Light at Light Speed

[Emil]

Sarcasm noted.
But, origin, by whose curriculum standards is this "high school algebra"? I think you have overestimated Emil's contributions to this thread. It looks like literally elementary school arithmetic, circa age 11, to me.

You have correctly observed. There is no need for more advanced mathematics.
I think I gave enough time to contest the dates.

But as you like more advanced mathematics,I recommend the following exercise.

Recommendations:
1. To put yourself in touch with the basic measurement units and derivatives. With special attention to the definition of speed.
2. To put yourself in touch with vectors and why speed is a vector.
Now you are able to define the relative velocity between two objects, considering the definition of speed and that speed is a vector.
3.Punctiform objects exist only in mathematics. You must leave this world and enter reality where objects have size.

The exercise itself:
Consider that you get close to a sphere with a high enough speed to be length contraction.
Are you close enough to the sphere so that the velocity vector, decomposed by the directions of the various points on the sphere have significantly different values.
Assuming you're as good at Mathematical Analysis and Special Mathematics, you calculate the shape of the sphere, taking into account the Lorentz transformation.

That has to do in two stages.
The distance until the all points on the "visible" hemisphere, considering the velocity vector for each point,
and the sphere "thickness" corresponding to each vector.

Now you've got a new geometric figure and you can play with him.
For example rotating sphere with a constant angular velocity and see the speed of different points on the surface of your new geometric figure.
Or try doing a triple integral on the surface of this new geometric figures.

What do you say, this satisfies your cravings for advanced mathematics?

 

[Motor Daddy]

I think what Motor Daddy is overlooking completely, probably because he hasn't studied physics at high school, is that you can be accelerating in time.

Although you have a speed of 0 m/s at the surface of the earth, you experience a force. To explain the force, you say gravity is accelerating your mass towards the centre of the earth. Since the universe is 4-dimensional, you can accelerate in one dimension; that leaves three in which you aren't accelerating.

On the surface of the earth the three remaining dimensions are spatial; you accelerate in the time dimension. This is the 'force' of gravity with acceleration g = F/m.

Describe what you mean by saying that I experience a force? Certainly there is no motion that can be measured, as far as a change in distance between myself and the center of the earth while I'm laying on the beach. So there is no change in distance, therefore there is no velocity. Acceleration is the rate of change of velocity. The velocity is NOT changing, therefore the acceleration rate is 0 m/s^2.

You say I accelerate in the time dimension. How do you suggest I measure that? What exactly do you mean by that? How do you quantify that statement?

 

[arfa brane]

Describe what you mean by saying that I experience a force?

I'm probably going to regret this, but:
the force you experience is called "weight".

Certainly there is no motion that can be measured, as far as a change in distance between myself and the center of the earth while I'm laying on the beach. So there is no change in distance, therefore there is no velocity. Acceleration is the rate of change of velocity. The velocity is NOT changing, therefore the acceleration rate is 0 m/s^2.

There is no apparent motion (velocity or acceleration) in any of the 3 spatial dimensions if you remain "still". But you experience the force of gravity; you accelerate at g, because of your mass m, where your "weight" W = mg.

You say I accelerate in the time dimension. How do you suggest I measure that?

It's easy. Become aware of your weight for a few seconds, wait for a bit, then repeat the process. For all the time you experience weight, you are being accelerated towards the centre of the earth at 9.81 m/s, in the time dimension.

It's more complicated than that, because the surface of the earth is in motion, but you can ignore this for smallish intervals of time and assume that you are motionless--since you are "at rest" on the surface to a good first approximation (that's a thing physicists say sometimes).

 

[Motor Daddy]

I'm probably going to regret this, but:
the force you experience is called "weight".
There is no apparent motion (velocity or acceleration) in any of the 3 spatial dimensions if you remain "still". But you experience the force of gravity; you accelerate at g, because of your mass m, where your "weight" W = mg.

It's easy. Become aware of your weight for a few seconds, wait for a bit, then repeat the process. For all the time you experience weight, you are being accelerated towards the centre of the earth at 9.81 m/s, in the time dimension.

It's more complicated than that, because the surface of the earth is in motion, but you can ignore this for smallish intervals of time and assume that you are motionless--since you are "at rest" on the surface to a good first approximation (that's a thing physicists say sometimes).

So where does the meter and the second come into play, and how do I use my ruler and clock to measure my acceleration at 9.81 m/s^2 while laying on the beach??

Are you pretending that if I were to be actually accelerating that is the rate I would be accelerating at?

How do I measure the pretend acceleration with my real meter stick and real stop watch in reality?

You mention weight. If I stand on a scale and it reads 200 lbs, and it remains at 200 lbs while I'm on the scale, there is no net force, correct? If there is no net force, then there is no acceleration, correct, since f=ma?

 

[arfa brane]

So where does the meter and the second come into play, and how do I use my ruler and clock to measure my acceleration at 9.81 m/s^2 while laying on the beach??

Well, it's like this: you are trying to explain why you have a sense of weight.
Your body has spatial extent in three dimensions, and it "exists" in time--you don't appear and disappear randomly, or at all. You have a sense of the continuous "existence" of your body.

