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Old 04-16-2018, 02:08 AM
Batano Batano is offline
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Relativity Question

Since there is no privileged frame of reference, what does it mean that an object's mass increases with speed? Presumably I'm traveling near the speed of light relative to photons and such and I don't feel infinitely massive.

Last edited by Batano; 04-16-2018 at 02:09 AM.
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Old 04-16-2018, 02:35 AM
Stranger On A Train Stranger On A Train is offline
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The mass of an object moving at relativistic speed increases with respect to the rest of the unaccelerated universe (which includes the outside observer) and is compensated by the momentum of the mass moving in the opposite direction. For the internal observer who is accelerated, the rest of the universe increases in mass.

Like all concepts involved in relativity, you really need to understand the math involved to grasp the concepts which are not intuitive to everyday experience. Fortunately, for special relativity, all you really need is a grasp of high school algebra and just a smidge of analytical geometry. General relativity requires considerably more mathematics but the basic concepts are understandable by anyone who has been through the basic calculus sequence through vector analysis, but applying the theory requires considerable experience with tensor calculus for anything but the most trivial of cases.

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Old 04-16-2018, 02:40 AM
DPRK DPRK is offline
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Originally Posted by Batano View Post
Since there is no privileged frame of reference, what does it mean that an object's mass increases with speed? Presumably I'm traveling near the speed of light relative to photons and such and I don't feel infinitely massive.
It just means that in a frame where you are going fast you will have more kinetic (and total) energy. If you now remember that E = mc , then you could define a "relativistic mass" m = E / c. However, as you yourself point out, your actual mass (i.e., rest mass) does not change. As an extreme example, you could have an extremely high-energy photon, even though photons have zero mass.
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Old 04-16-2018, 03:21 AM
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Like all concepts involved in relativity, you really need to understand the math involved to grasp the concepts which are not intuitive to everyday experience. Fortunately, for special relativity, all you really need is a grasp of high school algebra and just a smidge of analytical geometry.
Special Relativity comes down to two facts: Accelerations can be described as rotations in a spacetime plane where one direction is spatial and one direction is time, and rotations in a spacetime plane are hyperbolic, as opposed to circular. Like all very high-level descriptions, this is more-or-less opaque to anyone who doesn't already know it, but, fortunately, there are some very good websites which teach it to you from, as you said, a foundation in high-school algebra and basic geometry: I happen to like this one.

Yes, it's mathematical. It's also simple, and it's simple because it's mathematical: In physics, and quantum physics is too often the victim of this, the "simple" non-mathematical overviews conceal more than they reveal by hiding simple concepts behind convoluted metaphors which probably make perfect sense to people who already know the concepts, but which leave the people they're ostensibly written for worse off than before, freighted down with useless conceptual baggage instead of a few fundamental mathematical concepts a bright teen could grasp.

People can work so much goddamned mysticism into a simple change-of-base operation when they dress up the Fourier transform into the Uncertainty Principle and pretend it means the Universe is Literally Consciousness.
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Old 04-16-2018, 04:53 AM
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Thanks all. I should look at the math, but you have posted helps
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Old 04-16-2018, 05:20 AM
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Simplest answer: It doesn't. The only reason to say that mass increases with speed is to make the momentum equation look pretty, and even if that is one's goal, there are other ways to make it look just as pretty but which make a lot more sense. As a result, actual physicists never talk about "relativistic mass" increasing, and the "fact" that it does lives on only in textbooks written by people who don't know what they're talking about. Who, unfortunately, write a lot of textbooks.
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Old 04-16-2018, 08:49 AM
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This is one good answer:
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Originally Posted by Chronos View Post
Simplest answer: It doesn't. The only reason to say that mass increases with speed is to make the momentum equation look pretty, and even if that is one's goal, there are other ways to make it look just as pretty but which make a lot more sense. As a result, actual physicists never talk about "relativistic mass" increasing, and the "fact" that it does lives on only in textbooks written by people who don't know what they're talking about. Who, unfortunately, write a lot of textbooks.
But there's another point:
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Originally Posted by Batano View Post
Presumably I'm traveling near the speed of light relative to photons and such
You actually can't do that. No matter how fast you're going with respect to, say Earth, you will always find that photons are moving at c with respect to you. Weird, right? But that's where all the fundamental weirdness of special relativity (time dilation and stuff like that) comes in. Which you don't have to understand if you don't want to, of course. There's lots of cool stuff to understand in this universe.
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Old 04-16-2018, 09:01 AM
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Simplest answer: It doesn't. The only reason to say that mass increases with speed is to make the momentum equation look pretty, and even if that is one's goal, there are other ways to make it look just as pretty but which make a lot more sense. As a result, actual physicists never talk about "relativistic mass" increasing, and the "fact" that it does lives on only in textbooks written by people who don't know what they're talking about. Who, unfortunately, write a lot of textbooks.
I won't dispute any of this but it does raise (not beg) the question: What about all those guys who say you can never reach c because by the time you get near c, your mass is increasing without limit and it would take an infinite amount of energy to accelerate an infinite amount of mass to reach c?

