Xplore Physics Online
Topic: Mach Principle
The Mach Effect (or Principle) describes a relationship between a particular mass and the universal mass. In the nineteenth century the physicist and philosopher Ernst Mach suggested that the inertia (a measure of mass) an object exhibited was caused by all the other masses in the universe.
This is easy to understand if one considers a single object in an otherwise empty universe. How do you measure its velocity? There is no reference (other object) by which to measure its coordinate change, therefore there can be no velocity. If there can be no velocity then there can be no resistance to a change in velocity, therefore no inertia. A subtle but logical argument.
In other words, the Mach effect states: inertia here is caused by mass there.
Ridgeview, Georgia, USA
Jack Williams had been crazy about rockets since he was a little kid. He started building bottle rockets at age seven. He had gone on to win several contests with his rockets starting at age nine. He was sure he would end up engineering rockets when he was grown and so he pursued all the necessary classes throughout high school to get into an aerospace engineering college. Shorter than the other kids, with dark brown hair and green eyes, he had just finished his junior year and was starting his summer plans when he read the daily space news:
The administration announced today a new goal in space. Speaking to reporters the President said, “We are going to make space a place for everyone, not just the well-to-do as it is now. Starting today, my administration is proposing a series of goals which will be pursued by the government. As each of these goals is reached we believe that space will become a more democratic and diverse place. I am today instructing all departments of this government to review their programs and bring them into alignment with this important initiative.”
After taking a few questions from reporters, the President continued, “We are also calling on all foreign governments as well as commercial space entities to sign on to the Space First Initiative. You can expect more details in the days ahead.”
With that the President boarded Marine One to begin his vacation.
Whenever Jack didn't understand something he would turn to his dad.
“I don't understand dad, what does it mean for space flight?”
“Jack, it's hard to say at this point. From what I've read I would say it will make it more expensive for aerospace companies to launch. They have to meet work force goals, environmental engineering goals, and there is a goal for international cooperation.”
“But dad, this country is almost the only one still pushing space exploration. They're going to stop it completely.”
“I know son, it looks that way. Since globalism fell apart a lot of what we thought would happen in space by now, hasn't happened. But even with this new initiative I think a lot of companies will still be determined to make their space dreams a reality.”
“I'm determined too dad,” said Jack.
Jack's plans for the summer were to research rockets and think. He wanted to find out why many of the dreams people had dreamt about space were still just dreams.
Men were on the Moon and, well that was it. After the first commercial mission to Mars failed when Jack was nine, no one had gone back, although the government was still talking about it. Jack wondered, was the cause technical, or political, or economical, or all the above? He suspected it might be all the above.
Technically, space was still hard and dangerous. Chemical rockets were still the workhorse, although some testing of nuclear rockets had occurred, but no one seemed interested in developing the technology beyond the prototype stage.
“Probably,” James thought, “ because it was too politically fraught and economically expensive. One failure could put a company into bankruptcy.
Something new was needed. Safe, environmentally sound, and, economical.
Home was a white two-story house in surrounded by hills on three sides. Jack's dad, Jose, was a working engineer who also spent time raising cattle and horses. His mom, Mildred, raised Jack and his three sisters, all of which were out of the house now, and kept the home going. Jack's room was as much as shrine to rocketry as a bedroom.
One day when he wasn't feeling particularly resourceful, Jack stumbled across some information on the net that he couldn't understand. It seemed to have something to do with using inertia for propulsion but he wasn't be sure. His reading sent him in search of something called the Mach Principle.
Ernst Mach had been a physicist/philosopher in the nineteenth century. He had proposed the curious idea that inertia, that is a body's resistance to a change in velocity, wasn't just related to the amount of mass it contained, but was also set by the amount of mass in the rest of the universe. In other words, the inertia of an object was related to all the other masses in the universe.
Jack thought it sounded a little bit like quantum entanglement which correlates some property of a particle here with some other particle across the universe and if a property of one of the particles is measured, it will cause that property in the distant particle to take a correlative value. A form of action-at-a-distance which the physicist Albert Einstein called “spooky.” But at the time Mach proposed his principle, quantum mechanics hadn't even been discovered. Maybe Mach was ahead of his time, and maybe it was an example of action-at-a-distance.
