Fun with Physics

[NealRaymond2]

[quote]lothario1132 wrote:
Okay, hearing you. But what about my assertion that there is such a thing as the smallest unit of time? Isn’t the fact that there is such a thing as a “fastest speed” indicative of this?
[/quote]
By itself, I don’t think a “fastest speed” necessarily implies a smallest amount of time. The equation is distance divided by speed equals time (assuming that actually is the equation, and it doesn’t change under some extreme circumstance of which I am ignorant). Therefore, given a fixed upper limit for speed, if we assume that the distance could be as small as we want, then according to the formula the time could also be as small as we want.

On the other hand, if we assume a fixed upper limit for speed and a fixed smallest amount for distance, those two things together would necessarily imply a fixed smallest amount for time. (Imagine the formula for time expressed as a fraction, with the distance as the numerator and the speed as the denominator.)

[boomerlu]

[quote]lothario1132 wrote:
True.

But what is the most precise and frighteningly predictable part of physics?

Quantum physics.

It is my guess that we will tack on relativity to this instead of the other way around.

[/quote]

What happens is that you have some relatively simple laws which govern the way things work. This is say…QM or maybe QFT. These laws can be solved in simple cases like a single particle etc. What happens however, as you add more particles, the problem becomes impossible to solve analytically.

Not “it’ll take some time but we can do it” but simply there doesn’t exist a solution. This is where the approximations come in.

In fact, some relatively simple looking integrals can’t be solved analytically…eg

Integral(cos(x)/x)

You must employ numerical methods to get an approximation.

[boomerlu]

[quote]NealRaymond2 wrote:
lothario1132 wrote:
Okay, hearing you. But what about my assertion that there is such a thing as the smallest unit of time? Isn’t the fact that there is such a thing as a “fastest speed” indicative of this?

By itself, I don’t think a “fastest speed” necessarily implies a smallest amount of time. The equation is distance divided by speed equals time (assuming that actually is the equation, and it doesn’t change under some extreme circumstance of which I am ignorant). Therefore, given a fixed upper limit for speed, if we assume that the distance could be as small as we want, then according to the formula the time could also be as small as we want.

On the other hand, if we assume a fixed upper limit for speed and a fixed smallest amount for distance, those two things together would necessarily imply a fixed smallest amount for time. (Imagine the formula for time expressed as a fraction, with the distance as the numerator and the speed as the denominator.)[/quote]

I think it’s been mentioned before, but this is where Heisenberg’s uncertainty principle comes in. hbar/2 <= delta x * delta p

hbar/2 is just a constant. Delta x and delta p are respectively the uncertainty in x and p.

In normal terms, this means that you can only measure up to a certain degree of accuracy. This I believe is where the Planck length and times arise.

ALSO, you have to realize that in special relativity, time and distance are the same unit, and the speed of light is defined to be 1. Actually Special Relativity is not that hard of a subject (I had it freshman year), and I recommend anybody interested to pick up a book and learn.

[Kailash]

[quote]swordthrower wrote:
I have no idea what you mean by a grainy nervous system… Are you referring to our role as observers, and the limitations of our senses?[/quote]

Yes. See the picture above. Imagine the large circle on the left is so large, that it looks flat. Just like earth was formerly believed to be flat by some peoples with shit for brains.

Now imagine the smallest circles (at right) are so small, that brushing against something on the scale of our nervous systems they appear like a flat, straight line. Just like atoms were formerly believe to be indivisble by some peoples with shit for brains.

Yes, anyone who believes in real limits has shit for brains, and that holds true still. The only thing limited is our perceptions, and to fall for that self-trick one might as well join the Flat Earth Society.

Just because science hasn’t yet shown proof, doesn’t mean that god didn’t give us brains with in-sight and a copy of the truth, now does it?

[quote]swordthrower wrote:
Why the mass difference between protons and electrons?[/quote]

Vive la Difference! It’s obviously so they’ll find each other sexy and be mutually attracted, for the purpose of breeding atoms.

