Space-time curvature is incorrect

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"it becomes important to treat the Earth as a sphere rather than as flat. "

I kinda detest when opinions are used as theories in science, for example the 2ond theory of thermodinamics which sites "organization", and when you just sited "importance". What is important? At the very least you need to revise that sentence.

I can understand the example, but the reason for the analogy to work is because earth is so big and we are so small, the smaller we get the more flat it will seem. A way it would be "important" for earth's surface to be recognized as curved is if we want to build a machine that takes two steps to get around the planet.

If we built it to the configurations of a flat surface, it would step out into space and create a big raucaus when it comes crashing down. But if we configured it to step in a curved pattern, the crash might not be quite so terrible.

This "importance" stuff is much more of an opinion than a scientific point of reference.

"Similarly, GR says that spacetime is locally flat, "

What is the significance of GR to recognize this?

"No matter accelerates in all directions at once."

you said: "In GR, the Earth's surface is accelerating the Earthbound observer upwards in spacetime towards the free-falling object. "

This would not work UNLESS the earth was accelerating in all directions at once. On page one and two of this very thread, me and Zanket discussed this, you might want to read it.

If the planet accelerates toward the free-fall object, then if there were free-fall objects on all sides of the earth, the earth would have to be accelerating in all directions at once.

"Very roughly, an inertial frame is one which is not accelerating."

So does this mean that two objects going at different speeds, but not accelerating with respect to eachother are in the same inertial reference?

-Would you mind giving an example of why that wouldn't work?-

"I already did."

You said: "the theory of quantum electrodynamics (QED) relies on the fact that photons have no rest mass."

Thats all you said. You did not give an example of why QED would not work unless light was massless. So, would you mind?

 

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"Yes. It is a beautiful theory precisely because it makes so few assumptions."

In that case, ill take a closer look at them

"1. Spacetime is a 4-dimensional manifold which has a locally flat (Minkowski) metric. "

From dictionary.com, manifold is something with diverse properties, so that either can be left out, or given a more specific definition.

What is a "metric" and what is Minkowski?

What I can glean from that is that spacetime is a 4-dimentional and locally flat something.

"2. Particles in free-fall follow timelike geodesics on the manifold. "

How is something "timelike"? Dictionary.com fails to provide a meaning of geodesics that would fit this sentence, so what is it? Manifold please?

"This means that without forces particles tend to follow free-fall trajectories."

Follow free-fall trajectories toward what. That is definately not specific enough.

"3. All physical laws that hold in flat Minkowski space and are expressible in terms of vectors and tensors, and are meaningful in the 4 dimensional manifold, continue to hold in every reference frame (provided we replace derivatives by a special type of derivative known as a "covariant derivative"). "

Tensor is what? It would probably be a good idea to define vector too. "meaningful" is an opinion, that needs to go. Reference frames need defining adn covariant derivative needs to be defined.

I think it is fair to say that my axioms were easy to understand, and relatively complete.

Your axioms lack many definitions, hardly mention forces, and form a contradtiction in the form of mentioning special and general relativity without explanation. What does it mean to apply locally? How local is local?

These look more like a short description of the theory of relativity than a description of the universe. Could you please revise the laws so they are more clear?

 

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"Set your allowable error bounds and I'll tell you whether you need to worry about the difference between a flat earth and a curved one"

I can understand that. But in your axiom, it is a bit vauge to say that space-time is locally flat. how locally?

"A way it would be "important" for earth's surface to be recognized as curved is if we want to build a machine that takes two steps to get around the planet.

If we built it to the configurations of a flat surface, it would step out into space and create a big raucaus when it comes crashing down. But if we configured it to step in a curved pattern, the crash might not be quite so terrible. "

Would you mind answering that?

"Different parts of the surface accelerate in different directions."

Im sorry, but if different parts of the surface accelerated in different directions, the earth would rip appart. I think you can understand that concept.

"In Euclidean (Minkowski) space, yes. "

You like to leave something incomplete don't you? In what space no?

"I cannot explain QED to you in a single post"

Great, so what your saying is you can't give me an example. The "example" you put down was in reference to something I don't have experience with, you have to explain the whole example to me not just a peice of it.

"I suggest you find out what the mathematical definition of the word "manifold""

Why do you have to put me down like that? Wouldn't it just be simpler to give me YOUR definition of manifold?

"I cannot teach you Riemannian geometry here. Look it up."