“If the inertia of a body was caused by all the other masses of the universe, then how did Mach suggest that the effect could be communicated?” Jack wondered.
That he couldn't discover, but he did discover something called a Mach Thruster, and that peaked his interest.
Xplore Physics Online
Topic: Mach Thrusters
A Mach thruster is constructed in layers. One of the end layers (let's call it the outer layer) is made up of a material (usually capacitive) which has a large capacity for internal energy changes when a voltage is applied.
Next is the actuator layer, usually made of a PZT (lead-zirconium-titanate) composite. This layer when driven by a increasing or decreasing voltage will expand and contract, respectively.
The final layer is made of a strong metal and provides the support and the local reaction mass for the rest of the stack.
If the capacitive layer is driven by the changing voltage its internal energy increases and decreases, and since according to relativity theory energy is equivalent to mass, the mass of this layer will also increase and decrease.
Now, if the actuator layer is in expansion as the capacitive layer increases in mass the stack will move a little in the direction opposite the capacitive layer, and if the actuator is in contraction as the capacitive layer decreases in mass then the stack will move towards the capacitive layer a little. Since the expansion and contraction are equal but the mass being pushed against is heavier than the mass being pulled, the whole stack will move slightly in the direction away from the capacitive layer. There will be a net force on the stack and an acceleration in the direction of the reaction mass.
By itself, the motion of the stack might seem to break some law of physics, after all, motion as a result of applied force usually requires that the force is “pushing” off something, at least there is some friction involved. So what is the stack “pushing off of or against?
The stack is “pushing” against the mass of the rest of the universe, according to the Mach Principle.
If Jack had read the article correctly, then he believed this “thruster” could be put on a load-bearing structure (that is a rocket body) and provide a kind of impulse engine using Newton's third law, action/reaction, to send that body upward, upward into space.
Could it? Jack couldn't believe it possible, and if it was possible, why had no one done such a thing before?
He kept looking until he came across a reference to an old book, apparently the one written by the physicist that developed the Mach Thruster, or almost developed the thruster. The professor must have come up short, since Jack had never heard of such a rocket engine. But right now he had to find a copy of that book written decades before, even before books were electronic. Since it was written by the inventor of the device, it should have the answers that Jack was seeking.
As Jack searched for a copy of the book he also found other articles that made reference to the drive. At first these articles were few but as the years went by they became more numerous. Finally seven years after the book was written online articles spiked as the inventor (now inventors) gave interviews to many websites. Then the articles ended.
Jack wondered why, then he found out. The inventor died and the China crisis hit immediately afterwards. With the descent of China into chaos and the resulting dislocations in the global network of trade, most countries were too busy trying to find a replacement for reduced availability of Chinese exports.
This took years and in the meantime other countries had trouble with their commitments to globalization. Those were the years when crisis led to crisis and widespread famine returned to the Earth. Governments worked to prevent food shortages in country after country as the world adapted to de-globalization. Spaceflight was not something that most governments considered critical throughout those times.
By the time Jack was born the world was very different than in his parents youth. Great countries such as China, Russia, Japan, Germany, Italy, South Korea and others, had lost much of their wealth trying to adapt to the changing circumstances and their governments were overthrown more than once as people became angry and discouraged. Because people had become poorer, their lives had become much more insecure. Even widespread pirating had returned to the world for a time.
In the USA things were not as difficult, a recession lasting years marred the countries progress, but no one starved and most people adjusted to the hard times. But that just meant that financial backing for a new method to power a spaceship was impossible to obtain, so the idea of the Mach drive withered and was forgotten.
“So that's that,” thought Jack. “No one pushed the design after the inventor died. But that means it may still be possible.”
Jack determined to try to learn enough to duplicate the old professor's experiment, and if it worked, to develop the drive further.
Since the math and theory behind the device was beyond him, he decided to concentrate on just duplicating the device and experiment. As he read more about the Mach thruster he began to understand how it operated. Part of the device, a capacitance usually, was driven by a voltage that increased and decreased, like a sinusoidal frequency of a tuning fork. Jack could understand this since he had a simple oscilloscope and a sound generator.
The voltage caused the capacitance to charge, grounding the capacitor caused it to discharge, essentially energy was added or drained from the capacitor. Since energy is equal to mass times the speed of light squared, and since the speed of light is constant, then an increase in energy meant an increase in mass. Likewise, during discharge, the decrease in energy meant a decrease in mass. Jack could follow the argument so far.
