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Procyan
2010-May-15, 11:31 PM
I don't think this has been addressed already...It seems like there are two distinct types. One you feel, like in a rocket and the other you don't as in falling towards a black hole. Are they infact different?

Would your mass increase as you approached c while in free fall? I know that it would in a fast rocket, but with a gravity well...well its not really accelleration is it? you know its warped space time or something?

thanks in advance.

John37309
2010-May-16, 02:03 AM
Einstein would tell us that your mass WOULD increase as you approach c. What i think you are asking, if you were accelerating the whole way as you approached c, would it be different? In that case, i believe that as you are accelerating, and approaching c, your mass would increase at a proportional rate to your rate of acceleration. Of coarse, you could never get to c ....LOL

John.

Ken G
2010-May-16, 02:37 AM
IIt seems like there are two distinct types. One you feel, like in a rocket and the other you don't as in falling towards a black hole. Are they infact different? Yes. What you are asking about is a very crucial concept in relativity, it is the difference between "proper acceleration" (that which an accelerometer in your pocket would read, and if the reading is nonzero, it means you need to take care in how you coordinatize your surroundings or the laws of physics won't seem to work for you-- alternatively, you can use naive coordinates but assert the presence of a kind of "fictitious gravity"), and "coordinate acceleration" (which just means that objects are accelerating in comparison to what you have arbitrarily chosen in your coordinate system to say are not accelerating, often things that are staying stationary with respect to you).

The former relates to the laws of physics, but the latter doesn't-- it just relates to your choice of coordinates, your decision about what objects to label as "not accelerating". A classic example of the latter is essentially every object in your vision right now-- they are all being acted on by a net force of some kind, so they should all be considered as accelerating from the point of view of the laws of physics, but you choose a coordinate system that says they are all stationary, just because they are stationary relative to you. This bias led Newton to imagine the presence of a "force of gravity", and he got a lot of mileage out of that idea, but it is fundamentally untrue. Gravity is a set of coordinates that allows you to ignore proper acceleration when it is right in front of your nose.

Procyan
2010-May-16, 04:54 AM
Thanks, I think this is really interesting because I was thinking along the same path that James seems to be on. But I think the sort of arbitrary coordinate system in the second part of Ken's *aptly named "g" * reply means...gulp... that objects in free fall CAN approach light speed relative to an attractor... because my reference frame includes the attractor. I think I'll call it Ground!

grapes
2010-May-16, 05:17 AM
Gravity is a set of coordinates that allows you to ignore proper acceleration when it is right in front of your nose.Get your nose out of my pocket! :)

Schneibster
2010-May-16, 12:19 PM
I don't think this has been addressed already...It seems like there are two distinct types. No; there is only one. In fact, one of the principles of General Relativity is that gravity and acceleration are equivalent. Historically, Einstein came to the theory of gravity by this route, but it isn't generally taught that way.


One you feel, like in a rocket and the other you don't as in falling towards a black hole. Are they infact different? You've confused two different things, but interestingly, you've chosen just the two things that are equivalent in GR. Because gravity acts on all objects, the acceleration it imposes on you if you're falling toward a black hole is relative to an observer in flat space. This is the gateway question to a fairly interesting conversation about the ways that, despite their equivalence, gravity and acceleration are different as we encounter them in reality; the main difference is tides. I'll leave that for later if you're interested; it's not down the main line of your questions. Moving right along, when you're accelerated in a rocket, what actually happens is that you accelerate some matter that was part of the rocket away from the rocket and the rocket undergoes equal-and-opposite acceleration; you have not thrown any matter away, so you do not intrinsically accelerate, but when the rocket does all around you, it transmits that acceleration to you by van der Waals forces and similar repulsive effects acting on your body. You experience a net force applied to you by the walls of the rocket, or some object you are in contact with that is accelerated by the rocket.

Another thing to keep in mind is that gravity is a warp in spacetime; so space is not flat in a gravity field. As a result, you appear to accelerate according to an observer in flat space. However, you do not agree you're accelerating; this is because you can perform a simple physics experiment (build an accelerometer) and determine that you are not accelerating. On the other hand, the same experiment performed in the rocket will have the different result that you are accelerating.

These are just a few ways they are different, though they are equivalent.


