Relativity, Einstein, Discover Magazine and Constants

So Discover magazine has a special “Einstein Issue” this month which I bought at the airport. I don’t normally read Discover, but found this issue unclear - it was a superficial lauding of the man and genius, but any attempts to explain relativity were thin at best. But it got me thinking about two questions:

1. Why does time slow when one approaches the speed of light? - so, I am driving a car at, say, 95% the speed of light. I know that, to my eye, light beams that I am racing will still be moving away from me at the speed of light relative to my point of observation and that time for me is slowing to enable that. But how does that work - if I am moving at a fixed percentage less than light, then at time x, I will only be 95% as far along (95 miles vs. 100 miles) and so on. How does time slowing down for me reconcile with the mathematical distance separating us and enable light to still be observably moving at c?

2. the Speed of light as a universal constant - it’s weird, but I am wondering if this analogy works: As a musician and music fan, I started with rock music. With rock, the bass drum (and sometimes snare) keep time; listen to them and you have the “constant” to focus on and figure out the rhythm. When I first heard jazz, I couldn’t “find” it, until I realized that (usually) the hi-hat cymbols were used by jazz drummers to keep time. Hi-hats are the constant for jazz I could fix on to “find” how jazz makes rhythmic sense. I wonder - is that similar to how scientists had to re-calibrate their thinking for relativity? Did Newtonian physicists key on time as the constant and then have to fix on light as the constant instead?

For number (1), this explanation of time dilation might be helpful:

thanks Liberal - interesting stuff, but doesn’t get at my question. I will try to rephrase:
Again, let’s say I am travelling at 95% the speed of light. That implies to me that, regardless of the time that passes, at any spot in elapsed time, I will have travelled 95% as far as the light beam I am racing. Therefore, how does time slowing down enable it to appear to me that light is still travelling at c relative to my position - no matter what, I will still be 5% away, but it appears to me that light is travelling at a much faster rate - a distance much greater than our 5% difference would be covered by light travelling at c away from me, right? That is what I cannot reconcile…

You’re forgetting about frame of reference – in your frame, you are not moving. You move at some fraction of the speed of light only in some other frame of reference. In both frames, light travels at c, and the apparent paradox is resolved by time dilation. There is also length contraction and mass, um…embiggening, which keep straight the other details that are bothering you (and which have similar math – all three are called Lorentz contractions).

That’s my point Nametag - I am fully aware of what you describe; I have read it in a bunch of Relativity explanations over the years. My question is: how does time dilation reconcile the paradox??.

I try to explain it to myself and have trouble: "okay, so in my frame of reference, I am stationary and light is moving at c away from me, so, even though I am travelling at 95% the speed of light, because time dilates…well, what if it does? I am still a set, quantifiable distance away from the light beam I am chasing, aren’t I (e.g., if moving at 95% the speed of light, I am 5% less along at any point in time)? I know that can’t be right, but, based on what I have read - and it’s been a lot - I can’t make this work in my head…

Thanks for trying and please continue if my question makes sense…

I’m not an expert, but I think of it this way:

Let’s say you’re on a rocket, and I’m on the ground. From my perspective, you are travelling parallel to a beam of light, and you are going 95% of the speed of light.

From your perspective, after 1 second the beam of light is ahead of you by 186,000 miles. From my perspective, it would take 20 seconds for the light to get so far ahead of you. This is resolved by time dilation, because 20 seconds to me is the same as one second to you.

To us in the lab (the at-rest reference frame), it’s true that the ratio of your distance from us and a light pulse’s distance from us will be fixed at a constant 95%. I’m assuming we’ve arranged things so that both you and the light pulse begin your “race” at the same time and place, the lab.

In your reference frame things are different. The lab is moving away from you in one direction at 95% c, and the light pulse is moving away from you, in the opposite direction, at 100% c. If you tried to compute the same distance ratio that we in the lab are watching, you might naively come up with 0.95ct / (0.95ct + 1.00ct) = 0.487. However, this ratio isn’t especially useful for anything.

If you and the light pulse are racing toward a particular destination (is wagering allowed?), say a star 10 light-years away, then to us at the starting gate the light pulse will make it in 10 years, and you’ll make it in 10 / 0.95 = 10.53 years.

In your frame however, the distance to cover is dilated. The distance between the starting line (the lab) and the finish line (the star) is shortened by a ratio of 3.2, to 3.12 light-years. By your observations then, the light pulse finishes the race in 3.12 years, and you finish it in 3.29 years. The ratio of these times is still 0.95.

Was that Scientific American actually? Or are both magazines celebrating Einstein this month?

Basically yes, I would say. Einstein was trying to make sense of Maxwell’s equations as they apply to a photon of light (among other things). The equations as given would tell you that photons should cease to exist in their own reference frames — the electric and magnetic fields, which reinforce each other’s mutual oscillation, would vanish. Einstein made the bold move to assume that Maxwell’s equations needed no adjustment, and that ordinary space and time were the things needing an overhaul.

A silly idea, were it not demonstrably true.

I meant contracted, sorry.

You might try Scientific American. They also have a special September issue devoted to Einstein.