Trying to detect or be aware of, say, the effect of gravity on the blood flowing through your body is a bit of a task, but for instance, your heart pumps blood to your brain against the downward force of gravity when you stand still.

It's probably easier to examine the effects of weight by using inert objects and weighing scales, or simple springs you can hang the weights from.
This will give you a distance (in metres) for each of the springs; if you have a set of "weights" with different mass you can see how far they each extend a single spring.
Measuring the time is irrelevant--all times are equivalent for an inert mass which is "at rest" in a graviational field because the forces are in equilibrium and there is no motion relative to the surface or the centre of gravity.

You now apply a simple formula for the displacement of a spring with a fixed elastic constant, k, which will give you a linear relation if the displacements are small. You need to either use weights with a known mass to determine k for each spring, or use springs with a known k. Since W = mg, you can plot this linear relation for each spring and determine another constant, G, Newton's constant.

Again, this all ignores the fact that the weights are in motion, because the earth is. That's why it's only a first approximation. It treats gravity as a one-dimensional interaction between masses. At equilibrium that single dimension of interaction is the time dimension.

 

[Motor Daddy]

Well, it's like this: you are trying to explain why you have a sense of weight.
Your body has spatial extent in three dimensions, and it "exists" in time--you don't appear and disappear randomly, or at all. You have a sense of the continuous "existence" of your body.

Trying to detect or be aware of, say, the effect of gravity on the blood flowing through your body is a bit of a task, but for instance, your heart pumps blood to your brain against the downward force of gravity when you stand still.

It's probably easier to examine the effects of weight by using inert objects and weighing scales, or simple springs you can hang the weights from.
This will give you a distance (in metres) for each of the springs; if you have a set of "weights" with different mass you can see how far they each extend a single spring.
Measuring the time is irrelevant--all times are equivalent for an inert mass which is "at rest" in a graviational field because the forces are in equilibrium and there is no motion relative to the surface or the centre of gravity.

You now apply a simple formula for the displacement of a spring with a fixed elastic constant, k, which will give you a linear relation if the displacements are small. You need to either use weights with a known mass to determine k for each spring, or use springs with a known k. Since W = mg, you can plot this linear relation for each spring and determine another constant, G, Newton's constant.

Again, this all ignores the fact that the weights are in motion, because the earth is. That's why it's only a first approximation. It treats gravity as a one-dimensional interaction between masses. At equilibrium that single dimension of interaction is the time dimension.

You should be a politician, you have many words but never answer the question.

How do I measure my acceleration while I'm laying on the beach with my ruler and my stop watch?

If f=ma is a net force, and I stand on a scale at it reads a constant 200 lbs, there is no net force, so therefore there is no acceleration. If there was an acceleration the scale would be changing, but is isn't.

Are you saying I am accelerating towards the center of the earth while the scale reads a constant 200 lbs?

Your numbers don't add up.

There is no net force while I'm on the beach, otherwise I would be accelerating, but I am not!

 

[arfa brane]

There is no net force while I'm on the beach, otherwise I would be accelerating, but I am not!

There is no net force that results in you having apparent motion in space, right? You are standing or lying "still", right?

But when you are still, you have a sense of weight, right? How come?
Why does your heart have to pump blood "uphill" to your brain--why do humans, who stand upright, have a physiological mechanism that maintains blood pressure in their brain "against" the force of gravity, huh?

Have you actually studied physics, and do you really understand what equilibrium means? I don't think so.

 

[Motor Daddy]

There is no net force that results in you having apparent motion in space, right? You are standing or lying "still", right?

But when you are still, you have a sense of weight, right? How come?
Why does your heart have to pump blood "uphill" to your brain--why do humans, who stand upright, have a physiological mechanism that maintains blood pressure in your brain "against" the force of gravity, huh?

Have you actually studied physics, and do you really understand what equilibrium means? I don't think so.

Do you agree the definition of acceleration is the rate of change of velocity?

 

[arfa brane]

'sigh'

Do you understand that when you're in space and not accelerating, you have no sense of weight? You are in equilibrium because otherwise a net force would be acting, you would accelerate and then you would notice "weight".

Try relating this scenario to what you notice lying on a beach.
But again, I don't think so . . .

 

[Motor Daddy]

'sigh'

Do you understand that when you're in space and not accelerating, you have no sense of weight? You are in equilibrium because otherwise a net force would be acting, you would accelerate and then you would notice "weight".

Try relating this scenario to what you notice lying on a beach.
But again, I don't think so . . .

Are you saying I could be in space a distance away from other massive objects, and I would not be accelerating towards an object?

Again you are living in a fantasy world. There is no circumstance in space where you wouldn't be in motion.

...and since you say on earth I am accelerating towards the center of the earth, that means I am getting closer to the center of the earth if I am accelerating, but my distance from the center of the earth is clearly not changing while I'm lying on the beach, because there is no net force, which means a zero acceleration!!

 

[arfa brane]

Motor Daddy: what's your explanation for the sense of weight that humans experience, when they stand still, lie on a beach or a sofa, or move around?

Do you have one? What does it look like? It's not small and kind of dangly, is it?

