Place to discuss the Theory of Relativity

[Daminc]

This forum is meant as a place to discuss the Theory of Relativity and is for the benefit of those who wish to learn about or expand their understanding of said theory. It is not meant as a soapbox for those who wish to argue Relativity's validity, or advertise their own personal theories. All future posts of this nature shall either be deleted or moved by the discretion of the Mentors.

I read this and I'm not sure if this is the right place to post. If it isn't then I appologise.

An object in space accelerates to 2/5 th the speed of light and then stops accelerating traveling at a steady pace. If it doid this 3 times it would travel 1.2c.

Now, if something cannot go faster than c then obviously the above situation has a flaw. But I'm walking through the scenario and I can't see it:

OK, I'm on the object in space and I hit the boost button to go to 2/5c and then switch of the boost and travel at a constant rate. I look around and the stars are too far away to see their movement, for all intensive purposes I'm stationary and so I hit the boost again...

Stepping away from the object an independant observer from a distant galaxy with a telescope that would make Patrick Moore wet his pants looks on as this mad idiot on an object accelerates once, twice and then disappears.

Where is the flaw?

 

[Pengwuino]

In special relativity, speeds do not add up like they do in our everyday experiences. Someone else will be better able to explain it but basically, as you approach the speed of light, time starts dilating instead of your velocity increasing. This is called 'time dilation'. The idea is basically that time is not a fixed-dimension

 

[Phobos]

I read this and I'm not sure if this is the right place to post. If it isn't then I appologise.

Note: Asking how the theory works is fine. ("...is for the benefit of those who wish to learn about or expand their understanding... ")

 

[EnumaElish]

An object in space accelerates to 2/5 th the speed of light and then stops accelerating traveling at a steady pace. If it doid this 3 times it would travel 1.2c.

Another way to look at the problem is perhaps as follows. In a pre-Einstein (Newtonian) world, after its 2nd bout of acceleration the object would be traveling at 80 percent of lightspeed. In this type of a world, it would take the object an identical amount of energy to get to 120% of c as was needed to get from 40% to 80%, as a non-physicist would put it. In a relativistic world, however, the object's relativistic mass (directional mass due to high velocity) would have increased to such an enormous amount that it would take an infinite amount of energy even to reach the speed of light -- let alone surpass it. As far as I know, this is why the only objects that can travel at the speed of light are photons; they are the only known particle not having a mass.

 

[Phobos]

for all intensive purposes I'm stationary

Relative to what?

Looks like you're trying to set up an absolute reference frame that you can keep calling your new baseline when in fact you're still moving through spacetime.

 

[εllipse]

I read this and I'm not sure if this is the right place to post. If it isn't then I appologise.

You've come to the right place!

An object in space accelerates to 2/5 th the speed of light and then stops accelerating traveling at a steady pace. If it doid this 3 times it would travel 1.2c.

Ok, in the special theory of relativity there is no such thing as absolute motion. If you're not familiar with this concept, here's a quick intro. I am standing on the side of the road and see a car go by at 30 km/h. But, am I correct in saying that everyone who has good tools for measuring speed will agree with me? Certainly not, because relative to the sun (if the sun had a point of view) the Earth is moving 107300 km/h, and it's also spinning at 1670 km/h, so the sun might say the car is moving at about 109000 km/h. But the sun is also moving around the center of our galaxy, and the galaxy is moving within the local galaxy cluster, and... So how fast is the car moving? According to the principle of relativity there is no such thing as absolute speed; it doesn't make sense to just say "the car is moving at 30 km/h" or "the car is moving at 109000 km/h". You must say "the car is moving 109000 km/h relative to the sun." But notice this, relative to the passengers in the car, the car is not moving.

So, having qualified the notion of speed, let's rewrite the scenario in a way that makes a little more sense:

I am in a spaceship, and you are on the Earth watching me from a powerful telescope. I am initially moving at a constant speed of 1/5 the speed of light relative to you. I have a button on my spaceship set up so that every time I press it the rockets turn on with the same amount of thrust for the same amount of time and then turn off. The first time I hit the button you see me accelerate to about 2/5 the speed of light. The second time I hit it, you see me accelerate to a little less than 3/5 the speed of light. I won't quite be going at 3/5 the speed of light. The third time I hit it, you'll see me accelerate even less, and the fourth time less still. After four pushes of the button, Newton would have declared me moving at 5/5, or 100%, the speed of light. However, Einstein realized that each time I pressed the button I'd accelerate less and less because as I get faster and faster, instead of the energy from the rockets increasing speed, it'd start increasing relativistic mass instead! As I get closer and closer to the speed of light, more and more of my rocket fuel will get converted into relativistic mass instead of speed (from your point of view), so I will never be able to reach the speed of light.

