Relative Understanding

lorentz transformation

If you understand this equation, this post is not for you.

I’m not much of an aural learner, so in college I generally didn’t garner much from lectures. In physics, I made it to class about three times (five, if you count the exams), preferring to learn from the textbook. The professor was incredibly dry, but he was a smart guy. At one point, after one of the few classes I attended, I asked him if he could explain relativity to me.

“If a ten foot ladder is traveling at the speed of light, and it flies through an eight foot barn, the whole thing will be inside the barn at once.”

Earlier, in high school, my physics teacher had attempted to explain relativity:

“If you went on a trip into space and traveled close to the speed of light, when you arrived back on Earth, everybody you know would be dead and gone.”

After college, my cousin’s girlfriend tried to explain it to me:

“If there’s a clock orbiting the Earth, it measures time more slowly relative to a clock on the surface.”

OK, I was getting a little closer to understanding what happens, but not why it happened. When I asked Neil deGrasse Tyson about relativity,* he showed a picture of how gravity bends the spacetime continuum:spacetime

 

 

 

 

 

 

 

 

This gave me a better visual understanding of how relativity works. Gravity bends the spacetime continuum, thus slowing time down relative to areas of less gravity. So, if we were in space looking at a clock on the surface of the Earth, that clock would appear to be ticking slower. Conversely, standing on Earth, if we were to look at a clock floating in space, it would appear to be sped up.

But, as it turns out, this is only part of the picture. What Neil showed me was a representation of general relativity, which Einstein posited 100 years ago. Not that I understand much of what he was saying, but it was fun to read it in Einstein’s own words. The relativity of time due to gravity is called gravitational time dilation. But it doesn’t address the three explanations I had over the years of what relativity is – in fact, it seems to contradict my cousin’s girlfriend (blast you, Melanie!).

That’s because general relativity is different from special relativity. Why didn’t anybody tell me there were two different kinds of this shit?** Special relativity, introduced by Einstein 110 years ago, deals with all that velocity stuff. My professors and Melanie were talking about special relativity. According to this, time is also relative depending on the velocity (relative, of course) of an object. This is called relative velocity time dilation. If you have two clocks and you throw one, the moving clock will tick less time off than the stationary one. Relative velocity time dilation explains why a guy traveling close to the speed of light will find that all of his friends and family have long since turned to dust when he returns from his space trip***; and it also explains why a clock orbiting the Earth tells time slower than a clock on Earth (good job, Melanie!). The fact that the orbiting clock is moving faster than the clock on Earth outweighs the opposite effect of gravitational time dilation (depending on how fast it’s going, relatively). In fact, the cosmonaut Sergei Avdeyev has aged about 20 milliseconds less than the rest of us, due to his time zooming around the Earth at about 7.7 km/s on the International Space Station – he has, in a sense, traveled forward in time. Personally, I’m going to run everywhere I go now, to slow aging (that should add a nanosecond or two to my life relative to the rest of you slouches).

Another component of special relativity is length contraction.**** This means that a relatively fast-moving object will be shorter than it was at rest. This explains the ladder-in-the-barn trick, I guess. But it’s all about perspective, right? If you’re on the ladder, shouldn’t the barn seem smaller? (Whoops, just saw that this is called the ladder paradox and that I’m suffering from the mistaken assumption of absolute simultaneity – simultaneity is also relative.) OK, well, at the speed of light, does everything seem infinitesimal to an observer? Maybe photons are just ladders and space travelers and universes and whatnot zipping past and through us all the time.

So where does this all leave me? Relatively lost still. Why does gravity bend spacetime? How the hell does gravity even work? Why does time move more slowly the faster one goes (relative to a stationary observer)? Magic, of course – Bill O’Reilly and I can agree on that.***** I guess I’ll have to be content accepting what smarter people than I have figured out – if I can’t wrap my mind around four dimensions, how am I going to do with ten or 26 dimensions?

 

*OK, I didn’t ask him so much as watch one of his shows. And, just as Neil himself has a fallible memory, mine may be misremembering the actual host of the show, but it’s nice to think that it was Neil.

**Well, they probably did but, y’know, the whole aural learning thing. My wife needs to draw me diagrams to get me to remember to feed the kids when she’s gone.

***What if, relative to a third object (say, a distant planet), the space traveler is actually not moving at all, but the Earth and the distant planet are moving apart at almost the speed of light? Is it not then the Earth moving close to the speed of light, relative to the space traveler, so wouldn’t the Earthlings be aging more slowly? Does the space guy need to return to Earth (necessitating even faster travel relative to the distant planet) to realize his slower aging? Ahh, I guess this is called the twin paradox, and apparently I’m using an incorrect naïve interpretation of time dilation and relativity – somehow relativity of simultaneity and length contraction and separate inertial frames come into play, and this goes beyond my ability to comprehend. But it does seem dependent on the space traveler making the return trip, right?

****To tie this in with my last post, one might also call this shrinkage.

*****Neil deGrasse Tyson, not so much.

3 thoughts on “Relative Understanding

  1. For further research:
    learning styles visual auditory kinesthetic tactile

    An auodidact, I’m a visual learner and do well with written instructions.

  2. I ended up with a bachelors in physics, went as far as a class in quantum mechanics using Dirac notation. Wish I kept up on it, lose a lot of memory in a few years.

    I always remembered why you can’t travel faster than the speed of light. The law of conservation of mass energy gets involved. Mass increases as you approach the speed of light. As your mass increases it takes an increasing amount of energy to move you faster. the problem ends in an exponential asymptote, if I remember correctly, in which you can never actually reach the speed of light, just get infinitely close to it.

    But if you could bend spacetime at will, well then you could move faster than the speed of light, without actually moving faster than the speed of light by contracting and expanding spacetime around you.

    • Does that mean I can lose weight if I go really slow? I’ll give it a shot. If that doesn’t work, I may try bending spacetime and see if that helps me lose these last 5 pounds. (Or I could follow my own advice and stop drinking so many carbs.)

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