# Quote about movement through spacetime that is confusing me:

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1. Apr 29, 2013

### VeryConfusedP

The quote is from Jake Goldberg's Albert Einstein: the rebel behind relativity:

p. 53: "As objects begin to move rapidly through the dimension of space, their movement throught the dimension of time must slow down, because no object can move through space-time faster than the speed of light."

So how does light's speed through spacetime dictate that bodies moving rapidly through the dimension of space must slow down in their movement through the dimension of time, relatively speaking?

2. Apr 29, 2013

### phinds

Using "the speed of light" in this context is misleading. It is not the speed of light per se, it is the universal speed limit which is followed by, among other thing, light. That is, it is not the "speed of light" that dictates this, it is the universal speed limit that dictates this, irrespective of light.

This is the fundamental basis of the "Twin Paradox", which you can Google if you are not already familiar with it. The traveling twin moves more through space and less through time than the stay-at-home twin, and thus is younger when they get back together.

3. Apr 29, 2013

### VeryConfusedP

Phinds:

First of all, thanks for your answer. Secondly, are you saying that the universal speed limit is the same as the speed of light but that using the phrase "the speed of light" in the aforementioned quote can be misleading to some?

Also, what kind of dog is that in your avatar? It looks like a yellow lab with some polar bear mixed in.

4. Apr 29, 2013

### phinds

Well, that's a bit backwards. The universal speed light is the fundamental thing. Light, and all massless objects, travel at that speed. That is, they "obey" the universal speed limit, so I wouldn't say "the universal speed limit is the same as the speed of light" rather I would say that "light obeys the universal speed limit. Saying the "speed of light" causes something implies that LIGHT has something to do with setting the limit, but it doesn't. The speed of light is an effect. The universal speed limit is the cause.

Great Pyrenees

5. Apr 29, 2013

### Staff: Mentor

This statement is actually incorrect. As objects begin to move rapidly through the dimension of space, their movement through the dimension of time actually increases also (by the relativity factor); this is because of the Minkowski metric, which differs from the Pythagorean relationship, in that it features a minus sign in the line element.

6. Apr 29, 2013

### PAllen

I don't believe Einstein ever said anything resembling this. Long after his death, some physicists have adopted an interpretation of SR that involves a constant 'speed through spacetime' of c. Other physicists find no value in this interpretation.

This statement is consistent with Brian Greene's approach to speed through spacetime which is based on a rearrangement of the standard Minkowski line element:

c^2 d$\tau$^2 = c^2dt^2 - dx^2 - dy^2 - dz^2

into:

c^2 (d $\tau$ / dt)^2 + (√(dx^2 + dy^2 + dz^2)/dt)^2 = c^2

or

√(c^2 (d $\tau$ / dt)^2 + v^2) = c

This is interpreted as the speed through spacetime is c, which is the sqrt of the sum of speed through time squared plus speed through space squared.

(In short, Brian Greene would agree with the statement Chestermiller finds false. However, I am one of those, like Einstein, who understood SR without ever introducing any concept of speed through spacetime. To me, looking at spacetime as a 4-dim geometry, speed through spacetime is as silly as asking what is the speed along a line drawn on a plane, in the context of plane geometry).

Last edited: Apr 29, 2013
7. Apr 29, 2013

### Staff: Mentor

This is not wrong, exactly, but it gives the impression that "speed through space" is not relative. It is. For any object with nonzero rest mass, there is some inertial frame in which it is at rest; so there is no absolute sense in which it is "moving through space". It depends on which frame you pick. The same applies to its "movement through time", i.e., to time dilation.

One can actually make a stronger statement than this; to the extent that an object's "speed through spacetime" can be defined (PAllen's post #6 explains how this works), it is *exactly* the speed of light; so not only can no object move through spacetime faster than light, no object can move through spacetime slower than light either.

But as PAllen points out, this whole business about "speed through spacetime" is not necessary; you can understand relativity and work out correct answers to any relativity problem without ever using it.

Looking up the book that you got this quote from, it appears to be primarily a biography, so I would not expect its treatment of the science to be very useful pedagogically. And if what you quoted is any indication, it isn't.