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Since we live in a 4D world (3 of space and 1 of time, my question extends to more, if there are any) does this mean the only "thing" experiments measure are spacetime coordinates and the rest of the variables/quantities have to be calculated by the relation between the variables and spacetime coordinates?

Examples

  • Velocity can be easily calculated from position and time measurements
  • Kinetic energy
  • Charge (using Coulomb's law and measuring the distance between charges)
  • Mass (by measuring how the length changes for the spring)

Is there a quantity that can be measured "directly" without measuring position or time?

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  • $\begingroup$ I think you have to define your definitions of "directly" more rigorously for this question. A photodiode connected to a voltmeter. Is the photodiode enough to count as direct measurement? Or do you include the readout for human senses? And if you do, does it make a difference if it is a digital readout made of semiconductors vs an analog one made of mechanical parts? $\endgroup$
    – DKNguyen
    Commented Oct 1, 2021 at 21:49
  • $\begingroup$ And what constitutes "position" to you? Hear me out, You can measure current by running it through a resistor, and then measuring the voltage using nothing but semiconductors by amplifying it, and feeding it to an analog-to-digital converter which then drives an ADC. No mechanical parts and just choose an ADC architecture that does not rely on time measurements. For example, one relies on sampling the voltage with a capacitor and then redistributing it between capacitors of known ratios. Does locating charge in different places count as position when you don't care about distance? $\endgroup$
    – DKNguyen
    Commented Oct 1, 2021 at 22:01
  • $\begingroup$ I would challenge the assertion that spacetime coordinates are measurable. How exactly would you use measurements to determine your $x$-coordinate right now? Coordinates are arbitrary labels, and nature couldn't care less how we label things. If you can clarify what you really mean by measuring spacetime coordinates, then maybe that would help clarify the question overall. $\endgroup$ Commented Oct 1, 2021 at 23:27
  • $\begingroup$ @Chiral Anomaly. I agree that coordinates are just labels. What I mean here is that we choose some inertial frame and we measure coordinates wrt to it. $\endgroup$
    – mum
    Commented Oct 2, 2021 at 5:07
  • $\begingroup$ @DKNguyen but isn't current density just amount of charge passing through unit area per unit time so aren't we indirectly measuring drift velocity of charges? Though I don't really know how should I define directly. $\endgroup$
    – mum
    Commented Oct 2, 2021 at 5:18

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Measurements evolved when humans developed from primates and started cultivating to supplement hunting and gathering. Then it became important to have an exact definition of quantities of produce, dimensions of fields etc etc and the "money" for produce system developed.

Geometry with its theorems was the first modeling of nature ordering the measurements of fields and predicting new measurements. The coordinates as such are arbitrary, it is the mathematical functional relationships that constrain the model.

Your examples are examples of the use of a theoretical model that can fit the data and be predictive, using space and time coordinates. There are more sophisticated models that use energy and momentum to predict a plethora of data in complicated experiments.

The data are not only measurements of space and time, as discussed in the comments, there are now complicated methods of getting numbers by experiment that can be fitted with models, the models have to be predictive to have any validity.

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  • $\begingroup$ See for example this answer . physics.stackexchange.com/a/316004/244281 here we have to , in the end, rely on the measurement of radius of circular path of charge to measure momentum. Could you cite an experiment where we measure momentum or energy without actually using data of position ? $\endgroup$
    – mum
    Commented Oct 2, 2021 at 5:22
  • $\begingroup$ In accelerators, where the geometry is fixed and introduced into the programs that gather the detector signals, also with fixed locations, etc etc In the link you give, there are programs using already mapped locations , not measuring locations. $\endgroup$
    – anna v
    Commented Oct 2, 2021 at 5:39

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