[quote]swordthrower wrote:
Why the matter anti-matter asymmetry?[/quote]

Because there are more things “not in being” than there are “being”.

Imagine everything that “is”. Like dogs having one tail. Now imagine everything that “is not”. Like dogs with two tails, or dogs with three tails, four tails, five tails, etc. There’s a hella lot more in the second category, am I right?

[quote]swordthrower wrote:
Oh, and how does a forest resemble the tree?[/quote]

When realizing that the forest is only one tree!

[lucasa]

[quote]boomerlu wrote:
Lucasa, he’s right.

Mathematics can perform outside of physics, but physics must be described by mathematics.[/quote]

Untrue, for us to say we understand physics we need to be able to describe it. Many times physicists will invent new mathematics to describe physics.

Sure pi is incalculable, but it exists and the logic behind it is there. We could theoretically calculate pi to any degree of precision we need.

However, we cannot necessarily calculate it to any degree of precision to which it exists.

Also, no “true” circles exist. “Smoothness” or “circles” in a mathematical sense don’t exist in the universe. Sure we can well approximate most things as smooth, but in truth they are not.

1. Not strengthening your case any.

2. When you consider the vast scope and composition (circles need not be composed of matter) of the universe to assume there are no perfect spheres seems just as likely and an abundance of them.

You bring up the fact that “time is not invertible”. This is untrue, since given a function of time, we can easily invert to see how time relates to another quantity. Whether or not we can travel backwards in time is a completely unrelated issue.

It’s not unrelated at all and actually proves my point, mathematical manipulation of time and energy is easy. Actually physically doing it is not. It’s easy to calculate the energy to convert diamonds to coal and back, that doesn’t mean it can be done.

In addition, there are easily cases of uninvertible functions. Just Google it and see.

Sorry, the nomenclature can be fuzzy and I’m being presumptuous, I was referring to a one-way function and it’s yet to be proven whether they do or don’t exist.

One-way function

[lucasa]

[quote]lothario1132 wrote:
lucasa wrote:
What I really want to know is if we’re a great big movie, when is intermission?

This is a good question. How about these:

If we’re living in a computer game generated by the sickest, most ludicrously fast computer imaginable:

Do I get a saved game to revert back to after I die? Can somebody control-alt-delete us?[/quote]

Should I really be fragging as many people as I can?

Reminds me of an article I read:

Monday, December 1 12:01 AM EST
Half-Life 2 Physics Engine
Contains Grand Unified Theory
By David Olsen

Ithaca, NY - Physicists at Cornel-Putnam University (CPU) confirmed yesterday the Holy Grail of Physics, the Grand Unified Theory, is contained in the Half-Life 2 source code. For decades Einstein attempted to weave together all aspects of physics into one grand unified theory, and although he failed many physicists have continued his work, seemingly in vain.

The Half-Life 2 source code leaked onto the Internet by an unknown hacker last month after he or she compromised one of the computers it was stored on. This allowed physicists at CPU to analyze the revolutionary physics engine.

Dr. Harvey McLeod said in his statement early yesterday, “I overheard one of my students talking in class, about how he was playing the Half-Life 2 beta and how exact the physics engine was. I became intrigued. I didn’t think that a computer had the processing power to compute all the different physics equations quickly enough to animate the game flawlessly. I was right, they were just computing one equation.”

Game Engine Software Engineer at Valve, Jose Garcia discovered the theory. “The game engine ran too slowly. I was assigned the job of speeding it up,” he said. “I started out by combining some of the gravity equations with some of the other force equations and found it all started to fit together. After a day, I had fine-tuned the entire physics-animation functions down to four lines of code, which ran a bit faster,” he added.

Game Engine Development Manager at Valve, David Price released a press briefing later in the day accusing Dr. McLeod of “theft of intellectual property” and “releasing of a trade secret”. He went on to state the internal workings of the Half-Life 2 physics engine were the sole property of Valve. Any equations it contained, and anybody creating derivative works or publishing the equation in any way would be sued.

