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Author Topic:   Speed of Light Barrier
JustinC
Member (Idle past 3743 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 1 of 178 (222953)
07-10-2005 1:15 PM


This is a question to all the physics gurus (Sylas, Eta, etc) on this board. I have a good background in physics, so try not to dumb down answers too much.

Why can't we exceed the speed of light? I've heard two explanations but I am not sure which one is right.

The first explanation is that mass increases as matter approaches the speed of light, so it would take more and more force to further accelerate an object as it approaches the speed of light. This seems wrong to me for some reason. One's mass doesn't objectively (from all reference frames) increase, does it? Only from a second observers. So why would the fact that there is a second observer affect how I can accelerate?

The second is the reason I think is correct, but I'm having trouble articulating it. Basically, it's a fundamental property of space-time. Velocities aren't additive according to special relativity. In order to add velocities, you use the equation:

u= (v1 + v2)/(1+ v1v2/c^2)

So from your referece frame you may add 2000 m/s on to your original velocity, but the second observer won't see it add that way due to the above equation.

Are these mutually exclusive explanations? Are they related?


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AdminAsgara
Administrator (Idle past 1202 days)
Posts: 2073
From: The Universe
Joined: 10-11-2003


Message 2 of 178 (222958)
07-10-2005 1:42 PM


Thread moved here from the Proposed New Topics forum.

  
Chiroptera
Inactive Member


Message 3 of 178 (222963)
07-10-2005 2:07 PM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


It is true that mass doesn't increase except from the point of view of a second observor. But then, you aren't moving at all except relative to another observor. As far as you are concerned, you are always remaining motionless.

The formula that you have at the end of your post (I am assuming that it is correct -- I'm too lazy to look it up and verify it) is correct. Suppose that I am observing you move at a velocity equal to v1. Now in your reference frame, you are motionless. Then you speed up to a velocity of v2. That means relative to your initial reference frame, your velocity is now v2; however I watch you accelerate to a velocity of u, given by the equation.

How does this work? I am watching you accelerate. Let us say that you are in a vessel ejecting mass from a rocket; this is increasing your momentum by some amount, perhaps by a large amount. However, to get your velocity I must divide your momentum by your mass -- since your momentum increases a lot but your velocity doesn't increase by very much (after all there is no limit to how much momentum you can have, but your velocity is constrained by the speed of light) that must mean that your mass has increased by a large amount.

However, this increase in mass is just what I, in my reference frame, is measuring. To an observer in another reference frame, you will have a different mass. You, of course, being motionless in your own reference frame, see no change in your own mass.


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Modulous
Member (Idle past 1003 days)
Posts: 7789
From: Manchester, UK
Joined: 05-01-2005


Message 4 of 178 (222966)
07-10-2005 2:45 PM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


The joker:
Don't forget as well the small issue of time, there simply isn't enough time in the universe to get to the speed of light (with the time dilation that occurs), the heat death of the universe would guarantee that there is no workable energy, so no more acceleration.

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Tony650
Member (Idle past 2932 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 5 of 178 (222973)
07-10-2005 3:37 PM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


Greene's time-dilated cars
I don't know if this is quite what you're asking but it was a great help to me in better understanding the light-speed barrier. I wrote about it in another post and, while it specifically deals with time dilation, it indirectly presents a fairly intuitive analogy of how the light-speed barrier works. I'll quote the relevant portion here.

I think the best explanation I've ever read of time dilation was by Brian Greene who describes it with the analogy of racing cars across a set distance out on a large, flat desert plane.

He shows how, assuming a constant speed for each trip, you will measure one time when travelling in only one dimension, say, north/south, between the start and finish line, but another time when travelling simultaneously in two dimensions, say, north/south and east/west, between the start and finish line. The time measures differently because, in the first scenario, your speed is dedicated to travel in one dimension, while in the second scenario, it is shared between travel in two dimensions.

In this way, he showed how our travel through space and time can be seen as both drawing on the same unchanging "reserve" of velocity, which works out to the speed of light. He said that this shows how our travel through space affects our travel through time and is another reason we can never travel faster than light through space. To do so would require a greater overall velocity than we have at our disposal.

