Is there a mathematical symbol or formula for this physics-related concept?

Question

I hope I can express this concept. . . Is there a symbol or a mathematical symbol or formula that means the speed and the place something occupies is the same? I don't mean zero movement, but where something is going so fast that it is in all places at once? Is there a point where a distance becomes so small that velocity and place are one without relation to the particle size? The concept I think has been addressed in quantum physics, but I was just wondering if there is a mathematical symbol or formula to describe it. Thank you.

Answer 1

Indeed there is a way to express this concept mathematically! And it lies with our old friend, Albert Einstein and his special theory of relativity. Quantum Mechanics may also hold an answer, which I will also address, but I believe the proof that if you are going fast enough you can be everywhere at once is a predominantly relativistic convept.

You might think that to be in all places in the universe at once, you'd have to be travelling infinitely fast. This is not true; one need only reach the speed of light. Before I continue, let me remind you that this is inherently impossible - it would take an infinite amount of energy to accelerate a body to the speed of light.
Now, let's take a look at the length contraction formula, originally proposed for Lorentz:
d0 = d * sqrt(1 - v^2/c^2)
where d is an observed distance relative to an observer like us (assume stationary) and d0 is the same distance observed by an observer moving with speed v relative to the first observer.

Okay, now put v = c (the speed of light) in that formula. You will immediately notice that this reduces sqrt(1 - v^2/c^2) to zero, and thus d0 = 0. Hence, if an object is travelling with the speed of light (like a photon) then all distances in the universes become zero, and the object can be anywhere at once. (Of course to the observer at rest it is still only travelling at a finite speed, but the moving observer can be anywhere in the universe! It might sound weird how it could be one result for one observer and a different one for a different observer, but that's why it's called RELATIVITY - it's relative.)

So I think that answers your question from a relativistic standpoint. If you wanted to be thorough you could also look at the relativistic time dilation formula and show that it always takes no time to reach a destination if you travel at the speed of light.

Now onto quantum mechanics - in my view, this is definitely more of a wordy proof, given that the mathematics required to prove this concept are beyond all but the most brilliant minds in modern physics.
Briefly, all particles can be described by waves, or, in quantum physics, wave functions. A main characteristic of a wave is that in its true sense, it has no beginning or end, and permeates all of space. Although the maximum of a wave function may be localised, the wave function itself should never fall to zero amplitude. This corresponds to the statement that there is a finite proability of the particle being located anywhere in space.
However, notice that this does not necessarily mean that it is in ALL places at once, but merely ANY place at once; it could appear to be in multiple positions given the Heisenburg uncertainty principle, but certainly not ALL.

This is why, in my view, relativity gives a much more satisfactory answer to your question. Hope this answers it!

Answer 2

Not sure what you are saying, so I will go through the various possibilities.

1)Speed and place are both relative, so 'both are the same' does not exist.

2) Distance becoming shorter is Einstein, not QM, but I disgress. In General Relativity, yes, you can make is so that there is zero distance between two given point by moving at the speed of light, as per your observation. However, this is only in the direction of motion, so you would get a large flat plane, with only one point occupied, not all.

3) Is there a "distance becomes so small that velocity and place are one" .... nope, they are two entirely seperate things! You cannot mingle them! (If I recall correctly)

Answer 3

Heisenberg Uncertainty Principle

In quantum physics, the Heisenberg uncertainty principle or the Heisenberg indeterminacy principle — the latter name given to it by Niels Bohr — states that one cannot measure values (with arbitrary precision) of certain conjugate quantities, which are pairs of observables of a single elementary particle. These pairs include the position and momentum.

Mathematics provides a positive lower bound for the product of the uncertainties of measurements of the conjugate quantities. The uncertainty principle is one of the cornerstones of quantum mechanics and was discovered by Werner Heisenberg in 1927.

http://en.wikipedia.org/wiki/Uncertainty_principle

Answer 4

How else? Look a bit through the answers on this website. Most problems (even in the physics section) occur because people don't understand wath other people say. The language of mathematics is much more suitable for saying thinks so that they can only be understood in one way.

Answer 5

In quantum physics, particles are described by a "wave function". Indeed, any particle can be anywhere, but some places have a higher probability than others.

The shape of the wave function is related to the "state" of the partcle. For various states of the electron in the hydrogen atom, look here:
http://abulafia.mt.ic.ac.uk/Bulatov/gallery/qmech/hydr/index.html

Answer 6

you cannot go so fast that you exist in all places at once. theoretically, traveling at the speed of light would allow you to occupy all points in time (except the past) at once, allowing you to instantly reach the end of existance.

if you are still rying to think of something that allows you to be in a state of unknon position, you might be thinking about Heisenburg's Uncertainty principle. lookup "hyperphysics" in google and click the link. there will be some information about heisenburg's theory there.

Answer 7

Maybe you refer to Heisenberg's uncertainly principle.
The capital delta symbol, a triangle, means here:
"the uncertainly in"
delta position x delta speed > Planck's constant
Th

Answer 8

The attached site may help you - it explains the Lorentz Transformation and gives cool animated examples as well as formulas.

Hope that's what you're looking for!