Rates of Change and Multiple Dimensions

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Discussion Overview

The discussion revolves around the concepts of rates of change, particularly in relation to displacement, velocity, acceleration, and the nature of time and motion. Participants explore the implications of these concepts in both theoretical and conceptual contexts, questioning the relationships between them and the dimensionality of space and time.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that with each layer of change (e.g., displacement, velocity, acceleration), a new dimension is added, leading to the idea of infinite dimensions of space or time.
  • Others argue that time and motion are distinct, suggesting that time is not simply a measure of change in displacement.
  • A participant questions whether time can be defined as the rate of displacement, leading to confusion about the definitions of velocity and acceleration.
  • There are claims that acceleration is the second derivative of position, while some participants mistakenly refer to it as the third derivative.
  • One participant suggests that rates of change may be limited by the number of dimensions, questioning if there can be a rate of change beyond acceleration that is not instantaneous.
  • Concerns are raised about the speculative nature of some contributions, with calls for grounding ideas in established physics.
  • Another participant reflects on the challenge of contributing meaningfully without a strong background in physics, expressing a desire to understand mainstream concepts better.

Areas of Agreement / Disagreement

Participants express a mix of agreement and disagreement, with some supporting the exploration of rates of change and dimensions, while others challenge the validity of certain claims and the speculative nature of the discussion. The conversation remains unresolved on several key points, particularly regarding the nature of time and the dimensionality of change.

Contextual Notes

Some discussions involve misunderstandings of mathematical definitions and relationships, particularly concerning derivatives and their physical interpretations. There is also a noted tension between speculative ideas and established physics principles.

Who May Find This Useful

This discussion may be of interest to those exploring foundational concepts in physics, particularly in relation to motion, time, and mathematical representations of change.

  • #31
lekh2003 said:
I often hear of teaching tactics where people ask questions first and then the teacher begins the class.
That's far too vague to prove things one way or another. It is not unusual for a teacher to ask students to prepare questions for next lesson but then the questions need to be within limits and they will be the result of some targeted homework.
Anything else would be idle chat and would risk wasting the other students' time.
I have a feeling that the OP expects to get a deep knowledge of Physics without any of the graft. He is destined to be disappointed - like many other 'visitors' we have had to PF.
 
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  • #32
Dale said:
Ask as many questions as you like! The problem isn’t in questions, it is in speculation. Speculation does not accelerate education, we have tried.

What is the fundamental difference between a string and a wave?
 
  • #33
paulo84 said:
What is the fundamental difference between a string and a wave?
A string transports a wave. It can act as a medium.
 
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  • #34
paulo84 said:
What is the fundamental difference between a string and a wave?
Here we go; you have just made my point. Have you read about the two and what would your own conclusion be?
 
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  • #36
lekh2003 said:
A string transports a wave. It can act as a medium.

Thank you, I'm already more clear.
 
  • #37
Another question - is there a part in physics which deals with strings carrying beta waves? Hope I don't get eaten!
 
  • #38
paulo84 said:
is there a part in physics which deals with strings carrying beta waves?
What is a beta wave?
 
  • #40
Dale said:
What is a beta wave?

Sorry I meant beta ray. I could have sworn they were called 'beta waves' in school. Woops.
 
  • #41
I withdraw my last question.
 
  • #42
I'm starting to think Sophie is right.
 
  • #43
paulo84 said:
I'm starting to think Sophie is right.
Yes, @sophiecentaur usually is right!
 
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  • #44
Dale said:
Yes, @sophiecentaur usually is right!

That somehow doesn't surprise me. :) One final thought (for now) - lekh2003's answer gave me a very basic understanding of one aspect of string theory. A wikipedia article would have been far, far harder to decipher.
 
  • #45
paulo84 said:
OK, so time is change of displacement. Speed is change of change of displacement.
It has already been discussed, but IMO bears repeating. Time is NOT change of displacement. If s represents the displacement of some object, then a change in displacement is usually represented as ##\Delta s##. Velocity is the instantaneous rate of change of displacement, and can be written either as s' or s'(t) or ##\frac {ds}{dt}##. This last notation is the derivative of s with respect to t. "Change of change of <whatever>" is not good terminology. We always talk about the "rate of change" of some variable with respect to some other variable. In this context, the "other variable" is time.

Without getting too deep into the weeds of calculus (which is what we're really talking about when we are discussing derivatives), ##\frac {ds}{dt}## is defined in terms of a limit. IOW, ##\frac{ds}{dt} = \lim_{\Delta t \to 0}\frac{\Delta s}{\Delta t} = \lim_{h \to 0}\frac{s(t_0 + h) - s(t_0)}{h}##. Suffice it to say, that we can approximate the velocity by taking smaller and smaller time increments in doing the calculation.

Speed and velocity are different. Velocity is usually taken as a vector quantity, as it indicates a rate of motion in some direction. Speed, on the other hand, is a scalar quantity, with speed = |velocity|. A car's speedometer records the magnitude of the car's velocity, but doesn't indicate the direction.

paulo84 said:
Acceleration is change of change of change of displacement (or of distance, sorry I'm not sure whether acceleration is a vector or a scalar).
No, accleleration the rate of change of the velocity with respect to time. Again, if s is displacement, then s'(t) is velocity, and s''(t) or ##\frac {d^2s}{dt^2}##, also a vector quantity, as direction is significant.

paulo84 said:
It seems to me, with each new layer of change you're adding a new dimension.
No. Dimension has nothing to do with any of this.

paulo84 said:
Therefore there must be an infinite number of dimensions of space. Or am I getting space mixed up with motion?
Yes.
 
  • #46
I agree with most of your post, but I don't understand how that proves that time is not change of displacement. But as has been noted, I'm not a physicist, I really don't know what I'm talking about.
 
  • #47
I'm sorry. I just don't understand the difference between time and space. As far as I can fathom, they're the same thing.
 
  • #48
paulo84 said:
I'm sorry. I just don't understand the difference between time and space. As far as I can fathom, they're the same thing.
Duration is what clocks measure, distance is what rulers measure. Clocks and rulers are different. If you are getting so far out in the weeds that the distinction escapes you, it's time to come back to the house.
 
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  • #49
jbriggs444 said:
Duration is what clocks measure, distance is what rulers measure. Clocks and rulers are different. If you are getting so far out in the weeds that the distinction escapes you, it's time to come back to the house.

Thanks, I am able to distinguish between space and time for the practical purposes of everyday living. I stand by my point.
 
  • #50
paulo84 said:
I am able to distinguish between space and time for the practical purposes of everyday living. I stand by my point.
This is logically inconsistent. If they were the same thing then you could not distinguish between them.
 
  • #51
Which one of us is making a circular argument?
 
  • #53
OK. So should I give up?
 
  • #54
I retract my previous statement. I am not able to distinguish between space and time. I just think I can due to an illusion caused by consciousness.
 
  • #55
There is not much we can do to help you then. If you can’t even distinguish between a clock and a ruler then you will have a very hard time with physics.

I think it is time to close this thread. If you wish to learn physics then please open a new thread with a substantive question
 
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