Can One Grasp Relativity Without Doing the Math?

[Uncayimmy]

The question is in the subject: Do you think relativity can be grasped without doing the math? I ask because it seems like the discussions here so often revolve around semantics and thought experiments on the part of those who, IMHO, don't grasp the concepts. It seems rare to find someone confused about it when they can actually perform the calculations and/or do the light cone thing with ease.

I'm not saying that I personally grasp it, but I will offer that I didn't get the whole "you can approach the speed of light but never exceed it" thing until I saw the addition of velocities formula. I didn't actually need to crunch any numbers. Just by looking at it I could tell what I would see should I plug in some values and chart the data.

I'd be interested to hear the comments of those who have experience trying to teach the concepts to others, either formally or informally.

 

[RossFW]

I have no clue on the Maths of relativity, but can start with "Mass is energy, an object with more energy has more mass" and enterpolate most of the consequences, e.g as motion is relative, an object has different KE and therefore different mass to different observers, therefore will accelerate at differnt rates for a given force, which means each observer must be measuring a different time etc. etc.

I take it on faith (Dirty word here?) that the relative mass of an object approaches infinity as it's velocity approaches C, but have read enough about experiments confirming this to consider it proven.

 

[Bearded One]

I won't speak for general relativity but you can get a pretty good grasp of special relativity without doing a lot of math. Some math is required, but it's basic level. What is very helpful is drawing space-time diagrams because it helps you see visually exactly what is going on.

There are a lot of misconceptions about relativity and a lot of them are propagated by people who do know better but are trying to make it easier for the layperson to understand. Instead of helping they actually confuse the issue even more. For example, the statement that you can't go faster than the speed of light because it would take an infinite amount of energy. That only applies to the outside observer yet that fact is not usually mentioned. It leads people into believing there is some sort of "brick wall" that you will come up against that will prevent you from going any faster.

Hollywood seems to have fallen for that misconception hook line and sinker. Thus we get spaceships with "speed gages" that climb quickly at first then start to move slower and slower as they near "light speed" until they stop just before the mark and no matter how much they gun the engines they go no faster. This also leads to the misconception that all we have to do is "jump over the hump" to break the light speed "barrier".

The truth is that no matter how hard you try you can never go any percentage of the speed of light. If you had a gage that registered your speed as a percentage of light speed it will always be stuck on the zero peg. That's the fundamental problem/concept.

Speed only makes sense when compared to other things/people.

 

[ben m]

Speed only makes sense when compared to other things/people.

That's true, but that is not why you can't go faster than light.

 

[Bearded One]

That's true, but that is not why you can't go faster than light.

I didn't imply that it was but I now realize that by putting that sentence at the end I could be adding to the confusion. The phrase "you can't travel faster than light" is not very informative. Perhaps "You can never appear to travel faster than light" might be better.

 

[Brian-M]

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?

Another one that confuses me is the one about two spaceships traveling towards each-other at a high fraction of the speed of light. If each traveler observes the other through a telescope, for both travelers time appears to be moving faster for the other person than it is for them.

My question is, what has this got to do with relativity? If both ships are traveling towards each-other, the time it takes light to travel from one to the other is constantly shrinking due to diminishing distance. Two events a set time apart will appear to happen closer together simply because it takes less time for the light to cross the distance for the second event than it did the first. An illusion explainable with Newtonian physics, but I've heard it being used as an example of the strangeness of relativity.

(Sorry for the rant, these things have been bugging me for a while.)

 

[Paulhoff]

Why can’t you one and/or anything go faster than the speed of light.

Well, let’s try to make that as simple as possible. OK, let’s look at something simple, a hydrogen atom, which has just one proton and one electron, we will not worry about the quarks and gluons that make up the proton. Now what makes the electron stay with the proton, it is an exchange partial called a virtual-photon, virtual because it is not seen outside the system of the atom. This photo is used to attract the two partials together and travels between the two partials and it travels at the speed of light and no faster. We will now make the hydrogen atom move thru space, has it moves so does the virtual-photon, the virtual-photon must now move between the electron and photo and also move along with the two, it now has less time that can be used as an exchange partial. So now, let’s pretended that we can make the hydrogen atom move at the speed of light. Now that virtual-photo total speed in the direction of the atom, it has no speed left to move between the two partials, time for that atom in a sense has stopped, the proton and electron can’t talk to each other. You can also take this idea to the proton and the quarks and gluons that make it, the gluons again travel at the speed of light. Also you can take that idea to everything else, time has stopped for anything moving at the speed of light because there is no speed left for any movement in any other direction.