Again, as an analogy, this description is inherently imperfect. But I must say, it is easily the most satisfying explanation of time dilation that I've ever read. I've known for a long time what happens, but not until I read that did I finally get a handle on how it happens. I don't know how closely this analogy reflects the reality, but it gave me a great mechanism by which to visualize the process.

So long as we're touching on this again I'd like to ask the resident physicists... Just how close is this analogy to the actual process? It is the best (read: most easily-perceptible) model of time dilation/the light-speed barrier that I've ever read, but is it an accurate illustration of what actually happens? Does mass indeed have an unchanging "reserve" of velocity that it shares between space and time, such that one must fall if the other rises and vice versa?


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Brad McFall
Member (Idle past 3932 days)
Posts: 3428
From: Ithaca,NY, USA
Joined: 12-20-2001


Message 6 of 178 (223000)
07-10-2005 7:20 PM
Reply to: Message 4 by Modulous
07-10-2005 2:45 PM


Re: The joker:
Hey Mod, perhaps you can help with this and tie it into the thread head.

I have been getting originally unsolicted e-mail from

From : Ozan Hasimi OKTAR Sorry I have deleted the contents as this author requested twice in email.

for some time now and I have been replying but I am starting to think that his ideas violate TIME in respect to the speed of light?

quote:
The story begins with a researcher called Giovanni Amelino-Camelia. Working on quantum gravity in Rome, he decided to find a theoretical solution to solve one of modern physics� big problems � unexpectedly high energies of cosmic rays. To do this, he formed a new addition to the theory of special relativity.

The basis of doubly special relativity, which this is now called, is that the universe possesses two, not one absolute values. In Einstein�s original relativity, we have the speed of light as a constant, independent of the frame of reference for the observer. In doubly special relativity, there is also a threshold energy/length, which is true for all observers.

So far, so simple? But this small change makes a huge difference. By SR, the length of an object is entirely dependent on the particular observer. If I were moving at a different speed from you, I would see an object entirely differently. But in certain branches of physics, the laws of physics around an object are very dependent on its length, resulting in the absurd suggestion that the laws of physics are different for each person. In attempting to unify the different laws of quantum mechanics, where the Planck length/energy represents the point where quantum laws become apparent, this is especially problematic. If we follow DSR, and use the Planck energy as a universe absolute threshold, all observers can determine the laws of physics in the same way, and this problem is solved. The unification of quantum theory and relativistic theory is made a lot easier.
http://physicspost.com/articles.php?articleId=129


I got that by googling his name today.

In particular he seems to have an extension that is against Poincare's notion of return point (in this time) or the clock of Einstein. I dont really know. I really cant tell if I'm just in South AMerica on this or if there really is something interesting here. Perhaps one of the physics people can respond as well and show up more in JustinC's question.

OKTAR has some material in two places here:
http://physicsastronomy.com/list.php?f=14&collapse=0

He has a dubious, to me,bye-bye line "Satan Trust uS"

Would the speed of light be a barrier in this kind of time?

Edited by Brad McFall, : No reason given.


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sidelined
Member (Idle past 4807 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 7 of 178 (223039)
07-10-2005 10:50 PM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


JustinC

The first explanation is that mass increases as matter approaches the speed of light, so it would take more and more force to further accelerate an object as it approaches the speed of light. This seems wrong to me for some reason. One's mass doesn't objectively (from all reference frames) increase, does it?

The mass does indeed increase since energy and mass are the same thing {E=mc^2}The "rest" mass of an object is different from one that is moving in accordance with this formula. m = m'/[sqrt{1-v2/c2}]This is the lorentz transformation of mass.

Since I cannot faithfully reproduce the formula m' is the rest mass while the m we seek is the relativistic mass.Now if the velocity {v}is equal to the speed of light {c} then our formula becomes m'/sqrt{1-1} which is the sqrt of 0 therefore division by zero not allowed means that the limiting case as a mass approaches the speed of light scales up exponentially and soon requires a greater amount of energy than is presemt within the universe.Thus an object with any mass at all must eventually become incapable of further acceleration due to the mass increase.

Photons of light avoid this by having no mass or rather by being simply energy with the characteristic that it can never go slower than the speed of light for the medium within which it travels.

