Revisiting the Definition of Speed: Is Distance/Time Arbitrary?

[Futobingoro]

1 universally relative second = 0 (second^2/segment of time) * infinite (segments of time/second)

So if you divide one second into an infinite amount of segments, then multiply by 0 time acceleration (s^2/segment), you get one second.

This operates on the principle that 1/0=infinity, so multiplying both sides by zero makes 1=infinity*0.

Mathematicians: don't despair, if division by 0 is in the problem proposed to me, multiplication by 0 is legal.

So in time acceleration, going from a standstill to motion involves an infinite increase in time relative to distance traveled.

 

[quantumdude]

Mathematicians: don't despair, if division by 0 is in the problem proposed to me, multiplication by 0 is legal.

Not when the other factor is infinite, it isn't. That's an indeterminate quantity.

 

[Futobingoro]

Infinity is definite because everything else is definite. Through deductive reasoning, one can subtract all the definite items and find an exact indefinite. There can only be one infinity, just as there can only be one place where an infinite indefinite belongs. Infinity exists because it belongs in the place where everything else does not belong.

One can define infinity just as one can "see" black.

If it is not finite, it is infinite. 1/0 is not finite, so it is infinite.

Square roots of negative quantities and similar "numbers" are intangible finite numbers.

Everybody knows that 1/0 and the tan (90 degrees) are infinite quantities.

 

[StatusX]

You can't just define infinity as "the only non-finite number". You need more axioms. For example, how would you know from that defintion that infinity>3, or infinity+infinity=infinity? Where does minus infinity fit in?

 

[quantumdude]

Infinity is definite because everything else is definite.

And q20[ruasvdojawro;mtf is definite because everything else is definite.

What's this got to do with what I said?

Through deductive reasoning, one can subtract all the definite items and find an exact indefinite. There can only be one infinity, just as there can only be one place where an infinite indefinite belongs. Infinity exists because it belongs in the place where everything else does not belong.

Take a course in calculus. Once you've done that, you will know how to deal with indeterminate forms such as the one you've presented here.

Two concrete examples:

\lim_{x \rightarrow \infty} e^{-x}x
\lim_{x \rightarrow \infty} x^{-1}e^x

Both limits lead to "0 times infinity". But when "deductive reasoning" (aka "L'Hopital's rule") is applied to them, you get two different results (zero in the first case, infinity in the second).

 

[FulhamFan3]

I think a better question is why isn't it d*t instead if d/t.

 

[jdm]

It is interesting to think of what d*t would mean physically, but it is mathematically in a different class from d/t or t/d so I cannot see it replacing either.

To clarify, d*t gives the area under a trajectory curve and d/t and t/d are rates of change of their respective trajectory curves.

That being said the implicit 1 in the dimensional expression (d*t)/1 is interesting. Also, 1/(d*t) is fun to think about. Any dimensional expression that couples space and time like d*t and 1/(d*t) is worth thinking about, especially as a possible fundamental unit in a background dependent theory.

 

[jdm]

Sorry, previous post should read background independent theory.

General relativity is a background independent theory, b/c the background is a dynamic part of the theory, not merely something the theory relies on for a frame of reference.

Newtonian mechanics is background dependent, b/c it relies on the presence of an
absolute space and time, sperate from the dynamics, that is used only as a refernece point.

A fundamental theory should ideally be background independent so that the existence of space and time can be explained, possibly as an emergent property of a more basic set of relationships (LQG), not just assumed as it is in a background dependent theory. For clearer, more intelligible discussions and explanations check out the relavant threads.

 

[jcsd]

Backgorund independce is over-hyped, to take soemthing that philosophically elegant and turn it into a physical requiremnt is going overboard. Many people would say that the geometricla treatemnt of gravity by theories like GR and LQG must ultimately fail at some point anyway and it seems entirely possible that in this case there could only be one possible background which makes the concept of background independence moot.

 

[Futobingoro]

When an object moves through space it does so as a function of time. That means that distance moved depends on the amount of time elapsed.
Now keeping that in mind, consider the inverse of that statement. For t/d to be valid, that would mean that the time elapsed in a given situation would depend on the distance covered. This is clearly absurd. Time contiues regardless whether you're standing still or running. It does not change depending on how much distance you've covered (notice how I say 'distance covered' and not 'velocity traveled at').

You attack t/d on the basis that traveling 5 meters does not determine the time elapsed. You are correct, but d/t is subject to the same limitation. Does traveling for 5 seconds determine the distance covered? Of course it does not! The other variable is required if the rate is to be found. D/T can not exist as a rate if elapsed time is not known just as T/D can not exist as a rate if distance is not known.
Many question t/d's ability to explain a static object's motion. The familiar d/t explains it: if a stationary person endeavors to move at his current velocity for one second he will move zero meters. The t/d view holds that if the same stationary person endeavors to move 1 meter at his current velocity he will wait for an infinite time period.
D/T answers the question: "How far does a stationary person move in one second?"
T/D answers the question: "How long does it take for a stationary person to move one meter?"
D/T has an advantage in that it better illustrates lower velocities, showing the viewer how the velocity approaches zero any time the graph approaches the x-axis.
T/D has an advantage in that it better illustrates higher velocities, showing the viewer how velocity approaches infinity as the graph approaches the x-axis.

 

[WarrenPlatts]

We need a new word for t/d. I propose "torpidity". Thus, a stationary object would have infinite torpidity; something traveling at an infinite velocity would have zero torpidity.

The weird thing, however, is if special relativity is true, a stationary object would not have infinite torpidity. Just as SR places a speed limit on how fast objects go, SR also places a torpidity limit on how slow objects go. At the speed of light an object travels 3 X 10^8 meters in one second. Thus, a stationary object would have a torpidity of 3 X 10^8 seconds per meter; i.e, a stationary object actually travels 1 meter in 3 X 10^8 seconds.

I think this explains the expansion of the universe.

 

[Son Goku]

The weird thing, however, is if special relativity is true, a stationary object would not have infinite torpidity. Just as SR places a speed limit on how fast objects go, SR also places a torpidity limit on how slow objects go. At the speed of light an object travels 3 X 10^8 meters in one second. Thus, a stationary object would have a torpidity of 3 X 10^8 seconds per meter; i.e, a stationary object actually travels 1 meter in 3 X 10^8 seconds.

Using t/d, the speed of light would be equivalent to 3.3x10^-9 s/m.
Meaning the minimum amount of time you can cover over one meter is 3.3 nanoseconds, which is equivalent to an upper speed limit.

A stationary object travels an infinite amount of seconds over every meter and in t/d notation this can be reduced to lower limit of 3.3 nanoseconds over every meter.
Which doesn't imply that a stationary object travels one meter every 3 X 10^8 seconds.

Another point is that in relativistic units t/d and d/t disappear.

So 300 million meters per second and 3.3 nanoseconds per meter both become just 1.

 

[Futobingoro]

This discussion needs more participation.

We must lower the torpidity of this thread if it is to move forward.

 

[hypnagogue]

I believe this thread has run its course.