# Strange character of space-time !

Suppose we are looking from an inertial frame at two events in a region of space-time.
The first event A (0,0,0,0) is the orign of our frame.
The second event is B(10,10,5,15/c) where the 4th corrordinate is time and c is the speed of light.
Then the total interval between the to event is ;
S = X^2 + Y^2+ Z^2- C ^2t^2
=100 + 100 + 25 - 225 = 0 But if look at Distance;
D = (100 + 100 + 25)^0.5 = 15m so the light needs 15/c second to go from A to B
So if the interval of space-time between two event is zero that does not mean that the two events are the the same
Is this strange or only that it is related to our inability to visulize the space-time?
Does this mean that any event in space-time represents unlimited number of events that are zero space-time interval distant from it ?

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JesseM
Suppose we are looking from an inertial frames at two events in a region of space-time.
The first event A (0,0,0,0) is the orign of our frame.
The second event is B(10,10,5,15/c) where the 4th corrordinate is time and c is the speed of light.
Then the to total interval between the to event is ;
S = X + Y + Z - C t
=10 + 10 + 5 - 15 = 0
But if look at Distance;
D = (10 + 10 + 5)^0.5 = 15mso the light needs 15/c second to go from A to B
So if the interval of space-time between two event is zero that does not mean that the two event are the the same
Yes, a space-time interval of zero represents what is called a "light-like separation" between a pair of events, see the discussion here about the three different types of spacetime intervals (the other two being 'time-like' and 'space-like').
Does this mean that any event in space-time represents unlimited number of events that are zero space-time interval distant from it ?
No, despite have a spacetime interval of zero between them they are really separate events, you can't say that one event "represents" the other one.

Dale
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So if the interval of space-time between two event is zero that does not mean that the two events are the the same
That is correct. The Minkowski inner product is bilinear, symmetric, and nondegenerate, but it is not positive definite.

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No, despite have a spacetime interval of zero between them they are really separate events, you can't say that one event "represents" the other one.

yes.. events are different of course when you divide the space-time into its four dimensions in different ways according to frames..but i mean when we look at space time
objectively as a unit (like looking to our three-dimension space before dividing it in arbitrary maner into three dimensions)
eg; if we take the surface of a paper as a part of two-dimension world then if the absolute distance between two points is zero then this mean that the two point must be the same regardless of the way we divide this 2D world into 2 dimentions ..but this is not the case in space-time.
This is what I mean by strange character of space-time.

Dale
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eg; if we take the surface of a paper as a part of two-dimension world then if the absolute distance between two points is zero then this mean that the two point must be the same regardless of the way we divide this 2D world into 2 dimentions.
Yes, this is because the Euclidean inner product is positive definite, which is a stronger condition than the nondegeneracy of the Minkowski inner product.

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That is correct. The Minkowski norm is bilinear, symmetric, and nondegenerate, but it is not positive definite.

please , give us short definitions to the three concepts underlined.

Dale
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Bilinear means that it is linear in the first and the second arguments. This in turn means that it can be written as a matrix.

Symmetric means that the order of the arguments doesn't matter.

Positive definite means that it is positive or zero, with zero only if at least one of the arguments is zero.

Dale
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Oops. I just noticed that I have been talking about the inner product but using the word "norm" instead. I went back and corrected it. The square of the norm is, of course, the inner product of a vector with itself.

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I am obviously way over my head even being on this forum, but maybe someone can answer this simple question for me. You are in a spaceship traveling at some minute fraction of a second less than the speed of light. Inside the spaceship you are traveling, you fire a gun. If the bullet leaves the gun at 600/ft per second, it, combined with the vehicle it is traveling inside of, will have a speed of 600 ft per secone PLUS the speed of the spaceship just a hair under the speed of light. Since the combined speed of the bulet and the space ship would exceed the speed of light, something the universe will not allow, what would happen? Same question if you simply turned on a flashlight, but in the flashlight example, the light leaving it would have no mass, as it would in the case of the bullet. But in both examples your are breaking the speed limiit of hte universe. Any answers?

Look up relativistic addition of velocities.

