# Why does moving through space at the speed of light automatically limit us from moving through time? [closed]

If I'm moving through MY reference frame at the speed of light, isn't time still passing by normally for me?

Help me think about this fourth dimension- space-time. I want to intuitively understand it. I understand some thought-experiments (Einstein's train experiment, for example, and why events occur slower/later for people that are farther away or moving from the event because of the infinitesimal amounts of time it takes for light to travel to them).

Another question I could ask here is what caused you to understand space-time when you finally got it (if you didn't immediately get it).

Thanks!

• You may not realize it, but your first question doesn't make any sense. In your own reference frame your velocity is precisely zero. From any other reference frame your speed will always be smaller than speed of light (because reference frames are defined by relative Lorentz transformation which only makes sense for speeds lower than speed of light). The second question is not a question at all. Think about what precisely you don't understand about space-time and then come back and make a concrete question. I am voting to close this one. – Marek Nov 25 '10 at 23:50
• I'd like to comment that thought experiments are a technique of limited value. No value, in fact, unless you have firm understanding of the math (and it's implication) that describes the stuff you're trying to think through. Einstein was able to Gedankenexperiment his way into relativity because he understood what Lorenz was saying about the symmetries of Maxwell's equations. Without that underling comprehension you're in a tough way. – dmckee --- ex-moderator kitten Nov 25 '10 at 23:54
• @dmckee: Not quite true. Einstein used his physical intuition in thought experiments long before he understood the maths problem! Admittedly, not everyone can however. He was a genius, and had a particular ability for thought experiments. – Noldorin Nov 26 '10 at 0:41
• @Noldorin: is that really so? As far as I know what dmckee's written is correct. Einstein was very familiar with electromagnetism and symmetries. Also his famous paper on foundations of SR is entitled "On the electrodynamics of moving bodies". It was no thought experiment. He was just extracting the relativistic content out of Maxwell's equations. I don't dispute the fact that he was a genius, but no physicist ever produced reasonable thought experiment out of thin air. – Marek Nov 26 '10 at 0:52
• @Marek: Noldorin is right that Einstein was running (hmm...the Real Experimenter in me wants that to be "running") thought experiments from early on. But they didn't lead to a theory until he had some math to hang them on. You could argue it either way. – dmckee --- ex-moderator kitten Nov 26 '10 at 1:00

I can answer both questions at the same time.

You have to realize that space-time is not merely space plus time. It's a unified concept, in which we create extra mathematical structures.

In particular, you may want to take a look at the definition of distance between events:

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$$

And start to ask yourself questions, like: what does $ds$ represent? What happens to $ds$ if an object is still with respect to the observer? What if the object is moving at the speed of light? What is represented by the locus of points defined by $ds=0$?

As noted in comments, your question is problematic because in your own frame of reference, your velocity would be zero. You will never see yourself moving at the speed of light.

There are a bunch of different ways to see that the speed of light is a limit, among them the fact that the relativistic velocity transformations prevent any object that is seen to be moving at a speed less than that of light from being seen at light speed by any other observer, the fact that an infinite amount of energy would be required to accelerate an object to light speed, and the fact that any object moving faster than the speed of light would create problems with causality, with effects happening before the things that caused them according to at least some observers.

The two best general books on Special Relativity that I've seen (and I've been reading a bunch of them as research for the book I'm writing) are David Mermin's It's About Time and Tatsu Takeuchi's An Illustrated Guide to Relativity. Both are aimed at non-scientists, but explain the underlying ideas in a really clear manner that can provide some additional insight even for physicists.

Here is my method for intuitively understanding space-time. Imagine you are holding a clock in front of you. At any given moment, you have the choice to allow the clock to tick at the correct pace (from your viewpoint) by holding the clock still, stop the clock by moving it at the speed of light, or somewhere in between. The "rate of observed time" is given by the Lorentz factor in all three cases.