However, it is important that the discussion above is from your point of view. I will still feel the same amount of acceleration for each time I press the button no matter how many times I press it and I will also always measure the same amount of mass for myself and my spaceship, so from my point of view things are a little different. Let's imagine that the reason I'm gunning my rockets is because I'm chasing a light ray and trying to catch up with it to see what it looks like when I'm moving beside it. At first I see the light ray moving at 300000 km/s away from me, which is extremely fast, but, no problem, I'm in a state-of-the-art spaceship in the year 5047 and I have no doubt of its ability to reach any speed I want it to. I hit the button, and after the rocket finishes its boost I measure the speed the light ray is moving away from me again, but am not amused to find that it still moving at 300000 km/s away. I hit the button a second time, but find the light ray is still moving away from me at the same speed. I become impatient and slam my accelerator down putting my rockets into full thrust, but no matter how fast I speed up, I can't seem to catch up with the light ray. And everytime I stop to measure its speed, its still moving at 300000 km/s away. This is because the speed of light is a universal constant. Light must propagate at c in any special relativistic reference frame. The reason it can get away with this is because time and space warp as I speed up, in just the right way so that light can travel at the same speed. As I speed up, time for me slows down and space contracts, and after every acceleration, no matter what clock I use or what measuring device I have to measure the speed with which the light is moving away from me, I always find the same value, c.

 

[George Jones]

An object in space accelerates to 2/5 th the speed of light and then stops accelerating traveling at a steady pace. If it doid this 3 times it would travel 1.2c.

If observer C is moving away from B with speed $v_{2}$, while observer B is moving (in the same direction) away from A with speed $v_{1}$ then the Newton/Galilean view says that C is moving away from A with speed $v = v_{1} + v_{2}$. Einstein radically changed our views of space and time, and since speed = space/time, this changed the way speeds are added. Relativity replaces the "common sense" Newtonian velocity addition formula by

[tex]
v = \frac{v_{1} + v_{2}}{1 + v_{1}v_{2}},
[/itex]

where all speeds are expressed as fractions of the speed of light.

Now apply this to your example. "Adding" 2 speeds of 0.4 gives

[tex]
\frac{0.4 + 0.4}{1 + (0.4)(0.4)} = 0.690.
[/itex]

"Adding" another 0.4 gives

[tex]
\frac{0.690 + 0.4}{1 + (0.690)(0.4)} = 0.85.
[/itex]

So, in your example, the final speed is 0.85 c with respect to the initial reference frame, not 1.2 c.

Regards,
George

 

[Daminc]

Wow, that's really counter intuitive isn't it.

Is it kind of like an object reaching a terminal velocity due to resistance and gravity?

 

[Daminc]

This is because the speed of light is a universal constant. Light must propagate at c in any special relativistic reference frame.

I must admit, I do have issues with this. The 'Speed of light' and the speed at which light propergates I think are different issues (I have a lot of ideas about this but there is a high probablitity that I'm wrong with all of them )

 

[εllipse]

Wow, that's really counter intuitive isn't it.

Yes, it is pretty counter intuitive at first because we don't have experience with such high speeds from every day life. But one of my favorite things about it is that it does become intuitive once you accept Einstein's two postulates (that the laws of physics are the same for all inertial reference frames and that the speed of light is constant in every inertial reference frame). One of the most amazing things about the special theory of relativity is that Einstein was able to produce the theory almost entire by thought. So in that sense, it is intuitive because you can understand it if you're willing to accept the postulates and take the time to think it through and read some of Einstein's arguments.

The special theory of relativity has been thoroughly proven by experiment since its publication in 1905. Many of the things in our world today wouldn't work right without an understanding of Einstein's theory of relativity. (One of the ones often mentioned is GPS statellites, which have to account for their clocks running a little slower than ours.)

 

[Daminc]

Thank's for taking the time to explain it to me (though it may take a bit longer for me to actually understand it though )

 

[Phobos]

kudos, εllipse

daminc - It's certainly counter intuitive, as εllipse noted, which makes it hard for many people to accept. The thing is that it keeps passing experimental tests (I encourage you to check out some examples in the literature).