 

[arfa brane]

I though I'd maybe covered this, but you seem to be suffering from recursive cognitive dissonance (that's a medical term I just made up).

...and since you say on earth I am accelerating towards the center of the earth, that means I am getting closer to the center of the earth if I am accelerating, but my distance from the center of the earth is clearly not changing while I'm lying on the beach, because there is no net force, which means a zero acceleration!!

I said you are accelerating towards the centre of gravity in one dimension. Get it right, pal.

The distance doesn't change because the surface of the earth "pushes" back on your mass with an opposite and equal force--that's an "equal to your weight" force.
You don't get closer to the centre because you're in equilibrium in three dimensions--at least to a first approximation, you are.

 

[Motor Daddy]

Motor Daddy: what's your explanation for the sense of weight that humans experience, when they stand still, lie on a beach or a sofa, or move around?

Do you have one? What does it look like? It's not small and kind of dangly, is it?

I measure distance and time with a ruler and clock. I measure force with a scale.

If I am laying on the beach, I am not getting closer to the center of the earth, so I am not accelerating towards the center of the earth.

If I were to jump in the air from the ground and start accelerating towards the earth, There would be a net force while I am accelerating towards the center of the earth unless I was already at a terminal velocity, which would be a zero net force. If I was accelerating and not yet reached terminal velocity when I impacted the ground, the ground resists my motion and the force builds until the forces are at equilibrium, at which point I will not be accelerating. The net force will be zero, and the acceleration will be zero!

 

[arfa brane]

Once again. When you reach equilibrium in THREE spatial dimensions--the same ones your body has--there is ONE dimension left, because there are 3+1 of these dimensions in total.

You accelerate continuously in this ONE dimension, and you call it time. Why? Because there are only 3 spatial dimensions (apparently). Why only 3? Who knows?

 

[Motor Daddy]

Once again. When you reach equilibrium in THREE spatial dimensions--the same ones your body has--there is ONE dimension left, because there are 3+1 of these dimensions in total.

You accelerate continuously in this ONE dimension, and you call it time. Why? Because there are only 3 spatial dimensions (apparently). Why only 3? Who knows?

Once again you are wrong. You do NOT accelerate in only the time dimension. Acceleration is the rate of change of velocity. Velocity involves distance (meter) and time (second). So why do you keep pretending you can accelerate with no measure of distance (meter)?

...and if you claim to be able to accelerate in only the time dimension, why do you say 9.81 METERS/s^2???

Are you implying you can accelerate using the unit seconds, so it would be 9.81 s^2???

What units do you use to accelerate in only the time dimension??

 

[arfa brane]

Once again you are wrong. You do NOT accelerate in only the time dimension.

Then WHY do you experience a "force" called weight?

What units do you use to accelerate in only the time dimension??

It's mind-boggling, eh? I guess "units of gravity", or something. There's a constant involved that tells you about the "strength" of the 1-dimensional interaction, which presumably acts in 4 dimensions (I mean, why wouldn't it?).

By extension, gravity also acts in n dimensions, since there is no reason other than our anthropocentric heuristics to assume the universe has only 4. This suggests that evolution has delivered a sense of three spatial dimensions and one of time because "that will do it". There is no evolutionary advantage in having a sense of more than this number, and why that is is a good question . . .

 

[Motor Daddy]

Then WHY do you experience a "force" called weight?

That is not motion, it is force. f=ma is a NET force, and when the NET FORCE is zero, there is ZERO acceleration.


Would you like to talk about torque and HP so I can clearly show you the error of your ways? I am well versed in rotational velocity and the acceleration of the rotational velocity, along with f=ma, torque, work, power, gear ratios, etc... Would you like to play hard ball?

 

[arfa brane]

Look what happens if I edit your statement:
"That is not motion through space, it is force. f=ma is a NET force, and when the NET FORCE is zero, there is ZERO acceleration through space.

What about the remaining dimension, what "happens" in time?

 

[Motor Daddy]

Look what happens if I edit your statement:
"That is not motion through space, it is force. f=ma is a NET force, and when the NET FORCE is zero, there is ZERO acceleration through space.

What about the remaining dimension, what "happens" in time?

Time is a measure of duration. You can sit in a chair for 1 second or three years.

You can travel 10 feet in one second or you can travel 10 feet in 30 minutes.

But you can not accelerate in only the time dimension. Time is a duration, you don't accelerate a duration, you measure it!

 

[arfa brane]

But you can not accelerate in only the time dimension. Time is a duration, you don't accelerate a duration, you measure it!

Yet, you have a sense of time. You can "measure" the passage of time without looking at a clock, or looking at anything. Not with what we call "good accuracy", but that's a mere detail.

There are four dimensions. When you have zero motion in three of these, there's still one left. This explains why, when you are motionless (in 3 dimensions) in a gravitational field, you accelerate, and this is your weight. You can sense your weight, right?

And, you have an EXPLANATION for this sense of weight, and why it's a continuous kind of sensation, and seems to be an external influence on the mass of your body, on the blood flowing "upwards" to your brain, and so on?

I would like to see what your explanation is. Do you have one? I don't think so.