This message has been edited by sidelined, Sun, 2005-07-10 08:51 PM


Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry

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cavediver
Member (Idle past 2543 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 8 of 178 (223078)
07-11-2005 5:27 AM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


Brian Greene's explanation mentioned further up the posts is a very good way of describing it... and the analogy is not so flawed as the poster inferred. But the idea of a "reserve" can be expressed better:

I use the following picture with my students...

Imagine the space around you (in your room, office, etc) is representing space-time, with left-right, and forward-backward as your space dimensions, and up-down as your time dimension.

Take a 1m (or 3ft) ruler. This is your 3-dimensional (2space +1time) velocity vector. Let's call its length "c". Point it straight up.

As you can see, your velocity vector is pointing entirely within the time-direction and not pointing in any spatial direction. This is you, moving through time with "time-velocity" c, and not moving through space at all.

Now tilt the ruler over by 5 degrees from vertical. Your velocity vector is pointing slightly sideways, and so you have a small spatial velocity, but your "time-velocity" is hardly changed. However, because of the magnitude of c, this small spatial velocity is actually enormous in our terms.

Now tilt the ruler further to 45 degrees. You have now made a measurable impact on your "time-velocity". You also have a large sideways, spatial velocity.

Finally, tilt the ruler until it is horizontal. You now have NO time-velocity at all, but all of your velocity is in the spatial direction. How much velocity? c of course... the length of the ruler is fixed.

You should now start to understand simultaneously the reason for a max speed limit and time-dilation (and if you think about it hard enough, length-contraction)...

The speed-of-light is a maximum simply becuase it is THE ONLY SPEED. It just depends in which direction of four-dimensional space it is pointing! You are always travelling at the speed-of-light, just not always spatially.

Can you now understand that what we call velocity is really just a ROTATION of a fixed length higher-dimensional vector?

Asking how to go faster than the speed-of-light is the same as asking "what angle can I turn my ruler through to make it longer than 1m?". As you can see, the question makes no sense. Our ideas of velocity are screwed becasue we think of it as a rate of translation, where-as it is actually a rotation.

Hold a second ruler perpendicular to the first, so it starts pointing in a purely sideways / spatial direction. As we start moving spatially, we rotate and now our spatial vector is pointing slightly downwards. The important point is that the ruler does not now point as far in the spatial direction because of its rotation. Rotate 90 degress to "the speed-of-light" and the spatial ruler no longer points spatially at all. This is length-contraction.

Once you realise that all the bizarre notions of special relativity simply come from having a restricted 3d viewpoint on a 4d universe, you are well on your way to learning the subject.

This message has been edited by cavediver, 07-11-2005 05:30 AM


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Replies to this message:
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cavediver
Member (Idle past 2543 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 9 of 178 (223101)
07-11-2005 8:50 AM
Reply to: Message 3 by Chiroptera
07-10-2005 2:07 PM


Just a quick addition to what I wrote above... this whole business with "relativistic" mass is just another example of measuring the wrong thing. We're looking at a 3d concept and expecting it to make sense in a 4d universe. Length, velocity, time and mass as we naively understand them are merely PROJECTIONS of the true 4d quantities which don't change. Think of shadows: shadows are 2d projections of actual 3d objects. The shadows themselves can change shape markedly, without the object doing so. In fact, this is why we see various quantities going to infinity... it is only the projection moving out of its range of validity.

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Chiroptera
Inactive Member


Message 10 of 178 (223108)
07-11-2005 9:59 AM
Reply to: Message 9 by cavediver
07-11-2005 8:50 AM


Yeah, I like to draw a line segment on a plane, then draw two different x- and y-axes, and explain how the same segment can have different "x-lengths" and "y-lengths.

Then, it it appears that people may understand this, I mentions stuff about rotating coordinate axes through imaginary angles.


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cavediver
Member (Idle past 2543 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 11 of 178 (223111)
07-11-2005 10:27 AM
Reply to: Message 10 by Chiroptera
07-11-2005 9:59 AM


Then, it it appears that people may understand this, I mentions stuff about rotating coordinate axes through imaginary angles.