Clayton Wilkins, a lawyer for Dr. McLeod, argued the equation cannot be intellectual property because it “describes physics itself, which has existed for 14 billion years from the time of The Big Bang to the present. Dr. McLeod’s right to free press governs his publishing of the equation under fair use laws.”

Lawyers for Valve responded to the arguments by filing a lawsuit against Dr. McLeod and asking a judge for an injunction against his publishing of the equation.

Dr. McLeod was stunned by the news. “Where would physics be today if other fundamental equations were copyrighted? E=MC^2 Copyright Albert Einstein, 1917! What of physics? Every theory is built on other theories and if we are legally bound against using the grand unified theory our entire field is in a stalemate. It’s not like we can just find another ‘one equation, which describes all of physics’ there is only one! There can be only one!”

Valve deferred all further questions to their legal department.

http://www.bbspot.com/News/2003/12/valve_unified_theory.html

[boomerlu]

[quote]lucasa wrote:

Untrue, for us to say we understand physics we need to be able to describe it. Many times physicists will invent new mathematics to describe physics.

[/quote]

Yes, physicists will “invent” new mathematics, but physics will always exist within the “realm” of mathematics. There is nothing in physics that some kind of mathematics does not describe. Whether or not we’ve invented the math is different and only a practical matter.

On the other hand, there is some kind of mathematics that doesn’t have any physical basis.

[quote]lucasa wrote:

However, we cannot necessarily calculate it to any degree of precision to which it exists.

[/quote]

Your argument as I saw it was that there is physics that math can’t describe. You then cite the fact that we can’t “calculate pi” yet it exists in every circle.

You’ve got it backwards. “Calculating pi” is a physical limitation, not a mathematical one. Mathematically, it exists to infinite precision. Given infinite computing power, you could determine pi to infinite precision.

[quote]lucasa wrote:

Also, no “true” circles exist. “Smoothness” or “circles” in a mathematical sense don’t exist in the universe. Sure we can well approximate most things as smooth, but in truth they are not.

1. Not strengthening your case any.

2. When you consider the vast scope and composition (circles need not be composed of matter) of the universe to assume there are no perfect spheres seems just as likely and an abundance of them.

[/quote]

1. This indeed strengthens my case. Basically it means that math conjured up something that doesn’t exist in the physical world.

2. Yeah, you are right that this is actually debatable. Let’s assume that the Planck length IS a limitation. Then you cannot draw or even have a perfect circle, as a circle is continuous, but such a length scale is discrete (ie not continuous).

Supposing however that the Planck scale is not a limitation, you are right on this point.

But, nobody knows for sure.

[quote]lucasa wrote:

It’s not unrelated at all and actually proves my point, mathematical manipulation of time and energy is easy. Actually physically doing it is not. It’s easy to calculate the energy to convert diamonds to coal and back, that doesn’t mean it can be done.

In addition, there are easily cases of uninvertible functions. Just Google it and see.

Sorry, the nomenclature can be fuzzy and I’m being presumptuous, I was referring to a one-way function and it’s yet to be proven whether they do or don’t exist.

One-way function

[/quote]

At this point, I think you are just contradicting yourself.

Some things are mathematically easy, yet physically hard. That’s exactly what I was trying to say.

Thus physics exists within the bounds of mathematics.

Math takes some assumptions and tells us what MUST be true if those assumptions are true. These assumptions don’t have to be physically tied to anything.

Physics is a matter of finding those assumptions which pertain to our universe. We may have to “invent” some math along the way, but the world already obeyed the math.

[onewall]

I think your starting formula,
speed = distance / time is not correct. I don’t know much about this, but I believe that according to Einstein’s special theory of relativity, in a moving frame of reference, length’s contract, i.e. the ‘distance’ in your formula should not be a constant.

[pookie]

[quote]Kailash wrote:
The point is that there are dimensions of scale too small or too large for humans to access.[/quote]

How do we know about them then?