Would your mass increase as you approached c while in free fall? According to whom? The answer is different for different observers.


I know that it would in a fast rocket, but with a gravity well...well its not really accelleration is it? you know its warped space time or something?Ah, I see what you mean now. It doesn't matter why the observer in flat space says you are accelerating, whether it is gravity or the rocket, all that matters is how fast you're going relative to the observer; it doesn't matter, in particular, whether it's because you're falling into a gravity well or being accelerated in a rocket. What does matter is whether you agree you are accelerating.


thanks in advance.You're welcome. My pleasure.

Ken G
2010-May-16, 06:52 PM
All the same, there are indeed two quite different types of acceleration that we could perceive objects as having, and both get used in physics parlance commonly: proper acceleration (which is actual acceleration of the object in question), and coordinate acceleration (which is either apparent acceleration of the object due to acceleration or rotation of the observer, or it is acceleration in just part of the mathematical expression in some coordinates-- in either case, the proper acceleration is being disguised or obfuscated in some way). It seems to me this is what the OP is asking. The former type obeys Newton's laws in the instantaneous frame of the object in question, whereas the latter only appears to depart from those laws if we fail to notice how our coordinates are playing tricks on us ("centrifugal forces" when you drive around a curve are a classic example). The big surprise was that even real gravity (tidal gravity) is like this latter type of "coordinate acceleration"-- we just didn't realize we shouldn't be coordinatizing flat spacetime. This is more or less in agreement with what Schneibster said, just replacing his answer "no" to the OP, with my answer "yes." I'll let the OPer decide which one-word answer is more appropriate, since it is really all the clarifying explanations that count.

Procyan
2010-May-16, 08:04 PM
I've thought it over and decided that you are both wrong! Just kidding. What I was wondering is if you throw a meteor at a massive object hard enough (instantaneous velocity) will it accelerate to c and beyond? Imagine both I and the object are stationary, the meteor is falling into the object with an initial velocity near relativistic speed. You don't read about FTL meteors in BA/UT too often so I'm pretty sure its not a goer.

George
2010-May-16, 08:33 PM
All the same, there are indeed two quite different types of acceleration that we could perceive objects as having, and both get used in physics parlance commonly: proper acceleration (which is actual acceleration of the object in question), and coordinate acceleration (which is either apparent acceleration of the object due to acceleration or rotation of the observer, or it is acceleration in just part of the mathematical expression in some coordinates-- in either case, the proper acceleration is being disguised or obfuscated in some way). No doubt that is the best way to describe it, but I'd like to play with this a little without deviating from the OP.

Another way to see it, or at least until you "fix me good" :), is that both rocketing acceleration and falling deeper into a gravity well are the same because both involve forces acting on the observer. At least, the latter case is a "maybe". I haven't read about gravitons but if these are exchange particles that act upon every atom within our body, could they be considered to behave as a non-fictious force? If so, how could our nerves sense any normal force acting upon us if the force is ubiquitous throughout the body. Of course, in the case of the rocket, we feel the force acting upon the surface of our body, which causes our nerves to sense the change.

Note: It is probably worth mentioning that in the special case of a black hole -- mentioned in the OP -- the falling person would indeed become quite aware he or she is accelerating since the gravity gradient is so strong it will rip the person to shreds (ie spaghettification). Ironically, if it is a supermassive blackhole, the trip into the event horizon isn't all that bad, as I understand. [Have we ever established an irony thread around here to point-out such poignant astronomical oddities?]

neilzero
2010-May-16, 08:45 PM
I certainly don't claim to understand the math, but let me try any way. Normally we feel 9.8 meters per second per second toward the center of Earth so we feel any other amount or direction including free fall or even half free fall = some air resistance. Obviously the air rushing past produces a feeling.
In your frame of reference, your velocity is always zero, even if you are traveling c in someone else's frame of reference (or the ground's frame of reference) so you experience no weight increase, nor length change, nor time shortening and you can continue to accelerate, If you collide with something moving almost c in your frame of reference, great damage occurs. Acceleration and velocity are two different things. Neil

Procyan
2010-May-16, 09:44 PM
I think I just worked it out. George mentioned the crazy effects of super strong gravity fields. I had forgotten the inverse square law. Even a black hole's gravity reduces at distance so nothing can accelerate to c in free fall. Right?