 

[Daminc]

Will do

Can you recommend anything to a layman?

 

[George Jones]

Can you recommend anything to a layman?

Try the excellent General Relativity from A to B by Robert Geroch, which details different views spacetime from Aristotle to Galileo to Einstein. Also very good, but at a slightly higher level is A Traveler's Guide to Spacetime by Thomas Moore.

Special relativity is very counterintuitive because the speed of light $c$ is so large. For example, the in the relativistic velocity "addition" expression

$$v = \frac{v_{1} + v_{2}}{1 + \frac{v_{1}v_{2}}{c^2}}$$

where speeds are expressed in everyday units, the term

$$\frac{v_{1}v_{2}}{c^2}}$$

is so small that in everyday life it is not noticed. If $c$ were smaller, this term would be larger and make more of a noticeable contribution, and thus be part of our intuition, i.e., experience.

Regards,
George

 

[Daminc]

Numbers don't bother me much. The bit that I find counter intuitive is the same objects having different speeds depending on all the other different objects which would also have different speeds which depends on ... etc, etc

p.s. I'll try General Relativity from A to B by Robert Geroch first I think :)

 

[Doc Al]

another book to read

Let me add a plug for N. David Mermin's pedagogical classic, "Space and Time in Special Relativity". (I recommend a few others here: https://www.physicsforums.com/showpost.php?p=255747&postcount=114)

 

[HallsofIvy]

I scanned this thread quickly and didn't see this point made: you can't just accelerate something indefinitely at a constant acceleration because the relativistic mass increases as speed increases. Since F= ma, in order to have constant acceleration with increasing mass, you would need to increase the force. As the speed nears c, the mass, and therefore force required to accelerate, goes to infinity.

 

[Daminc]

can't just accelerate something indefinitely at a constant acceleration because the relativistic mass increases as speed increases.

I've heard this before (although I don't know exactly why this is true) which is why I staggered it with a period of non-acceleration.

The fact that you can't (as far as we're aware to date) get that speed is acceptable. I'm taken that as a given because people a lot smarter than I said there is a lot of evidence showing this to be true. I was asking why this is so.

Which is why these kind people have volunteered to try and enlighten me

Let me add a plug for N. David Mermin's pedagogical classic, "Space and Time in Special Relativity".

Thank's, I'll try that one as well (I haven't got a big enough budget to get everything )

 

[Aer]

Wow, that's really counter intuitive isn't it.

Is it kind of like an object reaching a terminal velocity due to resistance and gravity?

No. In the case of terminal velocity, the force of gravity is countered by the force of air resistance. So your acceleration approaches 0, as measured by your instantaneous velocity. Whereas accelerating to reach to speed c, you can accelerate at a constant, a, measured at the instantaneous velocity at any point in time and your instantaneous velocity will constantly increase but it will never surpass c. A rough example would be accelerating such that your velocity increased in the following way: .90c, .990c, .9990c, .99990c, etc.

The bit that I find counter intuitive is the same objects having different speeds depending on all the other different objects which would also have different speeds which depends on ... etc, etc

Quite a few details are lacking for this to make any sense - maybe that is why you find it counterintuitive.

I scanned this thread quickly and didn't see this point made: you can't just accelerate something indefinitely at a constant acceleration because the relativistic mass increases as speed increases. Since F= ma, in order to have constant acceleration with increasing mass, you would need to increase the force. As the speed nears c, the mass, and therefore force required to accelerate, goes to infinity.

Perhaps you didn't see that brought up because what you just said just isn't so. Let's say a spaceship and yourself start in an inertial reference frame at t=0. The spaceship begins to accelerate away from you such that it feels a constant acceleration. While it is true that the spaceship cannot consider itself an inertial reference frame, the instantaneous velocity it has with respect to the inertial reference frame you are in is itself an inertial reference frame from which the acceleration felt by the spaceship is measured. In this instantaneous inertial reference frame, the spaceship is at rest at that specific instant in time in that frame. So the relativistic mass you refer to is the rest mass of the spaceship and as you can see, the acceleration is always constant. There are only a handful of people around here that still use the concept of relativistic mass for one reason or another. But this is prime case of when the concept of relativistic mass is misused.

I've heard this before (although I don't know exactly why this is true) which is why I staggered it with a period of non-acceleration.

See my response above to clarify this issue.

