Physics Question

U

ussfletcher

Chrono Cadet
I asked my physics teacher a question and his answer sounded like he was bsing it so I've decided to ask you!

You are onboard a spaceship traveling 1 mph under the speed of light, when you decide to walk from the rear of the ship to the front of the ship. Your walking speed is greater than 1 mph so what happens? (from the perspective of a static observer specifically)
 
The static reference frame is in a time flow state that is much more rapid than the reference frame inside the ship. At speeds close to that of light time slows down. So if the guy in the ship was moving just a little more than i mph in his reference frame, it would appear that he was moving at rate much slower to the static observer. Maybe an inch per week to the static observer.
 
Yep. Einstein (the real one, and our poster) got it right. Relative flow of time is the key point here, as our Einstein pointed out.

However, this question points to the underlying assumption of relativity and Minkowski spacetime which might be good to discuss. It deals with observability and whether or not there are absolutes with respect to simultaneity of events. This shows that it is the observer's position and motion that determine whether two events are simultaneous or not. It is often a difficult concept to grasp, but it is one which helps validate that you cannot (accurately) treat Space as separate and distinct from Time. Instead, for complete accuracy, we must deal with the combined "field" of SpaceTime.

HERE is a good website to help understand relative simultaneity.

Once one understands this principle of how Einstein and Minkowski merged Space with Time to define SpaceTime, then one might be able to understand where I am going with Massive SpaceTime. I am simply extending this notion one more level to encompass Mass. IOW, you cannot (accurately) treat Mass as separate and distinct from SpaceTime. If we wish to advance further beyond the work of Einstein we must take his ideas further, and that means dealing with Massive SpaceTime as a whole. And conveniently, the physical measure we use to do just that is Energy.

RMT
 
Hi Newbie,
So he appears to be just walking there in space without the ship??
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No, not really. But your question brings up another good topic to discuss about the practicality of the "GedankenExperiments" (Thought Experiments) that Einstein used to help visualize the path to his equations. In this case, we assume that the ship itself is constructed of a transparent material so we could see inside and observe the timeframe of the person on the ship.

But Einstein did point out that you can't just keep thinking in the GedankenExperiment, as it is not practical and could lead to wrong conclusions. You must move from the GedankenExperiment, as a thought process helper, to the hard and fast mathematics that describe the physical situations that you presume from the GedankenExperiment. This is how he used Minkowski's idea of SpaceTime to develop the mathematics of Relativity. This is the reason that I so often point out how important it is to be able to formulate the math when it comes to any sort of scientific advancements.

If we look at the practicality of this particular thought experiment, we realize that the ability for a human observer in a relatively stationary (inertial) reference frame to be able to actually track and discern the details of a ship flying at 1 mph below the speed of light is impractical. Such a ship, traveling at such a speed across our human field of view, would be nothing more than a flash of light in our timeframe. This is an important practical view to consider, and in my opinion (and in my models) this is what gives rise to the importance of the observer as the "tenth dimension" (tenth string?) which is immersed within the 3x3 Matrix (Tensor Field) of Massive SpaceTime.

The big problem that Einstein did not (and likely could not) attack was the issue of separating the observer from the totality of the observable universe. This is where a certain aspect of spiritual traditions comes into play (IMO). Most human spiritual traditions hold it as a basic truth that you cannot, accurately, separate the human observation process (our spirit/soul/mind) from the rest of the observable universe. In other words: All is One. Since the entirety of a true "Grand Unified Theory" of physics must consider the observer and the observed combined, this is where the concept of closed-loop, non-linear mathematics comes into play.

RMT
 
So does the person walking on the ship actually hit the speed of light? (even if it does not appear so)
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The answer in the SpaceTime reference frame of the ship itself is an obvious "not even close". But I know you are talking about the SpaceTime reference of the inertial observer. And the answer there is still "no" because you must account for the contraction of space that goes with the time dilation as you approach the speed of light. This is why we have the Lorentz Transformation, and this is the purpose of the "c^2" term in this famous transformations.

