# Q & A: time dilation, meaning of time

Q:
If nothing ever moved, changed, or decayed, would time exist? I recently had a discussion with my wife about what time actually was, and we came to the conclusion there is not a flow of time, rather time is simply a measurement of change. I've been puzzled by Einstein's theory that time slows as you approach the speed of light. Does this simply mean that matter traveling at a higher rate of speed changes less than that of matter at slower speeds? That seems counter-intuitive. And in a universe where everything is moving all the time, how do you accurately judge speed on a universal scale without a non-moving frame of reference?
- Nate (age 32)
Alexandria, VA
A:
Let me take your easier question first. We cannot and do not pretend to "judge speed on a universal scale". The basic assumption of Special Relativity is that you can describe things from the point of view of any inertial (non-accelerating) observer using exactly the same laws of physics. That means that any one of those observers could say with equal justification that he was at rest.

Now what happens to stuff that is traveling quickly, according to us? As you surmised, all processes on that traveler happen slow, according to our assignments of times to the events on the traveler. But wait- from their point of view, it's us who are traveling. Does that mean that from their point of view, it's our events (watches, heartbeats...) that are running slow? Yes, exactly. From your own point of view, it's them who is traveling fast, and that doesn't affect your clocks.

How  can that be consistent? If the observers have fixed velocity with respect to each other, the distance between them keeps changing. The lengths of time it takes to observe events on the other keeps changing. Each observer must allow for that length of time in calculating when things he sees happened at the other one. However, because each observer treats the signal as traveling at the speed of light with respect to himself, not the other observer, they disagree on those observation-lag corrections. The sum of that disagreement and the disagreement about how long the events are taking just cancels out. So it's all self-consistent.

Now you might wonder about observers circling each other at fixed distance, where the signal time doesn't keep changing. Something else must be going on. Yes- that's the path to General Relativity, also self-consistent but even stranger.

Finally, what about your philosophical question on the meaning of time? It sounds like you and your wife came to a nice working definition.

Mike W.

(published on 04/15/2011)

## Follow-Up #1: relativity: perception ot time?

Q:
Hmm.. I think I need to read up more on Einstein's theories because it's now starting to make sense. I think I had it backwards for quite some time. For some reason I was under the impression that his theory said if you traveled at the speed of light, you could sort of skip forward in time. As if the speed of light traveler would be removed from time(aka stop/slow changing) while everyone else moved through time at the normal rate. After reading your response I'm getting the impression that his theory describes more the perception time. I think I saw where you or someone recommended a book that explained the theories in more layman's terms. I'll have to find that again.
- Nate (age 32)
Alexandria, VA
A:
There are good introductory relativity books. One by my late colleague, James Smith, "Introduction to special relativity", is quite readable.

Just to be clear on the "perception" issue, relativistic effects are very real. To pick the standard example, muons have such short a half-life that, if they decayed at the stand-still rates, almost none would make it to earth from the upper atmosphere, where they are made by cosmic rays. However, plenty do make it here because they decay by their own rates, which seem slow to us.  From the muons' point of view, the earth manages to make it up to collide with them in their short lifetime only because the earth and its atmosphere have been flattened into a pancake by the relativistic length contraction. If the muons thought the atmosphere was as thick as we see it,  the earth wouldn't have time to get to the muons even traveling at c.

Mike W.

(published on 04/15/2011)

## Follow-Up #2: meaning of relativity applied

Q:
I actually want to follow up on this question, but I think I'm getting confused by the words being chosen. When you say "point of view", that means the same as perception to me. There is also other terminology that I think I'm missing like stand still rates. Does that mean that the muon(something I had to look up but I still don't think I understand) is decaying slower due to it's fast rate of speed, and if it were to slow it's travel, it's decay would increase in speed? You also confused me with what the muon's "thinking" due to the language implications. I looked up relativistic length contraction and I'm starting to grasp that, though I'm not sure why that would happen. My first inclination is to think of it like a pilot being compressed by the g-forces when at high speeds but I don't know if speed compresses you in the vacuum of space without gravity pulling on you. It also seems like the faster should look flattened to the slower, and the slower should look elongated to the faster, but from what you said it sounds like each looks flattened to the other. I guess this is the reason why everything comes down to math. Language is too messy. I got as far as calc 2 back in school, but once math became all math theory, my interest waned. I have this tendency to want things in black and white, right or wrong, works or doesn't. So if the theory didn't work every time, then it seemed wrong to me all of the time. I think i'm looking for the truth of the universe that noone has fully yet understood.I should go pick up that book because I need a better base of understanding to enter into discussions or questions on these subjects.
- Nate (age 32)
Alexandria, VA
A:
Before getting into the specific answers, here's perhaps a good way to start thinking about this. You know that when you look at a rectangular box from different directions, things like "width" and "depth" change. It takes some effort to figure out what is a matter of perspective and what is invariant, independent of how you look at it. For simple rotations of viewing angles, volume and area would be among the invariants and width and depth would be relative.