This is because our nervous systems are either too “grainy” or too “fine”, and our instruments themselves suffer from this same limitation, since they eventually have to connect to these limited senses.

That doesn’t really make sense, does it? An electron microscope can render viruses visible. And while my naked eye will never be able to see a single virus, I can see it fine if I use an electron microscope to look at it. For a simpler example, I cannot feel the magnetic field of the earth; but by using a simple compass, I can not only detect it, I can use it to orient myself.

You seem to be under the assumption that our instruments must necessarily suffer from the same limitations as our senses do. That’s simply not so. If something can be detected in some way, we can build an instrument that will detect it and present the information in a manner accessible to us.

Radio waves, infrared, X-Rays, radar, etc. The electromagnetic spectrum is filled with wavelengths we can’t perceive with our senses. Yet, we know the other wavelenghts exists and we use them daily for miriads of uses. Never directly with our senses though.

Therefore, “microaliens” COULD abound.

Well, yes. So could invisible pink unicorns or out-of-phase flying ninja monkeys.

My question is why should we accept their existence? If there’s no way to confirm their existence, either directly or indirectly, then whether they exist or not is inconsequential to us and assuming they don’t prevents useless clutter in our theories.

That they probably do abound is not so essential to this point, which defers “grainy time” to be mere perceptual limitation.

Actually, grainy time is a consequence of our best current theories to explain “reality.” Those theories may be wrong, but for now, they’re the best we’ve got. Simply dismissing them because “grainy time” bothers you is not actually science. If you can present a better theory, one that explains everything QM does and then some and involves larger/smaller dimensions, then we may have something.

But - If there’s one thing that we can learn from observing nature, it’s that everything is somehow fractalline.

Not really, but let’s move on…

A section of a tree resembles the entire tree. The tree resembles the forest.

A branch with leaves does ressemble a smaller example of a tree. I don’t think a forest looks like a tree. A forest looks like a group of trees; not like a tree itself. A forest doesn’t have “a trunk” or “branches” or “leaves.” It’s just an area of ground covered by trees.

Even inorganically, the mountain side has rocks of similar slope and a gem is made of similarly shaped crystals, right on down to the molecular level.

Not really. At least, not unless you really try hard to see the patterns you want to see.

But even if it were true that nature is always self-similar at all scale; that still doesn’t mean that there isn’t a smallest and largest scale.

And so you are likely considered a cluster of universes, to those in other (smaller) dimensions. And they can’t even see through, to each other, haha!

I could imagine a different model of universe/metaverse/multiverses every day for the rest of my life. That doesn’t mean that any of them actually reflects reality.

Isn’t this shit grand?

I think it’s just shit.

[rawda]

[quote]pookie wrote:
Kailash wrote:
I used to call that my “microaliens” theory. That we are microscopic aliens to beings of a different dimension (that is, too a large for our nervous systems to register) just as we are populated by infinite levels of microaliens of smaller dimensions (being too small for our nervous systems to register).

Since there’s no way of registering those smaller/larger alien beings, then there’s no way to tell if they’re actually there or not. Correct me if I’m wrong.

If there’s no way of detecting the presence of those smaller/larger beings at all, why suppose that they exist? Why invent undetectable entities that have no interaction with this universe? What benefit does it bring? Is it simply because the concept of infinite regression towards smaller and smaller / larger and larger universes is somehow pleasing to you?

[/quote]

if certain physicists had used that line of reasoning, they would have never discovered quarks.

[brucevangeorge]

[quote]if certain physicists had used that line of reasoning, they would have never discovered quarks.
[/quote]

I believe in male and female atoms and when they get together… they make electrons which are just baby atoms.

Fuck the microalien theory! This is where the shit’s at!

[lucasa]

[quote]boomerlu wrote:

Yes, physicists will “invent” new mathematics, but physics will always exist within the “realm” of mathematics. There is nothing in physics that some kind of mathematics does not describe. Whether or not we’ve invented the math is different and only a practical matter.[/quote]

Doesn’t this agree 100% with what I’m saying? Just because we can’t divide something by nothing doesn’t mean that there isn’t concepts out there to describe it and physical phenomenon to perform it?

