white cat, and a hairier jet black cat. If I call the second cat "the hairiest", that kind of implies that it's possible in principle to examine both cats and count the hairs. If nobody is allowed to measure both cats' hairiness then using an "-est" word on them is kind of meaningless, no?

In my frame of reference I will get some value for the smallest possible volume of space. If physical limits allow such a measurement by creatures on our scale.

And in your frame of reference you could possibly get a different value.

So what?

It is the same volume.

Space has structure. Something with structure can only be broken apart so many times until the structure is destroyed. You can only divide matter so far before you destroy the structure of the matter and it is no longer matter you are talking about.

Sure, What I'm trying to find out from you is whether the structure you're saying space has is observer-relative or is an absolute property that's the same for all observers. If some particular region is a single quantum and I can't halve it, is that same region a single quantum from the point of view of a different observer? Or is it possible that that same region is two or more quanta to him and he can still break it down. If two observers break down the structure of space all the way to individual quanta, do they wind up with the same partitioning into the same quanta? Or can they get different partitions? Is the following scenario possible?

Observer 1's partition: |_____|_____|
Observer 2's partition: |___|___|___|

 

[untermensche]

I have answered that.

The same thing can have two different measurements. Because all measurements are relative and are made by observers trapped in a specific frame of reference.

There can be no meaningful partitions of the smallest possible volume of space. It cannot be broken apart. If you tried to somehow break it apart you would not have space anymore. You would destroy the structure.

 

[Speakpigeon]

And like it or not, that's all you'll ever get.
EB

 

[beero1000]

I have answered that.

The same thing can have two different measurements. Because all measurements are relative and are made by observers trapped in a specific frame of reference.

Wrong.

There can be no meaningful partitions of the smallest possible volume of space. It cannot be broken apart. If you tried to somehow break it apart you would not have space anymore. You would destroy the structure.

Unsupported, and contrary to experimental results supporting Lorentz invariance. So, wrong.

 

[bilby]

I have answered that.

The same thing can have two different measurements. Because all measurements are relative and are made by observers trapped in a specific frame of reference.

Wrong.

There can be no meaningful partitions of the smallest possible volume of space. It cannot be broken apart. If you tried to somehow break it apart you would not have space anymore. You would destroy the structure.

Unsupported, and contrary to experimental results supporting Lorentz invariance. So, wrong.

Sorry, but this is the twenty first century. Facts are subordinate to beliefs now, so as unter believes it with all has heart, it becomes the truth.

Apparently.

 

[untermensche]

I have answered that.

The same thing can have two different measurements. Because all measurements are relative and are made by observers trapped in a specific frame of reference.

Wrong.

Very Wrong. As wrong as a human can be.

Boy this is easy!

And totally fucking worthless.

 

[beero1000]

I have answered that.

The same thing can have two different measurements. Because all measurements are relative and are made by observers trapped in a specific frame of reference.

Wrong.

Very Wrong. As wrong as a human can be.

Boy this is easy!

And totally fucking worthless.

Except that my statement is supported by the most well-evidenced physical theories of all time, and yours is based on what you think makes sense at the time. I'm pretty sure you're completely ignorant of relativistic  Lorentz scalars, but that's really no excuse for the sheer confidence with which you are continually wrong...