Is it that this statement
a) Has been misunderstood by me all these years and the theory never really said this
b) Used to be the prevalent thinking but our understanding has evolved
c) Is a myth perpetuated by laymen on message boards
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Old 04-16-2018, 09:16 AM
Francis Vaughan Francis Vaughan is offline
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I won't dispute any of this but it does raise (not beg) the question: What about all those guys who say you can never reach c because by the time you get near c, your mass is increasing without limit and it would take an infinite amount of energy to accelerate an infinite amount of mass to reach c?
It is a slight but critical misquote. You can't get some other object to c because that object would have an unbounded mass. That is just, as chronos points out, a cheap way of making the momentum equation work. It never said anything about you raising your own speed.
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Old 04-16-2018, 11:46 AM
md2000 md2000 is offline
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The simple result is that in a situation where everything is moving at a steady state, nobody can "stop and compare". So relativistic mass goes up, clocks run slower, distances contract in the direction of motion. My clock is faster than yours, your clock is faster than mine, and "simultaneous" is a relative term; what seems simultaneous to you may not to me.

If one of us stops to compare with the other, see who got older and who stayed younger - then one of us (or both) underwent acceleration. That's the difference between special and general relativity, and hence the much much more complex math. The twin who stayed home got older, the one who accelerated to .9C and then stopped, turned around, and came back at .9c then stopped when they got home - experienced acceleration and thus their frame of reference and age is different from the twin who stayed home. But if all we have is two (space)ships passing in the night at constant velocity, each thinks the other is the weird one.

And unless you want to get into the math, that's the main distinction you need to know about Relativity.

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Old 04-16-2018, 12:45 PM
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The simple result is that in a situation where everything is moving at a steady state, nobody can "stop and compare". So relativistic mass goes up, clocks run slower, distances contract in the direction of motion. My clock is faster than yours, your clock is faster than mine, and "simultaneous" is a relative term; what seems simultaneous to you may not to me.

If one of us stops to compare with the other, see who got older and who stayed younger - then one of us (or both) underwent acceleration. That's the difference between special and general relativity, and hence the much much more complex math. The twin who stayed home got older, the one who accelerated to .9C and then stopped, turned around, and came back at .9c then stopped when they got home - experienced acceleration and thus their frame of reference and age is different from the twin who stayed home. But if all we have is two (space)ships passing in the night at constant velocity, each thinks the other is the weird one.

And unless you want to get into the math, that's the main distinction you need to know about Relativity.
While the acceleration model is a common explanation it is not the correct answer to the twin paradox. Unfortunately the acceleration explanation is a common point of confusion due to the common stopping point in most peoples introduction to Relativity, and the classical version of the twin paradox really leads to this very common misunderstanding. Unfortunately this misunderstanding also tends to intersect with the terminus of most physics education tracks and is often taught as the answer by very well meaning educators but this is purely an artifact of the common curriculum.

It is the motion and the lack of a universal reference frame that is important and not the acceleration.

Don Lincoln of Fermilab actually produced what I think is the most accessible explanations of the twin paradox I have found.

https://youtu.be/noaGNuQCW8A

If anyone is more interested in the why, it will require math but luckily as it can be explained within the framework of Special Relativity you really don't need much more than the Pythagorean theorem and the hardest part will be abandoning our assumptions.