The bullet goes 600ft/sec when measured using a very very slow clock. So slow in fact that the bullet doesn't go faster than light.

So if the interval of space-time between two event is zero that does not mean that the two events are the the same
Is this strange or only that it is related to our inability to visulize the space-time?
Does this mean that any event in space-time represents unlimited number of events that are zero space-time interval distant from it ?
In an informal way, you can regard the spacetime interval as the proper time (squared) that elapses on a hypothetical clock that is transported from one event to the other. An interval of zero means that a hypothetical clock transported between the two events has to be travelling at the speed of light, and the path is lightlike and the path is on the surface of a light cone. If the separation is spacelike, a hypothetical clock that is present at both events would have to be travelling at greater than the speed of light and its elapsed proper time would be imaginary and since the interval is the proper time squared, the interval is negative. The imaginary time of the clock in the spacelike case is a clear indication that you could not actually transport a real clock at greater than the speed of light.

Look up relativistic addition of velocities.

The bullet goes 600ft/sec when measured using a very very slow clock. So slow in fact that the bullet doesn't go faster than light.

Thanks. I read your link (or at least tried to). I get the basic premise that things are not the same when you approach the speed of light as they are when you are traveling much less than the speed of light. I understand that premise that the combined velocities can never exceed the speed of light.

Here is my follow up question:

As I understand it, it takes about one light second to travel around the earth 7 times. So, if a special train were built on a special theoretical v e r y high speed track around the circumference of the earth and you got on this train and it traveled at a velocity just the smallest fraction of a hair under the speed of light. So, if there are 31,536,000 seconds in a year, then, you would have traveled around the earth approximately 220,752,000 times in one year, as a passenger on this train, traveling at a velocity of just under the speed of light. When you got off this train, you would be much less than a year older then when you got on, while everyone and everything on earth would be a year older. I do not know what they exact ratio is, but let's say, for argument's sake, that you were one month older because the near light speed had made time slow down for the passengers on that train. So you would have essentially traveled the distance for light to travel around the earth 220,752,000 times going at 186,000 miles per second, in only 1/12th the time it should have taken you from the passenger's perspective since you still would have made that trip of 220,752,000 revolutions, but you would have aged only one month and the watch you were wearing on your wrist would only show that you have been on that train for one month instead of one year. So, according to the passenger's watch, it would have traversed a distance it would take a velocity of 186,000 per second to achieve in a year, but you would have done it in only a month from your perspective, which would mean you would have had to have been traveling at 12 times the speed of light, form your perspective, to achieve that distance in such a short period of time.

Now, in the last fraction of a second of your trip, you stand at the front of your train, which is already traveling as close to the speed of light as the universe will allow, and you fire a bullet from your gun at a target in front of you, will the bullet get to your target before you and your train will? If the answer is yes, then that bullet just traveled faster than the speed of light. Can you explain please? Thanks.

Thanks. I read your link (or at least tried to). I get the basic premise that things are not the same when you approach the speed of light as they are when you are traveling much less than the speed of light. I understand that premise that the combined velocities can never exceed the speed of light.

Here is my follow up question:

As I understand it, it takes about one light second to travel around the earth 7 times. So, if a special train were built on a special theoretical v e r y high speed track around the circumference of the earth and you got on this train and it traveled at a velocity just the smallest fraction of a hair under the speed of light. So, if there are 31,536,000 seconds in a year, then, you would have traveled around the earth approximately 220,752,000 times in one year, as a passenger on this train, traveling at a velocity of just under the speed of light. When you got off this train, you would be much less than a year older then when you got on, while everyone and everything on earth would be a year older. I do not know what they exact ratio is, but let's say, for argument's sake, that you were one month older because the near light speed had made time slow down for the passengers on that train. So you would have essentially traveled the distance for light to travel around the earth 220,752,000 times going at 186,000 miles per second, in only 1/12th the time it should have taken you from the passenger's perspective since you still would have made that trip of 220,752,000 revolutions, but you would have aged only one month and the watch you were wearing on your wrist would only show that you have been on that train for one month instead of one year. So, according to the passenger's watch, it would have traversed a distance it would take a velocity of 186,000 per second to achieve in a year, but you would have done it in only a month from your perspective, which would mean you would have had to have been traveling at 12 times the speed of light, form your perspective, to achieve that distance in such a short period of time.