Im not asking you for a lesson, buddy. Im asking you for a definition. Your axioms were hard to understand, to say the least. My axioms were very easily and understandably layed out, that is what I want from you.

"to explain metrics and spacetime intervals here would take too much effort and space."

No pain no gain. What are you posting on here for anyway? Im posting to learn something, but if you don't back up what you say, then I can't do but wait for it.

I think you think im stupid. If you give me simple definitions of these things, ill probably be able to understand them.

"Towards whatever is creating the local gravitational curvature."

Don't you think there needs to be some sort of force involved in either accelerating whatever is creating the dent toward the freefall object?

"A tensor is similar to a matrix in mathematical terms."

Thank you, but that is not a definition. I know what a vector is, if you didn't catch it, I was saying it would be good to define it for peole who might be less knowlegable.

"The fact that you don't understand something doesn't render it meaningless."

This is irrelevant, meaningful is an opinion. Period. May I say that you lack explaining skills, I may not be able to understand what your talking about because you don't care about actually teaching me something, you just try to belittle me with extravegant words and phrases that have different meaning than normal. Why don't you just give up on me, sinse I can't understand the explanations you aren't giving.

"Easy to understand? Yes. Well-defined? No. Complete? Not even close."

Did I say my axioms were the end all be all of the universe? NO. I gave them as an example of my understanding of the universe. They were easy to understand, unlike yours. They were a well-defined set of axioms that explain my thinking very clearly. Complete, thats all i got, im not saying they are perfect, but yours are definately screwed too.

"You seem to be confusing what is true with what you presently understand. "

Are you saying that you know everything? You know how the universe works completely? Im sorry, but you can not take a godly stand on this matter. I am saying that what I presently understand is the best theory I have and you haven't given me anything to change it.

"anything you don't currently know is suspicious "

How can a good scientist think any differently? If you take things for granted, your not a scientist, your a mysticist.

"That's what you asked for. "

No, actually. I asked for axioms describing the universe according to relativity. I DID NOT ask for axioms describing relativity according to you.

Im glad you care nothing whatsoever about actually explaining yourself.

By the way, I am on AIM with the name Frencheneesz, if you want we can discuss it real time.

One more thing is that it would probably be a lot easier for the forum if we discuss one thing at a time. Let me nominate gravity as the first line of discussion.

 

Hi Frencheneesz,

"If you give me simple definitions of these things, ill probably be able to understand them."

The problem is that physics or maths cannot always be put into simple words without loosing a lot of information. The reason why I think James (and I try to do that myself aswel) doesn't just explain things to you in simplified scenarios is because those are simply incomplete. Actually, you should see it as a compliment, because he/we are trying to explain things to you as a whole, and not just some fancy story

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.

Bye!

Crisp

 

Crisp:

Sure, i see your point. But I think if you use a word you should be able to define it, don't you think?

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Im sorry. I kinda flipped out. The stupid thing delete my ENTIRE message yet again. I hate having to copy my thing into a text file every time I write one of these things.

"You have yet to grasp the GR description, which explains how the surface does not need to rip apart."

Here you have to explain yourself. I assume that if particles are moving in different directions they will eventually get farther apart. Did you read our posts when I was arguing with Zanket on the spherical outward acceleration of a gravitational body?

"I think you want to be spoon fed, though."

Quite right.

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. Although I did take a few seconds to try and look up EVERY word you had on those axioms that confused me.

"You haven't given me enough to pick holes in your ideas yet. Also, I get the impression you don't want your ideas challenged."

Hmm, what more should I give? And I most definately do want my ideas challenged. Im not the church! I just would like an explanation that I can understand. I know that is asking a bit much, but I seriously do try to understand what you are saying. When I find contradictions in what you say, then im suspicious.

"Pragmatically, you have no option but to take some things for granted. "

I see your point, but in retrospect, somethings need to be inspected before you can believe their truth.

"Unfortunately my time is limited. "

I understand. But if anyone else wants to discuss with me these things, my AIM screen name is Frencheneesz.

"You've picked a hard place to start. "

Ok ok. How bout we start with light. As I understand it that was one of the first things one Einstein's mind.

 

Ok light. Ill make this short. As I understand it, light supposedly goes at the same speed for all references.

You have hinted at these refference, but I am still not clear on all of them. You have specified the speed as a frame of reference, the first derivative of speed (acceleration) as another frame, so are the third fouth and fifth derivative of speed also frames?

