Can One Grasp Relativity Without Doing the Math?

[Reality Check]

If the math of Relativity is a credible and valid representation of reality then a non-math explanation of what the reality that the math represents should be able to be provided and understood.

The math of Relativity is a credible and valid representation of reality since we have many observations that validate it.
Whether there is a possible non-math explanation of math depends on the math. What is the non-math explanation of modular forms?

For SR we could forget about equations and present it as geometry. But that is maths too!

We could just state the results of SR as what the reality that the math represents:

• Nothing with mass can travel reach the speed of light.
• Objects without mass will travel at the speed of light.
• Time dilation happens.
• Length contraction happens.
• etc.

We could just state the reality is that the universe obeys the SR postulates and so there are the above consequences.

 

[Uncayimmy]

If the math of Relativity is a credible and valid representation of reality then a non-math explanation of what the reality that the math represents should be able to be provided and understood.

Should. That's the key word, eh? I'm more familiar with financial calculations and somewhat familiar with statistical ones. I think it can be very difficult to explain some of those concepts without showing the math, and by that I mean not giving example calculations as well as not showing the formulas. I've seen people get stuck over Annual Percentage Yield and Annual Percentage Rate. I've seen people perplexed over amortization tables. And let's not get into p-values and standard deviations.

I think physics is a lot more complex. The example calculations for APR and APY are not that difficult to grasp once I give you a chart showing simple interest versus compound interest. Show them that after a verbal explanation, and it starts to click. Explain relativity and then show somebody a Lorentz transformation, and you're likely to still get a glassy eyed stare.

 

[Uncayimmy]

I also think there are different levels of understanding, which is probably a factor in all this. Simply stating the "rules" that Reality Check posted is a very basic level. I think there's a scale that goes all the way up to what I consider "getting it" for lack of a better term.

I think most of us have had moments where we could work with something and then finally "got it" or had it "click" or some other moment where it all seemed to come together. It's like you repeat what you already know, but this time in italics. For example, when you learn that ^2 is squared and ^3 is cubed and then suddenly say, "right, it's squared like in a square and cubed like in a cube!"

To me when you really "get" something you can manipulate it in your mind and understand it from any point of view. Think of a cube. In your mind you can take a cube, rotate it on any axis and know what it will look like. You can imagine what you would see if you stood on any point on the surface or from any point within it. Now try the same thing with a human heart. Yeh, I know what a heart looks like and roughly what it does, but I don't fully get it.

Some of the people here seem to understand relativity like most of us understand a cube. I'm nowhere near that level. I wonder if you can get there without the math...

 

[The Man]

Vectors and vector addition is really not that hard to understand either it is just basically a triangle. The square of the hypotenuse (the resulting vector) is equal to the sum of the squares of the sides (or the orthogonal vectors being added). With the vectors being added tip to tail the resulting vector is directed from the exposed tail to the exposed tip of the vectors being added. Such graphical solutions, drawing the vectors in some unit of scale, can often be just as effective as actually doing the calculation.

 

[Uncayimmy]

Vectors and vector addition is really not that hard to understand either it is just basically a triangle. The square of the hypotenuse (the resulting vector) is equal to the sum of the squares of the sides (or the orthogonal vectors being added). With the vectors being added tip to tail the resulting vector is directed from the exposed tail to the exposed tip of the vectors being added. Such graphical solutions, drawing the vectors in some unit of scale, can often be just as effective as actually doing the calculation.

Did you understand this explanation before you ever did the calculations or do you explain this to people without doing the calculations?

Also, as someone else mentioned, that graphical solution is using geometry, which is math. And your explanation itself relies on math (sum of the squares). Of course, there's nothing wrong with that nor am I trying to be pedantic. I'm pointing it out because a lot of the discussions I see about relativity don't even go that far. It's all twins, rockets, garages, clocks and so forth. It's almost always the experts who bring in the math (be it simplified or complex), not the ones who don't seem to grasp it.

 

[The Man]

Did you understand this explanation before you ever did the calculations or do you explain this to people without doing the calculations?

Also, as someone else mentioned, that graphical solution is using geometry, which is math. And your explanation itself relies on math (sum of the squares). Of course, there's nothing wrong with that nor am I trying to be pedantic. I'm pointing it out because a lot of the discussions I see about relativity don't even go that far. It's all twins, rockets, garages, clocks and so forth. It's almost always the experts who bring in the math (be it simplified or complex), not the ones who don't seem to grasp it.