Now, in the last fraction of a second of your trip, you stand at the front of your train, which is already traveling as close to the speed of light as the universe will allow, and you fire a bullet from your gun at a target in front of you, will the bullet get to your target before you and your train will? If the answer is yes, then that bullet just traveled faster than the speed of light. Can you explain please? Thanks.

It seems to me that, if time slows down as you approach the speed of light, then you could travel to some destination say one light year away,, and it would take two earth years to make the roundtrip, but you may have only aged 2 months, which, from your perspective, you would have had to have been traveling at 12 times the speed of light to cover that distance in that period of time. These may be all basic questions that have been asked a thousand times before, but i would appreciate any explanation. thanks.

It seems to me that, if time slows down as you approach the speed of light, then you could travel to some destination say one light year away,, and it would take two earth years to make the roundtrip, but you may have only aged 2 months, which, from your perspective, you would have had to have been traveling at 12 times the speed of light to cover that distance in that period of time. These may be all basic questions that have been asked a thousand times before, but i would appreciate any explanation. thanks.

From your perspective the distance has length contracted to 2 light months, so you have travelled 2 light months in (just over) two months and so your speed is less than the speed of light. You are making the mistake of calculating velocity using time measured in your reference frame and distance measured in in the the Earth frame.

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From your perspective the distance has length contracted to light months, so you have travelled 2 light months in (just over) two months and so your speed is less than the speed of light. You are making the mistake of calculating velocity using time measured in your reference frame and distance measured in in the the Earth frame.

omg, this is driving me crazy. OK, so what you are saying is that if I want to travel to some distant star and back which is 100 light years away, the distance in miles I would have to travel would be 31,536,000 (the number of seconds in a year) X 186,000 (the number of miles light travels in one second) X 100 ( the number of years it would take light to reach my destination traveling at $186,000 per second) X 2 (roundtrip - not accounting for any accelerating or decelerating time in my example). So if you were 25 years old and set out on this journey, normally your lifetime would expire before you even made it to your destination much less survived for the trip back home to Earth). However, because time has slowed down for you traveling at near light speed, you can actually traverse a distance far greater than what light, traveling at 186,000 mps, would transverse and maybe you can travel this distance in only 10, for example, of your years even though 200 years would have passed on Earth while you were away. My other question that is still not answered is that, if you were traveling at that near light speed and you: A. stood at the front of your spaceship and fired a gun in front of you, at some object, would the bullet go faster than your already near light speed ship and hit this object before you did OR B you turned on your headlights, in which case my question is would the object light up in front of you which would mean the light from your headlights would have to be traveling faster than you are, when you are already at the maximum speed permitted by the universe. The only difference between example A and example B is that the bullet has mass whereas the light from your headlights does not. I am sure there is a simple explanation and I would appreciate if anyone can tell me what it is. thanks. JesseM Science Advisor omg, this is driving me crazy. OK, so what you are saying is that if I want to travel to some distant star and back which is 100 light years away, the distance in miles I would have to travel would be 31,536,000 (the number of seconds in a year) X 186,000 (the number of miles light travels in one second) X 100 ( the number of years it would take light to reach my destination traveling at$186,000 per second) X 2 (roundtrip - not accounting for any accelerating or decelerating time in my example). So if you were 25 years old and set out on this journey, normally your lifetime would expire before you even made it to your destination much less survived for the trip back home to Earth). However, because time has slowed down for you traveling at near light speed, you can actually traverse a distance far greater than what light, traveling at 186,000 mps, would transverse and maybe you can travel this distance in only 10, for example, of your years even though 200 years would have passed on Earth while you were away.
yuiop was talking about length contraction in your own frame, not time dilation. If the distance between the Earth and star is 100 light years in the frame where the Earth and star are at rest, then in your frame, traveling at say 0.8c relative to the Earth and star, the distance between the Earth and star is shrunk down to only 60 light years. So in your frame, your clock is running at the normal rate, but with the star moving towards you at 0.8c, it only takes you 60/0.8=75 years to get from the Earth to the star.
A. stood at the front of your spaceship and fired a gun in front of you, at some object, would the bullet go faster than your already near light speed ship and hit this object before you did OR
The bullet would go faster than you and hit the object before you did, but the bullet's speed would still be slower than light in all inertial frames, that follows from the relativistic velocity formula. If you are traveling at speed u relative to some observer, and you fire the bullet at speed v in your own frame, in the observer's frame the bullet is traveling at speed w = (u + v)/(1 + uv/c^2). As long as both u and v are slower than light, w will be too according to this formula (and if we replace the bullet with a laser so that v=c, then w=c as well).
B you turned on your headlights, in which case my question is would the object light up in front of you which would mean the light from your headlights would have to be traveling faster than you are, when you are already at the maximum speed permitted by the universe.
You can't be traveling at "the maximum speed permitted by the universe" because no object with nonzero rest mass (i.e. all atoms) can travel at light speed. You can travel arbitrarily close to light speed as seen in any given inertial frame, though.

