Can you measure voltage along a wire a multiple points simultaneously?
Your question assumes 2 things.1) The signal is a constant current DC, typical for measuring ohms. 2) A low frequency ac signal, such that the wavelength is at least 20 times the length of the wire. I mention these first because your question also having simultaneous measurements at different points along the wire. With DC current and LF AC readings will be stable and predictable. Above a few hundred MHZ you will see dips and peaks in signal amplitude along the length of the wire, due to standing waves. If you keep the same sample points and increase the frequency these peaks and dips will move along the wire. At some point, when the wire is equal to 1/8th to 1/4 wavelength, grounding one end is a moot point because so much energy is radiant, and the very connections you make for testing begin to affect the signal. At some point your equipment becomes very expensive and you would use a spectrum analyser (about $30,000 USD) to probe the wires RF performance.Readings along the length of the wire will always be different as long as there is current flowing, whether its DC, or LF AC. HF AC or VHF/UHF frequencies will have peaks and dips in the signal, until your outside (too high or too low) of the resonant frequency of the wire.