Paul

 

[Eyeron]

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.

 

[JHGRedekop]

The question is in the subject: Do you think relativity can be grasped without doing the math?

You can get a basic outline, but as Mark Chu-Carroll says at the Good Math, Bad Math blog, the worst math is no math. The most common reason why someone is an "Einstein was wrong!" crank is that he doesn't understand the math, or thinks the math is unnecessary. (The same goes for many other types of "<famous scientist> was wrong" types.)

 

[ben m]

Two events a set time apart will appear to happen closer together simply because it takes less time for the light to cross the distance for the second event than it did the first. An illusion explainable with Newtonian physics, but I've heard it being used as an example of the strangeness of relativity.

Nope, that (as you've stated it) should never be used an example of special relativity. The interesting relativistic time-dilations and simulteneity-changes are there after you've accounted for any signal-travel delays.

 

[Bearded One]

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?

I'm not going to go to deep here because frankly I'm not motivated enough this evening and I feel rather stoopid today. It does seem to me that you are mixing some things up here. You may be confusing the equivalence of gravity and acceleration with the explanation of the twin paradox. The time difference occurs because one undergoes an acceleration whereas the other doesn't. Which one does determines who is going to be younger. The gravity field and the actual acceleration do not relate in this example.

Another one that confuses me is the one about two spaceships traveling towards each-other at a high fraction of the speed of light. If each traveler observes the other through a telescope, for both travelers time appears to be moving faster for the other person than it is for them.

My question is, what has this got to do with relativity? If both ships are traveling towards each-other, the time it takes light to travel from one to the other is constantly shrinking due to diminishing distance. Two events a set time apart will appear to happen closer together simply because it takes less time for the light to cross the distance for the second event than it did the first. An illusion explainable with Newtonian physics, but I've heard it being used as an example of the strangeness of relativity.

I seem to relate better to things moving apart. Get away from me Universe!

The essence of these "thought experiments" is that any effects from the limited transmission speed are already eliminated. That alone doesn't explain the results anyhow. Simply add the phrase "after all speed of light delays are taken into account" to the description of the problem.

The one thing a lot of people don't seem to grasp about relativity is that it affects apparent simultaneity. We are used to living in a world in which the concept of a moment in time can be defined using external events. We tend to define moments in time by what events occurred simultaneously within that moment. For example, I sneeze and at the same time a batter in New York hit a ball and an astronaut on Mars kicked a rock. We would tend to say all those events occurred at the same "time". Once again, all light travel times are taken into account. Truth is that to another observer, say one moving through the Solar System at 90% of light speed relative to the Solar System, those events would occur at different moments in time. They would not be simultaneous to that observer. Therein lies the essence of almost all apparent "paradoxes". They only appear to be paradoxes if you consider simultaneity to be absolute.

The barn and pole paradox is probably the easiest to explain. The story goes that you have a barn 10 meters long and a pole 11 meters long. If things really do appear shortened at high velocities you should be able to move the pole fast enough to get it contained entirely within the barn at the same time. At that time you should be able to close doors on the barn and trap the pole in the barn without damaging the barn.

The experiment works as far as the observers at the barn are concerned. They wait till the pole is entirely within the barn and cycle the doors. the pole is trapped and the barn survives. (These doors open and close real fast BTW)

The problem is that from the poles POV the doors were not closed at the same time. As the pole approaches the far door it closes and the pole is still sticking out the back. Then the far door opens and the pole starts to exit the barn and only after the front of the pole is already outside of the barn does the back door close. Yet the folks by the barn insist that doors opened and closed simultaneously.

Time is not as absolute as it may appear.

 

[athon]

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.

People often tend to see science as a static philosophy, meaning the perspectives we once held which turned out to be false equally mean we could just as easily be wrong today. In truth, given the progress of science as a methodology, it is less likely that we are wrong today about certain accepted theories than we were in the past.