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yuiop was talking about length contraction in your own frame, not time dilation. If the distance between the Earth and star is 100 light years in the frame where the Earth and star are at rest, then in your frame, traveling at say 0.8c relative to the Earth and star, the distance between the Earth and star is shrunk down to only 60 light years. So in your frame, your clock is running at the normal rate, but with the star moving towards you at 0.8c, it only takes you 60/0.8=75 years to get from the Earth to the star.

The bullet would go faster than you and hit the object before you did, but the bullet's speed would still be slower than light in all inertial frames, that follows from the relativistic velocity formula. If you are traveling at speed u relative to some observer, and you fire the bullet at speed v in your own frame, in the observer's frame the bullet is traveling at speed w = (u + v)/(1 + uv/c^2). As long as both u and v are slower than light, w will be too according to this formula (and if we replace the bullet with a laser so that v=c, then w=c as well).

You can't be traveling at "the maximum speed permitted by the universe" because no object with nonzero rest mass (i.e. all atoms) can travel at light speed. You can travel arbitrarily close to light speed as seen in any given inertial frame, though.

Yes I understand you cannot travel AT the speed of light, because mass cannot exist at that speed. What I meant by my phrase "maximum speed permitted by the universe" was the highest SUB light speed that would not be breaking any laws. in other words, as close to light speed as possible without actually reaching it is what I meant. I just don't understand how, if the light from your taser, combined with your SUB light speed exceeds the speed of light, how the light from the taser, can fly out ahead of your spaceship traveling at just a hair under the speed of light.

I also do not understand the concept that if you want to travel to someplace say 1000 light seconds away, which would mean it would be 186 million miles away (186,000 x 1000). From the perspective of the observer on earth, it has to take your space ship 1000 seconds to get there traveling at the rate of 186,000 per second. Simple. BUT from the reference of you as a passenger on that ship traveling at just a hair under light speed, you make the trip is say around only 100 seconds. When you reach your destination, the passenger's watch shows 100 seconds and the watch on the earth observer shows 1000 seconds. How can you travel 186 million miles at 186,000 miles per second and get there in only 100 seconds when it should have taken you 1000 seconds? You could not have been going 10 times the speed of light?

the other concept that is difficult to grasp is the one where you stay right here on earth but you board a train that runs the cirucumference of the earth an just a hair under light speed. Disregarding g forces and say we can accelerate to maximum speed in an instant, you should be able to circle the earth about 7 times per second. BUT if I see my friend off before he gets on that train and come back to pick him up 10 years later, I will have aged 10 years but he may have aged only one year or less and the ONLY difference between him and me is that he went very fast for the last 10 years in a circle, and his watch only registered one year whereas mine registered 10 as a result. Wow. So then, if the passenger on this train were able to look at a video monitor showing the train station he was whizzing past 7 times a second each time he circled the globe, everyone and everything he would be seeing should be going in fast motion, in my example, 10 times faster than normal, correct? And if that is the case, if the planet were exploding one day far far into the future and we all boarded our armada of a million sub light speed space ships we had built for just this occasion to take us to an earth like planet we had found 1000 light years away, we may make the journey in maybe only 10 years, or even 1 year, even though 1000 years will have to have passed on the earth we left and the same 1000 years would have passed on the destiination earth like planet we were going to, but we would only have aged a few years, or whatever the exact ratio is on the formula for the rate of time slowing down relative to how close you approach the speed of light.

