Can Objects Move with Complex, Infinity Velocities?

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Discussion Overview

The discussion revolves around the concept of whether objects, real or theoretical, can move with complex or infinite velocities as described by various mathematical functions of position over time, x(t). Participants explore the implications of different conditions on the derivative of x(t), including undefined, indeterminate, and complex values, and consider the physical feasibility of such motions in the context of theoretical physics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions if objects can have a velocity function x'(t) that is undefined at all points, suggesting that it is possible, citing Brownian motion as an example.
  • Another participant argues that an indeterminate form at one point is not possible, stating that physics does not align with such mathematical constructs.
  • There is uncertainty regarding whether x'(t) can be defined at some points but undefined in others, with one participant suggesting it may be possible.
  • One participant asserts that the speed of an object must always be real, challenging the idea of x'(t) having a range of complex numbers.
  • Concerns are raised about the possibility of velocities approaching infinity, with a participant stating that the speed limit of any object is the speed of light (c), thus ruling out infinity.
  • A follow-up question is posed regarding the continuity of x'(t) and its implications for the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of various velocity functions, with no consensus reached on the physical reality of such motions or the implications of complex and infinite velocities.

Contextual Notes

Participants highlight the distinction between mathematical constructs and physical reality, indicating that certain theoretical motions may not align with established physical laws.

madah12
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I know some people might think this topic is stupid but I am asking about it anyway.
Can any object real or theoretical move with a function x(t) where:
1_ x'(t) is undefined at all points
2_ x'(t) is an indeterminate form at one point
3_ x'(t) is defined at some points but undefined in others
4_ x'(t) have range of complex numbers
5_x'(t) approaches infinity
So can theoretical objects move with theoretical motion with such crazy velocities exists? if the velocity is infinity will an object exist in two places at the same time? can any real astronomic object move with such velocities because of effects of wormholes or black holes? Is it physically impossible within any universe for such motions to exist. If it isn't physically impossible is there a mathematical way to describe such motions?
I know I am asking about stupid stuff but it is just for curiosity.
Thanks for replying.
 
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The velocity is a smooth function F.A.P.P. (for all practical purposes) The mentioned artifacts can exist in limiting cases of physical toy models. They are not physical reality and never will be. Nature doesn't like divergences.
There are mathematical ways to describe such functions, but for these you need a deeper understanding of the types of derivatives that exist and the theory of measures.
 
I try to answer your questions:

madah12 said:
I know some people might think this topic is stupid but I am asking about it anyway.
Can any object real or theoretical move with a function x(t) where:
1_ x'(t) is undefined at all points
Yes, it can. Eg. Brownian motion,

2_ x'(t) is an indeterminate form at one point
It cannot. Physics is not mathematics

3_ x'(t) is defined at some points but undefined in others
May be.

4_ x'(t) have range of complex numbers
Speed of the object is always real.

5_x'(t) approaches infinity
No, the speed limit of any object is c. It cannot be infinity.

So can theoretical objects move with theoretical motion with such crazy velocities exists? if the velocity is infinity will an object exist in two places at the same time? can any real astronomic object move with such velocities because of effects of wormholes or black holes? Is it physically impossible within any universe for such motions to exist. If it isn't physically impossible is there a mathematical way to describe such motions?
I know I am asking about stupid stuff but it is just for curiosity.
Thanks for replying.
 
What about if x'(t) is not continuous?
 

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