You’ve got it backwards. “Calculating pi” is a physical limitation, not a mathematical one. Mathematically, it exists to infinite precision. Given infinite computing power, you could determine pi to infinite precision.

If infinite calculating power doesn’t exist physically, this would conscribe the existence of pi to finite precision, no? Thus, physics bounding mathematics? I guess it would depend more on your definition of the word ‘exist’…

…But, nobody knows for sure…

I can agree on this, and I think until something unheard of happens wrt things like P=NP and Godel’s Theorems, we’ll just have to leave it there.

[pookie]

[quote]rawda wrote:
if certain physicists had used that line of reasoning, they would have never discovered quarks.[/quote]

Huh? Care to explain why, because I can’t understand your reasoning here.

Quarks were first theorized (in the 1960s) and then later confirmed when predicted particles where detected in experiments. The existence of quarks seemed probable from certain analysis of the existing theoritical model at the time. There where two competing theories, if memory serves, with the term “partons” (ie, “parts” of elementary particles) being used. I believe those two theories where eventually merged and led to modern quantum chromodynamics.

Quarks are not the result of physicists believing in infinite regression towards the small, they are accepted because the theoritical models that posits their existence made predictions that went on to be verified.

Quarks, as “small” as they are, leave detectable signs of their presence. Micro/macro aliens (and their supposed universes) do not.

Microaliens “theories” predict nothing and have no way to be experimentally confirmed. (Sadly, it has much in common with String Theory) That’s why quarks are accepted and microaliens ridiculed.

[JonP]

[quote]lothario1132 wrote:
swordthrower wrote:
Ok kids, here comes the disgruntled physics graduate student…

First of all, the Planck time has nothing to do with the speed of light directly. It really has to do with reconciling gravity with quantum field theory. The fundamental “Planck” quantity is the Planck energy, which is the energy at which quantum field theory breaks down becuase gravity starts to have a non-negligible effect. A complete description of quantum gravity would be required, which we don’t have right now.

The reason this is an interesting quantity is becuase it really is a maximum energy that a photon can have, because if it had any more, it would create a particle massive enough to become a black hole. Therefore, bye-bye photon, and no observations can be made.

Using the uncertainty principle, you can derive the Planck scale, or Planck length, which corresponds to the Schwarzchild radius of a black hole of the Planck mass.

I think everyone also needs to be reminded that physics is a mathematical description of reality, and any non-mathematical speculation, while useful from a pedagagical or philosophical perspective, is not scientifically valid.

P.S. I just checked out the Wikipedia entry for the Planck scale, and it’s pretty good. Take a look.

Planck units

Okay, hearing you. But what about my assertion that there is such a thing as the smallest unit of time? Isn’t the fact that there is such a thing as a “fastest speed” indicative of this?

Or is my caffeine buzz just making me even more full of shit than I normally am? :)[/quote]

First, your entire theory is based on the assumption that if there’s a max speed there must be a minimum speed. A doesn’t necessarily follow from B. It’s something that sounds good, but has no logical basis behind it.

Second, the limit isn’t even on speed, but on energy. The reason you can’t go faster than the speed of light is because your mass increases with speed and at the speed of light your mass would be infinite meaning the energy required to accelerate you further would be infinite. Like how your tires on your car only go as fast as your engine can push them.

And the whole micro-alien thing is highly unlikely. First they’d be smaller than any wavelength of light or any soundwave so they’d all be blind and deaf. There’s also the whole issue of what possible energy source could they use and a host of other problems that take this theory from ever being taken seriously.

[Dr_E_Nigma]

OK, looks like I need to step in again and explain a couple things concerning maximum and minimum speed.