Here is a "back of the envelope" math version I shared last year related to this, and is probably the best I can try do do within the limitations of the dopes supported features.

https://boards.straightdope.com/sdmb...1&postcount=24

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Old 04-16-2018, 01:02 PM
Andy L Andy L is offline
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Here's a discussion of the twin paradox that doesn't need acceleration https://boards.straightdope.com/sdmb...8&postcount=31
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Old 04-16-2018, 01:05 PM
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I won't dispute any of this but it does raise (not beg) the question: What about all those guys who say you can never reach c because by the time you get near c, your mass is increasing without limit and it would take an infinite amount of energy to accelerate an infinite amount of mass to reach c?

Is it that this statement
a) Has been misunderstood by me all these years and the theory never really said this
b) Used to be the prevalent thinking but our understanding has evolved
c) Is a myth perpetuated by laymen on message boards
I'd say (a) and (c). IIRC, the first mention of "relativistic mass" in the literature was promptly followed by a disclaimer that it was just a way to make the equations look a bit like their Newtonian version and not a useful way to think about the situation -- it was never "prevalent thinking".

I think an obvious riposte to relativistic mass as a reason why we can't reach c is that whenever we want something to move fast we don't throw it, we use a rocket. And a rocket engine is always at rest relative to what it is pushing so it shouldn't experience the relativistic mass of its payload. So relativistic mass provides no explanation of why we can't push things faster than c with a rocket.
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Old 04-16-2018, 01:08 PM
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Originally Posted by CookingWithGas View Post
I won't dispute any of this but it does raise (not beg) the question: What about all those guys who say you can never reach c because by the time you get near c, your mass is increasing without limit and it would take an infinite amount of energy to accelerate an infinite amount of mass to reach c?

Is it that this statement
a) Has been misunderstood by me all these years and the theory never really said this
b) Used to be the prevalent thinking but our understanding has evolved
c) Is a myth perpetuated by laymen on message boards
Your rest mass or invariant mass does not increase, but your total energy does.

Part of the confusion here is he often quoted "E = mc^2" is a simplified version of the formula, but E = mc^2 only works if one assumes the momentum term is zero.

The more complete form is

E^2 - (pc)^2 = (mc^2)^2

For objects like us who are not traveling close to the speed of light E = MC^2 works, but for a photon you can use simple algebra above to reduce it to E = pc if you just simplify assuming m = 0.

If you try out the above formula accounting for rest mass, total energy, and momentum; you will see that no massive particle can reach the speed of light, and mass-less particles cannot travel slower than the speed of light.

It may be helpful to read about you light cone and the implications for the concept of causality. The speed of light is not about light, but really about the speed of causality.
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Old 04-16-2018, 01:59 PM
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I'd say (a) and (c). IIRC, the first mention of "relativistic mass" in the literature was promptly followed by a disclaimer that it was just a way to make the equations look a bit like their Newtonian version and not a useful way to think about the situation -- it was never "prevalent thinking".

I think an obvious riposte to relativistic mass as a reason why we can't reach c is that whenever we want something to move fast we don't throw it, we use a rocket. And a rocket engine is always at rest relative to what it is pushing so it shouldn't experience the relativistic mass of its payload. So relativistic mass provides no explanation of why we can't push things faster than c with a rocket.
"relativistic mass" has grown in disfavor in recent years due to the issues with it being extremely overloaded but yes, it is mostly maintained because Newton's second law is useful and his model is accurate enough in most cases. There is a tenancy to use momentum and to avoid "relativistic mass" which really depends on the "fictional force" of gravitation.

Unfortunately "fictional force" as a term has the problem that is best demonstrated in how people often say that "centrifugal force" is fake. It is not fake, but just a pseudo force that is observed to being in an accelerated reference frame. The Newtonian model is extremely useful, and much simpler than more correct models but it assumes that gravitation is "real" and a superluminal, instantaneous force. As the concept of mass is tied to weight in common interpretations of Newton's model it does cause confusion.


This film, while long will be helpful for understanding the implications of "frame of reference".

https://www.youtube.com/watch?v=bJMYoj4hHqU


Remember that due to Einstein's Equivalence Principle, Gravity is just an observed force caused by being in an accelerated reference frame, it is a "fictional force" or "pseudo force" but that jumps to GR which is not needed for the twins paradox.

I found it useful to translate "Relativistic mass" to Lorentz factor or the overloaded use of the term gamma (γ) when ever I see it in this domain.