Or just teach them the hyberbolic trig... they always wondered what that sinh and cosh stuff was on their calculators! You haven't done the barn paradox until you've drawn it on a hyberbolic grid :-)


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Tony650
Member (Idle past 2932 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 12 of 178 (223259)
07-11-2005 8:47 PM
Reply to: Message 8 by cavediver
07-11-2005 5:27 AM


Hi cavediver.

cavediver writes:

Brian Greene's explanation mentioned further up the posts is a very good way of describing it... and the analogy is not so flawed as the poster inferred.

I apologize if I gave the impression that I personally thought it was flawed. That truly wasn't my intention. The reason I asked is because, in my experience, such explanations are usually simplified descriptions which are specifically designed to be more palatable to our intuitive way of thinking than the actual descriptions otherwise would be. As such, they often convey a more intuitive sense of what is happening at the expense of total accuracy.

But this is just something that I'm cautious about. As a scientific layman, I try to be careful not to take these kinds of analogies too literally, lest I get a skewed idea of the actual models. As I've said previously, it's frustrating not understanding the underlying mathematical theory. Mathematically, the models can be shown with such accuracy, yet when asking what the math "really" means, it so often has to be translated via statements like, "Well... Try to think about it like this..."

Anyway, my point is that I'm just wary of how closely I associate intuitive physical analogies with the actual phenomena they describe. It seems, from what I've heard, that the only way to really understand certain physical models is mathematically.

That said, if this analogy is indeed an accurate description of the actual model, that's great. It gave me a deeper insight into the process than any other description I've ever read, so I'm pleased to hear that I have the correct understanding.

I also appreciate your explanation of the "reserve" of velocity. I couldn't really think of any other way to phrase this, but no problem; your description was very much along the lines I was thinking. Thanks for the confirmation.

cavediver writes:

Once you realise that all the bizarre notions of special relativity simply come from having a restricted 3d viewpoint on a 4d universe, you are well on your way to learning the subject.

Off-topic here, but you've just touched on my personal obsession. You seem quite knowledgeable of this so, if you can help me in any way, please feel free to contribute your own thoughts. I'm always on the lookout for anybody I can learn from in this area.:)


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cavediver
Member (Idle past 2543 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 13 of 178 (223316)
07-12-2005 7:13 AM
Reply to: Message 12 by Tony650
07-11-2005 8:47 PM


Anyway, my point is that I'm just wary of how closely I associate intuitive physical analogies with the actual phenomena they describe. It seems, from what I've heard, that the only way to really understand certain physical models is mathematically.

Absolutely. This is the key to getting over all the naive preconceptions and objections. My description was not an analogy. It was an actual depiction of the 3+1 dimensional mathematics (with a little simplification of course!)

You can produce analogy upon anaology, but until you understand the mathematics, you cannot see how it all fits together as one incredible whole.

Off-topic here, but you've just touched on my personal obsession. You seem quite knowledgeable of this so, if you can help me in any way, please feel free to contribute your own thoughts.

Hmmm, interesting thread. Shame I wasn't around for it. The funny thing is that as you get more into the mathematics, topics such as extra dimensions lose their mystique and become the ordinary!

The best way to learn is to devote your first three decades to the subject :-) That's how I did it. Otherwise, if you have a desire and the patience to get into the mathematics, try "The Road to Reality" by Roger Penrose. It's an attempt to bridge the enormous gap between the layman approach to fundemental physics and the post-graduate. I'm not sure it quite suceeds, but he writes well and he sees a lot further and deeper than many of the others out there, even if he does have some quite bizarre ideas.


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Tony650
Member (Idle past 2932 days)
Posts: 450
From: Australia
Joined: 01-30-2004


Message 14 of 178 (223504)
07-12-2005 8:47 PM
Reply to: Message 13 by cavediver
07-12-2005 7:13 AM


Hi cavediver.

cavediver writes:

My description was not an analogy.

Again, I apologize for my lack of clarity. I wasn't referring to your description; I was referring to Greene's. The cars racing across the desert is clearly a "commonplace" illustration that Greene uses to describe the actual phenomenon in a more easily-perceivable way. It was this description to which the word "analogy" was directed.

