Wave function, units in the argument

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Discussion Overview

The discussion centers around the interpretation of the wave function f = f(x–ct), specifically addressing the meaning of the minus sign and the role of the speed of light (c) in the argument. Participants explore the interchangeability of time and space in this context, as well as the implications of unit conversions in special relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant explains that time and space can be treated interchangeably if time is measured in appropriate units, specifically relating to the distance light travels in one meter.
  • Another participant expresses confusion about how multiplying time in seconds by the speed of light (c) results in a unit of time that corresponds to one meter.
  • A different participant challenges the notion that time and space are interchangeable, suggesting that special relativity involves transformations between inertial frames rather than a direct interchangeability.
  • One participant provides a link to a derivation of Lorentz transformations, implying that a proper understanding of these transformations is necessary for clarity.
  • Another participant uses an analogy involving a rod and a door to illustrate the concept of interpreting ct as a distance, suggesting that this interpretation can simplify the understanding of certain equations.

Areas of Agreement / Disagreement

Participants express differing views on the interchangeability of time and space, with some supporting the idea while others contest it. The discussion remains unresolved regarding the clarity of the relationship between time, space, and the wave function argument.

Contextual Notes

Participants have not reached a consensus on the interpretation of the wave function or the implications of unit conversions. There are also unresolved questions about the arithmetic involved in relating time and distance through the speed of light.

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I will be very grateful if someone could explain to me the following, in the most simple terms, f being a wave function :

" ...f = f(x–ct). Let me explain the minus sign and the c in the argument.
Time and space are interchangeable in the argument, provided we measure time in the ‘right’ units, and so that’s why we multiply the time in seconds with c, so the new unit of time becomes the time that light needs to travel a distance of one meter. That also explains the minus sign in front of ct: if we add one distance unit (i.e. one meter) to the argument, we have to subtract one time unit from it – the new time unit of course, so that’s the time that light needs to travel one meter – in order to get the same value for f."
 
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Starting from the beginning, where is the first place that you get "stuck", and why?

It will help people in giving you well-targeted answers, if you can be as specific as possible about what your difficulties are.
 
I guess I am stuck with the arithmetic : if I multiply time in sec. with speed c which is meters over second , how arithmetically do I get a unit of time corresponding to a 1 meter distance ?
 
I don't understand : ".. we multiply the time in seconds with c, so the new unit of time becomes the time that light needs to travel a distance of one meter." thank you if you can rephrase this for me !
 
Time and space are not interchangeable, all SR is is some transformations between so called inertial frames.

I think you first need to see a proper derivation of the transformations:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

We sometimes like to write our equations in forms applicable to all inertial frames. In that case sometimes people get loose and say distances are like c times time because in equation 29 above is invariant under such an interpretation.

Its like you have a rod too big for a door so you rotate it to fit through. The length of the rod hasn't changed - just its x and y coordinates. Same with equation 29 if you are being a bit loose in your thinking - thinking of ct as a distance makes the equation seem more sensible. Its just like the Pythagoras theorem of geometry but you have a minus sign. This is given the fancy name of hyperbolic rotation.

Thanks
Bill
 
:smile::smile::smile:
 

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