I should frame the question this way: At what height must a ball be released over a given attractor such that its velocity on impact is 3000000000 m/s? Are there any known bodies so massive as to be able to do this at all?

Ken G
2010-May-16, 10:55 PM
I think I just worked it out. George mentioned the crazy effects of super strong gravity fields. I had forgotten the inverse square law. Even a black hole's gravity reduces at distance so nothing can accelerate to c in free fall. Right?
I would say you are still tripping over the difference between coordinate acceleration and proper acceleration. There are coordinate systems where an object accelerates faster than c as it enters a black hole, but it isn't proper acceleration that is doing it-- indeed, there is no proper acceleration at all. Spaghettification is an effect that occurs in the absence of any proper acceleration-- it happens when a body is moving in a spacetime that is so warped, the body cannot maintain its rigidity. It would require proper acceleration for parts of the body to keep the same distance from other parts-- in the absence of proper acceleration (from internal forces), the parts of the body diverge from each other. These are all ramifications of being deceived by one's own coordinate system-- in coordinates where only proper acceleration looks like acceleration, the falling object isn't accelerating at all, what is happening is more akin to the "expanding space" often used to picture the Big Bang model (in the case of black hole gravity, it isn't isotropic expansion, it's expansion in the direction toward the black hole, and compression in the sideways directions). When "space itself" is pictured as expanding, you need forces to keep from spaghettifying, you don't need forces to create spaghettification.

But George is right, this is all in the general relativity picture-- if gravity is to be unified with the other forces, there will need to be a graviton and a different way of thinking about all this, where gravity is a real force. I really don't understand why many physicists expect it to turn out that way-- if the big breakthrough of GR was in not treating gravity like the other forces, I'm not so sure why we need to unify it. But it is always the goal to achieve the highest level of unification, so it's natural to look for it.


I should frame the question this way: At what height must a ball be released over a given attractor such that its velocity on impact is 3000000000 m/s? Are there any known bodies so massive as to be able to do this at all?It gets tricky, because c is a kind of singular limit. That's the speed that anything that falls into a black hole from infinity would reach at the event horizon, relative to an object that was hovering at the event horizon. You might ask, isn't it impossible to reach c, but I think the answer is, what is impossible there is to have an object hovering at the event horizon! Such an object would need to be a little above the event horizon, and then the falling body would not quite have a relative speed of c. Note also that it is just as reasonable to say the hovering object is the one that is responsible for the speed, and the falling object never really acquired any speed at all. The latter is all about coordinatization, and the difference between coordinate acceleration (the kind of acceleration we normally expect the falling body to exhibit) versus proper acceleration (the kind of acceleration the hovering body actually experiences).

mugaliens
2010-May-17, 02:11 AM
I would contend that if you can't measure it with an on-board accelerometer, it's not acceleration. Thus, free-fall movement caused by gravity is not an acceleration, but the warping of the reference frame (space-time).

On the other hand, sitting here in my chair, I'm under 1 g of constant acceleration through the warped space-time around me. Speaking of which, my backside needs a two-minute walk...

George
2010-May-17, 01:28 PM
I would contend that if you can't measure it with an on-board accelerometer, it's not acceleration. Thus, free-fall movement caused by gravity is not an acceleration, but the warping of the reference frame (space-time). If acceleration is defined as dv/dt, and you notice that your rate of velocity is increasing relative to your surroundings, are you, or your surrondings, not accelerating? "Falling" is certainly different as you point out due to the lack of readings from a traditional accelerometer, but then dv/dt is no longer an accurate definition for acceleration, if you make "falling" a non-acceleration experience.

If gravitons are found then acceleration might be considered either external or internal, or physicists might choose to classify them in some more appropriate way. For me, I would like to know where all the force vectors get placed: externally or on every internal atom.


On the other hand, sitting here in my chair, I'm under 1 g of constant acceleration through the warped space-time around me. Speaking of which, my backside needs a two-minute walk... :) You have both accelerations at work: gravitons (hypothetically) pulling you down and the chair pushing you up. Lucky for you they balance exactly. *wink* If you can somehow adjust the graviton flow, your backside will be thankful. :)