Can One Grasp Relativity Without Doing the Math?

[ben m]

Gravitational fields fall off with distance but accelerating frames don't.

How gravity falls off depends on the source. The gravitational force above a infinite massive plane, for example, is constant everywhere in space. You can construct a planet whose density increases as 1/r; the acceleration due to gravity has a constant magnitude anywhere inside this planet. (The direction varies, of course, since it always points inwards)

How acceleration behaves depends on ... well, on why you're accelerating. If you're standing in a space elevator in a textbook relativity problem, you're accelerating because of a normal force on your feet (which goes to zero if you step out of the elevator). If you're positively charged and getting pulled towards a large negative point charge, your acceleration varies as 1/r^2.

Anyway: as a purely practical matter, yes, you can probably determine the cause of a force by looking for commonsense external clues, like "Am I standing on a space elevator or not?" and "Are there familiar gradients in this force?"

 

[Ziggurat]

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?

Depends. Presumably you mean not only teleportation, but faster-than-light teleportation. In relativity, faster-than-light travel (of any form) is equivalent to time travel.

However, since this would require new physics, we wouldn't necessarily need to stick with relativity alone in this hypothetical experiment. If this new physics imposed a locally preferred reference frame on the universe, then it would be possible to have faster-than-light travel without having time travel.

 

[sol invictus]

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.

If there is no mass or energy in the universe at all and you can make precise measurements over long distances, then you can determine that there is no mass and from there that the acceleration field must be purely due to, well, acceleration. But if there is mass, you cannot distinguish "real" gravity from acceleration.

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

Global measurements don't help (except in special cases). Try this: I give you two metrics. That's complete information about the spacetime, far more than you could ever hope to get from measurements. Your job is to tell me if they describe the same configuration of matter. If you cn distinguish gravity from acceleration that should be easy, but AFAIK there is no known way to do it.

Gravitational fields fall off with distance but accelerating frames don't.

I just gave you a counterexample. You're thinking of a simple constant acceleration field. But there's no reason to restrict yourself to that.

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

What?

 

[sol invictus]

Anyway: as a purely practical matter, yes, you can probably determine the cause of a force by looking for commonsense external clues, like "Am I standing on a space elevator or not?" and "Are there familiar gradients in this force?"

In simple cases that will work. But suppose you're inside a sealed lab. You don't know if the lab is firing its rockets in various directions or simply being pulled and stretched by tidal forces because it's near a complex configuration of masses. Now try to figure out which it is .

 

[Hokulele]

I think Brian Greene does a relatively good job, without a lot of math.

Seconded. His descriptions in one of the early chapter in The Elegant Universe are about as good as one can get without math.

 

[Uncayimmy]

Anyway: as a purely practical matter, yes, you can probably determine the cause of a force by looking for commonsense external clues, like "Am I standing on a space elevator or not?" and "Are there familiar gradients in this force?"

Serious question here: How do you know? Doesn't it kind of presume that you know something is already gravity and not acceleration? Like in the building, we assume it's the pull of the earth based on these other clues. What were the clues that told us earth is not accelerating?

I have not thought this through for more than 10 seconds, but I wanted to post the question before I took off for dinner.

 

[ben m]

Serious question here: How do you know? Doesn't it kind of presume that you know something is already gravity and not acceleration? Like in the building, we assume it's the pull of the earth based on these other clues. What were the clues that told us earth is not accelerating?

I have not thought this through for more than 10 seconds, but I wanted to post the question before I took off for dinner.

In what direction could the Earth accelerate to provide a gravity-mimicking force everywhere on the surface?

 

[daenku32]

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

See, why can't they just call this the Grand Unification Theory? It combines both relativity and quantum mechanics.

 

[ben m]

See, why can't they just call this the Grand Unification Theory? It combines both relativity and quantum mechanics.

Special relativity is easy. It's general relativity that causes the problems.

 

[Uncayimmy]

In what direction could the Earth accelerate to provide a gravity-mimicking force everywhere on the surface?

Right. However, I was thinking locally and doing one measurement. It's an arbirtrary and meaningless (in a practical sense) distinction that I didn't tell anyone about. I should never post when I'm in a hurry like that.

 

[leon_heller]

Einstein came up with his concepts by performing "thought experiments", he then sorted out the maths later.

Leon

 

[ponderingturtle]

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.

That is because math is the true language of physics. English is a poor imprecise substitute.

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?

Depends on how the departial and arival where seperated. If it was a light like seperation it would be reference frame invarient.

 

[ponderingturtle]

Einstein came up with his concepts by performing "thought experiments", he then sorted out the maths later.

Leon

Yes and no. The thought experiments are geometric in nature. If you think geometery is math then they are mathmatical in nature. If not then you can get reletivity with out the math.

 

[Fredrik]

Do you think relativity can be grasped without doing the math?

Special relativity, yes. General relativity, no.

If you learn about spacetime diagrams (which is easy and mostly involves drawing straight lines on a piece of paper), you can understand special relativity very well. You can even develop a better intuitive understanding of the subject than university students who studied Lorentz transformations algebraically in classes on classical mechanics and classical electrodynamics.

This will give you some intuition about general relativity too, but there are lots of things in GR that you will never be able to understand without a solid understanding of differential geometry.

 

[Dorfl]

If there is no mass or energy in the universe at all and you can make precise measurements over long distances, then you can determine that there is no mass and from there that the acceleration field must be purely due to, well, acceleration. But if there is mass, you cannot distinguish "real" gravity from acceleration.

You're probably right, but I still have this mental picture of the researcher in the lab seeing that the field lines are not parallel and not radiating from an axis, and therefore concluding that no kind of acceleration could be behind them, meaning that they must be due to gravity. Maybe there is in general some really complicated way of accelerating the lab to replicate the effects of gravity from any specific mass. I don't see how, though.

 

[Cuddles]

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.

You have it exactly backwards. The maths is logical understanding. Go back and read my last post. What you're effectively saying is that someone doesn't understand the sentence "The cat sat on the mat." because they can't translate it into German. Their inability to translate says nothing about their understanding of the phrase in English. Similarly, a person's inability to translate maths and physics into English (specifically, into English that you, personally, can understand) says nothing about their understanding of the actual maths and physics.

 

[Buckaroo]

A couple of animations I did about five years ago for the NSF (the Earbot.com URL was pasted on by whoever posted them on youtube; I have no affiliation). Minimal math, but I still found it necessary, even if I'm only using a geometric explanation:

 

[The Man]

A couple of animations I did about five years ago for the NSF (the Earbot.com URL was pasted on by whoever posted them on youtube; I have no affiliation). Minimal math, but I still found it necessary, even if I'm only using a geometric explanation:

Very nice work.

 

[Uncayimmy]

Yes and no. The thought experiments are geometric in nature. If you think geometery is math then they are mathmatical in nature. If not then you can get reletivity with out the math.

Einstein was a physicist who was well versed in the related math before he ever started his thought experiments, and I'm sure the math was on his mind the whole time.

 

[ponderingturtle]

Einstein was a physicist who was well versed in the related math before he ever started his thought experiments, and I'm sure the math was on his mind the whole time.

Sure, but the point stands that they are really geometery, so you could show a lot of it with out numbers or equations.