While I hesitate to mention it as it is at risk of derailing the thread, it is important to remember that in GR, which is where you have to go when gravity is involved, weight and mass which are different in the Newtonian model are measures of the same underlying fundamental property. I am only mentioning it because contemplating that fact will help move past the Newtonian model assumptions, and here is a video that is also more "accessible" that will function as a cite that doesn't involve math that no one will read anyway.

https://youtu.be/QSIuTxnBuJk

Think of "mass" in relativity as purely the mass of an object or collection of objects that is independent of the overall motion of that system and the concepts will be easier to understand.

Once you start to think more about momentum, the implications of Alpha particles, which are a helium-4 nucleus traveling at ~5% of the speed of light or higher, and how energetic those particles interact with our cells, or other massive objects with less momentum this will start to make more sense.

While not exact, if you think about how kinetic energy increases with velocity in a non-linear fashion, it takes more and more energy to accelerate an object.

When you use the version of the above mass-energy equivalence formula, where p is the momentum and avoid using the simplified form of the stationary object that is E=mc^2 it should be more clear why objects with mass will never reach the speed of light.

This is also going to be a bummer for long distance space travel, because if you could accelerate to any meaningful percentage of the speed of light the star system you are approaching would have most of it's energy blue-shifted into high energy forms. You will need to have some form of shielding that will withstand x-rays and gamma radiation in a proportion that is far higher than would be assumed.

I am writing another novel here, so I will stop but really relativity, and in particular general relativity is truly a thing of beauty, and encourage everyone to dig into it as much as possible.

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Old 04-16-2018, 05:27 PM
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The first video is interesting, but... An important note is that because each frame of reference sees time and distance differently; and "simultaneous" is different for different observers - the only definite simultaneity for all observers is when two objects are at the same location. If A watches B and C moving - A does not necessarily see B and C pass their start points at the same time, and ditto B for A and C, and so on. Only when A passes B (to start) or B passes C at the midpoint can one say the event happened at the same time on both clocks.
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Old 04-16-2018, 05:44 PM
Asympotically fat Asympotically fat is offline
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Relativistic mass is simply not used because it is confusing: in Newtonian physics mass is a measure of how difficult it is to accelerate and object, but in special relativity there is a directional dependence and relativistic mass (as usually defined) is a measure of how difficult it is to accelerate an object perpendicular to its direction of motion. It's at best a footnote in any decent relativity textbook.
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Old 04-16-2018, 05:53 PM
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"relativistic mass" has grown in disfavor in recent years due to the issues with it being extremely overloaded but yes, it is mostly maintained because Newton's second law is useful and his model is accurate enough in most cases. There is a tenancy to use momentum and to avoid "relativistic mass" which really depends on the "fictional force" of gravitation.
Momentum is nice for other reasons, at least when you get into quantum physics: It has a simple relationship with photon frequency, and it explains how massless particles can impart momentum and, indeed, more firmly fixes in the mind the centrality of the energy-momentum four-vector.

Quote:
Unfortunately "fictional force" as a term has the problem that is best demonstrated in how people often say that "centrifugal force" is fake. It is not fake, but just a pseudo force that is observed to being in an accelerated reference frame.
As far as I'm concerned, we should dump the "fictional force" and "pseudo force" terms and just call them frame-dependent forces. It has no implication that they're not real, and it, again, firmly fixes in the mind the importance of reference frames and distinguishing between inertial frames and accelerating ones.
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Old 04-16-2018, 07:24 PM
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Whatever you call them, centrifugal force is exactly as real as gravity. If you want to say that they're both real, that's fine. If you want to say that they're both "fictitious" in a way that, say, the electromagnetic force isn't, well, then you get into questions of just what you mean by "fictitious", but sure, you can say that too. But what you can't say is that gravity is "real" but that centrifugal force isn't.

Back to relativistic mass, a further explanation:

First of all, there's a quantity called gamma, or γ, that shows up a lot in relativity. γ = 1/sqrt(1-v^2/c^2). Or, what's important to note about it, is it depends on speed, and for small speeds (much less than the speed of light), it's very close to 1, but as v approaches c, γ approaches infinity.