Now, if the capacitor happened to be pushed upon as it was gaining energy then the “pusher” would find the increase in mass to be an increase in inertia and according to Newton's third law would experience an equal and opposite reaction. Then, if the capacitor was “pulled” upon when it was discharged, the “puller” would move toward the capacitor, but not with the same acceleration as before because the capacitor was now lighter and not as resistant to being moved.
Except that the capacitor seemed to have been done away with by the time of the articles Jack was reading, he could still understand how to build the “gadget” as he called it, while not completely understanding how such a system could impart motion to a rocket ship, or itself for that matter. He just followed the explanation of the device in the articles, joining what was called PZT disks together to create the “stack.”
The disks were actually piezoelectric and would expand and contract as a voltage was applied to them, they also gained and lost weight during the cycle, similar to the capacitors in the analogy Jack had studied. Such piezoelectric materials are often used in electronic crystals which, in combination with a clock circuit, provide timekeeping for electronic devices.
The piezoelectric disks had to be assembled in a certain way, the sides with the same polarity (similar to a polarized battery) facing each other. Then they were wired for a voltage by placing one wire between the two sandwiched disks and connecting two wires to the other sides of the disks. Several of these PZT cells were assembled back to back with one end attached to a brass disk and the other end an aluminum cap. It resembled a cylindrical sandwich.
All of this had to be placed in a vacuum chamber to prevent any air currents from drowning out the expected signal which would be in the range of microvolts per micronewtons, the last being a measure of force. His physics teacher was able to find a chamber and pump for the experiment.
Jack also had to be careful about vibrations drowing out the signal, so a special and very expensive bench had been engineered by his dad. This almost ended the experiment as Jack's dad balked at the expense. Only because it might find use in his business was he able to justify the expense.
Jack built his gadget in the large cellar at one end of the family home among his mother's canned goods. Once finished, he planned on testing it Friday after school but had to wait for the following morning as one of his sisters showed up with her husband that evening.
Saturday morning was clear in the hollows of North Georgia and after breakfast, Jack was in the cellar. He setup a camera to record the device during the test. Switching on the sinusoidal power supply, he heard the familiar whumpf as the circuits rang with power. A fundamental sinusoidal voltage with a frequency of 32.35 kilohertz would be applied to the gadget. The vacuum chamber was already prepared.
Jack was watching the computer screen as he brought the power up remotely from across the room. He didn't see what was happening with the gadget until he heard a ripping sound in that direction. Looking up he saw through the shimmering air, the gadget which appeared to vibrate and to hop in a lurch within the chamber. Then a light, too bright to look at, forced Jack to close his eyes and turn away. The explosive sound was the last thing he heard and the heat from the explosion was the last thing he felt before being knocked unconscious.
His mom heard the muted sound of the explosion, and while she didn't expect it was close by, her motherly instinct prompted her to make sure everyone was alright. That included Jack, she headed for the cellar. As she neared, she sensed the acrid smell of burnt electronics. When she opened the door a cloud of smoke exited, she entered, even though it was now dark she knew the layout well and where her son had setup his test bench.
Pulling her blouse up over her nose she felt her way to his table where she almost tripped over the unconscious boy. His mother thought nothing of picking her son up, even though he outweighed her, and carrying him out of the cellar, placing him on the still cool grass in the sunshine. Jack coughed and tried to setup but lay back down, continuing to cough. By this time his father was at his side with a first-aid kit and a water bottle. He raised Jack's head and lifted the bottle to his lips, Jack took a sip and then a deeper drink. Then he sat up.
“What happened, how did I get out here?” he said.
“Your experiment exploded son,” said Jack's dad, “and your mom carried you out of the cellar, you were unconscious.”
“Mom carried me?” said Jack. “There was no reason for it to explode.”
“Well it did,” said his mom, “and I think we are going to have to take you to urgent care to make sure you are all right.”
“Ah mom,” said Jack. “I've got to put the lab back in order.”
“Do as your mom says Jack,” said his dad.
Jack knew if his dad was agreeing with his mom then he would have to do as they said, even if he was feeling fine.
“Okay,” was all he said.
“Good, let's go,” said his mom. “Can you walk or do we need to carry you?”