The 'we once thought we could go no faster than X' is thrown out there as often as Lord Kelvin's 'heavier than air flying machines' gaff. We can always find somebody who makes a bold claim. In truth, there was never any theoretical model proposed that limited speed. There was a fear amongst the layman during the 19th century (when engineers were competing in building the fastest locomotive) that believed at a given speed, it would be impossible to breathe. Yet science literacy being what it was back then, common thought was far from the same thing as an educated statement on what was and wasn't possible.

Certainty has no place in science. However, if put logically, we could exceed the speed of light only if certain laws we have deduced turn out to be completely wrong, or if we discover a new field of science that creates an exemption for those laws (such as the sci-fi notion of hyperspace). We have no reason to suspect either is the case.

Athon

 

[Dancing David]

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.

Not by today theories.

Mass increases as one approached c therefore the energy required to accelerate further increases. Otherwise particle accelerators would break light speed all the time.

 

[Brian-M]

The gravity field and the actual acceleration do not relate in this example.

I thought the equivilance principle meant gravity and acceleration was the same thing. Let's move the stay at home twin off the planet and try again...

You're saying that if the stay-at-home twin lived on a space-station rotating fast enough for it's occupants to constantly experience 1g of acceleration and the traveling twin was in a space-ship constantly accelerating at 1g, both twins would remain the same age?

 

[Paulhoff]

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.

One cannot get one electron to go faster than the speed of light. 15 mph is not a physical speed limit, the speed of light is.

Paul

 

[Bearded One]

I thought the equivilance principle meant gravity and acceleration was the same thing. Let's move the stay at home twin off the planet and try again...

You're saying that if the stay-at-home twin lived on a space-station rotating fast enough for it's occupants to constantly experience 1g of acceleration and the traveling twin was in a space-ship constantly accelerating at 1g, both twins would remain the same age?

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.

The real point is that none of that has anything to do with the twin paradox. Gravity does affect time but that is not significant to the twin paradox. When people say the acceleration is key they are not referring to the equivalence principle. They are referring to the fact that one person goes through an acceleration phase (has momentum applied) compared to the other person that doesn't.

 

[Bearded One]

The 'we once thought we could go no faster than X' is thrown out there as often as Lord Kelvin's 'heavier than air flying machines' gaff.

I will add: Much of that had to do with short sighted views on the limits on engineering. We always knew heavier than air things could fly, birds do it. We also knew things could go faster than the speed of sound, bullets and whip tips have been doing it for a long time. The issue was whether we could ever actually build something that could do it.

In the case of the speed of light we have observed nothing that can do it. At this point in time, considering our current understanding of the Universe, it's not just a matter of insufficient engineering skills, it's a matter of it being a logically impossible situation. It's a true paradox to science right now. Not just an apparent paradox, a real one. It creates the potential for backwards time travel or at least communication. We just can't handle that right now with our current science.

 

[ynot]

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.

 

[Wowbagger]

I think Brian Greene does a relatively good job, without a lot of math. He uses a lot of Itchy & Scratchy, instead.

 

[The Man]

The question is in the subject: Do you think relativity can be grasped without doing the math? I ask because it seems like the discussions here so often revolve around semantics and thought experiments on the part of those who, IMHO, don't grasp the concepts. It seems rare to find someone confused about it when they can actually perform the calculations and/or do the light cone thing with ease.

I'm not saying that I personally grasp it, but I will offer that I didn't get the whole "you can approach the speed of light but never exceed it" thing until I saw the addition of velocities formula. I didn't actually need to crunch any numbers. Just by looking at it I could tell what I would see should I plug in some values and chart the data.

I'd be interested to hear the comments of those who have experience trying to teach the concepts to others, either formally or informally.

No, unfortunately I do not think it can. Certainly generally relativity takes more complex math to gain a good understanding, but even special relativity requires, at the very least, an understanding of vectors and vector addition in order to gain a fundamental understanding. Motion has direction as well as magnitude and thus is a vector. Unlike scalars such a temperature, pressure or even speed (a representation of distance per time without consideration of direction) vectors such as velocity represent direction as well as magnitude. Ignoring that can tend to result in confusion not only about the importance of direction when considering relative motion, but also confusion about the nature of time and its differentiation from the spatial dimensions.