OK, set that aside for now. Let's take a step back to ordinary Newtonian mechanics. In Newtonian mechanics, momentum is given by p = m0*v (I don't know why the letter 'p' is used for momentum; just roll with it). Momentum is a useful concept, so this formula is useful, and it's nice and simple, so everyone is happy. What I called m0 is the "rest mass", and is the mass an object has when it's at rest. In Newtonian mechanics, that's the only mass we ever deal with, so we usually just call it 'm', but I'm explicitly calling it out as the rest mass for convenience in comparing to the relativistic case.

Back to relativity. In relativity, it turns out that the correct form for the momentum formula is p = m0*γ*v. When v is much smaller than c (as it is for the sorts of things that Newton was dealing with), γ is almost equal to 1, so this ends up looking like m*v for those cases, but in cases with higher speeds, that doesn't work any more. Well, some people wanted the formula to still be simple, so they said "Let's define something called relativistic mass, mr = γ*m0, and then p = mr*v, and it looks just like it used to.".

But this quantity, "relativistic mass", isn't useful very often in relativity. And even when it is useful, we already had a perfectly good term for it, "energy". Well, technically, it's energy divided by c squared, but nobody who actually does relativity worries too much about factors of c. So it's not all that helpful.

On the other hand, rest mass turns out to be a very useful quantity, in relativity. For one thing, it's what's called an invariant: Any two observers, no matter what reference frames they're in, will always agree as to the rest mass of an object. And the easy way to do relativity is to do all (or at least, most) of your work in terms of the various invariant quantities.

So, does that mean that we have to give up on that nice pretty momentum equation? No, it doesn't even mean that. We can take that equation, p = m0*γ*v, and instead of defining a new kind of mass, let's define a new kind of velocity: Proper velocity, abbreviated u, is given by u = γ*v, and then we can say that p = m0*u. This makes more sense than attaching the γ to the m, because after all, γ is something that relates to velocity in the first place. And it's also more useful, because proper velocity (and its derivative, proper acceleration) turns out to have other applications besides just momentum.

So again, we're left with rest mass being the only mass anyone talks about, and so, just like in Newtonian physics, it makes sense to just call it 'm', without the subscript.
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Old 04-16-2018, 08:04 PM
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The first video is interesting, but... An important note is that because each frame of reference sees time and distance differently; and "simultaneous" is different for different observers - the only definite simultaneity for all observers is when two objects are at the same location. If A watches B and C moving - A does not necessarily see B and C pass their start points at the same time, and ditto B for A and C, and so on. Only when A passes B (to start) or B passes C at the midpoint can one say the event happened at the same time on both clocks.
Minkowski space is so different that we use "acceleration" as a crutch.

The challenge in explaining how it works under space-time is hard when many won't believe it.

But yes there is no paradox under of special and general relativity and the solutions to the classic version will be identical in the case of a round trip.

There are some fun versions with the round trip model, equating the acceleration experienced traveling twin in the spaceship can be made equal with the stationary twin who is being accelerated in a gravitational field.

Even in the simpler SR context the acceleration explanation often ignores the still SR concept of the "clock postulate"
.

The clocks rate may be affected by acceleration but the rate of the accelerated clock doesn't depend on its acceleration.
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Old 04-17-2018, 04:13 AM
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In Newtonian mechanics, momentum is given by p = m0*v (I don't know why the letter 'p' is used for momentum; just roll with it).
I had the name related to this pop in my head, as to why it is p, while letting my dog out to pee

Before Newton/Galileo there was no momentum and impetus would be the closest term, I don't know if 'i' and 'm' were already in use but it is probably because the Latin root of impetus is petere so 'p' was used.

So blame Buridan
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Old 04-17-2018, 05:36 PM
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Thanks, everybody! I am now 7% closer to understanding this musical joke I heard on Mountain Stage.

From Stewed Mulligan's song about Albert Einstein:
"Had a frame of reference,
Set it on the fence.
Showed it relativity,
Ain't seen the damn thing since.
(chorus)
Albert, dance around,
Albert, be profound.
Albert, let your hair stick out,
And your socks fall down."
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Old 04-17-2018, 08:16 PM
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Ah, let me try and clarify some things.


Under Newtonian and SR you have "initial frames" which really can just be thought of as locations that don't have external forces acting on them. So if you think of a location billions of light years away from other objects as an example. These are "privileged" frames and in Newtonian physics these privileged frames are interchangeable and you can reference a universal frame that basically ignores the complicated bits but includes all of these privileged frames.