First we need to re-visit the Planck squat. If you are unfamiliar with this movement, please re-read through this thread. Now, maximum speed is the rate at which the person will get buried under the weight if they accidently perform the movement for a ROM larger than the Planck distance. Conversely, the minimum speed would be the rate at which they would return to standing following the previous movement. Therefore, the maximum speed would be the eccentric portion and the minimum speed would be the concentric portion. Hope this has helped shed some light on the situation.

[Split]

thats why they say if you can go faster than the speed of light you can travel time, however time does not even exist it is just a word humans made up ;o

[gendou57]

You can’t divide by zero for a very simple reason.

Let x and y be numbers not equal to zero such that

x=y/0

So x is the value of y divided by zero. This is the same as saying

0x=y

But we all know that anything multiplied by zero is zero. This violates our assumption that neither number is equal to zero.

Now, for fun, lets define x and different way.

x=0/0

This yields

0x=0

Now this is correct, but what is x? Well, it could be anything, now couldn’t it, since every number multiplied by zero is equal to zero. This solution is not solvable to a single solution. Hence why, if you ever took calculus, you always had to put up with a ton of crap when using the definition of derivative to keep the limits from all approaching zeros.

Now, as to whether or not you could divise a system of numbers that would allow you to divide by zero, I suppose it would be possible, but only by sacrificing other important properties of numbers.

Oh, look, wikipedia!

Division by zero

-Gen (Mathematics is the foundation from which all science is raised) to the Dou

[chillain]

I just skimmed this thread, and I did seem some really good posts. I’ll add the following, which are mostly on-topic:

-The experimentally confirmed phenomenon of time dilation, based on the effects of gravity on spacetime and maybe also the inverse relationship between speed and time. (two twins, one stays on Earth and one leaves on a rocket ship that travels near the speed of light and later returns to find the Earthbound twin has aged faster/is older)

-The weak anthropic principle: as incredibly miraculous as our observable universe seems, its physical laws and constants must eventually allow intelligent life to evolve and observe this universe. So then, is our universe really that miraculous after all?

I highly recommend Paul Davies’ works: God and the New Physics and About Time among others.

[boomerlu]

[quote]lucasa wrote:

Doesn’t this agree 100% with what I’m saying? Just because we can’t divide something by nothing doesn’t mean that there isn’t concepts out there to describe it and physical phenomenon to perform it?

[/quote]

Well if there are concepts that exist that describe dividing by nothing, then it is allowed by math. Whether or not the physical world obeys THAT math is different. Actually, I think the mathematical systems that physics is based on don’t allow it.

Now, if there exists the concept of being able to divide by zero, as somebody posted, then it is possible MATHEMATICALLY.

Here is the key. As long as the math allows it, the physics is possible. Not necessarily true, because the math behind the physics must obey the physics (note, that isn’t to say all math must obey physics, just the math we choose to describe the physics).

As far as inventing math, technically that math always existed, we just hadn’t discovered it. So if we find physics that isn’t described by current math, we “invent” new math, but that doesn’t mean we “created” new math, rather we simply discovered it. Again, the underlying math was always there.

[quote]lucasa wrote:
If infinite calculating power doesn’t exist physically, this would conscribe the existence of pi to finite precision, no? Thus, physics bounding mathematics? I guess it would depend more on your definition of the word ‘exist’…
[/quote]

It’s a physical limitation on our abilities to calculate pi, which doesn’t limit the infinite precision of pi itself. It just means WE can’t hold in our minds infinite precision of “pi”. Here you are mistaking computation for logical reasoning.

And again, don’t ignore the fact that there is plenty of math that doesn’t rely on physical reality at all.

[boomerlu]

[quote]gendou57 wrote:
Now, as to whether or not you could divise a system of numbers that would allow you to divide by zero, I suppose it would be possible, but only by sacrificing other important properties of numbers.

Oh, look, wikipedia!

Division by zero

-Gen (Mathematics is the foundation from which all science is raised) to the Dou[/quote]

Yup, abstract algebra, the math which doesn’t have a physical basis.