As you start looking at things from different points of view in motion with respect to each other, there are also quantities that turn out to be relative and ones that turn out to be invariant. Our gut instincts about this are summarized by the rules of what is called Galilean invariance. Those rules include that the distance between events is relative (Breakfast and lunch are at the same place, the dining car, in the train frame but at different places, Champaign and Chicago, in the earth frame.) They also include that the time interval between events is invariant, and thus that the speed of any object is relative.  It just turns out that those rules of perspective are false. The actual rules have different invariants (the speed of light is in, but the time intervals are out, etc.) It's not surprising that our instincts lock on to the simplest perspective rules which work well enough for small changes in motion, rather than the slightly more complicated rules needed to include larger changes in perspective.

By "point of view" we  mean "reference frame" or "coordinate system with oneself assigned the spatial coordinate (0,0,0)".

Your interpretation of what we meant about muon decay rate is exactly right. It's also a fully confirmed experimental fact. Sorry for getting cute about what the muon is "thinking".  What I meant would be "what a person traveling along with the muon and using that reference frame is thinking."

On the length contraction: Yes, each looks flattened to the other. Neither one is faster or slower in any absolute sense. Exactly the same laws of physics work for each observer. On the g-forces etc.- that's another topic, General Relativity, and not directly needed for our discussion here.

Mike W.

(published on 04/22/2011)

## Follow-Up #3: interpretation of Special Relativity

Q:
Special relativity has been proved beyond doubt, but the spacetime interpretation has not been proved. It looks like 4-dimensional geometry, and has internal consistency in places that make that look convincing. But there are too many unknowns to be sure about it, and the truth is we just don't know. To give an example of something that is absolutely central, but we don't know why it's there - the constant speed of c though 4 dimensions, which we find all matter has. When matter's speed is adjusted in one place, its time rate is immediately adjusted in a way that ALWAYS keeps the overall speed at c. That fact led us to the 4-dimensional geometry in the first place, but we have no idea why it's there. It just looks significant. But why is all matter moving at the speed of light through 4 dimensions? We have no idea.
- Ellen Davis (age 37)
Arizona
A:
I'm not sure what it means to say that SR "has been proved beyond a doubt" but not its spacetime interpretation. The spacetime description is just a mathematical rephrasing of the same content contained in the SR transformation laws. It's only a matter of taste whether you prefer that language.

I assume you're referring to the invariant  4-interval, c2t2-d2, when you write about "all matter moving at the speed of light", which it certainly doesn't. What your real point seems to be is that there's not a deeper theory from which the rules, such as that invariance, are derived. I suppose, with minor quibbles, that's true, but won't any description of nature reach a point at which we just say "them's the rules" without being able to go deeper, at least for a while?

Mike W.

(published on 06/11/2011)

## Follow-Up #4: relativistic

Q:
Yes, point taken that sooner or later we have to say 'that's just the way it is'. But some of the basis of the spacetime interpretation of SR is later shown not to exist - by that very picture. For instance, the idea that there is a moment called 'now' moving along through time at a given place in the universe was absolutely central to what gave us the 4-dimensional geometry. But by 1966 a proof of block time was published that meant there could be no moment called 'now', and no motion through time at all, and many decided it must be some sort of illusion. And yet it had led us to that point. Philosophers have been worried about this, but some think the arguments apply anyway. But like an electric drill that risks cutting its own power cable, the spacetime interpretation is in danger of being inconsistent with its own foundations.
- Ellen Davis (age 37)
Arizona
A:
I won't claim to understand that. The philosophical mystery of what constitutes now-ness in time is not removed by relativity. In fact, relativity tends to refocus our attention on that old problem.

Mike W.

(published on 06/13/2011)