“I can walk mom.”
Jack got up with the help of his father and slowly walked to the car which took him to the nearest doctor.
A doctor's check up, including x-rays, found nothing wrong with Jack. But his mom was not eager to have him go back to his experimentation. The cellar was a mess, and even though not too many of her canned goods were damaged, she wouldn't agree that the experiments could continue. Jack's dad, as he had done with Jack's bottle rocket tests years before, came to the rescue.
“Okay,” he said, at the family meeting with Jack and Jack's mom. “What if I build a wall to protect the canned goods and what if Jack assembles his experiment in the cellar but automates it so that he can test it remotely?”
“I don't know Jose,” said his mom. “What if the explosion is bigger next time? Could it damage the house?”
“Well,” said Jack's dad, “no one can say for sure what might happen but I think once Jack is sure of what went wrong, then we can make it safe, for him and the house.”
“I don't know, honey,” said Jack's mom. “I want him to pursue his interests but it has to be safe for him and for us.”
“Alright, let's just wait to see what Jack finds during his investigation and we'll go from there.”
They all agreed.
After a week Jack's dad asked, “Tell me son, have you figured out what went wrong?”
Jack was silent for a moment.
“Something happened with the piezo cell,” he said. “It got so hot during expansion that it blew itself apart. I'm going to experiment with the voltage ramp, the material obviously has a limit to the power it can handle.”
“But your power supply wasn't all that powerful, was it son?”
“No, not really dad. But these PZT disks aren't the same as the ones the professor used. I think they must be more sensitive to the power input, they expanded too fast.”
“Okay son, you have a hypothesis to test. I'll tell Mildred and we'll start building.”
Jack's dad rented a robotic 3D builder and drew up the plans that would isolate Jack's experiments from the rest of the cellar. Jack's room would be in one corner of the cellar with two walls built into the earth. Another wall would be built by the 3D builder and would be one foot thick and reinforced by steel. The last wall would be the outside berm. Through the berm Jack's dad designed a pressure release tunnel a foot in diameter. In the chance that there was another explosion the pressure relief door would open and release the gases and smoke to the outside.
Once the 3D builder was finished and on it's way back to the home improvement store Jack got to see his new room.
“This is great dad. It really feels like a lab. Thanks.”
The room was about eight foot by ten foot with a reinforced door. The lighting was recessed and electromagnetically quiet so as to not interfere. The room itself was a Faraday shield, that is it was shielded from any radio or other electromagnetic interference. The table had been restored and Jack's physic's professor had come through with a clear vacuum chamber made out of a tough plastic which was a Faraday shield itself. Everything coupled to the gadget inside the chamber was properly grounded to prevent antenna-like effects The walls were clean without shelving, the only thing in the room was the table and necessary equipment. Everything was better than the last time.
“Your welcome son, Now we need to have your mother tour the cellar and approve it.”
“Right dad.”
Jack's mom reluctantly approved the new arrangement with the understanding that Jack would go more slowly with his experiments. Since that was exactly what he planned, Jack quickly agreed.
Jack spent the next couple of weeks setting up the remote control for his experiment. Unlike before, he sought out equipment that could be controlled remotely over a network. The expense was a little more significant this time, but Jack's dad came through, although he didn't inform his wife of every purchase he made for Jack.
Fall was approaching and the air was cool in the mornings as Jack rose and got started on his project each day after his dad had left for work. The walk outside and into the cellar reminded Jack of the changing seasons and the amount of time he had spent on this project. It would be a shame, if after all that time and everyone's efforts, he was unable to at least reproduce the results of the earlier experiment.
The interruption had given Jack time to study the gadget some more. One morning while he was reading through the articles for a third time he got a notice that the old professor's book had been found. The price was high, but it was as important to the experiment as any of the equipment Jack had purchased, so with a large part of the money that remained after buying other equipment and supplies, he purchased the book.
A couple of days later after receiving the book, Jack could see that between the time the book was written and the time the articles he had read were published exactly how the design had changed. There was no capacitors in the new design, just PZT disks. But with the book at hand, it was conceptually easier to see how the older design worked.
But it still didn't seem right to Jack. He felt that there should be something more involved. The whole thing seemed to need something to push against during the expansion cycle, and yet there was nothing there, or rather it was supposedly provided by the universal inertia, the Mach effect. But Jack couldn't understand that part, and the book and all the math didn't help.