Indeed geometry is basically math, although some people seem to have less problem with graphical explanations then the mathematical ones and the graphical explanation often helps to better understand the mathematical one. For me trigonometry (in math) was before vector addition in (physics) and both were explained mathematically and geometrically. However even though such simplifications and explanations can help one gain a better understanding of the underlying relations it can also lead to additional confusion. For example the special relativity velocity addition you mentioned in the OP it is not a simple vector addition (as a trigonometric function) but an addition of hyperbolic tangents and trigonometry is a good place to start to try and understand the hyperbolic functions.


http://en.wikipedia.org/wiki/Velocity-addition_formula

http://en.wikipedia.org/wiki/Hyperbolic_function

Check out the animation in the following link for a graphical representation of both hyperbolic and trigonometric functions.

http://en.wikipedia.org/wiki/File:HyperbolicAnimation.gif

 

[Dorfl]

I think most of the "layperson" explanations confuse the issue too.

Can anyone explain to me how the "twin paradox" actually works?
Is the difference in age supposed to be from different acceleration or different velocities? I've heard the same thing explained both ways at different times. In other words, if the traveling twin flies away at 1g acceleration while the stay-at-home twin waits on a planet with 1g gravity, will they or won't they be the same age when the traveling twin returns.

The resolution to the paradox doesn't really have very much to do with acceleration at all. The formula for time dilation, which implies that they both should be younger than the other, is derived on the assumption that neither changes his velocity. Since one of them does, you have to do slightly more complicated calculations which end up showing that the travelling twin is younger.

Hm... Maybe it was a bit misleading to say that acceleration in unimportant, since it does depend on one of the twins changing velocity. My point is that it does not depend on the amount of change per unit time, just on the fact that he ends up going the other direction. It has nothing to do with the general relativistic effect of time dilation due to acceleration.

ps. Want to travel centuries into the future? Just become really acceleration-resistant, then travel in a circle at near c. You will age much more slowly than the rest of the planet.

 

[Dorfl]

If the math of Relativity is a credible and valid representation of reality then a non-math explanation of what the reality that the math represents should be able to be provided and understood.

Why? The reason people invented mathematics in the first place is that many things aren't understandable without it. I agree that the universe would be nicer if it were possible to understand it without doing mathematics, but it doesn't seem to care how I think it "should" be.

This is not a problem limited to SR. Most of modern physics can't be understood fully unless you are willing to do the maths. Does that make it invalid?

 

[Mojo]

I personally believe that we can go faster than the speed of light, we just have to find out how. At one time it was said that 15mph was the upper limit. So the same thing is happening here.

Ten points, plus a bonus for including a "they laughed at the Wright Brothers" argument.

 

[edd]

The maths, maybe arguably not so much, but that's not really a standpoint I'd back. The rigour in problem solving you learn along the way definitely is a help, however.

 

[Dancing David]

If the math of Relativity is a credible and valid representation of reality then a non-math explanation of what the reality that the math represents should be able to be provided and understood.

So how would you express the relationship of distance in Newton's gravitational theory without using math?
Or the Kepler relationship in elliptical orbits?

 

[sol invictus]

Gravity and acceleration are equivalent... to a point. It's actually trivial to determine the difference between a gravitational field and acceleration. The lines of force for an accelerating body are parallel yet for a gravitating body they point towards the center of mass. An accelerating body also has equal force at different altitudes where a gravitating mass does not.

A rotating frame has acceleration force lines that point towards an axis and have a strength that varies with distance from it. And gravitational field lines do not usually point to the center of mass (center of mass of what?).

Not only is it not "trivial" to tell acceleration and gravity apart, I don't think it's possible at all except in very special cases.

As for the OP, I think the answer is that you can understand something but not everything, and you will much more often be wrong. Knowing the math means you can check your intuition, and so eventually your intuition matches the math (more or less). Not knowing the math means that's much harder to do.

 

[ponderingturtle]

I personally believe that we can go faster than the speed of light, we just have to find out how. At one time it was said that 15mph was the upper limit. So the same thing is happening here.

After all, rules and traditions are made to be broken.

This is not likely. We can accelerate things to near the speed of light and then add a lot of energy to them and they do not go beyond the speed of light. This along with many other predictions of SR are well studdied and shown to be accurate. As one of the other predictions is that you can go backward in time if you go faster than light there are some very good reasons to think that this will not change.