This is precisely why it is important to move to math and not linger terribly long in the visualization. The "practical" view that made you pose the question includes an underlying assumption you are making, which is that space itself remains unchanged when you transfer from the ship's reference frame to your inertial reference frame. This is the more simple Galilean Transformation. The built-in assumption is invalid, even though it seems "practical" from the way you view the universe at very low relative sublight speeds. It is when you move to the math, and the reality that the speed of light is allegedly constant, that you come to the conclusion that the Lorentz Transformation is necessary to account for the space contraction that occurs as you approach the speed of light.

Now, that being said, I posted a link to another website which discusses that Special Relativity's "constant speed of light in all reference frames" may not be required if we consider the speed of light to be comprised of the vector sum of its linear velocity and the angular velocity component associated with its wave structure.

RMT
 
Perhaps this is a stupid question, but why is the speed of light the maximum attainable speed of anything? I suppose im assuming that the theory of relativity is just that, a theory not a law.
 
Hiya Fletch,
(Sorry, I can't resist...I am a big fan of the Chevy Chase movies with this name!)


Perhaps this is a stupid question, but why is the speed of light the maximum attainable speed of anything? I suppose im assuming that the theory of relativity is just that, a theory not a law.
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Not only is this not a stupid question, but it is one that speaks to the heart of the distinction between Einstein's General Relativity and Special Relativity. The former has been verified with experimental observations more than once, and no one has been able to falsify it as yet. However, the latter form of Relativity (Special Theory of Relativity) depends on a constant speed of light. Furthermore, as far as I am aware, there are some discussions and perhaps even some evidence that may end up falsifying one of STR's primary postulates.

My own, personal opinion as a person who practices engineering science is that GTR will never fall, but that STR may be flawed and therefore it may someday fall, conclusively. I haven't done it mathematically, as yet, but I am hopeful that my Massive SpaceTime may be able to falsify, yet also contain, Einstein's STR. But that's just my wacky thinking, so far. /ttiforum/images/graemlins/smile.gif

The Wikipedia review of the Two Primary Postulates of STR provides a good introduction to why Einstein believed the speed of light is constant in a vacuum.

RMT
 
Alright, here's a marginally different question:

Hypothetically, suppose I was placed in a space-pod just large enough to contain me, and ejected into space. Then, I fire my pod's engines at a constant thrust, accelerating at a constant 10ms_2.

If I could (somehow, I said it's a hypothetical question for this reason) maintain that acceleration for a whole year, would I, from my own POV, have reached lightspeed?

I know that from a static reference point, I would appear to be barely moving at all and getting slower all the time, but I'm not sure about from my own point of reference.

I studied Relativity - Special, and then General - at Uni for the final year of my degree, and I must confess that I still don't understand it! Most of my final year, I don't understand actually (also included Intro Quantum Theory and Quantum Mechanics 2 - all bad choices in retrospect...)
 
Ahh I see, so would it be like a red-shift effect, or would they both be invisible because no light is able to catch up to the ship to bounce off in the first place?
 
Hi newbie,

Ahh I see, so would it be like a red-shift effect, or would they both be invisible because no light is able to catch up to the ship to bounce off in the first place?
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I think I need more description of what you are getting at (and/or quoting of what you are responding to), as I am not sure what you are referring to by "they both". However:

Any object that is moving away from you is red-shifted, so if in this analogy we are assuming the ship is moving away from us, then yes, it would be red-shifted by quite a bit. And on the flipside, if the ship is coming towards us it would be heavily blue-shifted.

RMT
 
Welcome KoopaCooper:
Hypothetically, suppose I was placed in a space-pod just large enough to contain me, and ejected into space. Then, I fire my pod's engines at a constant thrust, accelerating at a constant 10ms_2.

If I could (somehow, I said it's a hypothetical question for this reason) maintain that acceleration for a whole year, would I, from my own POV, have reached lightspeed?