This is improtant, I think, in discussing the constnacy of the speed of light. Also, how is it theorised that light decellerate, because it must if it bounces off of something. There must be one point in teh bounce when the light is stationary, right?

 

"That is not a strictly correct way of visualising things"

I suppose you are implying that a correct way of visualising things would not be easy enough to do in this forum....?

"I can give you that roughly."

Well, As long as i understand that it is superficial, it WOULD help.

"that is due to your incomplete understanding at this stage. "

I can believe it.

"Ok then. What do you want to know [about light]?"

Well, you must have just missed my post ON light. You can look up if you want.

 

Note: I backtracked on this post in my next post below.

Frencheneesz:

I’m glad you brought this up. You had me thinking about this all weekend. I hope James R can confirm or deny my suspicion below.

Einstein’s chapter The Relativity of Simultaneity seems misleading. I believe this is the way it is: The observer on the train (the “passenger”) sees the lightning strikes as simultaneous. So does the observer on the ground (the “bystander”). This is true because either observer is midpoint between the strikes and either can take themselves to be stationary (the principle of relativity says that neither can determine absolutely who is moving, only that they are moving relative to each other).

But the bystander determines that the passenger observes strike B first, because from the bystander’s perspective the passenger is rushing to meet the light from strike B. Likewise the passenger determines that the bystander observes stike A first because from the passenger’s perspective, the bystander is rushing to meet the light from strike A. If the bystander and the passenger later meet to compare their observations, they will disagree about what the other observed.

Einstein’s chapter is misleading because it leads one to believe that the passenger does not see the strikes as simultaneous. I inserted some clarifying qualifiers here in brackets: “Now in reality (considered with reference to the railway embankment [from the bystander’s perspective]) he [the passenger] is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence [from the bystander’s perspective] the [passenger] observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

What follows from the observers’ disagreement about what the other observes is remarkable. For example, each observer sees the other’s clock as running slow. There is a far better thought experiment for this in the book Relativity Visualized. For any objection you have to Einstein's thought experiment, I refer you to this book.

I recommend you get that one, and also Relativity Simply Explained and Understanding Einstein's Theories of Relativity. These books have only simple equations within yet do an excellent job of explaining (as an introduction) what James R is telling you about general relativity. Do what you want, but I think you’d learn “light years” faster with the books than this forum. I’ve been studying relativity for a year now, and I’m only beginning to grasp what James R is explaining. Starting with the axioms, for example, is ill advised because they are saying in the most concise way possible what any mere mortal would require some chapters from a good author to understand.

[Edited to include the note at top.]

 

Frencheneesz:

I’m gonna backtrack on my previous post. Upon further inspection all my sources agree that the train passenger would observe strike B first. That was confusing to me because both the bystander and passenger are midpoint between the strikes, and either can take themselves to be a stationary observer.

However, if the bystander is midpoint between the strikes when they hit the track, the passenger cannot be. The passenger is moving relative to the lightning. If the bystander sees the lightning come straight down, the passenger sees it slant, because he is moving toward the strike as it comes down. Strike A slants away from him, and strike B slants towards him. Strike B hits the track closer to the passenger than strike A does. So the passenger sees strike B first.

I was thinking, what if the lightning was replaced by flashes of strobe lights on the ends of the train itself? Surely then both the passenger and bystander would see the flashes as simultaneous. But the bystander would see light A flash first. If the strobes were controlled by a device at the midpoint of the train, the bystander would see the signal from the device hit light A first, because, from his perspective, light A is moving towards the signal, whilst light B is moving away from the signal.

Now suppose the strobe lights were controlled by atomic clocks at each end of the train, attached directly to the lights. The clocks are synchronized by the device at the midpoint. Now the bystander would see the flashes as simultaneous, right? No. We just determined that if the lights were directly controlled by the device, the bystander would not see the flashes as simultaneous. Likewise if the device was used to synchronize the endpoint clocks, the bystander would see the synchronization signal get to light A first, so the clock at light A would show a later time than the clock at light B from the bystander’s perspective. The bystander would see clock A reach the designated flash time first, and so see light A flash first.

Going back to the point you made:

If the passenger measures the distance between the lightning strikes, he finds that strike B hit the track closer to him than strike A did. He could use this information to determine that the strikes happened simultaneously, but that would be true only from the bystander's perspective. Likewise, if the light pulses came from strobe lights on the train as above, the bystander could determine that the pulses happened simultaneously, but that would be true only from the passenger’s perspective. The order of events depends on your perspective.