Basically these "privileged" frames go away under GR. But this really doesn't relate to the speed you are going in that privileged context (massive oversimplification)

To help with the speed of light question in your original question can be visualized with a spacetime diagram.

Think of it as an normal X + Y 2D graph, where up is you traveling through time and Y is any movement you make in the normal non-time dimensions.

The units here are natural units, so +1 in the X axis is the distance that a photon would travel in X time. This results in a photon's world line being exactly 45 degrees from all observers viewpoint.

This is where it is critical to understand that the speed of light is the speed of causality, that just happens to be the speed that mass-less particles like light must travel.

You also have a "world line" and even when you are "stationary" you are still moving through time.

Here is where things get interesting, because you are still in the traditional space dimensions you are actually following the shortest path possible through time, which means your clock is moving "fast" as possible to an external observer. But that photon, which looks like it is going at a 45 degree angle will actually experience no time at all.

Lets say that you are way out in the middle of space and had no references to anything else but were moving at a significant portion of the speed of light. You wouldn't notice anything, but because everyone views the speed of light the same, even if you were moving at 1/2c you still can't interact with other objects in front of you faster than the speed of causality. Basically you are not following the shortest path through time, so for an external observer your clock would be running slower.

If we could violate the speed of causality and send information faster than speed of light and lets say you held a white lamp up and some how looked at the light from a position ahead of where you are. That white light would be blue shifted from that slower for a FTL front observer and red shifted fro a FTL rear observer.

The speed of causality, which really limits the ability to exchange information wouldn't allow for that, but the energy levels of the light would change, but the user wouldn't notice.

Thus the Einstein equivalence principle.
Quote:
The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.
Tests to find violations of this principle, basically showing that a privileged frame exists are where some of the more seemingly crazy ideas like the universe is a hologram come from.

Please note this is the cliff notes version, and the above analogies won't be exact.

The implications are kind of cool though. For example, if you ignore air resistance, if you toss a base ball it is actually following a path that is straighter in spacetime than you are experiencing, as the pressure you feel on your feet from what we call gravity is actually the earth accelerating you away from your preferred shortest path through space-time.

Or the one that makes people get riled up: The international space station (once again ignoring friction and tidal forces) is not "falling and missing" the earth, it is actually traveling in the straightest (geodesic) path through spacetime, as is the earth when orbiting the sun.

The crazy thing here is that the earth spinning, actually twists space time too, resulting in frame dragging. So light traveling in the direction of rotation of the earth will move faster than light moving against the rotation. The effect is tiny but it will induce math panic attacks for people studying black holes.

If you use the simple Schwarzschild black hole's which don't spin the math is hard, but once you introduce spin and have to bump up to the Kerr metric things get crazy.

This is an example of the "geodesic" shortest possible line for a body orbiting a spinning black hole

As a reminder, to the body in the above orbit, it is not undergoing acceleration!!

How cool is that.

Remember that these effects are all experimentally verified, so even if we do find a unifying theory it will still be a crazy weird world that will be a challenge and fun to work through.

TL;DR there is no privileged reference frame as we know it today in GR, all of our clocks and reference frames are just as valid yet the man or the speed of causality is still the boss.
  #24  
Old 04-17-2018, 09:25 PM
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Chronos Chronos is offline
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Inertial reference frames are still just as "special" in general relativity as they are in special relativity. The lack of "privileged" reference frames means that no one inertial reference frame is in any way preferred over any other. The reference frame in which I'm at rest is no more nor less valid than one in which a cosmic ray is at rest, with a relative speed of .99999999c to each other.
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Old 04-18-2018, 11:48 AM
Asympotically fat Asympotically fat is offline
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In special relativity it is always possible to choose a global coordinate system where the Christoffel symbols vanish everywhere, these are the 'privileged' inertial frames of special relativity. In an accelerated frames of reference in SR the Christoffel symbols do not vanish and there's not obvious procedure for extending such a frame spatially.

In general relativity the Christoffel symbols can always be made to vanish locally to construct a local free-falling frame, but, except in the special case of flat spacetime, the Christoffel symbols cannot be made to vanish globally and there's no general procedure for constructing global frames.

Locally the inertial and/or gravitational forces felt by an observer are directly dependent on the Christoffel symbols of their frame.
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