The distinction is of what is possible vs what can be done practicaly. It is different saying that you do not think there will ever be an engineering solution to X as opposed to thinking X is impossible because good well tested theories that are tested in the region of X have shown that X is impossible.

For example I think it would be nice if we could find a material that screens out gravit so you would float over a plate of it. I can think it would be nice to find that, but I know that it would never be something that could be made.

 

[ponderingturtle]

If the math of Relativity is a credible and valid representation of reality then a non-math explanation of what the reality that the math represents should be able to be provided and understood.

Depends, when people talk in non math they often draw analogies. These can be useful but they can also be confusing. I think this is because language is not as precise as math and if you are describing it fully you are describing all the math, so then why not just use the math?

I will also add that the math in SR is basic high school geometry and algebra. You do not need a lot of math background to understand the math of SR. SR is difficult because people try to intuit the answer, and not sit back and trust the math. Well using non mathmatical explanations removes the possibly to do the math and leaves just intuition.

 

[Cuddles]

As for the OP, I think the answer is that you can understand something but not everything, and you will much more often be wrong.

This. You can certainly understand some of the concepts of relativity without knowing the maths, but I've never seen anyone who couldn't do the maths who actually understood most of it, let alone all.

The problem, as with quantum physics, cosmology and many other things, is scale. Humans are evolved to understand the human scale. We can deal with millimetres up metres, milliseconds up to years, and speeds from stationary up to hundreds of miles per hour. All of our instinct, intuition and, importantly, language has developed in an environment where nothing happens on a relativistic or quantum scale. We not only don't have the tools built in to understand these things easily, we don't even have the tools to describe them.

And that's where maths comes in. Maths is, in essence, the tool we have developed to understand things that we have difficulty understanding. This is what people often fail to understand. Maths is not science. Maths is a language and tool used for doing science. And it is used because it is the only tool we've found that allows to actually understand large parts of science.

Just as you can't study the Bible seriously without reading the original words in ancient Hebrew, you can't study science seriously without reading the original "words" in maths. You can translate both into English to gain some understanding, but you will always lose something in the translation. Often the something that is lost is enough to make the whole thing meaningless.

 

[orange31]

It's actually easier to understand with the math, once I took the time to learn it (it's simple algebra).
Prior to that, I'd 'understand' it while reading the non-math explanations, like Brian Greene's. Then an hour later, I couldn't explain it to myself, let alone someone else.

http://meshula.net/wordpress/?p=222

 

[Dorfl]

A rotating frame has acceleration force lines that point towards an axis and have a strength that varies with distance from it. And gravitational field lines do not usually point to the center of mass (center of mass of what?).

Not only is it not "trivial" to tell acceleration and gravity apart, I don't think it's possible at all except in very special cases.

Really? I'd have thought that gravity would lead to field lines pointing in a way which simply wouldn't be consistent with any kind of acceleration, in nearly all cases. Of course, making equipment sensitive enough to tell might be near–impossible anyway.

 

[Ziggurat]

Not only is it not "trivial" to tell acceleration and gravity apart, I don't think it's possible at all except in very special cases.

I don't believe that's true. Local measurements cannot distinguish them, but there's no reason we need confine ourselves to local measurements.

 

[Bearded One]

Not only is it not "trivial" to tell acceleration and gravity apart, I don't think it's possible at all except in very special cases.

Don't worry, I'm not saying Einstein was wrong.

It's trivial if you can examine the situation from multiple points as I alluded to in my post. If you are limited to one point in space then you can't tell them apart. The very tall building is the easiest example. Gravitational fields fall off with distance but accelerating frames don't. The force of gravity on the top of a 100 story building is slightly less than it is on the first floor. If that building was in an accelerating frame then the force would be equal throughout the building. This doesn't go against the equivalence principle but it does expand upon it. The principle deals with experiments you can do within an theoretically infinitesimally small area.

It's another case of science educators trying to simplify things and in doing so eliminating some rather important aspects.

To bad it's not true, if it was we could handle huge accelerations just by building really long spaceships.

 

[Speed of Light]

In my experience, it is the other way round -
I've had discussions with people who are well versed in the maths, and when I've tried to discuss it on the intuitive or logical level, all they've done is quote one formula after another, to try to illustrate things -
So in my experience, formulae may be a good tool, but it is also a crutch, which enables them to work out things without any real philosophical or logical understanding.of what is actually going on.

I have a question - If teleportation ever became a reality, would we end up travelling backwards in time?
Would this be a way of building a time machine?