 

[EnumaElish]

... There are only a handful of people around here that still use the concept of relativistic mass for one reason or another. But this is prime case of when the concept of relativistic mass is misused.

Which of the following are you saying?

(a) A certain type of mass can be described as relativistic or directional mass, but this is not one of those cases
(b) Mass by definition cannot be relativistic or directional, I advise you to improve (or improvise) your vocabulary
(c) None of the above.

 

[Aer]

Which of the following are you saying?

(a) A certain type of mass can be described as relativistic or directional mass, but this is not one of those cases
(b) Mass by definition cannot be relativistic or directional, I advise you to improve (or improvise) your vocabulary
(c) None of the above.

I cannot tell you the reason some people still use relativistic mass or what they use it for. I will have to refer you to those who do use relativistic mass to explain why they use it. I cannot rule out the possibility that they are also in error when applying relativistic mass as well but I don't know as I am not familiar with the details of why they use it.

 

[EnumaElish]

I cannot tell you the reason some people still use relativistic mass or what they use it for. I will have to refer you to those who do use relativistic mass to explain why they use it. I cannot rule out the possibility that they are also in error when applying relativistic mass as well but I don't know as I am not familiar with the details of why they use it.

I have used it in the past and will continue to use it in the future until someone can make the definitive case against it in a language that I, a non-physicist (and no math wiz either), can understand. I have not seen such a case made. Not in these forums, anyway.

 

[Aer]

I have used it in the past and will continue to use it in the future until someone can make the definitive case against it in a language that I, a non-physicist (and no math wiz either), can understand. I have not seen such a case made. Not in these forums, anyway.

Very well, use relativisitic mass as you please. I will even give you an opportunity to do so now.

There are two ships, S1 and S2. The relativisitic velocity between them is .9c. That is, if S1 considers itself at rest, S2 is moving at .9c and if S2 considers itself at rest, S1 is moving at -.9c. Either frame is an inertial reference frame so neither frame is preffered over the other. What is the relativistic mass of S1 and S2 and what is the importance of this relativisitic mass as seen by either S1 or S2. To rephrase, in what situations might I apply these relativistic masses?

 

[EnumaElish]

There are two ships, S1 and S2. The relativisitic velocity between them is .9c. That is, if S1 considers itself at rest, S2 is moving at .9c and if S2 considers itself at rest, S1 is moving at -.9c. Either frame is an inertial reference frame so neither frame is preffered over the other. What is the relativistic mass of S1 and S2 and what is the importance of this relativisitic mass as seen by either S1 or S2. To rephrase, in what situations might I apply these relativistic masses?

My lay understanding is that from S2's point of view (POV) S1 has a large relativistic (directional) mass. From S1's POV, S2 has a relativistic (directional) mass with the same magnitude but in the opposite direction. Burdened with such colossal relativistic masses, either ship needs ever increasing amounts of energy to increase speed in ever decreasing increments. Okay, where am I wrong?

 

[Aer]

My lay understanding is that from S2's point of view (POV) S1 has a large relativistic (directional) mass. From S1's POV, S2 has a relativistic (directional) mass with the same magnitude but in the opposite direction. Burdened with such colossal relativistic masses, either ship needs ever increasing amounts of energy to increase speed in ever decreasing increments. Okay, where am I wrong?

Your explanation is too vague to unequivically say that you are wrong. However, that does not mean you are right, because depending on how one interprets what you are saying - they could be either right or wrong.

If I assume when you say "ever increasing amounts of energy" that you mean, the ship expends an increased amount of energy to achieve the same task as time increases, then your explanation is wrong.

Now if I assume that you mean the above to mean that the ship expends a continuous and constant rate of energy such that the energy supplies decrease to achieve the same task as time increases, then your explanation is correct. However, this means that the force driving the ship is constant and hence F=ma means that mass, m, is constant for a constant acceleration. Therefore if you are to adopt this perspective, you've effectively disproven relativistic mass.

Now the point that is often misunderstood is the fact that it takes an infinite amount of energy to accelerate to c. This is the case because of the fact that you can accelerate forever and never reach c. It is not because of the often misinterpreted explanation that you must expend increasing amounts of energy to increase velocity at a constant acceleration.

 

[EnumaElish]

If I assume when you say "ever increasing amounts of energy" that you mean, the ship expends an increased amount of energy to achieve the same task as time increases, then your explanation is wrong.

I see. And why am I wrong in this interpretation?

 

[Aer]

I see. And why am I wrong in this interpretation?

