How can we have motion through time with Relativity?

Question

How can anything actually move through time if Relativity is correct? It seems everything is just a Lorentz Transformation to a different reference frame and 4D spacetime keeps track of all of these transformations simultaneously. The speed of light would then be the speed of the projector. It would be the fastest speed you could change reference frames.

So we would be projected through these different reference frames because we can't experience whatever time is in its fullness. So in 4D spacetime, all points we consider past, present and future exist simultaneously and they would be static points in 4D spacetime. We experience time from 3D from moment to moment but it only seems that way because we can only experience time within our 3D frame of reference but if you looked at our worldline from a higher dimension, you would see all points that we call past, present and future in 4D spacetime. Einstein said this in his book Relativity.

Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence.

So we don't move through time. We only change frames of reference in space. This would be why the faster you move through space the slower you appear to move in time but you're never moving through time. You just can't see all of time which includes all events we call past, present and future. You can just experience time from moment to moment which gives you the illusion of a passage of time.

Is this picture of Relativity correct?

Answer 1

Can you define what you mean by "project"? My answer is that we do move through time. First, an observer's worldline can be parameterized by its own arclength, the internal aging of the observer also known as proper time. So, in what I would consider the active picture of relativity, the observer's clock, like an odometer, reads out the arclength (proper time) of the worldline $$\tau_2-\tau_1=\int_{p_1}^{p_2}\sqrt{-ds^2}$$ between any two events as they actively move from the past event to the future event in spacetime along their worldline. I can assure you this is not an illusion because one actually experiences aging as one goes from an event to the next on their worldline. This picture is perfectly in line with the spacetime view.

This also relates to the universal speed limit in special relativity. Let $U$ be the tangent vector field along a worldline $G(\tau)$, then $ds=|U|d\tau$. But because the arclength is $\tau$ itself, the tangent vector has to be of unit norm (or the speed of light $c$ in the conventional unit system). This vector field is the 4-dimensional velocity of a massive particle, and its components can be written: $U^\mu = \gamma (1,u_1,u_2,u_3)$ according to an inertial coordinate system. Thus, the unit norm condition sets constraints on the speed of a particle. What you said about "the faster you move through space the slower you appear to move in time" follows immediately from previous results.

Actually, "moving through time" is perfectly in line with "changing reference frames". Consider the 4-velocity again. How is this vector field transported along a worldline? In general, if the acceleration is nonzero, the 4-velocity field would rotate because acceleration makes the worldline curve. Mathematically, (See Misner et al.(1973) P.170) this specific rotation is determined a 2-form $A_a\wedge U_b$ that is associated with a boost in the 4-velocity vector field. This is exactly the type of transformation between two reference frames that are moving relative to each other. So, I guess you could really see motion in spacetime as series of different frames that are, at each point on the worldline, characterized by a 4-velocity, which point in the direction of time, and three orthonormal spatial vectors, which could be three arrows that the observer is holding in front of their chest.

Answer 2

No, you have misunderstood the meaning of a reference frame. A reference frame is a set of four coordinates that are used to label points in spacetime. If you are coasting through flat spacetime (ie in a region of space in which the effects of gravity can be ignored), then you are stationary in your own spatial frame but moving directly along your own time axis at a fixed (from your perspective) rate. If I am moving relative to you at some fixed velocity, I too am stationary in my spatial frame and moving along my time axis, which will be tilted relative to yours (our respective time axes will only point in the same direction of we are stationary relative to each other).

The Lorenz transforms are equations that relate the coordinates of an event in your frame with the coordinates of the same event in mine.

You only change your reference frame if you accelerate.

When you say that all points in spacetime- whether past, present or future- exist simultaneously, you are either wrong or you are using the word simultaneous to mean something quite different to its normal meaning in physics.

Whether we actually move through time, or time is just a counter of change, is a matter of interpretation. As you say, we exist in the present. However, the idea of coasting through spacetime is an easy one to visualise. The present is wherever you happen to be, analogous to 'here' in space. The future is the region of spacetime you have yet to reach, and the past is the region of spacetime you have left.