Not sure I fully understand your question, but time does not slow down for you. You don’t notice anything different. Someone observing you from a reference frame that is “stationary” will observe you as if time had slowed down.

I don’t understand your lead in about rock and jazz, but your last sentence seems to be right. Newtonian physics assumes that time moves forward at a constant, unchanging rate. Experiments in the late 19th and early 20th centrury showed that the speed of light was invarient, and Einstein reconciled that by showing that time was, in fact, not constant.

Bytegeist - I am almost there; your explanation hits it. My last question is: Why is the distance “dilated” from 10 light years to 3.12 light years? I am assuming that this dilated distance is what keeps light moving at c away from me - the shorter relative distance “enables” light to be moving at c away from me??? Did I just answer my own question?

yes - it is definitely Discover, so both it and SA must be in sync…

And thank you for speaking to my music analogy - it helps me understand given my music brain…

Thanks!!

This won’t explain the “how or the why” of Relativity Theory, but this page (my website) shows the formula and has a calculator for computing time dilation, Lorenz contraction, etc.
http://www.1728.com/reltivty.htm

…and this page has some good derivations of the Lorentz equation et al, that may help with the “how” and “why” behind the math…

http://www.geocities.com/physics_world/sr/sr.htm

I think you did, but I’ll answer anyway, because I love seeing my name in pixels.

As you’ve read, there are two counter-intuitive distortions that you’ll observe when moving with respect to other objects: (1) lengths and distances are shortened along your direction of motion (though not perpendicular to that direction), and (2) time slows down for other objects; they age more slowly than you. The coefficient for both these distortions, usually symbolized by a Greek gamma, is the same, and is a simple function of the speed. (See Wolf’s page, the very top.) The example speed you tossed out was 0.95c, for which gamma is about 3.2.

As to why all this happens — the big “Why”, as in why are things this way, and not some other way — that’s harder to answer. Well, harder for me to answer anyway. Einstein was led to it by his assumption that the speed of photon is a constant for all observers, which indeed turns out to be the case. There are other confirmations as well, such as the extended lifetimes of unstable particles moving at near light speed. (That wasn’t seen until later though.) Once you accept that objects moving at a particular speed are moving at that speed for all observers, regardless, well then, you know your simplistic Galilean model of space and time needs rethinking.

Others have mentioned some good web pages. I’ll also recommend the book Relativity Visualized by Epstein, which sits on my shelves even today.

Cool - thanks. Consider it bought.

Gargoyle
Impressive website.
Seems you got the explainables and I got the calculables. … oh sorry - had a “Dubya” moment there. You realize this may be the first time “Dubya” and Relativity Theory have been mentioned on the same page?

Okay, I just thought, since we’re talking about Einstein, might as well bring in the legendary E=mc² equation. Of course there’s a web page calculator for that:
www.1728.com/einstein.htm

I’m confused…I thought that if a person travels close to the speed of light, time speeds up for other objects, and other people age more quickly. That’s why, in science fiction, when a space traveler returns to Earth everyone else is long dead. Also, I thought that it was the acceleration relative to a certain eference frame that causes the time dilation, and not the actual speed one is traveling at. Thus, photons, which do not have to accelerate, never experience this dilation–only matter does.

read: “It’s a rag, but this time particularly bad.” I wanted to pit Discover for this particular “Special Issue” because I’m a subscriber and I though it was completely lame and inadequate at clarifying what A.E. was about. Usually it’s a decent enough source to keep your eyes trained on, if not hard, cutting edge science at least what’s up in multiple disciplines.

MaceMan
Yes, you are right.
Quoting from my own website here:

www.1728.com/reltivty.htm

One thing that has always puzzled me about the space traveler case is why isn’t it symmetric. One of the basic underpinnings of relativity is the concept of, well, relativity. That is, why don’t things work both ways based on the reference frame you pick?

In the space traveler example, Dude gets in a rocket, heads towards Alpha Centauri at a high fraction of the speed of light. Then, he turns around and heads back home at a similarly high speed. Since he has been moving at a high rate of speed, the resulting time dilation causes thousands of years to have gone by on earth, while only handful of years have passed for Dude (considerably shorter than his lifespan.)

But, based on the whole notion of relativity, it is just as correct to say this: from the frame of reference of the traveler, the earth has moved away and returned at a high speed, while you (Dude the traveler) have remained still in your reference frame. So, given that all the roles are completely reversed, why doesn’t the time dilation happen the other way. Why doesn’t the earth return to see Dude long dead, while only a few years have passsed for the Earthlings? Or why don’t both points of view cancel out and cause the time to pass symmetrically (perhaps much longer than a simple *time time = distance / velocity * calculation would indicate) ?

I’ve always understood the notion of time dilation. Or maybe understood isn’t the right word. I’ve had it explained so much that I accept it as true without a fundamental understanding. I’m long past the point of trying to wrap my mind around the cause, and have moved on to simply accepting the results as dogma. But being an engineer, that bothers me. And my lack of a real understanding is probably what’s leading me to the paradox described above.

Anyone care to explain?