If I've understood you correctly, though, Greene's analogy very closely reflects the actual model anyway. Your description is exactly the impression I got from Greene's cars. So it seems that I did understand it correctly. I was, perhaps, just not explaining it well (the "velocity vector," for example, being a more useful description than the "reserve of velocity").

cavediver writes:

You can produce analogy upon anaology, but until you understand the mathematics, you cannot see how it all fits together as one incredible whole.

Ugh! I know; it's frustrating. I wish I did understand the math. Unfortunately, like many amateur scientists, I rely on the nearest approximations that can be described in physical terms to understand the models. As a rule, if it can be described in a way that I can somehow picture in my head, I can understand it within reason. If it can only be shown through abstract mathematics, though, I'm pretty much screwed.

I find it to be a kind of double-edged sword, really. I like descriptions, such as Greene's cars, that are clear and easy to understand. At the same time, though, I worry that the more simplified the description (for ease of understanding), the less accurate it will be in describing the actual model. It's tough trying to understand physics purely through the concepts themselves, and knowing none of the math.:P

cavediver writes:

Hmmm, interesting thread. Shame I wasn't around for it.

Oh, please don't let that stop you. Unless it's been closed unbeknownst to me, you should still be able to post there. If you have anything you can add to it you're more than welcome.

cavediver writes:

The funny thing is that as you get more into the mathematics, topics such as extra dimensions lose their mystique and become the ordinary!

So I understand. From what I've heard, performing mathematical calculations in more than three dimensions is not the least bit unusual. Three dimensions or three hundred dimensions... they're all just numbers as far as the math is concerned.

cavediver writes:

The best way to learn is to devote your first three decades to the subject :-)

Heh heh!:D

Well, I haven't devoted that much time to it, but I have devoted quite a bit. I've been fascinated by dimensional concepts for many years now and I've read a lot of material on the subject. I still know essentially nothing of the math, but I do believe I have a fairly solid grasp of the basic principles (at least for a layman).

cavediver writes:

Otherwise, if you have a desire and the patience to get into the mathematics, try "The Road to Reality" by Roger Penrose.

Hmm... Could be worth a try. Thanks for the recommendation.:)

Just to be clear, though, my interest is not really in the underlying mathematics; it is to gain a clearer physical perception of higher dimensions. My ultimate goal, though a long shot admittedly, is to achieve the same intuitive perception of four-space that I have of three-space.


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JustinC
Member (Idle past 3743 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 15 of 178 (223850)
07-15-2005 2:42 AM
Reply to: Message 8 by cavediver
07-11-2005 5:27 AM


Thanks for the analogy. I never heard it put that way, though I like to think I'm pretty well read on the subject. That "time-velocity" does really clarify what's going on. I'm having trouble understanding the "length-contraction" in that analogy.
quote:

Hold a second ruler perpendicular to the first, so it starts pointing in a purely sideways / spatial direction. As we start moving spatially, we rotate and now our spatial vector is pointing slightly downwards. The important point is that the ruler does not now point as far in the spatial direction because of its rotation. Rotate 90 degress to "the speed-of-light" and the spatial ruler no longer points spatially at all. This is length-contraction.


Is the first ruler pointed up? Why does the vector point downwards, wouldn't that be going backwards in time? I'm missing something.

Back to the original question, though. I'm not sure you guys really answered it.

Chiroptera showed that mass will increase as velocity increases, but only by assuming there is a limit to the speed of light. I took that post as "mass will increase since there is a speed of light limit," not "there is a speed of light limit because mass increases."

You gave me a good way of visualizing special relativity concepts, but only by assuming a fixed length to the ruler.

Is the answer just: Assuming there is a speed of light limit, various predictions would be made such as time dilation, etc. These have been observed or inferred by experiments, supporting the assumption.

Another way I like to think about it, though I'm not sure it is correct, is similar to how Einstein first thought about the problem.

Based on Maxwell's equations, light is a self-propogating E-Field and B-field. The only way it is self propogating is for it to be moving, but if you were traveling at the speed of light it wouldn't be moving relative to you, so it wouldn't exist. Then if you slowed down, it would either: 1.) reappear (something from nothing) or 2.) continue to not exist, although from another persons reference frame (whose was moving slower than c the whole time) it would still be there, right next to you. These scenerios seem pretty illogical, and it seems intuitive to assume one simply can't go faster than c.


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