Is worldline a real, physical trace of an object or just an imaginary trajectory? And what is movement in spacetime?

Question

I'm not a physicist so all my understanding comes from educational content online.

I think I understand how transformations for switching perspectives between moving frames of reference work, and if this understanding is correct, it should imply that each object must exist at all times, forming a sort of "stack of frames" along its trajectory (worldline).

Here's my reasoning:

Imagine the example of two static light bulbs, A and B, some distance away from each other, that light up at the same time (from their perspective). From the perspective of a rocket moving away from them, the light bulb that is further away (A) would light up later than B, so the rocket will observe both light bulbs at slightly different moments in their lifetime.

If each object existed only at a single point in its time, that would be impossible: the rocket wouldn't see the bulb A when bulb B lights up, as bulb A would only exist in the future - the moment it lights up. In fact, a lot more things would break if that was the case; I had to ignore them to convey the idea.

If, however, each object existed at all times, this example would make sense: when the bulb B lights up, the rocket observes a slightly older version of the bulb A, while the version that lit up also exists in the future (and so does every other version of the light bulb across its worldline)

Questions

Is my understanding correct?

If it is, this rises another question: what is movement? It seems like objects are NOT moving along their worldlines, but just exist at all positions (on their woldline) simultaneously.

If an object was actually moving through spacetime, wouldn't "moving" mean that its position is changing over time? Wouldn't that require a second time?

Answer 1

Based on the comments, I will try and give some (extremely brief) insight on the everlasting dispute between imagination, linguistics, physics, and reality.

Physics provides frameworks whose job is to reproduce observations through the behavior of mathematical objects. By postulating some laws/constraints that restrict all the possible outcomes of a mathematical model, you can sort out all physically plausible outcomes and call it a theory that describes reality. \

If your framework gets more and more complex, you have to invent new maths, new terms that unambiguously refer to other objects.
We talk about "spin", "color" charge, "virtual particles" because they are terms that make sense to the human mind and carry a level of intuition that is coherent with the framework at hand, but they are NOT things by themselves. There are no balls spinning, no colored (in the electromagnetic spectrum sense) quarks, and no invisible, evanescent, wrong-massed things zipping around. It is just a way of expressing the framework through words that make sense.

It becomes even more complicated if your whole framework is embedded in four dimensions, which we cannot fully imagine. We can think of sections of 4d space changing, make animations etc, but it is NOT 4d space.
-"Movement" is the change in relative position, and it changes from observer to observer.
-Your last question implies the existence of a preferred, universal clock, which is the exact opposite of the principle of relativity.

You are trying too hard to understand these concepts through diagrams and simplifications. The future is not a place, it is a point in a dimension that stands at a certain distance FROM YOU. You and all other observers are moving in this 4d space, and the relative motion of each pair give rise to the weird observations we call "length contraction", "time dilation" etc. There is no rods being squished, and no clocks being slowed, just effects that are emergent from the framework, and that we experimentally see. The words and figure you use to get closer and closer to it are NOT the theory itself

Answer 2

Your understanding is not correct. You seem to be overlooking the transit time of light from distant objects. To illustrate the point, suppose your two bulbs A and B are a light-year apart and have clocks synchronised to Earth time. Now imagine that they each flash once on the first of January 2024. To an observer stationary at A, the flash from B will not arrive until the first of January 2025, a year after A has flashed. So the observer at A sees B as it was when it flashed a year earlier. In the meantime, clocks at B will have continued ticking, so that in the common frame of A and B it is the first of January 2025, Earth time, at both A and B when the flash from B arrives at A.

Now, imagine a rocket that is passing A when the flash from B arrives. The observer in the rocket sees exactly the same light as the stationary observer at A sees- ie, they both see B as it was on the first of January 2024 Earth time. Of course, in the frame of the rocket, B's flash might have occurred at some other date in rocket time, but that is just a labelling issue. The flash was the flash- it was an event at a given point on B's world-line. The fact that the event occurred on first of January 2024 Earth time, and on a different date in rocket time, is irrelevant- that just means that the same instant in time is labelled in different ways in each of the two frames.

Answer 3

I am kind of annoyed at how dismissive the people replying have been on you. Your ideas are not too bad.

I like to introduce beginners to relativity via Minkowski diagrams, and if you do it properly, you can see that your argument is not too wrong.

Let us start with only constant velocities. Then each observer has their own worldline = timeline. You can see them as moving forward in time at velocity $c$ if you so wish. Before you define the space surrounding the one observer you care about, these are purely moving forward in time, for some naïve understanding of these things.

Later, when you use clocks and mirrors to define space, you can then consider one observer observing another observer moving, and thereby obtain all the interesting stuff happening in Special Theory of Relativity. You can then see that observers are moving in spacetime, and the coördinate time i.e. the observer kept stationary at infinitely far away (so no interaction with anybody nearby) serves as the second time that you can use to quantify everything, if you want. It is just not as interesting as you might think. We tend to only care about the proper time as measured by each observer inside the arena we are looking at.

As for whether worldlines are imaginary or not, they should be imaginary, but approximately real. For example, you can predict that a clock will measure the proper time as its worldline would measure. In fact, each electron would have to have its own proper time, which is a headache that we have to actually compute when the spacetime is really curved. The atoms making up your head starting to feel different time from the atoms in your feet is the thing to study when we consider spaghettification when you fall into a black hole. Now, since each electron has an extended wavefunction and not just one point-like thing we can draw worldlines, there is a lot of digusting complications to take care of.

You can have a lot of fun with such views. But beware that it is difficult to get correct answers and stay within standard physics. It is very easy to make mistakes.