I know that from a static reference point, I would appear to be barely moving at all and getting slower all the time, but I'm not sure about from my own point of reference.
Click to expand...
The issue with your hypothetical is that it defies the accepted principles of Relativity. So if you are asking your question with respect to what Relativity tells us would happen, then your hypothetical would not be possible. The reason is that a constant thrust would not result in you maintaining a constant acceleration as relativistic effects kick-in. Relativity tells us that the energy required to continue to accelerate becomes exponential as you approach the speed of light. So for smaller and smaller increases in velocity as you approach "c" you will need much larger inputs of energy, which translates (in the simplistic view) to more thrust.

Beyond this, from your own point of reference things would appear normal because you are in an accelerated frame. It is when you look outside your reference frame that you would notice the "blue tunnel" effect (looking in the direction of your velocity vector) or the "red tunnel" effect (looking in the opposite direction of your velocity vector). If you could actually segregate the light into discernable objects, you would see them flitting around at hyperspeeds. IOW you would see the inertial frame's time passing much more quickly than your accelerated frame. This matches the fact that an inertial observer would perceive you as moving slower than molasses.

IMO this very effect is what convinces me that Time is not a "real" quantity, but rather a perceived quantity. If you take the limit as you approach the speed of light (even though we are told we cannot physically achieve it), Time would cease to exist in the rest of the universe as perceived from that frame. And to me, this is what makes the "veil" of the speed of light so interesting.


RMT
 
I think I need more description of what you are getting at (and/or quoting of what you are responding to), as I am not sure what you are referring to by "they both".
Click to expand...

By "they both" I meant the ship and the guy walking forward. But I should have only said the the guy hehe. Would the guy appear redshifted as he walked? or would he go invisible because no light would reach him to bouce off? (the hull of the ship is already invisible, made out of real super clear 0% refraction glass or something).
 
D5 extractive, the issue in a larger sense. is to conditons that would allow you to make the at 1 mph, in the first place, the a number of empirical constants, that must be in place, you can't decouple the driver from the machine!! spaceship are held to the same fundamentals, as centers of gravity and moments of inertial, by definition the static observer, is just that static!!, but does not preclude the ability of motion in the static reference frame, but changes in velocity of the static reference frame, in relationship the observed frame does limit the abilIty to move within a as an observed event time interval ( lets say 1 second ) due to the effects of Lorentzian invariance, and time dilation/contraction EFFECTS , So that you would not be able to move at any speed, 1mph, 20mph or infinity, because of changes within your local space (relative to one frame to another)as you approach the speed of light /ttiforum/images/graemlins/mad.gif
 
Koopa,

Hypothetically, suppose I was placed in a space-pod just large enough to contain me, and ejected into space. Then, I fire my pod's engines at a constant thrust, accelerating at a constant 10ms_2.
Click to expand...

That's the problem - constant thrust to get constant acceleration.

When you started the journey you calculated the thrust that you need to have a constant acceleration of 10 m/s/s. That thrust was based on your total mass.

But in the Special Theory of Relativity mass is not a constant. Relativistic mass is defined as:

m = m_0/sqrt(1-v^2) where c=1 and m_0 is the rest mass that you measured before you started to accelerate.

That's the limit problem that Rainman refered to. The mass tends to infinity as the limit of "v" approaches 1 (where v=c).

To maintain your constant acceleration you have to increase the thrust to compensate for the increased relativistic mass. But thrust increases linerally and mass increases as a function of the square of the increase in velocity. Your thrust can never catch up with the increased mass.

If you do the differential and graph it you see that the slope of the acceleration curve flattens out drastically as" v "approaches the limit. (This is from the POV of the rest frame observer.)

As to your original question about how velocities are added in the Special Theory of Relativity I would suggest that you go to Borders (or any major book store) and buy a little book called "Relativity: The Special and General Theory". Albert Einstein himself wrote the book. Its a pop-sci treatment that only assumes that you have a good high school general education. He deals directly with your problem. In the book the man is walking on the floor of a train car and the train is moving in the same direction.

As I recall, the book goes for about $10.00. Good stuff and you don't have to know partial differential calculus or analytic geometry to understand it. What little math there is is stated in basic high school Algebra I terms.

By the way, you didn't say what your teacher told you that sounded like "BS". What was his/her explanation?
 
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