The acceleration is measured by the object accelerating. Regardless of any acceleration that may have happened in the past (the ship may be moving at 0c, .5c, .9c, etc relative to another ship), according to the ship accelerating, in it's reference frame it is moving at 0c by definition. So the acceleration at any of the relative velocities listed above will be constant for a constant amount of expended energy. There is not an increase in the amount of expended energy to achieve a constant acceleration. However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

 

[Pengwuino]

Guess I am wrong because i stopped understanding what was going on about 9 posts ago

 

[pervect]

I have used it in the past and will continue to use it in the future until someone can make the definitive case against it in a language that I, a non-physicist (and no math wiz either), can understand. I have not seen such a case made. Not in these forums, anyway.

Have you read the sci.physics.faq entry on the topic?

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Assuming you did read it, did you regard it as non-definitive (in that it only made recommendations), or did you clasify it as "incomprehensible to a non-physicist"?

 

[pervect]

Guess I am wrong because i stopped understanding what was going on about 9 posts ago

Your original post wasn't very detailed, but was basically on the right track IMO.

 

[pervect]

I scanned this thread quickly and didn't see this point made: you can't just accelerate something indefinitely at a constant acceleration because the relativistic mass increases as speed increases. Since F= ma, in order to have constant acceleration with increasing mass, you would need to increase the force. As the speed nears c, the mass, and therefore force required to accelerate, goes to infinity.

There is a potential for confusion here even with such a simple statement. You can't accelerate indefinitely with a constant coordinate acceleration, d^2x/dt^2, but you _can_ accelerate indefinitely with a constant proper acceleration (the sort an acceleromter mounted on a space-ship would measure, i.e. dv/dt, where v and t are measured from an instantaneously co-moving frame.

 

[Aer]

Have you read the sci.physics.faq entry on the topic?

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Assuming you did read it, did you regard it as non-definitive (in that it only made recommendations), or did you clasify it as "incomprehensible to a non-physicist"?

You seem to like that page a lot as I've seen you link it many times. However I must admit that I've done little more than skim over it as I don't find it to contain anything interesting. That is, there doesn't seem to be any real use for relativisitic mass and the uses that it is used for are valid only because the end result is the same whether you consider relativistic mass or invariant mass with kinetic energy. But the former can lead to non-physical situations as I've pointed out in a few threads so I would argue that the latter is the correct interpretation. Please point out any errors in this line of thinking.

 

[EnumaElish]

Have you read the sci.physics.faq entry on the topic?

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Assuming you did read it, did you regard it as non-definitive (in that it only made recommendations), or did you clasify it as "incomprehensible to a non-physicist"?

I read the Addendum. I understand relativistic mass is directional and I am okay with it. This makes perfect sense to me: relativistic mass results from velocity which is directional. I use the term "relativistic mass" while acknowledging its directional connotation.

 

[EnumaElish]

... However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

But, from the other ship's point of view, the first ship is not only maintaining a constant acceleration but increasing its relativistic mass as it gains speed. And surely, accelerating a relativistically more massive object would require more energy than accelerating (by the same amount) a relativistically less massive object, wouldn't it? In the limit, as the first ship's velocity approaches c, its relativistic mass will have approximated infinity. At that point it will require an approximately infinite amount of energy to accelerate it even a bit further.

 

[Aer]

But, from the other ship's point of view, the first ship is not only maintaining a constant acceleration but increasing its relativistic mass as it gains speed. And surely, accelerating a relativistically more massive object would require more energy than accelerating (by the same amount) a relativistically less massive object, wouldn't it?

This is not what is generally meant when something is said to constantly accelerate. However you may specify this condition if you so wish, but as I pointed out previously:

However, if you wish to say that the constant acceleration is in the other ship's reference frame, then the acceleration felt by the ship accelerating is increasing (but note that this scenario is not physical as it would evenutally require the ship to exceed the speed of light). So as you can see, the interpretation that a constant increase in energy expendature, leads to a non-physical reality.

(See, I did point it out previously) As I pointed out previously, this situation is not physical, pervect will testify to this as well.

There is a potential for confusion here even with such a simple statement. You can't accelerate indefinitely with a constant coordinate acceleration, d^2x/dt^2, but you _can_ accelerate indefinitely with a constant proper acceleration (the sort an acceleromter mounted on a space-ship would measure, i.e. dv/dt, where v and t are measured from an instantaneously co-moving frame.

See.