Additionally, if you are traveling at say almost the speed of light, say if you went 300 feet per second faster, you would be at light speed (and you would cease to exist since mass cannot exist at light speed). Now you stand at the front of your very fast ship and you fire your gun, the bullet from which will travel at 600 feet per second, which, combined with the momemtum of your sub light speed space ship, would exceed the 186,000 per second barrier by 300 fps, how can that be? Yet if you fire that gun, it will hit the target in front of you before your ship will.

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JesseM
Yes I understand you cannot travel AT the speed of light, because mass cannot exist at that speed. What I meant by my phrase "maximum speed permitted by the universe" was the highest SUB light speed that would not be breaking any laws.
Well, there is no such highest sublight speed in relativity, because relativity assumes speed can vary continuously. It's just like asking what the largest real number is that's smaller than 1 (can't be 0.999, because 0.9999 is larger...can't be 0.9999, because 0.99999 is larger...etc. etc.) Also, do you understand that speed is relative in relativity? There is no absolute sense in which any sublight object is moving at very close to the speed of light, you can only say that its speed is close to c in some choice of inertial frame, but you can always find another frame where its speed is much smaller, even zero.
uniqueland said:
I just don't understand how, if the light from your taser, combined with your SUB light speed exceeds the speed of light, how the light from the taser, can fly out ahead of your spaceship traveling at just a hair under the speed of light.
Laser, not taser! A taser is one of these, it shoots out wires that deliver a shock.

Anyway, the whole point is that the way velocities are "combined" in relativity doesn't match the way they are combined in Newtonian physics. In Newtonian physics, if the laser moved at 1c relative to me, and I was moving at 0.8c relative to you, we could just add the speeds to find the speed of the laser relative to you, in this case 1.8c. But in relativity we would have to instead use the formula (u + v)/(1 + uv/c^2) I mentioned earlier, which in this example gives:

(0.8c + 1c)/(1 + ((0.8c*1c)/c^2)) = 1.8c/1.8 = 1c.

The basic reason velocities don't add the same way in relativity is that each observer is using his own ruler and synchronized clocks to measure the "speed" of anything as distance/time, but each observer will see the other guy's rulers as shrunken down due to length contraction, and see the other guy's clocks as slowed-down and out-of-sync due to time dilation and the relativity of simultaneity. If this point doesn't help clear up your confusion, please take a look at the numerical example I offered in [post=2489746]this post[/post] to show how two observers would both measure the same light beam to travel at c using their own rulers and clocks, and tell me if there's anything about it you can't follow.
uniqueland said:
I also do not understand the concept that if you want to travel to someplace say 1000 light seconds away, which would mean it would be 186 million miles away (186,000 x 1000). From the perspective of the observer on earth, it has to take your space ship 1000 seconds to get there traveling at the rate of 186,000 per second.
I assume you mean it takes a hair over 1000 seconds if you are traveling at very close to light speed?
uniqueland said:
Simple. BUT from the reference of you as a passenger on that ship traveling at just a hair under light speed, you make the trip is say around only 100 seconds. When you reach your destination, the passenger's watch shows 100 seconds and the watch on the earth observer shows 1000 seconds. How can you travel 186 million miles at 186,000 miles per second and get there in only 100 seconds when it should have taken you 1000 seconds? You could not have been going 10 times the speed of light?
Do you understand the point about "length contraction", that in your frame the distance between the Earth and destination is not 1000 light-seconds, but is shrunk to a smaller distance, in this case about 99.503719021 light-seconds*? Length contraction is not just a different way of talking about time dilation, it's a separate relativistic phenomenon so it's important you understand that it exists and that the distance between Earth and the destination therefore depends on your choice of reference frame.