 

The light hitting the train would be the same as having strobe lights, because when the lighting hits the trains metal, the metal bounces some of the residual lightning blast towards the observers, and when a strobe light turns on, the same thing happens.

To be technical, If we are involving light in this analogy, we must refer to the assumed relativistic properties of light which say that light goes the same speed for every observer. SO, if both observers are equidistant from both lightning flashes, then both must actually see both light flashes at the same time.

As another insight, the defining process of this analogy assumes the clasical view of simulanuity in its proof that that very happening has no meaning. When shall each clock be set if we don't know when the times will be simultanious? I don't know how to fix this, but if things were absolutely simultanious, it would fix the problem....

I see the time dialation stuff as not actually relating to "time" persay, but relating to the speed of the forces in a given frame. For example, time is constant, but when one speeds up, the rate at which atoms move and forces exchange is slowed down, thus slowing down a mechanical clock. By using measurements and theories, we can calculate what rate of our clocks is equivelant to what rate on an outside clock. So instead of time slowing down, the four fundemental forces just work slower. This would make sence of simultanuity for different frames of refference.

Back to the point. let us imagine a particle called SHWING that maintained a constant speed relative to the its emission point. This would be just like the light analogy, but excludes the complicating factor of the constancy of c. I will explalin a new analogy for thoroughness:

There is a train traveling perpendicular to a road, on which observer MOVE stands. On the road stands the unmoving observer STAND. Two SHWING emittors are hung from the sky in a fasion that, when connecting them by a straight line, this straight line will also be perpendicular to road and rail-line. Each observer carries a shwing particle detector that has an infinite computer clock-speed (meaning it does not approximate simultanuity).

As the train moves MOVE next to STAND, one burst of SWING particles from each emittor is emmitted. Since the emittors are stationary as compared to the road and thus observer STAND, the observer MOVE sees the SHWING particle he is moving toward first, and the one he is moving away from second, while observer STAND sees both simultaniously. But the MOVE observer can easily calculate that the particles were emmitted simultaniously because he can measure newtonian distances and speeds and calculate it, as long as he doesn't care about the miniscule error his calculations will have.

According to James R, these two observers will always agree on the simultanuity if they are in the same frame of reference. So what we disagree on is wheather that deduction of simultanuity occurs for both observer at relativistic frames of reference. For that we need to discuss frames of reference and how different things can make it.

"He could use this information to determine that the strikes happened simultaneously, but that would be true only from the bystander's perspective. "

If the bystander did not exist, the traveler could still calculate the same results.

 

James R:

I think I hit on that in my previous post. I made an alternate set up of the example. I think that this example with incongruity of the simultanuity of light is a help to prove that light DOES NOT go at a constant speed for all frames of reference. The only time simultanuity is questionable is when an object is going at the same speed for different frames of reference, which could also be said to be going two different speeds for ONE frame of reference. The contradictions and exeptions keep piling up.

By the way, what does Quantum theory say about the speed of light?

 

"The constancy of the speed of light is counter-intuitive, so you dismiss it out of hand."

Yup. Sorry. I find places in it that don't make sence to me, I already have a theory in my head about how stuff works. When you contradict my theory, I have to dismiss the new theory if that new theory is without explanation. I haven't found sufficient explanation for this stuff. Im sure I can incorperate at least some of it, but as of yet I don't know which part to do that with.

How bout lets discuss light. This is a great place to start. What I was saying is that if the constancy of the speed of light is "special" to light only, then the incoruent simmultanious observations is also "special" to light only. So it really wouldn't go against any relativistic ideas.

Well, you decided no to read my questions on light? You posted right below it but didn't see it I guess.

"You have hinted at these refference, but I am still not clear on all of them. You have specified the speed as a frame of reference, the first derivative of speed (acceleration) as another frame, so are the third fouth and fifth derivative of speed also frames? "

Thats me! What are your thoughts on the "real" positions of objects in space? Do you think that observations define reality, or does reality define observations?

My idea of this is that a particle in space can only be occupying one spot at a time, not multiple spots(I also disbelieve the reality of that quantum self interference theory it has). Light contradicts this thought. Given that there are an infinite number of frames of reference, then there are an infinite number of positions that a SINGLE particle of light can be, can you agree?

I don't want to go on forever, so you can play with these questions.

 

James R:

That does clear things up, thanks for the explanation. I realize how you are right that both observers would find the strikes points equidistant. I've been taking for granted the consequences of non-simultaneity. It's nice to really understand how this works.