In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin.


Suppose Planck is in some frame of reference, moving at such and such a way relative to what he is observing (he's watching Bohr in this example)

Is whatever we work out about that frame of reference (e.g. his distance from Bohr after 3 seconds) only true for Planck, or is it also true for us, who are not in that frame of reference?

I ask because all the introductory literature uses phrases like

An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.


Which is also badly worded: substitute 'man' for 'subject'. However there are 6,000 hits for "at" physics" and 500,000 for "in" "physics". You'd have thought that "at" would be more suitable, if frames of reference can be accurately calculated outside them?

So I just wanted to check that what holds for Planck holds for us about Planck.

  • 2
    Question should be moved to the physics stackexchange. Also the answer is that of course you can calculate about a frame of reference you are not in.
    – causative
    Mar 9 '21 at 20:46
  • weird @causative ... it's too basic for physics stack
    – anon
    Mar 9 '21 at 20:47
  • 1
    It would sound strange to use "at."
    – causative
    Mar 9 '21 at 20:51
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    Some quantities in relativity are frame-invariant (like the proper time between two events on a given worldline), others are frame-dependent (like the distance an object moves in a given time). A frame-dependent quantity is only defined relative to a frame, but that doesn't mean there are truths that are relative to particular people--when physicists say something like "Planck's frame" that's just a shorthand for "the inertial frame where Planck is at rest", Planck himself has no obligation to use that frame when doing calculations, & no physicists judges one frame more "true" than any other.
    – Hypnosifl
    Mar 9 '21 at 22:17
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    As an analogy, if you have some curves on a 2D plane, you can describe them with different equations in different coordinate systems, like a polar coordinate system vs. a cartesian coordinate system, or two different cartesian coordinate systems with the x and y axes oriented at different angles. The equation for a curve is going to be relative to the choice of coordinate system, but that doesn't imply any differences of opinion about "truth", it's just a matter of description, like different systems of units (metric vs. imperial for ex.)
    – Hypnosifl
    Mar 9 '21 at 22:20

Suppose Planck is in some frame of reference, …

… who are not in that frame of reference?

I think you're confused about what reference frames are. A reference frame is just a coordinate system attached to (presumably all of) the universe, so it doesn't make sense to say that something is in some frame of reference or is not in another. One can define the position, velocity, etc of any object in any reference frame. For that reason, everyone with access to the relevant information will agree on the value of Planck's distance from Bohr after 3 seconds, in Planck's frame of reference, regardless of where anyone is in relation to Planck or Bohr. However, this does not mean that everyone will measure the same values in their own reference frames, just that they can apply Lorentz transformations to obtain the values in another reference frame, but details about that would be better suited for Physics.

  • It absolutely makes sense to describe an observer as being in one reference frame and not another. Different observers in different reference frames will measure different distances between Planck and Bohr. Whatever measurement tools they use won't produce the same number. They can convert between reference frames with the right information, but there's no reason why Observer A should agree that Observer B's measure is correct any more than Observer B should agree that Observer A is correct. How far away Planck sees Bohr is just treating all observers as being in Planck's reference frame. Mar 9 '21 at 22:18
  • @NuclearHoagie - "Whatever measurement tools they use won't produce the same number" That isn't exactly true, nothing is physically stopping Planck from using a system of rulers and clocks that are in motion relative to himself but at rest relative to Bohr, and if Bohr uses a system of rulers and clocks at rest relative to himself, they will both get the same answer to frame-dependent questions. It is merely a matter of convention that when we say "Planck's ruler" or "Planck's clock" it's normally understood that we're talking about a ruler and clock at rest relative to Planck.
    – Hypnosifl
    Mar 9 '21 at 22:58
  • @NuclearHoagie As I stated, while different observers may get different values in their own rest frames, they can still effectively take measurements in Planck's frame by applying Lorentz transformations to their measurements.
    – Sandejo
    Mar 9 '21 at 23:33
  • @Hypnosifl Right, it just strikes me as very weird to talk about an observer who is measuring things in someone else's reference frame - at that point, he's just an observer in the other frame. If Planck is using a meter stick in Bohr's frame, he's simply in Bohr's frame, since as far as Planck's frame is concerned, that meter stick is not actually 1m long. Mar 10 '21 at 14:17
  • @NuclearHoagie - But it's just a matter of linguistic convention that physicists use the wording of being "in" a frame as shorthand for "at rest in that frame", and likewise "Bohr's frame" as shorthand for "the frame where Bohr is at rest". Would you still find anything weird about the idea that Planck can use rulers and clocks moving relative to himself if we didn't have these linguistic shorthands? Can you phrase what you find weird about it without using these shorthands yourself? If not, it may just be a matter of the wording giving misleading intuitions about measurement restrictions.
    – Hypnosifl
    Mar 10 '21 at 17:27

Is whatever we work out about that frame of reference (e.g. his distance from Bohr after 3 seconds) only true for Planck, or is it also true for us, who are not in that frame of reference?

Length contraction formula Where v is the relative velocity between the observer and the moving object, and contraction is seen along the line of motion. So distance measurements can depend on relative motion.

What you need is the concept of invariance in physics. A good example is the speed of light in a vacuum, which is the same in all inertial (non-accelerating) frames of reference. This invariant speed doesn't cause conflicts with our experiences & our intuitions, until we approach speeds of the order of magnitude of light. When that happens, we find time isn't the same for all observers, and because of that we need transformations between different observers, that account for their changed clocks.

What has happened, is we had assumed a spacial symmetry, that speed looks the same for all observers plus or minus theirs in a linear way; and a time symmetry, that events can all be related to one clock regardless of speed. Then, we found at high speeds these linear symmetries-under-transformation between observer viewpoints, fail, and turn out to be linked, and high speeds relative to an observer cause some of the dimensions to swap so their combination keeps certain qualities, rather than each dimension we measure. There isn't space, and time, instead there is space-time. The space-time view is the same for all observers, but space & time may shift in related ways. This explorable explanation helps get an intuition for how things squash and rotate, and how event information moves.

Accelerated frames, involve forces, which means varying energy, requiring the energy momentum relation, which means general relativity. Then our intuitions become even less useful.

We thought we had some other separate things we can observe about a system, time-reversability, charge, and parity ('handedness'). It turns out these are also linked, in CPT symmetry, meaning one can be violated if one or more of the others is also, in a special way such that a combination of the three is still conserved.

Continuous symmetries-under-transformation and conservation laws, are related by Noether's theorem. Translational symmetry and conservation of momentum. Time symmetry and conservation of energy. Using this we can start to understand how time & space may not be 'out there', but be patterns of symmetry 'in' each local point. Quantum gravity theories like Loop Quantum Gravity build the dimensional symmetries from something simpler, a spin network of quantum information. It's not the only option, but space-time is expected not to be continuous, and must mesh somehow with wider quantum symmetries like CPT.

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