*In case you're curious where I got this number, I'm assuming of your velocity relative to Earth is v = (1/sqrt(1.01))*c = about 0.99503719021c, in which case the gamma factor is 1/sqrt(1 - v^2/c^2) = 1/sqrt(1 - (1/sqrt(1.01))^2) = 1/sqrt(1 - (1/1.01)) = 1/sqrt((1.01/1.01) - (1/1.01)) = 1/sqrt(0.01/1.01) = sqrt(1.01)/sqrt(0.01) = 10*sqrt(1.01), and length contraction says the distance is (distance in rest frame)/gamma = 1000/(10*sqrt(1.01)) = 100/sqrt(1.01) light-seconds, meaning the time for the destination to reach you is given by distance/velocity = [100/sqrt(1.01)] / [1/sqrt(1.01)] = 100 seconds. It's not important to follow the details of these calculations though.
uniqueland said:
the other concept that is difficult to grasp is the one where you stay right here on earth but you board a train that runs the cirucumference of the earth an just a hair under light speed. Disregarding g forces and say we can accelerate to maximum speed in an instant, you should be able to circle the earth about 7 times per second. BUT if I see my friend off before he gets on that train and come back to pick him up 10 years later, I will have aged 10 years but he may have aged only one year or less and the ONLY difference between him and me is that he went very fast for the last 10 years in a circle, and his watch only registered one year whereas mine registered 10 as a result. Wow. So then, if the passenger on this train were able to look at a video monitor showing the train station he was whizzing past 7 times a second each time he circled the globe, everyone and everything he would be seeing should be going in fast motion, in my example, 10 times faster than normal, correct?
On average over the course of a full trip around the Earth he'll see the station running 10 times faster than normal, although if his video monitor is receiving images from light or radio waves sent from the station, the exact speed will depend on his direction relative to the station due to the Doppler effect.
uniqueland said:
And if that is the case, if the planet were exploding one day far far into the future and we all boarded our armada of a million sub light speed space ships we had built for just this occasion to take us to an earth like planet we had found 1000 light years away, we may make the journey in maybe only 10 years, or even 1 year, even though 1000 years will have to have passed on the earth we left and the same 1000 years would have passed on the destiination earth like planet we were going to, but we would only have aged a few years, or whatever the exact ratio is on the formula for the rate of time slowing down relative to how close you approach the speed of light.
If we travel inertially from Earth to the new planet, then in our inertial rest frame as we travel, time on Earth is running slower, not faster (again, velocity is relative, and time dilation just says that clocks in motion in a given inertial frame run slow relative to that frame, so we are free to pick the inertial frame where the ship is at rest and the Earth is moving, and in this frame it must be the Earth's clock that is running slow). But it is true that once we reach our destination, if we decelerate so we are at rest relative to the Earth, then in our new inertial rest frame (also the frame of the Earth), it would now be true that 1000 years had passed on Earth even though our own clocks had only elapsed 100 years. This difference has to do with the relativity of simultaneity which says different frames disagree about which pairs of distant events happened "at the same moment" (same time-coordinate in that frame). If the ship left the Earth in the year 2000 according to Earth clocks, then in the frame where the ship was at rest during its journey while the Earth was moving away from it, the event of the ship arriving at the destination (with 10 years having passed on the ship clocks) was simultaneous with the event of Earth clocks showing a date of 2000.1; but in the frame where the Earth is at rest and the ship was moving, the event of the ship arriving at the destination was simultaneous with the event of Earth clocks showing a date of 3000.
uniqueland said:
Additionally, if you are traveling at say almost the speed of light, say if you went 300 feet per second faster, you would be at light speed (and you would cease to exist since mass cannot exist at light speed). Now you stand at the front of your very fast ship and you fire your gun, the bullet from which will travel at 600 feet per second, which, combined with the momemtum of your sub light speed space ship, would exceed the 186,000 per second barrier by 300 fps, how can that be? Yet if you fire that gun, it will hit the target in front of you before your ship will.
See above about addition of velocities. If the bullet from the gun is traveling at 600 feet per second relative to you (in the frame where you are at rest), then in the frame of the observer who sees you traveling close to light speed, the bullet is not traveling at (your speed) + (600 feet per second), velocities don't add this way in relativity. Instead, if u=(your speed in the observer's frame) and v=600 feet per second, the observer sees the bullet traveling at (u + v)/(1 + u*v/c^2), which will give an answer smaller than the speed of light.