So, he would just proceed and see what happened.
The next weekend after several preliminary runs, Jack was in his bedroom, he had the app he had written open. From this one program he could run and monitor his experiment in the cellar. So far the experiment had yielded no results. Each time he had run it he had decreased the ramp up of the voltage signal while increasing the power. This time he would be close to the settings that were used during the first, explosive attempt.
He touched the screen to turn on the power supply and heard the familar whumpf through his speakers as the currents surged into the large capacitors of the supply. Jack glanced at another screen showing his experiment room, everything looked good. Another screen showed the strain gauge widget and other readouts. Nothing but the power supply indicator, which showed the supply was on, had changed.
Jack prepared to touch the button on the screen that would start ramping up voltage to the PZT stack. He pressed it and then quickly looked at the screen showing his room in the cellar. Everything looked normal, so he turned to the readout screen. Meter and bar widgets were starting to move. Jack was particularly focused on the strain gauge widget.
It began to move and then he heard a noise. Before he could pivot to the camera screen he heard a strange sound coming from the speakers. It wasn't easy to place, Jack had not expected any sound. It started as a low hum and proceeded up the scale quickly, at the same time a loud buzz commenced. Then he heard what sounded like a large firecracker going off, then he thought he heard a swooshing sound from outside.
Looking at the camera screen he saw nothing unusual, at first, but then noticed something falling on the table on which he had placed the gadget. Or rather, on the table which had held the gadget, because now Jack saw nothing there but the debris falling from above.
“Jack,” he heard his mother yelling for him.
He ran and opened his bedroom door.
“I'm coming mother,” he yelled back.
Jack raced down the steps and down the hall and out the back door. He saw his mother standing near the berm that covered the entrance to the cellar. She was pointing up the embankment.
“Jack, something fell through the roof.”
Jack knew that the hole she was pointing to was just above the experiment table.
“I'll check it out Mom,” he said as he rushed past her and into the cellar.
Jack could smell hot electronics but no smoke. He opened the thick door that separated his experiment room from the rest of the cellar and rushed up to the table. As he looked up he could see the hole directly above where the gadget had been. Everything looked normal except the gadget, the vacuum chamber that had held it, and power supply were missing. The hole in the roof seemed to be about the same size as the missing chamber.
“That ain't good,” he thought.
“No more Jack,” said his mom.
Jack hung his head.
“I'm afraid I've got to agree son,” said his dad. “This experiment is just too unpredictable to allow you to continue, something we would all regret could happen.”
“I know,” said Jack. “I'll start cleaning out the room tomorrow.”
“Thank you son,” said his mom.
Jack and his dad were in the cellar the next day finishing the cleanup.
“Did you come up with what went wrong Jack?” asked his father.
“Well, I looked through the data from the instrumentation last night and I think it might have worked dad.”
“Really?”
“Yeah, everything looked like I would expect, except that the data was off the chart, literally.”
“So, if it worked, where is the gadget?”
“Well my guess is that, if it did work, it is somewhere west of here. But how far, I don't know.”
“You mean you think it lifted off and carried the vacuum chamber with it?” his dad asked.
“Yes, and it dragged the power supply with it too.”
“That's several pounds Jack, that power supply was heavy.”
“I know dad, I wish I could find it, to prove my hypothesis.”
“That's a wooded area Jack. Make your best distance estimate and we'll go looking for it.”
“You think we can find it dad?”
“I don't know son, but we can give it a try.”
The next weekend they took the four-wheel drive and a drone with them and headed west. Jack had figured that the device had taken a parabolic trajectory and was no more than a mile from the house. Jack's dad got them as close to the suspected area as possible and parked the four-wheeler. He put up the drone and they both watched the camera feed. They were looking for any broken or bent tree branches that might indicate where the vacuum chamber had fallen.
But after two hours of buzzing back and forth, they saw nothing.
“Sorry, son,” said his father as he put the drone back in the four-wheeler.”
“That's okay dad, at least we tried. I know my calculations weren't very accurate, who knows where the thing is.”
Meanwhile, just a few hundred yards to the south, at the bottom of a neighbor's pond, set a strange looking chamber with an even stranger looking gadget inside.
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