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So let me see if I have this right now. If you boarded a light speed train that traveled around the earth at just under the speed of light, time for you as the passenger on that train, would slow to a crawl relative to the rest of the earth that you were circling around. Of course to you on the train, everything would seem normal. If you were watching a monitor with a live video feed of your neighborhood, for example, and let's not even get into the logistical problems of actually making such a video feed possible, the images you would be watching should look like they are all going in fast motion. Sort of like if you were zipping thru a commercial for a football game that you recorded on your dvr. What gets really interesting is if you could actually make a telephone call to your friend who is not on the train with you, but rather is sitting home in his living room. Wouldn't he sound like a chipmunk to you since his voice would be sped up to whatever time difference ratio the two of you are experiencing from your different places? If time slowed down to 1/10th, for example, Wouldn't he be talking in fast motion, 10 times his normal speed, relative to what you are hearing on your end of the phone, and wouldn't your friend sitting in his living room talking to you, be hearing you in super slow motion at 1/10th speed. If you could video chat with each other wouldn't you both experience this 10 times difference in perception of your conversation?

JesseM
So let me see if I have this right now. If you boarded a light speed train that traveled around the earth at just under the speed of light, time for you as the passenger on that train, would slow to a crawl relative to the rest of the earth that you were circling around. Of course to you on the train, everything would seem normal. If you were watching a monitor with a live video feed of your neighborhood, for example, and let's not even get into the logistical problems of actually making such a video feed possible, the images you would be watching should look like they are all going in fast motion. Sort of like if you were zipping thru a commercial for a football game that you recorded on your dvr. What gets really interesting is if you could actually make a telephone call to your friend who is not on the train with you, but rather is sitting home in his living room. Wouldn't he sound like a chipmunk to you since his voice would be sped up to whatever time difference ratio the two of you are experiencing from your different places? If time slowed down to 1/10th, for example, Wouldn't he be talking in fast motion, 10 times his normal speed, relative to what you are hearing on your end of the phone, and wouldn't your friend sitting in his living room talking to you, be hearing you in super slow motion at 1/10th speed. If you could video chat with each other wouldn't you both experience this 10 times difference in perception of your conversation?
Yes, right on all counts.

OK, so then why, whenever I see a program on the science channel talking about interstellar space travel, they always talk about how it would take generations to get from one place to another given the enormous distances. I just watched a program about the universe with Steven Hawking and it said the nearest star system with earth like properties was over 70 light years away. BUT, if we were able to accelerate to near light speed, while 70 years may have elapsed waaaaay back on Earth, to the passengers of this near light speed interstellar craft, maybe only 5 or 10 years elapsed. since this would be a one way trip anyway, what would it matter to the passengers how many years had elapsed on earth. If they can get to a planet that is 70 light years away and only age by 5 years because of the slowing down effect that traveling at near light speed would have on them, wouldn't this be a huge factor in possibly resolving the problem of how it would normally take more than a lifetime to get from one place to another? Also is there any specific math calculation that determines the amount of time slow down relative to approaching the speed of light. I know that the closer you get to the speed of light, the more time slows down, but there must be some formula that tells you whether the ratio of time to speed is 2:1, 20:1 or 200:1.

JesseM
Yes, if you a clock is traveling at speed v relative to any given inertial frame, then relative to that frame it only ticks at $$\sqrt{1 - v^2/c^2}$$ the rate of clocks at rest in that frame. For example, if you are traveling at 0.6c relative to the Earth's frame, then in the Earth's frame your clock is ticking at sqrt(1 - 0.6^2) = sqrt(1 - 0.36) = sqrt(0.64) = 0.8 the normal rate, meaning your clock ticks 8 seconds for every 10 seconds of time that pass in that frame.